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Created: Sat, May 4, 20:40

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	diff --git a/.codeclimate.yml b/.codeclimate.yml
	index ed1c1d15c..fc0df9490 100644
	--- a/.codeclimate.yml
	+++ b/.codeclimate.yml
	@@ -1,55 +1,39 @@
	checks:
	duplicate:
	enabled: true
	exclude_patterns:
	- "test/"
	- "examples/"
	structure:
	enabled: true
	exclude_patterns:
	- "test/"

	plugins:
	editorconfig:
	enabled: false
	config:
	editorconfig: .editorconfig
	exclude_patterns:
	- ".clangd/"
	- ".cache/"
	pep8:
	enabled: true
	exclude_patterns:
	- "test/test_fe_engine/py_engine/py_engine.py"
	cppcheck:
	enabled: false
	- project: compile_commands.json
	+ project: build/compile_commands.json
	language: c++
	check: warning, style, performance
	stds: [c++14]
	+ exclude_patterns:
	+ - "python/"
	+
	fixme:
	enabled: true
	exclude_patterns:
	- "doc/"
	- clang-tidy:
	- enabled: false
	- checks:
	- extra-arg:
	- - -std=c++14
	- - -Ithird-party/akantu_iterators/include
	- - -Ithird-party/iohelper/src
	- - -Itest/ci/includes_for_ci
	- - -Isrc/mesh
	- checks:
	- - '-*'
	- - 'modernize-*'
	- exclude_patterns:
	- - test/
	- - cmake/
	- - examples/
	- - extra_packages/
	- - .clangd/
	-
	exclude_patterns:
	- "third-party/"
	- "build*/"
	diff --git a/.gitignore b/.gitignore
	index 3a53eaa50..7dd72dc48 100644
	--- a/.gitignore
	+++ b/.gitignore
	@@ -1,25 +1,26 @@
	build*
	.dir-locals.el
	TAGS
	third-party/*/
	!third-party/cmake/*
	!third-party/akantu-iterators
	!third-party/iohelper
	*~
	release
	.*.swp
	*.tar.gz
	*.tgz
	*.tbz
	*.tar.bz2
	.idea
	__pycache__
	.mailmap
	paraview/*
	*.vtu
	*.pvd
	*.pvtu
	*.vtk
	compile_commands.json
	.clangd
	.iwyu.imp
	+.cache
	diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
	index b0c336627..f49003d93 100644
	--- a/.gitlab-ci.yml
	+++ b/.gitlab-ci.yml
	@@ -1,350 +1,445 @@
	stages:
	- configure
	- build
	- - check-warnings
	- test
	- deploy

	.docker_build:
	image: 'docker:19.03.11'
	stage: .pre
	services:
	- docker:19.03.11-dind
	variables:
	# Use TLS https://docs.gitlab.com/ee/ci/docker/using_docker_build.html#tls-enabled
	DOCKER_HOST: tcp://docker:2376
	DOCKER_TLS_CERTDIR: "/certs"
	before_script:
	- docker login -u $CI_REGISTRY_USER -p $CI_REGISTRY_PASSWORD $CI_REGISTRY
	script:
	- cd test/ci/${IMAGE_NAME}/
	- docker build -t registry.gitlab.com/akantu/akantu/${IMAGE_NAME} .
	- docker push registry.gitlab.com/akantu/akantu/${IMAGE_NAME}

	docker build:debian-testing:
	variables:
	IMAGE_NAME: debian:testing
	extends: .docker_build
	rules:
	- changes:
	- test/ci/debian:testing/Dockerfile

	docker build:ubuntu-lts:
	variables:
	IMAGE_NAME: ubuntu:lts
	extends: .docker_build
	rules:
	- changes:
	- test/ci/ubuntu:lts/Dockerfile

	.configure:
	stage: configure
	except:
	- tags
	variables:
	BLA_VENDOR: 'Generic'
	script:
	- cmake -E make_directory build
	- cd build
	- cmake -DAKANTU_COHESIVE_ELEMENT:BOOL=TRUE
	-DAKANTU_IMPLICIT:BOOL=TRUE
	-DAKANTU_PARALLEL:BOOL=TRUE
	-DAKANTU_STRUCTURAL_MECHANICS:BOOL=TRUE
	-DAKANTU_HEAT_TRANSFER:BOOL=TRUE
	-DAKANTU_DAMAGE_NON_LOCAL:BOOL=TRUE
	-DAKANTU_PHASE_FIELD:BOOL=TRUE
	-DAKANTU_PYTHON_INTERFACE:BOOL=TRUE
	-DAKANTU_CONTACT_MECHANICS:BOOL=TRUE
	-DAKANTU_EXAMPLES:BOOL=TRUE
	-DAKANTU_BUILD_ALL_EXAMPLES:BOOL=TRUE
	- -DAKANTU_TEST_EXAMPLES:BOOL=TRUE
	-DAKANTU_TESTS:BOOL=TRUE
	-DAKANTU_RUN_IN_DOCKER:BOOL=TRUE
	- -DCMAKE_BUILD_TYPE:STRING=Coverage ..
	+ -DAKANTU_TEST_EXAMPLES:BOOL=${TEST_EXAMPLES}
	+ -DCMAKE_BUILD_TYPE:STRING=${BUILD_TYPE} ..
	- cp compile_commmands.json ..
	artifacts:
	when: on_success
	paths:
	- build
	- compile_commands.json
	expire_in: 10h

	.build:
	stage: build
	script:
	- - cmake --build build/src > >(tee -a ${output}-out.log) 2> >(tee -a ${output}-err.log >&2)
	- - cmake --build build/python > >(tee -a ${output}-out.log) 2> >(tee -a ${output}-err.log >&2)
	- - cmake --build build/test/ > >(tee -a ${output}-out.log) 2> >(tee -a ${output}-err.log >&2)
	- - cmake --build build/examples > >(tee -a ${output}-out.log) 2> >(tee -a ${output}-err.log >&2)
	+ - cmake --build build/src > >(tee -a build-${output}-out.log) 2> >(tee -a build-${output}-err.log >&2)
	+ - cmake --build build/python > >(tee -a build-${output}-out.log) 2> >(tee -a build-${output}-err.log >&2)
	+ - cmake --build build/test/ > >(tee -a build-${output}-out.log) 2> >(tee -a build-${output}-err.log >&2)
	+ - cmake --build build/examples > >(tee -a build-${output}-out.log) 2> >(tee -a build-${output}-err.log >&2)
	artifacts:
	when: on_success
	paths:
	- build/
	- #- ${output}-out.log
	- - ${output}-err.log
	+ - build-${output}-err.log
	- compile_commands.json
	+ exclude:
	+ - build/*/.o
	expire_in: 10h

	.tests:
	stage: test
	script:
	- cd build
	- - ctest -T test --no-compress-output --timeout 1800
	+ - ctest -T test --output-on-failure --no-compress-output --timeout 1800
	after_script:
	- cd build
	- tag=$(head -n 1 < Testing/TAG)
	- if [ -e Testing/${tag}/Test.xml ]; then
	- xsltproc -o ./juint.xml ${CI_PROJECT_DIR}/test/ci/ctest2junit.xsl Testing/${tag}/Test.xml;
	- fi
	- - gcovr --xml
	- --gcov-executable "${GCOV_EXECUTABLE}"
	- --output coverage.xml
	- --object-directory ${CI_PROJECT_DIR}/build
	- --root ${CI_PROJECT_DIR} -s \|\| true
	+ - if [ ${CMAKE_BUILD_TYPE} = "Coverage" ]; then
	+ - gcovr --xml
	+ --gcov-executable "${GCOV_EXECUTABLE}"
	+ --output coverage.xml
	+ --object-directory ${CI_PROJECT_DIR}/build
	+ --root ${CI_PROJECT_DIR} -s \|\| true
	+ - fi
	artifacts:
	when: always
	paths:
	- build/juint.xml
	- build/coverage.xml
	reports:
	junit:
	- build/juint.xml
	cobertura:
	- build/coverage.xml

	-.analyse_build:
	- stage: check-warnings
	- script:
	- - if [[ $(cat ${output}-err.log \| grep warning -i) ]]; then
	- - cat ${output}-err.log;
	- - exit 1;
	- - fi
	- allow_failure: true
	- artifacts:
	- when: on_failure
	- paths:
	- - "$output-err.log"
	-
	# ------------------------------------------------------------------------------
	.cache_build:
	variables:
	- CCACHE_BASEDIR: ${CI_PROJECT_DIR}/build
	+ CCACHE_BASEDIR: ${CI_PROJECT_DIR}/
	CCACHE_DIR: ${CI_PROJECT_DIR}/.ccache
	- CCACHE_NOHASHDIR: 1
	- CCACHE_COMPILERCHECK: content
	+ #CCACHE_NOHASHDIR: 1
	+ #CCACHE_COMPILERCHECK: content
	cache:
	- key: ${output}
	+ key: ${output}_${BUILD_TYPE}
	policy: pull-push
	paths:
	- .ccache/
	- third-party/google-test
	- third-party/pybind11
	before_script:
	- ccache --zero-stats \|\| true
	after_script:
	- ccache --show-stats \|\| true

	# ------------------------------------------------------------------------------
	.image_debian_testing:
	image: registry.gitlab.com/akantu/akantu/debian:testing

	.image_ubuntu_lts:
	image: registry.gitlab.com/akantu/akantu/ubuntu:lts

	# ------------------------------------------------------------------------------
	.compiler_gcc:
	variables:
	CC: /usr/lib/ccache/gcc
	CXX: /usr/lib/ccache/g++
	FC: gfortran
	GCOV_EXECUTABLE: gcov

	.compiler_clang:
	variables:
	CC: /usr/lib/ccache/clang
	CXX: /usr/lib/ccache/clang++
	FC: gfortran
	GCOV_EXECUTABLE: llvm-cov gcov

	+.build_coverage:
	+ variables:
	+ TEST_EXAMPLES: 'FALSE'
	+ BUILD_TYPE: 'Coverage'
	+
	+.build_release:
	+ variables:
	+ TEST_EXAMPLES: 'TRUE'
	+ BUILD_TYPE: 'Release'
	+
	+.build_valgrind:
	+ variables:
	+ TEST_EXAMPLES: 'FALSE'
	+ BUILD_TYPE: 'Valgrind'
	+
	# ------------------------------------------------------------------------------
	.debian_testing_gcc:
	variables:
	output: debian_testing_gcc
	extends:
	- .compiler_gcc
	- .image_debian_testing
	- .cache_build

	.debian_testing_clang:
	variables:
	output: debian_testing_clang
	extends:
	- .compiler_clang
	- .image_debian_testing
	- .cache_build

	.ubuntu_lts_gcc:
	variables:
	output: ubuntu_lts_gcc
	extends:
	- .compiler_gcc
	- .image_ubuntu_lts
	- .cache_build

	# ------------------------------------------------------------------------------
	# ------------------------------------------------------------------------------
	configure:debian_testing_gcc:
	extends:
	- .debian_testing_gcc
	+ - .build_coverage
	- .configure
	- cache:
	- policy: pull-push

	build:debian_testing_gcc:
	extends:
	- .debian_testing_gcc
	+ - .build_coverage
	- .build
	- dependencies:
	- - configure:debian_testing_gcc
	+ needs:
	+ - job: configure:debian_testing_gcc

	test:debian_testing_gcc:
	extends:
	- .debian_testing_gcc
	+ - .build_coverage
	- .tests
	- dependencies:
	- - build:debian_testing_gcc
	+ needs:
	+ - job: build:debian_testing_gcc
	+
	+# ------------------------------------------------------------------------------
	+configure:debian_testing_gcc_valgrind:
	+ extends:
	+ - .debian_testing_gcc
	+ - .build_valgrind
	+ - .configure
	+
	+build:debian_testing_gcc_valgrind:
	+ extends:
	+ - .debian_testing_gcc
	+ - .build_valgrind
	+ - .build
	+ needs:
	+ - job: configure:debian_testing_gcc_valgrind

	-analyse_build:debian_testing_gcc:
	+test:debian_testing_gcc_valgrind:
	extends:
	- .debian_testing_gcc
	- - .analyse_build
	- dependencies:
	- - build:debian_testing_gcc
	+ - .build_valgrind
	+ - .tests
	+ needs:
	+ - job: build:debian_testing_gcc_valgrind

	# ------------------------------------------------------------------------------
	configure:debian_testing_clang:
	extends:
	- .debian_testing_clang
	+ - .build_coverage
	- .configure
	- cache:
	- policy: pull-push

	build:debian_testing_clang:
	extends:
	- .debian_testing_clang
	+ - .build_coverage
	- .build
	- dependencies:
	- - configure:debian_testing_clang
	+ needs:
	+ - job: configure:debian_testing_clang

	test:debian_testing_clang:
	extends:
	- .debian_testing_clang
	+ - .build_coverage
	- .tests
	- dependencies:
	- - build:debian_testing_clang
	-
	-analyse_build:debian_testing_clang:
	- extends:
	- - .debian_testing_clang
	- - .analyse_build
	- dependencies:
	- - build:debian_testing_clang
	+ needs:
	+ - job: build:debian_testing_clang

	# ------------------------------------------------------------------------------
	configure:ubuntu_lts_gcc:
	extends:
	- .ubuntu_lts_gcc
	+ - .build_release
	- .configure
	- cache:
	- policy: pull-push

	build:ubuntu_lts_gcc:
	extends:
	- .ubuntu_lts_gcc
	+ - .build_release
	- .build
	- dependencies:
	- - configure:ubuntu_lts_gcc
	-
	-analyse_build:ubuntu_lts_gcc:
	- extends:
	- - .ubuntu_lts_gcc
	- - .analyse_build
	- dependencies:
	- - build:ubuntu_lts_gcc
	+ needs:
	+ - job: configure:ubuntu_lts_gcc

	test:ubuntu_lts_gcc:
	extends:
	- .ubuntu_lts_gcc
	+ - .build_release
	- .tests
	- dependencies:
	- - build:ubuntu_lts_gcc
	+ needs:
	+ - job: build:ubuntu_lts_gcc

	# ------------------------------------------------------------------------------
	-code_quality:
	+cq:code_quality:
	stage: test
	image: docker:19.03.12
	allow_failure: true
	services:
	- docker:19.03.12-dind
	variables:
	DOCKER_DRIVER: overlay2
	- DOCKER_HOST: tcp://docker:2376
	- DOCKER_TLS_CERTDIR: "/certs"
	- CODECLIMATE_DEV: 1
	- CODE_QUALITY_IMAGE: "registry.gitlab.com/gitlab-org/ci-cd/codequality:0.85.22"
	+ DOCKER_TLS_CERTDIR: ""
	+ CODE_QUALITY_IMAGE: "registry.gitlab.com/gitlab-org/ci-cd/codequality:0.85.24"
	needs: []
	script:
	- export SOURCE_CODE=$PWD
	+ - \|
	+ if ! docker info &>/dev/null; then
	+ if [ -z "$DOCKER_HOST" -a "$KUBERNETES_PORT" ]; then
	+ export DOCKER_HOST='tcp://localhost:2375'
	+ fi
	+ fi
	- \| # this is required to avoid undesirable reset of Docker image ENV variables being set on build stage
	function propagate_env_vars() {
	CURRENT_ENV=$(printenv)
	+
	for VAR_NAME; do
	echo $CURRENT_ENV \| grep "${VAR_NAME}=" > /dev/null && echo "--env $VAR_NAME "
	done
	}
	- docker pull --quiet "$CODE_QUALITY_IMAGE"
	- \|
	- - docker build -t codeclimate/codeclimate-clang-tidy test/ci/codeclimate/codeclimate-clang-tidy
	- - \|
	- docker run \
	+ docker run --rm \
	$(propagate_env_vars \
	SOURCE_CODE \
	TIMEOUT_SECONDS \
	CODECLIMATE_DEBUG \
	CODECLIMATE_DEV \
	REPORT_STDOUT \
	REPORT_FORMAT \
	ENGINE_MEMORY_LIMIT_BYTES \
	+ CODECLIMATE_PREFIX \
	) \
	--volume "$PWD":/code \
	--volume /var/run/docker.sock:/var/run/docker.sock \
	"$CODE_QUALITY_IMAGE" /code
	artifacts:
	paths:
	- gl-code-quality-report.json
	- reports:
	- codequality: gl-code-quality-report.json
	expire_in: 1 week
	- dependencies: []
	+ needs:
	+ - job: build:debian_testing_clang
	rules:
	- if: '$CODE_QUALITY_DISABLED'
	when: never
	- if: '$CI_COMMIT_TAG \|\| $CI_COMMIT_BRANCH'

	+.clang_tools:
	+ stage: test
	+ extends:
	+ - .debian_testing_clang
	+ before_script:
	+ - if [ 'x${CI_MERGE_REQUEST_ID}' != 'x' ]; then
	+ - git fetch origin $CI_MERGE_REQUEST_TARGET_BRANCH_NAME
	+ - git diff --name-only $CI_COMMIT_SHA $CI_MERGE_REQUEST_TARGET_BRANCH_NAME > file_list
	+ - FILE_LIST_ARG='-f file_list'
	+ - fi
	+ needs:
	+ - job: build:debian_testing_clang
	+ allow_failure: true
	+ rules:
	+ - if: '$CODE_QUALITY_DISABLED'
	+ when: never
	+ - if: '$CI_COMMIT_TAG \|\| $CI_COMMIT_BRANCH'
	+
	+cq:clang_tidy:
	+ extends:
	+ - .clang_tools
	+ script:
	+ - test/ci/scripts/cq
	+ -x third-party
	+ -x extra-packages
	+ -x pybind11
	+ -x test
	+ ${FILE_LIST_ARG}
	+ clang-tidy
	+ -p ${CI_PROJECT_DIR}/build > gl-clang-tidy-report.json
	+ artifacts:
	+ paths:
	+ - gl-clang-tidy-report.json
	+
	+cq:clang_format:
	+ extends:
	+ - .clang_tools
	+ script:
	+ - test/ci/scripts/cq
	+ -x third-party
	+ -x extra-packages
	+ clang-format
	+ -p ${CI_PROJECT_DIR}/build > gl-clang-format-report.json
	+ artifacts:
	+ paths:
	+ - gl-clang-format-report.json
	+
	+cq:compilation_warnings:
	+ stage: test
	+ image: python:latest
	+ script:
	+ - pip install warning-parser termcolor Click
	+ - ls build-*-err.log
	+ - test/ci/scripts/cq
	+ -x third-party
	+ -x extra-packages
	+ warnings
	+ build-*-err.log > gl-warnings-report.json
	+ needs:
	+ - job: build:debian_testing_clang
	+ - job: build:debian_testing_gcc
	+ - job: build:ubuntu_lts_gcc
	+ artifacts:
	+ paths:
	+ - gl-warnings-report.json
	+
	+cq:merge_code_quality:
	+ stage: deploy
	+ extends:
	+ - .debian_testing_clang
	+ script:
	+ - jq -Ms '[.[][]]' gl-*-report.json \| tee gl-codequality.json \| jq -C
	+ needs:
	+ - job: cq:code_quality
	+ - job: cq:clang_tidy
	+ - job: cq:clang_format
	+ - job: cq:compilation_warnings
	+ artifacts:
	+ paths:
	+ - gl-codequality.json
	+ artifacts:
	+ reports:
	+ codequality: [gl-codequality.json]
	# ------------------------------------------------------------------------------
	pages:
	stage: deploy
	extends:
	- .debian_testing_gcc
	script:
	- cd build
	- cmake -DAKANTU_DOCUMENTATION=ON ..
	- cmake --build . -t sphinx-doc
	- mv doc/dev-doc/html ../public
	- dependencies:
	- - build:debian_testing_gcc
	+ needs:
	+ - job: build:debian_testing_gcc
	artifacts:
	paths:
	- public
	only:
	- master
	diff --git a/CHANGELOG.md b/CHANGELOG.md
	new file mode 100644
	index 000000000..76c42c153
	--- /dev/null
	+++ b/CHANGELOG.md
	@@ -0,0 +1,91 @@
	+## Version 4.0 (09-21-2021)
	+
	+### Added
	+
	+- pybind11 binding
	+- contact mechanics model
	+- phase field model
	+- Added a Changelog
	+
	+### Changed
	+
	+- transferred CI from jenkinsfile to gitlab CI/CD
	+- API changes to make container mode STL compatible
	+ - clear does not set to 0 anymore but empties containers
	+ - empty does not empty containers but tells if the container is empty
	+ - zero replace the old empty and set containers to 0
	+
	+### Deprecated
	+
	+- `getForce` in the `SolidMechanicsModel` becomes `getExternalForce`
	+- `firstType()`, `lastType()` replaced by `elementTypes()`
	+
	+## Version 3.2 (not released)
	+
	+### Added
	+
	+- Activating PETSc solver back with the new solver interface
	+
	+### Deprecated
	+
	+- deprecating old C++ 03 code
	+
	+
	+## 3.0 (2018-03)
	+
	+### Added
	+
	+- Parallel cohesive elements
	+- Element groups created by default for “physical_names”
	+- Named arguments for functions (e.g. model.initFull(_analysis_method = _static))
	+
	+### Changed
	+
	+- Models using new interface for solvers
	+ - Same configuration for all models
	+ - Solver can be configured in input file
	+- Only one function to solve a step model.solveStep()
	+- Simplification of the parallel simulation with the mesh.distribute() function
	+- Switch from C++ standard 2003 to 2014 Example of changes implied by this:
	+
	+ for (UInt g = _not_ghost; g <= _ghost; ++g) {
	+ GhostType gt = (GhostType)g;
	+ Mesh::type_iterator it = this->mesh.firstType(spatial_dimension, gt);
	+ Mesh::type_iterator end = this->mesh.lastType(spatial_dimension, gt);
	+ for (; it != end; ++it) {
	+ ElementType & type = *it;
	+ ...
	+ }
	+ }
	+
	+ becomes:
	+
	+ for (auto ghost_type : ghost_types) {
	+ for (auto type : mesh.elementTypes(spatial_dimension,
	+ ghost_type)) {
	+ ...
	+ }
	+ }
	+
	+### Deleted
	+
	+- PETSc interface temporary inactive
	+- Periodic boundary condition temporary inactive
	+
	+## 2.3 (2016-03)
	+
	+### Added
	+
	+- swig python interface
	+
	+## 2.2 (2014-09)
	+
	+### Added
	+- Cohesive elements
	+
	+## 1.0 (2012-06)
	+
	+### Added
	+- Continuum damage local and non-local
	+- Models: solid mechanics, structural mechanics, heat transfer
	+
	diff --git a/cmake/AkantuExtraCompilationProfiles.cmake b/cmake/AkantuExtraCompilationProfiles.cmake
	index c39ff7480..80d648a6b 100644
	--- a/cmake/AkantuExtraCompilationProfiles.cmake
	+++ b/cmake/AkantuExtraCompilationProfiles.cmake
	@@ -1,143 +1,119 @@
	#===============================================================================
	# @file AkantuExtraCompilationProfiles.cmake
	#
	# @author Nicolas Richart <nicolas.richart@epfl.ch>
	#
	# @date creation: Fri Dec 02 2016
	# @date last modification: Wed Feb 03 2021
	#
	# @brief Compilation profiles
	#
	#
	# @section LICENSE
	#
	# Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	#
	# Akantu is free software: you can redistribute it and/or modify it under the
	# terms of the GNU Lesser General Public License as published by the Free
	# Software Foundation, either version 3 of the License, or (at your option) any
	# later version.
	#
	# Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	# A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	# details.
	#
	# You should have received a copy of the GNU Lesser General Public License along
	# with Akantu. If not, see <http://www.gnu.org/licenses/>.
	#
	#===============================================================================

	option (FORCE_COLORED_OUTPUT "Always produce ANSI-colored output (GNU/Clang only)." FALSE)
	mark_as_advanced(FORCE_COLORED_OUTPUT)
	if(FORCE_COLORED_OUTPUT)
	if (CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
	add_flags(cxx "-fcolor-diagnostics")
	else()
	add_flags(cxx "-fdiagnostics-color=always")
	endif()
	endif()


	+
	set(CMAKE_CXX_FLAGS_RELEASE "-O3 -DNDEBUG -DAKANTU_NDEBUG"
	CACHE STRING "Flags used by the compiler during release builds" FORCE)
	if (CMAKE_CXX_COMPILER_ID STREQUAL "GNU" OR CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
	set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG_INIT} -ggdb3"
	CACHE STRING "Flags used by the compiler during debug builds" FORCE)
	set(CMAKE_CXX_FLAGS_RELWITHDEBINFO "${CMAKE_CXX_FLAGS_RELWITHDEBINFO_INIT} -ggdb3"
	CACHE STRING "Flags used by the compiler during debug builds" FORCE)
	endif()

	-#Profiling
	-set(_profiling "-g -ggdb3 -pg -DNDEBUG -DAKANTU_NDEBUG -O2")
	-set(CMAKE_CXX_FLAGS_PROFILING ${_profiling}
	- CACHE STRING "Flags used by the compiler during profiling builds")
	-set(CMAKE_C_FLAGS_PROFILING ${_profiling}
	- CACHE STRING "Flags used by the compiler during profiling builds")
	-set(CMAKE_Fortran_FLAGS_PROFILING ${_profiling}
	- CACHE STRING "Flags used by the compiler during profiling builds")
	-set(CMAKE_EXE_LINKER_FLAGS_PROFILING "-pg"
	- CACHE STRING "Flags used by the linker during profiling builds")
	-set(CMAKE_SHARED_LINKER_FLAGS_PROFILING "-pg"
	- CACHE STRING "Flags used by the linker during profiling builds")
	-
	-mark_as_advanced(
	- CMAKE_CXX_FLAGS_PROFILING
	- CMAKE_C_FLAGS_PROFILING
	- CMAKE_Fortran_FLAGS_PROFILING
	- CMAKE_EXE_LINKER_FLAGS_PROFILING
	- CMAKE_SHARED_LINKER_FLAGS_PROFILING
	- )
	-
	-set(_coverage "-g -ggdb3 -DNDEBUG -DAKANTU_NDEBUG -O2 --coverage")
	-set(CMAKE_CXX_FLAGS_COVERAGE ${_coverage}
	- CACHE STRING "Flags used by the compiler during profiling builds" FORCE)
	-set(CMAKE_C_FLAGS_COVERAGE ${_coverage}
	- CACHE STRING "Flags used by the compiler during profiling builds" FORCE)
	-set(CMAKE_Fortran_FLAGS_COVERAGE ${_coverage}
	- CACHE STRING "Flags used by the compiler during profiling builds" FORCE)
	-set(CMAKE_SHARED_LINKER_FLAGS_COVERAGE ${_coverage}
	- CACHE STRING "Flags used by the compiler during profiling builds" FORCE)
	-set(CMAKE_EXE_LINKER_FLAGS_COVERAGE ${_coverage}
	- CACHE STRING "Flags used by the linker during sanitizing builds" FORCE)
	-
	-mark_as_advanced(
	- CMAKE_CXX_FLAGS_COVERAGE
	- CMAKE_C_FLAGS_COVERAGE
	- CMAKE_Fortran_FLAGS_COVERAGE
	- CMAKE_SHARED_LINKER_FLAGS_COVERAGE
	- CMAKE_EXE_LINKER_FLAGS_COVERAGE
	- )
	+function(declare_compilation_profile name)
	+ include(CMakeParseArguments)
	+
	+ cmake_parse_arguments(_args
	+ "" "COMPILER;LINKER;DOC" "" ${ARGN})
	+
	+ string(TOUPPER "${name}" _u_name)
	+
	+ if(NOT _args_DOC)
	+ string(TOLOWER "${name}" _args_DOC)
	+ endif()
	+
	+ if(NOT _args_COMPILER)
	+ message(FATAL_ERROR "declare_compilation_profile: you should at least give COMPILER flags")
	+ endif()
	+
	+ if(NOT _args_LINKER)
	+ set(_args_LINKER ${_args_COMPILER})
	+ endif()
	+
	+ foreach(_flag CXX C Fortran SHARED_LINKER EXE_LINKER)
	+ set(_stage "compiler")
	+ set(_flags ${_args_COMPILER})
	+ if(_stage MATCHES ".*LINKER")
	+ set(_stage "linker")
	+ set(_flags ${_args_LINKER})
	+ endif()
	+ set(CMAKE_${_flag}_FLAGS_${_u_name} ${_flags}
	+ CACHE STRING "Flags used by the ${_stage} during coverage builds" FORCE)
	+ mark_as_advanced(CMAKE_${_flag}_FLAGS_${_u_name})
	+ endforeach()
	+endfunction()
	+
	+
	+# Profiling
	+declare_compilation_profile(PROFILING
	+ COMPILER "-g -ggdb3 -pg -DNDEBUG -DAKANTU_NDEBUG -O3")
	+
	+# Valgrind
	+declare_compilation_profile(VALGRIND
	+ COMPILER "-g -ggdb3 -DNDEBUG -DAKANTU_NDEBUG -O3")
	+
	+# Coverage
	+declare_compilation_profile(COVERAGE
	+ COMPILER "-g -ggdb3 -DNDEBUG -DAKANTU_NDEBUG -O2 --coverage")

	# Sanitize the code
	if ((CMAKE_CXX_COMPILER_ID STREQUAL "GNU" AND CMAKE_CXX_COMPILER_VERSION VERSION_GREATER "5.2") OR
	CMAKE_CXX_COMPILER_ID STREQUAL "Clang")

	if(CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
	set(_blacklist " -fsanitize-blacklist=${PROJECT_SOURCE_DIR}/cmake/sanitize-blacklist.txt")
	endif()
	- set(_sanitize "-g -ggdb3 -O2 -fsanitize=address -fsanitize=leak -fsanitize=undefined -fno-omit-frame-pointer${_blacklist}")
	-
	- set(CMAKE_CXX_FLAGS_SANITIZE ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_C_FLAGS_SANITIZE ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_Fortran_FLAGS_SANITIZE ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_EXE_LINKER_FLAGS_SANITIZE ${_sanitize}
	- CACHE STRING "Flags used by the linker during sanitizing builds")
	- set(CMAKE_SHARED_LINKER_FLAGS_SANITIZE ${_sanitize}
	- CACHE STRING "Flags used by the linker during sanitizing builds")
	-
	- mark_as_advanced(
	- CMAKE_CXX_FLAGS_SANITIZE
	- CMAKE_C_FLAGS_SANITIZE
	- CMAKE_Fortran_FLAGS_SANITIZE
	- CMAKE_SHARED_LINKER_FLAGS_SANITIZE
	- CMAKE_EXE_LINKER_FLAGS_SANITIZE
	- )
	+
	+ declare_compilation_profile(SANITIZE
	+ COMPILER "-g -ggdb3 -O2 -fsanitize=address -fsanitize=leak -fsanitize=undefined -fno-omit-frame-pointer${_blacklist}")
	endif()

	if (CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
	- set(_sanitize "-g -ggdb3 -O2 -fPIE -fsanitize=memory -fsanitize-memory-track-origins -fsanitize-recover=all -fno-omit-frame-pointer -fsanitize-blacklist=${PROJECT_SOURCE_DIR}/cmake/sanitize-blacklist.txt")
	-
	- set(CMAKE_CXX_FLAGS_SANITIZEMEMORY ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_C_FLAGS_SANITIZEMEMORY ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_Fortran_FLAGS_SANITIZEMEMORY ${_sanitize}
	- CACHE STRING "Flags used by the compiler during sanitizing builds")
	- set(CMAKE_EXE_LINKER_FLAGS_SANITIZEMEMORY ${_sanitize}
	- CACHE STRING "Flags used by the linker during sanitizing builds")
	- set(CMAKE_SHARED_LINKER_FLAGS_SANITIZEMEMORY ${_sanitize}
	- CACHE STRING "Flags used by the linker during sanitizing builds")
	-
	- mark_as_advanced(
	- CMAKE_CXX_FLAGS_SANITIZEMEMORY
	- CMAKE_C_FLAGS_SANITIZEMEMORY
	- CMAKE_Fortran_FLAGS_SANITIZEMEMORY
	- CMAKE_SHARED_LINKER_FLAGS_SANITIZEMEMORY
	- CMAKE_EXE_LINKER_FLAGS_SANITIZEMEMORY
	- )
	+ declare_compilation_profile(SANITIZEMEMORY
	+ COMPILER "-g -ggdb3 -O2 -fPIE -fsanitize=memory -fsanitize-memory-track-origins -fsanitize-recover=all -fno-omit-frame-pointer -fsanitize-blacklist=${PROJECT_SOURCE_DIR}/cmake/sanitize-blacklist.txt"
	+ DOC "\"sanitize memory\"")
	+endif()
	+
	+if (CMAKE_BUILD_TYPE MATCHES "[Vv][Aa][Ll][Gg][Rr][Ii][Nn][Dd]")
	+ find_program(VALGRIND_EXECUTABLE valgrind)
	endif()
	diff --git a/cmake/AkantuTestsMacros.cmake b/cmake/AkantuTestsMacros.cmake
	index 5103e28cb..319e10f97 100644
	--- a/cmake/AkantuTestsMacros.cmake
	+++ b/cmake/AkantuTestsMacros.cmake
	@@ -1,653 +1,657 @@
	#===============================================================================
	# @file AkantuTestsMacros.cmake
	#
	# @author Nicolas Richart <nicolas.richart@epfl.ch>
	#
	# @date creation: Fri Sep 03 2010
	# @date last modification: Tue Jun 30 2020
	#
	# @brief macros for tests
	#
	#
	# @section LICENSE
	#
	# Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	#
	# Akantu is free software: you can redistribute it and/or modify it under the
	# terms of the GNU Lesser General Public License as published by the Free
	# Software Foundation, either version 3 of the License, or (at your option) any
	# later version.
	#
	# Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	# A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	# details.
	#
	# You should have received a copy of the GNU Lesser General Public License along
	# with Akantu. If not, see <http://www.gnu.org/licenses/>.
	#
	#===============================================================================


	#[=======================================================================[.rst:
	AkantuTestsMacros
	-----------------

	This modules provides the functions to helper to declare tests and folders
	containing tests in akantu

	.. command:: add_test_tree

	add_test_tree(<test_direcotry>)

	``<test_directory>`` is the entry direcroty of the full structure of
	subfolders containing tests

	.. command:: add_akantu_test

	add_akantu_test(<dir> <desc>)

	This function add a subdirectory ``<dir>`` of tests that will be conditionnaly
	activable and will be visible only if the parent folder as been activated An
	option ``AKANTU_BUILD_TEST_<dir>`` will appear in ccmake with the description
	``<desc>``. The compilation of all tests can be forced with the option
	``AKANTU_BUILD_ALL_TESTS``

	.. command:: register_test

	register_test(<test_name>
	SOURCES <sources>...
	PACKAGE <akantu_packages>...
	SCRIPT <scirpt>
	[FILES_TO_COPY <filenames>...]
	[DEPENDS <targets>...]
	[DIRECTORIES_TO_CREATE <directories>...]
	[COMPILE_OPTIONS <flags>...]
	[EXTRA_FILES <filnames>...]
	[LINK_LIBRARIES <libraries>...]
	[INCLUDE_DIRECTORIES <include>...]
	[UNSABLE]
	[PARALLEL]
	[PARALLEL_LEVEL <procs>...]
	)

	This function defines a test ``<test_name>_run`` this test could be of
	different nature depending on the context. If Just sources are provided the
	test consist of running the executable generated. If a file ``<test_name>.sh``
	is present the test will execute the script. And if a ``<test_name>.verified``
	exists the output of the test will be compared to this reference file

	The options are:

	``SOURCES <sources>...``
	The list of source files to compile to generate the executable of the test

	``PACKAGE <akantu_packages>...``
	The list of package to which this test belongs. The test will be activable
	only of all the packages listed are activated

	``SCRIPT <script>``
	The script to execute instead of the executable

	``FILES_TO_COPY <filenames>...``
	List of files to copy from the source directory to the build directory

	``DEPENDS <targets>...``
	List of targets the test depends on, for example if a mesh as to be generated

	``DIRECTORIES_TO_CREATE <directories>...``
	Obsolete. This specifies a list of directories that have to be created in
	the build folder

	``COMPILE_OPTIONS <flags>...``
	List of extra compilations options to pass to the compiler

	``EXTRA_FILES <filnames>...``
	Files to consider when generating a package_source

	``UNSABLE``
	If this option is specified the test can be unacitivated by the glocal option
	``AKANTU_BUILD_UNSTABLE_TESTS``, this is mainly intendeed to remove test
	under developement from the continious integration

	``PARALLEL``
	This specifies that this test should be run in parallel. It will generate a
	series of test for different number of processors. This automaticaly adds a
	dependency to the package ``AKANTU_PARALLEL``

	``PARALLEL_LEVEL``
	This defines the different processor numbers to use, if not defined the
	macro tries to determine it in a "clever" way

	]=======================================================================]

	set(AKANTU_DRIVER_SCRIPT ${AKANTU_CMAKE_DIR}/akantu_test_driver.sh)

	# ==============================================================================
	macro(add_test_tree dir)
	if(AKANTU_TESTS)
	enable_testing()
	include(CTest)
	mark_as_advanced(BUILD_TESTING)

	set(_akantu_current_parent_test ${dir} CACHE INTERNAL "Current test folder" FORCE)
	set(_akantu_${dir}_tests_count 0 CACHE INTERNAL "" FORCE)

	string(TOUPPER ${dir} _u_dir)
	set(AKANTU_BUILD_${_u_dir} ON CACHE INTERNAL "${desc}" FORCE)

	package_get_all_test_folders(_test_dirs)

	foreach(_dir ${_test_dirs})
	add_subdirectory(${_dir})
	endforeach()
	endif()
	endmacro()


	set(_test_flags
	UNSTABLE
	PARALLEL
	PYTHON
	GTEST
	HEADER_ONLY
	)

	set(_test_one_variables
	POSTPROCESS
	SCRIPT
	)

	set(_test_multi_variables
	SOURCES
	FILES_TO_COPY
	DEPENDS
	DIRECTORIES_TO_CREATE
	COMPILE_OPTIONS
	EXTRA_FILES
	LINK_LIBRARIES
	INCLUDE_DIRECTORIES
	PACKAGE
	PARALLEL_LEVEL
	)


	# ==============================================================================
	function(add_akantu_test dir desc)
	if(NOT EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/${dir})
	return()
	endif()

	set(_my_parent_dir ${_akantu_current_parent_test})

	# initialize variables
	set(_akantu_current_parent_test ${dir} CACHE INTERNAL "Current test folder" FORCE)
	set(_akantu_${dir}_tests_count 0 CACHE INTERNAL "" FORCE)

	# set the option for this directory
	string(TOUPPER ${dir} _u_dir)
	option(AKANTU_BUILD_${_u_dir} "${desc}")
	mark_as_advanced(AKANTU_BUILD_${_u_dir})

	# add the sub-directory
	add_subdirectory(${dir})

	# if no test can be activated make the option disappear
	set(_force_deactivate_count FALSE)
	if(${_akantu_${dir}_tests_count} EQUAL 0)
	set(_force_deactivate_count TRUE)
	endif()

	# if parent off make the option disappear
	set(_force_deactivate_parent FALSE)
	string(TOUPPER ${_my_parent_dir} _u_parent_dir)
	if(NOT AKANTU_BUILD_${_u_parent_dir})
	set(_force_deactivate_parent TRUE)
	endif()

	if(_force_deactivate_parent OR _force_deactivate_count OR AKANTU_BUILD_ALL_TESTS)
	if(NOT DEFINED _AKANTU_BUILD_${_u_dir}_SAVE)
	set(_AKANTU_BUILD_${_u_dir}_SAVE ${AKANTU_BUILD_${_u_dir}} CACHE INTERNAL "" FORCE)
	endif()
	unset(AKANTU_BUILD_${_u_dir} CACHE)
	if(AKANTU_BUILD_ALL_TESTS AND NOT _force_deactivate_count)
	set(AKANTU_BUILD_${_u_dir} ON CACHE INTERNAL "${desc}" FORCE)
	else()
	set(AKANTU_BUILD_${_u_dir} OFF CACHE INTERNAL "${desc}" FORCE)
	endif()
	else()
	if(DEFINED _AKANTU_BUILD_${_u_dir}_SAVE)
	unset(AKANTU_BUILD_${_u_dir} CACHE)
	set(AKANTU_BUILD_${_u_dir} ${_AKANTU_BUILD_${_u_dir}_SAVE} CACHE BOOL "${desc}")
	unset(_AKANTU_BUILD_${_u_dir}_SAVE CACHE)
	endif()
	endif()

	# adding up to the parent count
	math(EXPR _tmp_parent_count "${_akantu_${dir}_tests_count} + ${_akantu_${_my_parent_dir}_tests_count}")
	set(_akantu_${_my_parent_dir}_tests_count ${_tmp_parent_count} CACHE INTERNAL "" FORCE)

	# restoring the parent current dir
	set(_akantu_current_parent_test ${_my_parent_dir} CACHE INTERNAL "Current test folder" FORCE)
	endfunction()

	function(is_test_active is_active)
	cmake_parse_arguments(_register_test
	"${_test_flags}"
	"${_test_one_variables}"
	"${_test_multi_variables}"
	${ARGN}
	)

	if(NOT _register_test_PACKAGE)
	message(FATAL_ERROR "No reference package was defined for the test"
	" ${test_name} in folder ${CMAKE_CURRENT_SOURCE_DIR}")
	endif()

	if(_register_test_PYTHON)
	list(APPEND _register_test_PACKAGE python_interface)
	endif()

	set(_test_act TRUE)
	# Activate the test anly if all packages associated to the test are activated
	foreach(_package ${_register_test_PACKAGE})
	package_is_activated(${_package} _act)
	if(NOT _act)
	set(_test_act FALSE)
	endif()
	endforeach()

	# check if the test is marked unstable and if the unstable test should be run
	if(_register_test_UNSTABLE AND NOT AKANTU_BUILD_UNSTABLE_TESTS)
	set(_test_act FALSE)
	endif()

	if(_test_act)
	# todo this should be checked for the build package_sources since the file will not be listed.
	math(EXPR _tmp_parent_count "${_akantu_${_akantu_current_parent_test}_tests_count} + 1")
	set(_akantu_${_akantu_current_parent_test}_tests_count ${_tmp_parent_count} CACHE INTERNAL "" FORCE)
	endif()

	string(TOUPPER ${_akantu_current_parent_test} _u_parent)
	if(NOT (AKANTU_BUILD_${_u_parent} OR AKANTU_BUILD_ALL_TESTS))
	set(_test_act FALSE)
	endif()

	set(${is_active} ${_test_act} PARENT_SCOPE)
	endfunction()

	# ------------------------------------------------------------------------------
	function(register_gtest_sources)
	cmake_parse_arguments(_register_test
	"${_test_flags}"
	"${_test_one_variables}"
	"${_test_multi_variables}"
	${ARGN}
	)

	is_test_active(_is_active ${ARGN})
	register_test_files_to_package(${ARGN})

	if(NOT _is_active)
	return()
	endif()

	if(_register_test_PACKAGE)
	set(_list ${_gtest_PACKAGE})
	list(APPEND _list ${_register_test_PACKAGE})
	list(REMOVE_DUPLICATES _list)
	set(_gtest_PACKAGE ${_list} PARENT_SCOPE)
	endif()

	foreach (_var ${_test_flags})
	if(_var STREQUAL "HEADER_ONLY")
	if(NOT DEFINED_register_test_${_var})
	set(_gtest_${_var} OFF PARENT_SCOPE)
	elseif(NOT DEFINED _gtest_${_var})
	set(_gtest_${_var} ON PARENT_SCOPE)
	endif()
	continue()
	endif()

	if(_register_test_${_var})
	set(_gtest_${_var} ON PARENT_SCOPE)
	else()
	if(_gtest_${_var})
	message("Another gtest file required ${_var} to be ON it will be globally set for this folder...")
	endif()
	endif()
	endforeach()

	if(_register_test_UNPARSED_ARGUMENTS)
	list(APPEND _register_test_SOURCES ${_register_test_UNPARSED_ARGUMENTS})
	endif()

	foreach (_var ${_test_multi_variables})
	if(_register_test_${_var})
	set(_list ${_gtest_${_var}})
	list(APPEND _list ${_register_test_${_var}})
	list(REMOVE_DUPLICATES _list)
	set(_gtest_${_var} ${_list} PARENT_SCOPE)
	endif()
	endforeach()
	endfunction()

	# ==============================================================================
	function(akantu_pybind11_add_module target)
	package_is_activated(pybind11 _pybind11_act)
	if(_pybind11_act)
	package_get_all_external_informations(
	INTERFACE_INCLUDE AKANTU_INTERFACE_EXTERNAL_INCLUDE_DIR
	)

	pybind11_add_module(${target} ${ARGN})
	target_link_libraries(${target} PRIVATE akantu)
	target_include_directories(${target} SYSTEM PRIVATE ${PYBIND11_INCLUDE_DIR} ${PROJECT_SOURCE_DIR}/python)
	set_property(TARGET ${target} PROPERTY DEBUG_POSTFIX "")
	endif()
	endfunction()

	# ==============================================================================
	function(register_gtest_test test_name)
	if(NOT _gtest_PACKAGE)
	return()
	endif()

	set(_argn ${test_name}_gtest)

	set(_link_libraries GTest::GTest GTest::Main)

	list(FIND _gtest_PACKAGE python_interface _pos)
	package_is_activated(python_interface _python_interface_act)

	if(_python_interface_act AND (NOT _pos EQUAL -1))
	list(APPEND _link_libraries pybind11::embed)
	set(_compile_flags COMPILE_OPTIONS "AKANTU_TEST_USE_PYBIND11")
	endif()

	is_test_active(_is_active ${ARGN} PACKAGE ${_gtest_PACKAGE})
	if(NOT _is_active)
	return()
	endif()

	register_gtest_sources(${ARGN}
	SOURCES ${PROJECT_SOURCE_DIR}/test/test_gtest_main.cc
	LINK_LIBRARIES ${_link_libraries}
	PACKAGE ${_gtest_PACKAGE}
	${_compile_flags}
	)

	foreach (_var ${_test_flags})
	if(_gtest_${_var})
	list(APPEND _argn ${_var})
	unset(_gtest_${_var})
	endif()
	endforeach()

	foreach (_var ${_test_multi_variables})
	if(_gtest_${_var})
	list(APPEND _argn ${_var} ${_gtest_${_var}})
	unset(_gtest_${_var})
	endif()
	endforeach()

	register_test(${_argn} GTEST)
	target_include_directories(${test_name}_gtest PRIVATE ${PROJECT_SOURCE_DIR}/test)
	endfunction()

	# ==============================================================================
	function(register_test test_name)
	cmake_parse_arguments(_register_test
	"${_test_flags}"
	"${_test_one_variables}"
	"${_test_multi_variables}"
	${ARGN}
	)

	register_test_files_to_package(${ARGN})
	is_test_active(_test_act ${ARGN})
	if(NOT _test_act)
	return()
	endif()

	set(_extra_args)

	# check that the sources are files that need to be compiled
	if(_register_test_SOURCES} OR _register_test_UNPARSED_ARGUMENTS)
	set(_need_to_compile TRUE)
	else()
	set(_need_to_compile FALSE)
	endif()

	set(_compile_source)
	foreach(_file ${_register_test_SOURCES} ${_register_test_UNPARSED_ARGUMENTS})
	if(_file MATCHES "\\.cc$" OR _file MATCHES "\\.hh$")
	list(APPEND _compile_source ${_file})
	endif()
	endforeach()

	if(_compile_source)
	# get the include directories for sources in activated directories
	package_get_all_include_directories(
	AKANTU_LIBRARY_INCLUDE_DIRS
	)

	# get the external packages compilation and linking informations
	package_get_all_external_informations(
	INTERFACE_INCLUDE AKANTU_EXTERNAL_INCLUDE_DIR
	)

	foreach(_pkg ${_register_test_PACKAGE})
	package_get_nature(${_pkg} _nature)
	if(_nature MATCHES "^external.*")
	package_get_include_dir(${_pkg} _incl)
	package_get_libraries(${_pkg} _libs)

	list(APPEND _register_test_INCLUDE_DIRECTORIES ${_incl})
	list(APPEND _register_test_LINK_LIBRARIES ${_libs})
	endif()
	endforeach()

	# Register the executable to compile
	add_executable(${test_name} ${_compile_source})

	# set the proper includes to build most of the tests
	target_include_directories(${test_name}
	PRIVATE ${AKANTU_LIBRARY_INCLUDE_DIRS}
	${AKANTU_EXTERNAL_INCLUDE_DIR}
	${PROJECT_BINARY_DIR}/src
	${_register_test_INCLUDE_DIRECTORIES})

	if(NOT _register_test_HEADER_ONLY)
	target_link_libraries(${test_name} PRIVATE akantu ${_register_test_LINK_LIBRARIES})
	else()
	get_target_property(_features akantu INTERFACE_COMPILE_FEATURES)
	target_link_libraries(${test_name} ${_register_test_LINK_LIBRARIES})
	target_compile_features(${test_name} PRIVATE ${_features})
	endif()

	# add the extra compilation options
	if(_register_test_COMPILE_OPTIONS)
	set_target_properties(${test_name}
	PROPERTIES COMPILE_DEFINITIONS "${_register_test_COMPILE_OPTIONS}")
	endif()

	if(AKANTU_EXTRA_CXX_FLAGS)
	set_target_properties(${test_name}
	PROPERTIES COMPILE_FLAGS "${AKANTU_EXTRA_CXX_FLAGS}")
	endif()
	else()
	add_custom_target(${test_name} ALL)
	if(_register_test_UNPARSED_ARGUMENTS AND NOT _register_test_SCRIPT)
	set(_register_test_SCRIPT ${_register_test_UNPARSED_ARGUMENTS})
	endif()
	endif()

	if(_register_test_DEPENDS)
	add_dependencies(${test_name} ${_register_test_DEPENDS})
	endif()

	# copy the needed files to the build folder
	if(_register_test_FILES_TO_COPY)
	foreach(_file ${_register_test_FILES_TO_COPY})
	_add_file_to_copy(${test_name} "${_file}")
	endforeach()
	endif()

	# create the needed folders in the build folder
	if(_register_test_DIRECTORIES_TO_CREATE)
	foreach(_dir ${_register_test_DIRECTORIES_TO_CREATE})
	if(IS_ABSOLUTE ${dir})
	file(MAKE_DIRECTORY "${_dir}")
	else()
	file(MAKE_DIRECTORY "${CMAKE_CURRENT_BINARY_DIR}/${_dir}")
	endif()
	endforeach()
	endif()

	# register the test for ctest
	set(_arguments -n "${test_name}")
	if(_register_test_SCRIPT)
	_add_file_to_copy(${test_name} ${_register_test_SCRIPT})
	if(_register_test_PYTHON)
	if(NOT PYTHONINTERP_FOUND)
	find_package(PythonInterp ${AKANTU_PREFERRED_PYTHON_VERSION} REQUIRED)
	endif()
	list(APPEND _arguments -e "${PYTHON_EXECUTABLE}")
	list(APPEND _extra_args "${_register_test_SCRIPT}")
	add_dependencies(${test_name} py11_akantu)
	else()
	list(APPEND _arguments -e "./${_register_test_SCRIPT}")
	endif()
	elseif(EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.sh")
	_add_file_to_copy(${test_name} ${test_name}.sh)
	list(APPEND _arguments -e "./${test_name}.sh")
	else()
	list(APPEND _arguments -e "./${test_name}")
	endif()

	if(_register_test_GTEST)
	list(APPEND _extra_args "--" "--gtest_output=xml:${PROJECT_BINARY_DIR}/gtest_reports/${test_name}.xml")
	endif()

	list(APPEND _arguments -E "${PROJECT_BINARY_DIR}/akantu_environement.sh")

	package_is_activated(parallel _is_parallel)
	if(_is_parallel AND AKANTU_TESTS_ALWAYS_USE_MPI AND NOT _register_test_PARALLEL)
	set(_register_test_PARALLEL TRUE)
	set(_register_test_PARALLEL_LEVEL 1)
	endif()

	if(_register_test_PARALLEL AND _is_parallel)
	set(_exe ${MPIEXEC})
	if(NOT _exe)
	set(_exe ${MPIEXEC_EXECUTABLE})
	endif()
	list(APPEND _arguments -p "${_exe} ${MPIEXEC_PREFLAGS} ${MPIEXEC_NUMPROC_FLAG}")
	if(_register_test_PARALLEL_LEVEL)
	set(_procs "${_register_test_PARALLEL_LEVEL}")
	elseif(CMAKE_VERSION VERSION_GREATER "3.0")
	set(_procs)
	if(MPIEXEC_MAX_NUMPROCS)
	- set(N MPIEXEC_MAX_NUMPROCS)
	+ set(N MPIEXEC_MAX_NUMPROCS)
	else()
	- include(ProcessorCount)
	- ProcessorCount(N)
	+ include(ProcessorCount)
	+ ProcessorCount(N)
	endif()

	while(N GREATER 1)
	list(APPEND _procs ${N})
	math(EXPR N "${N} / 2")
	endwhile()
	list(APPEND _procs 1)
	endif()

	if(NOT _procs)
	set(_procs 2)
	endif()
	endif()

	if(_register_test_POSTPROCESS)
	list(APPEND _arguments -s "${_register_test_POSTPROCESS}")
	file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${_register_test_POSTPROCESS}
	FILE_PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE
	DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
	endif()

	list(APPEND _arguments -w "${CMAKE_CURRENT_BINARY_DIR}")

	if(EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.verified")
	list(APPEND _arguments -r "${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.verified")
	endif()

	+ if(CMAKE_BUILD_TYPE MATCHES "[Vv][Aa][Ll][Gg][Rr][Ii][Nn][Dd]" AND VALGRINDXECUTABLE)
	+ list(APPEND _arguments -v "${VALGRIND_EXECUTABLE} --error-exitcode=111 --leak-check=full --suppressions=${PROJECT_SOURCE_DIR}/test/ci/ompi_init.supp")
	+ endif()
	+
	string(REPLACE ";" " " _command "${_arguments}")

	# register them test
	if(_procs)
	foreach(p ${_procs})
	add_test(NAME ${test_name}_${p} COMMAND ${AKANTU_DRIVER_SCRIPT} ${_arguments} -N ${p} ${_extra_args})
	set_property(TEST ${test_name}_${p} PROPERTY PROCESSORS ${p})
	endforeach()
	else()
	add_test(NAME ${test_name} COMMAND ${AKANTU_DRIVER_SCRIPT} ${_arguments} ${_extra_args})
	set_property(TEST ${test_name} PROPERTY PROCESSORS 1)
	endif()
	endfunction()


	function(register_test_files_to_package)
	cmake_parse_arguments(_register_test
	"${_test_flags}"
	"${_test_one_variables}"
	"${_test_multi_variables}"
	${ARGN}
	)

	if(_register_test_PYTHON)
	list(APPEND _register_test_PACKAGE python_interface)
	endif()

	set(_test_all_files)
	# add the source files in the list of all files
	foreach(_file ${_register_test_SOURCES} ${_register_test_UNPARSED_ARGUMENTS}
	${_register_test_EXTRA_FILES} ${_register_test_SOURCES} ${_register_test_SCRIPT}
	${_register_test_POSTPROCESS} ${_register_test_FILES_TO_COPY})
	if(EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/${_file} OR EXISTS ${_file})
	list(APPEND _test_all_files "${_file}")
	else()
	message("The file \"${_file}\" registred by the test \"${test_name}\" does not exists")
	endif()
	endforeach()

	# add the different dependencies files (meshes, local libraries, ...)
	foreach(_dep ${_register_test_DEPENDS})
	get_target_list_of_associated_files(${_dep} _dep_ressources)
	if(_dep_ressources)
	list(APPEND _test_all_files "${_dep_ressources}")
	endif()
	endforeach()

	# add extra files to the list of files referenced by a given test
	if(EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.sh")
	list(APPEND _test_all_files "${test_name}.sh")
	endif()
	if(EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.verified")
	list(APPEND _test_all_files "${test_name}.verified")
	endif()
	if(_register_test_SCRIPT)
	list(APPEND _test_all_files "${_register_test_SCRIPT}")
	endif()

	# clean the list of all files for this test and add them in the total list
	foreach(_file ${_test_all_files})
	get_filename_component(_full ${_file} ABSOLUTE)
	file(RELATIVE_PATH __file ${PROJECT_SOURCE_DIR} ${_full})
	list(APPEND _tmp "${__file}")
	endforeach()

	foreach(_pkg ${_register_test_PACKAGE})
	package_get_name(${_pkg} _pkg_name)
	_package_add_to_variable(TESTS_FILES ${_pkg_name} ${_tmp})
	endforeach()
	endfunction()
	diff --git a/cmake/akantu_test_driver.sh b/cmake/akantu_test_driver.sh
	index 452591ed8..eb675c9da 100755
	--- a/cmake/akantu_test_driver.sh
	+++ b/cmake/akantu_test_driver.sh
	@@ -1,145 +1,150 @@
	#!/bin/bash

	set -o errexit
	set -o pipefail

	show_help() {
	cat << EOF
	Usage: ${0##*/} -n NAME -e EXECUTABLE [-p MPI_WRAPPER] [-s SCRIPT_FILE]
	[-r REFERENCE_FILE] [-w WORKING_DIR] [ARGS]
	Execute the test in the good configuration according to the options given

	-e EXECUTABLE Main executable of the test
	-n NAME Name of the test
	-p MPI_WRAPPER Executes the test for multiple parallel configuration
	-s SCRIPT_FILE Script to execute after the execution of the test to
	postprocess the results
	+ -v VALGRIND_PATH Running the test using valgrind
	-r REFERENCE_FILE Reference file to compare with if the name of the file
	contains a <nb_proc> this will be used for the different
	configuration when -p is given
	-w WORKING_DIR The directory in which to execute the test
	-E ENVIRONMENT_FILE File to source before running tests
	-h Print this helps
	EOF
	}

	full_redirect() {
	- local nproc=$1
	- shift
	- local name=$1
	- shift
	-
	- local sout=".lastout"
	- local serr=".lasterr"
	- if [ ${nproc} -ne 0 ]; then
	- sout="-${nproc}${sout}"
	- serr="-${nproc}${serr}"
	- fi
	- echo "Run $*"
	- (($* \| tee "${name}${sout}") 3>&1 1>&2 2>&3 \| tee "${name}${serr}") 3>&1 1>&2 2>&3
	-
	- lastout="${name}${sout}"
	+ local nproc=$1
	+ shift
	+ local name=$1
	+ shift
	+
	+ local sout=".lastout"
	+ local serr=".lasterr"
	+ if [ "${nproc}" -ne 0 ]; then
	+ sout="-${nproc}${sout}"
	+ serr="-${nproc}${serr}"
	+ fi
	+ echo "Run $*"
	+ ( ($* \| tee "${name}${sout}") 3>&1 1>&2 2>&3 \| tee "${name}${serr}") 3>&1 1>&2 2>&3
	+
	+ lastout="${name}${sout}"
	}

	name=
	executable=
	parallel=
	postprocess_script=
	reference=
	working_dir=
	envi=
	parallel_processes="2"
	-
	+valgrind=""

	while :
	do
	case "$1" in
	-e)
	executable=$2
	shift 2
	;;
	-E)
	envi="$2"
	shift 2
	;;
	-h \| --help)
	show_help
	exit 0
	;;
	-n)
	name="$2"
	shift 2
	;;
	-N)
	parallel_processes="$2"
	shift 2
	;;
	-p)
	parallel="$2"
	shift 2
	;;
	-r)
	reference="$2"
	shift 2
	;;
	-s)
	postprocess_script="$2"
	shift 2
	;;
	-w)
	working_dir="$2"
	shift 2
	;;
	+ -v)
	+ valgrind="$2"
	+ shift 2
	+ ;;
	--) # End of all options
	shift
	break
	;;
	-*)
	echo "Error: Unknown option: $1" >&2
	show_help
	exit 1
	;;
	*) #No more options
	break
	;;
	esac
	done

	-_args=$@
	+_args=$*

	if [ -n "${envi}" ]; then
	- source ${envi}
	+ source "${envi}"
	fi

	-if [ -z "${name}" -o -z "${executable}" ]; then
	- echo "Missing executable or name"
	- show_help
	- exit 1
	+if [ -z "${name}" ] \|\| [ -z "${executable}" ]; then
	+ echo "Missing executable or name"
	+ show_help
	+ exit 1
	fi

	if [ -n "${working_dir}" ]; then
	- current_directory=$PWD
	- echo "Entering directory ${working_dir}"
	- cd "${working_dir}"
	+# current_directory=$PWD
	+ echo "Entering directory ${working_dir}"
	+ cd "${working_dir}"
	fi

	if [ -z "${parallel}" ]; then
	- echo "Executing the test ${name}"
	- full_redirect 0 ${name} "${executable} ${_args}"
	+ echo "Executing the test ${name}"
	+ full_redirect 0 "${name}" "${valgrind} ${executable} ${_args}"
	else
	#for i in ${parallel_processes}; do
	i=${parallel_processes}
	echo "Executing the test ${name} for ${i} procs"
	- full_redirect $i ${name}_$i "${parallel} ${i} ${executable} ${_args}"
	+ full_redirect "$i" "${name}"_"$i" "${parallel} ${i} ${valgrind} ${executable} ${_args}"
	#done
	fi

	if [ -n "${postprocess_script}" ]; then
	echo "Executing the test ${name} post-processing"
	- full_redirect 0 ${name}_pp ./${postprocess_script}
	+ full_redirect 0 "${name}_pp" "./${postprocess_script}"
	fi

	if [ -n "${reference}" ]; then
	- echo "Comparing last generated output to the reference file"
	- diff -w ${lastout} ${reference}
	+ echo "Comparing last generated output to the reference file"
	+ diff -w "${lastout}" "${reference}"
	fi
	diff --git a/examples/boundary_conditions/predefined_bc/predefined_bc.cc b/examples/boundary_conditions/predefined_bc/predefined_bc.cc
	index 4294771ef..59ae792b8 100644
	--- a/examples/boundary_conditions/predefined_bc/predefined_bc.cc
	+++ b/examples/boundary_conditions/predefined_bc/predefined_bc.cc
	@@ -1,64 +1,64 @@
	/**
	* @file predefined_bc.cc
	*
	* @author Zineb Fouad <zineb.fouad@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Wed Feb 06 2019
	*
	* @brief Example showing how to set boundary conditions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	Mesh mesh(2);
	mesh.read("square.msh");

	// model initialization
	SolidMechanicsModel model(mesh);
	model.initFull();

	// Dirichlet boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "Fixed_x");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "Fixed_y");

	// output in a paraview file
	model.setBaseName("plate");
	model.addDumpFieldVector("displacement");
	model.addDumpField("blocked_dofs");
	model.addDumpField("external_force");
	model.dump();

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/boundary_conditions/python_user_defined_bc/python_user_defined_bc.cc b/examples/boundary_conditions/python_user_defined_bc/python_user_defined_bc.cc
	index 215ad901f..e3d3bede3 100644
	--- a/examples/boundary_conditions/python_user_defined_bc/python_user_defined_bc.cc
	+++ b/examples/boundary_conditions/python_user_defined_bc/python_user_defined_bc.cc
	@@ -1,97 +1,97 @@
	/**
	* @file python_user_defined_bc.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Tue Sep 08 2020
	*
	* @brief user define boundary condition example
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <iostream>
	#include <pybind11/embed.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class PYBIND11_EXPORT SineBoundary : public BC::Dirichlet::DirichletFunctor {
	public:
	SineBoundary(Real amplitude, Real phase) {
	py_module = py::module::import("boundary_condition");
	py_sin_boundary = py_module.attr("SinBoundary")(amplitude, phase);
	}

	public:
	inline void operator()(__attribute__((unused)) UInt node,
	Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	py_sin_boundary.attr("compute")(primal, coord, flags);
	}

	protected:
	py::object py_sin_boundary;
	py::module py_module;
	};

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	py::scoped_interpreter guard{};

	UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);
	mesh.read("fine_mesh.msh");

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull();

	/// boundary conditions
	Vector<Real> traction(2, 0.2);
	SineBoundary sin_boundary(.2, 10.);

	model.applyBC(sin_boundary, "Fixed_x");
	model.applyBC(BC::Dirichlet::FixedValue(0., _y), "Fixed_y");
	model.applyBC(BC::Neumann::FromTraction(traction), "Traction");

	// output a paraview file with the boundary conditions
	model.setBaseName("plate");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("external_force");
	model.addDumpField("blocked_dofs");
	model.dump();

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/boundary_conditions/user_defined_bc/user_defined_bc.cc b/examples/boundary_conditions/user_defined_bc/user_defined_bc.cc
	index e098d96f1..e31557e7d 100644
	--- a/examples/boundary_conditions/user_defined_bc/user_defined_bc.cc
	+++ b/examples/boundary_conditions/user_defined_bc/user_defined_bc.cc
	@@ -1,90 +1,90 @@
	/**
	* @file user_defined_bc.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Wed Feb 06 2019
	*
	* @brief example of boundary conditions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class SineBoundary : public BC::Dirichlet::DirichletFunctor {
	public:
	SineBoundary(Real amp, Real phase, BC::Axis ax = _x)
	: DirichletFunctor(ax), amplitude(amp), phase(phase) {}

	public:
	inline void operator()(__attribute__((unused)) UInt node,
	Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	DIRICHLET_SANITY_CHECK;
	flags(axis) = true;
	primal(axis) = -amplitude * std::sin(phase * coord(1));
	}

	protected:
	Real amplitude;
	Real phase;
	};

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);
	mesh.read("fine_mesh.msh");

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull();

	/// boundary conditions
	Vector<Real> traction(2, 0.2);
	model.applyBC(SineBoundary(.2, 10., _x), "Fixed_x");
	model.applyBC(BC::Dirichlet::FixedValue(0., _y), "Fixed_y");
	model.applyBC(BC::Neumann::FromTraction(traction), "Traction");

	// output a paraview file with the boundary conditions
	model.setBaseName("plate");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("external_force");
	model.addDumpField("blocked_dofs");
	model.dump();

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/cohesive_element/cohesive_extrinsic/cohesive_extrinsic.cc b/examples/cohesive_element/cohesive_extrinsic/cohesive_extrinsic.cc
	index 7b347c4d5..899e6b598 100644
	--- a/examples/cohesive_element/cohesive_extrinsic/cohesive_extrinsic.cc
	+++ b/examples/cohesive_element/cohesive_extrinsic/cohesive_extrinsic.cc
	@@ -1,129 +1,129 @@
	/**
	* @file cohesive_extrinsic.cc
	*
	* @author Zineb Fouad <zineb.fouad@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Wed Feb 06 2019
	*
	* @brief Cohesive element examples in extrinsic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 1000;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = true);

	Real time_step = model.getStableTimeStep() * 0.05;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	CohesiveElementInserter & inserter = model.getElementInserter();
	inserter.setLimit(_y, 0.30, 0.20);
	model.updateAutomaticInsertion();

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	boundary(n, 1) = true;

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99)
	boundary(n, 0) = true;
	}

	model.setBaseName("extrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.dump();

	/// initial conditions
	Real loading_rate = 0.5;
	Real disp_update = loading_rate * time_step;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 1) = loading_rate * position(n, 1);
	}

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	/// update displacement on extreme nodes
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	displacement(n, 1) += disp_update * position(n, 1);
	}

	model.checkCohesiveStress();
	model.solveStep();

	if (s % 10 == 0) {
	model.dump();

	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	}

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 200 * std::sqrt(2);
	std::cout << Ed << " " << Edt << std::endl;
	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/examples/cohesive_element/cohesive_extrinsic_ig_tg/cohesive_extrinsic_ig_tg.cc b/examples/cohesive_element/cohesive_extrinsic_ig_tg/cohesive_extrinsic_ig_tg.cc
	index 5c548a019..d992c288b 100644
	--- a/examples/cohesive_element/cohesive_extrinsic_ig_tg/cohesive_extrinsic_ig_tg.cc
	+++ b/examples/cohesive_element/cohesive_extrinsic_ig_tg/cohesive_extrinsic_ig_tg.cc
	@@ -1,153 +1,154 @@
	/**
	* @file cohesive_extrinsic_ig_tg.cc
	*
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Jan 19 2021
	*
	- * @brief Cohesive element examples in extrinsic with 2 different bulk materials
	+ * @brief Cohesive element examples in extrinsic with 2 different bulk
	+ * materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	class Velocity : public BC::Dirichlet::DirichletFunctor {
	public:
	explicit Velocity(SolidMechanicsModel & model, Real vel, BC::Axis ax = _x)
	: DirichletFunctor(ax), model(model), vel(vel) {
	disp = vel * model.getTimeStep();
	}

	public:
	inline void operator()(UInt node, Vector<bool> & /flags/,
	Vector<Real> & disp,
	const Vector<Real> & coord) const {
	Real sign = std::signbit(coord(axis)) ? -1. : 1.;
	disp(axis) += sign * this->disp;
	model.getVelocity()(node, axis) = sign * vel;
	}

	private:
	SolidMechanicsModel & model;
	Real vel, disp;
	};

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 1000;

	Mesh mesh(spatial_dimension);
	mesh.read("square.msh");

	SolidMechanicsModelCohesive model(mesh);
	MaterialCohesiveRules rules{{{"btop", "bbottom"}, "tg_cohesive"},
	{{"btop", "btop"}, "ig_cohesive"},
	{{"bbottom", "bbottom"}, "ig_cohesive"}};

	/// model initialization
	auto cohesive_material_selector =
	std::make_shared<MaterialCohesiveRulesSelector>(model, rules);
	auto bulk_material_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	auto && current_selector = model.getMaterialSelector();

	cohesive_material_selector->setFallback(bulk_material_selector);
	bulk_material_selector->setFallback(current_selector);

	model.setMaterialSelector(cohesive_material_selector);

	model.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = true);

	Real time_step = model.getStableTimeStep() * 0.05;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	auto & position = mesh.getNodes();
	auto & velocity = model.getVelocity();

	model.applyBC(BC::Dirichlet::FlagOnly(_y), "top");
	model.applyBC(BC::Dirichlet::FlagOnly(_y), "bottom");

	model.applyBC(BC::Dirichlet::FlagOnly(_x), "left");
	model.applyBC(BC::Dirichlet::FlagOnly(_x), "right");

	model.setBaseName("extrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpField("material_index");
	model.dump();

	/// initial conditions
	Real loading_rate = 0.1;
	// bar_height = 2
	Real VI = loading_rate * 2 * 0.5;
	for (auto && data : zip(make_view(position, spatial_dimension),
	make_view(velocity, spatial_dimension))) {
	std::get<1>(data) = loading_rate * std::get<0>(data);
	}

	model.dump();

	Velocity vely(model, VI, _y);
	Velocity velx(model, VI, _x);

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	model.applyBC(vely, "top");
	model.applyBC(vely, "bottom");

	model.applyBC(velx, "left");
	model.applyBC(velx, "right");

	model.checkCohesiveStress();

	model.solveStep();

	if (s % 10 == 0) {
	model.dump();
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	}

	return 0;
	}
	diff --git a/examples/cohesive_element/cohesive_intrinsic/cohesive_intrinsic.cc b/examples/cohesive_element/cohesive_intrinsic/cohesive_intrinsic.cc
	index 0fc8340e7..a35ee428b 100644
	--- a/examples/cohesive_element/cohesive_intrinsic/cohesive_intrinsic.cc
	+++ b/examples/cohesive_element/cohesive_intrinsic/cohesive_intrinsic.cc
	@@ -1,138 +1,139 @@
	/**
	* @file cohesive_intrinsic.cc
	*
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Fri Jul 19 2019
	*
	* @brief Cohesive element example in intrinsic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "mesh_iterators.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	static void updateDisplacement(SolidMechanicsModelCohesive &,
	const ElementGroup &, Real);

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 350;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	SolidMechanicsModelCohesive model(mesh);
	model.getElementInserter().setLimit(_x, -0.26, -0.24);

	/// model initialization
	model.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = false);

	Real time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	Array<bool> & boundary = model.getBlockedDOFs();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	for (UInt n = 0; n < nb_nodes; ++n) {
	boundary(n, dim) = true;
	}
	}

	model.setBaseName("intrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.dump();

	/// update displacement
	auto && elements = mesh.createElementGroup("diplacement");
	Vector<Real> barycenter(spatial_dimension);

	- for_each_element(mesh,
	- [&](auto && el) {
	- mesh.getBarycenter(el, barycenter);
	- if (barycenter(_x) > -0.25)
	- elements.add(el, true);
	- },
	- _element_kind = _ek_regular);
	+ for_each_element(
	+ mesh,
	+ [&](auto && el) {
	+ mesh.getBarycenter(el, barycenter);
	+ if (barycenter(_x) > -0.25)
	+ elements.add(el, true);
	+ },
	+ _element_kind = _ek_regular);

	Real increment = 0.01;

	updateDisplacement(model, elements, increment);

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {
	model.solveStep();

	updateDisplacement(model, elements, increment);
	if (s % 1 == 0) {
	model.dump();
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	}

	Real Ed = model.getEnergy("dissipated");
	Real Edt = 2 * sqrt(2);

	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	static void updateDisplacement(SolidMechanicsModelCohesive & model,
	const ElementGroup & group, Real increment) {
	Array<Real> & displacement = model.getDisplacement();

	for (auto && node : group.getNodeGroup().getNodes()) {
	displacement(node, 0) += increment;
	}
	}
	diff --git a/examples/contact_mechanics/cohesive_contact_explicit_dynamic.cc b/examples/contact_mechanics/cohesive_contact_explicit_dynamic.cc
	index d8027083a..67ab7ef25 100644
	--- a/examples/contact_mechanics/cohesive_contact_explicit_dynamic.cc
	+++ b/examples/contact_mechanics/cohesive_contact_explicit_dynamic.cc
	@@ -1,159 +1,159 @@
	/**
	* @file cohesive_contact_explicit_dynamic.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sat Jun 19 2021
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Contact mechanics test with cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_cohesive_contact.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {

	const UInt spatial_dimension = 2;
	initialize("material-cohesive.dat", argc, argv);

	Real time_step{0.};
	Real time_factor = 0.1;
	UInt max_steps = 25000;
	Real max_displacement = 1e-3;

	Mesh mesh(spatial_dimension);
	mesh.read("cohesive-contact.msh");

	CouplerSolidCohesiveContact coupler(mesh);

	auto & solid = coupler.getSolidMechanicsModelCohesive();
	auto & contact = coupler.getContactMechanicsModel();

	auto && material_selector =
	std::make_shared<MeshDataMaterialCohesiveSelector>(solid);
	material_selector->setFallback(solid.getMaterialSelector());
	solid.setMaterialSelector(material_selector);

	auto && surface_selector = std::make_shared<CohesiveSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);

	coupler.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = true);

	coupler.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "sides");

	time_step = solid.getStableTimeStep();
	time_step *= time_factor;
	std::cout << "Time Step = " << time_step << "s (" << time_step << "s)"
	<< std::endl;
	coupler.setTimeStep(time_step);

	coupler.setBaseName("cohesive-contact-explicit-dynamic");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("velocity");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("grad_u");
	coupler.addDumpField("stress");
	coupler.addDumpField("gaps");
	coupler.addDumpField("areas");

	auto & velocity = solid.getVelocity();
	auto & gaps = contact.getGaps();

	Real damping_ratio = 0.99;
	auto increment = max_displacement / max_steps;

	for (auto i : arange(max_steps)) {

	coupler.applyBC(BC::Dirichlet::IncrementValue(increment, _y), "loading");
	coupler.applyBC(BC::Dirichlet::IncrementValue(-increment, _y), "fixed");

	coupler.solveStep();

	solid.checkCohesiveStress();

	// damping velocities only along the contacting zone
	for (auto && tuple : zip(gaps, make_view(velocity, spatial_dimension))) {
	auto & gap = std::get<0>(tuple);
	auto & vel = std::get<1>(tuple);
	if (gap > 0) {
	vel *= damping_ratio;
	}
	}

	// dumping energies
	if (i % 1000 == 0) {

	Real epot = solid.getEnergy("potential");
	Real ekin = solid.getEnergy("kinetic");

	std::cerr << i << "," << i * increment << "," << epot << "," << ekin
	<< "," << epot + ekin << "," << std::endl;
	}

	if (i % 1000 == 0) {
	coupler.dump();
	}
	}

	for (auto i : arange(max_steps)) {

	solid.applyBC(BC::Dirichlet::IncrementValue(-increment, _y), "loading");
	solid.applyBC(BC::Dirichlet::IncrementValue(increment, _y), "fixed");

	coupler.solveStep();

	coupler.checkCohesiveStress();

	// damping velocities only along the contacting zone
	for (auto && tuple : zip(gaps, make_view(velocity, spatial_dimension))) {
	auto & gap = std::get<0>(tuple);
	auto & vel = std::get<1>(tuple);
	if (gap > 0) {
	vel *= damping_ratio;
	}
	}

	// dumping energies
	if (i % 1000 == 0) {

	Real epot = solid.getEnergy("potential");
	Real ekin = solid.getEnergy("kinetic");

	std::cerr << i << "," << i * increment << "," << epot << "," << ekin
	<< "," << epot + ekin << "," << std::endl;
	}

	if (i % 1000 == 0) {
	coupler.dump();
	}
	}
	}
	diff --git a/examples/contact_mechanics/contact_explicit_dynamic.cc b/examples/contact_mechanics/contact_explicit_dynamic.cc
	index da9406eff..6e6e36d5b 100644
	--- a/examples/contact_mechanics/contact_explicit_dynamic.cc
	+++ b/examples/contact_mechanics/contact_explicit_dynamic.cc
	@@ -1,135 +1,132 @@
	/**
	* @file contact_explicit_dynamic.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Sun Jun 06 2021
	*
	* @brief Contact mechanics example in dynamic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	-#include "solid_mechanics_model.hh"
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_contact.hh"
	#include "non_linear_solver.hh"
	+#include "solid_mechanics_model.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	-int main(int argc, char *argv[]) {
	+int main(int argc, char * argv[]) {

	-
	const UInt spatial_dimension = 2;
	initialize("material.dat", argc, argv);

	Real time_step;
	Real time_factor = 0.1;
	UInt max_steps = 20000;
	- Real max_displacement = 5e-3;
	-
	+ Real max_displacement = 5e-3;
	+
	Mesh mesh(spatial_dimension);
	mesh.read("hertz.msh");
	-
	+
	CouplerSolidContact coupler(mesh);

	- auto & solid = coupler.getSolidMechanicsModel();
	+ auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	auto && selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	- "physical_names",solid);
	+ "physical_names", solid);
	solid.setMaterialSelector(selector);
	-
	- coupler.initFull( _analysis_method = _explicit_lumped_mass);
	-
	+
	+ coupler.initFull(_analysis_method = _explicit_lumped_mass);
	+
	auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);
	-
	+
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "fixed");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "fixed");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "loading");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "symmetry");
	-
	+
	time_step = solid.getStableTimeStep();
	time_step *= time_factor;
	- std::cout << "Time Step = " << time_step << "s (" << time_step
	- << "s)" << std::endl;
	+ std::cout << "Time Step = " << time_step << "s (" << time_step << "s)"
	+ << std::endl;
	coupler.setTimeStep(time_step);

	coupler.setBaseName("contact-explicit-dynamic");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("velocity");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpFieldVector("contact_force");
	coupler.addDumpFieldVector("external_force");
	coupler.addDumpFieldVector("internal_force");
	coupler.addDumpField("gaps");
	coupler.addDumpField("areas");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("grad_u");
	coupler.addDumpField("stress");

	auto & velocity = solid.getVelocity();
	auto & gaps = contact.getGaps();
	-
	+
	Real damping_ratio = 0.99;
	- auto increment = max_displacement/max_steps;
	-
	+ auto increment = max_displacement / max_steps;
	+
	for (auto i : arange(max_steps)) {
	-
	- solid.applyBC(BC::Dirichlet::IncrementValue(-increment, _y), "loading");
	+
	+ solid.applyBC(BC::Dirichlet::IncrementValue(-increment, _y), "loading");

	coupler.solveStep();

	- // damping velocities only along the contacting zone
	- for(auto && tuple : zip(gaps,
	- make_view(velocity, spatial_dimension))){
	+ // damping velocities only along the contacting zone
	+ for (auto && tuple : zip(gaps, make_view(velocity, spatial_dimension))) {
	auto & gap = std::get<0>(tuple);
	auto & vel = std::get<1>(tuple);
	- if(gap > 0) {
	- vel *= damping_ratio;
	+ if (gap > 0) {
	+ vel *= damping_ratio;
	}
	}

	- // dumping energies
	+ // dumping energies
	if (i % 1000 == 0) {
	-
	+
	Real epot = solid.getEnergy("potential");
	Real ekin = solid.getEnergy("kinetic");

	- std::cerr << i << "," << i * increment << "," << epot << "," << ekin << ","
	- << epot + ekin << "," << std::endl;
	+ std::cerr << i << "," << i * increment << "," << epot << "," << ekin
	+ << "," << epot + ekin << "," << std::endl;
	}

	if (i % 1000 == 0) {
	coupler.dump();
	}
	}

	finalize();
	return EXIT_SUCCESS;
	}
	-
	diff --git a/examples/contact_mechanics/contact_explicit_static.cc b/examples/contact_mechanics/contact_explicit_static.cc
	index b72b5895f..9344e0306 100644
	--- a/examples/contact_mechanics/contact_explicit_static.cc
	+++ b/examples/contact_mechanics/contact_explicit_static.cc
	@@ -1,97 +1,95 @@
	/**
	* @file contact_explicit_static.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Example of contact mechanics in static
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	-#include "solid_mechanics_model.hh"
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_contact.hh"
	#include "non_linear_solver.hh"
	+#include "solid_mechanics_model.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	-int main(int argc, char *argv[]) {
	+int main(int argc, char * argv[]) {

	-
	const UInt spatial_dimension = 2;
	initialize("material.dat", argc, argv);
	-
	+
	Mesh mesh(spatial_dimension);
	mesh.read("hertz.msh");
	-
	+
	CouplerSolidContact coupler(mesh);

	- auto & solid = coupler.getSolidMechanicsModel();
	+ auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	auto && selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	- "physical_names",solid);
	+ "physical_names", solid);
	solid.setMaterialSelector(selector);

	coupler.initFull(_analysis_method = _static);

	auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);

	coupler.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "fixed");
	coupler.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "fixed");
	coupler.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "loading");
	coupler.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "symmetry");

	coupler.setBaseName("contact-explicit-static");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpFieldVector("contact_force");
	coupler.addDumpFieldVector("external_force");
	coupler.addDumpFieldVector("internal_force");
	coupler.addDumpField("gaps");
	coupler.addDumpField("areas");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("grad_u");
	coupler.addDumpField("stress");

	auto max_steps = 100u;

	for (auto _ [[gnu::unused]] : arange(max_steps)) {

	auto increment = 1e-4;
	coupler.applyBC(BC::Dirichlet::IncrementValue(-increment, _y), "loading");

	- coupler.solveStep();
	+ coupler.solveStep();
	coupler.dump();
	}

	finalize();
	return EXIT_SUCCESS;
	}
	-
	diff --git a/examples/embedded/embedded.cc b/examples/embedded/embedded.cc
	index 4785076c5..6d3bdd6b0 100644
	--- a/examples/embedded/embedded.cc
	+++ b/examples/embedded/embedded.cc
	@@ -1,99 +1,99 @@
	/**
	* @file embedded.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Tue Dec 01 2015
	* @date last modification: Wed Feb 06 2019
	*
	* @brief Embedded solid mechanis model example
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "embedded_interface_model.hh"
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt dim = 2;

	// Loading the concrete mesh
	Mesh mesh(dim);
	mesh.read("concrete.msh");

	// Loading the reinforcement mesh
	Mesh reinforcement_mesh(dim, "reinforcement_mesh");

	// Exception is raised because reinforcement
	// mesh contains only segments, i.e. 1D elements
	try {
	reinforcement_mesh.read("reinforcement.msh");
	} catch (debug::Exception & e) {
	}

	// Model creation
	EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);
	model.initFull(EmbeddedInterfaceModelOptions(_static));

	// Boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "XBlocked");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "YBlocked");

	Vector<Real> force(dim);
	force(0) = 0.0;
	force(1) = -1.0;

	model.applyBC(BC::Neumann::FromTraction(force), "Force");

	// Dumping the concrete
	model.setBaseName("concrete");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.addDumpFieldTensor("stress");

	// Dumping the reinforcement
	model.setBaseNameToDumper("reinforcement", "reinforcement");
	model.addDumpFieldTensorToDumper(
	"reinforcement", "stress_embedded"); // dumping stress in reinforcement

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 1);
	solver.set("threshold", 1e-6);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	model.solveStep();

	// Dumping model
	model.dump();
	model.dump("reinforcement");

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/explicit/explicit_dynamic.cc b/examples/explicit/explicit_dynamic.cc
	index 5b09505fc..24a38bdcd 100644
	--- a/examples/explicit/explicit_dynamic.cc
	+++ b/examples/explicit/explicit_dynamic.cc
	@@ -1,110 +1,110 @@
	/**
	* @file explicit_dynamic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Jan 28 2021
	*
	* @brief Example of explicit dynamic simulation in solid mechanics
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 3;
	const Real pulse_width = 2.;
	const Real A = 0.01;
	Real time_step;
	Real time_factor = 0.8;
	UInt max_steps = 1000;

	Mesh mesh(spatial_dimension);

	if (Communicator::getStaticCommunicator().whoAmI() == 0)
	mesh.read("bar.msh");

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _explicit_lumped_mass);

	time_step = model.getStableTimeStep();
	std::cout << "Time Step = " << time_step * time_factor << "s (" << time_step
	<< "s)" << std::endl;
	time_step *= time_factor;
	model.setTimeStep(time_step);

	/// boundary and initial conditions
	Array<Real> & displacement = model.getDisplacement();
	const Array<Real> & nodes = mesh.getNodes();

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	Real x = nodes(n) - 2;
	// Sinus * Gaussian
	Real L = pulse_width;
	Real k = 0.1 * 2 * M_PI * 3 / L;
	displacement(n) = A * sin(k * x) * exp(-(k * x) * (k * x) / (L * L));
	}

	std::ofstream energy;
	energy.open("energy.csv");

	energy << "id,rtime,epot,ekin,tot" << std::endl;

	model.setBaseName("explicit_dynamic");
	model.addDumpField("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("stress");
	model.dump();

	for (UInt s = 1; s <= max_steps; ++s) {
	model.solveStep();

	Real epot = model.getEnergy("potential");
	Real ekin = model.getEnergy("kinetic");

	energy << s << "," << s * time_step << "," << epot << "," << ekin << ","
	<< epot + ekin << "," << std::endl;

	if (s % 10 == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	model.dump();
	}

	energy.close();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/examples/heat_transfer/heat_transfer_dynamics_2d.cc b/examples/heat_transfer/heat_transfer_dynamics_2d.cc
	index e674486c0..f6f2c3528 100644
	--- a/examples/heat_transfer/heat_transfer_dynamics_2d.cc
	+++ b/examples/heat_transfer/heat_transfer_dynamics_2d.cc
	@@ -1,104 +1,104 @@
	/**
	* @file heat_transfer_dynamics_2d.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun May 01 2011
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Example of heat transfer model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "heat_transfer_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	const UInt spatial_dimension = 2;
	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	// create mesh
	Mesh mesh(spatial_dimension);
	mesh.read("square.msh");

	HeatTransferModel model(mesh);

	// initialize everything
	model.initFull();

	// get stable time step
	Real time_step = model.getStableTimeStep() * 0.8;
	std::cout << "time step is:" << time_step << std::endl;
	model.setTimeStep(time_step);

	// boundary conditions
	const Array<Real> & nodes = model.getFEEngine().getMesh().getNodes();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & temperature = model.getTemperature();
	double length = 1.;

	UInt nb_nodes = model.getFEEngine().getMesh().getNbNodes();
	for (UInt i = 0; i < nb_nodes; ++i) {
	temperature(i) = 100.;

	Real dx = nodes(i, 0) - length / 4.;
	Real dy = 0.0;
	Real dz = 0.0;

	if (spatial_dimension > 1)
	dy = nodes(i, 1) - length / 4.;
	if (spatial_dimension == 3)
	dz = nodes(i, 2) - length / 4.;
	Real d = sqrt(dx * dx + dy * dy + dz * dz);
	if (d < 0.1) {
	boundary(i) = true;
	temperature(i) = 300.;
	}
	}

	model.setBaseName("heat_transfer_square2d");
	model.addDumpField("temperature");
	model.addDumpField("temperature_rate");
	model.addDumpField("internal_heat_rate");

	// main loop
	int max_steps = 15000;
	for (int i = 0; i < max_steps; i++) {
	model.solveStep();

	if (i % 100 == 0)
	model.dump();
	if (i % 10 == 0)
	std::cout << "Step " << i << "/" << max_steps << std::endl;
	}
	std::cout << "\n\n Stable Time Step is : " << time_step << "\n \n"
	<< std::endl;

	return 0;
	}
	diff --git a/examples/heat_transfer/heat_transfer_dynamics_3d.cc b/examples/heat_transfer/heat_transfer_dynamics_3d.cc
	index db061c6fc..fa6490b60 100644
	--- a/examples/heat_transfer/heat_transfer_dynamics_3d.cc
	+++ b/examples/heat_transfer/heat_transfer_dynamics_3d.cc
	@@ -1,110 +1,110 @@
	/**
	* @file heat_transfer_dynamics_3d.cc
	*
	* @author Srinivasa Babu Ramisetti <srinivasa.ramisetti@epfl.ch>
	* @author Rui Wang <rui.wang@epfl.ch>
	*
	* @date creation: Sun May 01 2011
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Heat transfer model example in 3D
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "heat_transfer_model.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	UInt spatial_dimension = 3;
	ElementType type = _tetrahedron_4;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read("cube.msh");

	HeatTransferModel model(mesh);
	// initialize everything
	model.initFull();

	// get and set stable time step
	Real time_step = model.getStableTimeStep() * 0.8;
	std::cout << "Stable Time Step is : " << time_step / .8 << std::endl;
	std::cout << "time step is:" << time_step << std::endl;
	model.setTimeStep(time_step);

	/// boundary conditions
	const Array<Real> & nodes = mesh.getNodes();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & temperature = model.getTemperature();
	UInt nb_nodes = mesh.getNbNodes();

	double length;
	length = 1.;

	for (UInt i = 0; i < nb_nodes; ++i) {
	temperature(i) = 100.;

	// to insert a heat source
	Real dx = nodes(i, 0) - length / 2.;
	Real dy = nodes(i, 1) - length / 2.;
	Real dz = nodes(i, 2) - length / 2.;
	Real d = sqrt(dx * dx + dy * dy + dz * dz);
	if (d < 0.1) {
	boundary(i) = true;
	temperature(i) = 300.;
	}
	}

	model.setBaseName("heat_transfer_cube3d");
	model.addDumpField("temperature");
	model.addDumpField("temperature_rate");
	model.addDumpField("internal_heat_rate");

	// //for testing
	int max_steps = 1000;

	for (int i = 0; i < max_steps; i++) {
	model.solveStep();

	if (i % 100 == 0)
	model.dump();

	if (i % 10 == 0) {
	std::cout << "Step " << i << "/" << max_steps << std::endl;
	}
	}

	return 0;
	}
	diff --git a/examples/heat_transfer/heat_transfer_static_2d.cc b/examples/heat_transfer/heat_transfer_static_2d.cc
	index b26e9f3dd..ba3ebc0a7 100644
	--- a/examples/heat_transfer/heat_transfer_static_2d.cc
	+++ b/examples/heat_transfer/heat_transfer_static_2d.cc
	@@ -1,95 +1,95 @@
	/**
	* @file heat_transfer_static_2d.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun May 01 2011
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Heat transfer model example in 2D
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "heat_transfer_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <fstream>
	#include <iostream>
	#include <string>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	UInt spatial_dimension = 2;
	std::string base_name;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	// create mesh
	Mesh mesh(spatial_dimension);
	mesh.read("square.msh");

	HeatTransferModel model(mesh);
	// initialize everything
	model.initFull(_analysis_method = _static);

	// boundary conditions
	const Array<Real> & nodes = mesh.getNodes();
	Array<bool> & blocked_dofs = model.getBlockedDOFs();
	Array<Real> & temperature = model.getTemperature();
	double length = 1.;
	UInt nb_nodes = nodes.size();
	for (UInt i = 0; i < nb_nodes; ++i) {
	temperature(i) = 100.;

	Real dx = nodes(i, 0);
	Real dy = nodes(i, 1);

	Vector<Real> dX = {dx, dy};
	dX -= length / 4.;
	Real d = dX.norm();
	if (d < 0.1) {
	blocked_dofs(i) = true;
	temperature(i) = 300.;
	}

	if (std::abs(dx) < 1e-4 \|\| std::abs(dy) < 1e-4)
	blocked_dofs(i) = true;
	if (std::abs(dx - length) < 1e-4 \|\| std::abs(dy - length) < 1e-4)
	blocked_dofs(i) = true;
	}

	model.setBaseName("heat_transfer_static_2d");
	model.addDumpField("temperature");
	model.addDumpField("internal_heat_rate");
	model.addDumpField("conductivity");
	model.addDumpField("blocked_dofs");
	model.dump();

	model.solveStep();
	model.dump();

	return 0;
	}
	diff --git a/examples/implicit/implicit_dynamic.cc b/examples/implicit/implicit_dynamic.cc
	index 16ed54d00..cb365da58 100644
	--- a/examples/implicit/implicit_dynamic.cc
	+++ b/examples/implicit/implicit_dynamic.cc
	@@ -1,151 +1,151 @@
	/**
	* @file implicit_dynamic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Example of solid mechanics in implicit dynamic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	const Real bar_length = 10.;
	const Real bar_height = 1.;
	const Real bar_depth = 1.;
	const Real F = 5e3;
	const Real L = bar_length;
	const Real I = bar_depth * bar_height * bar_height * bar_height / 12.;
	const Real E = 12e7;
	const Real rho = 1000;
	const Real m = rho * bar_height * bar_depth;

	static Real w(UInt n) {
	return n * n * M_PI * M_PI / (L * L) * sqrt(E * I / m);
	}

	static Real analytical_solution(Real time) {
	return 2 * F * L * L * L / (pow(M_PI, 4) * E * I) *
	((1. - cos(w(1) * time)) + (1. - cos(w(3) * time)) / 81. +
	(1. - cos(w(5) * time)) / 625.);
	}

	const UInt spatial_dimension = 2;
	const Real time_step = 1e-4;
	const Real max_time = 0.62;
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {

	initialize("material_dynamic.dat", argc, argv);

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	if (prank == 0)
	mesh.read("beam.msh");

	mesh.distribute();

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _implicit_dynamic);
	Material & mat = model.getMaterial(0);
	mat.setParam("E", E);
	mat.setParam("rho", rho);

	Array<Real> & force = model.getExternalForce();
	Array<Real> & displacment = model.getDisplacement();

	// boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "blocked");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "blocked");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "roller");

	const Array<UInt> & trac_nodes =
	mesh.getElementGroup("traction").getNodeGroup().getNodes();

	bool dump_node = false;
	if (trac_nodes.size() > 0 && mesh.isLocalOrMasterNode(trac_nodes(0))) {
	force(trac_nodes(0), 1) = F;
	dump_node = true;
	}

	// output setup
	std::ofstream pos;
	pos.open("position.csv");
	if (!pos.good())
	AKANTU_ERROR("Cannot open file \"position.csv\"");

	pos << "id,time,position,solution" << std::endl;

	model.setBaseName("dynamic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.dump();

	model.setTimeStep(time_step);

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 100);
	solver.set("threshold", 1e-12);
	solver.set("convergence_type", SolveConvergenceCriteria::_solution);

	/// time loop
	Real time = 0.;
	for (UInt s = 1; time < max_time; ++s, time += time_step) {
	if (prank == 0)
	std::cout << s << "\r" << std::flush;

	model.solveStep();

	if (dump_node)
	pos << s << "," << time << "," << displacment(trac_nodes(0), 1) << ","
	<< analytical_solution(s * time_step) << std::endl;

	if (s % 100 == 0)
	model.dump();
	}

	std::cout << std::endl;
	pos.close();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/examples/io/dumper/dumpable_interface.cc b/examples/io/dumper/dumpable_interface.cc
	index fa5b6d2ea..961c1db3a 100644
	--- a/examples/io/dumper/dumpable_interface.cc
	+++ b/examples/io/dumper/dumpable_interface.cc
	@@ -1,191 +1,192 @@
	/**
	* @file dumpable_interface.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Aug 17 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Example usnig the dumper interface directly
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "group_manager_inline_impl.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include "dumpable_inline_impl.hh"
	#include "dumper_iohelper_paraview.hh"
	/* -------------------------------------------------------------------------- */
	#include "locomotive_tools.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {

	/*
	In this example, we present dumpers::Dumpable which is an interface
	for other classes who want to dump themselves.
	Several classes of Akantu inheritate from Dumpable (Model, Mesh, ...).
	In this example we reproduce the same tasks as example_dumper_low_level.cc
	using this time Dumpable interface inherted by Mesh, NodeGroup and
	ElementGroup.
	It is then advised to read first example_dumper_low_level.cc.
	*/

	initialize(argc, argv);

	// To start let us load the swiss train mesh and its mesh data information.
	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("swiss_train.msh");

	/*
	swiss_train.msh has the following physical groups that can be viewed with
	GMSH:
	"$MeshFormat
	2.2 0 8
	$EndMeshFormat
	$PhysicalNames
	6
	2 1 "red"
	2 2 "white"
	2 3 "lwheel_1"
	2 4 "lwheel_2"
	2 5 "rwheel_2"
	2 6 "rwheel_1"
	$EndPhysicalNames
	..."
	*/

	// Grouping nodes and elements belonging to train wheels (=four mesh data).
	ElementGroup & wheels_elements =
	mesh.createElementGroup("wheels", spatial_dimension);
	wheels_elements.append(mesh.getElementGroup("lwheel_1"));
	wheels_elements.append(mesh.getElementGroup("lwheel_2"));
	wheels_elements.append(mesh.getElementGroup("rwheel_1"));
	wheels_elements.append(mesh.getElementGroup("rwheel_2"));

	const Array<UInt> & lnode_1 =
	(mesh.getElementGroup("lwheel_1")).getNodeGroup().getNodes();
	const Array<UInt> & lnode_2 =
	(mesh.getElementGroup("lwheel_2")).getNodeGroup().getNodes();
	const Array<UInt> & rnode_1 =
	(mesh.getElementGroup("rwheel_1")).getNodeGroup().getNodes();
	const Array<UInt> & rnode_2 =
	(mesh.getElementGroup("rwheel_2")).getNodeGroup().getNodes();

	Array<Real> & node = mesh.getNodes();
	UInt nb_nodes = mesh.getNbNodes();

	// This time a 2D Array is created and a padding size of 3 is passed to
	// NodalField in order to warp train deformation on Paraview.
	Array<Real> displacement(nb_nodes, spatial_dimension);

	// Create an ElementTypeMapArray for the colour
	ElementTypeMapArray<UInt> colour("colour");
	colour.initialize(mesh, _with_nb_element = true);

	/* ------------------------------------------------------------------------ */
	/* Creating dumpers */
	/* ------------------------------------------------------------------------ */

	// Create dumper for the complete mesh and register it as default dumper.
	- auto && dumper = std::make_shared<DumperParaview>("train", "./paraview/dumpable", false);
	+ auto && dumper =
	+ std::make_shared<DumperParaview>("train", "./paraview/dumpable", false);
	mesh.registerExternalDumper(dumper, "train", true);
	mesh.addDumpMesh(mesh);

	// The dumper for the filtered mesh can be directly taken from the
	// ElementGroup and then registered as "wheels_elements" dumper.
	auto && wheels = mesh.getGroupDumper("paraview_wheels", "wheels");

	mesh.registerExternalDumper(wheels.shared_from_this(), "wheels");
	mesh.setDirectoryToDumper("wheels", "./paraview/dumpable");

	// Arrays and ElementTypeMapArrays can be added as external fields directly
	mesh.addDumpFieldExternal("displacement", displacement);

	ElementTypeMapArrayFilter<UInt> filtered_colour(
	colour, wheels_elements.getElements());

	auto colour_field_wheel =
	std::make_shared<dumpers::ElementalField<UInt, Vector, true>>(
	filtered_colour);
	mesh.addDumpFieldExternal("color", colour_field_wheel);

	mesh.addDumpFieldExternalToDumper("wheels", "displacement", displacement);
	mesh.addDumpFieldExternalToDumper("wheels", "colour", colour);

	// For some specific cases the Fields should be created, as when you want to
	// pad an array
	auto displacement_vector_field =
	mesh.createNodalField(&displacement, "all", 3);
	mesh.addDumpFieldExternal("displacement_as_paraview_vector",
	displacement_vector_field);
	mesh.addDumpFieldExternalToDumper("wheels", "displacement_as_paraview_vector",
	displacement_vector_field);

	/* ------------------------------------------------------------------------ */
	/* ------------------------------------------------------------------------ */

	// Fill the ElementTypeMapArray colour.
	fillColour(mesh, colour);

	/// Apply displacement and wheels rotation.
	Real tot_displacement = 50.;
	Real radius = 1.;
	UInt nb_steps = 100;
	Real theta = tot_displacement / radius;

	Vector<Real> l_center(spatial_dimension);
	Vector<Real> r_center(spatial_dimension);

	for (UInt i = 0; i < spatial_dimension; ++i) {
	l_center(i) = node(14, i);
	r_center(i) = node(2, i);
	}

	for (UInt i = 0; i < nb_steps; ++i) {
	displacement.zero();

	Real step_ratio = Real(i) / Real(nb_steps);
	Real angle = step_ratio * theta;

	applyRotation(l_center, angle, node, displacement, lnode_1);
	applyRotation(l_center, angle, node, displacement, lnode_2);
	applyRotation(r_center, angle, node, displacement, rnode_1);
	applyRotation(r_center, angle, node, displacement, rnode_2);

	for (UInt j = 0; j < nb_nodes; ++j) {
	displacement(j, _x) += step_ratio * tot_displacement;
	}
	/// Dump call is finally made through Dumpable interface.
	mesh.dump();
	mesh.dump("wheels");
	}

	finalize();

	return 0;
	}
	diff --git a/examples/io/dumper/dumper_low_level.cc b/examples/io/dumper/dumper_low_level.cc
	index 820834668..3d31ba3ba 100644
	--- a/examples/io/dumper/dumper_low_level.cc
	+++ b/examples/io/dumper/dumper_low_level.cc
	@@ -1,200 +1,200 @@
	/**
	* @file dumper_low_level.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Aug 17 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Example using the low level dumper interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "group_manager.hh"
	#include "mesh.hh"

	#include "dumper_elemental_field.hh"
	#include "dumper_nodal_field.hh"

	#include "dumper_iohelper_paraview.hh"
	#include "locomotive_tools.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {

	/* This example aims at illustrating how to manipulate low-level methods of
	DumperIOHelper.
	The aims is to visualize a colorized moving train with Paraview */

	initialize(argc, argv);

	// To start let us load the swiss train mesh and its mesh data information.
	// We aknowledge here a weel-known swiss industry for mesh donation.
	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("swiss_train.msh");

	Array<Real> & nodes = mesh.getNodes();
	UInt nb_nodes = mesh.getNbNodes();

	/* swiss_train.msh has the following physical groups that can be viewed with
	GMSH:
	"$MeshFormat
	2.2 0 8
	$EndMeshFormat
	$PhysicalNames
	6
	2 1 "red"
	2 2 "white"
	2 3 "lwheel_1"
	2 4 "lwheel_2"
	2 5 "rwheel_2"
	2 6 "rwheel_1"
	$EndPhysicalNames
	..."
	*/

	// Grouping nodes and elements belonging to train wheels (=four mesh data)
	ElementGroup & wheels_elements =
	mesh.createElementGroup("wheels", spatial_dimension);
	wheels_elements.append(mesh.getElementGroup("lwheel_1"));
	wheels_elements.append(mesh.getElementGroup("lwheel_2"));
	wheels_elements.append(mesh.getElementGroup("rwheel_1"));
	wheels_elements.append(mesh.getElementGroup("rwheel_2"));

	const Array<UInt> & lnode_1 =
	(mesh.getElementGroup("lwheel_1")).getNodeGroup().getNodes();
	const Array<UInt> & lnode_2 =
	(mesh.getElementGroup("lwheel_2")).getNodeGroup().getNodes();
	const Array<UInt> & rnode_1 =
	(mesh.getElementGroup("rwheel_1")).getNodeGroup().getNodes();
	const Array<UInt> & rnode_2 =
	(mesh.getElementGroup("rwheel_2")).getNodeGroup().getNodes();

	/* Note this Array is constructed with three components in order to warp train
	deformation on Paraview. A more appropriate way to do this is to set a
	padding in the NodalField (See example_dumpable_interface.cc.) */
	Array<Real> displacement(nb_nodes, 3);

	// ElementalField are constructed with an ElementTypeMapArray.
	ElementTypeMapArray<UInt> colour;
	colour.initialize(mesh, _with_nb_element = true);

	/* ------------------------------------------------------------------------ */
	/* Dumper creation */
	/* ------------------------------------------------------------------------ */

	// Creation of two DumperParaview. One for full mesh, one for a filtered
	// mesh.
	DumperParaview dumper("train", "./paraview/dumper", false);
	DumperParaview wheels("wheels", "./paraview/dumper", false);

	// Register the full mesh
	dumper.registerMesh(mesh);

	// Register a filtered mesh limited to nodes and elements from wheels groups
	wheels.registerFilteredMesh(mesh, wheels_elements.getElements(),
	wheels_elements.getNodeGroup().getNodes());

	// Generate an output file of the two mesh registered.
	dumper.dump();
	wheels.dump();

	/* At this stage no fields are attached to the two dumpers. To do so, a
	dumpers::Field object has to be created. Several types of dumpers::Field
	exist. In this example we present two of them.

	NodalField to describe nodal displacements of our train.
	ElementalField handling the color of our different part.
	*/

	// NodalField are constructed with an Array.
	auto displ_field = std::make_shared<dumpers::NodalField<Real>>(displacement);
	auto colour_field = std::make_shared<dumpers::ElementalField<UInt>>(colour);

	// Register the freshly created fields to our dumper.
	dumper.registerField("displacement", displ_field);
	dumper.registerField("colour", colour_field);

	// For the dumper wheels, fields have to be filtered at registration.
	// Filtered NodalField can be simply registered by adding an Array<UInt>
	// listing the nodes.
	auto displ_field_wheel = std::make_shared<dumpers::NodalField<Real, true>>(
	displacement, 0, 0, &(wheels_elements.getNodeGroup().getNodes()));
	wheels.registerField("displacement", displ_field_wheel);

	// For the ElementalField, an ElementTypeMapArrayFilter has to be created.
	ElementTypeMapArrayFilter<UInt> filtered_colour(
	colour, wheels_elements.getElements());

	auto colour_field_wheel =
	std::make_shared<dumpers::ElementalField<UInt, Vector, true>>(
	filtered_colour);
	wheels.registerField("colour", colour_field_wheel);

	/* ------------------------------------------------------------------------ */
	// Now that the dumpers are created and the fields are associated, let's
	// paint and move the train!

	// Fill the ElementTypeMapArray colour according to mesh data information.
	fillColour(mesh, colour);

	// Apply displacement and wheels rotation.
	Real tot_displacement = 50.;
	Real radius = 1.;
	UInt nb_steps = 100;
	Real theta = tot_displacement / radius;

	Vector<Real> l_center(3);
	Vector<Real> r_center(3);

	for (UInt i = 0; i < spatial_dimension; ++i) {
	l_center(i) = nodes(14, i);
	r_center(i) = nodes(2, i);
	}

	for (UInt i = 0; i < nb_steps; ++i) {
	displacement.zero();

	Real angle = (Real)i / (Real)nb_steps * theta;
	applyRotation(l_center, angle, nodes, displacement, lnode_1);
	applyRotation(l_center, angle, nodes, displacement, lnode_2);
	applyRotation(r_center, angle, nodes, displacement, rnode_1);
	applyRotation(r_center, angle, nodes, displacement, rnode_2);

	for (UInt j = 0; j < nb_nodes; ++j) {
	displacement(j, 0) += (Real)i / (Real)nb_steps * tot_displacement;
	}
	// Output results after each moving steps for main and wheel dumpers.
	dumper.dump();
	wheels.dump();
	}

	finalize();

	return 0;
	}
	diff --git a/examples/io/dumper/locomotive_tools.cc b/examples/io/dumper/locomotive_tools.cc
	index bc550fdfa..03a31bf90 100644
	--- a/examples/io/dumper/locomotive_tools.cc
	+++ b/examples/io/dumper/locomotive_tools.cc
	@@ -1,92 +1,92 @@
	/**
	* @file locomotive_tools.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	*
	* @date creation: Mon Aug 17 2015
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Small helper code for the dumper examples
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include "locomotive_tools.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	void applyRotation(const Vector<Real> & center, Real angle,
	const Array<Real> & nodes, Array<Real> & displacement,
	const Array<UInt> & node_group) {
	auto nodes_it = nodes.begin(nodes.getNbComponent());
	auto disp_it = displacement.begin(center.size());
	Array<UInt>::const_scalar_iterator node_num_it = node_group.begin();
	Array<UInt>::const_scalar_iterator node_num_end = node_group.end();

	Vector<Real> pos_rel(center.size());

	for (; node_num_it != node_num_end; ++node_num_it) {
	const Vector<Real> pos = nodes_it[*node_num_it];
	for (UInt i = 0; i < pos.size(); ++i)
	pos_rel(i) = pos(i);

	Vector<Real> dis = disp_it[*node_num_it];

	pos_rel -= center;
	Real radius = pos_rel.norm();

	if (std::abs(radius) < Math::getTolerance())
	continue;

	Real phi_i = std::acos(pos_rel(_x) / radius);
	if (pos_rel(_y) < 0)
	phi_i *= -1;

	dis(_x) = std::cos(phi_i - angle) * radius - pos_rel(_x);
	dis(_y) = std::sin(phi_i - angle) * radius - pos_rel(_y);
	}
	}

	/* -------------------------------------------------------------------------- */
	void fillColour(const Mesh & mesh, ElementTypeMapArray<UInt> & colour) {
	const ElementTypeMapArray<std::string> & phys_data =
	mesh.getData<std::string>("physical_names");
	const Array<std::string> & txt_colour = phys_data(_triangle_3);
	Array<UInt> & id_colour = colour(_triangle_3);

	for (UInt i = 0; i < txt_colour.size(); ++i) {
	std::string phy_name = txt_colour(i);

	if (phy_name == "red")
	id_colour(i) = 3;
	else if (phy_name == "white" \|\| phy_name == "lwheel_1" \|\|
	phy_name == "rwheel_1")
	id_colour(i) = 2;
	else
	id_colour(i) = 1;
	}
	}
	diff --git a/examples/io/dumper/locomotive_tools.hh b/examples/io/dumper/locomotive_tools.hh
	index e15f5d62b..cdf6d2c40 100644
	--- a/examples/io/dumper/locomotive_tools.hh
	+++ b/examples/io/dumper/locomotive_tools.hh
	@@ -1,40 +1,40 @@
	/**
	* @file locomotive_tools.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Mon Aug 24 2015
	*
	* @brief Header for the locomotive helper for the dumpers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	void applyRotation(const ::akantu::Vector<::akantu::Real> & center,
	::akantu::Real angle,
	const ::akantu::Array<::akantu::Real> & nodes,
	::akantu::Array<::akantu::Real> & displacement,
	const ::akantu::Array<::akantu::UInt> & node_group);

	void fillColour(const ::akantu::Mesh & mesh,
	::akantu::ElementTypeMapArray<::akantu::UInt> & colour);
	diff --git a/examples/io/parser/example_parser.cc b/examples/io/parser/example_parser.cc
	index 40fda7f77..ac4c5fcfd 100644
	--- a/examples/io/parser/example_parser.cc
	+++ b/examples/io/parser/example_parser.cc
	@@ -1,88 +1,88 @@
	/**
	* @file example_parser.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	*
	* @date creation: Mon Dec 14 2015
	* @date last modification: Wed Feb 06 2019
	*
	* @brief Example of using the user parameter parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {

	// Precise in initialize the name of the text input file to parse.
	initialize("input_file.dat", argc, argv);

	// Get the user ParserSection.
	const ParserSection & usersect = getUserParser();

	// getParameterValue() allows to extract data associated to a given parameter
	// name
	// and cast it in the desired type set as template paramter.
	Mesh mesh(usersect.getParameterValue<UInt>("spatial_dimension"));
	mesh.read(usersect.getParameterValue<std::string>("mesh_file"));

	// getParameter() can be used with variable declaration (destination type is
	// explicitly known).
	Int max_iter = usersect.getParameter("max_nb_iterations");
	Real precision = usersect.getParameter("precision");

	// Following NumPy convention, data can be interpreted as Vector or Matrix
	// structures.
	Matrix<Real> eigen_stress = usersect.getParameter("stress");

	SolidMechanicsModel model(mesh);
	model.initFull(SolidMechanicsModelOptions(_static));

	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x),
	usersect.getParameterValue<std::string>("outter_crust"));
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y),
	usersect.getParameterValue<std::string>("outter_crust"));
	model.applyBC(BC::Neumann::FromStress(eigen_stress),
	usersect.getParameterValue<std::string>("inner_holes"));

	model.setDirectory("./paraview");
	model.setBaseName("swiss_cheese");
	model.addDumpFieldVector("displacement");

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", max_iter);
	solver.set("threshold", precision);

	model.solveStep();

	model.dump();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/examples/new_material/local_material_damage.cc b/examples/new_material/local_material_damage.cc
	index e3fa26252..86ea0cda9 100644
	--- a/examples/new_material/local_material_damage.cc
	+++ b/examples/new_material/local_material_damage.cc
	@@ -1,111 +1,111 @@
	/**
	* @file local_material_damage.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Specialization of the material class for the damage material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "local_material_damage.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	LocalMaterialDamage::LocalMaterialDamage(SolidMechanicsModel & model,
	const ID & id)
	: Material(model, id), damage("damage", *this) {
	AKANTU_DEBUG_IN();

	this->registerParam("E", E, 0., _pat_parsable, "Young's modulus");
	this->registerParam("nu", nu, 0.5, _pat_parsable, "Poisson's ratio");
	this->registerParam("lambda", lambda, _pat_readable,
	"First Lamé coefficient");
	this->registerParam("mu", mu, _pat_readable, "Second Lamé coefficient");
	this->registerParam("kapa", kpa, _pat_readable, "Bulk coefficient");
	this->registerParam("Yd", Yd, 50., _pat_parsmod);
	this->registerParam("Sd", Sd, 5000., _pat_parsmod);

	damage.initialize(1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::initMaterial() {
	AKANTU_DEBUG_IN();
	Material::initMaterial();

	lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
	mu = E / (2 * (1 + nu));
	kpa = lambda + 2. / 3. * mu;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * dam = damage(el_type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	computeStressOnQuad(grad_u, sigma, *dam);
	++dam;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::computePotentialEnergy(ElementType el_type) {
	AKANTU_DEBUG_IN();

	Real * epot = potential_energy(el_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);
	computePotentialEnergyOnQuad(grad_u, sigma, *epot);
	epot++;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	static bool material_is_alocated_local_damage [[gnu::unused]] =
	MaterialFactory::getInstance().registerAllocator(
	"local_damage",
	[](UInt, const ID &, SolidMechanicsModel & model,
	const ID & id) -> std::unique_ptr<Material> {
	return std::make_unique<LocalMaterialDamage>(model, id);
	});

	} // namespace akantu
	diff --git a/examples/new_material/local_material_damage.hh b/examples/new_material/local_material_damage.hh
	index 923e17a00..914d4f98e 100644
	--- a/examples/new_material/local_material_damage.hh
	+++ b/examples/new_material/local_material_damage.hh
	@@ -1,119 +1,119 @@
	/**
	* @file local_material_damage.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Material isotropic elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_LOCAL_MATERIAL_DAMAGE_HH_
	#define AKANTU_LOCAL_MATERIAL_DAMAGE_HH_
	namespace akantu {

	class LocalMaterialDamage : public Material {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	LocalMaterialDamage(SolidMechanicsModel & model, const ID & id = "");

	virtual ~LocalMaterialDamage(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the potential energy for all elements
	void computePotentialEnergy(ElementType el_type) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & sigma,
	Real & damage);

	/// compute the potential energy for on element
	inline void computePotentialEnergyOnQuad(Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & epot);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute the celerity of the fastest wave in the material
	inline Real getCelerity(const Element & element) const override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real);

	private:
	/// the young modulus
	Real E;

	/// Poisson coefficient
	Real nu;

	/// First Lamé coefficient
	Real lambda;

	/// Second Lamé coefficient (shear modulus)
	Real mu;

	/// resistance to damage
	Real Yd;

	/// damage threshold
	Real Sd;

	/// Bulk modulus
	Real kpa;

	/// damage internal variable
	InternalField<Real> damage;
	};

	} // namespace akantu
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "local_material_damage_inline_impl.hh"

	#endif /* AKANTU_LOCAL_MATERIAL_DAMAGE_HH_ */
	diff --git a/examples/new_material/local_material_damage_inline_impl.hh b/examples/new_material/local_material_damage_inline_impl.hh
	index 646c7a9b9..aa5f42b0f 100644
	--- a/examples/new_material/local_material_damage_inline_impl.hh
	+++ b/examples/new_material/local_material_damage_inline_impl.hh
	@@ -1,92 +1,92 @@
	/**
	* @file local_material_damage_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Implementation of the inline functions of the material damage
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_LOCAL_MATERIAL_DAMAGE_INLINE_IMPL_HH_
	#define AKANTU_LOCAL_MATERIAL_DAMAGE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline void LocalMaterialDamage::computeStressOnQuad(Matrix<Real> & grad_u,
	Matrix<Real> & sigma,
	Real & dam) {

	Real trace = grad_u.trace();

	/// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
	/// u_{ij} + \nabla u_{ji})
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	sigma(i, j) =
	(i == j) * lambda * trace + mu * (grad_u(i, j) + grad_u(j, i));
	}
	}

	Real Y = 0;
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	Y += sigma(i, j) * grad_u(i, j);
	}
	}
	Y *= 0.5;

	Real Fd = Y - Yd - Sd * dam;

	if (Fd > 0)
	dam = (Y - Yd) / Sd;
	dam = std::min(dam, 1.);

	sigma *= 1 - dam;
	}

	/* -------------------------------------------------------------------------- */
	inline void LocalMaterialDamage::computePotentialEnergyOnQuad(
	Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & epot) {
	epot = 0.;
	for (UInt i = 0, t = 0; i < spatial_dimension; ++i)
	for (UInt j = 0; j < spatial_dimension; ++j, ++t)
	epot += sigma(i, j) * (grad_u(i, j) - (i == j));
	epot *= .5;
	}

	/* -------------------------------------------------------------------------- */
	inline Real LocalMaterialDamage::getCelerity(__attribute__((unused))
	const Element & element) const {
	// Here the fastest celerity is the push wave speed
	return (std::sqrt((2 * mu + lambda) / rho));
	}

	} // namespace akantu

	#endif /* AKANTU_LOCAL_MATERIAL_DAMAGE_INLINE_IMPL_HH_ */
	diff --git a/examples/new_material/new_local_material.cc b/examples/new_material/new_local_material.cc
	index e885e4e90..96a2a0414 100644
	--- a/examples/new_material/new_local_material.cc
	+++ b/examples/new_material/new_local_material.cc
	@@ -1,104 +1,104 @@
	/**
	* @file new_local_material.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Wed Jan 15 2020
	*
	* @brief test of the class SolidMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "local_material_damage.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	#define bar_length 10.
	#define bar_height 4.
	akantu::Real eps = 1e-10;

	int main(int argc, char * argv[]) {
	akantu::initialize("material.dat", argc, argv);

	UInt max_steps = 10000;
	Real epot, ekin;

	const UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);
	mesh.read("barre_trou.msh");

	/// model creation
	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _explicit_lumped_mass);

	std::cout << model.getMaterial(0) << std::endl;

	Real time_step = model.getStableTimeStep();
	model.setTimeStep(time_step / 10.);

	/// Dirichlet boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "Fixed_x");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "Fixed_y");

	// Neumann boundary condition
	Matrix<Real> stress(2, 2);
	stress.eye(3e2);
	model.applyBC(BC::Neumann::FromStress(stress), "Traction");

	model.setBaseName("local_material");
	model.addDumpField("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.addDumpField("grad_u");
	model.addDumpField("stress");
	model.addDumpField("damage");
	model.dump();

	for (UInt s = 0; s < max_steps; ++s) {
	model.solveStep();

	epot = model.getEnergy("potential");
	ekin = model.getEnergy("kinetic");

	if (s % 100 == 0)
	std::cout << s << " " << epot << " " << ekin << " " << epot + ekin
	<< std::endl;

	if (s % 1000 == 0)
	model.dump();
	}

	akantu::finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/new_material/viscoelastic_maxwell/material_viscoelastic_maxwell_energies.cc b/examples/new_material/viscoelastic_maxwell/material_viscoelastic_maxwell_energies.cc
	index c614045d2..a1087207d 100644
	--- a/examples/new_material/viscoelastic_maxwell/material_viscoelastic_maxwell_energies.cc
	+++ b/examples/new_material/viscoelastic_maxwell/material_viscoelastic_maxwell_energies.cc
	@@ -1,179 +1,179 @@
	/**
	* @file material_viscoelastic_maxwell_energies.cc
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	*
	* @date creation: Tue Nov 20 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Example of using viscoelastic material and computing energies
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	#include <sstream>
	/* -------------------------------------------------------------------------- */
	#include "material_viscoelastic_maxwell.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	#include "sparse_matrix.hh"

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	akantu::initialize("material_viscoelastic_maxwell.dat", argc, argv);

	// sim data
	Real eps = 0.1;

	const UInt dim = 2;
	Real sim_time = 100.;
	Real T = 10.;
	Mesh mesh(dim);
	mesh.read("material_viscoelastic_maxwell_mesh.msh");

	SolidMechanicsModel model(mesh);

	/* ------------------------------------------------------------------------ */
	/* Initialization */
	/* ------------------------------------------------------------------------ */
	model.initFull(_analysis_method = _static);
	std::cout << model.getMaterial(0) << std::endl;

	std::stringstream filename_sstr;
	filename_sstr << "material_viscoelastic_maxwell_output.out";
	std::ofstream output_data;
	output_data.open(filename_sstr.str().c_str());

	Material & mat = model.getMaterial(0);

	Real time_step = 0.1;

	UInt nb_nodes = mesh.getNbNodes();
	const Array<Real> & coordinate = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> & blocked = model.getBlockedDOFs();

	/// Setting time step

	model.setTimeStep(time_step);

	model.setBaseName("dynamic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("blocked_dofs");
	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.addDumpField("grad_u");
	model.addDumpField("stress");
	model.addDumpField("strain");

	UInt max_steps = sim_time / time_step + 1;
	Real time = 0.;

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 10);
	solver.set("threshold", 1e-7);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	/* ------------------------------------------------------------------------ */
	/* Main loop */
	/* ------------------------------------------------------------------------ */
	for (UInt s = 0; s <= max_steps; ++s) {

	std::cout << "Time Step = " << time_step << "s" << std::endl;
	std::cout << "Time = " << time << std::endl;

	// impose displacement
	Real epsilon = 0;
	if (time < T) {
	epsilon = eps * time / T;
	} else {
	epsilon = eps;
	}

	for (UInt n = 0; n < nb_nodes; ++n) {
	if (Math::are_float_equal(coordinate(n, 0), 0.0)) {
	displacement(n, 0) = 0;
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 1), 0.0)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = 0;
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 0), 0.001)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 1), 0.001)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	}
	}

	try {
	model.solveStep();
	} catch (debug::Exception & e) {
	}

	// for debugging
	// auto int_force = model.getInternalForce();
	// auto &K = model.getDOFManager().getMatrix("K");
	// K.saveMatrix("K.mtx");

	Int nb_iter = solver.get("nb_iterations");
	Real error = solver.get("error");
	bool converged = solver.get("converged");

	if (converged) {
	std::cout << "Converged in " << nb_iter << " iterations" << std::endl;
	} else {
	std::cout << "Didn't converge after " << nb_iter
	<< " iterations. Error is " << error << std::endl;
	return EXIT_FAILURE;
	}

	model.dump();

	Real epot = mat.getEnergy("potential");
	Real edis = mat.getEnergy("dissipated");
	Real work = mat.getEnergy("work");

	// data output
	output_data << s * time_step << " " << epsilon << " " << epot << " " << edis
	<< " " << work << std::endl;
	time += time_step;
	}
	output_data.close();
	finalize();
	}
	diff --git a/examples/parallel/parallel_2d.cc b/examples/parallel/parallel_2d.cc
	index 007fac130..e08a0074f 100644
	--- a/examples/parallel/parallel_2d.cc
	+++ b/examples/parallel/parallel_2d.cc
	@@ -1,108 +1,108 @@
	/**
	* @file parallel_2d.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Aug 09 2010
	* @date last modification: Thu Mar 22 2018
	*
	* @brief Parallel example
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	UInt spatial_dimension = 2;
	UInt max_steps = 10000;
	Real time_factor = 0.8;
	Real max_disp = 1e-6;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();
	if (prank == 0) {
	// Read the mesh
	mesh.read("square_2d.msh");
	}

	mesh.distribute();

	SolidMechanicsModel model(mesh);
	model.initFull();

	if (prank == 0)
	std::cout << model.getMaterial(0) << std::endl;

	model.setBaseName("multi");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("velocity");
	model.addDumpFieldVector("acceleration");
	model.addDumpFieldTensor("stress");
	model.addDumpFieldTensor("grad_u");

	/// boundary conditions
	Real eps = 1e-16;
	const Array<Real> & pos = mesh.getNodes();
	Array<Real> & disp = model.getDisplacement();
	Array<bool> & boun = model.getBlockedDOFs();

	Real left_side = mesh.getLowerBounds()(0);
	Real right_side = mesh.getUpperBounds()(0);

	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	if (std::abs(pos(i, 0) - left_side) < eps) {
	disp(i, 0) = max_disp;
	boun(i, 0) = true;
	}

	if (std::abs(pos(i, 0) - right_side) < eps) {
	disp(i, 0) = -max_disp;
	boun(i, 0) = true;
	}
	}

	Real time_step = model.getStableTimeStep() * time_factor;
	std::cout << "Time Step = " << time_step << "s" << std::endl;
	model.setTimeStep(time_step);

	model.dump();
	for (UInt s = 1; s <= max_steps; ++s) {
	model.solveStep();
	if (s % 200 == 0)
	model.dump();

	if (prank == 0 && s % 100 == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/phase_field/phase_field_notch.cc b/examples/phase_field/phase_field_notch.cc
	index 8f76a5ba5..14deb3da7 100644
	--- a/examples/phase_field/phase_field_notch.cc
	+++ b/examples/phase_field/phase_field_notch.cc
	@@ -1,123 +1,120 @@
	/**
	* @file phase_field_notch.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Tue Oct 02 2018
	* @date last modification: Wed Apr 07 2021
	*
	* @brief Example of phase field model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	+#include "coupler_solid_phasefield.hh"
	#include "non_linear_solver.hh"
	#include "phase_field_model.hh"
	#include "solid_mechanics_model.hh"
	-#include "coupler_solid_phasefield.hh"
	/* -------------------------------------------------------------------------- */
	-#include <iostream>
	-#include <fstream>
	#include <chrono>
	+#include <fstream>
	+#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	using clk = std::chrono::high_resolution_clock;
	using second = std::chrono::duration<double>;
	using millisecond = std::chrono::duration<double, std::milli>;

	const UInt spatial_dimension = 2;

	/* -------------------------------------------------------------------------- */

	-int main(int argc, char *argv[]){
	-
	+int main(int argc, char * argv[]) {
	+
	initialize("material_notch.dat", argc, argv);

	// create mesh
	Mesh mesh(spatial_dimension);
	mesh.read("square_notch.msh");

	CouplerSolidPhaseField coupler(mesh);
	auto & model = coupler.getSolidMechanicsModel();
	auto & phase = coupler.getPhaseFieldModel();

	model.initFull(_analysis_method = _static);
	- auto && mat_selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	- "physical_names", model);
	+ auto && mat_selector =
	+ std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	+ model);
	model.setMaterialSelector(mat_selector);

	auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
	- "physical_names", phase);
	+ "physical_names", phase);
	phase.setPhaseFieldSelector(selector);

	phase.initFull(_analysis_method = _static);

	model.applyBC(BC::Dirichlet::FixedValue(0., _y), "bottom");
	- model.applyBC(BC::Dirichlet::FixedValue(0., _x), "left");
	-
	+ model.applyBC(BC::Dirichlet::FixedValue(0., _x), "left");
	+
	model.setBaseName("phase_notch");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpFieldVector("displacement");
	model.addDumpField("damage");
	model.dump();

	UInt nbSteps = 1500;
	Real increment = 1e-5;
	-
	- auto start_time = clk::now();

	+ auto start_time = clk::now();

	for (UInt s = 1; s < nbSteps; ++s) {

	if (s >= 500) {
	increment = 1.e-6;
	}
	-
	- if (s % 10 == 0 ) {
	+
	+ if (s % 10 == 0) {
	constexpr char wheel[] = "/-\\\|";
	auto elapsed = clk::now() - start_time;
	auto time_per_step = elapsed / s;
	std::cout << "\r[" << wheel[(s / 10) % 4] << "] " << std::setw(5) << s
	- << "/" << nbSteps << " (" << std::setprecision(2)
	- << std::fixed << std::setw(8)
	- << millisecond(time_per_step).count()
	+ << "/" << nbSteps << " (" << std::setprecision(2) << std::fixed
	+ << std::setw(8) << millisecond(time_per_step).count()
	<< "ms/step - elapsed: " << std::setw(8)
	<< second(elapsed).count() << "s - ETA: " << std::setw(8)
	<< second((nbSteps - s) * time_per_step).count() << "s)"
	<< std::string(' ', 20) << std::flush;
	}
	model.applyBC(BC::Dirichlet::IncrementValue(increment, _y), "top");
	-
	+
	coupler.solve();

	- if ( s % 100 == 0) {
	+ if (s % 100 == 0) {
	model.dump();
	}
	-
	}

	-
	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/examples/static/static.cc b/examples/static/static.cc
	index db9199bfd..a1bddacf2 100644
	--- a/examples/static/static.cc
	+++ b/examples/static/static.cc
	@@ -1,81 +1,81 @@
	/**
	* @file static.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Oumaima Sabir <oumaima.sabir@epfl.ch>
	*
	* @date creation: Mon Aug 09 2010
	* @date last modification: Sun Dec 30 2018
	*
	* @brief This code refers to the implicit static example from the user manual
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	#define bar_length 0.01
	#define bar_height 0.01

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);
	mesh.read("square.msh");

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _static);

	model.setBaseName("static");
	model.addDumpFieldVector("displacement");
	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.addDumpField("grad_u");

	/// Dirichlet boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "Fixed_x");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "Fixed_y");
	model.applyBC(BC::Dirichlet::FixedValue(0.0001, _y), "Traction");
	model.dump();

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 2);
	solver.set("threshold", 2e-4);
	solver.set("convergence_type", SolveConvergenceCriteria::_solution);

	model.solveStep();

	model.dump();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/examples/structural_mechanics/bernoulli_beam_2_example.cc b/examples/structural_mechanics/bernoulli_beam_2_example.cc
	index 24712a721..be255f5c3 100644
	--- a/examples/structural_mechanics/bernoulli_beam_2_example.cc
	+++ b/examples/structural_mechanics/bernoulli_beam_2_example.cc
	@@ -1,142 +1,142 @@
	/**
	* @file bernoulli_beam_2_example.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	*
	* @date creation: Fri Jul 15 2011
	* @date last modification: Mon Mar 15 2021
	*
	* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	-#include "structural_mechanics_model.hh"
	#include "mesh_accessor.hh"
	+#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	#define TYPE _bernoulli_beam_2

	using namespace akantu;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize(argc, argv);
	// Defining the mesh
	Mesh beams(2);

	const auto q = 6000.;
	const auto L = 10.;
	const auto M = -3600.; // Momentum at 3

	auto nb_nodes = 3;
	auto nb_element = nb_nodes - 1;

	MeshAccessor mesh_accessor(beams);
	Array<Real> & nodes = mesh_accessor.getNodes();
	nodes.resize(nb_nodes);

	beams.addConnectivityType(_bernoulli_beam_2);
	Array<UInt> & connectivity = mesh_accessor.getConnectivity(_bernoulli_beam_2);
	connectivity.resize(nb_element);

	nodes.zero();
	nodes(1, 0) = 10;
	nodes(2, 0) = 18;

	for (int i = 0; i < nb_element; ++i) {
	connectivity(i, 0) = i;
	connectivity(i, 1) = i + 1;
	}

	mesh_accessor.makeReady();

	// Defining the materials
	StructuralMechanicsModel model(beams);

	StructuralMaterial mat1;
	mat1.E = 3e10;
	mat1.I = 0.0025;
	mat1.A = 0.01;

	model.addMaterial(mat1);

	StructuralMaterial mat2;
	mat2.E = 3e10;
	mat2.I = 0.00128;
	mat2.A = 0.01;

	model.addMaterial(mat2);

	// Defining the forces
	model.initFull();

	auto & forces = model.getExternalForce();
	auto & displacement = model.getDisplacement();
	auto & boundary = model.getBlockedDOFs();
	const auto & N_M = model.getStress(_bernoulli_beam_2);

	auto & element_material = model.getElementMaterial(_bernoulli_beam_2);

	boundary.set(false);
	forces.zero();
	displacement.zero();

	element_material(1) = 1;

	forces(0, 1) = -q * L / 2.;
	forces(0, 2) = -q * L * L / 12.;
	forces(1, 1) = -q * L / 2.;
	- forces(1, 2) = q * L * L / 12.;
	+ forces(1, 2) = q * L * L / 12.;
	forces(2, 2) = M;
	forces(2, 0) = mat2.E * mat2.A / 18;

	// Defining the boundary conditions
	boundary(0, 0) = true;
	boundary(0, 1) = true;
	boundary(0, 2) = true;
	boundary(1, 1) = true;
	boundary(2, 1) = true;

	model.addDumpFieldVector("displacement");
	model.addDumpField("rotation");
	model.addDumpFieldVector("force");
	model.addDumpField("momentum");

	model.solveStep();

	model.assembleResidual();

	// Post-Processing
	std::cout << " d1 = " << displacement(1, 2) << std::endl;
	std::cout << " d2 = " << displacement(2, 2) << std::endl;
	std::cout << " d3 = " << displacement(1, 0) << std::endl;
	std::cout << " M1 = " << N_M(0, 1) << std::endl;
	std::cout << " M2 = " << N_M(2 * (nb_nodes - 2), 1) << std::endl;

	model.dump();

	finalize();
	}
	diff --git a/extra_packages/extra-materials/src/material_FE2/material_FE2.cc b/extra_packages/extra-materials/src/material_FE2/material_FE2.cc
	index 68dd33e7f..31ba698b5 100644
	--- a/extra_packages/extra-materials/src/material_FE2/material_FE2.cc
	+++ b/extra_packages/extra-materials/src/material_FE2/material_FE2.cc
	@@ -1,199 +1,198 @@
	/**
	* @file material_FE2.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @brief Material for multi-scale simulations. It stores an
	* underlying RVE on each integration point of the material.
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_FE2.hh"
	#include "communicator.hh"
	#include "solid_mechanics_model_RVE.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialFE2<spatial_dimension>::MaterialFE2(SolidMechanicsModel & model,
	const ID & id)
	: Parent(model, id), C("material_stiffness", *this) {
	AKANTU_DEBUG_IN();

	this->C.initialize(voigt_h::size * voigt_h::size);
	this->initialize();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialFE2<spatial_dimension>::~MaterialFE2() = default;

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialFE2<dim>::initialize() {
	this->registerParam("element_type", el_type, _triangle_3,
	_pat_parsable \| _pat_modifiable,
	"element type in RVE mesh");
	this->registerParam("mesh_file", mesh_file, _pat_parsable \| _pat_modifiable,
	"the mesh file for the RVE");
	this->registerParam("nb_gel_pockets", nb_gel_pockets,
	_pat_parsable \| _pat_modifiable,
	"the number of gel pockets in each RVE");
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialFE2<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();
	Parent::initMaterial();

	/// create a Mesh and SolidMechanicsModel on each integration point of the
	/// material
	auto C_it = this->C(this->el_type).begin(voigt_h::size, voigt_h::size);

	for (auto && data :
	enumerate(make_view(C(this->el_type), voigt_h::size, voigt_h::size))) {
	auto q = std::get<0>(data);
	auto & C = std::get<1>(data);

	meshes.emplace_back(std::make_unique<Mesh>(
	spatial_dimension, "RVE_mesh_" + std::to_string(q), q + 1));

	auto & mesh = *meshes.back();
	mesh.read(mesh_file);

	RVEs.emplace_back(std::make_unique<SolidMechanicsModelRVE>(
	mesh, true, this->nb_gel_pockets, _all_dimensions,
	"SMM_RVE_" + std::to_string(q), q + 1));

	auto & RVE = *RVEs.back();
	RVE.initFull(_analysis_method = _static);

	/// compute intial stiffness of the RVE
	RVE.homogenizeStiffness(C);
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialFE2<spatial_dimension>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// Compute thermal stresses first

	Parent::computeStress(el_type, ghost_type);
	Array<Real>::const_scalar_iterator sigma_th_it =
	this->sigma_th(el_type, ghost_type).begin();

	// Wikipedia convention:
	// 2*eps_ij (i!=j) = voigt_eps_I
	// http://en.wikipedia.org/wiki/Voigt_notation

	Array<Real>::const_matrix_iterator C_it =
	this->C(el_type, ghost_type).begin(voigt_h::size, voigt_h::size);

	// create vectors to store stress and strain in Voigt notation
	// for efficient computation of stress
	Vector<Real> voigt_strain(voigt_h::size);
	Vector<Real> voigt_stress(voigt_h::size);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	const Matrix<Real> & C_mat = *C_it;
	const Real & sigma_th = *sigma_th_it;

	/// copy strains in Voigt notation
	for (UInt I = 0; I < voigt_h::size; ++I) {
	/// copy stress in
	Real voigt_factor = voigt_h::factors[I];
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_strain(I) = voigt_factor * (grad_u(i, j) + grad_u(j, i)) / 2.;
	}

	// compute stresses in Voigt notation
	voigt_stress.mul<false>(C_mat, voigt_strain);

	/// copy stresses back in full vectorised notation
	for (UInt I = 0; I < voigt_h::size; ++I) {
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];
	sigma(i, j) = sigma(j, i) = voigt_stress(I) + (i == j) * sigma_th;
	}

	++C_it;
	++sigma_th_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialFE2<spatial_dimension>::computeTangentModuli(
	- ElementType el_type, Array<Real> & tangent_matrix,
	- GhostType ghost_type) {
	+ ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Array<Real>::const_matrix_iterator C_it =
	this->C(el_type, ghost_type).begin(voigt_h::size, voigt_h::size);

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	tangent.copy(*C_it);
	++C_it;
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialFE2<spatial_dimension>::advanceASR(
	const Matrix<Real> & prestrain) {
	AKANTU_DEBUG_IN();

	for (auto && data :
	zip(RVEs,
	make_view(this->gradu(this->el_type), spatial_dimension,
	spatial_dimension),
	make_view(this->eigengradu(this->el_type), spatial_dimension,
	spatial_dimension),
	make_view(this->C(this->el_type), voigt_h::size, voigt_h::size),
	this->delta_T(this->el_type))) {
	auto & RVE = *(std::get<0>(data));

	/// apply boundary conditions based on the current macroscopic displ.
	/// gradient
	RVE.applyBoundaryConditions(std::get<1>(data));

	/// apply homogeneous temperature field to each RVE to obtain thermoelastic
	/// effect
	RVE.applyHomogeneousTemperature(std::get<4>(data));

	/// advance the ASR in every RVE
	RVE.advanceASR(prestrain);

	/// compute the average eigen_grad_u
	RVE.homogenizeEigenGradU(std::get<2>(data));

	/// compute the new effective stiffness of the RVE
	RVE.homogenizeStiffness(std::get<3>(data));
	}

	AKANTU_DEBUG_OUT();
	}

	INSTANTIATE_MATERIAL(material_FE2, MaterialFE2);

	} // namespace akantu
	diff --git a/extra_packages/extra-materials/src/material_FE2/material_FE2.hh b/extra_packages/extra-materials/src/material_FE2/material_FE2.hh
	index 084f40da7..d886cfbc2 100644
	--- a/extra_packages/extra-materials/src/material_FE2/material_FE2.hh
	+++ b/extra_packages/extra-materials/src/material_FE2/material_FE2.hh
	@@ -1,111 +1,110 @@
	/**
	* @file material_FE2.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Material for multi-scale simulations. It stores an
	* underlying RVE on each integration point of the material.
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	#include "material_thermal.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_FE_2_HH_
	#define AKANTU_MATERIAL_FE_2_HH_

	namespace akantu {
	class SolidMechanicsModelRVE;
	}

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/// /!\ This material works ONLY for meshes with a single element type!!!!!
	/* -------------------------------------------------------------------------- */

	/**
	* MaterialFE2
	*
	* parameters in the material files :
	* - mesh_file
	*/
	template <UInt DIM> class MaterialFE2 : public MaterialThermal<DIM> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	private:
	typedef MaterialThermal<DIM> Parent;

	public:
	MaterialFE2(SolidMechanicsModel & model, const ID & id = "");

	virtual ~MaterialFE2();

	typedef VoigtHelper<DIM> voigt_h;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	virtual void initMaterial();

	/// constitutive law for all element of a type
	virtual void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost);

	/// advance alkali-silica reaction
	void advanceASR(const Matrix<Real> & prestrain);

	private:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Underlying RVE at each integration point
	std::vector<std::unique_ptr<SolidMechanicsModelRVE>> RVEs;

	/// Meshes for all RVEs
	std::vector<std::unique_ptr<Mesh>> meshes;

	/// the element type of the associated mesh (this material handles only one
	/// type!!)
	ElementType el_type;

	/// the name of RVE mesh file
	ID mesh_file;

	/// Elastic stiffness tensor at each Gauss point (in voigt notation)
	InternalField<Real> C;

	/// number of gel pockets in each underlying RVE
	UInt nb_gel_pockets;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "material_FE2_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_FE_2_HH_ */
	diff --git a/extra_packages/extra-materials/src/material_damage/material_brittle.hh b/extra_packages/extra-materials/src/material_damage/material_brittle.hh
	index 5466e2c56..89df33608 100644
	--- a/extra_packages/extra-materials/src/material_damage/material_brittle.hh
	+++ b/extra_packages/extra-materials/src/material_damage/material_brittle.hh
	@@ -1,110 +1,111 @@
	/**
	* @file material_brittle.hh
	*
	* @author Aranda Ruiz Josue <josue.arandaruiz@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	*
	*
	* @brief Brittle damage law
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_BRITTLE_HH_
	#define AKANTU_MATERIAL_BRITTLE_HH_

	namespace akantu {

	/**
	* Material brittle
	*
	* parameters in the material files :
	* - S_0 : Critical stress at low strain rate (default: 157e6)
	* - E_0 : Low strain rate threshold (default: 27e3)
	* - A,B,C,D : Fitting parameters for the critical stress at high strain
	* rates
	* (default: 1.622e-11, -1.3274e-6, 3.6544e-2, -181.38)
	*/
	template <UInt spatial_dimension>
	class MaterialBrittle : public MaterialDamage<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialBrittle(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	void updateInternalParameters() override;

	/// constitutive law for all element of a type
	- void computeStress(ElementType el_type, GhostType ghost_type = _not_ghost) override;
	+ void computeStress(ElementType el_type,
	+ GhostType ghost_type = _not_ghost) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & grad_v,
	Matrix<Real> & sigma, Real & dam,
	Real & sigma_equivalent,
	Real & fracture_stress);

	inline void computeDamageAndStressOnQuad(Matrix<Real> & sigma, Real & dam,
	Real & sigma_c,
	Real & fracture_stress);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// strain rate arrays ordered by element types
	InternalField<Real> strain_rate_brittle;

	// polynome constants for critical stress value
	Real A;
	Real B;
	Real C;
	Real D;

	// minimum strain rate
	Real E_0;

	// Critical stress at low strain rates
	Real S_0;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "material_brittle_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_brittle_HH_ */
	diff --git a/extra_packages/extra-materials/src/material_damage/material_damage_iterative.hh b/extra_packages/extra-materials/src/material_damage/material_damage_iterative.hh
	index c844568f1..a9f2e05a7 100644
	--- a/extra_packages/extra-materials/src/material_damage/material_damage_iterative.hh
	+++ b/extra_packages/extra-materials/src/material_damage/material_damage_iterative.hh
	@@ -1,145 +1,145 @@
	/**
	* @file material_damage_iterative.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Specialization of the class material damage to damage only one gauss
	* point at a time and propagate damage in a linear way. Max principal stress
	* criterion is used as a failure criterion.
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_DAMAGE_ITERATIVE_HH_
	#define AKANTU_MATERIAL_DAMAGE_ITERATIVE_HH_

	namespace akantu {

	/**
	* Material damage iterative
	*
	* parameters in the material files :
	* - Sc
	*/
	template <UInt spatial_dimension>
	class MaterialDamageIterative : public MaterialDamage<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialDamageIterative(SolidMechanicsModel & model, const ID & id = "");

	~MaterialDamageIterative() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// virtual void updateInternalParameters();

	void computeAllStresses(GhostType ghost_type = _not_ghost) override;

	/// update internal field damage
	virtual UInt updateDamage();

	- UInt updateDamage(UInt quad_index, Real eq_stress,
	- ElementType el_type, GhostType ghost_type);
	+ UInt updateDamage(UInt quad_index, Real eq_stress, ElementType el_type,
	+ GhostType ghost_type);

	/// update energies after damage has been updated
	void updateEnergiesAfterDamage(ElementType el_type) override;

	/// compute the equivalent stress on each Gauss point (i.e. the max prinicpal
	/// stress) and normalize it by the tensile strength
	virtual void
	computeNormalizedEquivalentStress(const Array<Real> & grad_u,
	ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// find max normalized equivalent stress
	void findMaxNormalizedEquivalentStress(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	protected:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	- GhostType ghost_type = _not_ghost) override;
	+ GhostType ghost_type = _not_ghost) override;

	inline void computeDamageAndStressOnQuad(Matrix<Real> & sigma, Real & dam);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */

	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get max normalized equivalent stress
	AKANTU_GET_MACRO(NormMaxEquivalentStress, norm_max_equivalent_stress, Real);

	/// get a non-const reference to the max normalized equivalent stress
	AKANTU_GET_MACRO_NOT_CONST(NormMaxEquivalentStress,
	norm_max_equivalent_stress, Real &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// resistance to damage
	RandomInternalField<Real> Sc;

	/// the reduction
	InternalField<UInt> reduction_step;

	/// internal field to store equivalent stress on each Gauss point
	InternalField<Real> equivalent_stress;

	/// the number of total reductions steps until complete failure
	UInt max_reductions;

	/// damage increment
	Real prescribed_dam;

	/// maximum equivalent stress
	Real norm_max_equivalent_stress;

	/// deviation from max stress at which Gauss point will still get damaged
	Real dam_tolerance;

	/// define damage threshold at which damage will be set to 1
	Real dam_threshold;

	/// maximum damage value
	Real max_damage;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "material_damage_iterative_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_DAMAGE_ITERATIVE_HH_ */
	diff --git a/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage.hh b/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage.hh
	index 6690943d3..d15c70cbc 100644
	--- a/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage.hh
	+++ b/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage.hh
	@@ -1,146 +1,145 @@
	/**
	* @file material_orthotropic_damage.hh
	* @author Aurelia Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @date Sun Mar 8 12:49:56 2015
	*
	* @brief Material for orthotropic damage
	*
	*
	* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ORTHOTROPIC_DAMAGE_HH_
	#define AKANTU_MATERIAL_ORTHOTROPIC_DAMAGE_HH_

	namespace akantu {
	template <UInt spatial_dimension,
	template <UInt> class Parent = MaterialElastic>
	class MaterialOrthotropicDamage : public Parent<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialOrthotropicDamage(SolidMechanicsModel & model, const ID & id = "");

	virtual ~MaterialOrthotropicDamage(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// update the dissipated energy, must be called after the stress have been
	/// computed
	void updateEnergies(ElementType el_type) override;

	/// compute the tangent stiffness matrix for a given quadrature point
	inline void computeTangentModuliOnQuad(
	Matrix<Real> & tangent, const Matrix<Real> C, const Matrix<Real> & dam,
	const Matrix<Real> & dam_directions, Matrix<Real> & O_prime,
	Matrix<Real> & S_prime, Matrix<Real> & O, Matrix<Real> & S,
	Matrix<Real> & rotation_tmp);

	inline void computeDamageAndStressOnQuad(Matrix<Real> & sigma,
	Matrix<Real> & one_minus_D,
	Matrix<Real> & root_one_minus_D,
	Matrix<Real> & damage,
	Matrix<Real> & first_term,
	Matrix<Real> & third_term);

	/// rotate a Matrix of size dim*dim into the coordinate system of the FE
	/// computation
	inline void rotateIntoComputationFrame(const Matrix<Real> & to_rotate,
	Matrix<Real> & rotated,
	const Matrix<Real> & damage_directions,
	Matrix<Real> & rotation_tmp);

	/// rotate a Matrix of size dim*dim into the coordinate system of the damage
	inline void rotateIntoNewFrame(const Matrix<Real> & to_rotate,
	Matrix<Real> & rotated,
	const Matrix<Real> & damage_directions,
	Matrix<Real> & rotation_tmp);

	/// compute (1-D)
	inline void computeOneMinusD(Matrix<Real> & one_minus_D,
	const Matrix<Real> & damage);

	/// compute (1-D)^(1/2)
	inline void computeSqrtOneMinusD(const Matrix<Real> & one_minus_D,
	Matrix<Real> & sqrt_one_minus_D);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// give the dissipated energy for the time step
	Real getDissipatedEnergy() const;

	// virtual Real getEnergy(std::string type);
	// virtual Real getEnergy(std::string energy_id, ElementType type, UInt index)
	// {
	// return Parent<spatial_dimension>::getEnergy(energy_id, type, index);
	// };

	AKANTU_GET_MACRO_NOT_CONST(Damage, damage, ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO(Damage, damage, const ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real)

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// damage internal variable
	InternalField<Real> damage;

	/// dissipated energy
	InternalField<Real> dissipated_energy;

	/// contain the current value of @f$ \int_0^{\epsilon}\sigma(\omega)d\omega
	/// @f$ the dissipated energy
	InternalField<Real> int_sigma;

	/// direction vectors for the damage frame
	InternalField<Real> damage_dir_vecs;

	Real eta;

	/// maximum damage value
	Real max_damage;
	};

	} // namespace akantu

	#include "material_orthotropic_damage_tmpl.hh"

	#endif /* AKANTU_MATERIAL_ORTHOTROPIC_DAMAGE_HH_ */
	diff --git a/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage_tmpl.hh b/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage_tmpl.hh
	index 2da4fcb7f..0d752a8d7 100644
	--- a/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage_tmpl.hh
	+++ b/extra_packages/extra-materials/src/material_damage/material_orthotropic_damage_tmpl.hh
	@@ -1,321 +1,320 @@
	/**
	* @file material_orthotropic_damage_tmpl.hh
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @date Sun Mar 8 12:54:30 2015
	*
	* @brief Specialization of the material class for the orthotropic
	* damage material
	*
	*
	* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_orthotropic_damage.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	MaterialOrthotropicDamage<spatial_dimension, Parent>::MaterialOrthotropicDamage(
	SolidMechanicsModel & model, const ID & id)
	: Parent<spatial_dimension>(model, id), damage("damage", *this),
	dissipated_energy("damage dissipated energy", *this),
	int_sigma("integral of sigma", *this),
	damage_dir_vecs("damage_principal_directions", *this) {
	AKANTU_DEBUG_IN();

	this->registerParam("eta", eta, 2., _pat_parsable \| _pat_modifiable,
	"Damage sensitivity parameter");
	this->registerParam("max_damage", max_damage, 0.99999,
	_pat_parsable \| _pat_modifiable, "maximum damage value");

	this->is_non_local = false;
	this->use_previous_stress = true;
	this->use_previous_gradu = true;

	/// use second order tensor for description of damage state
	this->damage.initialize(spatial_dimension * spatial_dimension);
	this->dissipated_energy.initialize(1);
	this->int_sigma.initialize(1);
	this->damage_dir_vecs.initialize(spatial_dimension * spatial_dimension);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialOrthotropicDamage<spatial_dimension, Parent>::initMaterial() {
	AKANTU_DEBUG_IN();
	Parent<spatial_dimension>::initMaterial();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Compute the dissipated energy in each element by a trapezoidal approximation
	* of
	* @f$ Ed = \int_0^{\epsilon}\sigma(\omega)d\omega -
	* \frac{1}{2}\sigma:\epsilon@f$
	*/
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialOrthotropicDamage<spatial_dimension, Parent>::updateEnergies(
	ElementType el_type) {
	Parent<spatial_dimension>::updateEnergies(el_type);

	this->computePotentialEnergy(el_type);

	auto epsilon_p =
	this->gradu.previous(el_type).begin(spatial_dimension, spatial_dimension);
	auto sigma_p = this->stress.previous(el_type).begin(spatial_dimension,
	spatial_dimension);

	auto epot = this->potential_energy(el_type).begin();

	auto ints = this->int_sigma(el_type).begin();
	auto ed = this->dissipated_energy(el_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	Matrix<Real> delta_gradu_it(grad_u);
	delta_gradu_it -= *epsilon_p;

	Matrix<Real> sigma_h(sigma);
	sigma_h += *sigma_p;

	Real dint = .5 * sigma_h.doubleDot(delta_gradu_it);

	*ints += dint;
	ed = ints - *epot;

	++epsilon_p;
	++sigma_p;
	++epot;
	++ints;
	++ed;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialOrthotropicDamage<spatial_dimension, Parent>::computeTangentModuli(
	- ElementType el_type, Array<Real> & tangent_matrix,
	- GhostType ghost_type) {
	+ ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Parent<spatial_dimension>::computeTangentModuli(el_type, tangent_matrix,
	ghost_type);

	/// get the damage array for current element type
	Array<Real> & dam = this->damage(el_type);
	auto dam_it = dam.begin(this->spatial_dimension, this->spatial_dimension);

	/// get the directions of damage for the current element type
	Array<Real> & dam_dirs = this->damage_dir_vecs(el_type);
	auto damage_directions_it =
	dam_dirs.begin(this->spatial_dimension, this->spatial_dimension);

	/// for the computation of the Cauchy stress the matrices (1-D) and
	/// (1-D)^(1/2) are needed. For the formulation see Engineering
	/// Damage Mechanics by Lemaitre and Desmorat.
	Matrix<Real> one_minus_D(this->spatial_dimension, this->spatial_dimension);
	Matrix<Real> sqrt_one_minus_D(this->spatial_dimension,
	this->spatial_dimension);
	Matrix<Real> one_minus_D_rot(spatial_dimension, spatial_dimension);
	Matrix<Real> sqrt_one_minus_D_rot(spatial_dimension, spatial_dimension);

	Matrix<Real> rotation_tmp(spatial_dimension, spatial_dimension);

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);

	if (!(Math::are_float_equal((*dam_it).trace(), 0)))
	computeTangentModuliOnQuad(tangent, tangent, dam_it, damage_directions_it,
	one_minus_D, sqrt_one_minus_D, one_minus_D_rot,
	sqrt_one_minus_D_rot, rotation_tmp);

	++dam_it;
	++damage_directions_it;

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialOrthotropicDamage<spatial_dimension, Parent>::
	computeTangentModuliOnQuad(Matrix<Real> & tangent, const Matrix<Real> C,
	const Matrix<Real> & dam,
	const Matrix<Real> & dam_directions,
	Matrix<Real> & O_prime, Matrix<Real> & S_prime,
	Matrix<Real> & O, Matrix<Real> & S,
	Matrix<Real> & rotation_tmp) {

	/// effect of damage on stiffness matrix: See Ragueneau et al. 2008, p. 423,
	/// ep. 7
	Real trace_D = dam.trace();
	this->computeOneMinusD(O_prime, dam);
	this->computeSqrtOneMinusD(O_prime, S_prime);
	this->rotateIntoComputationFrame(O_prime, O, dam_directions, rotation_tmp);
	this->rotateIntoComputationFrame(S_prime, S, dam_directions, rotation_tmp);

	/// compute new stiffness matrix in damage coordinate system
	if (spatial_dimension == 1)
	tangent *= (1 - dam(0, 0));

	if (spatial_dimension == 2) {
	Real min_val =
	std::min((this->eta / spatial_dimension * trace_D), this->max_damage);

	/// first row
	tangent(0, 0) =
	(C(0, 0) * S(0, 0) * S(0, 0) + C(1, 0) * S(0, 1) * S(0, 1) -
	(min_val / 2. - 1. / 2) * (C(0, 0) + C(1, 0)) +
	(O(0, 0) * (C(0, 0) * O(0, 0) + C(1, 0) * O(1, 1))) / (trace_D - 2.));

	tangent(0, 1) =
	(C(0, 1) * S(0, 0) * S(0, 0) + C(1, 1) * S(0, 1) * S(0, 1) -
	(min_val / 2. - 1. / 2) * (C(0, 1) + C(1, 1)) +
	(O(0, 0) * (C(0, 1) * O(0, 0) + C(1, 1) * O(1, 1))) / (trace_D - 2.));

	tangent(0, 2) = (2. * C(2, 2) * S(0, 0) * S(0, 1) +
	(2. * C(2, 2) * O(0, 0) * O(0, 1)) / (trace_D - 2.));

	/// second row
	tangent(1, 0) =
	(C(0, 0) * S(0, 1) * S(0, 1) + C(1, 0) * S(1, 1) * S(1, 1) -
	(min_val / 2. - 1. / 2) * (C(0, 0) + C(1, 0)) +
	(O(1, 1) * (C(0, 0) * O(0, 0) + C(1, 0) * O(1, 1))) / (trace_D - 2.));

	tangent(1, 1) =
	(C(0, 1) * S(0, 1) * S(0, 1) + C(1, 1) * S(1, 1) * S(1, 1) -
	(min_val / 2. - 1. / 2) * (C(0, 1) + C(1, 1)) +
	(O(1, 1) * (C(0, 1) * O(0, 0) + C(1, 1) * O(1, 1))) / (trace_D - 2.));

	tangent(1, 2) = (2. * C(2, 2) * S(0, 1) * S(1, 1) +
	(2. * C(2, 2) * O(0, 1) * O(1, 1)) / (trace_D - 2.));

	/// third row
	tangent(2, 0) =
	((O(0, 1) * (C(0, 0) * O(0, 0) + C(1, 0) * O(1, 1))) / (trace_D - 2.) +
	C(0, 0) * S(0, 0) * S(0, 1) + C(1, 0) * S(0, 1) * S(1, 1));

	tangent(2, 1) =
	((O(0, 1) * (C(0, 1) * O(0, 0) + C(1, 1) * O(1, 1))) / (trace_D - 2.) +
	C(0, 1) * S(0, 0) * S(0, 1) + C(1, 1) * S(0, 1) * S(1, 1));
	tangent(2, 2) = ((2. * C(2, 2) * O(0, 1) * O(0, 1)) / (trace_D - 2.) +
	C(2, 2) * S(0, 1) * S(0, 1) + C(2, 2) * S(0, 0) * S(1, 1));
	}

	if (spatial_dimension == 3) {
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void MaterialOrthotropicDamage<spatial_dimension, Parent>::
	computeDamageAndStressOnQuad(Matrix<Real> & sigma,
	Matrix<Real> & one_minus_D,
	Matrix<Real> & sqrt_one_minus_D,
	Matrix<Real> & damage,
	Matrix<Real> & first_term,
	Matrix<Real> & third_term) {
	/// Definition of Cauchy stress based on second order damage tensor:
	/// "Anisotropic damage modelling of biaxial behaviour and rupture
	/// of concrete strucutres", Ragueneau et al., 2008, Eq. 7
	first_term.mul<false, false>(sqrt_one_minus_D, sigma);
	first_term *= sqrt_one_minus_D;

	Real second_term = 0;
	for (UInt i = 0; i < this->spatial_dimension; ++i) {
	for (UInt j = 0; j < this->spatial_dimension; ++j)
	second_term += sigma(i, j) * one_minus_D(i, j);
	}

	second_term /= (this->spatial_dimension - damage.trace());

	one_minus_D *= second_term;

	third_term.eye(1. / this->spatial_dimension * sigma.trace() *
	(1 - eta / (this->spatial_dimension) * damage.trace()));

	sigma.copy(first_term);
	sigma -= one_minus_D;
	sigma += third_term;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void MaterialOrthotropicDamage<spatial_dimension, Parent>::
	rotateIntoComputationFrame(const Matrix<Real> & to_rotate,
	Matrix<Real> & rotated,
	const Matrix<Real> & damage_directions,
	Matrix<Real> & rotation_tmp) {
	rotation_tmp.mul<false, true>(to_rotate, damage_directions);
	rotated.mul<false, false>(damage_directions, rotation_tmp);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialOrthotropicDamage<spatial_dimension, Parent>::rotateIntoNewFrame(
	const Matrix<Real> & to_rotate, Matrix<Real> & rotated,
	const Matrix<Real> & damage_directions, Matrix<Real> & rotation_tmp) {
	rotation_tmp.mul<false, false>(to_rotate, damage_directions);
	rotated.mul<true, false>(damage_directions, rotation_tmp);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialOrthotropicDamage<spatial_dimension, Parent>::computeOneMinusD(
	Matrix<Real> & one_minus_D, const Matrix<Real> & damage) {
	/// compute one minus
	one_minus_D.eye();
	one_minus_D -= damage;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialOrthotropicDamage<spatial_dimension, Parent>::computeSqrtOneMinusD(
	const Matrix<Real> & one_minus_D, Matrix<Real> & sqrt_one_minus_D) {

	/// To compute (1-D)^1/2 we need to check that we are in the
	/// principal coordinate system of the damage
	#ifndef AKANTU_NDEBUG
	for (UInt i = 0; i < this->spatial_dimension; ++i) {
	for (UInt j = 0; j < this->spatial_dimension; ++j) {
	if (i != j)
	AKANTU_DEBUG_ASSERT(Math::are_float_equal(one_minus_D(i, j), 0),
	"The damage tensor has off-diagonal parts");
	}
	}
	#endif // AKANTU_NDEBUG

	/// compute (1-D)^1/2
	sqrt_one_minus_D.copy(one_minus_D);
	for (UInt i = 0; i < this->spatial_dimension; ++i)
	sqrt_one_minus_D(i, i) = std::sqrt(sqrt_one_minus_D(i, i));
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.cc b/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.cc
	index 1068fa7a4..e93deff2c 100644
	--- a/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.cc
	+++ b/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.cc
	@@ -1,107 +1,106 @@
	/**
	* @file material_viscoplastic.cc
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	*
	*
	* @brief Specialization of the material class for isotropic viscoplastic
	* (small deformation)
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/
	/* -------------------------------------------------------------------------- */
	#include "material_viscoplastic.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialViscoPlastic<dim>::MaterialViscoPlastic(SolidMechanicsModel & model,
	const ID & id)
	: MaterialPlastic<dim>(model, id) {
	AKANTU_DEBUG_IN();

	this->registerParam("rate", rate, 0., _pat_parsable \| _pat_modifiable,
	"Rate sensitivity component");
	this->registerParam("edot0", edot0, 0., _pat_parsable \| _pat_modifiable,
	"Reference strain rate");
	this->registerParam("ts", ts, 0., _pat_parsable \| _pat_modifiable,
	"Time Step");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialViscoPlastic<dim>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * iso_hardening = this->iso_hardening(el_type, ghost_type).storage();

	auto previous_grad_u_it =
	this->gradu.previous(el_type, ghost_type).begin(dim, dim);

	auto previous_sigma_it =
	this->stress.previous(el_type, ghost_type).begin(dim, dim);

	auto inelastic_strain_it =
	this->inelastic_strain(el_type, ghost_type).begin(dim, dim);

	auto previous_inelastic_strain_it =
	this->inelastic_strain.previous(el_type, ghost_type).begin(dim, dim);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	computeStressOnQuad(grad_u, previous_grad_u_it, sigma, previous_sigma_it,
	inelastic_strain_it, previous_inelastic_strain_it,
	*iso_hardening);

	++inelastic_strain_it;
	++iso_hardening;
	++previous_grad_u_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialViscoPlastic<dim>::computeTangentModuli(
	- __attribute__((unused)) ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ __attribute__((unused)) ElementType el_type, Array<Real> & tangent_matrix,
	__attribute__((unused)) GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto previous_sigma_it =
	this->stress.previous(el_type, ghost_type).begin(dim, dim);

	auto previous_strain_it =
	this->gradu.previous(el_type, ghost_type).begin(dim, dim);

	Real * iso_hardening = this->iso_hardening(el_type, ghost_type).storage();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);

	Matrix<Real> & previous_grad_u = *previous_strain_it;
	Matrix<Real> & previous_sigma_tensor = *previous_sigma_it;

	computeTangentModuliOnQuad(tangent, grad_u, previous_grad_u, sigma,
	previous_sigma_tensor, *iso_hardening);
	++previous_sigma_it;
	++previous_strain_it;
	++iso_hardening;
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	INSTANTIATE_MATERIAL(visco_plastic, MaterialViscoPlastic);

	} // namespace akantu
	diff --git a/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.hh b/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.hh
	index eabfd8768..31976de37 100644
	--- a/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.hh
	+++ b/extra_packages/extra-materials/src/material_plastic/material_viscoplastic.hh
	@@ -1,99 +1,98 @@
	/**
	* @file material_viscoplastic.hh
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	*
	*
	* @brief Specialization of the material class for
	* MaterialLinearIsotropicHardening to include viscous effects (small
	* deformation)
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	#include "material_plastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_VISCOPLASTIC_HH_
	#define AKANTU_MATERIAL_VISCOPLASTIC_HH_

	namespace akantu {

	/**
	* Material plastic isotropic
	*
	* parameters in the material files :
	* - h : Hardening parameter (default: 0)
	* - sigmay : Yield stress
	* - rate : Rate sensitivity
	* - edot0 : Reference strain rate
	*
	* - ts: Time step
	*/

	template <UInt spatial_dimension>
	class MaterialViscoPlastic : public MaterialPlastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialViscoPlastic(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	virtual void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost);

	protected:
	inline void
	computeStressOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	Real & iso_hardening) const;

	inline void computeTangentModuliOnQuad(
	Matrix<Real> & tangent, const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u, const Matrix<Real> & sigma_tensor,
	const Matrix<Real> & previous_sigma_tensor,
	const Real & iso_hardening) const;
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// Rate sensitivity component (rate)
	Real rate;

	/// Reference strain rate (edot0)
	Real edot0;

	/// Time step (ts)
	Real ts;
	};
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "material_viscoplastic_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_VISCOPLASTIC_HH_ */
	diff --git a/extra_packages/extra-materials/src/material_viscoelastic/material_stiffness_proportional.hh b/extra_packages/extra-materials/src/material_viscoelastic/material_stiffness_proportional.hh
	index dbb3bac45..4b40c5f6f 100644
	--- a/extra_packages/extra-materials/src/material_viscoelastic/material_stiffness_proportional.hh
	+++ b/extra_packages/extra-materials/src/material_viscoelastic/material_stiffness_proportional.hh
	@@ -1,98 +1,99 @@
	/**
	* @file material_stiffness_proportional.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	*
	* @brief Material isotropic visco-elastic with viscosity proportional to the
	* stiffness
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_STIFFNESS_PROPORTIONAL_HH_
	#define AKANTU_MATERIAL_STIFFNESS_PROPORTIONAL_HH_

	namespace akantu {

	/**
	* Material visco-elastic @f[\sigma = E\epsilon + \alpha E*
	* \frac{d\epsilon}{dt}@f]
	* it can be seen as a Kelvin-Voigt solid with @f[\eta = \alpha E @f]
	*
	* The material satisfies the Caughey condition, the visco-elastic solid has the
	* same eigen-modes as the elastic one. (T.K. Caughey 1960 - Journal of Applied
	* Mechanics 27, 269-271. Classical normal modes in damped linear systems.)
	*
	* parameters in the material files :
	* - rho : density (default: 0)
	* - E : Young's modulus (default: 0)
	* - nu : Poisson's ratio (default: 1/2)
	* - Plane_Stress : if 0: plane strain, else: plane stress (default: 0)
	* - alpha : viscous ratio
	*/
	template <UInt spatial_dimension>
	class MaterialStiffnessProportional
	: public MaterialElastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialStiffnessProportional(SolidMechanicsModel & model,
	const ID & id = "");

	virtual ~MaterialStiffnessProportional(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// constitutive law for all element of a type
	- void computeStress(ElementType el_type, GhostType ghost_type = _not_ghost) override;
	+ void computeStress(ElementType el_type,
	+ GhostType ghost_type = _not_ghost) override;

	/// compute the potential energy for all elements
	void computePotentialEnergy(ElementType el_type) override;

	protected:
	/// constitutive law for a given quadrature point
	// inline void computeStress(Real * F, Real * sigma);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// stress due to viscosity
	InternalField<Real> stress_viscosity;

	/// stress due to elasticity
	InternalField<Real> stress_elastic;

	/// viscous ratio
	Real alpha;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "material_elastic_caughey_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_STIFFNESS_PROPORTIONAL_HH_ */
	diff --git a/extra_packages/igfem/src/dumper_igfem_connectivity.hh b/extra_packages/igfem/src/dumper_igfem_connectivity.hh
	index 42191d61b..3f2c4c99e 100644
	--- a/extra_packages/igfem/src/dumper_igfem_connectivity.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_connectivity.hh
	@@ -1,116 +1,133 @@
	/**
	* @file dumper_igfem_connectivity.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Iterator for the IGFEM connectivity
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_DUMPER_IGFEM_CONNECTIVITY_HH_
	#define AKANTU_DUMPER_IGFEM_CONNECTIVITY_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_igfem_element_iterator.hh"
	#include "dumper_igfem_generic_elemental_field.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-
	-template <class types>
	-class igfem_connectivity_field_iterator
	- : public igfem_element_iterator<types, igfem_connectivity_field_iterator> {
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	- typedef igfem_element_iterator<types,
	- dumpers::igfem_connectivity_field_iterator>
	- parent;
	- typedef typename types::return_type return_type;
	- typedef typename types::field_type field_type;
	- typedef typename types::array_iterator array_iterator;
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- igfem_connectivity_field_iterator(
	- const field_type & field, const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it, const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	- sub_element) {}
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	- return_type operator*() {
	- const Vector<UInt> & element_connect = *this->array_it;
	-
	- /// get the local sub_element connectivity and the nodes per sub-element
	- UInt * sub_connec_ptr =
	- IGFEMHelper::getSubElementConnectivity(*this->tit, this->sub_element);
	- UInt nb_nodes_sub_el =
	- IGFEMHelper::getNbNodesPerSubElement(*this->tit, this->sub_element);
	-
	- /// get the global sub element connectivity
	- Vector<UInt> sub_element_connect(nb_nodes_sub_el);
	- for (UInt i = 0; i < nb_nodes_sub_el; ++i) {
	- UInt lc = sub_connec_ptr[i];
	- sub_element_connect(i) = element_connect(lc);
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <class types>
	+ class igfem_connectivity_field_iterator
	+ : public igfem_element_iterator<types,
	+ igfem_connectivity_field_iterator> {
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ typedef igfem_element_iterator<types,
	+ dumpers::igfem_connectivity_field_iterator>
	+ parent;
	+ typedef typename types::return_type return_type;
	+ typedef typename types::field_type field_type;
	+ typedef typename types::array_iterator array_iterator;
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ igfem_connectivity_field_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	+ sub_element) {}
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ return_type operator*() {
	+ const Vector<UInt> & element_connect = *this->array_it;
	+
	+ /// get the local sub_element connectivity and the nodes per sub-element
	+ UInt * sub_connec_ptr =
	+ IGFEMHelper::getSubElementConnectivity(*this->tit, this->sub_element);
	+ UInt nb_nodes_sub_el =
	+ IGFEMHelper::getNbNodesPerSubElement(*this->tit, this->sub_element);
	+
	+ /// get the global sub element connectivity
	+ Vector<UInt> sub_element_connect(nb_nodes_sub_el);
	+ for (UInt i = 0; i < nb_nodes_sub_el; ++i) {
	+ UInt lc = sub_connec_ptr[i];
	+ sub_element_connect(i) = element_connect(lc);
	+ }
	+
	+ return sub_element_connect;
	}

	- return sub_element_connect;
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-
	-private:
	-};
	-
	-/* -------------------------------------------------------------------------- */
	-class IGFEMConnectivityField
	- : public IGFEMGenericElementalField<SingleType<UInt, Vector, false>,
	- igfem_connectivity_field_iterator> {
	-
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- typedef SingleType<UInt, Vector, false> types;
	- typedef igfem_connectivity_field_iterator<types> iterator;
	- typedef types::field_type field_type;
	- typedef IGFEMGenericElementalField<types, igfem_connectivity_field_iterator>
	- parent;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- IGFEMConnectivityField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost)
	- : parent(field, spatial_dimension, ghost_type) {}
	-};
	-
	-/* -------------------------------------------------------------------------- */
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ private:
	+ };
	+
	+ /* --------------------------------------------------------------------------
	+ */
	+ class IGFEMConnectivityField
	+ : public IGFEMGenericElementalField<SingleType<UInt, Vector, false>,
	+ igfem_connectivity_field_iterator> {
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ typedef SingleType<UInt, Vector, false> types;
	+ typedef igfem_connectivity_field_iterator<types> iterator;
	+ typedef types::field_type field_type;
	+ typedef IGFEMGenericElementalField<types, igfem_connectivity_field_iterator>
	+ parent;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ IGFEMConnectivityField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost)
	+ : parent(field, spatial_dimension, ghost_type) {}
	+ };
	+
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#endif /AKANTU_DUMPER_IGFEM_CONNECTIVITY_HH_ /
	diff --git a/extra_packages/igfem/src/dumper_igfem_element_iterator.hh b/extra_packages/igfem/src/dumper_igfem_element_iterator.hh
	index 09a320438..a044f8522 100644
	--- a/extra_packages/igfem/src/dumper_igfem_element_iterator.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_element_iterator.hh
	@@ -1,181 +1,199 @@
	/**
	* @file dumper_igfem_element_iterator.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Iterators for IGFEM elemental fields
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_DUMPER_IGFEM_ELEMENT_ITERATOR_HH_
	#define AKANTU_DUMPER_IGFEM_ELEMENT_ITERATOR_HH_
	/* -------------------------------------------------------------------------- */
	#include "element.hh"
	#include "igfem_helper.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <class types, template <class> class final_iterator>
	+ class igfem_element_iterator {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ typedef typename types::it_type it_type;
	+ typedef typename types::field_type field_type;
	+ typedef typename types::array_type array_type;
	+ typedef typename types::array_iterator array_iterator;
	+ typedef final_iterator<types> iterator;
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ igfem_element_iterator(const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it,
	+ const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost,
	+ UInt sub_element = 0)
	+ : field(field), tit(t_it), tit_end(t_it_end), array_it(array_it),
	+ array_it_end(array_it_end), ghost_type(ghost_type),
	+ sub_element(sub_element) {}
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ bool operator!=(const iterator & it) const {
	+ return (ghost_type != it.ghost_type) \|\|
	+ (tit != it.tit \|\|
	+ ((array_it != it.array_it) \|\| sub_element != it.sub_element));
	+ }

	-template <class types, template <class> class final_iterator>
	-class igfem_element_iterator {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- typedef typename types::it_type it_type;
	- typedef typename types::field_type field_type;
	- typedef typename types::array_type array_type;
	- typedef typename types::array_iterator array_iterator;
	- typedef final_iterator<types> iterator;
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- igfem_element_iterator(const field_type & field,
	- const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it,
	- const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost,
	- UInt sub_element = 0)
	- : field(field), tit(t_it), tit_end(t_it_end), array_it(array_it),
	- array_it_end(array_it_end), ghost_type(ghost_type),
	- sub_element(sub_element) {}
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- bool operator!=(const iterator & it) const {
	- return (ghost_type != it.ghost_type) \|\|
	- (tit != it.tit \|\|
	- ((array_it != it.array_it) \|\| sub_element != it.sub_element));
	- }
	-
	- iterator & operator++() {
	- if (!this->sub_element)
	- this->sub_element += 1;
	- else {
	- ++array_it;
	- this->sub_element = 0;
	- while (array_it == array_it_end && tit != tit_end) {
	- ++tit;
	- if (tit != tit_end) {
	- const array_type & vect = field(*tit, ghost_type);
	- UInt _nb_data_per_elem = getNbDataPerElem(*tit);
	- UInt nb_component = vect.getNbComponent();
	- UInt size = (vect.getSize() * nb_component) / _nb_data_per_elem;
	-
	- array_it = vect.begin_reinterpret(_nb_data_per_elem, size);
	- array_it_end = vect.end_reinterpret(_nb_data_per_elem, size);
	+ iterator & operator++() {
	+ if (!this->sub_element)
	+ this->sub_element += 1;
	+ else {
	+ ++array_it;
	+ this->sub_element = 0;
	+ while (array_it == array_it_end && tit != tit_end) {
	+ ++tit;
	+ if (tit != tit_end) {
	+ const array_type & vect = field(*tit, ghost_type);
	+ UInt _nb_data_per_elem = getNbDataPerElem(*tit);
	+ UInt nb_component = vect.getNbComponent();
	+ UInt size = (vect.getSize() * nb_component) / _nb_data_per_elem;
	+
	+ array_it = vect.begin_reinterpret(_nb_data_per_elem, size);
	+ array_it_end = vect.end_reinterpret(_nb_data_per_elem, size);
	+ }
	}
	}
	+ return (static_cast<iterator >(this));
	}
	- return (static_cast<iterator >(this));
	- }
	-
	- ElementType getType() {
	- ElementType sub_type = IGFEMHelper::getSubElementType(*tit, sub_element);
	- return sub_type;
	- }
	-
	- /// get IOHelperType for sub-element
	- UInt element_type() { return getIOHelperType(this->getType()); }
	-
	- /// get current parent element????
	- Element getCurrentElement() {
	- return Element(*tit, array_it.getCurrentIndex());
	- }
	-
	- UInt getNbDataPerElem(ElementType type) const {
	- /// nb of data per parent element!
	- if (!nb_data_per_elem.exists(type, ghost_type))
	- return field(type, ghost_type).getNbComponent();
	-
	- return nb_data_per_elem(type, ghost_type);
	- }
	-
	- void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) {
	- /// nb of data per parent element!
	- this->nb_data_per_elem = nb_data;
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-
	-protected:
	- /// the field to iterate on
	- const field_type & field;
	- /// field iterator
	- typename field_type::type_iterator tit;
	- /// field iterator end
	- typename field_type::type_iterator tit_end;
	- /// array iterator
	- array_iterator array_it;
	- /// internal iterator end
	- array_iterator array_it_end;
	- /// ghost type identification
	- const GhostType ghost_type;
	- /// number of data per element
	- ElementTypeMap<UInt> nb_data_per_elem;
	- /// index of sub-element
	- UInt sub_element;
	- /// sub_element end
	- UInt sub_element_end;
	-};

	-/* -------------------------------------------------------------------------- */
	-template <typename types>
	-class igfem_elemental_field_iterator
	- : public igfem_element_iterator<types, igfem_elemental_field_iterator> {
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	- typedef igfem_element_iterator<
	- types, ::akantu::dumpers::igfem_elemental_field_iterator>
	- parent;
	- typedef typename types::it_type it_type;
	- typedef typename types::return_type return_type;
	- typedef typename types::field_type field_type;
	- typedef typename types::array_iterator array_iterator;
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- igfem_elemental_field_iterator(
	- const field_type & field, const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it, const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	- sub_element) {}
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	- return_type operator() { return this->array_it; }
	-
	-private:
	-};
	+ ElementType getType() {
	+ ElementType sub_type = IGFEMHelper::getSubElementType(*tit, sub_element);
	+ return sub_type;
	+ }

	-/* -------------------------------------------------------------------------- */
	+ /// get IOHelperType for sub-element
	+ UInt element_type() { return getIOHelperType(this->getType()); }
	+
	+ /// get current parent element????
	+ Element getCurrentElement() {
	+ return Element(*tit, array_it.getCurrentIndex());
	+ }
	+
	+ UInt getNbDataPerElem(ElementType type) const {
	+ /// nb of data per parent element!
	+ if (!nb_data_per_elem.exists(type, ghost_type))
	+ return field(type, ghost_type).getNbComponent();
	+
	+ return nb_data_per_elem(type, ghost_type);
	+ }
	+
	+ void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) {
	+ /// nb of data per parent element!
	+ this->nb_data_per_elem = nb_data;
	+ }
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ protected:
	+ /// the field to iterate on
	+ const field_type & field;
	+ /// field iterator
	+ typename field_type::type_iterator tit;
	+ /// field iterator end
	+ typename field_type::type_iterator tit_end;
	+ /// array iterator
	+ array_iterator array_it;
	+ /// internal iterator end
	+ array_iterator array_it_end;
	+ /// ghost type identification
	+ const GhostType ghost_type;
	+ /// number of data per element
	+ ElementTypeMap<UInt> nb_data_per_elem;
	+ /// index of sub-element
	+ UInt sub_element;
	+ /// sub_element end
	+ UInt sub_element_end;
	+ };
	+
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <typename types>
	+ class igfem_elemental_field_iterator
	+ : public igfem_element_iterator<types, igfem_elemental_field_iterator> {
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ typedef igfem_element_iterator<
	+ types, ::akantu::dumpers::igfem_elemental_field_iterator>
	+ parent;
	+ typedef typename types::it_type it_type;
	+ typedef typename types::return_type return_type;
	+ typedef typename types::field_type field_type;
	+ typedef typename types::array_iterator array_iterator;
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ igfem_elemental_field_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	+ sub_element) {}
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ return_type operator() { return this->array_it; }
	+
	+ private:
	+ };
	+
	+ /* --------------------------------------------------------------------------
	+ */
	} // namespace dumpers
	} // namespace akantu
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_DUMPER_IGFEM_ELEMENT_ITERATOR_HH_ */
	diff --git a/extra_packages/igfem/src/dumper_igfem_element_partition.hh b/extra_packages/igfem/src/dumper_igfem_element_partition.hh
	index 88acea1ef..e098b69d0 100644
	--- a/extra_packages/igfem/src/dumper_igfem_element_partition.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_element_partition.hh
	@@ -1,103 +1,122 @@
	/**
	* @file dumper_igfem_element_partition.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Element partition field for IGFEM sub-elements
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {

	-/* -------------------------------------------------------------------------- */
	-template <class types>
	-class igfem_element_partition_field_iterator
	- : public igfem_element_iterator<types,
	- igfem_element_partition_field_iterator> {
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <class types>
	+ class igfem_element_partition_field_iterator
	+ : public igfem_element_iterator<types,
	+ igfem_element_partition_field_iterator> {

	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- typedef igfem_element_iterator<types,
	- dumpers::igfem_element_partition_field_iterator>
	- parent;
	- typedef typename types::return_type return_type;
	- typedef typename types::array_iterator array_iterator;
	- typedef typename types::field_type field_type;
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ typedef igfem_element_iterator<
	+ types, dumpers::igfem_element_partition_field_iterator>
	+ parent;
	+ typedef typename types::return_type return_type;
	+ typedef typename types::array_iterator array_iterator;
	+ typedef typename types::field_type field_type;

	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- igfem_element_partition_field_iterator(
	- const field_type & field, const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it, const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	- sub_element) {
	- prank = StaticCommunicator::getStaticCommunicator().whoAmI();
	- }
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ igfem_element_partition_field_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	+ sub_element) {
	+ prank = StaticCommunicator::getStaticCommunicator().whoAmI();
	+ }

	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-public:
	- return_type operator*() { return return_type(1, prank); }
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ return_type operator*() { return return_type(1, prank); }

	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-protected:
	- UInt prank;
	-};
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+ protected:
	+ UInt prank;
	+ };

	-/* -------------------------------------------------------------------------- */
	-template <bool filtered = false>
	-class IGFEMElementPartitionField : public IGFEMGenericElementalField<
	- SingleType<UInt, Vector, filtered>,
	- igfem_element_partition_field_iterator> {
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <bool filtered = false>
	+ class IGFEMElementPartitionField
	+ : public IGFEMGenericElementalField<
	+ SingleType<UInt, Vector, filtered>,
	+ igfem_element_partition_field_iterator> {
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */

	- typedef SingleType<UInt, Vector, filtered> types;
	- typedef igfem_element_partition_field_iterator<types> iterator;
	- typedef IGFEMGenericElementalField<types,
	- igfem_element_partition_field_iterator>
	- parent;
	- typedef typename types::field_type field_type;
	+ typedef SingleType<UInt, Vector, filtered> types;
	+ typedef igfem_element_partition_field_iterator<types> iterator;
	+ typedef IGFEMGenericElementalField<types,
	+ igfem_element_partition_field_iterator>
	+ parent;
	+ typedef typename types::field_type field_type;

	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */

	- IGFEMElementPartitionField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind kind = _ek_igfem)
	- : parent(field, spatial_dimension, ghost_type, kind) {
	- this->homogeneous = true;
	- }
	+ IGFEMElementPartitionField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind kind = _ek_igfem)
	+ : parent(field, spatial_dimension, ghost_type, kind) {
	+ this->homogeneous = true;
	+ }

	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */

	- UInt getDim() { return 1; }
	-};
	+ UInt getDim() { return 1; }
	+ };

	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu
	diff --git a/extra_packages/igfem/src/dumper_igfem_elemental_field.hh b/extra_packages/igfem/src/dumper_igfem_elemental_field.hh
	index 323c2dc7e..c3e53d4f6 100644
	--- a/extra_packages/igfem/src/dumper_igfem_elemental_field.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_elemental_field.hh
	@@ -1,56 +1,61 @@
	/**
	* @file dumper_igfem_elemental_field.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief description of IGFEM elemental fields
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_DUMPER_IGFEM_ELEMENTAL_FIELD_HH_
	#define AKANTU_DUMPER_IGFEM_ELEMENTAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_field.hh"
	#include "dumper_igfem_generic_elemental_field.hh"
	#include "static_communicator.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-
	-template <typename T, template <class> class ret = Vector,
	- bool filtered = false>
	-class IGFEMElementalField
	- : public IGFEMGenericElementalField<SingleType<T, ret, filtered>,
	- igfem_elemental_field_iterator> {
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	- typedef SingleType<T, ret, filtered> types;
	- typedef typename types::field_type field_type;
	- typedef elemental_field_iterator<types> iterator;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- IGFEMElementalField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_igfem)
	- : IGFEMGenericElementalField<types, igfem_elemental_field_iterator>(
	- field, spatial_dimension, ghost_type, element_kind) {}
	-};
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <typename T, template <class> class ret = Vector,
	+ bool filtered = false>
	+ class IGFEMElementalField
	+ : public IGFEMGenericElementalField<SingleType<T, ret, filtered>,
	+ igfem_elemental_field_iterator> {
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ typedef SingleType<T, ret, filtered> types;
	+ typedef typename types::field_type field_type;
	+ typedef elemental_field_iterator<types> iterator;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ IGFEMElementalField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_igfem)
	+ : IGFEMGenericElementalField<types, igfem_elemental_field_iterator>(
	+ field, spatial_dimension, ghost_type, element_kind) {}
	+ };

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_IGFEM_ELEMENTAL_FIELD_HH_ */
	diff --git a/extra_packages/igfem/src/dumper_igfem_generic_elemental_field.hh b/extra_packages/igfem/src/dumper_igfem_generic_elemental_field.hh
	index 66bb3bf07..b88a98a72 100644
	--- a/extra_packages/igfem/src/dumper_igfem_generic_elemental_field.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_generic_elemental_field.hh
	@@ -1,143 +1,152 @@
	/**
	* @file dumper_igfem_generic_elemental_field.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief generic interface IGFEM elemental fields
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DUMPER_IGFEM_GENERIC_ELEMENTAL_FIELD_HH_
	#define AKANTU_DUMPER_IGFEM_GENERIC_ELEMENTAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_generic_elemental_field.hh"
	#include "dumper_igfem_element_iterator.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-template <class _types, template <class> class iterator_type>
	-class IGFEMGenericElementalField
	- : public GenericElementalField<_types, iterator_type> {
	-
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- typedef _types types;
	- typedef typename types::data_type data_type;
	- typedef typename types::it_type it_type;
	- typedef typename types::field_type field_type;
	- typedef typename types::array_type array_type;
	- typedef typename types::array_iterator array_iterator;
	- typedef typename field_type::type_iterator field_type_iterator;
	- typedef iterator_type<types> iterator;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- IGFEMGenericElementalField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind kind = _ek_igfem)
	- :
	-
	- GenericElementalField<types, iterator_type>(field, spatial_dimension,
	- ghost_type, kind) {
	- this->checkHomogeneity();
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- /// return the size of the contained data: i.e. the number of elements ?
	- virtual UInt size() {
	- this->checkHomogeneity();
	- return ((this->nb_total_element) * 2);
	- }
	-
	- virtual iterator begin() {
	- field_type_iterator tit;
	- field_type_iterator end;
	- UInt sub_element = 0;
	-
	- /// type iterators on the elemental field
	- tit = this->field.firstType(this->spatial_dimension, this->ghost_type,
	- this->element_kind);
	- end = this->field.lastType(this->spatial_dimension, this->ghost_type,
	- this->element_kind);
	-
	- /// skip all types without data
	- ElementType type = *tit;
	- for (; tit != end && this->field(*tit, this->ghost_type).getSize() == 0;
	- ++tit) {
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <class _types, template <class> class iterator_type>
	+ class IGFEMGenericElementalField
	+ : public GenericElementalField<_types, iterator_type> {
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ typedef _types types;
	+ typedef typename types::data_type data_type;
	+ typedef typename types::it_type it_type;
	+ typedef typename types::field_type field_type;
	+ typedef typename types::array_type array_type;
	+ typedef typename types::array_iterator array_iterator;
	+ typedef typename field_type::type_iterator field_type_iterator;
	+ typedef iterator_type<types> iterator;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ IGFEMGenericElementalField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind kind = _ek_igfem)
	+ :
	+
	+ GenericElementalField<types, iterator_type>(field, spatial_dimension,
	+ ghost_type, kind) {
	+ this->checkHomogeneity();
	+ }
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ /// return the size of the contained data: i.e. the number of elements ?
	+ virtual UInt size() {
	+ this->checkHomogeneity();
	+ return ((this->nb_total_element) * 2);
	}
	- type = *tit;
	-
	- if (tit == end)
	- return this->end();
	-
	- /// getting information for the field of the given type
	- const array_type & vect = this->field(type, this->ghost_type);
	- UInt nb_data_per_elem = this->getNbDataPerElem(type);
	- UInt nb_component = vect.getNbComponent();
	- UInt size = (vect.getSize() * nb_component) / nb_data_per_elem;
	-
	- /// define element-wise iterator
	- array_iterator it = vect.begin_reinterpret(nb_data_per_elem, size);
	- array_iterator it_end = vect.end_reinterpret(nb_data_per_elem, size);
	- /// define data iterator
	- iterator rit = iterator(this->field, tit, end, it, it_end, this->ghost_type,
	- sub_element);
	- rit.setNbDataPerElem(this->nb_data_per_elem);
	- return rit;
	- }
	-
	- virtual iterator end() {
	- field_type_iterator tit;
	- field_type_iterator end;
	- UInt sub_element = 0;
	-
	- tit = this->field.firstType(this->spatial_dimension, this->ghost_type,
	- this->element_kind);
	- end = this->field.lastType(this->spatial_dimension, this->ghost_type,
	- this->element_kind);
	-
	- ElementType type = *tit;
	- for (; tit != end; ++tit)
	+
	+ virtual iterator begin() {
	+ field_type_iterator tit;
	+ field_type_iterator end;
	+ UInt sub_element = 0;
	+
	+ /// type iterators on the elemental field
	+ tit = this->field.firstType(this->spatial_dimension, this->ghost_type,
	+ this->element_kind);
	+ end = this->field.lastType(this->spatial_dimension, this->ghost_type,
	+ this->element_kind);
	+
	+ /// skip all types without data
	+ ElementType type = *tit;
	+ for (; tit != end && this->field(*tit, this->ghost_type).getSize() == 0;
	+ ++tit) {
	+ }
	type = *tit;

	- const array_type & vect = this->field(type, this->ghost_type);
	- UInt nb_data = this->getNbDataPerElem(type);
	- UInt nb_component = vect.getNbComponent();
	- UInt size = (vect.getSize() * nb_component) / nb_data;
	- array_iterator it = vect.end_reinterpret(nb_data, size);
	+ if (tit == end)
	+ return this->end();
	+
	+ /// getting information for the field of the given type
	+ const array_type & vect = this->field(type, this->ghost_type);
	+ UInt nb_data_per_elem = this->getNbDataPerElem(type);
	+ UInt nb_component = vect.getNbComponent();
	+ UInt size = (vect.getSize() * nb_component) / nb_data_per_elem;
	+
	+ /// define element-wise iterator
	+ array_iterator it = vect.begin_reinterpret(nb_data_per_elem, size);
	+ array_iterator it_end = vect.end_reinterpret(nb_data_per_elem, size);
	+ /// define data iterator
	+ iterator rit = iterator(this->field, tit, end, it, it_end,
	+ this->ghost_type, sub_element);
	+ rit.setNbDataPerElem(this->nb_data_per_elem);
	+ return rit;
	+ }

	- iterator rit =
	- iterator(this->field, end, end, it, it, this->ghost_type, sub_element);
	- rit.setNbDataPerElem(this->nb_data_per_elem);
	- return rit;
	- }
	+ virtual iterator end() {
	+ field_type_iterator tit;
	+ field_type_iterator end;
	+ UInt sub_element = 0;
	+
	+ tit = this->field.firstType(this->spatial_dimension, this->ghost_type,
	+ this->element_kind);
	+ end = this->field.lastType(this->spatial_dimension, this->ghost_type,
	+ this->element_kind);
	+
	+ ElementType type = *tit;
	+ for (; tit != end; ++tit)
	+ type = *tit;
	+
	+ const array_type & vect = this->field(type, this->ghost_type);
	+ UInt nb_data = this->getNbDataPerElem(type);
	+ UInt nb_component = vect.getNbComponent();
	+ UInt size = (vect.getSize() * nb_component) / nb_data;
	+ array_iterator it = vect.end_reinterpret(nb_data, size);
	+
	+ iterator rit = iterator(this->field, end, end, it, it, this->ghost_type,
	+ sub_element);
	+ rit.setNbDataPerElem(this->nb_data_per_elem);
	+ return rit;
	+ }

	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */

	-protected:
	-};
	+ protected:
	+ };

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_IGFEM_GENERIC_ELEMENTAL_FIELD_HH_ */
	diff --git a/extra_packages/igfem/src/dumper_igfem_material_internal_field.hh b/extra_packages/igfem/src/dumper_igfem_material_internal_field.hh
	index 80c602966..5af3c8299 100644
	--- a/extra_packages/igfem/src/dumper_igfem_material_internal_field.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_material_internal_field.hh
	@@ -1,53 +1,58 @@
	/**
	* @file dumper_igfem_material_internal_field.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief description of IGFEM material internal field
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_DUMPER_IGFEM_MATERIAL_INTERNAL_FIELD_HH_
	#define AKANTU_DUMPER_IGFEM_MATERIAL_INTERNAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_igfem_quadrature_points_field.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-
	-template <typename T, bool filtered = false>
	-class IGFEMInternalMaterialField
	- : public IGFEMGenericElementalField<SingleType<T, Vector, filtered>,
	- igfem_quadrature_point_iterator> {
	-
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- typedef SingleType<T, Vector, filtered> types;
	- typedef IGFEMGenericElementalField<types, igfem_quadrature_point_iterator>
	- parent;
	- typedef typename types::field_type field_type;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- IGFEMInternalMaterialField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind kind = _ek_igfem)
	- : parent(field, spatial_dimension, ghost_type, kind) {}
	-};
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <typename T, bool filtered = false>
	+ class IGFEMInternalMaterialField
	+ : public IGFEMGenericElementalField<SingleType<T, Vector, filtered>,
	+ igfem_quadrature_point_iterator> {
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ typedef SingleType<T, Vector, filtered> types;
	+ typedef IGFEMGenericElementalField<types, igfem_quadrature_point_iterator>
	+ parent;
	+ typedef typename types::field_type field_type;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ IGFEMInternalMaterialField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind kind = _ek_igfem)
	+ : parent(field, spatial_dimension, ghost_type, kind) {}
	+ };

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_IGFEM_MATERIAL_INTERNAL_FIELD_HH_ */
	diff --git a/extra_packages/igfem/src/dumper_igfem_quadrature_points_field.hh b/extra_packages/igfem/src/dumper_igfem_quadrature_points_field.hh
	index 38b060bba..ca9d90dce 100644
	--- a/extra_packages/igfem/src/dumper_igfem_quadrature_points_field.hh
	+++ b/extra_packages/igfem/src/dumper_igfem_quadrature_points_field.hh
	@@ -1,140 +1,156 @@
	/**
	* @file dumper_igfem_quadrature_points_field.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief description of IGFEM quadrature points field
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_DUMPER_IGFEM_QUADRATURE_POINTS_FIELD_HH_
	#define AKANTU_DUMPER_IGFEM_QUADRATURE_POINTS_FIELD_HH_

	/* -------------------------------------------------------------------------- */
	#include "dumper_igfem_elemental_field.hh"

	namespace akantu {
	namespace dumpers {

	-/* -------------------------------------------------------------------------- */
	-template <typename types>
	-class igfem_quadrature_point_iterator
	- : public igfem_element_iterator<types, igfem_quadrature_point_iterator> {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- typedef igfem_element_iterator<types, dumpers::igfem_quadrature_point_iterator>
	- parent;
	- typedef typename types::data_type data_type;
	- typedef typename types::return_type return_type;
	- typedef typename types::field_type field_type;
	- typedef typename types::array_iterator array_iterator;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- igfem_quadrature_point_iterator(
	- const field_type & field, const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it, const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	- sub_element) {}
	-
	- return_type operator*() {
	- const Vector<data_type> & mat_internal_field = *this->array_it;
	- /// get nb data per sub element
	- UInt nb_sub_1_internal_points =
	- IGFEMHelper::getNbQuadraturePoints(*this->tit, 0);
	- UInt nb_sub_2_internal_points =
	- IGFEMHelper::getNbQuadraturePoints(*this->tit, 1);
	-
	- UInt nb_data = this->getNbDataPerElem(*(this->tit)) /
	- (nb_sub_1_internal_points + nb_sub_2_internal_points);
	-
	- UInt nb_sub_components = 0;
	- if (!(this->sub_element))
	- nb_sub_components = nb_data * nb_sub_1_internal_points;
	- else
	- nb_sub_components = nb_data * nb_sub_2_internal_points;
	-
	- Vector<data_type> sub_mat_internal_field(nb_sub_components);
	-
	- if (!(this->sub_element)) {
	- for (UInt i = 0; i < nb_sub_components; ++i)
	- sub_mat_internal_field(i) = mat_internal_field(i);
	- } else {
	- for (UInt i = 0; i < nb_sub_components; ++i)
	- sub_mat_internal_field(i) =
	- mat_internal_field(nb_data * nb_sub_1_internal_points + i);
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <typename types>
	+ class igfem_quadrature_point_iterator
	+ : public igfem_element_iterator<types, igfem_quadrature_point_iterator> {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ typedef igfem_element_iterator<types,
	+ dumpers::igfem_quadrature_point_iterator>
	+ parent;
	+ typedef typename types::data_type data_type;
	+ typedef typename types::return_type return_type;
	+ typedef typename types::field_type field_type;
	+ typedef typename types::array_iterator array_iterator;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ igfem_quadrature_point_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost, UInt sub_element = 0)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type,
	+ sub_element) {}
	+
	+ return_type operator*() {
	+ const Vector<data_type> & mat_internal_field = *this->array_it;
	+ /// get nb data per sub element
	+ UInt nb_sub_1_internal_points =
	+ IGFEMHelper::getNbQuadraturePoints(*this->tit, 0);
	+ UInt nb_sub_2_internal_points =
	+ IGFEMHelper::getNbQuadraturePoints(*this->tit, 1);
	+
	+ UInt nb_data = this->getNbDataPerElem(*(this->tit)) /
	+ (nb_sub_1_internal_points + nb_sub_2_internal_points);
	+
	+ UInt nb_sub_components = 0;
	+ if (!(this->sub_element))
	+ nb_sub_components = nb_data * nb_sub_1_internal_points;
	+ else
	+ nb_sub_components = nb_data * nb_sub_2_internal_points;
	+
	+ Vector<data_type> sub_mat_internal_field(nb_sub_components);
	+
	+ if (!(this->sub_element)) {
	+ for (UInt i = 0; i < nb_sub_components; ++i)
	+ sub_mat_internal_field(i) = mat_internal_field(i);
	+ } else {
	+ for (UInt i = 0; i < nb_sub_components; ++i)
	+ sub_mat_internal_field(i) =
	+ mat_internal_field(nb_data * nb_sub_1_internal_points + i);
	+ }
	+
	+ return sub_mat_internal_field;
	}
	-
	- return sub_mat_internal_field;
	- }
	-};
	-
	-// /* --------------------------------------------------------------------------
	-// */
	-// /* Fields type description */
	-// /* --------------------------------------------------------------------------
	-// */
	-// template<class types, template <class> class iterator_type>
	-// class GenericQuadraturePointsField :
	-// public GenericElementalField<types,iterator_type> {
	-
	-// public:
	-
	-// /* ------------------------------------------------------------------------
	-// */
	-// /* Typedefs */
	-// /* ------------------------------------------------------------------------
	-// */
	-
	-// typedef iterator_type<types> iterator;
	-// typedef typename types::field_type field_type;
	-// typedef typename iterator::it_type T;
	-// typedef GenericElementalField<types,iterator_type> parent;
	-
	-// /* ------------------------------------------------------------------------
	-// */
	-// /* Constructors/Destructors */
	-// /* ------------------------------------------------------------------------
	-// */
	-
	-// GenericQuadraturePointsField(const field_type & field,
	-// UInt spatial_dimension = _all_dimensions,
	-// GhostType ghost_type = _not_ghost,
	-// ElementKind element_kind = _ek_not_defined) :
	-// parent(field, spatial_dimension, ghost_type, element_kind) { }
	-
	-// /* ------------------------------------------------------------------------
	-// */
	-// /* Methods */
	-// /* ------------------------------------------------------------------------
	-// */
	-
	-// virtual iterator begin() {
	-// iterator it = parent::begin();
	-// return it;
	-// }
	-
	-// virtual iterator end () {
	-// iterator it = parent::end();
	-// return it;
	-// }
	-
	-// };
	-
	-/* -------------------------------------------------------------------------- */
	+ };
	+
	+ // /*
	+ // --------------------------------------------------------------------------
	+ // */
	+ // /* Fields type description */
	+ // /*
	+ // --------------------------------------------------------------------------
	+ // */
	+ // template<class types, template <class> class iterator_type>
	+ // class GenericQuadraturePointsField :
	+ // public GenericElementalField<types,iterator_type> {
	+
	+ // public:
	+
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+ // /* Typedefs */
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+
	+ // typedef iterator_type<types> iterator;
	+ // typedef typename types::field_type field_type;
	+ // typedef typename iterator::it_type T;
	+ // typedef GenericElementalField<types,iterator_type> parent;
	+
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+ // /* Constructors/Destructors */
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+
	+ // GenericQuadraturePointsField(const field_type & field,
	+ // UInt spatial_dimension = _all_dimensions,
	+ // GhostType ghost_type = _not_ghost,
	+ // ElementKind element_kind = _ek_not_defined) :
	+ // parent(field, spatial_dimension, ghost_type, element_kind) { }
	+
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+ // /* Methods */
	+ // /*
	+ // ------------------------------------------------------------------------
	+ // */
	+
	+ // virtual iterator begin() {
	+ // iterator it = parent::begin();
	+ // return it;
	+ // }
	+
	+ // virtual iterator end () {
	+ // iterator it = parent::end();
	+ // return it;
	+ // }
	+
	+ // };
	+
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_IGFEM_QUADRATURE_POINTS_FIELD_HH_ */
	diff --git a/extra_packages/igfem/src/element_class_igfem.hh b/extra_packages/igfem/src/element_class_igfem.hh
	index 69b7ca250..c98cc6cf6 100644
	--- a/extra_packages/igfem/src/element_class_igfem.hh
	+++ b/extra_packages/igfem/src/element_class_igfem.hh
	@@ -1,297 +1,304 @@
	/**
	* @file element_class_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	*
	* @brief Specialization for interface-enriched finite elements
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_IGFEM_HH_
	#define AKANTU_ELEMENT_CLASS_IGFEM_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <InterpolationType interpolation_type>
	class InterpolationElement<interpolation_type, _itk_igfem> {
	public:
	using interpolation_property = InterpolationProperty<interpolation_type>;
	/* ------------------------------------------------------------------------ */
	/* Member functions */
	/* ------------------------------------------------------------------------ */
	public:
	static void assembleShapes(const Vector<Real> & parent_interpolation,
	const Vector<Real> & sub_interpolation,
	Vector<Real> & interpolation,
	UInt sub_element = 0) {
	/// N1, N2, N3 of parent triangle
	UInt nb_nodes_parent = InterpolationElement<
	interpolation_property::parent_interpolation_type>::getShapeSize();

	for (UInt i = 0; i < nb_nodes_parent; ++i) {
	interpolation(i) = parent_interpolation(i);
	}
	/// add the enrichment
	UInt * enriched_node = enrichments[sub_element];
	for (UInt e = 0; e < nb_enrichments; ++e) {
	interpolation(nb_nodes_parent + e) = sub_interpolation(enriched_node[e]);
	}
	}
	static void
	assembleShapeDerivatives(const Matrix<Real> & parent_interpolation,
	const Matrix<Real> & sub_interpolation,
	Matrix<Real> & interpolation, UInt sub_element = 0) {

	/// N1, N2, N3 of parent triangle
	UInt nb_nodes_parent = InterpolationElement<
	interpolation_property::parent_interpolation_type>::getShapeSize();

	for (UInt i = 0; i < nb_nodes_parent; ++i) {
	Vector<Real> ip(interpolation(i));
	ip = parent_interpolation(i);
	}
	/// add the enrichment
	UInt * enriched_node = enrichments[sub_element];
	for (UInt e = 0; e < nb_enrichments; ++e) {
	Vector<Real> ip(interpolation(nb_nodes_parent + e));
	ip = sub_interpolation(enriched_node[e]);
	}
	}

	static void interpolate(const Matrix<Real> & nodal_values,
	const Vector<Real> & shapes,
	Vector<Real> & interpolated) {
	Matrix<Real> interpm(interpolated.storage(), nodal_values.rows(), 1);
	Matrix<Real> shapesm(shapes.storage(),
	interpolation_property::nb_nodes_per_element, 1);
	interpm.mul<false, false>(nodal_values, shapesm);
	}

	public:
	static AKANTU_GET_MACRO_NOT_CONST(
	ShapeSize, interpolation_property::nb_nodes_per_element, UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	ShapeDerivativesSize,
	(interpolation_property::nb_nodes_per_element *
	interpolation_property::natural_space_dimension),
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NaturalSpaceDimension, interpolation_property::natural_space_dimension,
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NbNodesPerInterpolationElement,
	interpolation_property::nb_nodes_per_element, UInt);
	- static AKANTU_GET_MACRO_NOT_CONST(NbSubElements, interpolation_property::nb_sub_elements, UInt);
	+ static AKANTU_GET_MACRO_NOT_CONST(NbSubElements,
	+ interpolation_property::nb_sub_elements,
	+ UInt);
	static UInt * getSubElementConnectivity(UInt t = 0) {
	return &(interpolation_property::sub_element_connectivity[t]);
	};
	- static UInt getNbEnrichments() { return interpolation_property::nb_enrichments; };
	- static UInt * getSubElementEnrichments(UInt t = 0) { return &(interpolation_property::enrichments[t]); };
	+ static UInt getNbEnrichments() {
	+ return interpolation_property::nb_enrichments;
	+ };
	+ static UInt * getSubElementEnrichments(UInt t = 0) {
	+ return &(interpolation_property::enrichments[t]);
	+ };

	protected:
	/// storage of the subelement local connectivity

	static UInt sub_element_connectivity_vect[];
	/// local connectivity of subelements
	static UInt * sub_element_connectivity[];
	/// nb of subelements
	static UInt nb_sub_elements;
	/// storage of enrichments
	static UInt enrichment_vect[];
	static UInt * enrichments[];
	static UInt nb_enrichments;
	};

	} // namespace akantu

	#include "interpolation_element_igfem_tmpl.hh"

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	#define AKANTU_DEFINE_IGFEM_ELEMENT_CLASS_PROPERTY( \
	elem_type, geom_type, interp_type, parent_el_type, sub_el_type_1, \
	sub_el_type_2, elem_kind, sp, min_int_order) \
	template <> struct ElementClassProperty<elem_type> { \
	static const GeometricalType geometrical_type{geom_type}; \
	static const InterpolationType interpolation_type{interp_type}; \
	static const ElementType parent_element_type{parent_el_type}; \
	static const ElementType sub_element_type_1{sub_el_type_1}; \
	static const ElementType sub_element_type_2{sub_el_type_2}; \
	static const ElementKind element_kind{elem_kind}; \
	static const UInt spatial_dimension{sp}; \
	static const UInt minimal_integration_order{min_int_order}; \
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType element_type>
	class ElementClass<element_type, _ek_igfem>
	: public GeometricalElement<
	ElementClassProperty<element_type>::geometrical_type>,
	public InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type> {
	protected:
	using geometrical_element =
	GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
	using interpolation_element = InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type>;
	using parent_element =
	ElementClass<ElementClassProperty<element_type>::parent_element_type>;
	using element_property = ElementClassProperty<element_type>;
	using interpolation_property =
	typename interpolation_element::interpolation_property;

	/* ------------------------------------------------------------------------ */
	/* Member functions */
	/* ------------------------------------------------------------------------ */
	public:
	static void getSubElementCoords(const Matrix<Real> & element_coords,
	Matrix<Real> & sub_coords,
	const UInt sub_element) {
	/// get the sub_element_type
	/// constexrp ElementType sub_el_type = getSubElementType(sub_element);
	UInt nb_nodes_sub_el = 0;
	switch (sub_element) {
	case 0:
	nb_nodes_sub_el =
	ElementClass<ElementClassProperty<element_type>::sub_element_type_1>::
	getNbNodesPerInterpolationElement();
	break;
	case 1:
	nb_nodes_sub_el =
	ElementClass<ElementClassProperty<element_type>::sub_element_type_2>::
	getNbNodesPerInterpolationElement();
	break;
	}

	for (UInt i = 0; i < nb_nodes_sub_el; ++i) {
	UInt lc = InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type>::
	sub_element_connectivity[sub_element][i];
	Vector<Real> sub_c(sub_coords(i));
	sub_c = element_coords(lc);
	}
	}

	static void getParentCoords(const Matrix<Real> & element_coords,
	Matrix<Real> & parent_coords) {
	const ElementType parent_type =
	ElementClassProperty<element_type>::parent_element_type;
	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	for (UInt i = 0; i < nb_nodes_parent_el; ++i) {
	Vector<Real> parent_c(parent_coords(i));
	parent_c = element_coords(i);
	}
	}

	/// map the points from the reference domain of the subelement to the physical
	/// domain
	static void mapToPhysicalDomain(const Matrix<Real> & element_coords,
	Matrix<Real> & sub_coords,
	Matrix<Real> & sub_shapes,
	Matrix<Real> & physical_points,
	UInt sub_element = 0) {
	/// get the sub_element_type

	getSubElementCoords(element_coords, sub_coords, sub_element);
	/// map the points of the subelements in the physical domain
	switch (sub_element) {
	case 0:
	ElementClass<ElementClassProperty<element_type>::sub_element_type_1>::
	interpolate(sub_coords, sub_shapes, physical_points);
	break;
	case 1:
	ElementClass<ElementClassProperty<element_type>::sub_element_type_2>::
	interpolate(sub_coords, sub_shapes, physical_points);
	break;
	}
	}

	/// map the points from the physical domain to the parent reference domain
	static void mapToParentRefDomain(const Matrix<Real> & element_coords,
	Matrix<Real> & parent_coords,
	Matrix<Real> & physical_points,
	Matrix<Real> & natural_coords) {
	const ElementType parent_type =
	ElementClassProperty<element_type>::parent_element_type;
	getParentCoords(element_coords, parent_coords);

	/// map the points from the physical domain into the parent reference domain
	ElementClass<parent_type>::inverseMap(physical_points, parent_coords,
	natural_coords);
	}

	/// map the points from the subelement reference domain to the parent
	/// reference domain
	static void mapFromSubRefToParentRef(const Matrix<Real> & element_coords,
	Matrix<Real> & parent_coords,
	Matrix<Real> & sub_coords,
	Matrix<Real> & sub_shapes,
	Matrix<Real> & physical_points,
	Matrix<Real> & natural_points,
	UInt /nb_points/, UInt sub_element) {
	mapToPhysicalDomain(element_coords, sub_coords, sub_shapes, physical_points,
	sub_element);
	mapToParentRefDomain(element_coords, parent_coords, physical_points,
	natural_points);
	}

	static void mapFromSubRefToParentRef(const Matrix<Real> & element_coords,
	Matrix<Real> & sub_coords,
	Matrix<Real> & parent_coords,
	Matrix<Real> & sub_shapes,
	Matrix<Real> & physical_points,
	Matrix<Real> & parent_el_natural_coords,
	UInt sub_element) {
	mapToPhysicalDomain(element_coords, sub_coords, sub_shapes, physical_points,
	sub_element);
	mapToParentRefDomain(element_coords, parent_coords, physical_points,
	parent_el_natural_coords);
	}

	/// compute the normal of a surface defined by the function f
	static inline void
	computeNormalsOnNaturalCoordinates(const Matrix<Real> & /coord/,
	Matrix<Real> & /f/,
	Matrix<Real> & /normals/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// determine orientation of the element with respect to the interface
	static inline UInt getOrientation(const Vector<bool> & is_inside);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	static AKANTU_GET_MACRO_NOT_CONST(Kind, _ek_igfem, ElementKind);
	static ElementType getP1ElementType() { AKANTU_TO_IMPLEMENT(); };
	static AKANTU_GET_MACRO_NOT_CONST(
	SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
	UInt);
	static ElementType & getFacetType(UInt /t/ = 0) { AKANTU_TO_IMPLEMENT(); }
	static ElementType * getFacetTypeInternal() { AKANTU_TO_IMPLEMENT(); }
	+
	private:
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "geometrical_element_igfem.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_class_igfem_segment_3_inline_impl.hh"
	#include "element_class_igfem_triangle_4_inline_impl.hh"
	#include "element_class_igfem_triangle_5_inline_impl.hh"
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_ELEMENT_CLASS_IGFEM_HH_ */
	diff --git a/extra_packages/igfem/src/fe_engine_template_tmpl_igfem.hh b/extra_packages/igfem/src/fe_engine_template_tmpl_igfem.hh
	index 3fe2d31a8..276ab296d 100644
	--- a/extra_packages/igfem/src/fe_engine_template_tmpl_igfem.hh
	+++ b/extra_packages/igfem/src/fe_engine_template_tmpl_igfem.hh
	@@ -1,117 +1,115 @@
	/**
	* @file shape_igfem_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @brief ShapeIGFEM inline implementation
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss_igfem.hh"
	#include "shape_igfem.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FE_ENGINE_TEMPLATE_TMPL_IGFEM_HH_
	#define AKANTU_FE_ENGINE_TEMPLATE_TMPL_IGFEM_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* compatibility functions */
	/* -------------------------------------------------------------------------- */

	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem,
	DefaultIntegrationOrderFunctor>::
	- initShapeFunctions(const Array<Real> & nodes,
	- GhostType ghost_type) {
	+ initShapeFunctions(const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh::type_iterator it =
	mesh.firstType(element_dimension, ghost_type, _ek_igfem);
	Mesh::type_iterator end =
	mesh.lastType(element_dimension, ghost_type, _ek_igfem);
	for (; it != end; ++it) {
	ElementType type = *it;
	integrator.initIntegrator(nodes, type, ghost_type);

	#define INIT(_type) \
	do { \
	const Matrix<Real> & all_quads = \
	integrator.getIntegrationPoints<_type>(ghost_type); \
	const Matrix<Real> & quads_1 = integrator.getIntegrationPoints< \
	ElementClassProperty<_type>::sub_element_type_1>(ghost_type); \
	const Matrix<Real> & quads_2 = integrator.getIntegrationPoints< \
	ElementClassProperty<_type>::sub_element_type_2>(ghost_type); \
	shape_functions.initShapeFunctions(nodes, all_quads, quads_1, quads_2, \
	_type, ghost_type); \
	} while (0)

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(INIT);
	#undef INIT
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem,
	DefaultIntegrationOrderFunctor>::
	computeIntegrationPointsCoordinates(
	Array<Real> & quadrature_points_coordinates, ElementType type,
	- GhostType ghost_type,
	- const Array<UInt> & filter_elements) const {
	+ GhostType ghost_type, const Array<UInt> & filter_elements) const {

	const Array<Real> & nodes_coordinates = mesh.getNodes();
	UInt spatial_dimension = mesh.getSpatialDimension();
	/// create an array with the nodal coordinates that need to be
	/// interpolated. The nodal coordinates of the enriched nodes need
	/// to be set to zero, because they represent the enrichment of the
	/// position field, and the enrichments for this field are all zero!
	/// There is no gap in the mesh!
	Array<Real> igfem_nodes(nodes_coordinates.getSize(), spatial_dimension);
	shape_functions.extractValuesAtStandardNodes(nodes_coordinates, igfem_nodes,
	ghost_type);

	interpolateOnIntegrationPoints(igfem_nodes, quadrature_points_coordinates,
	spatial_dimension, type, ghost_type,
	filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem,
	DefaultIntegrationOrderFunctor>::
	computeIntegrationPointsCoordinates(
	ElementTypeMapArray<Real> & quadrature_points_coordinates,
	const ElementTypeMapArray<UInt> * filter_elements) const {

	const Array<Real> & nodes_coordinates = mesh.getNodes();
	UInt spatial_dimension = mesh.getSpatialDimension();
	/// create an array with the nodal coordinates that need to be
	/// interpolated. The nodal coordinates of the enriched nodes need
	/// to be set to zero, because they represent the enrichment of the
	/// position field, and the enrichments for this field are all zero!
	/// There is no gap in the mesh!
	Array<Real> igfem_nodes(nodes_coordinates.getSize(), spatial_dimension);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {
	GhostType ghost_type = *gt;
	shape_functions.extractValuesAtStandardNodes(nodes_coordinates, igfem_nodes,
	ghost_type);
	}

	interpolateOnIntegrationPoints(igfem_nodes, quadrature_points_coordinates,
	filter_elements);
	}

	} // namespace akantu

	#endif /* AKANTU_FE_ENGINE_TEMPLATE_TMPL_IGFEM_HH_ */
	diff --git a/extra_packages/igfem/src/igfem_helper.hh b/extra_packages/igfem/src/igfem_helper.hh
	index 687e9653b..01a103fa5 100644
	--- a/extra_packages/igfem/src/igfem_helper.hh
	+++ b/extra_packages/igfem/src/igfem_helper.hh
	@@ -1,148 +1,147 @@
	/**
	* @file dumper_igfem_element_iterator.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Helper class to return sub element information
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	#ifndef AKANTU_IGFEM_HELPER_HH_
	#define AKANTU_IGFEM_HELPER_HH_
	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class FEEngine;

	template <ElementType type> struct ElementTypeIGFEMData {
	static ElementType igfem_element_types[];
	static UInt nb_igfem_types;
	};

	struct IGFEMHelper {
	template <ElementType type>
	static VectorProxy<ElementType> getIGFEMElementTypes() {
	return VectorProxy<ElementType>(
	ElementTypeIGFEMData<type>::igfem_element_types,
	ElementTypeIGFEMData<type>::nb_igfem_types);
	}

	/// get the number of nodes for a given sub-element
	static UInt getNbNodesPerSubElement(ElementType type,
	const UInt sub_element) {
	UInt nb_nodes_per_sub_element = 0;
	#define GET_NB_NODES_PER_SUB_ELEMENT(type) \
	switch (sub_element) { \
	case 0: \
	nb_nodes_per_sub_element = \
	ElementClass<ElementClassProperty<type>::sub_element_type_1>:: \
	getNbNodesPerInterpolationElement(); \
	break; \
	case 1: \
	nb_nodes_per_sub_element = \
	ElementClass<ElementClassProperty<type>::sub_element_type_2>:: \
	getNbNodesPerInterpolationElement(); \
	break; \
	}
	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_NB_NODES_PER_SUB_ELEMENT);
	#undef GET_NB_NODES_PER_SUB_ELEMENT
	return nb_nodes_per_sub_element;
	}

	/// get the connectivity for a given sub-element
	static UInt * getSubElementConnectivity(ElementType type,
	const UInt sub_element) {
	UInt * sub_element_connectivity = NULL;
	#define GET_SUB_ELEMENT_CONNECTIVITY(type) \
	sub_element_connectivity = \
	ElementClass<type>::getSubElementConnectivity(sub_element);
	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_SUB_ELEMENT_CONNECTIVITY);
	#undef GET_SUB_ELEMENT_CONNECTIVITY
	return sub_element_connectivity;
	}

	/// get the sub-element type
	static ElementType getSubElementType(ElementType type,
	const UInt sub_element) {
	ElementType sub_type = _not_defined;
	#define GET_SUB_ELEMENT_TYPE(type) \
	switch (sub_element) { \
	case 0: \
	sub_type = ElementClassProperty<type>::sub_element_type_1; \
	break; \
	case 1: \
	sub_type = ElementClassProperty<type>::sub_element_type_2; \
	break; \
	}
	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_SUB_ELEMENT_TYPE);
	#undef GET_SUB_ELEMENT_TYPE
	return sub_type;
	}

	/// get the nb of quads for one sub element type
	- static UInt getNbQuadraturePoints(ElementType type,
	- const UInt sub_element) {
	+ static UInt getNbQuadraturePoints(ElementType type, const UInt sub_element) {
	UInt nb_quad_points = 0;
	#define GET_NB_QUADS(type) \
	switch (sub_element) { \
	case 0: \
	nb_quad_points = GaussIntegrationElement<ElementClassProperty< \
	type>::sub_element_type_1>::getNbQuadraturePoints(); \
	break; \
	case 1: \
	nb_quad_points = GaussIntegrationElement<ElementClassProperty< \
	type>::sub_element_type_2>::getNbQuadraturePoints(); \
	break; \
	}
	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_NB_QUADS);
	#undef GET_NB_QUADS
	return nb_quad_points;
	}

	/// get the nb of parent nodes of a given igfem element type
	static UInt getNbParentNodes(ElementType type) {
	UInt nb_parent_nodes = 0;
	#define GET_NB_PARENT_NODES(type) \
	nb_parent_nodes = \
	ElementClass<ElementClassProperty<type>::parent_element_type>:: \
	getNbNodesPerInterpolationElement();

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_NB_PARENT_NODES);
	#undef GET_NB_PARENT_NODES
	return nb_parent_nodes;
	}

	/// get the nb of parent nodes of a given igfem element type
	static UInt getNbEnrichedNodes(ElementType type) {
	UInt nb_enriched_nodes = 0;
	#define GET_NB_ENRICHED_NODES(type) \
	nb_enriched_nodes = ElementClass<type>::getNbEnrichments();

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_NB_ENRICHED_NODES);
	#undef GET_NB_ENRICHED_NODES
	return nb_enriched_nodes;
	}

	/// get the nb of quads for one sub element type
	static UInt getElementOrientation(ElementType type,
	const Vector<bool> & is_inside) {
	UInt orientation = 0;

	#define GET_ORIENTATION(type) \
	orientation = ElementClass<type>::getOrientation(is_inside);

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_ORIENTATION);
	#undef GET_ORIENTATION
	return orientation;
	}
	};

	} // namespace akantu
	#endif /* AKANTU_IGFEM_HELPER_HH_ */
	diff --git a/extra_packages/igfem/src/integrator_gauss_igfem.hh b/extra_packages/igfem/src/integrator_gauss_igfem.hh
	index c32092989..02f75885d 100644
	--- a/extra_packages/igfem/src/integrator_gauss_igfem.hh
	+++ b/extra_packages/igfem/src/integrator_gauss_igfem.hh
	@@ -1,123 +1,119 @@
	/**
	* @file integrator_gauss_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Gauss integration facilities for IGFEM
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTEGRATOR_IGFEM_HH_
	#define AKANTU_INTEGRATOR_IGFEM_HH_

	/* -------------------------------------------------------------------------- */
	#include "integrator.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	template <class IOF> class IntegratorGauss<_ek_igfem, IOF> : public Integrator {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	IntegratorGauss(const Mesh & mesh, const ID & id = "integrator_gauss");

	virtual ~IntegratorGauss(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	- inline void initIntegrator(const Array<Real> & nodes,
	- ElementType type,
	+ inline void initIntegrator(const Array<Real> & nodes, ElementType type,
	GhostType ghost_type);

	/// precompute jacobians on elements of type "type"
	template <ElementType type>
	void precomputeJacobiansOnQuadraturePoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// integrate f on the element "elem" of type "type"
	template <ElementType type>
	inline void integrateOnElement(const Array<Real> & f, Real * intf,
	UInt nb_degree_of_freedom, UInt elem,
	GhostType ghost_type) const;

	/// integrate f for all elements of type "type"
	template <ElementType type>
	void integrate(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom, GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// integrate one element scalar value on all elements of type "type"
	template <ElementType type>
	Real integrate(const Vector<Real> & in_f, UInt index,
	GhostType ghost_type) const;

	/// integrate scalar field in_f
	template <ElementType type>
	Real integrate(const Array<Real> & in_f, GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// integrate partially around a quadrature point (@f$ intf_q = f_q * J_q *
	/// w_q @f$)
	template <ElementType type>
	- void integrateOnIntegrationPoints(const Array<Real> & in_f,
	- Array<Real> & intf,
	- UInt nb_degree_of_freedom,
	- GhostType ghost_type,
	- const Array<UInt> & filter_elements) const;
	+ void
	+ integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	+ UInt nb_degree_of_freedom, GhostType ghost_type,
	+ const Array<UInt> & filter_elements) const;
	/// return a vector with quadrature points natural coordinates
	template <ElementType type>
	const Matrix<Real> & getIntegrationPoints(GhostType ghost_type) const;

	/// return the number of quadrature points for a given element type
	template <ElementType type>
	- inline UInt
	- getNbIntegrationPoints(GhostType ghost_type = _not_ghost) const;
	+ inline UInt getNbIntegrationPoints(GhostType ghost_type = _not_ghost) const;

	/// compute the vector of quadrature points natural coordinates
	template <ElementType type>
	void computeQuadraturePoints(GhostType ghost_type);

	/// check that the jacobians are not negative
	- template <ElementType type>
	- void checkJacobians(GhostType ghost_type) const;
	+ template <ElementType type> void checkJacobians(GhostType ghost_type) const;

	public:
	/// compute the jacobians on quad points for a given element
	template <ElementType type>
	void computeJacobianOnQuadPointsByElement(const Matrix<Real> & node_coords,
	Vector<Real> & jacobians);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	inline void integrate(Real * f, Real * jac, Real * inte,
	UInt nb_degree_of_freedom,
	UInt nb_quadrature_points) const;

	private:
	ElementTypeMap<Matrix<Real>> quadrature_points;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "integrator_gauss_igfem_inline_impl.hh"

	} // namespace akantu

	#endif /AKANTU_INTEGRATOR_IGFEM_HH_ /
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	diff --git a/extra_packages/igfem/src/integrator_gauss_igfem_inline_impl.hh b/extra_packages/igfem/src/integrator_gauss_igfem_inline_impl.hh
	index 376ccba79..6d182f7e6 100644
	--- a/extra_packages/igfem/src/integrator_gauss_igfem_inline_impl.hh
	+++ b/extra_packages/igfem/src/integrator_gauss_igfem_inline_impl.hh
	@@ -1,451 +1,449 @@
	/**
	* @file integrator_gauss_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Inline functions of gauss integrator for the case of IGFEM
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "fe_engine.hh"
	#if defined(AKANTU_DEBUG_TOOLS)
	#include "aka_debug_tools.hh"
	#endif

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define INIT_INTEGRATOR(type) \
	computeQuadraturePoints<type>(ghost_type); \
	precomputeJacobiansOnQuadraturePoints<type>(nodes, ghost_type); \
	checkJacobians<type>(ghost_type);

	template <class IOF>
	-inline void
	-IntegratorGauss<_ek_igfem, IOF>::initIntegrator(const Array<Real> & nodes,
	- ElementType type,
	- GhostType ghost_type) {
	+inline void IntegratorGauss<_ek_igfem, IOF>::initIntegrator(
	+ const Array<Real> & nodes, ElementType type, GhostType ghost_type) {
	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(INIT_INTEGRATOR);
	}

	#undef INIT_INTEGRATOR

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	-inline UInt IntegratorGauss<_ek_igfem, IOF>::getNbIntegrationPoints(
	- GhostType) const {
	+inline UInt
	+IntegratorGauss<_ek_igfem, IOF>::getNbIntegrationPoints(GhostType) const {
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	UInt nb_quad_points_sub_1 =
	GaussIntegrationElement<sub_type_1>::getNbQuadraturePoints();
	UInt nb_quad_points_sub_2 =
	GaussIntegrationElement<sub_type_2>::getNbQuadraturePoints();
	return (nb_quad_points_sub_1 + nb_quad_points_sub_2);
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline void IntegratorGauss<_ek_igfem, IOF>::integrateOnElement(
	const Array<Real> & f, Real * intf, UInt nb_degree_of_freedom,
	const UInt elem, GhostType ghost_type) const {

	Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points = getNbIntegrationPoints<type>();
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f do not have the good number of component.");

	Real * f_val = f.storage() + elem * f.getNbComponent();
	Real * jac_val = jac_loc.storage() + elem * nb_quadrature_points;

	integrate(f_val, jac_val, intf, nb_degree_of_freedom, nb_quadrature_points);
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline Real IntegratorGauss<_ek_igfem, IOF>::integrate(
	const Vector<Real> & in_f, UInt index, GhostType ghost_type) const {
	const Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points = getNbIntegrationPoints<type>();
	AKANTU_DEBUG_ASSERT(in_f.size() == nb_quadrature_points,
	"The vector f do not have nb_quadrature_points entries.");

	Real * jac_val = jac_loc.storage() + index * nb_quadrature_points;
	Real intf;

	integrate(in_f.storage(), jac_val, &intf, 1, nb_quadrature_points);

	return intf;
	return 0.;
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	inline void
	IntegratorGauss<_ek_igfem, IOF>::integrate(Real * f, Real * jac, Real * inte,
	UInt nb_degree_of_freedom,
	UInt nb_quadrature_points) const {
	memset(inte, 0, nb_degree_of_freedom * sizeof(Real));

	Real * cjac = jac;
	for (UInt q = 0; q < nb_quadrature_points; ++q) {
	for (UInt dof = 0; dof < nb_degree_of_freedom; ++dof) {
	inte[dof] += f *cjac;
	++f;
	}
	++cjac;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline const Matrix<Real> &
	IntegratorGauss<_ek_igfem, IOF>::getIntegrationPoints(
	GhostType ghost_type) const {
	AKANTU_DEBUG_ASSERT(
	quadrature_points.exists(type, ghost_type),
	"Quadrature points for type "
	<< quadrature_points.printType(type, ghost_type)
	<< " have not been initialized."
	<< " Did you use 'computeQuadraturePoints' function ?");
	return quadrature_points(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	-inline void IntegratorGauss<_ek_igfem, IOF>::computeQuadraturePoints(
	- GhostType ghost_type) {
	+inline void
	+IntegratorGauss<_ek_igfem, IOF>::computeQuadraturePoints(GhostType ghost_type) {
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;

	/// store the quadrature points on the two subelements
	Matrix<Real> & quads_sub_1 = quadrature_points(sub_type_1, ghost_type);
	Matrix<Real> & quads_sub_2 = quadrature_points(sub_type_2, ghost_type);
	quads_sub_1 = GaussIntegrationElement<sub_type_1>::getQuadraturePoints();
	quads_sub_2 = GaussIntegrationElement<sub_type_2>::getQuadraturePoints();

	/// store all quad points for the current type
	UInt nb_quad_points_sub_1 =
	GaussIntegrationElement<sub_type_1>::getNbQuadraturePoints();
	UInt nb_quad_points_sub_2 =
	GaussIntegrationElement<sub_type_2>::getNbQuadraturePoints();

	UInt spatial_dimension = mesh.getSpatialDimension();

	Matrix<Real> & quads = quadrature_points(type, ghost_type);
	quads = Matrix<Real>(spatial_dimension,
	nb_quad_points_sub_1 + nb_quad_points_sub_2);

	Matrix<Real> quads_1(quads.storage(), quads.rows(), nb_quad_points_sub_1);
	quads_1 = quads_sub_1;

	Matrix<Real> quads_2(quads.storage() + quads.rows() * nb_quad_points_sub_1,
	quads.rows(), nb_quad_points_sub_2);

	quads_2 = quads_sub_2;
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline void
	IntegratorGauss<_ek_igfem, IOF>::computeJacobianOnQuadPointsByElement(
	const Matrix<Real> & node_coords, Vector<Real> & jacobians) {

	/// optimize: get the matrix from the ElementTypeMap
	Matrix<Real> quad = GaussIntegrationElement<type>::getQuadraturePoints();
	// jacobian
	ElementClass<type>::computeJacobian(quad, node_coords, jacobians);
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	-inline IntegratorGauss<_ek_igfem, IOF>::IntegratorGauss(
	- const Mesh & mesh, const ID & id)
	+inline IntegratorGauss<_ek_igfem, IOF>::IntegratorGauss(const Mesh & mesh,
	+ const ID & id)
	: Integrator(mesh, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	-inline void IntegratorGauss<_ek_igfem, IOF>::checkJacobians(
	- GhostType ghost_type) const {
	+inline void
	+IntegratorGauss<_ek_igfem, IOF>::checkJacobians(GhostType ghost_type) const {
	AKANTU_DEBUG_IN();
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	UInt nb_quad_points_sub_1 =
	GaussIntegrationElement<sub_type_1>::getNbQuadraturePoints();
	UInt nb_quad_points_sub_2 =
	GaussIntegrationElement<sub_type_2>::getNbQuadraturePoints();
	UInt nb_quadrature_points = nb_quad_points_sub_1 + nb_quad_points_sub_2;

	UInt nb_element;

	nb_element = mesh.getConnectivity(type, ghost_type).getSize();

	Real * jacobians_val = jacobians(type, ghost_type).storage();

	for (UInt i = 0; i < nb_element * nb_quadrature_points;
	++i, ++jacobians_val) {
	if (*jacobians_val < 0)
	AKANTU_ERROR(
	"Negative jacobian computed,"
	<< " possible problem in the element node ordering (Quadrature Point "
	<< i % nb_quadrature_points << ":" << i / nb_quadrature_points << ":"
	<< type << ":" << ghost_type << ")");
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline void
	IntegratorGauss<_ek_igfem, IOF>::precomputeJacobiansOnQuadraturePoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	/// get the number of nodes for the subelements and the parent element
	UInt nb_nodes_sub_1 =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_2 =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	UInt nb_quadrature_points_sub_1 =
	GaussIntegrationElement<sub_type_1>::getNbQuadraturePoints();
	UInt nb_quadrature_points_sub_2 =
	GaussIntegrationElement<sub_type_2>::getNbQuadraturePoints();
	UInt nb_quadrature_points =
	nb_quadrature_points_sub_1 + nb_quadrature_points_sub_2;

	UInt nb_element = mesh.getNbElement(type, ghost_type);

	Array<Real> * jacobians_tmp;
	if (!jacobians.exists(type, ghost_type))
	jacobians_tmp = &jacobians.alloc(nb_element * nb_quadrature_points, 1, type,
	ghost_type);
	else {
	jacobians_tmp = &jacobians(type, ghost_type);
	jacobians_tmp->resize(nb_element * nb_quadrature_points);
	}

	Array<Real>::vector_iterator jacobians_it =
	jacobians_tmp->begin_reinterpret(nb_quadrature_points, nb_element);

	Vector<Real> weights_sub_1 =
	GaussIntegrationElement<sub_type_1>::getWeights();
	Vector<Real> weights_sub_2 =
	GaussIntegrationElement<sub_type_2>::getWeights();

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

	Array<Real>::const_matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element; ++elem, ++jacobians_it, ++x_it) {
	const Matrix<Real> & X = *x_it;

	Matrix<Real> sub_1_coords(spatial_dimension, nb_nodes_sub_1);
	Matrix<Real> sub_2_coords(spatial_dimension, nb_nodes_sub_2);

	ElementClass<type>::getSubElementCoords(X, sub_1_coords, 0);
	ElementClass<type>::getSubElementCoords(X, sub_2_coords, 1);

	Vector<Real> & J = *jacobians_it;
	/// initialize vectors to store the jacobians for each subelement
	Vector<Real> J_sub_1(nb_quadrature_points_sub_1);
	Vector<Real> J_sub_2(nb_quadrature_points_sub_2);
	computeJacobianOnQuadPointsByElement<sub_type_1>(sub_1_coords, J_sub_1);
	computeJacobianOnQuadPointsByElement<sub_type_2>(sub_2_coords, J_sub_2);
	J_sub_1 *= weights_sub_1;
	J_sub_2 *= weights_sub_2;

	/// copy results into the jacobian vector for this element
	for (UInt i = 0; i < nb_quadrature_points_sub_1; ++i) {
	J(i) = J_sub_1(i);
	}

	for (UInt i = 0; i < nb_quadrature_points_sub_2; ++i) {
	J(i + nb_quadrature_points_sub_1) = J_sub_2(i);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline void IntegratorGauss<_ek_igfem, IOF>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	const Matrix<Real> & quads = quadrature_points(type, ghost_type);

	UInt nb_points = quads.cols();

	const Array<Real> & jac_loc = jacobians(type, ghost_type);

	Array<Real>::const_matrix_iterator J_it;
	Array<Real>::matrix_iterator inte_it;
	Array<Real>::const_matrix_iterator f_it;

	UInt nb_element;
	Array<Real> * filtered_J = NULL;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.getSize();
	filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);
	const Array<Real> & cfiltered_J = *filtered_J; // \todo temporary patch
	J_it = cfiltered_J.begin_reinterpret(nb_points, 1, nb_element);
	} else {
	nb_element = mesh.getNbElement(type, ghost_type);
	J_it = jac_loc.begin_reinterpret(nb_points, 1, nb_element);
	}

	intf.resize(nb_element);

	f_it = in_f.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);
	inte_it = intf.begin_reinterpret(nb_degree_of_freedom, 1, nb_element);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Matrix<Real> & f = *f_it;
	const Matrix<Real> & J = *J_it;
	Matrix<Real> & inte_f = *inte_it;

	inte_f.mul<false, false>(f, J);
	}

	delete filtered_J;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline Real IntegratorGauss<_ek_igfem, IOF>::integrate(
	const Array<Real> & in_f, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	Array<Real> intfv(0, 1);
	integrate<type>(in_f, intfv, 1, ghost_type, filter_elements);

	UInt nb_values = intfv.getSize();
	if (nb_values == 0)
	return 0.;

	UInt nb_values_to_sum = nb_values >> 1;

	std::sort(intfv.begin(), intfv.end());

	// as long as the half is not empty
	while (nb_values_to_sum) {
	UInt remaining = (nb_values - 2 * nb_values_to_sum);
	if (remaining)
	intfv(nb_values - 2) += intfv(nb_values - 1);

	// sum to consecutive values and store the sum in the first half
	for (UInt i = 0; i < nb_values_to_sum; ++i) {
	intfv(i) = intfv(2 * i) + intfv(2 * i + 1);
	}

	nb_values = nb_values_to_sum;
	nb_values_to_sum >>= 1;
	}

	AKANTU_DEBUG_OUT();
	return intfv(0);
	}

	/* -------------------------------------------------------------------------- */
	template <class IOF>
	template <ElementType type>
	inline void IntegratorGauss<_ek_igfem, IOF>::integrateOnIntegrationPoints(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	UInt nb_element;
	const Matrix<Real> & quads = quadrature_points(type, ghost_type);

	UInt nb_points = quads.cols();

	const Array<Real> & jac_loc = jacobians(type, ghost_type);

	Array<Real>::const_scalar_iterator J_it;
	Array<Real>::vector_iterator inte_it;
	Array<Real>::const_vector_iterator f_it;

	Array<Real> * filtered_J = NULL;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.getSize();
	filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);
	J_it = filtered_J->begin();
	} else {
	nb_element = mesh.getNbElement(type, ghost_type);
	J_it = jac_loc.begin();
	}

	intf.resize(nb_element * nb_points);

	f_it = in_f.begin(nb_degree_of_freedom);
	inte_it = intf.begin(nb_degree_of_freedom);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Real & J = *J_it;
	const Vector<Real> & f = *f_it;
	Vector<Real> & inte_f = *inte_it;

	inte_f = f;
	inte_f *= J;
	}

	delete filtered_J;

	AKANTU_DEBUG_OUT();
	}
	diff --git a/extra_packages/igfem/src/material_igfem/material_igfem_elastic.cc b/extra_packages/igfem/src/material_igfem/material_igfem_elastic.cc
	index 33435cecb..16413e09b 100644
	--- a/extra_packages/igfem/src/material_igfem/material_igfem_elastic.cc
	+++ b/extra_packages/igfem/src/material_igfem/material_igfem_elastic.cc
	@@ -1,241 +1,240 @@
	/**
	* @file material_igfem_elastic.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Specializaton of material class for the igfem elastic material
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/
	/* -------------------------------------------------------------------------- */
	#include "material_igfem_elastic.hh"
	#include "material_elastic.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialIGFEMElastic<dim>::MaterialIGFEMElastic(SolidMechanicsModel & model,
	const ID & id)
	: Material(model, id), Parent(model, id), lambda("lambda", *this),
	mu("mu", this), kpa("kappa", this) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialIGFEMElastic<dim>::initialize() {
	this->lambda.initialize(1);
	this->mu.initialize(1);
	this->kpa.initialize(1);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialIGFEMElastic<dim>::initMaterial() {
	AKANTU_DEBUG_IN();

	Parent::initMaterial();

	/// insert the sub_material names into the map
	this->sub_material_names[0] = this->name_sub_mat_1;
	this->sub_material_names[1] = this->name_sub_mat_2;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::updateElasticInternals(
	const Array<Element> & element_list) {

	/// compute the Lamé constants for both sub-materials
	Vector<Real> lambda_per_sub_mat(this->nb_sub_materials);
	Vector<Real> mu_per_sub_mat(this->nb_sub_materials);
	Vector<Real> kpa_per_sub_mat(this->nb_sub_materials);
	for (UInt i = 0; i < this->nb_sub_materials; ++i) {
	ID mat_name = this->sub_material_names[i];
	const MaterialElastic<spatial_dimension> & mat =
	dynamic_cast<MaterialElastic<spatial_dimension> &>(
	this->model->getMaterial(mat_name));
	lambda_per_sub_mat(i) = mat.getLambda();
	mu_per_sub_mat(i) = mat.getMu();
	kpa_per_sub_mat(i) = mat.getKappa();
	}

	for (ghost_type_t::iterator g = ghost_type_t::begin();
	g != ghost_type_t::end(); ++g) {
	GhostType ghost_type = *g;
	/// loop over all types in the material
	typedef ElementTypeMapArray<UInt>::type_iterator iterator;
	iterator it = this->element_filter.firstType(spatial_dimension, ghost_type,
	_ek_igfem);
	iterator last_type =
	this->element_filter.lastType(spatial_dimension, ghost_type, _ek_igfem);
	/// loop over all types in the filter
	for (; it != last_type; ++it) {
	ElementType el_type = *it;
	if (el_type == _igfem_triangle_4)
	this->template setSubMaterial<_igfem_triangle_4>(element_list,
	ghost_type);
	else if (el_type == _igfem_triangle_5)
	this->template setSubMaterial<_igfem_triangle_5>(element_list,
	ghost_type);
	else
	AKANTU_ERROR("There is currently no other IGFEM type implemented");

	UInt nb_element = this->element_filter(el_type, ghost_type).getSize();
	UInt nb_quads = this->fem->getNbIntegrationPoints(el_type);
	/// get pointer to internals for given type
	Real * lambda_ptr = this->lambda(el_type, ghost_type).storage();
	Real * mu_ptr = this->mu(el_type, ghost_type).storage();
	Real * kpa_ptr = this->kpa(el_type, ghost_type).storage();
	UInt * sub_mat_ptr = this->sub_material(el_type, ghost_type).storage();
	for (UInt q = 0; q < nb_element * nb_quads;
	++q, ++lambda_ptr, ++mu_ptr, ++kpa_ptr, ++sub_mat_ptr) {
	UInt index = *sub_mat_ptr;
	*lambda_ptr = lambda_per_sub_mat(index);
	*mu_ptr = mu_per_sub_mat(index);
	*kpa_ptr = kpa_per_sub_mat(index);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Parent::computeStress(el_type, ghost_type);

	if (!this->finite_deformation) {
	/// get pointer to internals
	Real * lambda_ptr = this->lambda(el_type, ghost_type).storage();
	Real * mu_ptr = this->mu(el_type, ghost_type).storage();
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	this->computeStressOnQuad(grad_u, sigma, lambda_ptr, mu_ptr);
	++lambda_ptr;
	++mu_ptr;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	} else {
	AKANTU_DEBUG_TO_IMPLEMENT();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::computeTangentModuli(
	- __attribute__((unused)) ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ __attribute__((unused)) ElementType el_type, Array<Real> & tangent_matrix,
	__attribute__((unused)) GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	/// get pointer to internals
	Real * lambda_ptr = this->lambda(el_type, ghost_type).storage();
	Real * mu_ptr = this->mu(el_type, ghost_type).storage();
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	this->computeTangentModuliOnQuad(tangent, lambda_ptr, mu_ptr);
	++lambda_ptr;
	++mu_ptr;
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::computePotentialEnergy(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// MaterialThermal<spatial_dimension>::computePotentialEnergy(el_type,
	// ghost_type);

	// if(ghost_type != _not_ghost) return;
	// Array<Real>::scalar_iterator epot = this->potential_energy(el_type,
	// ghost_type).begin();

	// if (!this->finite_deformation) {
	// MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	// this->computePotentialEnergyOnQuad(grad_u, sigma, *epot);
	// ++epot;

	// MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	// } else {
	// Matrix<Real> E(spatial_dimension, spatial_dimension);

	// MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	// this->template gradUToGreenStrain<spatial_dimension>(grad_u, E);

	// this->computePotentialEnergyOnQuad(E, sigma, *epot);
	// ++epot;

	// MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	// }

	AKANTU_DEBUG_TO_IMPLEMENT();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::computePotentialEnergyByElement(
	ElementType type, UInt index, Vector<Real> & epot_on_quad_points) {
	// Array<Real>::matrix_iterator gradu_it =
	// this->gradu(type).begin(spatial_dimension,
	// spatial_dimension);
	// Array<Real>::matrix_iterator gradu_end =
	// this->gradu(type).begin(spatial_dimension,
	// spatial_dimension);
	// Array<Real>::matrix_iterator stress_it =
	// this->stress(type).begin(spatial_dimension,
	// spatial_dimension);

	// if (this->finite_deformation)
	// stress_it = this->piola_kirchhoff_2(type).begin(spatial_dimension,
	// spatial_dimension);

	// UInt nb_quadrature_points =
	// this->model->getFEEngine().getNbQuadraturePoints(type);

	// gradu_it += index*nb_quadrature_points;
	// gradu_end += (index+1)*nb_quadrature_points;
	// stress_it += index*nb_quadrature_points;

	// Real * epot_quad = epot_on_quad_points.storage();

	// Matrix<Real> grad_u(spatial_dimension, spatial_dimension);

	// for(;gradu_it != gradu_end; ++gradu_it, ++stress_it, ++epot_quad) {

	// if (this->finite_deformation)
	// this->template gradUToGreenStrain<spatial_dimension>(*gradu_it,
	// grad_u);
	// else
	// grad_u.copy(*gradu_it);

	// this->computePotentialEnergyOnQuad(grad_u, stress_it, epot_quad);
	// }
	AKANTU_DEBUG_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialIGFEMElastic<spatial_dimension>::onElementsAdded(
	const Array<Element> & element_list, const NewElementsEvent & event) {

	Parent::onElementsAdded(element_list, event);
	updateElasticInternals(element_list);
	};

	INSTANTIATE_MATERIAL(MaterialIGFEMElastic);

	} // namespace akantu
	diff --git a/extra_packages/igfem/src/material_igfem/material_igfem_saw_tooth_damage.hh b/extra_packages/igfem/src/material_igfem/material_igfem_saw_tooth_damage.hh
	index 04ecc8063..479abdbd9 100644
	--- a/extra_packages/igfem/src/material_igfem/material_igfem_saw_tooth_damage.hh
	+++ b/extra_packages/igfem/src/material_igfem/material_igfem_saw_tooth_damage.hh
	@@ -1,138 +1,138 @@
	/**
	* @file material_igfem_saw_tooth_damage.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief Linear saw-tooth softening material model for IGFEM elements
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_damage.hh"
	#include "material_igfem_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_IGFEM_SAW_TOOTH_DAMAGE_HH_
	#define AKANTU_MATERIAL_IGFEM_SAW_TOOTH_DAMAGE_HH_

	namespace akantu {

	template <UInt spatial_dimension>
	class MaterialIGFEMSawToothDamage
	: public MaterialDamage<spatial_dimension, MaterialIGFEMElastic> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	private:
	typedef MaterialDamage<spatial_dimension, MaterialIGFEMElastic> Parent;

	public:
	typedef std::pair<Element, Element> ElementPair;
	MaterialIGFEMSawToothDamage(SolidMechanicsModel & model, const ID & id = "");
	MaterialIGFEMSawToothDamage(SolidMechanicsModel & model, UInt dim,
	const Mesh & mesh, FEEngine & fe_engine,
	const ID & id = "");

	virtual ~MaterialIGFEMSawToothDamage() {}

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	virtual void initMaterial();

	/// virtual void updateInternalParameters();

	virtual void computeAllStresses(GhostType ghost_type = _not_ghost);

	/// update internal field damage
	virtual UInt updateDamage();

	- UInt updateDamage(UInt quad_index, const Real eq_stress,
	- ElementType el_type, GhostType ghost_type);
	+ UInt updateDamage(UInt quad_index, const Real eq_stress, ElementType el_type,
	+ GhostType ghost_type);

	/// update energies after damage has been updated
	// virtual void updateEnergiesAfterDamage(ElementType el_type, GhostType
	// ghost_typ);

	virtual void onBeginningSolveStep(const AnalysisMethod & method){};

	virtual void onEndSolveStep(const AnalysisMethod & method){};

	protected:
	/// constitutive law for all element of a type
	virtual void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// compute the equivalent stress on each Gauss point (i.e. the max prinicpal
	/// stress) and normalize it by the tensile strength
	virtual void
	computeNormalizedEquivalentStress(const Array<Real> & grad_u,
	ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// find max normalized equivalent stress
	void findMaxNormalizedEquivalentStress(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	inline void computeDamageAndStressOnQuad(Matrix<Real> & sigma, Real & dam);

	protected:
	/* ------------------------------------------------------------------------ */
	/* MeshEventHandler inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	virtual void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get max normalized equivalent stress
	AKANTU_GET_MACRO(NormMaxEquivalentStress, norm_max_equivalent_stress, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// resistance to damage
	IGFEMInternalField<Real> Sc;

	/// internal field to store equivalent stress on each Gauss point
	IGFEMInternalField<Real> equivalent_stress;

	/// damage increment
	Real prescribed_dam;

	/// maximum equivalent stress
	Real norm_max_equivalent_stress;

	/// deviation from max stress at which Gauss point will still get damaged
	Real dam_tolerance;

	/// define damage threshold at which damage will be set to 1
	Real dam_threshold;

	/// maximum damage value
	Real max_damage;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "material_igfem_saw_tooth_damage_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_IGFEM_SAW_TOOTH_DAMAGE_HH_ */
	diff --git a/extra_packages/igfem/src/non_local_manager_igfem.cc b/extra_packages/igfem/src/non_local_manager_igfem.cc
	index c530c2e90..3ad164423 100644
	--- a/extra_packages/igfem/src/non_local_manager_igfem.cc
	+++ b/extra_packages/igfem/src/non_local_manager_igfem.cc
	@@ -1,306 +1,306 @@
	/**
	* @file non_local_manager_igfem.cc
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @date Mon Sep 21 15:32:10 2015
	*
	* @brief Implementation of non-local manager igfem
	*
	*
	* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_DAMAGE_NON_LOCAL
	#include "non_local_manager_igfem.hh"
	#include "material_non_local.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLocalManagerIGFEM::NonLocalManagerIGFEM(SolidMechanicsModelIGFEM & model,
	const ID & id)
	: NonLocalManager(model, id) {

	Mesh & mesh = this->model.getMesh();

	/// initialize the element type map array
	/// it will be resized to nb_quad * nb_element during the computation of
	/// coords
	mesh.initElementTypeMapArray(quad_positions, spatial_dimension,
	spatial_dimension, false, _ek_igfem, true);
	}

	/* -------------------------------------------------------------------------- */
	-NonLocalManagerIGFEM::~NonLocalManagerIGFEM() =default;
	+NonLocalManagerIGFEM::~NonLocalManagerIGFEM() = default;

	/* -------------------------------------------------------------------------- */
	void NonLocalManagerIGFEM::init() {

	/// store the number of current ghost elements for each type in the mesh
	ElementTypeMap<UInt> nb_ghost_protected;
	Mesh & mesh = this->model.getMesh();
	for (UInt k = _ek_regular; k <= _ek_igfem; ++k) {
	ElementKind el_kind = (ElementKind)k;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, _ghost, el_kind);
	Mesh::type_iterator last_type =
	mesh.lastType(spatial_dimension, _ghost, el_kind);
	for (; it != last_type; ++it)
	nb_ghost_protected(mesh.getNbElement(it, _ghost), it, _ghost);
	}

	/// exchange the missing ghosts for the non-local neighborhoods
	this->createNeighborhoodSynchronizers();

	/// insert the ghost quadrature points of the non-local materials into the
	/// non-local neighborhoods
	for (UInt m = 0; m < this->non_local_materials.size(); ++m) {
	switch (spatial_dimension) {
	case 1:
	dynamic_cast<MaterialNonLocal<1> &>(*(this->non_local_materials[m]))
	.insertQuadsInNeighborhoods(_ghost);
	break;
	case 2:
	dynamic_cast<MaterialNonLocal<2> &>(*(this->non_local_materials[m]))
	.insertQuadsInNeighborhoods(_ghost);
	break;
	case 3:
	dynamic_cast<MaterialNonLocal<3> &>(*(this->non_local_materials[m]))
	.insertQuadsInNeighborhoods(_ghost);
	break;
	}
	}

	FEEngine & fee_regular = this->model.getFEEngine();
	FEEngine & fee_igfem = this->model.getFEEngine("IGFEMFEEngine");

	this->updatePairLists();
	/// cleanup the unneccessary ghost elements
	this->cleanupExtraGhostElements(nb_ghost_protected);
	this->initElementTypeMap(1, volumes, fee_regular, _ek_regular);
	this->initElementTypeMap(1, volumes, fee_igfem, _ek_igfem);
	this->setJacobians(fee_regular, _ek_regular);
	this->setJacobians(fee_igfem, _ek_igfem);
	this->initNonLocalVariables();
	this->computeWeights();
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManagerIGFEM::computeAllNonLocalStresses() {

	/// update the flattened version of the internals
	std::map<ID, NonLocalVariable *>::iterator non_local_variable_it =
	non_local_variables.begin();
	std::map<ID, NonLocalVariable *>::iterator non_local_variable_end =
	non_local_variables.end();

	for (; non_local_variable_it != non_local_variable_end;
	++non_local_variable_it) {
	non_local_variable_it->second->local.zero();
	non_local_variable_it->second->non_local.zero();
	for (UInt gt = _not_ghost; gt <= _ghost; ++gt) {
	GhostType ghost_type = (GhostType)gt;
	this->flattenInternal(non_local_variable_it->second->local, ghost_type,
	_ek_regular);
	this->flattenInternal(non_local_variable_it->second->local, ghost_type,
	_ek_igfem);
	}
	}

	this->volumes.zero();
	/// loop over all the neighborhoods and compute intiate the
	/// exchange of the non-local_variables
	std::set<ID>::const_iterator global_neighborhood_it =
	global_neighborhoods.begin();
	NeighborhoodMap::iterator it;
	for (; global_neighborhood_it != global_neighborhoods.end();
	++global_neighborhood_it) {
	it = neighborhoods.find(*global_neighborhood_it);
	if (it != neighborhoods.end())
	it->second->getSynchronizerRegistry().asynchronousSynchronize(
	SynchronizationTag::_mnl_for_average);
	else
	dummy_synchronizers[*global_neighborhood_it]->asynchronousSynchronize(
	dummy_accessor, SynchronizationTag::_mnl_for_average);
	}

	this->averageInternals(_not_ghost);

	AKANTU_DEBUG_INFO("Wait distant non local stresses");

	/// loop over all the neighborhoods and block until all non-local
	/// variables have been exchanged
	global_neighborhood_it = global_neighborhoods.begin();
	it = neighborhoods.begin();
	for (; global_neighborhood_it != global_neighborhoods.end();
	++global_neighborhood_it) {
	it = neighborhoods.find(*global_neighborhood_it);
	if (it != neighborhoods.end())
	it->second->getSynchronizerRegistry().waitEndSynchronize(
	SynchronizationTag::_mnl_for_average);
	else
	dummy_synchronizers[*global_neighborhood_it]->waitEndSynchronize(
	dummy_accessor, SynchronizationTag::_mnl_for_average);
	}

	this->averageInternals(_ghost);

	/// copy the results in the materials
	this->distributeInternals(_ek_regular);
	/// loop over all the materials and update the weights
	for (UInt m = 0; m < this->non_local_materials.size(); ++m) {
	switch (spatial_dimension) {
	case 1:
	dynamic_cast<MaterialNonLocal<1> &>(*(this->non_local_materials[m]))
	.computeNonLocalStresses(_not_ghost);
	break;
	case 2:
	dynamic_cast<MaterialNonLocal<2> &>(*(this->non_local_materials[m]))
	.computeNonLocalStresses(_not_ghost);
	break;
	case 3:
	dynamic_cast<MaterialNonLocal<3> &>(*(this->non_local_materials[m]))
	.computeNonLocalStresses(_not_ghost);
	break;
	}
	}

	++this->compute_stress_calls;
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManagerIGFEM::cleanupExtraGhostElements(
	ElementTypeMap<UInt> & nb_ghost_protected) {

	typedef std::set<Element> ElementSet;
	ElementSet relevant_ghost_elements;
	ElementSet to_keep_per_neighborhood;
	/// loop over all the neighborhoods and get their protected ghosts
	NeighborhoodMap::iterator neighborhood_it = neighborhoods.begin();
	NeighborhoodMap::iterator neighborhood_end = neighborhoods.end();
	for (; neighborhood_it != neighborhood_end; ++neighborhood_it) {
	neighborhood_it->second->cleanupExtraGhostElements(
	to_keep_per_neighborhood);
	ElementSet::const_iterator it = to_keep_per_neighborhood.begin();
	for (; it != to_keep_per_neighborhood.end(); ++it)
	relevant_ghost_elements.insert(*it);
	to_keep_per_neighborhood.zero();
	}

	/// remove all unneccessary ghosts from the mesh
	/// Create list of element to remove and new numbering for element to keep
	Mesh & mesh = this->model.getMesh();
	ElementSet ghost_to_erase;
	RemovedElementsEvent remove_elem(mesh);
	Element element;

	for (UInt k = _ek_regular; k < _ek_igfem; ++k) {
	ElementKind el_kind = (ElementKind)k;
	element.kind = _ek_igfem;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, _ghost, el_kind);
	Mesh::type_iterator last_type =
	mesh.lastType(spatial_dimension, _ghost, el_kind);

	element.ghost_type = _ghost;

	for (; it != last_type; ++it) {
	element.type = *it;
	UInt nb_ghost_elem = mesh.getNbElement(*it, _ghost);
	UInt nb_ghost_elem_protected = 0;
	try {
	nb_ghost_elem_protected = nb_ghost_protected(*it, _ghost);
	} catch (...) {
	}

	if (!remove_elem.getNewNumbering().exists(*it, _ghost))
	remove_elem.getNewNumbering().alloc(nb_ghost_elem, 1, *it, _ghost);
	else
	remove_elem.getNewNumbering(*it, _ghost).resize(nb_ghost_elem);
	Array<UInt> & new_numbering = remove_elem.getNewNumbering(*it, _ghost);
	for (UInt g = 0; g < nb_ghost_elem; ++g) {
	element.element = g;
	if (element.element >= nb_ghost_elem_protected &&
	relevant_ghost_elements.find(element) ==
	relevant_ghost_elements.end()) {
	remove_elem.getList().push_back(element);
	new_numbering(element.element) = UInt(-1);
	}
	}
	/// renumber remaining ghosts
	UInt ng = 0;
	for (UInt g = 0; g < nb_ghost_elem; ++g) {
	if (new_numbering(g) != UInt(-1)) {
	new_numbering(g) = ng;
	++ng;
	}
	}
	}
	}

	for (UInt k = _ek_regular; k < _ek_igfem; ++k) {
	ElementKind el_kind = (ElementKind)k;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, _ghost, el_kind);
	Mesh::type_iterator last_type =
	mesh.lastType(spatial_dimension, _ghost, el_kind);
	for (; it != last_type; ++it) {
	UInt nb_elem = mesh.getNbElement(*it, _not_ghost);
	if (!remove_elem.getNewNumbering().exists(*it, _not_ghost))
	remove_elem.getNewNumbering().alloc(nb_elem, 1, *it, _not_ghost);
	Array<UInt> & new_numbering =
	remove_elem.getNewNumbering(*it, _not_ghost);
	for (UInt e = 0; e < nb_elem; ++e) {
	new_numbering(e) = e;
	}
	}
	}

	mesh.sendEvent(remove_elem);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManagerIGFEM::onElementsAdded(__attribute__((unused))
	const Array<Element> & element_list,
	__attribute__((unused))
	const NewElementsEvent & event) {

	FEEngine & fee = this->model.getFEEngine("IGFEMFEEngine");
	this->resizeElementTypeMap(1, volumes, fee, _ek_igfem);
	this->resizeElementTypeMap(spatial_dimension, quad_positions, fee, _ek_igfem);

	NonLocalManager::onElementsAdded(element_list, event);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManagerIGFEM::onElementsRemoved(
	const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	__attribute__((unused)) const RemovedElementsEvent & event) {

	FEEngine & fee = this->model.getFEEngine("IGFEMFEEngine");

	this->removeIntegrationPointsFromMap(event.getNewNumbering(),
	spatial_dimension, quad_positions, fee,
	_ek_igfem);
	this->removeIntegrationPointsFromMap(event.getNewNumbering(), 1, volumes, fee,
	_ek_igfem);

	NonLocalManager::onElementsRemoved(element_list, new_numbering, event);
	}

	} // namespace akantu

	#endif /* AKANTU_DAMAGE_NON_LOCAL */
	diff --git a/extra_packages/igfem/src/shape_igfem.cc b/extra_packages/igfem/src/shape_igfem.cc
	index f75a5407e..38fd32a18 100644
	--- a/extra_packages/igfem/src/shape_igfem.cc
	+++ b/extra_packages/igfem/src/shape_igfem.cc
	@@ -1,94 +1,93 @@
	/**
	* @file shape_igfem_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief ShapeIGFEM inline implementation
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	//#include "mesh.hh"
	#include "shape_igfem.hh"
	/* -------------------------------------------------------------------------- */

	#if defined(AKANTU_IGFEM)

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ShapeLagrange<_ek_igfem>::ShapeLagrange(const Mesh & mesh, const ID & id)
	- : ShapeFunctions(mesh, id),
	- shapes("shapes_generic", id),
	+ : ShapeFunctions(mesh, id), shapes("shapes_generic", id),
	shapes_derivatives("shapes_derivatives_generic", id),
	igfem_integration_points("igfem_integration_points", id),
	shapes_at_enrichments("shapes_at_enrichments", id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/-------------------------------------------------------------------------- /
	void ShapeLagrange<_ek_igfem>::extractValuesAtStandardNodes(
	const Array<Real> & nodal_values, Array<Real> & extracted_values,
	GhostType ghost_type) const {

	AKANTU_DEBUG_ASSERT(nodal_values.getNbComponent() ==
	extracted_values.getNbComponent(),
	"The arrays are not of the same size!!!!!");
	extracted_values.zero();
	UInt spatial_dimension = mesh.getSpatialDimension();
	Mesh::type_iterator it =
	mesh.firstType(spatial_dimension, ghost_type, _ek_igfem);
	Mesh::type_iterator end =
	mesh.lastType(spatial_dimension, ghost_type, _ek_igfem);
	for (; it != end; ++it) {
	ElementType type = *it;
	UInt nb_elements = mesh.getNbElement(type, ghost_type);
	UInt nb_parent_nodes = 0;
	UInt nb_nodes_per_element = 0;
	#define GET_NODES_INFO(type) \
	const ElementType parent_type = \
	ElementClassProperty<type>::parent_element_type; \
	nb_parent_nodes = \
	ElementClass<parent_type>::getNbNodesPerInterpolationElement(); \
	nb_nodes_per_element = \
	ElementClass<type>::getNbNodesPerInterpolationElement();

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(GET_NODES_INFO);
	#undef GET_NODES_INFO

	UInt * conn_val = mesh.getConnectivity(type, ghost_type).storage();
	for (UInt e = 0; e < nb_elements; ++e) {
	/// copy the value at standard nodes
	UInt offset = e * nb_nodes_per_element;
	for (UInt n = 0; n < nb_parent_nodes; ++n) {
	UInt node = conn_val[offset + n];
	for (UInt i = 0; i < nodal_values.getNbComponent(); ++i)
	extracted_values(node, i) = nodal_values(node, i);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ShapeLagrange<_ek_igfem>::printself(std::ostream & stream,
	int indent) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	;

	stream << space << "Shapes Lagrange [" << std::endl;
	ShapeFunctions::printself(stream, indent + 1);
	shapes.printself(stream, indent + 1);
	shapes_derivatives.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}
	} // namespace akantu

	#endif
	diff --git a/extra_packages/igfem/src/shape_igfem.hh b/extra_packages/igfem/src/shape_igfem.hh
	index 537f6b401..93dd84432 100644
	--- a/extra_packages/igfem/src/shape_igfem.hh
	+++ b/extra_packages/igfem/src/shape_igfem.hh
	@@ -1,199 +1,196 @@
	/**
	* @file shape_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief shape functions for interface-enriched generalized FEM
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "shape_functions.hh"

	#ifndef AKANTU_SHAPE_IGFEM_HH_
	#define AKANTU_SHAPE_IGFEM_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <> class ShapeLagrange<_ek_igfem> : public ShapeFunctions {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ShapeLagrange(const Mesh & mesh, const ID & id = "shape_igfem");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline void initShapeFunctions(const Array<Real> & nodes,
	const Matrix<Real> & integration_points,
	const Matrix<Real> & integration_points_1,
	const Matrix<Real> & integration_points_2,
	- ElementType type,
	- GhostType ghost_type);
	+ ElementType type, GhostType ghost_type);

	- inline void
	- interpolateEnrichmentsAllTypes(const Array<Real> & src, Array<Real> & dst,
	- ElementType type,
	- GhostType ghost_type) const;
	+ inline void interpolateEnrichmentsAllTypes(const Array<Real> & src,
	+ Array<Real> & dst,
	+ ElementType type,
	+ GhostType ghost_type) const;

	template <ElementType type>
	inline void precomputeShapesOnEnrichedNodes(const Array<Real> & nodes,
	GhostType ghost_type);

	template <ElementType type>
	void interpolateAtEnrichedNodes(const Array<Real> & src, Array<Real> & dst,
	GhostType ghost_type) const;

	/// pre compute all shapes on the element integration points from natural
	/// coordinates
	template <ElementType type>
	void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// pre compute all shape derivatives on the element integration points from
	/// natural coordinates
	template <ElementType type>
	void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// interpolate nodal values on the integration points
	template <ElementType type>
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// interpolate on physical point
	template <ElementType type>
	void interpolate(const Vector<Real> & real_coords, UInt elem,
	const Matrix<Real> & nodal_values,
	- Vector<Real> & interpolated,
	- GhostType ghost_type) const;
	+ Vector<Real> & interpolated, GhostType ghost_type) const;

	/// compute the gradient of u on the integration points
	template <ElementType type>
	void gradientOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// multiply a field by shape functions @f$ fts_{ij} = f_i * \varphi_j @f$
	template <ElementType type>
	void fieldTimesShapes(const Array<Real> & field,
	Array<Real> & field_times_shapes,
	GhostType ghost_type) const;

	/// find natural coords in parent element from real coords provided an element
	template <ElementType type>
	void inverseMap(const Vector<Real> & real_coords, UInt element,
	Vector<Real> & natural_coords,
	GhostType ghost_type = _not_ghost) const;

	/// find natural coords in sub-element from real coords provided an element
	template <ElementType type>
	void inverseMap(const Vector<Real> & real_coords, UInt element,
	Vector<Real> & natural_coords, UInt sub_element,
	GhostType ghost_type = _not_ghost) const;

	/// return true if the coordinates provided are inside the element, false
	/// otherwise
	template <ElementType type>
	bool contains(const Vector<Real> & real_coords, UInt elem,
	GhostType ghost_type) const;

	/// compute the shape on a provided point
	template <ElementType type>
	void computeShapes(const Vector<Real> & real_coords, UInt elem,
	Vector<Real> & shapes, GhostType ghost_type) const;

	/// compute the shape derivatives on a provided point
	template <ElementType type>
	void computeShapeDerivatives(const Matrix<Real> & real_coords, UInt elem,
	Tensor3<Real> & shapes,
	GhostType ghost_type) const;

	/// interpolate a field on a given physical point
	template <ElementType type>
	void interpolateOnPhysicalPoint(const Vector<Real> & real_coords, UInt elem,
	const Array<Real> & field,
	Vector<Real> & interpolated,
	GhostType ghost_type) const;

	/// function to extract values at standard nodes and zero-out enriched values
	/// of a nodal field
	void extractValuesAtStandardNodes(const Array<Real> & nodal_values,
	Array<Real> & extracted_values,
	GhostType ghost_type) const;

	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	protected:
	/// compute the shape derivatives on integration points for a given element
	template <ElementType type>
	inline void
	computeShapeDerivativesOnCPointsByElement(const Matrix<Real> & node_coords,
	const Matrix<Real> & natural_coords,
	Tensor3<Real> & shapesd) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get a the shapes vector
	- inline const Array<Real> &
	- getShapes(ElementType el_type,
	- GhostType ghost_type = _not_ghost) const;
	+ inline const Array<Real> & getShapes(ElementType el_type,
	+ GhostType ghost_type = _not_ghost) const;

	/// get a the shapes derivatives vector
	inline const Array<Real> &
	getShapesDerivatives(ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	/// get a the shapes vector
	inline const Array<Real> &
	getShapesAtEnrichedNodes(ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// shape functions for all elements
	ElementTypeMapArray<Real, InterpolationType> shapes;

	/// shape functions derivatives for all elements
	ElementTypeMapArray<Real, InterpolationType> shapes_derivatives;

	/// additional integration points for the IGFEM formulation
	ElementTypeMapArray<Real> igfem_integration_points;

	/// values of shape functions for all elements on the enriched nodes
	ElementTypeMapArray<Real, InterpolationType> shapes_at_enrichments;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "shape_igfem_inline_impl.hh"
	/// standard output stream operator
	// template <class ShapeFunction>
	// inline std::ostream & operator <<(std::ostream & stream, const
	// ShapeIGFEM<ShapeFunction> & _this)
	// {
	// _this.printself(stream);
	// return stream;
	// }

	#endif /* AKANTU_SHAPE_IGFEM_HH_ */
	diff --git a/extra_packages/igfem/src/shape_igfem_inline_impl.hh b/extra_packages/igfem/src/shape_igfem_inline_impl.hh
	index e72aaba33..a7febdfdf 100644
	--- a/extra_packages/igfem/src/shape_igfem_inline_impl.hh
	+++ b/extra_packages/igfem/src/shape_igfem_inline_impl.hh
	@@ -1,733 +1,731 @@
	/**
	* @file shape_igfem_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief ShapeIGFEM inline implementation
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> &
	ShapeLagrange<_ek_igfem>::getShapes(ElementType el_type,
	GhostType ghost_type) const {
	return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	-inline const Array<Real> & ShapeLagrange<_ek_igfem>::getShapesDerivatives(
	- ElementType el_type, GhostType ghost_type) const {
	+inline const Array<Real> &
	+ShapeLagrange<_ek_igfem>::getShapesDerivatives(ElementType el_type,
	+ GhostType ghost_type) const {
	return shapes_derivatives(FEEngine::getInterpolationType(el_type),
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_1>( \
	integration_points_1, ghost_type); \
	setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_2>( \
	integration_points_2, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	if (ElementClass<type>::getNaturalSpaceDimension() == \
	mesh.getSpatialDimension()) \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type); \
	precomputeShapesOnEnrichedNodes<type>(nodes, ghost_type);

	inline void ShapeLagrange<_ek_igfem>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	const Matrix<Real> & integration_points_1,
	const Matrix<Real> & integration_points_2, ElementType type,
	GhostType ghost_type) {

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}
	#undef INIT_SHAPE_FUNCTIONS

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void ShapeLagrange<_ek_igfem>::computeShapeDerivativesOnCPointsByElement(
	const Matrix<Real> & node_coords, const Matrix<Real> & natural_coords,
	Tensor3<Real> & shapesd) const {
	AKANTU_DEBUG_IN();

	// compute dnds
	Tensor3<Real> dnds(node_coords.rows(), node_coords.cols(),
	natural_coords.cols());
	ElementClass<type>::computeDNDS(natural_coords, dnds);
	// compute dxds
	Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
	natural_coords.cols());
	ElementClass<type>::computeJMat(dnds, node_coords, J);

	// compute shape derivatives
	ElementClass<type>::computeShapeDerivatives(J, dnds, shapesd);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
	UInt elem,
	Vector<Real> & natural_coords,
	UInt sub_element,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	if (!sub_element) {
	UInt nb_nodes_sub_el =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
	ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords,
	sub_element);
	ElementClass<sub_type_1>::inverseMap(real_coords, sub_el_coords,
	natural_coords);
	}

	else {
	UInt nb_nodes_sub_el =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
	ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords,
	sub_element);
	ElementClass<sub_type_2>::inverseMap(real_coords, sub_el_coords,
	natural_coords);
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
	UInt elem,
	Vector<Real> & natural_coords,
	GhostType ghost_type) const {

	/// map point into parent reference domain
	AKANTU_DEBUG_IN();

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	ElementClass<type>::getParentCoords(nodes_coord, parent_coords);
	ElementClass<parent_type>::inverseMap(real_coords, parent_coords,
	natural_coords);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	bool ShapeLagrange<_ek_igfem>::contains(const Vector<Real> & real_coords,
	- UInt elem,
	- GhostType ghost_type) const {
	+ UInt elem, GhostType ghost_type) const {

	UInt spatial_dimension = mesh.getSpatialDimension();
	Vector<Real> natural_coords(spatial_dimension);

	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	return ElementClass<type>::contains(natural_coords);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolate(const Vector<Real> & real_coords,
	UInt elem,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated,
	GhostType ghost_type) const {
	UInt nb_shapes = ElementClass<type>::getShapeSize();
	Vector<Real> shapes(nb_shapes);
	computeShapes<type>(real_coords, elem, shapes, ghost_type);
	ElementClass<type>::interpolate(nodal_values, shapes, interpolated);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	-void ShapeLagrange<_ek_igfem>::computeShapes(
	- const Vector<Real> & real_coords, UInt elem, Vector<Real> & shapes,
	- GhostType ghost_type) const {
	+void ShapeLagrange<_ek_igfem>::computeShapes(const Vector<Real> & real_coords,
	+ UInt elem, Vector<Real> & shapes,
	+ GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt spatial_dimension = mesh.getSpatialDimension();

	/// parent contribution
	/// get the size of the parent shapes
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	Vector<Real> parent_shapes(size_of_parent_shapes);

	/// compute parent shapes -> map shapes in the physical domain of the parent
	Vector<Real> natural_coords(spatial_dimension);
	Real tol = Math::getTolerance();
	Math::setTolerance(1e-14);
	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
	natural_coords.zero();

	/// sub-element contribution
	/// check which sub-element contains the physical point
	/// check if point is in sub-element 1
	inverseMap<type>(real_coords, elem, natural_coords, 0, ghost_type);
	if (ElementClass<sub_type_1>::contains(natural_coords)) {
	UInt size_of_sub_shapes = ElementClass<sub_type_1>::getShapeSize();
	Vector<Real> sub_shapes(size_of_sub_shapes);
	ElementClass<sub_type_1>::computeShapes(natural_coords, sub_shapes);
	/// assemble shape functions
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
	} else {
	natural_coords.zero();
	inverseMap<type>(real_coords, elem, natural_coords, 1, ghost_type);

	AKANTU_DEBUG_ASSERT(ElementClass<sub_type_2>::contains(natural_coords),
	"Physical point not contained in any element");

	UInt size_of_sub_shapes = ElementClass<sub_type_2>::getShapeSize();
	Vector<Real> sub_shapes(size_of_sub_shapes);
	ElementClass<sub_type_2>::computeShapes(natural_coords, sub_shapes);
	/// assemble shape functions
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 1);
	}

	Math::setTolerance(tol);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::computeShapeDerivatives(
	const Matrix<Real> & real_coords, UInt elem, Tensor3<Real> & shapesd,
	GhostType ghost_type) const {

	AKANTU_DEBUG_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapesOnIntegrationPoints(
	__attribute__((unused)) const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	/// get the spatial dimension for the given element type
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
	/// get the integration points for the subelements
	Matrix<Real> & natural_coords_sub_1 =
	integration_points(sub_type_1, ghost_type);
	Matrix<Real> & natural_coords_sub_2 =
	integration_points(sub_type_2, ghost_type);

	/// store the number of quadrature points on each subelement and the toal
	/// number
	UInt nb_points_sub_1 = natural_coords_sub_1.cols();
	UInt nb_points_sub_2 = natural_coords_sub_2.cols();
	UInt nb_total_points = nb_points_sub_1 + nb_points_sub_2;

	// get the integration points for the parent element
	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
	Array<Real> & natural_coords_parent = igfem_integration_points.alloc(
	nb_element * nb_total_points, spatial_dimension, type, ghost_type);
	Array<Real>::matrix_iterator natural_coords_parent_it =
	natural_coords_parent.begin_reinterpret(spatial_dimension,
	nb_total_points, nb_element);

	/// get the size of the shapes
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	UInt size_of_sub_1_shapes = ElementClass<sub_type_1>::getShapeSize();
	UInt size_of_sub_2_shapes = ElementClass<sub_type_2>::getShapeSize();

	/// initialize the matrices to store the shape functions of the subelements
	/// and the parent
	Matrix<Real> sub_1_shapes(size_of_sub_1_shapes, nb_points_sub_1);
	Matrix<Real> sub_2_shapes(size_of_sub_2_shapes, nb_points_sub_2);
	Matrix<Real> parent_1_shapes(size_of_parent_shapes, nb_points_sub_1);
	Matrix<Real> parent_2_shapes(size_of_parent_shapes, nb_points_sub_2);
	/// compute the shape functions of the subelements
	ElementClass<sub_type_1>::computeShapes(natural_coords_sub_1, sub_1_shapes);
	ElementClass<sub_type_2>::computeShapes(natural_coords_sub_2, sub_2_shapes);

	/// get the nodal coordinates per element
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// allocate the shapes for the given element type
	Array<Real> & shapes_tmp = shapes.alloc(nb_element * nb_total_points,
	size_of_shapes, itp_type, ghost_type);

	Array<Real>::matrix_iterator shapes_it = shapes_tmp.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(), nb_total_points,
	nb_element);

	Matrix<Real> physical_points_1(spatial_dimension, nb_points_sub_1);
	Matrix<Real> physical_points_2(spatial_dimension, nb_points_sub_2);
	Matrix<Real> parent_natural_coords_1(spatial_dimension, nb_points_sub_1);
	Matrix<Real> parent_natural_coords_2(spatial_dimension, nb_points_sub_2);

	/// intialize the matrices for the parent and subelement coordinates
	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_1 =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_2 =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
	Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);

	/// loop over all elements of the given type and compute the shape functions
	Vector<Real> all_shapes(size_of_shapes);

	for (UInt elem = 0; elem < nb_element;
	++elem, ++shapes_it, ++x_it, ++natural_coords_parent_it) {
	Matrix<Real> & N = *shapes_it;
	const Matrix<Real> & X = *x_it;
	Matrix<Real> & nc_parent = *natural_coords_parent_it;

	/// map the sub element integration points into the parent reference domain
	ElementClass<type>::mapFromSubRefToParentRef(
	X, sub_el_1_coords, parent_coords, sub_1_shapes, physical_points_1,
	parent_natural_coords_1, 0);
	ElementClass<type>::mapFromSubRefToParentRef(
	X, sub_el_2_coords, parent_coords, sub_2_shapes, physical_points_2,
	parent_natural_coords_2, 1);

	/// compute the parent shape functions on all integration points
	ElementClass<sub_type_1>::computeShapes(parent_natural_coords_1,
	parent_1_shapes);
	ElementClass<sub_type_1>::computeShapes(parent_natural_coords_2,
	parent_2_shapes);

	/// copy the results into the shape functions iterator and natural coords
	/// iterator
	for (UInt i = 0; i < nb_points_sub_1; ++i) {
	ElementClass<type>::assembleShapes(parent_1_shapes(i), sub_1_shapes(i),
	all_shapes, 0);
	N(i) = all_shapes;
	nc_parent(i) = parent_natural_coords_1(i);
	}
	for (UInt i = 0; i < nb_points_sub_2; ++i) {
	ElementClass<type>::assembleShapes(parent_2_shapes(i), sub_2_shapes(i),
	all_shapes, 1);
	N(i + nb_points_sub_1) = all_shapes;

	/// N(i + nb_points_sub_2) = all_shapes;
	nc_parent(i + nb_points_sub_1) = parent_natural_coords_2(i);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	UInt spatial_dimension = mesh.getSpatialDimension();

	/// get the integration points for the subelements
	Matrix<Real> & natural_coords_sub_1 =
	integration_points(sub_type_1, ghost_type);
	Matrix<Real> & natural_coords_sub_2 =
	integration_points(sub_type_2, ghost_type);
	/// store the number of quadrature points on each subelement and the toal
	/// number
	UInt nb_points_sub_1 = natural_coords_sub_1.cols();
	UInt nb_points_sub_2 = natural_coords_sub_2.cols();
	UInt nb_points_total = nb_points_sub_1 + nb_points_sub_2;

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();

	/// intialize the matrices for the parent and subelement coordinates
	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_1 =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_2 =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
	Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);

	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
	Array<Real> & shapes_derivatives_tmp = shapes_derivatives.alloc(
	nb_element * nb_points_total, size_of_shapesd, itp_type, ghost_type);

	/// get an iterator to the coordiantes of the elements
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

	Real * shapesd_val = shapes_derivatives_tmp.storage();
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// get an iterator to the integration points of the parent element
	Array<Real> & natural_coords_parent =
	igfem_integration_points(type, ghost_type);
	Array<Real>::matrix_iterator natural_coords_parent_it =
	natural_coords_parent.begin_reinterpret(spatial_dimension,
	nb_points_total, nb_element);

	Tensor3<Real> B_sub_1(spatial_dimension, nb_nodes_sub_el_1, nb_points_sub_1);
	Tensor3<Real> B_sub_2(spatial_dimension, nb_nodes_sub_el_2, nb_points_sub_2);
	Tensor3<Real> B_parent(spatial_dimension, nb_nodes_parent_el,
	nb_points_total);
	/// assemble the shape derivatives
	Matrix<Real> all_shapes(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element;
	++elem, ++x_it, ++natural_coords_parent_it) {
	Matrix<Real> & X = *x_it;
	Matrix<Real> & nc_parent = *natural_coords_parent_it;

	Tensor3<Real> B(shapesd_val, spatial_dimension, nb_nodes_per_element,
	nb_points_total);

	/// get the coordinates of the two sub elements and the parent element
	ElementClass<type>::getSubElementCoords(X, sub_el_1_coords, 0);
	ElementClass<type>::getSubElementCoords(X, sub_el_2_coords, 1);
	ElementClass<type>::getParentCoords(X, parent_coords);

	/// compute the subelements' shape derivatives and the parent shape
	/// derivatives
	computeShapeDerivativesOnCPointsByElement<sub_type_1>(
	sub_el_1_coords, natural_coords_sub_1, B_sub_1);
	computeShapeDerivativesOnCPointsByElement<sub_type_2>(
	sub_el_2_coords, natural_coords_sub_2, B_sub_2);
	computeShapeDerivativesOnCPointsByElement<parent_type>(parent_coords,
	nc_parent, B_parent);

	for (UInt i = 0; i < nb_points_sub_1; ++i) {
	ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_1(i),
	all_shapes, 0);
	B(i) = all_shapes;
	}

	for (UInt i = 0; i < nb_points_sub_2; ++i) {
	ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_2(i),
	all_shapes, 1);
	B(i + nb_points_sub_1) = all_shapes;
	}

	shapesd_val += size_of_shapesd * nb_points_total;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(shapes.exists(itp_type, ghost_type),
	"No shapes for the type "
	<< shapes.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->interpolateElementalFieldOnIntegrationPoints<type>(
	u_el, out_uq, ghost_type, shapes(itp_type, ghost_type), filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::gradientOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_nablauq,
	UInt nb_degree_of_freedom, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(
	shapes_derivatives.exists(itp_type, ghost_type),
	"No shapes derivatives for the type "
	<< shapes_derivatives.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->gradientElementalFieldOnIntegrationPoints<type>(
	u_el, out_nablauq, ghost_type, shapes_derivatives(itp_type, ghost_type),
	filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::fieldTimesShapes(
	const Array<Real> & field, Array<Real> & field_times_shapes,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	field_times_shapes.resize(field.getSize());

	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	UInt nb_degree_of_freedom = field.getNbComponent();

	const Array<Real> & shape = shapes(itp_type, ghost_type);

	Array<Real>::const_matrix_iterator field_it =
	field.begin(nb_degree_of_freedom, 1);
	Array<Real>::const_matrix_iterator shapes_it = shape.begin(1, size_of_shapes);

	Array<Real>::matrix_iterator it =
	field_times_shapes.begin(nb_degree_of_freedom, size_of_shapes);
	Array<Real>::matrix_iterator end =
	field_times_shapes.end(nb_degree_of_freedom, size_of_shapes);

	for (; it != end; ++it, ++field_it, ++shapes_it) {
	it->mul<false, false>(field_it, shapes_it);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateOnPhysicalPoint(
	const Vector<Real> & real_coords, UInt elem, const Array<Real> & field,
	Vector<Real> & interpolated, GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	Vector<Real> shapes(ElementClass<type>::getShapeSize());
	computeShapes<type>(real_coords, elem, shapes, ghost_type);

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_val(spatial_dimension, nb_nodes_per_element);
	mesh.extractNodalValuesFromElement(field, nodes_val.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	ElementClass<type>::interpolate(nodes_val, shapes, interpolated);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapesOnEnrichedNodes(
	- __attribute__((unused)) const Array<Real> & nodes,
	- GhostType ghost_type) {
	+ __attribute__((unused)) const Array<Real> & nodes, GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;
	const ElementType sub_type = ElementClassProperty<type>::sub_element_type_1;

	/// get the spatial dimension for the given element type
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();

	// get the integration points for the parent element
	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();

	/// get the size of the shapes
	UInt nb_enriched_nodes = ElementClass<type>::getNbEnrichments();
	UInt nb_parent_nodes =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	UInt size_of_sub_shapes = ElementClass<sub_type>::getShapeSize();

	Vector<Real> parent_shapes(size_of_parent_shapes);
	Vector<Real> sub_shapes(size_of_sub_shapes);

	Vector<Real> shapes(size_of_shapes);

	/// get the nodal coordinates per element
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// allocate the shapes for the given element type
	Array<Real> & shapes_tmp = shapes_at_enrichments.alloc(
	nb_element * nb_enriched_nodes, size_of_shapes, itp_type, ghost_type);

	Array<Real>::matrix_iterator shapes_it = shapes_tmp.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(),
	nb_enriched_nodes, nb_element);

	Vector<Real> real_coords(spatial_dimension);
	Vector<Real> natural_coords(spatial_dimension);
	Matrix<Real> parent_coords(spatial_dimension, nb_parent_nodes);
	UInt * sub_element_enrichments =
	ElementClass<type>::getSubElementEnrichments();

	/// loop over all elements
	for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it, ++x_it) {
	Matrix<Real> & N = *shapes_it;
	const Matrix<Real> & X = *x_it;
	for (UInt i = 0; i < nb_enriched_nodes; ++i) {
	/// get the parent element coordinates
	ElementClass<type>::getParentCoords(X, parent_coords);
	/// get the physical coords of the enriched node
	real_coords = X(nb_parent_nodes + i);
	/// map the physical point into the parent ref domain
	ElementClass<parent_type>::inverseMap(real_coords, parent_coords,
	natural_coords);
	/// compute the parent shape functions
	ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
	/// Sub-element contribution
	sub_shapes.zero();
	sub_shapes(sub_element_enrichments[i]) = 1.;
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
	N(i) = shapes;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateAtEnrichedNodes(
	- const Array<Real> & src, Array<Real> & dst,
	- GhostType ghost_type) const {
	+ const Array<Real> & src, Array<Real> & dst, GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	UInt nb_parent_nodes =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_enrichments = ElementClass<type>::getNbEnrichments();
	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	UInt spatial_dimension = mesh.getSpatialDimension();
	Matrix<Real> nodes_val(spatial_dimension, nb_nodes_per_element);
	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	const Array<Real> & shapes = shapes_at_enrichments(itp_type, ghost_type);
	Array<Real>::const_matrix_iterator shapes_it = shapes.begin_reinterpret(
	nb_nodes_per_element, nb_enrichments, nb_element);
	Array<Real>::vector_iterator dst_vect = dst.begin(spatial_dimension);

	Vector<Real> interpolated(spatial_dimension);
	for (UInt e = 0; e < nb_element; ++e, ++shapes_it) {
	const Matrix<Real> & el_shapes = *shapes_it;
	mesh.extractNodalValuesFromElement(src, nodes_val.storage(),
	elem_val + e * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);
	;
	for (UInt i = 0; i < nb_enrichments; ++i) {
	ElementClass<type>::interpolate(nodes_val, el_shapes(i), interpolated);
	UInt enr_node_idx =
	elem_val[e * nb_nodes_per_element + nb_parent_nodes + i];
	dst_vect[enr_node_idx] = interpolated;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	#define COMPUTE_ENRICHED_VALUES(type) \
	interpolateAtEnrichedNodes<type>(src, dst, ghost_type);

	inline void ShapeLagrange<_ek_igfem>::interpolateEnrichmentsAllTypes(
	const Array<Real> & src, Array<Real> & dst, ElementType type,
	GhostType ghost_type) const {

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(COMPUTE_ENRICHED_VALUES);
	}
	#undef COMPUTE_ENRICHED_VALUES

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_ */
	diff --git a/extra_packages/igfem/src/solid_mechanics_model_igfem.cc b/extra_packages/igfem/src/solid_mechanics_model_igfem.cc
	index 8422cb2d2..04d5a63d6 100644
	--- a/extra_packages/igfem/src/solid_mechanics_model_igfem.cc
	+++ b/extra_packages/igfem/src/solid_mechanics_model_igfem.cc
	@@ -1,585 +1,583 @@
	/**
	* @file solid_mechanics_model_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief solid mechanics model for IGFEM analysis
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_igfem.hh"
	#include "dumpable_inline_impl.hh"
	#include "group_manager_inline_impl.hh"
	#include "igfem_helper.hh"
	#include "material_igfem.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_igfem_element_partition.hh"
	#include "dumper_igfem_elemental_field.hh"
	#include "dumper_igfem_material_internal_field.hh"
	#include "dumper_material_padders.hh"
	#include "dumper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	const SolidMechanicsModelIGFEMOptions
	default_solid_mechanics_model_igfem_options(_static, false);

	SolidMechanicsModelIGFEM::SolidMechanicsModelIGFEM(Mesh & mesh, UInt dim,
	const ID & id)
	: SolidMechanicsModel(mesh, dim, id), IGFEMEnrichment(mesh),
	global_ids_updater(NULL) {
	AKANTU_DEBUG_IN();

	delete material_selector;
	material_selector = new DefaultMaterialIGFEMSelector(*this);

	this->registerEventHandler(*this);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("igfem elements", id);
	this->mesh.addDumpMeshToDumper("igfem elements", mesh, spatial_dimension,
	_not_ghost, _ek_igfem);
	#endif

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SolidMechanicsModelIGFEM::~SolidMechanicsModelIGFEM() {
	AKANTU_DEBUG_IN();
	if (global_ids_updater)
	delete global_ids_updater;
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::initFull(const ModelOptions & options) {
	AKANTU_DEBUG_IN();

	/// intialize the IGFEM enrichment
	this->initialize();

	SolidMechanicsModel::initFull(options);

	// set the initial condition to 0
	real_force->clear();
	real_displacement->clear();
	real_residual->clear();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Allocate all the needed vectors. By default their are not necessarily set to
	* 0
	*
	*/
	void SolidMechanicsModelIGFEM::initArrays() {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = mesh.getNbNodes();
	std::stringstream sstr_rdisp;
	sstr_rdisp << id << ":real_displacement";
	std::stringstream sstr_rforc;
	sstr_rforc << id << ":real_force";
	std::stringstream sstr_rresi;
	sstr_rresi << id << ":real_residual";

	real_displacement = &(alloc<Real>(sstr_rdisp.str(), nb_nodes,
	spatial_dimension, REAL_INIT_VALUE));
	real_force = &(alloc<Real>(sstr_rforc.str(), nb_nodes, spatial_dimension,
	REAL_INIT_VALUE));
	real_residual = &(alloc<Real>(sstr_rresi.str(), nb_nodes, spatial_dimension,
	REAL_INIT_VALUE));

	SolidMechanicsModel::initArrays();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::initParallel(MeshPartition * partition,
	DataAccessor * data_accessor) {
	SolidMechanicsModel::initParallel(partition, data_accessor);
	this->intersector_sphere.setDistributedSynchronizer(synch_parallel);
	if (mesh.isDistributed())
	global_ids_updater = new GlobalIdsUpdater(mesh, synch_parallel);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::initMaterials() {
	AKANTU_DEBUG_IN();

	// make sure the material are instantiated
	if (!are_materials_instantiated)
	instantiateMaterials();

	/// find the first igfem material
	UInt igfem_index = 0;

	while ((dynamic_cast<MaterialIGFEM *>(materials[igfem_index]) == NULL) &&
	igfem_index <= materials.size())
	++igfem_index;

	AKANTU_DEBUG_ASSERT(igfem_index != materials.size(),
	"No igfem materials in the material input file");

	DefaultMaterialIGFEMSelector * igfem_mat_selector =
	dynamic_cast<DefaultMaterialIGFEMSelector *>(material_selector);
	if (igfem_mat_selector != NULL)
	igfem_mat_selector->setIGFEMFallback(igfem_index);

	SolidMechanicsModel::initMaterials();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the model, basically pre-compute the shapes, shapes derivatives
	* and jacobian
	*
	*/
	void SolidMechanicsModelIGFEM::initModel() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel::initModel();

	registerFEEngineObject<MyFEEngineIGFEMType>("IGFEMFEEngine", mesh,
	spatial_dimension);
	/// insert the two feengines associated with the model in the map
	this->fe_engines_per_kind[_ek_regular] = &(this->getFEEngine());
	this->fe_engines_per_kind[_ek_igfem] = &(this->getFEEngine("IGFEMFEEngine"));

	/// add the igfem type connectivities

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	GhostType type_ghost = *gt;

	Mesh::type_iterator it = mesh.firstType(spatial_dimension, type_ghost);
	Mesh::type_iterator last = mesh.lastType(spatial_dimension, type_ghost);

	for (; it != last; ++it) {
	const Array<UInt> & connectivity = mesh.getConnectivity(*it, type_ghost);
	if (connectivity.getSize() != 0) {
	ElementType type = *it;
	Vector<ElementType> types_igfem = FEEngine::getIGFEMElementTypes(type);
	for (UInt i = 0; i < types_igfem.size(); ++i)
	mesh.addConnectivityType(types_igfem(i), type_ghost);
	}
	}
	}

	getFEEngine("IGFEMFEEngine").initShapeFunctions(_not_ghost);
	getFEEngine("IGFEMFEEngine").initShapeFunctions(_ghost);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::onElementsAdded(const Array<Element> & elements,
	const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	const NewIGFEMElementsEvent * igfem_event =
	dynamic_cast<const NewIGFEMElementsEvent *>(&event);
	/// insert the new and old elements in the map
	if (igfem_event != NULL) {
	this->element_map.zero();
	const Array<Element> & old_elements = igfem_event->getOldElementsList();
	for (UInt e = 0; e < elements.getSize(); ++e) {
	this->element_map[elements(e)] = old_elements(e);
	}
	}

	/// update shape functions
	getFEEngine("IGFEMFEEngine").initShapeFunctions(_not_ghost);
	getFEEngine("IGFEMFEEngine").initShapeFunctions(_ghost);

	SolidMechanicsModel::onElementsAdded(elements, event);
	this->reassignMaterial();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::onElementsRemoved(
	const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) {

	this->getFEEngine("IGFEMFEEngine").initShapeFunctions(_not_ghost);
	this->getFEEngine("IGFEMFEEngine").initShapeFunctions(_ghost);
	SolidMechanicsModel::onElementsRemoved(element_list, new_numbering, event);
	if (synch_parallel)
	synch_parallel->computeAllBufferSizes(*this);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) {
	AKANTU_DEBUG_IN();

	const NewIGFEMNodesEvent * igfem_event =
	dynamic_cast<const NewIGFEMNodesEvent *>(&event);
	// update the node type
	if (igfem_event != NULL) {
	intersector_sphere.updateNodeType(
	nodes_list, igfem_event->getNewNodePerElem(),
	igfem_event->getElementType(), igfem_event->getGhostType());
	}

	UInt nb_nodes = mesh.getNbNodes();

	if (real_displacement)
	real_displacement->resize(nb_nodes);
	if (real_force)
	real_force->resize(nb_nodes);
	if (real_residual)
	real_residual->resize(nb_nodes);

	if (mesh.isDistributed())
	mesh.getGlobalNodesIds().resize(mesh.getNbNodes());

	if (displacement)
	displacement->resize(nb_nodes);
	if (mass)
	mass->resize(nb_nodes);
	if (velocity)
	velocity->resize(nb_nodes);
	if (acceleration)
	acceleration->resize(nb_nodes);
	if (force)
	force->resize(nb_nodes);
	if (residual)
	residual->resize(nb_nodes);
	if (blocked_dofs)
	blocked_dofs->resize(nb_nodes);

	if (previous_displacement)
	previous_displacement->resize(nb_nodes);
	if (increment_acceleration)
	increment_acceleration->resize(nb_nodes);
	if (increment)
	increment->resize(nb_nodes);

	if (current_position)
	current_position->resize(nb_nodes);

	std::vector<Material *>::iterator mat_it;
	for (mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	(*mat_it)->onNodesAdded(nodes_list, event);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::onNodesRemoved(const Array<UInt> & nodes_list,
	const Array<UInt> & new_numbering,
	const RemovedNodesEvent & event) {
	if (real_displacement)
	mesh.removeNodesFromArray(*real_displacement, new_numbering);
	if (real_force)
	mesh.removeNodesFromArray(*real_force, new_numbering);
	if (real_residual)
	mesh.removeNodesFromArray(*real_residual, new_numbering);

	// communicate global connectivity for slave nodes
	if (global_ids_updater)
	global_ids_updater->updateGlobalIDs(
	mesh.getNbNodes() - intersector_sphere.getNbStandardNodes());

	SolidMechanicsModel::onNodesRemoved(nodes_list, new_numbering, event);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::addDumpGroupFieldToDumper(
	const std::string & dumper_name, const std::string & field_id,
	const std::string & group_name, ElementKind element_kind,
	bool padding_flag) {
	AKANTU_DEBUG_IN();

	ElementKind _element_kind = element_kind;
	if (dumper_name == "igfem elements") {
	_element_kind = _ek_igfem;
	}

	SolidMechanicsModel::addDumpGroupFieldToDumper(
	dumper_name, field_id, group_name, _element_kind, padding_flag);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::onDump() {
	this->computeValuesOnEnrichedNodes();
	this->flattenAllRegisteredInternals(_ek_igfem);
	SolidMechanicsModel::onDump();
	}

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	dumpers::Field * SolidMechanicsModelIGFEM::createElementalField(
	const std::string & field_name, const std::string & group_name,
	- bool padding_flag, const UInt & spatial_dimension,
	- ElementKind kind) {
	+ bool padding_flag, const UInt & spatial_dimension, ElementKind kind) {

	dumpers::Field * field = NULL;

	if (kind != _ek_igfem)
	field = SolidMechanicsModel::createElementalField(
	field_name, group_name, padding_flag, spatial_dimension, kind);

	else {

	if (field_name == "partitions")
	field =
	mesh.createElementalField<UInt, dumpers::IGFEMElementPartitionField>(
	mesh.getConnectivities(), group_name, spatial_dimension, kind);
	else if (field_name == "material_index")
	field =
	mesh.createElementalField<UInt, Vector, dumpers::IGFEMElementalField>(
	material_index, group_name, spatial_dimension, kind);
	else {
	// this copy of field_name is used to compute derivated data such as
	// strain and von mises stress that are based on grad_u and stress
	std::string field_name_copy(field_name);

	if (field_name == "strain" \|\| field_name == "Green strain" \|\|
	field_name == "principal strain" \|\|
	field_name == "principal Green strain")
	field_name_copy = "grad_u";
	else if (field_name == "Von Mises stress")
	field_name_copy = "stress";

	bool is_internal = this->isInternal(field_name_copy, kind);

	if (is_internal) {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->getInternalDataPerElem(field_name_copy, kind);
	ElementTypeMapArray<Real> & internal_flat =
	this->flattenInternal(field_name_copy, kind);
	- field =
	- mesh.createElementalField<Real, dumpers::IGFEMInternalMaterialField>(
	- internal_flat, group_name, spatial_dimension, kind,
	- nb_data_per_elem);
	+ field = mesh.createElementalField<Real,
	+ dumpers::IGFEMInternalMaterialField>(
	+ internal_flat, group_name, spatial_dimension, kind,
	+ nb_data_per_elem);
	if (field_name == "strain") {
	dumpers::ComputeStrain<false> * foo =
	new dumpers::ComputeStrain<false>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	} else if (field_name == "Von Mises stress") {
	dumpers::ComputeVonMisesStress * foo =
	new dumpers::ComputeVonMisesStress(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	} else if (field_name == "Green strain") {
	dumpers::ComputeStrain<true> * foo =
	new dumpers::ComputeStrain<true>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	} else if (field_name == "principal strain") {
	dumpers::ComputePrincipalStrain<false> * foo =
	new dumpers::ComputePrincipalStrain<false>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	} else if (field_name == "principal Green strain") {
	dumpers::ComputePrincipalStrain<true> * foo =
	new dumpers::ComputePrincipalStrain<true>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	}

	/// treat the paddings
	if (padding_flag) {
	if (field_name == "stress") {
	if (spatial_dimension == 2) {
	dumpers::StressPadder<2> * foo =
	new dumpers::StressPadder<2>(*this);
	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	}
	} else if (field_name == "strain" \|\| field_name == "Green strain") {
	if (spatial_dimension == 2) {
	dumpers::StrainPadder<2> * foo =
	new dumpers::StrainPadder<2>(*this);
	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	}
	}
	}
	// homogenize the field
	dumpers::ComputeFunctorInterface * foo =
	dumpers::HomogenizerProxy::createHomogenizer(*field);

	field = dumpers::FieldComputeProxy::createFieldCompute(field, *foo);
	}
	}
	}
	// }
	return field;
	}

	/* -------------------------------------------------------------------------- */

	dumpers::Field *
	SolidMechanicsModelIGFEM::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["real_displacement"] = real_displacement;

	dumpers::Field * field = NULL;
	if (padding_flag)
	field = mesh.createNodalField(real_nodal_fields[field_name], group_name, 3);
	else
	field = mesh.createNodalField(real_nodal_fields[field_name], group_name);

	if (field == NULL)
	return SolidMechanicsModel::createNodalFieldReal(field_name, group_name,
	padding_flag);

	return field;
	}

	#else
	/* -------------------------------------------------------------------------- */
	dumpers::Field * SolidMechanicsModelIGFEM::createElementalField(
	const std::string & field_name, const std::string & group_name,
	- bool padding_flag, const UInt & spatial_dimension,
	- ElementKind kind) {
	+ bool padding_flag, const UInt & spatial_dimension, ElementKind kind) {
	return NULL;
	}

	/* -------------------------------------------------------------------------- */

	dumpers::Field *
	SolidMechanicsModelIGFEM::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {
	return NULL;
	}

	#endif
	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::computeValuesOnEnrichedNodes() {

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	for (UInt s = 0; s < spatial_dimension; ++s)
	(real_displacement)(n, s) = (displacement)(n, s);
	}

	Element element;
	Vector<Real> real_coords(spatial_dimension);
	Vector<Real> interpolated(spatial_dimension);
	Array<Real>::const_vector_iterator r_displ_it =
	this->real_displacement->begin(spatial_dimension);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {
	element.ghost_type = *gt;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, *gt, _ek_igfem);
	Mesh::type_iterator last = mesh.lastType(spatial_dimension, *gt, _ek_igfem);
	for (; it != last; ++it) {
	element.type = *it;
	UInt nb_element = mesh.getNbElement(it, gt);
	if (!nb_element)
	continue;
	UInt * elem_val = mesh.getConnectivity(it, gt).storage();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(*it);
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);
	Matrix<Real> displ_val(spatial_dimension, nb_nodes_per_element);

	UInt nb_enriched_nodes = IGFEMHelper::getNbEnrichedNodes(*it);
	UInt nb_parent_nodes = IGFEMHelper::getNbParentNodes(*it);
	for (UInt el = 0; el < nb_element; ++el) {
	element.element = el;
	/// get the node coordinates of the element
	mesh.extractNodalValuesFromElement(
	mesh.getNodes(), nodes_coord.storage(),
	elem_val + el * nb_nodes_per_element, nb_nodes_per_element,
	spatial_dimension);

	/// get the displacement values at the nodes of the element
	mesh.extractNodalValuesFromElement(
	*(this->displacement), displ_val.storage(),
	elem_val + el * nb_nodes_per_element, nb_nodes_per_element,
	spatial_dimension);

	for (UInt i = 0; i < nb_enriched_nodes; ++i) {
	/// coordinates of enriched node
	real_coords = nodes_coord(nb_parent_nodes + i);
	/// global index of the enriched node
	UInt idx = elem_val[el * nb_nodes_per_element + nb_parent_nodes + i];
	/// compute the real displacement value
	this->getFEEngine("IGFEMFEEngine")
	.interpolate(real_coords, displ_val, interpolated, element);
	r_displ_it[idx] = interpolated;
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::transferInternalValues(
	const ID & internal, std::vector<Element> & new_elements,
	Array<Real> & added_quads, Array<Real> & internal_values) {

	/// @todo sort the new elements by their corresponding old element type and
	/// old material!!!

	/// get the number of elements for which iternals need to be transfered
	UInt nb_new_elements = new_elements.size();
	UInt nb_new_quads = added_quads.getSize() / nb_new_elements;

	Array<Real>::const_matrix_iterator quad_coords =
	added_quads.begin_reinterpret(this->spatial_dimension, nb_new_quads,
	nb_new_elements);
	UInt nb_internal_component = internal_values.getNbComponent();
	Array<Real>::matrix_iterator internal_val = internal_values.begin_reinterpret(
	nb_internal_component, nb_new_quads, nb_new_elements);
	Vector<Real> default_values(nb_internal_component, 0.);

	for (UInt e = 0; e < nb_new_elements; ++e, ++quad_coords, ++internal_val) {
	Element new_element = new_elements[e];
	Element old_element = this->element_map[new_element];
	UInt mat_idx = (this->material_index(
	old_element.type, old_element.ghost_type))(old_element.element);
	Material & old_material = *(this->materials[mat_idx]);
	old_material.extrapolateInternal(internal, old_element, *quad_coords,
	*internal_val);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelIGFEM::applyEigenGradU(
	const Matrix<Real> & prescribed_eigen_grad_u, const ID & material_name,
	const GhostType ghost_type) {

	AKANTU_DEBUG_ASSERT(prescribed_eigen_grad_u.size() ==
	spatial_dimension * spatial_dimension,
	"The prescribed grad_u is not of the good size");
	std::vector<Material *>::iterator mat_it;
	for (mat_it = this->materials.begin(); mat_it != this->materials.end();
	++mat_it) {
	MaterialIGFEM * mat_igfem = dynamic_cast<MaterialIGFEM >(mat_it);
	if (mat_igfem != NULL)
	mat_igfem->applyEigenGradU(prescribed_eigen_grad_u, material_name,
	ghost_type);
	else if ((*mat_it)->getName() == material_name)
	(*mat_it)->applyEigenGradU(prescribed_eigen_grad_u, ghost_type);
	}
	}

	} // namespace akantu
	diff --git a/extra_packages/igfem/src/solid_mechanics_model_igfem.hh b/extra_packages/igfem/src/solid_mechanics_model_igfem.hh
	index 4933932f8..c9f893958 100644
	--- a/extra_packages/igfem/src/solid_mechanics_model_igfem.hh
	+++ b/extra_packages/igfem/src/solid_mechanics_model_igfem.hh
	@@ -1,196 +1,196 @@
	/**
	* @file solid_mechanics_model_igfem.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief solid mechanics model for IGFEM analysis
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_SOLID_MECHANICS_MODEL_IGFEM_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_IGFEM_HH_
	#include "global_ids_updater.hh"
	#include "igfem_enrichment.hh"
	#include "solid_mechanics_model.hh"
	#include "solid_mechanics_model_event_handler.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	struct SolidMechanicsModelIGFEMOptions : public SolidMechanicsModelOptions {
	SolidMechanicsModelIGFEMOptions(AnalysisMethod analysis_method = _static,
	bool no_init_materials = false)
	: SolidMechanicsModelOptions(analysis_method, no_init_materials) {}
	};

	extern const SolidMechanicsModelIGFEMOptions
	default_solid_mechanics_model_igfem_options;

	/* -------------------------------------------------------------------------- */
	/* Solid Mechanics Model for IGFEM analysis */
	/* -------------------------------------------------------------------------- */
	class SolidMechanicsModelIGFEM : public SolidMechanicsModel,
	public SolidMechanicsModelEventHandler,
	public IGFEMEnrichment {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	typedef FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem>
	MyFEEngineIGFEMType;
	typedef std::map<Element, Element> ElementMap;
	typedef std::map<ElementKind, FEEngine *> FEEnginesPerKindMap;

	SolidMechanicsModelIGFEM(Mesh & mesh,
	UInt spatial_dimension = _all_dimensions,
	const ID & id = "solid_mechanics_model_igfem");

	virtual ~SolidMechanicsModelIGFEM();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the cohesive model
	virtual void initFull(const ModelOptions & options =
	default_solid_mechanics_model_igfem_options);

	/// initialize the model
	virtual void initModel();

	/// initialize igfem material
	virtual void initMaterials();

	/// register the tags associated with the parallel synchronizer
	virtual void initParallel(MeshPartition * partition,
	DataAccessor * data_accessor = NULL);

	/// allocate all vectors
	virtual void initArrays();

	/// transfer internals from old to new elements
	void transferInternalValues(const ID & internal,
	std::vector<Element> & new_elements,
	Array<Real> & added_quads,
	Array<Real> & internal_values);

	/// compute the barycenter for a sub-element
	inline void getSubElementBarycenter(UInt element, UInt sub_element,
	ElementType type,
	Vector<Real> & barycenter,
	GhostType ghost_type) const;

	/// apply a constant eigen_grad_u on all quadrature points of a given material
	virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
	const ID & material_name,
	const GhostType ghost_type = _not_ghost);

	private:
	/// compute the real values of displacement, force, etc. on the enriched nodes
	void computeValuesOnEnrichedNodes();

	/* ------------------------------------------------------------------------ */
	/* Mesh Event Handler inherited members */
	/* ------------------------------------------------------------------------ */

	protected:
	virtual void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event);
	virtual void onNodesRemoved(const Array<UInt> & element_list,
	const Array<UInt> & new_numbering,
	const RemovedNodesEvent & event);
	virtual void onElementsAdded(const Array<Element> & nodes_list,
	const NewElementsEvent & event);
	virtual void
	onElementsRemoved(const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event);

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	virtual void onDump();

	virtual void addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind,
	bool padding_flag);

	virtual dumpers::Field * createElementalField(const std::string & field_name,
	- const std::string & group_name,
	- bool padding_flag,
	- const UInt & spatial_dimension,
	- ElementKind kind);
	+ const std::string & group_name,
	+ bool padding_flag,
	+ const UInt & spatial_dimension,
	+ ElementKind kind);

	virtual dumpers::Field * createNodalFieldReal(const std::string & field_name,
	- const std::string & group_name,
	- bool padding_flag);
	+ const std::string & group_name,
	+ bool padding_flag);

	/* --------------------------------------------------------------------------
	*/
	/* Accessors */
	/* --------------------------------------------------------------------------
	*/
	public:
	/// get the fe-engines per kind
	AKANTU_GET_MACRO(FEEnginesPerKind, fe_engines_per_kind,
	const FEEnginesPerKindMap &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// real displacements array
	Array<Real> * real_displacement;
	/// real forces array
	Array<Real> * real_force;
	/// real residuals array
	Array<Real> * real_residual;
	/// map between and new elements (needed when the interface is moving)
	ElementMap element_map;
	/// global connectivity ids updater
	GlobalIdsUpdater * global_ids_updater;
	/// map between element kind and corresponding FEEngine object
	FEEnginesPerKindMap fe_engines_per_kind;
	};

	/* -------------------------------------------------------------------------- */
	/* IGFEMMaterialSelector */
	/* -------------------------------------------------------------------------- */

	class DefaultMaterialIGFEMSelector : public DefaultMaterialSelector {
	public:
	DefaultMaterialIGFEMSelector(const SolidMechanicsModelIGFEM & model)
	: DefaultMaterialSelector(model.getMaterialByElement()),
	fallback_value_igfem(0) {}

	virtual UInt operator()(const Element & element) {
	if (Mesh::getKind(element.type) == _ek_igfem)
	return fallback_value_igfem;
	else
	return DefaultMaterialSelector::operator()(element);
	}

	void setIGFEMFallback(UInt f) { this->fallback_value_igfem = f; }

	protected:
	UInt fallback_value_igfem;
	};

	} // namespace akantu

	#if defined(AKANTU_INCLUDE_INLINE_IMPL)
	#include "solid_mechanics_model_igfem_inline_impl.hh"
	#endif

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_IGFEM_HH_ */
	diff --git a/extra_packages/igfem/src/solid_mechanics_model_igfem_inline_impl.hh b/extra_packages/igfem/src/solid_mechanics_model_igfem_inline_impl.hh
	index 4c708c938..3158409f9 100644
	--- a/extra_packages/igfem/src/solid_mechanics_model_igfem_inline_impl.hh
	+++ b/extra_packages/igfem/src/solid_mechanics_model_igfem_inline_impl.hh
	@@ -1,59 +1,59 @@
	/**
	* @file solid_mechanics_model_igfem_inline_impl.hh
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @date Wed Nov 4 15:53:52 2015
	*
	* @brief Implementation on inline functions for SMMIGFEM
	*
	*
	* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_SOLID_MECHANICS_MODEL_IGFEM_INLINE_IMPL_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_IGFEM_INLINE_IMPL_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	inline void SolidMechanicsModelIGFEM::getSubElementBarycenter(
	- UInt element, UInt sub_element, ElementType type,
	- Vector<Real> & barycenter, GhostType ghost_type) const {
	+ UInt element, UInt sub_element, ElementType type, Vector<Real> & barycenter,
	+ GhostType ghost_type) const {
	UInt * conn_val = this->mesh.getConnectivity(type, ghost_type).storage();
	UInt nb_sub_element_nodes =
	IGFEMHelper::getNbNodesPerSubElement(type, sub_element);
	UInt * sub_el_conn =
	IGFEMHelper::getSubElementConnectivity(type, sub_element);
	UInt nb_nodes_per_element = this->mesh.getNbNodesPerElement(type);
	const Array<Real> & node_coords = this->mesh.getNodes();

	Real local_coord[spatial_dimension * nb_sub_element_nodes];

	UInt offset = element * nb_nodes_per_element;
	for (UInt n = 0; n < nb_sub_element_nodes; ++n) {
	UInt index = conn_val[offset + sub_el_conn[n]];
	memcpy(local_coord + n * spatial_dimension,
	node_coords.storage() + index * spatial_dimension,
	spatial_dimension * sizeof(Real));
	}
	Math::barycenter(local_coord, nb_sub_element_nodes, spatial_dimension,
	barycenter.storage());
	}

	} // namespace akantu

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_IGFEM_INLINE_IMPL_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/force_based_dirichlet.hh b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/force_based_dirichlet.hh
	index 3839869bf..a859105fa 100644
	--- a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/force_based_dirichlet.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/force_based_dirichlet.hh
	@@ -1,130 +1,130 @@
	/**
	* @file force_based_dirichlet.hh
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief dirichlet boundary condition that tries to keep the force at a given
	* value
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_FORCE_BASED_DIRICHLET_HH_
	#define AST_FORCE_BASED_DIRICHLET_HH_

	// akantu
	#include "aka_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class ForceBasedDirichlet : public BC::Dirichlet::IncrementValue {

	protected:
	typedef const Array<Real> * RealArrayPtr;
	typedef const Array<Int> * IntArrayPtr;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ForceBasedDirichlet(SolidMechanicsModel & model, BC::Axis ax, Real target_f,
	Real mass = 0.)
	: IncrementValue(0., ax), model(model), mass(mass), velocity(0.),
	target_force(target_f), total_residual(0.) {}

	virtual ~ForceBasedDirichlet() {}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void updateTotalResidual() {
	this->total_residual = 0.;
	for (auto && subboundary : this->subboundaries) {
	this->total_residual +=
	integrateResidual(subboundary, this->model, this->axis);
	}
	}

	virtual Real update() {
	AKANTU_DEBUG_IN();

	this->updateTotalResidual();
	Real total_force = this->target_force + this->total_residual;

	Real a = total_force / this->mass;
	Real dt = model.getTimeStep();
	this->velocity += 0.5 * dt * a;
	this->value =
	this->velocity * dt + 0.5 * dt * dt * a; // increment position dx
	this->velocity += 0.5 * dt * a;

	AKANTU_DEBUG_OUT();
	return this->total_residual;
	}

	Real applyYourself() {
	AKANTU_DEBUG_IN();
	Real reaction = this->update();

	for (auto && subboundary : this->subboundaries) {
	this->model.applyBC(*this, subboundary);
	}

	AKANTU_DEBUG_OUT();
	return reaction;
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_SET_MACRO(Mass, mass, Real);
	AKANTU_SET_MACRO(TargetForce, target_force, Real);

	void insertSubBoundary(const std::string & sb_name) {
	this->subboundaries.insert(sb_name);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	typedef std::set<std::string> SubBoundarySet;

	protected:
	SolidMechanicsModel & model;
	SubBoundarySet subboundaries;

	Real mass;
	Real velocity;
	Real target_force;
	Real total_residual;
	};

	} // namespace akantu

	#endif /* AST_FORCE_BASED_DIRICHLET_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/inclined_flat_dirichlet.hh b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/inclined_flat_dirichlet.hh
	index 513ea3549..10b378ee2 100644
	--- a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/inclined_flat_dirichlet.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/inclined_flat_dirichlet.hh
	@@ -1,82 +1,82 @@
	/**
	* @file inclined_flat_dirichlet.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief inclined dirichlet
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_INCLINED_FLAT_DIRICHLET_HH_
	#define AST_INCLINED_FLAT_DIRICHLET_HH_

	// akantu
	#include "aka_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class InclinedFlatDirichlet : public BC::Dirichlet::DirichletFunctor {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	InclinedFlatDirichlet(Real val, BC::Axis ax, BC::Axis incl_ax,
	Real center_coord, Real tang)
	: DirichletFunctor(ax), value(val), incl_ax(incl_ax),
	center_coord(center_coord), tang(tang){};

	virtual ~InclinedFlatDirichlet() {}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline void operator()(UInt node, Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	AKANTU_DEBUG_IN();

	Real dist = coord(incl_ax) - this->center_coord;
	flags(axis) = true;
	primal(axis) = this->value + this->tang * dist;

	AKANTU_DEBUG_OUT();
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	Real value;
	BC::Axis incl_ax;
	Real center_coord;
	Real tang;
	};

	} // namespace akantu

	#endif /* AST_INCLINED_FLAT_DIRICHLET_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/spring_bc.hh b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/spring_bc.hh
	index e6105c662..05afbadbc 100644
	--- a/extra_packages/traction-at-split-node-contact/src/boundary_conditions/spring_bc.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/boundary_conditions/spring_bc.hh
	@@ -1,143 +1,143 @@
	/**
	* @file spring_bc.hh
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief spring boundary condition
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_SPRING_BC_HH_
	#define AST_SPRING_BC_HH_

	// simtools
	#include "force_based_dirichlet.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class SpringBC : public ForceBasedDirichlet {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SpringBC(SolidMechanicsModel & model, BC::Axis ax, Real stiffness,
	Real mass = 0.)
	: ForceBasedDirichlet(model, ax, 0., mass), stiffness(stiffness),
	elongation(0.) {}

	virtual ~SpringBC() {}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	virtual Real update() {
	AKANTU_DEBUG_IN();

	this->target_force = -this->stiffness * this->elongation;
	Real reaction = ForceBasedDirichlet::update();
	this->elongation += this->value;

	AKANTU_DEBUG_OUT();
	return reaction;
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Elongation, elongation, Real);

	inline void setToEquilibrium() {
	AKANTU_DEBUG_IN();

	this->updateTotalResidual();

	this->target_force = -this->total_residual;
	this->elongation = -this->target_force / this->stiffness;

	AKANTU_DEBUG_OUT();
	}

	/// change elongation
	/// dx > 0 -> target_force < 0
	inline void incrementElongation(Real dx) {
	AKANTU_DEBUG_IN();

	this->elongation += dx;

	AKANTU_DEBUG_OUT();
	}
	// friend std::ostream& operator<<(std::ostream& out, const SpringBC &
	// spring);
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	Real stiffness;
	Real elongation;
	};

	// class SpringBCRestricted : public SpringBC {
	// public:
	// SpringBCRestricted(BC::Axis ax, Real target_force, BC::Axis surface_axis,
	// Real min, Real max)
	// :SpringBC(ax, target_force), surface_axis(surface_axis), min(min),
	// max(max) {}

	// virtual ~SpringBCRestricted() {}

	// public:
	// inline void operator()(UInt node, Vector<bool> & flags, Vector<Real> &
	// primal, const Vector<Real> & coord) const {
	// if(coord(surface_axis) > min && coord(surface_axis) < max) {
	// SpringBC::operator()(node, flags, primal, coord);
	// }
	// }
	// private:
	// BC::Axis surface_axis;
	// Real min;
	// Real max;
	// };

	// std::ostream& operator<<(std::ostream& out, const SpringBC & spring) {
	// out << "Real total_residual: " << *spring.total_residual << std::endl;
	// out << "Real mass: " << spring.mass << std::endl;
	// out << "Real k: " << spring.k << std::endl;
	// out << "Real delta_x: " << spring.delta_x << std::endl;
	// out << "Real dt: " << spring.dt << std::endl;
	// out << "Real v: " << spring.v << std::endl;
	// out << "Real dx: " << spring.dx << std::endl;
	// out << "Real forcing_vel: " << spring.forcing_vel << std::endl;
	// return out;
	// }

	} // namespace akantu

	#endif /* AST_SPRING_BC_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/manual_restart.cc b/extra_packages/traction-at-split-node-contact/src/common/manual_restart.cc
	index 4af44dc70..73acca78f 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/manual_restart.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/common/manual_restart.cc
	@@ -1,135 +1,136 @@
	/**
	* @file manual_restart.cc
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Tools to do a restart
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "manual_restart.hh"
	#include "dof_manager_default.hh"
	#include "dof_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	void dumpArray(const Array<Real> & array, const std::string & fname) {
	std::ofstream outFile;
	outFile.open(fname.c_str());
	outFile.precision(9);
	outFile.setf(std::ios::scientific);
	UInt size = array.size();
	UInt nb_component = array.getNbComponent();
	outFile << size << std::endl;
	outFile << nb_component << std::endl;
	Array<Real>::const_iterator<Vector<Real>> tit = array.begin(nb_component);
	Array<Real>::const_iterator<Vector<Real>> tend = array.end(nb_component);
	for (; tit != tend; ++tit) {
	for (UInt c = 0; c < nb_component; ++c) {
	- if (c != 0)
	+ if (c != 0) {
	outFile << " ";
	+ }
	outFile << (*tit)(c);
	}
	outFile << std::endl;
	}
	outFile.close();
	}

	void loadArray(Array<Real> & array, const std::string & fname) {
	std::ifstream inFile;
	inFile.open(fname.c_str());
	inFile.precision(9);
	inFile.setf(std::ios::scientific);
	UInt size(0), nb_comp(0);
	inFile >> size;
	inFile >> nb_comp;
	AKANTU_DEBUG_ASSERT(array.getNbComponent() == nb_comp,
	"BAD NUM OF COMPONENTS");
	AKANTU_DEBUG_ASSERT(array.size() == size,
	"loadArray: number of data points in file ("
	<< size << ") does not correspond to array size ("
	<< array.size() << ")!!");
	Array<Real>::iterator<Vector<Real>> tit = array.begin(nb_comp);
	Array<Real>::iterator<Vector<Real>> tend = array.end(nb_comp);
	array.resize(size);
	for (UInt i(0); i < size; ++i, ++tit) {
	for (UInt c = 0; c < nb_comp; ++c) {
	inFile >> (*tit)(c);
	}
	}
	inFile.close();
	}

	/* -------------------------------------------------------------------------- */
	void loadRestart(akantu::SolidMechanicsModel & model, const std::string & fname,
	akantu::UInt prank) {

	const akantu::Mesh & mesh = model.getMesh();
	const akantu::UInt spatial_dimension = model.getMesh().getSpatialDimension();
	auto & dof_manager = dynamic_cast<DOFManagerDefault &>(model.getDOFManager());
	if (prank == 0) {
	akantu::Array<akantu::Real> full_reload_array(mesh.getNbGlobalNodes(),
	spatial_dimension);
	loadArray(full_reload_array, fname);
	dof_manager.getSynchronizer().scatter(model.getDisplacement(),
	full_reload_array);
	} else {
	dof_manager.getSynchronizer().scatter(model.getDisplacement());
	}
	}

	/* -------------------------------------------------------------------------- */
	void loadRestart(akantu::SolidMechanicsModel & model,
	const std::string & fname) {
	loadArray(model.getDisplacement(), fname);
	}

	/* -------------------------------------------------------------------------- */
	void dumpRestart(akantu::SolidMechanicsModel & model, const std::string & fname,
	akantu::UInt prank) {

	const akantu::Mesh & mesh = model.getMesh();
	const akantu::UInt spatial_dimension = model.getMesh().getSpatialDimension();
	auto & dof_manager = dynamic_cast<DOFManagerDefault &>(model.getDOFManager());

	if (prank == 0) {
	akantu::Array<akantu::Real> full_array(mesh.getNbGlobalNodes(),
	spatial_dimension);
	dof_manager.getSynchronizer().gather(model.getDisplacement(), full_array);
	dumpArray(full_array, fname);
	} else {
	dof_manager.getSynchronizer().gather(model.getDisplacement());
	}
	}

	/* -------------------------------------------------------------------------- */
	void dumpRestart(akantu::SolidMechanicsModel & model,
	const std::string & fname) {
	dumpArray(model.getDisplacement(), fname);
	}
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/manual_restart.hh b/extra_packages/traction-at-split-node-contact/src/common/manual_restart.hh
	index 5ee0ff94e..26d7126e0 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/manual_restart.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/common/manual_restart.hh
	@@ -1,53 +1,53 @@
	/**
	* @file manual_restart.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Restart tools header
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @file manual_restart.hh
	* @author Dana Christen <dana.christen@epfl.ch>
	* @date May 15, 2013
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "solid_mechanics_model.hh"

	void dumpArray(const akantu::Array<akantu::Real> & array,
	const std::string & fname);

	void loadArray(akantu::Array<akantu::Real> & array, const std::string & fname);
	void loadRestart(akantu::SolidMechanicsModel & model, const std::string & fname,
	akantu::UInt prank);
	void loadRestart(akantu::SolidMechanicsModel & model,
	const std::string & fname);
	void dumpRestart(akantu::SolidMechanicsModel & model, const std::string & fname,
	akantu::UInt prank);
	void dumpRestart(akantu::SolidMechanicsModel & model,
	const std::string & fname);
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.cc b/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.cc
	index 2727837d0..a79cbce8e 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.cc
	@@ -1,457 +1,461 @@
	/**
	* @file parameter_reader.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Mar 16 2018
	*
	* @brief implementation of parameter reader
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// std
	#include <algorithm>
	#include <fstream>
	#include <iostream>
	#include <utility>

	// simtools
	#include "parameter_reader.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-ParameterReader::ParameterReader()
	- : data_types(), element_type_data(), string_data(), int_data(), uint_data(),
	- real_data(), bool_data() {
	+ParameterReader::ParameterReader() {
	AKANTU_DEBUG_IN();

	// setup of types of element
	data_types.insert("elementtype");
	data_types.insert("string");
	data_types.insert("uint");
	data_types.insert("int");
	data_types.insert("real");
	data_types.insert("bool");
	// data_types.insert("surface");

	// define conversion maps
	_input_to_akantu_element_types["_segment_2"] = akantu::_segment_2;
	_input_to_akantu_element_types["_segment_3"] = akantu::_segment_3;
	_input_to_akantu_element_types["_triangle_3"] = akantu::_triangle_3;
	_input_to_akantu_element_types["_triangle_6"] = akantu::_triangle_6;
	_input_to_akantu_element_types["_tetrahedron_4"] = akantu::_tetrahedron_4;
	_input_to_akantu_element_types["_tetrahedron_10"] = akantu::_tetrahedron_10;
	_input_to_akantu_element_types["_quadrangle_4"] = akantu::_quadrangle_4;
	_input_to_akantu_element_types["_quadrangle_8"] = akantu::_quadrangle_8;
	_input_to_akantu_element_types["_hexahedron_8"] = akantu::_hexahedron_8;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ParameterReader::readInputFile(std::string file_name) {
	AKANTU_DEBUG_IN();

	char comment_char = '#';
	char equal_char = '=';

	// open a file called file name
	std::ifstream infile;
	infile.open(file_name.c_str());

	if (!infile.good()) {
	std::cerr << "Cannot open file " << file_name << "!!!" << std::endl;
	exit(EXIT_FAILURE);
	}

	std::string line;
	std::string clean_line;
	while (infile.good()) {
	getline(infile, line);
	clean_line = line;

	// take out comments
	size_t found_comment;
	found_comment = line.find_first_of(comment_char);
	- if (found_comment != std::string::npos)
	+ if (found_comment != std::string::npos) {
	clean_line = line.substr(0, found_comment);
	- if (clean_line.empty())
	+ }
	+ if (clean_line.empty()) {
	continue;
	+ }

	std::stringstream sstr(clean_line);

	// check if data type exists
	std::string type;
	sstr >> type;
	std::transform(type.begin(), type.end(), type.begin(), ::tolower);
	if (this->data_types.find(type) == this->data_types.end()) {
	std::cerr << " * WARNING * Data type " << type << " does not exist"
	<< " in this input data structure. Ignore line: ";
	std::cerr << clean_line << std::endl;
	continue;
	}

	std::string keyword;
	std::string equal;
	std::string value;

	// get keyword
	sstr >> keyword;
	size_t equal_p = keyword.find_first_of(equal_char);
	if (equal_p != std::string::npos) {
	equal = keyword.substr(equal_p, std::string::npos);
	keyword = keyword.substr(0, equal_p);
	}

	// get equal
	- if (equal.empty())
	+ if (equal.empty()) {
	sstr >> equal;
	+ }
	if (equal.length() != 1) {
	value = equal.substr(1, std::string::npos);
	equal = equal[0];
	}
	if (equal[0] != equal_char) {
	std::cerr << " * WARNING * Unrespected convention! Ignore line: ";
	std::cerr << clean_line << std::endl;
	continue;
	}

	// get value
	- if (value.empty())
	+ if (value.empty()) {
	sstr >> value;
	+ }

	// no value
	if (value.empty()) {
	std::cerr << " * WARNING * No value given! Ignore line: ";
	std::cerr << clean_line << std::endl;
	continue;
	}

	// put value in map
	std::stringstream convert(value);
	- if (type.compare("elementtype") == 0) {
	+ if (type == "elementtype") {
	std::map<std::string, akantu::ElementType>::const_iterator it;
	it = this->_input_to_akantu_element_types.find(value);
	- if (it != this->_input_to_akantu_element_types.end())
	+ if (it != this->_input_to_akantu_element_types.end()) {
	this->element_type_data.insert(std::make_pair(keyword, it->second));
	- else {
	+ } else {
	std::cerr << " * WARNING * ElementType " << value
	<< " does not exist. Ignore line: ";
	std::cerr << clean_line << std::endl;
	continue;
	}
	- } else if (type.compare("string") == 0) {
	+ } else if (type == "string") {
	this->string_data.insert(std::make_pair(keyword, value));
	}
	/*
	else if (type.compare("surface") == 0) {
	//Surface surf;
	UInt surf;
	convert >> surf;
	//this->surface_data.insert(std::make_pair(keyword,surf));
	this->uint_data.insert(std::make_pair(keyword,surf));
	}
	*/
	- else if (type.compare("int") == 0) {
	+ else if (type == "int") {
	Int i;
	convert >> i;
	this->int_data.insert(std::make_pair(keyword, i));
	- } else if (type.compare("uint") == 0) {
	+ } else if (type == "uint") {
	UInt i;
	convert >> i;
	this->uint_data.insert(std::make_pair(keyword, i));
	- } else if (type.compare("real") == 0) {
	+ } else if (type == "real") {
	Real r;
	convert >> r;
	this->real_data.insert(std::make_pair(keyword, r));
	- } else if (type.compare("bool") == 0) {
	+ } else if (type == "bool") {
	std::transform(value.begin(), value.end(), value.begin(), ::tolower);
	bool b;
	- if (value.compare("true") == 0)
	+ if (value == "true") {
	b = true;
	- else if (value.compare("false") == 0)
	+ } else if (value == "false") {
	b = false;
	- else {
	+ } else {
	std::cerr << " * WARNING * boolean cannot be " << value
	<< ". Ignore line: ";
	std::cerr << clean_line << std::endl;
	continue;
	}
	this->bool_data.insert(std::make_pair(keyword, b));
	} else {
	std::cerr << " * ERROR * Could not add data to InputData for line: ";
	std::cerr << clean_line << std::endl;
	continue;
	exit(EXIT_FAILURE);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ParameterReader::writeInputFile(std::string file_name) const {
	AKANTU_DEBUG_IN();

	// open file to write input information
	std::ofstream outfile;
	outfile.open(file_name.c_str());

	// element type
	- for (std::map<std::string, akantu::ElementType>::const_iterator it =
	- element_type_data.begin();
	- it != element_type_data.end(); ++it) {
	- for (std::map<std::string, ElementType>::const_iterator et =
	- _input_to_akantu_element_types.begin();
	+ for (auto it = element_type_data.begin(); it != element_type_data.end();
	+ ++it) {
	+ for (auto et = _input_to_akantu_element_types.begin();
	et != _input_to_akantu_element_types.end(); ++et) {
	if (it->second == et->second) {
	outfile << "ElementType " << it->first << " = " << et->first
	<< std::endl;
	continue;
	}
	}
	}

	// string
	- for (std::map<std::string, std::string>::const_iterator it =
	- string_data.begin();
	- it != string_data.end(); ++it)
	+ for (auto it = string_data.begin(); it != string_data.end(); ++it) {
	outfile << "string " << it->first << " = " << it->second << std::endl;
	+ }

	// Surface
	/*
	for (std::map<std::string, akantu::Surface>::const_iterator it =
	surface_data.begin();
	it != surface_data.end(); ++it)
	outfile << "Surface " << it->first << " = " << it->second << std::endl;
	*/
	// Int
	- for (std::map<std::string, akantu::Int>::const_iterator it = int_data.begin();
	- it != int_data.end(); ++it)
	+ for (auto it = int_data.begin(); it != int_data.end(); ++it) {
	outfile << "Int " << it->first << " = " << it->second << std::endl;
	+ }

	// UInt
	- for (std::map<std::string, akantu::UInt>::const_iterator it =
	- uint_data.begin();
	- it != uint_data.end(); ++it)
	+ for (auto it = uint_data.begin(); it != uint_data.end(); ++it) {
	outfile << "UInt " << it->first << " = " << it->second << std::endl;
	+ }

	// Real
	- for (std::map<std::string, akantu::Real>::const_iterator it =
	- real_data.begin();
	- it != real_data.end(); ++it)
	+ for (auto it = real_data.begin(); it != real_data.end(); ++it) {
	outfile << "Real " << it->first << " = " << it->second << std::endl;
	+ }

	// Bool
	- for (std::map<std::string, bool>::const_iterator it = bool_data.begin();
	- it != bool_data.end(); ++it) {
	+ for (auto it = bool_data.begin(); it != bool_data.end(); ++it) {
	std::string b = "false";
	- if (it->second)
	+ if (it->second) {
	b = "true";
	+ }
	outfile << "bool " << it->first << " = " << b << std::endl;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	akantu::UInt ParameterReader::get<akantu::UInt>(std::string key) const {
	std::map<std::string, akantu::UInt>::const_iterator it;
	it = this->uint_data.find(key);

	// if not in map
	if (it == this->uint_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "UInt " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <>
	akantu::ElementType
	ParameterReader::get<akantu::ElementType>(std::string key) const {
	std::map<std::string, akantu::ElementType>::const_iterator it;
	it = this->element_type_data.find(key);

	// if not in map
	if (it == this->element_type_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "ElementType " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <>
	std::string ParameterReader::get<std::string>(std::string key) const {
	std::map<std::string, std::string>::const_iterator it;
	it = this->string_data.find(key);

	// if not in map
	if (it == this->string_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "string " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	/*
	template<>
	akantu::Surface ParameterData::get<akantu::Surface>(std::string key) const {
	std::map<std::string,akantu::Surface>::const_iterator it;
	it = this->surface_data.find(key);

	// if not in map
	if (it == this->surface_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "Surface " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	else
	return it->second;
	}
	*/

	/* -------------------------------------------------------------------------- */
	template <>
	akantu::Int ParameterReader::get<akantu::Int>(std::string key) const {
	std::map<std::string, akantu::Int>::const_iterator it;
	it = this->int_data.find(key);

	// if not in map
	if (it == this->int_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "Int " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <>
	akantu::Real ParameterReader::get<akantu::Real>(std::string key) const {
	std::map<std::string, akantu::Real>::const_iterator it;
	it = this->real_data.find(key);

	// if not in map
	if (it == this->real_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "Real " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <> bool ParameterReader::get<bool>(std::string key) const {
	std::map<std::string, bool>::const_iterator it;
	it = this->bool_data.find(key);

	// if not in map
	if (it == this->bool_data.end()) {
	std::cerr << " * ERROR * This data was not in input file. "
	<< "You need the following line in your input file: ";
	std::cerr << "bool " << key << " = ???" << std::endl;
	exit(EXIT_FAILURE);
	}

	- else
	+ else {
	return it->second;
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <> bool ParameterReader::has<bool>(std::string key) const {
	std::map<std::string, bool>::const_iterator it;
	it = this->bool_data.find(key);
	return (it != this->bool_data.end());
	}
	template <> bool ParameterReader::has<std::string>(std::string key) const {
	std::map<std::string, std::string>::const_iterator it;
	it = this->string_data.find(key);
	return (it != this->string_data.end());
	}
	template <> bool ParameterReader::has<akantu::Int>(std::string key) const {
	std::map<std::string, akantu::Int>::const_iterator it;
	it = this->int_data.find(key);
	return (it != this->int_data.end());
	}
	template <> bool ParameterReader::has<akantu::UInt>(std::string key) const {
	std::map<std::string, akantu::UInt>::const_iterator it;
	it = this->uint_data.find(key);
	return (it != this->uint_data.end());
	}
	template <> bool ParameterReader::has<akantu::Real>(std::string key) const {
	std::map<std::string, akantu::Real>::const_iterator it;
	it = this->real_data.find(key);
	return (it != this->real_data.end());
	}

	/* -------------------------------------------------------------------------- */
	void ParameterReader::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();

	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "ParameterReader [" << std::endl;
	/*
	stream << space << this->element_type_data << std::endl;
	stream << space << this->string_data << std::endl;
	stream << space << this->surface_data << std::endl;
	stream << space << this->int_data << std::endl;
	stream << space << this->uint_data << std::endl;
	stream << space << this->real_data << std::endl;
	stream << space << this->bool_data << std::endl;
	*/
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.hh b/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.hh
	index 504218710..d8e9ef118 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/common/parameter_reader.hh
	@@ -1,111 +1,111 @@
	/**
	* @file parameter_reader.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief for simulations to read parameters from an input file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_PARAMETER_READER_HH_
	#define AST_PARAMETER_READER_HH_

	/* -------------------------------------------------------------------------- */
	// std
	#include <map>
	#include <set>

	// akantu
	#include "aka_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class ParameterReader {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ParameterReader();
	- virtual ~ParameterReader(){};
	+ virtual ~ParameterReader() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// read input file
	void readInputFile(std::string file_name);

	/// write input file
	void writeInputFile(std::string file_name) const;

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	///
	template <typename T> T get(std::string key) const;

	template <typename T> bool has(std::string key) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// type of data available
	std::set<std::string> data_types;

	/// data
	std::map<std::string, akantu::ElementType> element_type_data;
	std::map<std::string, std::string> string_data;
	std::map<std::string, akantu::Int> int_data;
	std::map<std::string, akantu::UInt> uint_data;
	std::map<std::string, akantu::Real> real_data;
	std::map<std::string, bool> bool_data;

	/// convert string to element type
	std::map<std::string, ElementType> _input_to_akantu_element_types;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "parameter_reader_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const ParameterReader & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_PARAMETER_READER_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/synchronized_array.hh b/extra_packages/traction-at-split-node-contact/src/common/synchronized_array.hh
	index 7b8757f76..a88c6ca35 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/synchronized_array.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/common/synchronized_array.hh
	@@ -1,204 +1,204 @@
	/**
	* @file synchronized_array.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief synchronized array: a array can be registered to another (hereafter
	* called top) array. If an element is added to or removed from the top array,
	* the registered array removes or adds at the same position an element. The two
	* arrays stay therefore synchronized.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_SYNCHRONIZED_ARRAY_HH_
	#define AST_SYNCHRONIZED_ARRAY_HH_

	/* -------------------------------------------------------------------------- */
	// std
	#include <vector>

	// akantu
	#include "aka_array.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	enum SyncChoice { _added, _deleted };

	/* -------------------------------------------------------------------------- */
	class SynchronizedArrayBase {
	public:
	SynchronizedArrayBase() = default;
	~SynchronizedArrayBase() = default;

	virtual ID getID() const { return "call should be virtual"; };

	virtual UInt syncDeletedElements(std::vector<UInt> & delete_el) = 0;
	virtual UInt syncAddedElements(UInt nb_added_el) = 0;
	};

	/* -------------------------------------------------------------------------- */
	template <class T>
	class SynchronizedArray : public SynchronizedArrayBase, protected Array<T> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using value_type = typename Array<T>::value_type;
	using reference = typename Array<T>::reference;
	using pointer_type = typename Array<T>::pointer_type;
	using const_reference = typename Array<T>::const_reference;

	SynchronizedArray(UInt size, UInt nb_component, const_reference value,
	const ID & id, const_reference default_value,
	const std::string & restart_name);
	~SynchronizedArray() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// push_back
	template <typename P> inline void push_back(P && value);

	/// erase
	inline void erase(UInt i);
	// template<typename R>
	// inline void erase(const iterator<R> & it);

	/// synchronize elements
	void syncElements(SyncChoice sync_choice);

	/// dump restart file
	void dumpRestartFile(const std::string & file_name) const;

	/// read restart file
	void readRestartFile(const std::string & file_name);

	/// register depending array
	void registerDependingArray(SynchronizedArrayBase & array);

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/// find position of element
	Int find(const T & elem) const { return Array<T>::find(elem); };

	/// set values to zero
	inline void zero() { Array<T>::zero(); };
	// inline void clear() { memset(values, 0, sizenb_componentsizeof(T)); };

	/// set all entries of the array to the value t
	/// @param t value to fill the array with
	inline void set(T t) { Array<T>::set(t); }

	/// set
	template <template <typename> class C> inline void set(const C<T> & vm) {
	Array<T>::set(vm);
	}

	/// set all entries of the array to value t and set default value
	inline void setAndChangeDefault(T t) {
	this->set(t);
	this->default_value = t;
	}

	/// copy the content of an other array
	void copy(const SynchronizedArray<T> & vect) { Array<T>::copy(vect); };

	/// give the address of the memory allocated for this array
	T * storage() const { return Array<T>::storage(); };
	// T * storage() const { return this->values; };

	// get nb component
	UInt getNbComponent() const { return Array<T>::getNbComponent(); };

	protected:
	UInt syncDeletedElements(std::vector<UInt> & del_elements) override;
	UInt syncAddedElements(UInt nb_add_elements) override;

	/* ------------------------------------------------------------------------ */
	/* Operators */
	/* ------------------------------------------------------------------------ */
	public:
	inline reference operator()(UInt i, UInt j = 0) {
	return Array<T>::operator()(i, j);
	}
	inline const_reference operator()(UInt i, UInt j = 0) const {
	return Array<T>::operator()(i, j);
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_SET_MACRO(DefaultValue, default_value, T);

	UInt size() const { return this->size_; };

	ID getID() const override { return Array<T>::getID(); };

	const Array<T> & getArray() const {
	const Array<T> & a = (dynamic_cast<const Array<T> >(this));
	return a;
	};

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// init value when new elements added
	T default_value;

	/// restart file_name
	const std::string restart_name;

	/// elements that have been deleted
	std::vector<UInt> deleted_elements;

	/// number of elements to add
	UInt nb_added_elements;

	/// pointers to arrays to be updated
	std::vector<SynchronizedArrayBase *> depending_arrays;
	};

	/// standard output stream operator
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const SynchronizedArray<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "synchronized_array_inline_impl.hh"

	#endif /* AST_SYNCHRONIZED_ARRAY_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/common/synchronized_array_inline_impl.hh b/extra_packages/traction-at-split-node-contact/src/common/synchronized_array_inline_impl.hh
	index bf5e6eadf..5bac674fd 100644
	--- a/extra_packages/traction-at-split-node-contact/src/common/synchronized_array_inline_impl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/common/synchronized_array_inline_impl.hh
	@@ -1,70 +1,71 @@
	/**
	* @file synchronized_array_inline_impl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Mar 16 2018
	*
	* @brief inlined methods for the synchronized array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "synchronized_array.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <typename T>
	template <typename P>
	inline void SynchronizedArray<T>::push_back(P && value) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(deleted_elements.size() == 0,
	"Cannot push_back element if SynchronizedArray"
	<< " is already modified without synchronization");

	Array<T>::push_back(std::forward<P>(value));
	this->nb_added_elements++;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> inline void SynchronizedArray<T>::erase(UInt i) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(nb_added_elements == 0,
	"Cannot erase element if SynchronizedArray"
	<< " is already modified without synchronization");

	- for (UInt j = 0; j < this->nb_component; ++j)
	+ for (UInt j = 0; j < this->nb_component; ++j) {
	this->values[i * this->nb_component + j] =
	this->values[(this->size_ - 1) * this->nb_component + j];
	+ }
	this->size_--;

	this->deleted_elements.push_back(i);

	AKANTU_DEBUG_OUT();
	}

	-}
	+} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.cc b/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.cc
	index b3250b05c..9bd6a1e21 100644
	--- a/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.cc
	@@ -1,73 +1,73 @@
	/**
	* @file boundary_functions.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Tue Feb 20 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief functions for boundaries
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_functions.hh"
	#include "communicator.hh"
	#include "element_group.hh"
	#include "node_group.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Real integrateResidual(const std::string & sub_boundary_name,
	const SolidMechanicsModel & model, UInt dir) {
	Real int_res = 0.;

	const Mesh & mesh = model.getMesh();
	const Array<Real> & residual = model.getInternalForce();

	const ElementGroup & boundary = mesh.getElementGroup(sub_boundary_name);
	- for (auto & node : boundary.getNodeGroup().getNodes()) {
	+ for (const auto & node : boundary.getNodeGroup().getNodes()) {
	bool is_local_node = mesh.isLocalOrMasterNode(node);
	if (is_local_node) {
	int_res += residual(node, dir);
	}
	}

	mesh.getCommunicator().allReduce(int_res, SynchronizerOperation::_sum);
	return int_res;
	}

	/* -------------------------------------------------------------------------- */
	void boundaryFix(Mesh & mesh,
	const std::vector<std::string> & sub_boundary_names) {
	for (auto && eg : sub_boundary_names) {
	if (mesh.elementGroupExists(eg)) {
	mesh.createElementGroup(eg, mesh.getSpatialDimension() -
	1); // empty element group
	}
	}
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.hh b/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.hh
	index 79505c795..07d05253b 100644
	--- a/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/functions/boundary_functions.hh
	@@ -1,56 +1,56 @@
	/**
	* @file boundary_functions.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief functions for boundaries
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BOUNDARY_FUNCTIONS_HH_
	#define AKANTU_BOUNDARY_FUNCTIONS_HH_

	namespace akantu {
	class SolidMechanicsModel;
	}

	namespace akantu {

	Real integrateResidual(const std::string & sub_boundary_name,
	const SolidMechanicsModel & model, UInt dir);

	/// this is a fix so that all subboundaries exist on all procs
	void boundaryFix(Mesh & mesh,
	const std::vector<std::string> & sub_boundary_names);

	} // namespace akantu

	#endif /* AKANTU_BOUNDARY_FUNCTIONS_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/functions/node_filter.hh b/extra_packages/traction-at-split-node-contact/src/functions/node_filter.hh
	index 038b219ad..86477fb8a 100644
	--- a/extra_packages/traction-at-split-node-contact/src/functions/node_filter.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/functions/node_filter.hh
	@@ -1,114 +1,114 @@
	/**
	* @file node_filter.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Tue Feb 20 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief to filter nodes with functors
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NODE_FILTER_HH_
	#define AST_NODE_FILTER_HH_

	/* -------------------------------------------------------------------------- */
	// akantu
	#include "aka_common.hh"
	#include "mesh_filter.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class GeometryFilter : public NodeFilterFunctor {

	public:
	GeometryFilter(const Mesh & mesh, UInt dir, Real limit)
	: NodeFilterFunctor(), mesh(mesh), dir(dir), limit(limit) {
	this->positions = &(mesh.getNodes());
	};
	~GeometryFilter(){};

	bool operator()(UInt node) { AKANTU_TO_IMPLEMENT(); };

	protected:
	const Mesh & mesh;
	UInt dir;
	Real limit;
	const Array<Real> * positions;
	};

	/* -------------------------------------------------------------------------- */
	class FilterPositionsGreaterThan : public GeometryFilter {
	public:
	FilterPositionsGreaterThan(const Mesh & mesh, UInt dir, Real limit)
	: GeometryFilter(mesh, dir, limit){};
	~FilterPositionsGreaterThan(){};

	bool operator()(UInt node) {
	AKANTU_DEBUG_IN();
	bool to_filter = true;
	if ((*this->positions)(node, this->dir) > this->limit)
	to_filter = false;
	AKANTU_DEBUG_OUT();
	return to_filter;
	};
	};

	/* -------------------------------------------------------------------------- */
	class FilterPositionsLessThan : public GeometryFilter {
	public:
	FilterPositionsLessThan(const Mesh & mesh, UInt dir, Real limit)
	: GeometryFilter(mesh, dir, limit){};
	~FilterPositionsLessThan(){};

	bool operator()(UInt node) {
	AKANTU_DEBUG_IN();
	bool to_filter = true;
	if ((*this->positions)(node, this->dir) < this->limit)
	to_filter = false;
	AKANTU_DEBUG_OUT();
	return to_filter;
	};
	};

	/* -------------------------------------------------------------------------- */
	// this filter is erase because the convention of filter has changed!!
	// filter == true -> keep node

	// template<class FilterType>
	// void applyNodeFilter(Array<UInt> & nodes, FilterType & filter) {

	// Array<UInt>::iterator<> it = nodes.begin();

	// for (; it != nodes.end(); ++it) {
	// if (filter(*it)) {
	// it = nodes.erase(it);
	// }
	// }
	// };

	} // namespace akantu

	#endif /* AST_NODE_FILTER_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb.hh
	index cbca0c8f5..29fca2046 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb.hh
	@@ -1,108 +1,108 @@
	/**
	* @file ntn_friclaw_coulomb.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief coulomb friction with \mu_s = \mu_k (constant)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICLAW_COULOMB_HH_
	#define AST_NTN_FRICLAW_COULOMB_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_no_regularisation.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation = NTNFricRegNoRegularisation>
	class NTNFricLawCoulomb : public Regularisation {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricLawCoulomb(NTNBaseContact & contact, const ID & id = "coulomb");
	- virtual ~NTNFricLawCoulomb(){};
	+ ~NTNFricLawCoulomb() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register synchronizedarrays for sync
	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;

	/// dump restart file
	- virtual void dumpRestart(const std::string & file_name) const;
	+ void dumpRestart(const std::string & file_name) const override;

	/// read restart file
	- virtual void readRestart(const std::string & file_name);
	+ void readRestart(const std::string & file_name) override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// compute frictional strength according to friction law
	- virtual void computeFrictionalStrength();
	+ void computeFrictionalStrength() override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	// friction coefficient
	SynchronizedArray<Real> mu;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <class Regularisation>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTNFricLawCoulomb<Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntn_friclaw_coulomb_tmpl.hh"

	#endif /* AST_NTN_FRICLAW_COULOMB_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb_tmpl.hh
	index df46a255d..29259fa32 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_coulomb_tmpl.hh
	@@ -1,168 +1,168 @@
	/**
	* @file ntn_friclaw_coulomb_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of coulomb friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_nodal_field.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	NTNFricLawCoulomb<Regularisation>::NTNFricLawCoulomb(NTNBaseContact & contact,
	const ID & id)
	- : Regularisation(contact, id),
	- mu(0, 1, 0., id + ":mu", 0., "mu") {
	+ : Regularisation(contact, id), mu(0, 1, 0., id + ":mu", 0., "mu") {
	AKANTU_DEBUG_IN();

	Regularisation::registerSynchronizedArray(this->mu);

	this->registerParam("mu", this->mu, _pat_parsmod, "friction coefficient");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::computeFrictionalStrength() {
	AKANTU_DEBUG_IN();

	// get contact arrays
	const SynchronizedArray<bool> & is_in_contact =
	this->internalGetIsInContact();
	const SynchronizedArray<Real> & pressure = this->internalGetContactPressure();

	// array to fill
	SynchronizedArray<Real> & strength = this->internalGetFrictionalStrength();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// node pair is NOT in contact
	- if (!is_in_contact(n))
	+ if (!is_in_contact(n)) {
	strength(n) = 0.;

	- // node pair is in contact
	- else {
	+ // node pair is in contact
	+ } else {
	// compute frictional strength
	strength(n) = this->mu(n) * pressure(n);
	}
	}

	Regularisation::computeFrictionalStrength();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->mu.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::dumpRestart(
	const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->mu.dumpRestartFile(file_name);

	Regularisation::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::readRestart(
	const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->mu.readRestartFile(file_name);

	Regularisation::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricLawCoulomb [" << std::endl;
	Regularisation::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawCoulomb<Regularisation>::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "mu") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->mu.getArray()));
	}
	/*
	else if (field_id == "frictional_contact_pressure") {
	this->internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new
	DumperIOHelper::NodalField<Real>(this->frictional_contact_pressure.getArray()));
	}
	*/
	else {
	Regularisation::addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive.hh
	index c1570427f..7fa178a28 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive.hh
	@@ -1,115 +1,115 @@
	/**
	* @file ntn_friclaw_linear_cohesive.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief linear cohesive law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICLAW_LINEAR_COHESIVE_HH_
	#define AST_NTN_FRICLAW_LINEAR_COHESIVE_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_no_regularisation.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation = NTNFricRegNoRegularisation>
	class NTNFricLawLinearCohesive : public Regularisation {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricLawLinearCohesive(NTNBaseContact & contact,
	const ID & id = "linear_cohesive");
	- virtual ~NTNFricLawLinearCohesive(){};
	+ ~NTNFricLawLinearCohesive() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register synchronizedarrays for sync
	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;

	/// dump restart file
	- virtual void dumpRestart(const std::string & file_name) const;
	+ void dumpRestart(const std::string & file_name) const override;

	/// read restart file
	- virtual void readRestart(const std::string & file_name);
	+ void readRestart(const std::string & file_name) override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// compute frictional strength according to friction law
	- virtual void computeFrictionalStrength();
	+ void computeFrictionalStrength() override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	// fracture energy
	SynchronizedArray<Real> G_c;

	// peak value of cohesive law
	SynchronizedArray<Real> tau_c;

	// residual value of cohesive law (for slip > d_c)
	SynchronizedArray<Real> tau_r;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <class Regularisation>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTNFricLawLinearCohesive<Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntn_friclaw_linear_cohesive_tmpl.hh"

	#endif /* AST_NTN_FRICLAW_LINEAR_COHESIVE_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive_tmpl.hh
	index fee59ce33..66d45c5f6 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_cohesive_tmpl.hh
	@@ -1,190 +1,190 @@
	/**
	* @file ntn_friclaw_linear_cohesive_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of linear cohesive law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	//#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	NTNFricLawLinearCohesive<Regularisation>::NTNFricLawLinearCohesive(
	NTNBaseContact & contact, const ID & id)
	- : Regularisation(contact, id),
	- G_c(0, 1, 0., id + ":G_c", 0., "G_c"),
	+ : Regularisation(contact, id), G_c(0, 1, 0., id + ":G_c", 0., "G_c"),
	tau_c(0, 1, 0., id + ":tau_c", 0., "tau_c"),
	tau_r(0, 1, 0., id + ":tau_r", 0., "tau_r") {
	AKANTU_DEBUG_IN();

	Regularisation::registerSynchronizedArray(this->G_c);
	Regularisation::registerSynchronizedArray(this->tau_c);
	Regularisation::registerSynchronizedArray(this->tau_r);

	this->registerParam("G_c", this->G_c, _pat_parsmod, "fracture energy");
	this->registerParam("tau_c", this->tau_c, _pat_parsmod,
	"peak shear strength");
	this->registerParam("tau_r", this->tau_r, _pat_parsmod,
	"residual shear strength");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::computeFrictionalStrength() {
	AKANTU_DEBUG_IN();

	// get arrays
	const SynchronizedArray<bool> & is_in_contact =
	this->internalGetIsInContact();
	// const SynchronizedArray<Real> & slip = this->internalGetSlip();
	const SynchronizedArray<Real> & slip = this->internalGetCumulativeSlip();

	// array to fill
	SynchronizedArray<Real> & strength = this->internalGetFrictionalStrength();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// node pair is NOT in contact
	- if (!is_in_contact(n))
	+ if (!is_in_contact(n)) {
	strength(n) = 0.;

	- // node pair is in contact
	- else {
	+ // node pair is in contact
	+ } else {
	if (this->G_c(n) == 0.) {
	// strength(n) = 0.;
	strength(n) = this->tau_r(n);
	} else {
	Real slope = (this->tau_c(n) - this->tau_r(n)) *
	(this->tau_c(n) - this->tau_r(n)) / (2 * this->G_c(n));
	// no strength < tau_r
	strength(n) =
	std::max(this->tau_c(n) - slope * slip(n), this->tau_r(n));
	// strength(n) = std::max(this->tau_c(n) - slope * slip(n), 0.); // no
	// negative strength
	}
	}
	}

	Regularisation::computeFrictionalStrength();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->G_c.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::dumpRestart(
	const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->G_c.dumpRestartFile(file_name);
	this->tau_c.dumpRestartFile(file_name);
	this->tau_r.dumpRestartFile(file_name);

	Regularisation::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::readRestart(
	const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->G_c.readRestartFile(file_name);
	this->tau_c.readRestartFile(file_name);
	this->tau_r.readRestartFile(file_name);

	Regularisation::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricLawLinearCohesive [" << std::endl;
	Regularisation::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearCohesive<Regularisation>::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "G_c") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->G_c.getArray()));
	} else if (field_id == "tau_c") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->tau_c.getArray()));
	} else if (field_id == "tau_r") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->tau_r.getArray()));
	} else {
	Regularisation::addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening.hh
	index 88edfca2a..31addae6e 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening.hh
	@@ -1,117 +1,117 @@
	/**
	* @file ntn_friclaw_linear_slip_weakening.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief linear slip weakening
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_HH_
	#define AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_friclaw_coulomb.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation = NTNFricRegNoRegularisation>
	class NTNFricLawLinearSlipWeakening : public NTNFricLawCoulomb<Regularisation> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricLawLinearSlipWeakening(NTNBaseContact & contact,
	const ID & id = "linear_slip_weakening");
	- virtual ~NTNFricLawLinearSlipWeakening(){};
	+ ~NTNFricLawLinearSlipWeakening() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register synchronizedarrays for sync
	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;

	/// dump restart file
	- virtual void dumpRestart(const std::string & file_name) const;
	+ void dumpRestart(const std::string & file_name) const override;

	/// read restart file
	- virtual void readRestart(const std::string & file_name);
	+ void readRestart(const std::string & file_name) override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// compute frictional strength according to friction law
	- virtual void computeFrictionalStrength();
	+ void computeFrictionalStrength() override;
	/// computes the friction coefficient as a function of slip
	virtual void computeFrictionCoefficient();

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	// static coefficient of friction
	SynchronizedArray<Real> mu_s;

	// kinetic coefficient of friction
	SynchronizedArray<Real> mu_k;

	// Dc the length over which slip weakening happens
	SynchronizedArray<Real> d_c;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <class Regularisation>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTNFricLawLinearSlipWeakening<Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntn_friclaw_linear_slip_weakening_tmpl.hh"

	#endif /* AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing.hh
	index 7a7590daf..ccd85cbb6 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing.hh
	@@ -1,96 +1,96 @@
	/**
	* @file ntn_friclaw_linear_slip_weakening_no_healing.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief linear slip weakening
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_NO_HEALING_HH_
	#define AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_NO_HEALING_HH_

	/* -------------------------------------------------------------------------- */
	#include "ntn_friclaw_linear_slip_weakening.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation = NTNFricRegNoRegularisation>
	class NTNFricLawLinearSlipWeakeningNoHealing
	: public NTNFricLawLinearSlipWeakening<Regularisation> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricLawLinearSlipWeakeningNoHealing(
	NTNBaseContact & contact,
	const ID & id = "linear_slip_weakening_no_healing");
	- virtual ~NTNFricLawLinearSlipWeakeningNoHealing(){};
	+ ~NTNFricLawLinearSlipWeakeningNoHealing() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// computes the friction coefficient as a function of slip
	- virtual void computeFrictionCoefficient();
	+ void computeFrictionCoefficient() override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <class Regularisation>
	inline std::ostream & operator<<(
	std::ostream & stream,
	const NTNFricLawLinearSlipWeakeningNoHealing<Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh"

	#endif /* AST_NTN_FRICLAW_LINEAR_SLIP_WEAKENING_NO_HEALING_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh
	index ceeb3dd89..20cd67bc1 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh
	@@ -1,86 +1,87 @@
	/**
	* @file ntn_friclaw_linear_slip_weakening_no_healing_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Wed Oct 17 2018
	*
	* @brief implementation of linear slip weakening
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	NTNFricLawLinearSlipWeakeningNoHealing<Regularisation>::
	NTNFricLawLinearSlipWeakeningNoHealing(NTNBaseContact & contact,
	const ID & id)
	: NTNFricLawLinearSlipWeakening<Regularisation>(contact, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakeningNoHealing<
	Regularisation>::computeFrictionCoefficient() {
	AKANTU_DEBUG_IN();

	// get arrays
	const SynchronizedArray<Real> & slip = this->internalGetCumulativeSlip();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	if (slip(n) >= this->d_c(n)) {
	this->mu(n) = this->mu_k(n);
	} else {
	// mu = mu_k + (1 - slip / Dc) * (mu_s - mu_k)
	this->mu(n) = this->mu_k(n) + (1 - (slip(n) / this->d_c(n))) *
	(this->mu_s(n) - this->mu_k(n));
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakeningNoHealing<Regularisation>::printself(
	std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricLawLinearSlipWeakeningNoHealing [" << std::endl;
	NTNFricLawLinearSlipWeakening<Regularisation>::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_tmpl.hh
	index 7f9c8fd0a..5101a1d16 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_laws/ntn_friclaw_linear_slip_weakening_tmpl.hh
	@@ -1,191 +1,192 @@
	/**
	* @file ntn_friclaw_linear_slip_weakening_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of linear slip weakening
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	NTNFricLawLinearSlipWeakening<Regularisation>::NTNFricLawLinearSlipWeakening(
	NTNBaseContact & contact, const ID & id)
	: NTNFricLawCoulomb<Regularisation>(contact, id),
	mu_s(0, 1, 0., id + ":mu_s", 0., "mu_s"),
	mu_k(0, 1, 0., id + ":mu_k", 0., "mu_k"),
	d_c(0, 1, 0., id + ":d_c", 0., "d_c") {
	AKANTU_DEBUG_IN();

	NTNFricLawCoulomb<Regularisation>::registerSynchronizedArray(this->mu_s);
	NTNFricLawCoulomb<Regularisation>::registerSynchronizedArray(this->mu_k);
	NTNFricLawCoulomb<Regularisation>::registerSynchronizedArray(this->d_c);

	this->registerParam("mu_s", this->mu_s, _pat_parsmod,
	"static friction coefficient");
	this->registerParam("mu_k", this->mu_k, _pat_parsmod,
	"kinetic friction coefficient");
	this->registerParam("d_c", this->d_c, _pat_parsmod, "slip weakening length");

	this->setParameterAccessType("mu", _pat_readable);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<
	Regularisation>::computeFrictionalStrength() {
	AKANTU_DEBUG_IN();

	computeFrictionCoefficient();
	NTNFricLawCoulomb<Regularisation>::computeFrictionalStrength();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<
	Regularisation>::computeFrictionCoefficient() {
	AKANTU_DEBUG_IN();

	// get arrays
	const SynchronizedArray<bool> & stick = this->internalGetIsSticking();
	const SynchronizedArray<Real> & slip = this->internalGetSlip();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	if (stick(n)) {
	this->mu(n) = this->mu_s(n);
	} else {
	if (slip(n) >= this->d_c(n)) {
	this->mu(n) = this->mu_k(n);
	} else {
	// mu = mu_k + (1 - slip / Dc) * (mu_s - mu_k)
	this->mu(n) = this->mu_k(n) + (1 - (slip(n) / this->d_c(n))) *
	(this->mu_s(n) - this->mu_k(n));
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<Regularisation>::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->mu_s.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<Regularisation>::dumpRestart(
	const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->mu_s.dumpRestartFile(file_name);
	this->mu_k.dumpRestartFile(file_name);
	this->d_c.dumpRestartFile(file_name);

	NTNFricLawCoulomb<Regularisation>::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<Regularisation>::readRestart(
	const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->mu_s.readRestartFile(file_name);
	this->mu_k.readRestartFile(file_name);
	this->d_c.readRestartFile(file_name);

	NTNFricLawCoulomb<Regularisation>::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<Regularisation>::printself(
	std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricLawLinearSlipWeakening [" << std::endl;
	NTNFricLawCoulomb<Regularisation>::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Regularisation>
	void NTNFricLawLinearSlipWeakening<Regularisation>::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "mu_s") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->mu_s.getArray()));
	} else if (field_id == "mu_k") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->mu_k.getArray()));
	} else if (field_id == "d_c") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->d_c.getArray()));
	} else {
	NTNFricLawCoulomb<Regularisation>::addDumpFieldToDumper(dumper_name,
	field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.cc
	index 31f888ae6..956812e85 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.cc
	@@ -1,169 +1,170 @@
	/**
	* @file ntn_fricreg_no_regularisation.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of no regularisation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_no_regularisation.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-NTNFricRegNoRegularisation::NTNFricRegNoRegularisation(
	- NTNBaseContact & contact, const ID & id)
	+NTNFricRegNoRegularisation::NTNFricRegNoRegularisation(NTNBaseContact & contact,
	+ const ID & id)
	: NTNBaseFriction(contact, id),
	frictional_contact_pressure(0, 1, 0., id + ":frictional_contact_pressure",
	0., "frictional_contact_pressure") {
	AKANTU_DEBUG_IN();

	NTNBaseFriction::registerSynchronizedArray(this->frictional_contact_pressure);

	this->registerParam("frictional_contact_pressure",
	this->frictional_contact_pressure, _pat_internal,
	"contact pressure used for friction law");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	const SynchronizedArray<Real> &
	NTNFricRegNoRegularisation::internalGetContactPressure() {
	AKANTU_DEBUG_IN();

	this->computeFrictionalContactPressure();

	AKANTU_DEBUG_OUT();
	return this->frictional_contact_pressure;
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::computeFrictionalContactPressure() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	UInt dim = model.getSpatialDimension();

	// get contact arrays
	const SynchronizedArray<bool> & is_in_contact =
	this->internalGetIsInContact();
	const Array<Real> & pressure = this->contact.getContactPressure().getArray();
	Array<Real>::const_iterator<Vector<Real>> it = pressure.begin(dim);

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// node pair is NOT in contact
	- if (!is_in_contact(n))
	+ if (!is_in_contact(n)) {
	this->frictional_contact_pressure(n) = 0.;

	- // node pair is in contact
	- else {
	+ // node pair is in contact
	+ } else {
	// compute frictional contact pressure
	const Vector<Real> & pres = it[n];
	this->frictional_contact_pressure(n) = pres.norm();
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->frictional_contact_pressure.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::dumpRestart(
	const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->frictional_contact_pressure.dumpRestartFile(file_name);

	NTNBaseFriction::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::readRestart(const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->frictional_contact_pressure.readRestartFile(file_name);

	NTNBaseFriction::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricRegNoRegularisation [" << std::endl;
	NTNBaseFriction::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegNoRegularisation::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "frictional_contact_pressure") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->frictional_contact_pressure.getArray()));
	} else {
	NTNBaseFriction::addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.hh
	index ffba2f5d5..cfc6319d9 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_no_regularisation.hh
	@@ -1,134 +1,134 @@
	/**
	* @file ntn_fricreg_no_regularisation.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief regularisation that does nothing
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_NTN_FRICREG_NO_REGULARISATION_HH_
	#define AST_NTN_FRICREG_NO_REGULARISATION_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_friction.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class NTNFricRegNoRegularisation : public NTNBaseFriction {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricRegNoRegularisation(NTNBaseContact & contact,
	const ID & id = "no_regularisation");
	- virtual ~NTNFricRegNoRegularisation(){};
	+ ~NTNFricRegNoRegularisation() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// set to steady state for no regularisation -> do nothing
	- virtual void setToSteadyState(){};
	+ void setToSteadyState() override{};

	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	- virtual void dumpRestart(const std::string & file_name) const;
	- virtual void readRestart(const std::string & file_name);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;
	+ void dumpRestart(const std::string & file_name) const override;
	+ void readRestart(const std::string & file_name) override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	virtual void computeFrictionalContactPressure();

	/// compute frictional strength according to friction law
	- virtual void computeFrictionalStrength(){};
	+ void computeFrictionalStrength() override{};

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	protected:
	/// get the is_in_contact array
	virtual const SynchronizedArray<bool> & internalGetIsInContact() {
	return this->contact.getIsInContact();
	};

	/// get the contact pressure (the norm: scalar value)
	virtual const SynchronizedArray<Real> & internalGetContactPressure();

	/// get the frictional strength array
	virtual SynchronizedArray<Real> & internalGetFrictionalStrength() {
	return this->frictional_strength;
	};

	/// get the is_sticking array
	virtual SynchronizedArray<bool> & internalGetIsSticking() {
	return this->is_sticking;
	}

	/// get the slip array
	virtual SynchronizedArray<Real> & internalGetSlip() { return this->slip; }

	/// get the slip array
	virtual SynchronizedArray<Real> & internalGetCumulativeSlip() {
	return this->cumulative_slip;
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	// contact pressure (absolut value) for computation of friction
	SynchronizedArray<Real> frictional_contact_pressure;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntn_fricreg_no_regularisation_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTNFricRegNoRegularisation & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTN_FRICREG_NO_REGULARISATION_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.cc
	index 55ff516f0..ba84f90f1 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.cc
	@@ -1,176 +1,177 @@
	/**
	* @file ntn_fricreg_rubin_ampuero.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of no regularisation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_rubin_ampuero.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NTNFricRegRubinAmpuero::NTNFricRegRubinAmpuero(NTNBaseContact & contact,
	const ID & id)
	: NTNFricRegNoRegularisation(contact, id),
	t_star(0, 1, 0., id + ":t_star", 0., "t_star") {
	AKANTU_DEBUG_IN();

	NTNFricRegNoRegularisation::registerSynchronizedArray(this->t_star);

	this->registerParam("t_star", this->t_star, _pat_parsmod,
	"time scale of regularization");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	const SynchronizedArray<Real> &
	NTNFricRegRubinAmpuero::internalGetContactPressure() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	UInt dim = model.getSpatialDimension();
	Real delta_t = model.getTimeStep();

	// get contact arrays
	const SynchronizedArray<bool> & is_in_contact =
	this->internalGetIsInContact();
	const Array<Real> & pressure = this->contact.getContactPressure().getArray();
	Array<Real>::const_iterator<Vector<Real>> it = pressure.begin(dim);

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// node pair is NOT in contact
	- if (!is_in_contact(n))
	+ if (!is_in_contact(n)) {
	this->frictional_contact_pressure(n) = 0.;

	- // if t_star is too small compute like Coulomb friction (without
	- // regularization)
	- else if (Math::are_float_equal(this->t_star(n), 0.)) {
	+ // if t_star is too small compute like Coulomb friction (without
	+ // regularization)
	+ } else if (Math::are_float_equal(this->t_star(n), 0.)) {
	const Vector<Real> & pres = it[n];
	this->frictional_contact_pressure(n) = pres.norm();
	}

	else {
	// compute frictional contact pressure
	// backward euler method: first order implicit numerical integration
	// method
	// \reg_pres_n+1 = (\reg_pres_n + \delta_t / \t_star * \cur_pres)
	// / (1 + \delta_t / \t_star)
	Real alpha = delta_t / this->t_star(n);
	const Vector<Real> & pres = it[n];
	this->frictional_contact_pressure(n) += alpha * pres.norm();
	this->frictional_contact_pressure(n) /= 1 + alpha;
	}
	}

	AKANTU_DEBUG_OUT();
	return this->frictional_contact_pressure;
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::setToSteadyState() {
	AKANTU_DEBUG_IN();
	NTNFricRegNoRegularisation::computeFrictionalContactPressure();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->t_star.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::dumpRestart(const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->t_star.dumpRestartFile(file_name);

	NTNFricRegNoRegularisation::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::readRestart(const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->t_star.readRestartFile(file_name);

	NTNFricRegNoRegularisation::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricRegRubinAmpuero [" << std::endl;
	NTNFricRegNoRegularisation::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegRubinAmpuero::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "t_star") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->t_star.getArray()));
	} else {
	NTNFricRegNoRegularisation::addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.hh
	index 7df44ab25..f23eec34d 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_rubin_ampuero.hh
	@@ -1,102 +1,102 @@
	/**
	* @file ntn_fricreg_rubin_ampuero.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief regularisation that regularizes the contact pressure
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICREG_RUBIN_AMPUERO_HH_
	#define AST_NTN_FRICREG_RUBIN_AMPUERO_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_no_regularisation.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class NTNFricRegRubinAmpuero : public NTNFricRegNoRegularisation {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricRegRubinAmpuero(NTNBaseContact & contact,
	const ID & id = "rubin_ampuero");
	- virtual ~NTNFricRegRubinAmpuero(){};
	+ ~NTNFricRegRubinAmpuero() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	- virtual void dumpRestart(const std::string & file_name) const;
	- virtual void readRestart(const std::string & file_name);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;
	+ void dumpRestart(const std::string & file_name) const override;
	+ void readRestart(const std::string & file_name) override;

	- virtual void setToSteadyState();
	+ void setToSteadyState() override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	protected:
	/// get the contact pressure (the norm: scalar value)
	- virtual const SynchronizedArray<Real> & internalGetContactPressure();
	+ const SynchronizedArray<Real> & internalGetContactPressure() override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	SynchronizedArray<Real> t_star;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntn_fricreg_rubin_ampuero_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTNFricRegRubinAmpuero & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTN_FRICREG_RUBIN_AMPUERO_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.cc
	index 0837acb38..c922aa14f 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.cc
	@@ -1,164 +1,165 @@
	/**
	* @file ntn_fricreg_simplified_prakash_clifton.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Jul 19 2019
	*
	* @brief implementation of simplified prakash clifton with one parameter
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_simplified_prakash_clifton.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NTNFricRegSimplifiedPrakashClifton::NTNFricRegSimplifiedPrakashClifton(
	NTNBaseContact & contact, const ID & id)
	: NTNFricRegNoRegularisation(contact, id),
	t_star(0, 1, 0., id + ":t_star", 0., "t_star"),
	spc_internal(0, 1, 0., id + ":spc_internal", 0., "spc_internal") {
	AKANTU_DEBUG_IN();

	NTNFricRegNoRegularisation::registerSynchronizedArray(this->t_star);
	NTNFricRegNoRegularisation::registerSynchronizedArray(this->spc_internal);

	this->registerParam("t_star", this->t_star, _pat_parsmod,
	"time scale of regularisation");
	this->registerParam("spc_internal", this->spc_internal, _pat_internal, "");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::computeFrictionalStrength() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	Real delta_t = model.getTimeStep();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	Real alpha = delta_t / this->t_star(n);
	this->frictional_strength(n) += alpha * this->spc_internal(n);
	this->frictional_strength(n) /= 1 + alpha;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::setToSteadyState() {
	AKANTU_DEBUG_IN();

	/// fill the spc_internal array
	computeFrictionalStrength();

	/// set strength without regularisation
	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	this->frictional_strength(n) = this->spc_internal(n);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::registerSynchronizedArray(
	SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->t_star.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::dumpRestart(
	const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->t_star.dumpRestartFile(file_name);
	this->spc_internal.dumpRestartFile(file_name);

	NTNFricRegNoRegularisation::dumpRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::readRestart(
	const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->t_star.readRestartFile(file_name);
	this->spc_internal.readRestartFile(file_name);

	NTNFricRegNoRegularisation::readRestart(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFricRegSimplifiedPrakashClifton [" << std::endl;
	NTNFricRegNoRegularisation::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNFricRegSimplifiedPrakashClifton::addDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "t_star") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->t_star.getArray()));
	} else {
	NTNFricRegNoRegularisation::addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.hh
	index ac7835dac..7db6e82ce 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/friction_regularisations/ntn_fricreg_simplified_prakash_clifton.hh
	@@ -1,113 +1,113 @@
	/**
	* @file ntn_fricreg_simplified_prakash_clifton.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief regularisation that regularizes the frictional strength with one
	* parameter
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_FRICREG_SIMPLIFIED_PRAKASH_CLIFTON_HH_
	#define AST_NTN_FRICREG_SIMPLIFIED_PRAKASH_CLIFTON_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_fricreg_no_regularisation.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class NTNFricRegSimplifiedPrakashClifton : public NTNFricRegNoRegularisation {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFricRegSimplifiedPrakashClifton(
	NTNBaseContact & contact, const ID & id = "simplified_prakash_clifton");
	- virtual ~NTNFricRegSimplifiedPrakashClifton(){};
	+ ~NTNFricRegSimplifiedPrakashClifton() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void registerSynchronizedArray(SynchronizedArrayBase & array);
	- virtual void dumpRestart(const std::string & file_name) const;
	- virtual void readRestart(const std::string & file_name);
	+ void registerSynchronizedArray(SynchronizedArrayBase & array) override;
	+ void dumpRestart(const std::string & file_name) const override;
	+ void readRestart(const std::string & file_name) override;

	- virtual void setToSteadyState();
	+ void setToSteadyState() override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// compute frictional strength according to friction law
	- virtual void computeFrictionalStrength();
	+ void computeFrictionalStrength() override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	protected:
	/// get the frictional strength array
	- virtual SynchronizedArray<Real> & internalGetFrictionalStrength() {
	+ SynchronizedArray<Real> & internalGetFrictionalStrength() override {
	return this->spc_internal;
	};

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	SynchronizedArray<Real> t_star;

	// to get the incremental frictional strength
	SynchronizedArray<Real> spc_internal;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntn_fricreg_simplified_prakash_clifton_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTNFricRegSimplifiedPrakashClifton & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTN_FRICREG_SIMPLIFIED_PRAKASH_CLIFTON_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.cc
	index cd059e956..2507ef9bd 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.cc
	@@ -1,120 +1,121 @@
	/**
	* @file mIIasym_contact.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Wed Oct 17 2018
	*
	* @brief contact for mode II anti-symmetric simulations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "mIIasym_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MIIASYMContact::MIIASYMContact(SolidMechanicsModel & model, const ID & id)
	: NTRFContact(model, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MIIASYMContact::updateImpedance() {
	AKANTU_DEBUG_IN();

	NTRFContact::updateImpedance();

	for (UInt i = 0; i < this->impedance.size(); ++i) {
	this->impedance(i) *= 0.5;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/// WARNING: this is only valid for the acceleration in equilibrium
	void MIIASYMContact::computeRelativeNormalField(
	const Array<Real> & field, Array<Real> & rel_normal_field) const {
	AKANTU_DEBUG_IN();

	NTRFContact::computeRelativeNormalField(field, rel_normal_field);

	for (auto it_rtfield = rel_normal_field.begin();
	it_rtfield != rel_normal_field.end(); ++it_rtfield) {

	// in the anti-symmetric case
	it_rtfield = 2.;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MIIASYMContact::computeRelativeTangentialField(
	const Array<Real> & field, Array<Real> & rel_tang_field) const {
	AKANTU_DEBUG_IN();

	NTRFContact::computeRelativeTangentialField(field, rel_tang_field);

	UInt dim = this->model.getSpatialDimension();

	for (Array<Real>::iterator<Vector<Real>> it_rtfield =
	rel_tang_field.begin(dim);
	it_rtfield != rel_tang_field.end(dim); ++it_rtfield) {

	// in the anti-symmetric case, the tangential fields become twice as large
	it_rtfield = 2.;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MIIASYMContact::computeContactPressureInEquilibrium() {
	AKANTU_DEBUG_IN();

	NTRFContact::computeContactPressure();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MIIASYMContact::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "MIIASYMContact [" << std::endl;
	NTRFContact::printself(stream, indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.hh
	index ac35c2ac1..bc35b37cb 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/mIIasym_contact.hh
	@@ -1,92 +1,92 @@
	/**
	* @file mIIasym_contact.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief contact for mode II anti-symmetric simulations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_MIIASYM_CONTACT_HH_
	#define AST_MIIASYM_CONTACT_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntrf_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class MIIASYMContact : public NTRFContact {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MIIASYMContact(SolidMechanicsModel & model, const ID & id = "contact");
	~MIIASYMContact() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// update the impedance matrix
	- virtual void updateImpedance();
	+ void updateImpedance() override;

	/// compute contact pressure -> do nothing because can only compute it in
	/// equilibrium
	void computeContactPressure() override{};

	/// compute relative normal field (only value that has to be multiplied with
	/// the normal)
	/// WARNING: this is only valid for the acceleration in equilibrium
	void
	computeRelativeNormalField(const Array<Real> & field,
	Array<Real> & rel_normal_field) const override;

	/// compute relative tangential field (complet array)
	/// relative to master nodes
	void
	computeRelativeTangentialField(const Array<Real> & field,
	Array<Real> & rel_tang_field) const override;

	/// compute contact pressure that is used over the entire time
	virtual void computeContactPressureInEquilibrium();

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const MIIASYMContact & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_MIIASYM_CONTACT_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.cc
	index fae762cb6..1051b1817 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.cc
	@@ -1,567 +1,569 @@
	/**
	* @file ntn_base_contact.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of ntn base contact
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "ntn_base_contact.hh"
	#include "dof_manager_default.hh"
	#include "dumpable_inline_impl.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"
	#include "element_synchronizer.hh"
	#include "mesh_utils.hh"
	#include "non_linear_solver_lumped.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	// NTNContactSynchElementFilter::NTNContactSynchElementFilter(
	// NTNBaseContact & contact)
	// : contact(contact),
	// connectivity(contact.getModel().getMesh().getConnectivities()) {
	// AKANTU_DEBUG_IN();

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	// bool NTNContactSynchElementFilter::operator()(const Element & e) {
	// AKANTU_DEBUG_IN();

	// ElementType type = e.type;
	// UInt element = e.element;
	// GhostType ghost_type = e.ghost_type;

	// // loop over all nodes of this element
	// bool need_element = false;
	// UInt nb_nodes = Mesh::getNbNodesPerElement(type);
	// for (UInt n = 0; n < nb_nodes; ++n) {
	// UInt nn = this->connectivity(type, ghost_type)(element, n);

	// // if one nodes is in this contact, we need this element
	// if (this->contact.getNodeIndex(nn) >= 0) {
	// need_element = true;
	// break;
	// }
	// }

	// AKANTU_DEBUG_OUT();
	// return need_element;
	// }

	/* -------------------------------------------------------------------------- */
	NTNBaseContact::NTNBaseContact(SolidMechanicsModel & model, const ID & id)
	: id(id), model(model),
	slaves(0, 1, 0, id + ":slaves", std::numeric_limits<UInt>::quiet_NaN(),
	"slaves"),
	normals(0, model.getSpatialDimension(), 0, id + ":normals",
	std::numeric_limits<Real>::quiet_NaN(), "normals"),
	contact_pressure(
	0, model.getSpatialDimension(), 0, id + ":contact_pressure",
	std::numeric_limits<Real>::quiet_NaN(), "contact_pressure"),
	is_in_contact(0, 1, false, id + ":is_in_contact", false, "is_in_contact"),
	lumped_boundary_slaves(0, 1, 0, id + ":lumped_boundary_slaves",
	std::numeric_limits<Real>::quiet_NaN(),
	"lumped_boundary_slaves"),
	impedance(0, 1, 0, id + ":impedance",
	std::numeric_limits<Real>::quiet_NaN(), "impedance"),
	slave_elements("slave_elements", id) {
	AKANTU_DEBUG_IN();

	auto & boundary_fem = this->model.getFEEngineBoundary();
	for (auto && ghost_type : ghost_types) {
	boundary_fem.initShapeFunctions(ghost_type);
	}

	auto & mesh = this->model.getMesh();
	auto spatial_dimension = this->model.getSpatialDimension();

	this->slave_elements.initialize(mesh,
	_spatial_dimension = spatial_dimension - 1);

	MeshUtils::buildNode2Elements(mesh, this->node_to_elements,
	spatial_dimension - 1);

	this->registerDumper<DumperText>("text_all", id, true);
	this->addDumpFilteredMesh(mesh, slave_elements, slaves.getArray(),
	spatial_dimension - 1, _not_ghost, _ek_regular);

	// parallelisation
	this->synch_registry = std::make_unique<SynchronizerRegistry>();
	this->synch_registry->registerDataAccessor(*this);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	NTNBaseContact::~NTNBaseContact() = default;

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::initParallel() {
	AKANTU_DEBUG_IN();

	this->synchronizer = std::make_unique<ElementSynchronizer>(
	this->model.getMesh().getElementSynchronizer());

	this->synchronizer->filterScheme([&](auto && element) {
	// loop over all nodes of this element
	Vector<UInt> conn = const_cast<const Mesh &>(this->model.getMesh())
	.getConnectivity(element);
	for (auto & node : conn) {
	// if one nodes is in this contact, we need this element
	if (this->getNodeIndex(node) >= 0) {
	return true;
	}
	}
	return false;
	});

	this->synch_registry->registerSynchronizer(*(this->synchronizer),
	SynchronizationTag::_cf_nodal);
	this->synch_registry->registerSynchronizer(*(this->synchronizer),
	SynchronizationTag::_cf_incr);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::findBoundaryElements(
	const Array<UInt> & interface_nodes, ElementTypeMapArray<UInt> & elements) {
	AKANTU_DEBUG_IN();

	// add connected boundary elements that have all nodes on this contact
	for (const auto & node : interface_nodes) {
	for (const auto & element : this->node_to_elements.getRow(node)) {
	Vector<UInt> conn = const_cast<const Mesh &>(this->model.getMesh())
	.getConnectivity(element);
	auto nb_nodes = conn.size();
	decltype(nb_nodes) nb_found_nodes = 0;

	for (auto & nn : conn) {
	if (interface_nodes.find(nn) != UInt(-1)) {
	nb_found_nodes++;
	} else {
	break;
	}
	}

	// this is an element between all contact nodes
	// and is not already in the elements
	if ((nb_found_nodes == nb_nodes) &&
	(elements(element.type, element.ghost_type).find(element.element) ==
	UInt(-1))) {
	elements(element.type, element.ghost_type).push_back(element.element);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	-void NTNBaseContact::addSplitNode(UInt node, UInt) {
	+void NTNBaseContact::addSplitNode(UInt node, UInt /unused/) {
	AKANTU_DEBUG_IN();

	UInt dim = this->model.getSpatialDimension();

	// add to node arrays
	this->slaves.push_back(node);

	// set contact as false
	this->is_in_contact.push_back(false);

	// before initializing
	// set contact pressure, normal, lumped_boundary to Nan
	this->contact_pressure.push_back(std::numeric_limits<Real>::quiet_NaN());
	this->impedance.push_back(std::numeric_limits<Real>::quiet_NaN());
	this->lumped_boundary_slaves.push_back(
	std::numeric_limits<Real>::quiet_NaN());

	Vector<Real> nan_normal(dim, std::numeric_limits<Real>::quiet_NaN());
	this->normals.push_back(nan_normal);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::registerSynchronizedArray(SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->slaves.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::dumpRestart(const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->slaves.dumpRestartFile(file_name);
	this->normals.dumpRestartFile(file_name);
	this->is_in_contact.dumpRestartFile(file_name);
	this->contact_pressure.dumpRestartFile(file_name);
	this->lumped_boundary_slaves.dumpRestartFile(file_name);
	this->impedance.dumpRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::readRestart(const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->slaves.readRestartFile(file_name);
	this->normals.readRestartFile(file_name);
	this->is_in_contact.readRestartFile(file_name);
	this->contact_pressure.readRestartFile(file_name);
	this->lumped_boundary_slaves.readRestartFile(file_name);
	this->impedance.readRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt NTNBaseContact::getNbNodesInContact() const {
	AKANTU_DEBUG_IN();

	UInt nb_contact = 0;

	UInt nb_nodes = this->getNbContactNodes();
	const Mesh & mesh = this->model.getMesh();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = mesh.isLocalOrMasterNode(this->slaves(n));
	bool is_pbc_slave_node = mesh.isPeriodicSlave(this->slaves(n));
	if (is_local_node && !is_pbc_slave_node && this->is_in_contact(n)) {
	nb_contact++;
	}
	}

	mesh.getCommunicator().allReduce(nb_contact, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return nb_contact;
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::updateInternalData() {
	AKANTU_DEBUG_IN();

	updateNormals();
	updateLumpedBoundary();
	updateImpedance();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::updateLumpedBoundary() {
	AKANTU_DEBUG_IN();

	this->internalUpdateLumpedBoundary(this->slaves.getArray(),
	this->slave_elements,
	this->lumped_boundary_slaves);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::internalUpdateLumpedBoundary(
	const Array<UInt> & nodes, const ElementTypeMapArray<UInt> & elements,
	SynchronizedArray<Real> & boundary) {
	AKANTU_DEBUG_IN();

	// set all values in lumped_boundary to zero
	boundary.zero();

	UInt dim = this->model.getSpatialDimension();
	// UInt nb_contact_nodes = getNbContactNodes();

	const FEEngine & boundary_fem = this->model.getFEEngineBoundary();

	const Mesh & mesh = this->model.getMesh();

	for (auto ghost_type : ghost_types) {
	- for (auto & type : mesh.elementTypes(dim - 1, ghost_type)) {
	+ for (const auto & type : mesh.elementTypes(dim - 1, ghost_type)) {
	UInt nb_elements = mesh.getNbElement(type, ghost_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);

	// get shapes and compute integral
	const Array<Real> & shapes = boundary_fem.getShapes(type, ghost_type);
	Array<Real> area(nb_elements, nb_nodes_per_element);
	boundary_fem.integrate(shapes, area, nb_nodes_per_element, type,
	ghost_type);

	- if (this->contact_surfaces.size() == 0) {
	+ if (this->contact_surfaces.empty()) {
	AKANTU_DEBUG_WARNING(
	"No surfaces in ntn base contact."
	<< " You have to define the lumped boundary by yourself.");
	}

	Array<UInt>::const_iterator<UInt> elem_it =
	(elements)(type, ghost_type).begin();
	Array<UInt>::const_iterator<UInt> elem_it_end =
	(elements)(type, ghost_type).end();
	// loop over contact nodes
	for (; elem_it != elem_it_end; ++elem_it) {
	for (UInt q = 0; q < nb_nodes_per_element; ++q) {
	UInt node = connectivity(*elem_it, q);
	UInt node_index = nodes.find(node);
	AKANTU_DEBUG_ASSERT(node_index != UInt(-1), "Could not find node "
	<< node
	<< " in the array!");
	Real area_to_add = area(*elem_it, q);
	boundary(node_index) += area_to_add;
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::computeAcceleration(Array<Real> & acceleration) const {
	auto && dof_manager =
	dynamic_cast<DOFManagerDefault &>(model.getDOFManager());
	const auto & b = dof_manager.getResidual();
	acceleration.resize(b.size());
	const auto & blocked_dofs = dof_manager.getGlobalBlockedDOFs();
	const auto & A = dof_manager.getLumpedMatrix("M");

	Array<bool> blocked_dofs_bool(blocked_dofs.size());
	for (auto && data : zip(blocked_dofs, blocked_dofs_bool)) {
	- std::get<1>(data) = std::get<0>(data);
	+ std::get<1>(data) = (std::get<0>(data) != 0);
	}

	// pre-compute the acceleration
	// (not increment acceleration, because residual is still Kf)
	NonLinearSolverLumped::solveLumped(A, acceleration, b, this->model.getF_M2A(),
	blocked_dofs_bool);
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::computeContactPressure() {
	AKANTU_DEBUG_IN();

	UInt dim = this->model.getSpatialDimension();
	Real delta_t = this->model.getTimeStep();
	UInt nb_contact_nodes = getNbContactNodes();

	AKANTU_DEBUG_ASSERT(delta_t > 0.,
	"Cannot compute contact pressure if no time step is set");

	// synchronize data
	this->synch_registry->synchronize(SynchronizationTag::_cf_nodal);

	Array<Real> acceleration(0, dim);
	this->computeAcceleration(acceleration);

	// compute relative normal fields of displacement, velocity and acceleration
	Array<Real> r_disp(0, 1);
	Array<Real> r_velo(0, 1);
	Array<Real> r_acce(0, 1);
	Array<Real> r_old_acce(0, 1);
	computeNormalGap(r_disp);
	// computeRelativeNormalField(this->model.getCurrentPosition(), r_disp);
	computeRelativeNormalField(this->model.getVelocity(), r_velo);
	computeRelativeNormalField(acceleration, r_acce);
	computeRelativeNormalField(this->model.getAcceleration(), r_old_acce);

	AKANTU_DEBUG_ASSERT(r_disp.size() == nb_contact_nodes,
	"computeRelativeNormalField does not give back arrays "
	<< "size == nb_contact_nodes. nb_contact_nodes = "
	<< nb_contact_nodes
	<< " \| array size = " << r_disp.size());

	// compute gap array for all nodes
	Array<Real> gap(nb_contact_nodes, 1);
	Real * gap_p = gap.storage();
	Real * r_disp_p = r_disp.storage();
	Real * r_velo_p = r_velo.storage();
	Real * r_acce_p = r_acce.storage();
	Real * r_old_acce_p = r_old_acce.storage();
	for (UInt i = 0; i < nb_contact_nodes; ++i) {
	gap_p = r_disp_p + delta_t * r_velo_p + delta_t delta_t * *r_acce_p -
	0.5 * delta_t * delta_t * *r_old_acce_p;
	// increment pointers
	gap_p++;
	r_disp_p++;
	r_velo_p++;
	r_acce_p++;
	r_old_acce_p++;
	}

	// check if gap is negative -> is in contact
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	if (gap(n) <= 0.) {
	for (UInt d = 0; d < dim; ++d) {
	this->contact_pressure(n, d) =
	this->impedance(n) * gap(n) / (2 * delta_t) * this->normals(n, d);
	}
	this->is_in_contact(n) = true;
	} else {
	- for (UInt d = 0; d < dim; ++d)
	+ for (UInt d = 0; d < dim; ++d) {
	this->contact_pressure(n, d) = 0.;
	+ }
	this->is_in_contact(n) = false;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::applyContactPressure() {
	AKANTU_DEBUG_IN();

	UInt nb_contact_nodes = getNbContactNodes();
	UInt dim = this->model.getSpatialDimension();

	Array<Real> & residual = this->model.getInternalForce();

	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	UInt slave = this->slaves(n);

	for (UInt d = 0; d < dim; ++d) {
	// residual(master,d) += this->lumped_boundary(n,0) *
	// this->contact_pressure(n,d);
	residual(slave, d) -=
	this->lumped_boundary_slaves(n) * this->contact_pressure(n, d);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Int NTNBaseContact::getNodeIndex(UInt node) const {
	return this->slaves.find(node);
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNBaseContact [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + slaves : " << std::endl;
	this->slaves.printself(stream, indent + 2);
	stream << space << " + normals : " << std::endl;
	this->normals.printself(stream, indent + 2);
	stream << space << " + contact_pressure : " << std::endl;
	this->contact_pressure.printself(stream, indent + 2);

	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::syncArrays(SyncChoice sync_choice) {
	AKANTU_DEBUG_IN();

	this->slaves.syncElements(sync_choice);
	this->normals.syncElements(sync_choice);
	this->is_in_contact.syncElements(sync_choice);
	this->contact_pressure.syncElements(sync_choice);
	this->lumped_boundary_slaves.syncElements(sync_choice);
	this->impedance.syncElements(sync_choice);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseContact::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	const Array<UInt> & nodal_filter = this->slaves.getArray();

	#define ADD_FIELD(field_id, field, type) \
	internalAddDumpFieldToDumper( \
	dumper_name, field_id, \
	std::make_unique< \
	dumpers::NodalField<type, true, Array<type>, Array<UInt>>>( \
	field, 0, 0, &nodal_filter))

	if (field_id == "displacement") {
	ADD_FIELD(field_id, this->model.getDisplacement(), Real);
	} else if (field_id == "mass") {
	ADD_FIELD(field_id, this->model.getMass(), Real);
	} else if (field_id == "velocity") {
	ADD_FIELD(field_id, this->model.getVelocity(), Real);
	} else if (field_id == "acceleration") {
	ADD_FIELD(field_id, this->model.getAcceleration(), Real);
	} else if (field_id == "external_force") {
	ADD_FIELD(field_id, this->model.getExternalForce(), Real);
	} else if (field_id == "internal_force") {
	ADD_FIELD(field_id, this->model.getInternalForce(), Real);
	} else if (field_id == "blocked_dofs") {
	ADD_FIELD(field_id, this->model.getBlockedDOFs(), bool);
	} else if (field_id == "increment") {
	ADD_FIELD(field_id, this->model.getIncrement(), Real);
	} else if (field_id == "normal") {
	internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->normals.getArray()));
	} else if (field_id == "contact_pressure") {
	internalAddDumpFieldToDumper(dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->contact_pressure.getArray()));
	} else if (field_id == "is_in_contact") {
	internalAddDumpFieldToDumper(dumper_name, field_id,
	std::make_unique<dumpers::NodalField<bool>>(
	this->is_in_contact.getArray()));
	} else if (field_id == "lumped_boundary_slave") {
	internalAddDumpFieldToDumper(dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->lumped_boundary_slaves.getArray()));
	} else if (field_id == "impedance") {
	internalAddDumpFieldToDumper(dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->impedance.getArray()));
	} else {
	std::cerr << "Could not add field '" << field_id
	<< "' to the dumper. Just ignored it." << std::endl;
	}

	#undef ADD_FIELD
	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.hh
	index 8bfc075fb..4aef66622 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact.hh
	@@ -1,252 +1,252 @@
	/**
	* @file ntn_base_contact.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief base contact for ntn and ntrf contact
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_BASE_CONTACT_HH_
	#define AST_NTN_BASE_CONTACT_HH_

	/* -------------------------------------------------------------------------- */
	// akantu
	#include "aka_csr.hh"
	#include "solid_mechanics_model.hh"

	// simtools
	#include "synchronized_array.hh"

	namespace akantu {

	class NTNBaseContact;

	/* -------------------------------------------------------------------------- */
	// class NTNContactSynchElementFilter : public SynchElementFilter {
	// public:
	// // constructor
	// NTNContactSynchElementFilter(NTNBaseContact & contact);

	// // answer to: do we need this element ?
	// virtual bool operator()(const Element & e);

	// private:
	// const NTNBaseContact & contact;
	// const ElementTypeMapArray<UInt> & connectivity;
	// };

	/* -------------------------------------------------------------------------- */
	class NTNBaseContact : public DataAccessor<Element>, public Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNBaseContact(SolidMechanicsModel & model, const ID & id = "contact");
	~NTNBaseContact() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initializes ntn contact parallel
	virtual void initParallel();

	/// add split node
	- virtual void addSplitNode(UInt node, UInt = 0);
	+ virtual void addSplitNode(UInt node, UInt /unused/ = 0);

	/// update normals, lumped boundary, and impedance
	virtual void updateInternalData();

	/// update (compute the normals)
	virtual void updateNormals() = 0;

	/// update the lumped boundary B matrix
	virtual void updateLumpedBoundary();

	/// update the impedance matrix
	virtual void updateImpedance() = 0;

	/// compute the normal contact force
	virtual void computeContactPressure();

	/// impose the normal contact force
	virtual void applyContactPressure();

	/// register synchronizedarrays for sync
	virtual void registerSynchronizedArray(SynchronizedArrayBase & array);

	/// dump restart file
	virtual void dumpRestart(const std::string & file_name) const;

	/// read restart file
	virtual void readRestart(const std::string & file_name);

	/// compute the normal gap
	virtual void computeNormalGap(Array<Real> & gap) const = 0;

	/// compute relative normal field (only value that has to be multiplied with
	/// the normal)
	/// relative to master nodes
	virtual void
	computeRelativeNormalField(const Array<Real> & field,
	Array<Real> & rel_normal_field) const = 0;

	/// compute relative tangential field (complet array)
	/// relative to master nodes
	virtual void
	computeRelativeTangentialField(const Array<Real> & field,
	Array<Real> & rel_tang_field) const = 0;

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/// computes the acceleration
	void computeAcceleration(Array<Real> & acceleration) const;

	protected:
	/// updateLumpedBoundary
	virtual void
	internalUpdateLumpedBoundary(const Array<UInt> & nodes,
	const ElementTypeMapArray<UInt> & elements,
	SynchronizedArray<Real> & boundary);

	// to find the slave_elements or master_elements
	virtual void findBoundaryElements(const Array<UInt> & interface_nodes,
	ElementTypeMapArray<UInt> & elements);

	/// synchronize arrays
	virtual void syncArrays(SyncChoice sync_choice);

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Model, model, SolidMechanicsModel &)

	AKANTU_GET_MACRO(Slaves, slaves, const SynchronizedArray<UInt> &)
	AKANTU_GET_MACRO(Normals, normals, const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(ContactPressure, contact_pressure,
	const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(LumpedBoundarySlaves, lumped_boundary_slaves,
	const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(Impedance, impedance, const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(IsInContact, is_in_contact, const SynchronizedArray<bool> &)

	AKANTU_GET_MACRO(SlaveElements, slave_elements,
	const ElementTypeMapArray<UInt> &)

	AKANTU_GET_MACRO(SynchronizerRegistry, *synch_registry,
	SynchronizerRegistry &)

	/// get number of nodes that are in contact (globally, on all procs together)
	/// is_in_contact = true
	virtual UInt getNbNodesInContact() const;

	/// get index of node in either slaves or masters array
	/// if node is in neither of them, return -1
	virtual Int getNodeIndex(UInt node) const;

	/// get number of contact nodes: nodes in the system locally (on this proc)
	/// is_in_contact = true and false, because just in the system
	virtual UInt getNbContactNodes() const { return this->slaves.size(); }

	bool isNTNContact() const { return this->is_ntn_contact; }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	using SurfacePtrSet = std::set<const ElementGroup *>;

	ID id;

	SolidMechanicsModel & model;

	/// array of slave nodes
	SynchronizedArray<UInt> slaves;
	/// array of normals
	SynchronizedArray<Real> normals;
	/// array indicating if nodes are in contact
	SynchronizedArray<Real> contact_pressure;
	/// array indicating if nodes are in contact
	SynchronizedArray<bool> is_in_contact;
	/// boundary matrix for slave nodes
	SynchronizedArray<Real> lumped_boundary_slaves;
	/// impedance matrix
	SynchronizedArray<Real> impedance;

	/// contact surface
	SurfacePtrSet contact_surfaces;

	/// element list for dump and lumped_boundary
	ElementTypeMapArray<UInt> slave_elements;
	CSR<Element> node_to_elements;

	/// parallelisation
	std::unique_ptr<SynchronizerRegistry> synch_registry;
	std::unique_ptr<ElementSynchronizer> synchronizer;

	bool is_ntn_contact{true};
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTNBaseContact & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "ntn_base_contact_inline_impl.hh"

	#endif /* AST_NTN_BASE_CONTACT_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact_inline_impl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact_inline_impl.hh
	index 9168f051a..1b6372f69 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact_inline_impl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_contact_inline_impl.hh
	@@ -1,129 +1,129 @@
	/**
	* @file ntn_base_contact_inline_impl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief ntn base contact inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "ntn_base_contact.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	inline UInt NTNBaseContact::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt spatial_dimension = this->model.getSpatialDimension();

	UInt nb_nodes = 0;
	Array<Element>::const_iterator<Element> it = elements.begin();
	Array<Element>::const_iterator<Element> end = elements.end();
	for (; it != end; ++it) {
	const Element & el = *it;
	nb_nodes += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_cf_nodal: {
	size += nb_nodes * spatial_dimension * sizeof(Real) *
	3; // disp, vel and cur_pos
	break;
	}
	case SynchronizationTag::_cf_incr: {
	size += nb_nodes * spatial_dimension * sizeof(Real) * 1;
	break;
	}
	default: {
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void NTNBaseContact::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	switch (tag) {

	case SynchronizationTag::_cf_nodal: {
	DataAccessor::packNodalDataHelper(this->model.getDisplacement(), buffer,
	elements, this->model.getMesh());
	DataAccessor::packNodalDataHelper(this->model.getCurrentPosition(), buffer,
	elements, this->model.getMesh());
	DataAccessor::packNodalDataHelper(this->model.getVelocity(), buffer,
	elements, this->model.getMesh());
	break;
	}
	case SynchronizationTag::_cf_incr: {
	DataAccessor::packNodalDataHelper(this->model.getIncrement(), buffer,
	elements, this->model.getMesh());
	break;
	}
	default: {
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline void NTNBaseContact::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	switch (tag) {

	case SynchronizationTag::_cf_nodal: {
	DataAccessor::unpackNodalDataHelper(this->model.getDisplacement(), buffer,
	elements, this->model.getMesh());
	DataAccessor::unpackNodalDataHelper(
	const_cast<Array<Real> &>(this->model.getCurrentPosition()), buffer,
	elements, this->model.getMesh());
	DataAccessor::unpackNodalDataHelper(this->model.getVelocity(), buffer,
	elements, this->model.getMesh());
	break;
	}
	case SynchronizationTag::_cf_incr: {
	DataAccessor::unpackNodalDataHelper(this->model.getIncrement(), buffer,
	elements, this->model.getMesh());
	break;
	}
	default: {
	}
	}

	AKANTU_DEBUG_OUT();
	}
	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.cc
	index c66837db1..79e07047f 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.cc
	@@ -1,381 +1,382 @@
	/**
	* @file ntn_base_friction.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of ntn base friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_friction.hh"
	#include "dof_manager_default.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"
	#include "non_linear_solver_lumped.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NTNBaseFriction::NTNBaseFriction(NTNBaseContact & contact, const ID & id)
	- : Parsable(ParserType::_friction, id), Dumpable(),
	- contact(contact),
	+ : Parsable(ParserType::_friction, id), contact(contact),
	is_sticking(0, 1, true, id + ":is_sticking", true, "is_sticking"),
	frictional_strength(0, 1, 0., id + ":frictional_strength", 0.,
	"frictional_strength"),
	friction_traction(0, contact.getModel().getSpatialDimension(), 0.,
	id + ":friction_traction", 0., "friction_traction"),
	slip(0, 1, 0., id + ":slip", 0., "slip"),
	cumulative_slip(0, 1, 0., id + ":cumulative_slip", 0., "cumulative_slip"),
	slip_velocity(0, contact.getModel().getSpatialDimension(), 0.,
	id + ":slip_velocity", 0., "slip_velocity") {
	AKANTU_DEBUG_IN();

	this->contact.registerSynchronizedArray(this->is_sticking);
	this->contact.registerSynchronizedArray(this->frictional_strength);
	this->contact.registerSynchronizedArray(this->friction_traction);
	this->contact.registerSynchronizedArray(this->slip);
	this->contact.registerSynchronizedArray(this->cumulative_slip);
	this->contact.registerSynchronizedArray(this->slip_velocity);

	this->registerExternalDumper(contact.getDumper().shared_from_this(),
	contact.getDefaultDumperName(), true);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::updateSlip() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	UInt dim = model.getSpatialDimension();

	// synchronize increment
	this->contact.getSynchronizerRegistry().synchronize(
	SynchronizationTag::_cf_incr);

	Array<Real> rel_tan_incr(0, dim);
	this->contact.computeRelativeTangentialField(model.getIncrement(),
	rel_tan_incr);
	Array<Real>::const_iterator<Vector<Real>> it = rel_tan_incr.begin(dim);

	UInt nb_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (this->is_sticking(n)) {
	this->slip(n) = 0.;
	} else {
	const Vector<Real> & rti = it[n];
	this->slip(n) += rti.norm();
	this->cumulative_slip(n) += rti.norm();
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::computeFrictionTraction() {
	AKANTU_DEBUG_IN();

	this->computeStickTraction();
	this->computeFrictionalStrength();

	SolidMechanicsModel & model = this->contact.getModel();
	UInt dim = model.getSpatialDimension();

	// get contact arrays
	const SynchronizedArray<bool> & is_in_contact =
	this->contact.getIsInContact();

	- Array<Real> & traction =
	+ auto & traction =
	const_cast<Array<Real> &>(this->friction_traction.getArray());
	Array<Real>::iterator<Vector<Real>> it_fric_trac = traction.begin(dim);

	this->is_sticking.zero(); // set to not sticking

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// node pair is in contact
	if (is_in_contact(n)) {
	Vector<Real> fric_trac = it_fric_trac[n];
	// check if it is larger than frictional strength
	Real abs_fric = fric_trac.norm();
	if (abs_fric != 0.) {
	Real alpha = this->frictional_strength(n) / abs_fric;

	// larger -> sliding
	if (alpha < 1.) {
	fric_trac *= alpha;
	- } else
	+ } else {
	this->is_sticking(n) = true;
	+ }
	} else {
	// frictional traction is already zero
	this->is_sticking(n) = true;
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::computeStickTraction() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	UInt dim = model.getSpatialDimension();
	Real delta_t = model.getTimeStep();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();

	// get contact arrays
	const SynchronizedArray<Real> & impedance = this->contact.getImpedance();
	const SynchronizedArray<bool> & is_in_contact =
	this->contact.getIsInContact();

	Array<Real> acceleration(0, dim);
	this->contact.computeAcceleration(acceleration);

	// compute relative normal fields of velocity and acceleration
	Array<Real> r_velo(0, dim);
	Array<Real> r_acce(0, dim);
	Array<Real> r_old_acce(0, dim);
	this->contact.computeRelativeTangentialField(model.getVelocity(), r_velo);
	this->contact.computeRelativeTangentialField(acceleration, r_acce);
	this->contact.computeRelativeTangentialField(model.getAcceleration(),
	r_old_acce);

	AKANTU_DEBUG_ASSERT(r_velo.size() == nb_contact_nodes,
	"computeRelativeNormalField does not give back arrays "
	<< "size == nb_contact_nodes. nb_contact_nodes = "
	<< nb_contact_nodes
	<< " \| array size = " << r_velo.size());

	// compute tangential gap_dot array for all nodes
	Array<Real> gap_dot(nb_contact_nodes, dim);
	for (auto && data : zip(make_view(gap_dot), make_view(r_velo),
	make_view(r_acce), make_view(r_old_acce))) {
	auto & gap_dot = std::get<0>(data);
	auto & r_velo = std::get<1>(data);
	auto & r_acce = std::get<2>(data);
	auto & r_old_acce = std::get<3>(data);

	gap_dot = r_velo + delta_t * r_acce - 1. / 2. * delta_t * r_old_acce;
	}

	// compute friction traction to stop sliding
	- Array<Real> & traction =
	+ auto & traction =
	const_cast<Array<Real> &>(this->friction_traction.getArray());
	auto it_fric_trac = traction.begin(dim);
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	Vector<Real> fric_trac = it_fric_trac[n];
	// node pair is NOT in contact
	if (!is_in_contact(n)) {
	fric_trac.zero(); // set to zero
	}

	// node pair is in contact
	else {
	// compute friction traction
	- for (UInt d = 0; d < dim; ++d)
	+ for (UInt d = 0; d < dim; ++d) {
	fric_trac(d) = impedance(n) * gap_dot(n, d) / 2.;
	+ }
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::applyFrictionTraction() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel & model = this->contact.getModel();
	Array<Real> & residual = model.getInternalForce();
	UInt dim = model.getSpatialDimension();

	const SynchronizedArray<UInt> & slaves = this->contact.getSlaves();
	const SynchronizedArray<Real> & lumped_boundary_slaves =
	this->contact.getLumpedBoundarySlaves();

	UInt nb_contact_nodes = this->contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	UInt slave = slaves(n);

	for (UInt d = 0; d < dim; ++d) {
	residual(slave, d) -=
	lumped_boundary_slaves(n) * this->friction_traction(n, d);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::registerSynchronizedArray(SynchronizedArrayBase & array) {
	AKANTU_DEBUG_IN();

	this->frictional_strength.registerDependingArray(array);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::dumpRestart(const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	this->is_sticking.dumpRestartFile(file_name);
	this->frictional_strength.dumpRestartFile(file_name);
	this->friction_traction.dumpRestartFile(file_name);
	this->slip.dumpRestartFile(file_name);
	this->cumulative_slip.dumpRestartFile(file_name);
	this->slip_velocity.dumpRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::readRestart(const std::string & file_name) {
	AKANTU_DEBUG_IN();

	this->is_sticking.readRestartFile(file_name);
	this->frictional_strength.readRestartFile(file_name);
	this->friction_traction.readRestartFile(file_name);
	this->cumulative_slip.readRestartFile(file_name);
	this->slip_velocity.readRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::setParam(const std::string & name, UInt node,
	Real value) {
	AKANTU_DEBUG_IN();

	- SynchronizedArray<Real> & array =
	- this->get(name).get<SynchronizedArray<Real>>();
	+ auto & array = this->get(name).get<SynchronizedArray<Real>>();
	Int index = this->contact.getNodeIndex(node);
	if (index < 0) {
	AKANTU_DEBUG_WARNING("Node "
	<< node << " is not a contact node. "
	<< "Therefore, cannot set interface parameter!!");
	} else {
	array(index) = value; // put value
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt NTNBaseFriction::getNbStickingNodes() const {
	AKANTU_DEBUG_IN();

	UInt nb_stick = 0;

	UInt nb_nodes = this->contact.getNbContactNodes();
	const SynchronizedArray<UInt> & nodes = this->contact.getSlaves();
	const SynchronizedArray<bool> & is_in_contact =
	this->contact.getIsInContact();

	const Mesh & mesh = this->contact.getModel().getMesh();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = mesh.isLocalOrMasterNode(nodes(n));
	bool is_pbc_slave_node = mesh.isPeriodicSlave(nodes(n));
	if (is_local_node && !is_pbc_slave_node && is_in_contact(n) &&
	this->is_sticking(n)) {
	nb_stick++;
	}
	}

	mesh.getCommunicator().allReduce(nb_stick, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return nb_stick;
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNBaseFriction [" << std::endl;
	Parsable::printself(stream, indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNBaseFriction::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	// &(this->contact.getSlaves());

	if (field_id == "is_sticking") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<bool>>(
	this->is_sticking.getArray()));
	} else if (field_id == "frictional_strength") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->frictional_strength.getArray()));
	} else if (field_id == "friction_traction") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->friction_traction.getArray()));
	} else if (field_id == "slip") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(this->slip.getArray()));
	} else if (field_id == "cumulative_slip") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->cumulative_slip.getArray()));
	} else if (field_id == "slip_velocity") {
	this->internalAddDumpFieldToDumper(
	dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->slip_velocity.getArray()));
	} else {
	this->contact.addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.hh
	index e36eef799..5ae355bd3 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_base_friction.hh
	@@ -1,178 +1,178 @@
	/**
	* @file ntn_base_friction.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Tue Feb 20 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief base class for ntn and ntrf friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AST_NTN_BASE_FRICTION_HH_
	#define AST_NTN_BASE_FRICTION_HH_

	/* -------------------------------------------------------------------------- */
	// akantu
	#include "parsable.hh"

	// simtools
	#include "ntn_base_contact.hh"

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ParameterTyped<akantu::SynchronizedArray<Real>>::setAuto(
	const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	Real r = in_param;
	param.setAndChangeDefault(r);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void ParameterTyped<akantu::SynchronizedArray<Real>>::setTyped<Real>(
	const Real & value) {
	param.setAndChangeDefault(value);
	}

	/* -------------------------------------------------------------------------- */
	class NTNBaseFriction : public Parsable, public Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNBaseFriction(NTNBaseContact & contact, const ID & id = "friction");
	- virtual ~NTNBaseFriction() = default;
	+ ~NTNBaseFriction() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute friction traction
	virtual void computeFrictionTraction();

	/// compute stick traction (friction traction needed to stick the nodes)
	virtual void computeStickTraction();

	/// apply the friction force
	virtual void applyFrictionTraction();

	/// compute slip
	virtual void updateSlip();

	/// register Syncronizedarrays for sync
	virtual void registerSynchronizedArray(SynchronizedArrayBase & array);

	/// dump restart file
	virtual void dumpRestart(const std::string & file_name) const;

	/// read restart file
	virtual void readRestart(const std::string & file_name);

	/// set to steady state
	virtual void setToSteadyState() { AKANTU_TO_IMPLEMENT(); };

	/// get the number of sticking nodes (in parallel)
	/// a node that is not in contact does not count as sticking
	virtual UInt getNbStickingNodes() const;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// compute frictional strength according to friction law
	virtual void computeFrictionalStrength() = 0;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	- virtual void addDumpFieldToDumper(const std::string & dumper_name,
	- const std::string & field_id);
	+ void addDumpFieldToDumper(const std::string & dumper_name,
	+ const std::string & field_id) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Contact, contact, const NTNBaseContact &)

	AKANTU_GET_MACRO(IsSticking, is_sticking, const SynchronizedArray<bool> &)
	AKANTU_GET_MACRO(FrictionalStrength, frictional_strength,
	const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(FrictionTraction, friction_traction,
	const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(Slip, slip, const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(CumulativeSlip, cumulative_slip,
	const SynchronizedArray<Real> &)
	AKANTU_GET_MACRO(SlipVelocity, slip_velocity, const SynchronizedArray<Real> &)

	/// set parameter of a given node
	/// (if you need to set to all: used the setMixed function of the Parsable).
	virtual void setParam(const std::string & name, UInt node, Real value);

	// replaced by the setMixed of the Parsable
	// virtual void setParam(const std::string & param, Real value) {
	// AKANTU_ERROR("Friction does not know the following parameter: " <<
	// param);
	// };

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	NTNBaseContact & contact;

	// if node is sticking
	SynchronizedArray<bool> is_sticking;
	// frictional strength
	SynchronizedArray<Real> frictional_strength;
	// friction force
	SynchronizedArray<Real> friction_traction;
	// slip
	SynchronizedArray<Real> slip;
	SynchronizedArray<Real> cumulative_slip;
	// slip velocity (tangential vector)
	SynchronizedArray<Real> slip_velocity;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntn_base_friction_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTNBaseFriction & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTN_BASE_FRICTION_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.cc
	index d633a0af8..c8297bc98 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.cc
	@@ -1,556 +1,558 @@
	/**
	* @file ntn_contact.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of ntn_contact
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_contact.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NTNContact::NTNContact(SolidMechanicsModel & model, const ID & id)
	: NTNBaseContact(model, id),
	masters(0, 1, 0, id + ":masters", std::numeric_limits<UInt>::quiet_NaN(),
	"masters"),
	lumped_boundary_masters(0, 1, 0, id + ":lumped_boundary_masters",
	std::numeric_limits<Real>::quiet_NaN(),
	"lumped_boundary_masters"),
	master_elements("master_elements", id) {
	AKANTU_DEBUG_IN();

	const Mesh & mesh = this->model.getMesh();
	UInt spatial_dimension = this->model.getSpatialDimension();

	this->master_elements.initialize(mesh, _nb_component = 1,
	_spatial_dimension = spatial_dimension - 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::pairInterfaceNodes(const ElementGroup & slave_boundary,
	const ElementGroup & master_boundary,
	UInt surface_normal_dir, const Mesh & mesh,
	Array<UInt> & pairs) {
	AKANTU_DEBUG_IN();

	pairs.resize(0);
	AKANTU_DEBUG_ASSERT(pairs.getNbComponent() == 2,
	"Array of node pairs should have nb_component = 2,"
	<< " but has nb_component = "
	<< pairs.getNbComponent());

	UInt dim = mesh.getSpatialDimension();
	AKANTU_DEBUG_ASSERT(surface_normal_dir < dim,
	"Mesh is of " << dim << " dimensions"
	<< " and cannot have direction "
	<< surface_normal_dir
	<< " for surface normal");

	// offset for projection computation
	Vector<UInt> offset(dim - 1);
	for (UInt i = 0, j = 0; i < dim; ++i) {
	if (surface_normal_dir != i) {
	offset(j) = i;
	++j;
	}
	}

	// find projected node coordinates
	const Array<Real> & coordinates = mesh.getNodes();

	// find slave nodes
	Array<Real> proj_slave_coord(slave_boundary.getNbNodes(), dim - 1, 0.);
	Array<UInt> slave_nodes(slave_boundary.getNbNodes());
	UInt n(0);
	for (auto && slave_node : slave_boundary.getNodeGroup().getNodes()) {
	for (UInt d = 0; d < dim - 1; ++d) {
	proj_slave_coord(n, d) = coordinates(slave_node, offset[d]);
	slave_nodes(n) = slave_node;
	}
	++n;
	}

	// find master nodes
	Array<Real> proj_master_coord(master_boundary.getNbNodes(), dim - 1, 0.);
	Array<UInt> master_nodes(master_boundary.getNbNodes());
	n = 0;
	for (auto && master_node : master_boundary.getNodeGroup().getNodes()) {
	for (UInt d = 0; d < dim - 1; ++d) {
	proj_master_coord(n, d) = coordinates(master_node, offset[d]);
	master_nodes(n) = master_node;
	}
	++n;
	}

	// find minimum distance between slave nodes to define tolerance
	Real min_dist = std::numeric_limits<Real>::max();
	for (UInt i = 0; i < proj_slave_coord.size(); ++i) {
	for (UInt j = i + 1; j < proj_slave_coord.size(); ++j) {
	Real dist = 0.;
	for (UInt d = 0; d < dim - 1; ++d) {
	dist += (proj_slave_coord(i, d) - proj_slave_coord(j, d)) *
	(proj_slave_coord(i, d) - proj_slave_coord(j, d));
	}
	if (dist < min_dist) {
	min_dist = dist;
	}
	}
	}
	min_dist = std::sqrt(min_dist);
	Real local_tol = 0.1 * min_dist;

	// find master slave node pairs
	for (UInt i = 0; i < proj_slave_coord.size(); ++i) {
	for (UInt j = 0; j < proj_master_coord.size(); ++j) {
	Real dist = 0.;
	for (UInt d = 0; d < dim - 1; ++d) {
	dist += (proj_slave_coord(i, d) - proj_master_coord(j, d)) *
	(proj_slave_coord(i, d) - proj_master_coord(j, d));
	}
	dist = std::sqrt(dist);
	if (dist < local_tol) { // it is a pair
	Vector<UInt> pair(2);
	pair[0] = slave_nodes(i);
	pair[1] = master_nodes(j);
	pairs.push_back(pair);
	continue; // found master do not need to search further for this slave
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::addSurfacePair(const ID & slave, const ID & master,
	UInt surface_normal_dir) {
	AKANTU_DEBUG_IN();

	const Mesh & mesh = this->model.getMesh();

	const ElementGroup & slave_boundary = mesh.getElementGroup(slave);
	const ElementGroup & master_boundary = mesh.getElementGroup(master);

	this->contact_surfaces.insert(&slave_boundary);
	this->contact_surfaces.insert(&master_boundary);

	Array<UInt> pairs(0, 2);
	NTNContact::pairInterfaceNodes(slave_boundary, master_boundary,
	surface_normal_dir, this->model.getMesh(),
	pairs);

	// eliminate pairs which contain a pbc slave node
	Array<UInt> pairs_no_PBC_slaves(0, 2);
	Array<UInt>::const_vector_iterator it = pairs.begin(2);
	Array<UInt>::const_vector_iterator end = pairs.end(2);
	for (; it != end; ++it) {
	const Vector<UInt> & pair = *it;
	if (not mesh.isPeriodicSlave(pair(0)) and
	not mesh.isPeriodicSlave(pair(1))) {
	pairs_no_PBC_slaves.push_back(pair);
	}
	}

	this->addNodePairs(pairs_no_PBC_slaves);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::addNodePairs(const Array<UInt> & pairs) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(pairs.getNbComponent() == 2,
	"Array of node pairs should have nb_component = 2,"
	<< " but has nb_component = "
	<< pairs.getNbComponent());
	UInt nb_pairs = pairs.size();
	for (UInt n = 0; n < nb_pairs; ++n) {
	this->addSplitNode(pairs(n, 0), pairs(n, 1));
	}

	// synchronize with depending nodes
	findBoundaryElements(this->slaves.getArray(), this->slave_elements);
	findBoundaryElements(this->masters.getArray(), this->master_elements);
	updateInternalData();
	syncArrays(_added);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::getNodePairs(Array<UInt> & pairs) const {
	AKANTU_DEBUG_IN();

	pairs.resize(0);
	AKANTU_DEBUG_ASSERT(pairs.getNbComponent() == 2,
	"Array of node pairs should have nb_component = 2,"
	<< " but has nb_component = "
	<< pairs.getNbComponent());
	UInt nb_pairs = this->getNbContactNodes();
	for (UInt n = 0; n < nb_pairs; ++n) {
	Vector<UInt> pair{this->slaves(n), this->masters(n)};
	pairs.push_back(pair);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::addSplitNode(UInt slave, UInt master) {
	AKANTU_DEBUG_IN();

	NTNBaseContact::addSplitNode(slave);

	this->masters.push_back(master);
	this->lumped_boundary_masters.push_back(
	std::numeric_limits<Real>::quiet_NaN());

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/*
	This function only works for surface elements with one quad point. For
	surface elements with more quad points, it computes still, but the result
	might not be what you are looking for.
	*/
	void NTNContact::updateNormals() {
	AKANTU_DEBUG_IN();

	// set normals to zero
	this->normals.zero();

	// contact information
	UInt dim = this->model.getSpatialDimension();
	UInt nb_contact_nodes = this->getNbContactNodes();

	this->synch_registry->synchronize(
	SynchronizationTag::_cf_nodal); // synchronize current pos
	const Array<Real> & cur_pos = this->model.getCurrentPosition();

	FEEngine & boundary_fem = this->model.getFEEngineBoundary();
	const Mesh & mesh = this->model.getMesh();

	for (auto ghost_type : ghost_types) {
	- for (auto & type : mesh.elementTypes(dim - 1, ghost_type)) {
	+ for (const auto & type : mesh.elementTypes(dim - 1, ghost_type)) {
	// compute the normals
	Array<Real> quad_normals(0, dim);
	boundary_fem.computeNormalsOnIntegrationPoints(cur_pos, quad_normals,
	type, ghost_type);

	UInt nb_quad_points =
	boundary_fem.getNbIntegrationPoints(type, ghost_type);

	// new version: compute normals only based on master elements (and not all
	// boundary elements)
	// -------------------------------------------------------------------------------------

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);

	// loop over contact nodes
	for (auto & element : (this->master_elements)(type, ghost_type)) {
	for (UInt q = 0; q < nb_nodes_per_element; ++q) {
	UInt node = connectivity(element, q);
	UInt node_index = this->masters.find(node);
	AKANTU_DEBUG_ASSERT(node_index != UInt(-1), "Could not find node "
	<< node
	<< " in the array!");

	for (UInt q = 0; q < nb_quad_points; ++q) {
	// add quad normal to master normal
	for (UInt d = 0; d < dim; ++d) {
	this->normals(node_index, d) +=
	quad_normals(element * nb_quad_points + q, d);
	}
	}
	}
	}
	}
	}

	Real * master_normals = this->normals.storage();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	- if (dim == 2)
	+ if (dim == 2) {
	Math::normalize2(&(master_normals[n * dim]));
	- else if (dim == 3)
	+ } else if (dim == 3) {
	Math::normalize3(&(master_normals[n * dim]));
	+ }
	}

	// // normalize normals
	// auto nit = this->normals.begin();
	// auto nend = this->normals.end();
	// for (; nit != nend; ++nit) {
	// nit->normalize();
	// }

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::dumpRestart(const std::string & file_name) const {
	AKANTU_DEBUG_IN();

	NTNBaseContact::dumpRestart(file_name);
	this->masters.dumpRestartFile(file_name);
	this->lumped_boundary_masters.dumpRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::readRestart(const std::string & file_name) {
	AKANTU_DEBUG_IN();

	NTNBaseContact::readRestart(file_name);
	this->masters.readRestartFile(file_name);
	this->lumped_boundary_masters.readRestartFile(file_name);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::updateImpedance() {
	AKANTU_DEBUG_IN();

	UInt nb_contact_nodes = getNbContactNodes();
	Real delta_t = this->model.getTimeStep();
	AKANTU_DEBUG_ASSERT(delta_t != NAN,
	"Time step is NAN. Have you set it already?");

	const Array<Real> & mass = this->model.getMass();

	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	UInt master = this->masters(n);
	UInt slave = this->slaves(n);

	Real imp = (this->lumped_boundary_masters(n) / mass(master)) +
	(this->lumped_boundary_slaves(n) / mass(slave));
	imp = 2 / delta_t / imp;
	this->impedance(n) = imp;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::updateLumpedBoundary() {
	AKANTU_DEBUG_IN();

	internalUpdateLumpedBoundary(this->slaves.getArray(), this->slave_elements,
	this->lumped_boundary_slaves);

	internalUpdateLumpedBoundary(this->masters.getArray(), this->master_elements,
	this->lumped_boundary_masters);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::applyContactPressure() {
	AKANTU_DEBUG_IN();

	UInt nb_ntn_pairs = getNbContactNodes();
	UInt dim = this->model.getSpatialDimension();

	Array<Real> & residual = this->model.getInternalForce();

	for (UInt n = 0; n < nb_ntn_pairs; ++n) {
	UInt master = this->masters(n);
	UInt slave = this->slaves(n);

	for (UInt d = 0; d < dim; ++d) {
	residual(master, d) +=
	this->lumped_boundary_masters(n) * this->contact_pressure(n, d);
	residual(slave, d) -=
	this->lumped_boundary_slaves(n) * this->contact_pressure(n, d);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::computeRelativeTangentialField(
	const Array<Real> & field, Array<Real> & rel_tang_field) const {
	AKANTU_DEBUG_IN();

	// resize arrays to zero
	rel_tang_field.resize(0);

	UInt dim = this->model.getSpatialDimension();

	auto it_field = field.begin(dim);
	auto it_normal = this->normals.getArray().begin(dim);

	Vector<Real> rfv(dim);
	Vector<Real> np_rfv(dim);

	UInt nb_contact_nodes = this->slaves.size();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// nodes
	UInt slave = this->slaves(n);
	UInt master = this->masters(n);

	// relative field vector (slave - master)
	rfv = Vector<Real>(it_field[slave]);
	rfv -= Vector<Real>(it_field[master]);

	// normal projection of relative field
	const Vector<Real> normal_v = it_normal[n];
	np_rfv = normal_v;
	np_rfv *= rfv.dot(normal_v);

	// subract normal projection from relative field to get the tangential
	// projection
	rfv -= np_rfv;
	rel_tang_field.push_back(rfv);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::computeRelativeNormalField(
	const Array<Real> & field, Array<Real> & rel_normal_field) const {
	AKANTU_DEBUG_IN();

	// resize arrays to zero
	rel_normal_field.resize(0);

	UInt dim = this->model.getSpatialDimension();
	// Real * field_p = field.storage();
	// Real * normals_p = this->normals.storage();

	Array<Real>::const_iterator<Vector<Real>> it_field = field.begin(dim);
	Array<Real>::const_iterator<Vector<Real>> it_normal =
	this->normals.getArray().begin(dim);

	Vector<Real> rfv(dim);

	UInt nb_contact_nodes = this->getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// nodes
	UInt slave = this->slaves(n);
	UInt master = this->masters(n);

	// relative field vector (slave - master)
	rfv = Vector<Real>(it_field[slave]);
	rfv -= Vector<Real>(it_field[master]);

	// length of normal projection of relative field
	const Vector<Real> normal_v = it_normal[n];
	rel_normal_field.push_back(rfv.dot(normal_v));
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Int NTNContact::getNodeIndex(UInt node) const {
	AKANTU_DEBUG_IN();

	Int slave_i = NTNBaseContact::getNodeIndex(node);
	Int master_i = this->masters.find(node);

	AKANTU_DEBUG_OUT();
	return std::max(slave_i, master_i);
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNContact [" << std::endl;
	NTNBaseContact::printself(stream, indent);
	stream << space << " + masters : " << std::endl;
	this->masters.printself(stream, indent + 2);
	stream << space << " + lumped_boundary_mastres : " << std::endl;
	this->lumped_boundary_masters.printself(stream, indent + 2);

	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::syncArrays(SyncChoice sync_choice) {
	AKANTU_DEBUG_IN();

	NTNBaseContact::syncArrays(sync_choice);

	this->masters.syncElements(sync_choice);
	this->lumped_boundary_masters.syncElements(sync_choice);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTNContact::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_IN();

	/*
	#ifdef AKANTU_USE_IOHELPER
	const Array<UInt> & nodal_filter = this->slaves.getArray();

	#define ADD_FIELD(field_id, field, type) \
	internalAddDumpFieldToDumper(dumper_name, \
	field_id, \
	new DumperIOHelper::NodalField< type, true, \
	Array<type>, \
	Array<UInt> >(field, 0, 0, &nodal_filter))
	*/

	if (field_id == "lumped_boundary_master") {
	internalAddDumpFieldToDumper(dumper_name, field_id,
	std::make_unique<dumpers::NodalField<Real>>(
	this->lumped_boundary_masters.getArray()));
	} else {
	NTNBaseContact::addDumpFieldToDumper(dumper_name, field_id);
	}

	/*
	#undef ADD_FIELD
	#endif
	*/

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.hh
	index 39f69c8c3..5c14da23b 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_contact.hh
	@@ -1,167 +1,167 @@
	/**
	* @file ntn_contact.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief contact for node to node discretization
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_NTN_CONTACT_HH_
	#define AST_NTN_CONTACT_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class NTNContact : public NTNBaseContact {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNContact(SolidMechanicsModel & model, const ID & id = "contact");
	~NTNContact() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// add surface pair and pair nodes according to the surface normal
	void addSurfacePair(const ID & slave, const ID & master,
	UInt surface_normal_dir);

	/// fills the pairs vector with interface node pairs (*,0)=slaves,
	/// (*,1)=masters
	static void pairInterfaceNodes(const ElementGroup & slave_boundary,
	const ElementGroup & master_boundary,
	UInt surface_normal_dir, const Mesh & mesh,
	Array<UInt> & pairs);

	// add node pairs from a list with pairs(,0)=slaves and pairs(,1)=masters
	void addNodePairs(const Array<UInt> & pairs);

	/// add node pair
	void addSplitNode(UInt slave, UInt master) override;

	/// update (compute the normals on the master nodes)
	void updateNormals() override;

	/// update the lumped boundary B matrix
	void updateLumpedBoundary() override;

	/// update the impedance matrix
	void updateImpedance() override;

	/// impose the normal contact force
	void applyContactPressure() override;

	/// dump restart file
	void dumpRestart(const std::string & file_name) const override;

	/// read restart file
	void readRestart(const std::string & file_name) override;

	/// compute the normal gap
	void computeNormalGap(Array<Real> & gap) const override {
	this->computeRelativeNormalField(this->model.getCurrentPosition(), gap);
	};

	/// compute relative normal field (only value that has to be multiplied with
	/// the normal)
	/// relative to master nodes
	void
	computeRelativeNormalField(const Array<Real> & field,
	Array<Real> & rel_normal_field) const override;

	/// compute relative tangential field (complet array)
	/// relative to master nodes
	void
	computeRelativeTangentialField(const Array<Real> & field,
	Array<Real> & rel_tang_field) const override;

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// synchronize arrays
	void syncArrays(SyncChoice sync_choice) override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) override;
	// virtual void addDumpFieldVector(const std::string & field_id);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Masters, masters, const SynchronizedArray<UInt> &)
	AKANTU_GET_MACRO(LumpedBoundaryMasters, lumped_boundary_masters,
	const SynchronizedArray<Real> &)

	/// get interface node pairs (,0) are slaves, (,1) are masters
	void getNodePairs(Array<UInt> & pairs) const;

	/// get index of node in either slaves or masters array
	/// if node is in neither of them, return -1
	Int getNodeIndex(UInt node) const override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// array of master nodes
	SynchronizedArray<UInt> masters;
	/// lumped boundary of master nodes
	SynchronizedArray<Real> lumped_boundary_masters;

	// element list for dump and lumped_boundary
	ElementTypeMapArray<UInt> master_elements;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntn_contact_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTNContact & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTN_CONTACT_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction.hh
	index 58de04336..82cf47e17 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction.hh
	@@ -1,100 +1,100 @@
	/**
	* @file ntn_friction.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of friction for node to node contact
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_NTN_FRICTION_HH_
	#define AST_NTN_FRICTION_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_friction.hh"
	#include "ntn_friclaw_coulomb.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw = NTNFricLawCoulomb,
	class Regularisation = NTNFricRegNoRegularisation>
	class NTNFriction : public FrictionLaw<Regularisation> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTNFriction(NTNBaseContact & contact, const ID & id = "friction");
	- virtual ~NTNFriction(){};
	+ ~NTNFriction() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// apply the friction force
	- virtual void applyFrictionTraction();
	+ void applyFrictionTraction() override;

	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	// virtual void addDumpFieldToDumper(const std::string & dumper_name,
	// const std::string & field_id);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <template <class> class FrictionLaw, class Regularisation>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTNFriction<FrictionLaw, Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntn_friction_tmpl.hh"

	#endif /* AST_NTN_FRICTION_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction_tmpl.hh
	index c2b3c46d6..473799932 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_friction_tmpl.hh
	@@ -1,97 +1,99 @@
	/**
	* @file ntn_friction_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Wed Oct 17 2018
	*
	- * @brief base class for ntn and ntrf friction (template functions implementation)
	+ * @brief base class for ntn and ntrf friction (template functions
	+ * implementation)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw, class Regularisation>
	-NTNFriction<FrictionLaw, Regularisation>::NTNFriction(
	- NTNBaseContact & contact, const ID & id)
	+NTNFriction<FrictionLaw, Regularisation>::NTNFriction(NTNBaseContact & contact,
	+ const ID & id)
	: FrictionLaw<Regularisation>(contact, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw, class Regularisation>
	void NTNFriction<FrictionLaw, Regularisation>::applyFrictionTraction() {
	AKANTU_DEBUG_IN();

	- NTNContact & ntn_contact = dynamic_cast<NTNContact &>(this->contact);
	+ auto & ntn_contact = dynamic_cast<NTNContact &>(this->contact);
	SolidMechanicsModel & model = ntn_contact.getModel();
	Array<Real> & residual = model.getInternalForce();
	UInt dim = model.getSpatialDimension();

	const SynchronizedArray<UInt> & masters = ntn_contact.getMasters();
	const SynchronizedArray<UInt> & slaves = ntn_contact.getSlaves();
	const SynchronizedArray<Real> & l_boundary_slaves =
	ntn_contact.getLumpedBoundarySlaves();
	const SynchronizedArray<Real> & l_boundary_masters =
	ntn_contact.getLumpedBoundaryMasters();

	UInt nb_contact_nodes = ntn_contact.getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	UInt master = masters(n);
	UInt slave = slaves(n);

	for (UInt d = 0; d < dim; ++d) {
	residual(master, d) +=
	l_boundary_masters(n) * this->friction_traction(n, d);
	residual(slave, d) -=
	l_boundary_slaves(n) * this->friction_traction(n, d);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw, class Regularisation>
	void NTNFriction<FrictionLaw, Regularisation>::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTNFriction [" << std::endl;
	FrictionLaw<Regularisation>::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.cc
	index 710905418..0cbb97ad6 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.cc
	@@ -1,155 +1,155 @@
	/**
	* @file ntn_initiation_function.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Tue Feb 20 2018
	* @date last modification: Wed Oct 17 2018
	*
	* @brief implementation of initializing ntn and ntrf friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_initiation_function.hh"
	#include "mIIasym_contact.hh"
	#include "ntn_friction.hh"
	#include "ntrf_friction.hh"

	// friction regularisations
	#include "ntn_fricreg_rubin_ampuero.hh"
	#include "ntn_fricreg_simplified_prakash_clifton.hh"

	// friction laws
	#include "ntn_friclaw_linear_cohesive.hh"
	#include "ntn_friclaw_linear_slip_weakening.hh"
	#include "ntn_friclaw_linear_slip_weakening_no_healing.hh"

	#include "aka_factory.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	std::unique_ptr<NTNBaseFriction>
	initializeNTNFriction(NTNBaseContact & contact) {
	AKANTU_DEBUG_IN();
	auto sub_sect = getStaticParser().getSubSections(ParserType::_friction);
	auto it = sub_sect.first;
	const ParserSection & section = *it;

	std::string friction_law = section.getName();
	std::string friction_reg = section.getOption("no_regularisation");

	std::unique_ptr<NTNBaseFriction> friction =
	initializeNTNFriction(contact, friction_law, friction_reg);

	friction->parseSection(section);

	if (++it != sub_sect.second) {
	AKANTU_DEBUG_WARNING("There were several friction sections in input file. "
	<< "Only first one was used and all others ignored.");
	}

	AKANTU_DEBUG_OUT();
	return friction;
	}

	namespace {
	using NTNFactory =
	Factory<NTNBaseFriction, std::tuple<bool, ID, ID>, NTNBaseContact &>;

	// std::ostream & operator<<(std::ostream & stream,
	// const std::tuple<bool, ID, ID> & tuple) {
	// stream << "[" << std::get<0>(tuple) << ", " << std::get<1>(tuple) << ", "
	// << std::get<2>(tuple) << ", "
	// << "]" << std::endl;
	// return stream;
	// }

	template <bool is_ntn, template <class> class FrictionLaw, class FrictionReg>
	bool registerFriction(const ID & friction_law, const ID & friction_reg) {
	NTNFactory::getInstance().registerAllocator(
	std::make_tuple(is_ntn, friction_law, friction_reg),
	[](NTNBaseContact & contact) -> std::unique_ptr<NTNBaseFriction> {
	return std::make_unique<
	std::conditional_t<is_ntn, NTNFriction<FrictionLaw, FrictionReg>,
	NTRFFriction<FrictionLaw, FrictionReg>>>(
	contact);
	});
	return true;
	}

	template <template <class> class FrictionLaw, class FrictionReg>
	bool registerFrictionNTNandNTRF(const ID & friction_law,
	const ID & friction_reg) {
	registerFriction<true, FrictionLaw, FrictionReg>(friction_law,
	friction_reg);
	registerFriction<false, FrictionLaw, FrictionReg>(friction_law,
	friction_reg);
	return true;
	}

	template <template <class> class FrictionLaw>
	bool registerFrictionRegs(const ID & friction_law) {
	registerFrictionNTNandNTRF<FrictionLaw, NTNFricRegRubinAmpuero>(
	friction_law, "no_regularisation");
	registerFrictionNTNandNTRF<FrictionLaw, NTNFricRegRubinAmpuero>(
	friction_law, "rubin_ampuero");
	registerFrictionNTNandNTRF<FrictionLaw, NTNFricRegSimplifiedPrakashClifton>(
	friction_law, "simplified_prakash_clifton");
	return true;
	}

	bool registerFrictionLaws() {
	registerFrictionRegs<NTNFricLawCoulomb>("coulomb");
	registerFrictionRegs<NTNFricLawLinearSlipWeakening>(
	"linear_slip_weakening");
	registerFrictionRegs<NTNFricLawLinearSlipWeakeningNoHealing>(
	"linear_slip_weakening_no_healing");
	registerFrictionRegs<NTNFricLawLinearCohesive>("linear_cohesive");
	return true;
	}

	- static bool _ = registerFrictionLaws();
	+ bool _ = registerFrictionLaws();
	} // namespace

	/* -------------------------------------------------------------------------- */
	std::unique_ptr<NTNBaseFriction>
	initializeNTNFriction(NTNBaseContact & contact,
	const std::string & friction_law,
	const std::string & friction_reg) {
	bool is_ntn_contact = contact.isNTNContact();
	return NTNFactory::getInstance().allocate(
	std::make_tuple(is_ntn_contact, friction_law, friction_reg), contact);
	}

	} // namespace akantu

	namespace std {
	inline ostream & operator<<(ostream & stream,
	const tuple<bool, string, string> & _this) {
	stream << "<" << get<0>(_this) << ", " << get<1>(_this) << ", "
	<< get<2>(_this) << ">";
	return stream;
	}
	} // namespace std
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.hh
	index 9cdc4e0b4..a9ed1d264 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntn_initiation_function.hh
	@@ -1,48 +1,48 @@
	/**
	* @file ntn_initiation_function.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Wed Oct 17 2018
	*
	* @brief initiation ntn and ntrf friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_friction.hh"
	#include "ntrf_contact.hh"
	#include "parameter_reader.hh"

	namespace akantu {

	std::unique_ptr<NTNBaseFriction>
	initializeNTNFriction(NTNBaseContact & contact);

	std::unique_ptr<NTNBaseFriction>
	initializeNTNFriction(NTNBaseContact & contact,
	const std::string & friction_law,
	const std::string & friction_reg);

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.cc b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.cc
	index c37967de4..a6d980b15 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.cc
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.cc
	@@ -1,322 +1,324 @@
	/**
	* @file ntrf_contact.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Tue May 21 2019
	*
	* @brief contact for node to rigid flat interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntrf_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NTRFContact::NTRFContact(SolidMechanicsModel & model, const ID & id)
	- : NTNBaseContact(model, id),
	- reference_point(model.getSpatialDimension()),
	+ : NTNBaseContact(model, id), reference_point(model.getSpatialDimension()),
	normal(model.getSpatialDimension()) {
	AKANTU_DEBUG_IN();

	is_ntn_contact = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::setReferencePoint(Real x, Real y, Real z) {
	AKANTU_DEBUG_IN();

	Real coord[3];
	coord[0] = x;
	coord[1] = y;
	coord[2] = z;

	UInt dim = this->model.getSpatialDimension();
	- for (UInt d = 0; d < dim; ++d)
	+ for (UInt d = 0; d < dim; ++d) {
	this->reference_point(d) = coord[d];
	+ }

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::setNormal(Real x, Real y, Real z) {
	AKANTU_DEBUG_IN();

	UInt dim = this->model.getSpatialDimension();

	Real coord[3];
	coord[0] = x;
	coord[1] = y;
	coord[2] = z;

	- for (UInt d = 0; d < dim; ++d)
	+ for (UInt d = 0; d < dim; ++d) {
	this->normal(d) = coord[d];
	+ }

	this->normal.normalize();

	this->updateNormals();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::addSurface(const ID & surf) {
	AKANTU_DEBUG_IN();

	const Mesh & mesh_ref = this->model.getMesh();

	try {
	const ElementGroup & boundary = mesh_ref.getElementGroup(surf);
	this->contact_surfaces.insert(&boundary);

	// find slave nodes
	for (auto && node : boundary.getNodeGroup().getNodes()) {
	if (not mesh_ref.isPeriodicSlave(node)) {
	this->addSplitNode(node);
	}
	}
	} catch (debug::Exception & e) {
	AKANTU_DEBUG_INFO("NTRFContact addSurface did not found subboundary "
	<< surf
	<< " and ignored it. Other procs might have it :)");
	}

	// synchronize with depending nodes
	findBoundaryElements(this->slaves.getArray(), this->slave_elements);
	updateInternalData();
	syncArrays(_added);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::addNodes(Array<UInt> & nodes) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = nodes.size();
	UInt nb_compo = nodes.getNbComponent();
	for (UInt n = 0; n < nb_nodes; ++n) {
	for (UInt c = 0; c < nb_compo; ++c) {
	this->addSplitNode(nodes(n, c));
	}
	}

	// synchronize with depending nodes
	findBoundaryElements(this->slaves.getArray(), this->slave_elements);
	updateInternalData();
	syncArrays(_added);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::updateNormals() {
	AKANTU_DEBUG_IN();

	// normal is the same for all slaves
	this->normals.set(this->normal);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::updateImpedance() {
	AKANTU_DEBUG_IN();

	UInt nb_contact_nodes = getNbContactNodes();
	Real delta_t = this->model.getTimeStep();
	AKANTU_DEBUG_ASSERT(delta_t != NAN,
	"Time step is NAN. Have you set it already?");

	const Array<Real> & mass = this->model.getMass();

	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	UInt slave = this->slaves(n);

	Real imp = this->lumped_boundary_slaves(n) / mass(slave);
	imp = 2 / delta_t / imp;
	this->impedance(n) = imp;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::computeRelativeTangentialField(
	const Array<Real> & field, Array<Real> & rel_tang_field) const {
	AKANTU_DEBUG_IN();

	// resize arrays to zero
	rel_tang_field.resize(0);

	UInt dim = this->model.getSpatialDimension();

	Array<Real>::const_iterator<Vector<Real>> it_field = field.begin(dim);
	Array<Real>::const_iterator<Vector<Real>> it_normal =
	this->normals.getArray().begin(dim);

	Vector<Real> rfv(dim);
	Vector<Real> np_rfv(dim);

	UInt nb_contact_nodes = this->slaves.size();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// nodes
	UInt node = this->slaves(n);

	// relative field vector
	rfv = it_field[node];
	;

	// normal projection of relative field
	const Vector<Real> & normal_v = it_normal[n];
	np_rfv = normal_v;
	np_rfv *= rfv.dot(normal_v);

	// subtract normal projection from relative field to get the tangential
	// projection
	rfv -= np_rfv;
	rel_tang_field.push_back(rfv);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::computeNormalGap(Array<Real> & gap) const {
	AKANTU_DEBUG_IN();

	gap.resize(0);

	UInt dim = this->model.getSpatialDimension();

	Array<Real>::const_iterator<Vector<Real>> it_cur_pos =
	this->model.getCurrentPosition().begin(dim);
	Array<Real>::const_iterator<Vector<Real>> it_normal =
	this->normals.getArray().begin(dim);

	Vector<Real> gap_v(dim);

	UInt nb_contact_nodes = this->getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// nodes
	UInt node = this->slaves(n);

	// gap vector
	gap_v = it_cur_pos[node];
	gap_v -= this->reference_point;

	// length of normal projection of gap vector
	const Vector<Real> & normal_v = it_normal[n];
	gap.push_back(gap_v.dot(normal_v));
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::computeRelativeNormalField(
	const Array<Real> & field, Array<Real> & rel_normal_field) const {
	AKANTU_DEBUG_IN();

	// resize arrays to zero
	rel_normal_field.resize(0);

	UInt dim = this->model.getSpatialDimension();

	Array<Real>::const_iterator<Vector<Real>> it_field = field.begin(dim);
	Array<Real>::const_iterator<Vector<Real>> it_normal =
	this->normals.getArray().begin(dim);

	UInt nb_contact_nodes = this->getNbContactNodes();
	for (UInt n = 0; n < nb_contact_nodes; ++n) {
	// nodes
	UInt node = this->slaves(n);

	const Vector<Real> & field_v = it_field[node];
	const Vector<Real> & normal_v = it_normal[n];

	rel_normal_field.push_back(field_v.dot(normal_v));
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::printself(std::ostream & stream, int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTRFContact [" << std::endl;
	NTNBaseContact::printself(stream, indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NTRFContact::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_IN();

	/*
	#ifdef AKANTU_USE_IOHELPER
	const Array<UInt> & nodal_filter = this->slaves.getArray();

	#define ADD_FIELD(field_id, field, type) \
	internalAddDumpFieldToDumper(dumper_name, \
	field_id, \
	new DumperIOHelper::NodalField< type, true, \
	Array<type>, \
	Array<UInt> >(field, 0, 0, &nodal_filter))
	*/

	/*
	if(field_id == "displacement") {
	ADD_FIELD(field_id, this->model.getDisplacement(), Real);
	}
	else if(field_id == "contact_pressure") {
	internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new
	DumperIOHelper::NodalField<Real>(this->contact_pressure.getArray()));
	}
	else {*/
	NTNBaseContact::addDumpFieldToDumper(dumper_name, field_id);
	//}

	/*
	#undef ADD_FIELD
	#endif
	*/

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.hh
	index c66b79f90..f4f5357fc 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_contact.hh
	@@ -1,127 +1,127 @@
	/**
	* @file ntrf_contact.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief contact for node to rigid flat interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_NTRF_CONTACT_HH_
	#define AST_NTRF_CONTACT_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_base_contact.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class NTRFContact : public NTNBaseContact {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTRFContact(SolidMechanicsModel & model, const ID & id = "contact");
	~NTRFContact() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void setReferencePoint(Real x = 0., Real y = 0., Real z = 0.);
	void setNormal(Real x = 1., Real y = 0., Real z = 0.);

	/// add surface and nodes according to the surface normal
	void addSurface(const ID & surf);

	// add nodes from a list
	void addNodes(Array<UInt> & nodes);

	/// update (copy the normal to all normals)
	void updateNormals() override;

	/// update the impedance matrix
	void updateImpedance() override;

	/// compute the normal gap
	void computeNormalGap(Array<Real> & gap) const override;

	/// compute relative normal field (only value that has to be multiplied with
	/// the normal)
	/// relative to master nodes
	void
	computeRelativeNormalField(const Array<Real> & field,
	Array<Real> & rel_normal_field) const override;

	/// compute relative tangential field (complet array)
	/// relative to master nodes
	void
	computeRelativeTangentialField(const Array<Real> & field,
	Array<Real> & rel_tang_field) const override;

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) override;
	// virtual void addDumpFieldVector(const std::string & field_id);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// reference point for rigid flat surface
	Vector<Real> reference_point;
	/// outpointing normal of rigid flat surface
	Vector<Real> normal;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "ntrf_contact_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NTRFContact & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AST_NTRF_CONTACT_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction.hh
	index d9bfbd10c..1780bdfd8 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction.hh
	@@ -1,92 +1,92 @@
	/**
	* @file ntrf_friction.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief friction for node to rigid flat interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AST_NTRF_FRICTION_HH_
	#define AST_NTRF_FRICTION_HH_

	/* -------------------------------------------------------------------------- */
	// simtools
	#include "ntn_friclaw_coulomb.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw = NTNFricLawCoulomb,
	class Regularisation = NTNFricRegNoRegularisation>
	class NTRFFriction : public FrictionLaw<Regularisation> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NTRFFriction(NTNBaseContact & contact, const ID & id = "friction");
	- virtual ~NTRFFriction(){};
	+ ~NTRFFriction() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to print the contain of the class
	- virtual void printself(std::ostream & stream, int indent = 0) const;
	+ void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operato
	template <template <class> class FrictionLaw, class Regularisation>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const NTRFFriction<FrictionLaw, Regularisation> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "ntrf_friction_tmpl.hh"

	#endif /* AST_NTRF_FRICTION_HH_ */
	diff --git a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction_tmpl.hh b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction_tmpl.hh
	index 00d8269bd..7697171bc 100644
	--- a/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction_tmpl.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/ntn_contact/ntrf_friction_tmpl.hh
	@@ -1,106 +1,107 @@
	/**
	* @file ntrf_friction_tmpl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Wed Oct 17 2018
	*
	* @brief implementation of node to rigid flat interface friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	//#include "ntrf_friction.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw, class Regularisation>
	NTRFFriction<FrictionLaw, Regularisation>::NTRFFriction(
	NTNBaseContact & contact, const ID & id)
	: FrictionLaw<Regularisation>(contact, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <class> class FrictionLaw, class Regularisation>
	void NTRFFriction<FrictionLaw, Regularisation>::printself(std::ostream & stream,
	int indent) const {
	AKANTU_DEBUG_IN();
	std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	+ for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	+ }

	stream << space << "NTRFFriction [" << std::endl;
	FrictionLaw<Regularisation>::printself(stream, ++indent);
	stream << space << "]" << std::endl;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/*
	void NTRFFriction::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_IN();

	#ifdef AKANTU_USE_IOHELPER
	// const SynchronizedArray<UInt> * nodal_filter =
	&(this->contact.getSlaves());

	if(field_id == "is_sticking") {
	this->internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new
	DumperIOHelper::NodalField<bool>(this->is_sticking.getArray()));
	}
	else if(field_id == "frictional_strength") {
	this->internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new
	DumperIOHelper::NodalField<Real>(this->frictional_strength.getArray()));
	}
	else if(field_id == "friction_traction") {
	this->internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new
	DumperIOHelper::NodalField<Real>(this->friction_traction.getArray()));
	}
	else if(field_id == "slip") {
	this->internalAddDumpFieldToDumper(dumper_name,
	field_id,
	new DumperIOHelper::NodalField<Real>(this->slip.getArray()));
	}
	else {
	this->contact.addDumpFieldToDumper(dumper_name, field_id);
	}

	#endif

	AKANTU_DEBUG_OUT();
	}
	*/

	} // namespace akantu
	diff --git a/extra_packages/traction-at-split-node-contact/src/tasn_contact.hh b/extra_packages/traction-at-split-node-contact/src/tasn_contact.hh
	index c6a5230b1..5467445c0 100644
	--- a/extra_packages/traction-at-split-node-contact/src/tasn_contact.hh
	+++ b/extra_packages/traction-at-split-node-contact/src/tasn_contact.hh
	@@ -1,69 +1,69 @@
	/**
	* @file tasn_contact.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Mar 16 2018
	* @date last modification: Fri Mar 16 2018
	*
	* @brief traction at split node main include
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	// ast common
	#include "manual_restart.hh"
	#include "parameter_reader.hh"
	#include "synchronized_array.hh"

	// functions
	#include "boundary_functions.hh"
	#include "node_filter.hh"

	// boundary conditions
	#include "force_based_dirichlet.hh"
	#include "inclined_flat_dirichlet.hh"
	#include "spring_bc.hh"

	// ntn/ntrf contact
	#include "mIIasym_contact.hh"
	#include "ntn_base_contact.hh"
	#include "ntn_contact.hh"
	#include "ntrf_contact.hh"

	// ntn/ntrf friction
	#include "ntn_base_friction.hh"
	#include "ntn_friction.hh"
	#include "ntrf_friction.hh"

	// friction regularisations
	#include "ntn_fricreg_no_regularisation.hh"
	#include "ntn_fricreg_rubin_ampuero.hh"
	#include "ntn_fricreg_simplified_prakash_clifton.hh"

	// friction laws
	#include "ntn_friclaw_coulomb.hh"
	#include "ntn_friclaw_linear_cohesive.hh"
	#include "ntn_friclaw_linear_slip_weakening.hh"
	#include "ntn_friclaw_linear_slip_weakening_no_healing.hh"

	// initiation of friction
	#include "ntn_initiation_function.hh"
	diff --git a/python/py_aka_array.hh b/python/py_aka_array.hh
	index e3868bd50..6da82a07c 100644
	--- a/python/py_aka_array.hh
	+++ b/python/py_aka_array.hh
	@@ -1,282 +1,282 @@
	/**
	* @file py_aka_array.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 31 2018
	* @date last modification: Fri Nov 13 2020
	*
	* @brief pybind11 interface to akantu Arrays
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <aka_array.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/numpy.h>
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */

	namespace py = pybind11;
	namespace _aka = akantu;

	namespace akantu {
	namespace detail {
	template <class T> struct is_array_type : public std::false_type {};
	template <class T> struct is_array_type<Vector<T>> : public std::true_type {};
	template <class T> struct is_array_type<Matrix<T>> : public std::true_type {};
	template <class T> struct is_array_type<Array<T>> : public std::true_type {};

	/* ------------------------------------------------------------------------ */
	template <typename T> class ArrayProxy : public Array<T> {
	protected:
	// deallocate the memory
	void deallocate() final {}

	// allocate the memory
	void allocate(UInt /size/, UInt /nb_component/) final {}

	// allocate and initialize the memory
	void allocate(UInt /size/, UInt /nb_component/,
	const T & /value/) final {}

	public:
	ArrayProxy(T * data, UInt size, UInt nb_component) {
	this->values = data;
	this->size_ = size;
	this->nb_component = nb_component;
	}

	ArrayProxy(const Array<T> & src) {
	this->values = src.storage();
	this->size_ = src.size();
	this->nb_component = src.getNbComponent();
	}

	~ArrayProxy() override { this->values = nullptr; }

	void resize(UInt size, const T & /val/) final {
	if (size != this->size()) {
	AKANTU_EXCEPTION("cannot resize a temporary array");
	}
	- //std::fill(this->begin(), this->end(), val);
	+ // std::fill(this->begin(), this->end(), val);
	}

	void resize(UInt new_size) final {
	if (new_size != this->size()) {
	AKANTU_EXCEPTION("cannot resize a temporary array");
	}
	}

	void reserve(UInt /size/, UInt /new_size/) final {
	AKANTU_EXCEPTION("cannot resize a temporary array");
	}
	};

	/* ------------------------------------------------------------------------ */
	template <typename T> struct ProxyType {};
	template <typename T> struct ProxyType<Vector<T>> { using type = Vector<T>; };
	template <typename T> struct ProxyType<Matrix<T>> { using type = Matrix<T>; };
	template <typename T> struct ProxyType<Array<T>> {
	using type = ArrayProxy<T>;
	};
	template <typename array> using ProxyType_t = typename ProxyType<array>::type;
	} // namespace detail
	} // namespace akantu

	namespace pybind11 {
	namespace detail {

	template <typename T> struct AkaArrayType {
	using type =
	array_t<typename T::value_type, array::c_style \| array::forcecast>;
	};

	template <typename T> struct AkaArrayType<_aka::Vector<T>> {
	using type = array_t<T, array::f_style \| array::forcecast>;
	};
	template <typename T> struct AkaArrayType<_aka::Matrix<T>> {
	using type = array_t<T, array::f_style \| array::forcecast>;
	};

	template <typename U> using array_type_t = typename AkaArrayType<U>::type;

	/* ------------------------------------------------------------------------ */
	template <typename T>
	decltype(auto) create_proxy(array_type_t<_aka::Vector<T>> & ref,
	const _aka::Vector<T> * /unused/) {
	return std::make_unique<_aka::detail::ProxyType_t<_aka::Vector<T>>>(
	ref.mutable_data(), ref.shape(0));
	}

	template <typename T>
	decltype(auto) create_proxy(array_type_t<_aka::Matrix<T>> & ref,
	const _aka::Matrix<T> * /unused/) {
	return std::make_unique<_aka::detail::ProxyType_t<_aka::Matrix<T>>>(
	ref.mutable_data(), ref.shape(0), ref.shape(1));
	}

	template <typename T>
	decltype(auto) create_proxy(array_type_t<_aka::Array<T>> & ref,
	const _aka::Array<T> * /unused/) {
	return std::make_unique<_aka::detail::ProxyType_t<_aka::Array<T>>>(
	ref.mutable_data(), ref.shape(0), ref.shape(1));
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	py::handle aka_array_cast(const _aka::Array<T> & src,
	py::handle base = handle(), bool writeable = true) {
	array a;
	a = array_type_t<_aka::Array<T>>({src.size(), src.getNbComponent()},
	src.storage(), base);

	if (not writeable) {
	array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;
	}

	return a.release();
	}

	template <typename T>
	py::handle aka_array_cast(const _aka::Vector<T> & src,
	py::handle base = handle(), bool writeable = true) {
	array a;
	a = array_type_t<_aka::Vector<T>>({src.size()}, src.storage(), base);

	if (not writeable) {
	array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;
	}

	return a.release();
	}

	template <typename T>
	py::handle aka_array_cast(const _aka::Matrix<T> & src,
	py::handle base = handle(), bool writeable = true) {
	array a;
	a = array_type_t<_aka::Matrix<T>>({src.size(0), src.size(1)}, src.storage(),
	base);

	if (not writeable) {
	array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;
	}

	return a.release();
	}

	/* ------------------------------------------------------------------------ */
	template <typename AkaArrayType>
	- class type_caster<
	+ class type_caster<
	AkaArrayType,
	std::enable_if_t<_aka::detail::is_array_type<AkaArrayType>::value>> {
	protected:
	using T = typename AkaArrayType::value_type;
	using type = AkaArrayType;
	using proxy_type = _aka::detail::ProxyType_t<AkaArrayType>;
	using array_type = array_type_t<AkaArrayType>;

	std::unique_ptr<proxy_type> array_proxy;
	array_type_t<AkaArrayType> copy_or_ref;

	public:
	#if PYBIND11_VERSION_MAJOR >= 2 && PYBIND11_VERSION_MINOR >= 3
	static constexpr auto name = _("AkaArray");
	operator type &&() && { return std::move(*array_proxy); }
	template <typename T_>
	using cast_op_type = pybind11::detail::movable_cast_op_type<T_>;
	#else
	static PYBIND11_DESCR name() { return type_descr(_("AkaArray")); };
	template <typename _T>
	using cast_op_type = pybind11::detail::cast_op_type<_T>;
	#endif
	operator type *() { return array_proxy.get(); }
	operator type &() { return *array_proxy; }

	/**
	* Conversion part 1 (Python->C++)
	*/
	bool load(handle src, bool convert) {
	bool need_copy = not isinstance<array_type>(src);

	auto && fits = [&](auto && aref) {
	auto && dims = aref.ndim();
	if (dims < 1 \|\| dims > 2) {
	return false;
	}

	return true;
	};

	if (not need_copy) {
	// We don't need a converting copy, but we also need to check whether
	// the strides are compatible with the Ref's stride requirements
	auto aref = py::cast<array_type>(src);

	if (not fits(aref)) {
	return false;
	}
	copy_or_ref = std::move(aref);
	} else {
	if (not convert) {
	return false;
	}

	auto copy = array_type::ensure(src);
	if (not copy) {
	return false;
	}

	if (not fits(copy)) {
	return false;
	}
	copy_or_ref = std::move(array_type::ensure(src));
	loader_life_support::add_patient(copy_or_ref);
	}

	AkaArrayType * dispatch = nullptr; // cannot detect T from the expression
	array_proxy = create_proxy(copy_or_ref, dispatch);
	return true;
	}

	/**
	* Conversion part 2 (C++ -> Python)
	*/
	static handle cast(const type & src, return_value_policy policy,
	handle parent) {
	switch (policy) {
	case return_value_policy::copy:
	return aka_array_cast<T>(src);
	case return_value_policy::reference_internal:
	return aka_array_cast<T>(src, parent);
	case return_value_policy::reference:
	case return_value_policy::automatic:
	case return_value_policy::automatic_reference:
	return aka_array_cast<T>(src, none());
	default:
	pybind11_fail("Invalid return_value_policy for ArrayProxy type");
	}
	}
	};
	} // namespace detail
	} // namespace pybind11
	diff --git a/python/py_aka_common.cc b/python/py_aka_common.cc
	index 9aa11d819..cf702fc00 100644
	--- a/python/py_aka_common.cc
	+++ b/python/py_aka_common.cc
	@@ -1,147 +1,147 @@
	/**
	* @file py_aka_common.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 31 2018
	* @date last modification: Tue Mar 02 2021
	*
	* @brief pybind11 interface to aka_common.hh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <aka_common.hh>
	/* -------------------------------------------------------------------------- */
	#include <boost/preprocessor.hpp>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define PY_AKANTU_PP_VALUE(s, data, elem) \
	.value(BOOST_PP_STRINGIZE(elem), BOOST_PP_CAT(data, elem))

	#define PY_AKANTU_REGISTER_ENUM_(type_name, list, prefix, mod) \
	py::enum_<type_name>(mod, BOOST_PP_STRINGIZE(type_name)) \
	- BOOST_PP_SEQ_FOR_EACH(PY_AKANTU_PP_VALUE, prefix, list) \
	- .export_values()
	+ BOOST_PP_SEQ_FOR_EACH(PY_AKANTU_PP_VALUE, \
	+ prefix, list) \
	+ .export_values()

	#define PY_AKANTU_REGISTER_CLASS_ENUM(type_name, list, mod) \
	PY_AKANTU_REGISTER_ENUM_(type_name, list, type_name::_, mod)

	#define PY_AKANTU_REGISTER_ENUM(type_name, list, mod) \
	PY_AKANTU_REGISTER_ENUM_(type_name, list, , mod)

	/* -------------------------------------------------------------------------- */
	void register_initialize(py::module & mod) {
	mod.def("__initialize", []() {
	int nb_args = 0;
	char ** null = nullptr;
	initialize(nb_args, null);
	});
	}

	void register_enums(py::module & mod) {
	py::enum_<SpatialDirection>(mod, "SpatialDirection")
	.value("_x", _x)
	.value("_y", _y)
	.value("_z", _z)
	.export_values();

	py::enum_<AnalysisMethod>(mod, "AnalysisMethod")
	.value("_static", _static)
	.value("_implicit_dynamic", _implicit_dynamic)
	.value("_explicit_lumped_mass", _explicit_lumped_mass)
	.value("_explicit_lumped_capacity", _explicit_lumped_capacity)
	.value("_explicit_consistent_mass", _explicit_consistent_mass)
	.value("_explicit_contact", _explicit_contact)
	.value("_implicit_contact", _implicit_contact)
	.export_values();
	-

	PY_AKANTU_REGISTER_CLASS_ENUM(ModelType, AKANTU_MODEL_TYPES, mod);
	PY_AKANTU_REGISTER_CLASS_ENUM(NonLinearSolverType,
	AKANTU_NON_LINEAR_SOLVER_TYPES, mod);
	PY_AKANTU_REGISTER_CLASS_ENUM(TimeStepSolverType,
	AKANTU_TIME_STEP_SOLVER_TYPE, mod);
	PY_AKANTU_REGISTER_CLASS_ENUM(IntegrationSchemeType,
	AKANTU_INTEGRATION_SCHEME_TYPE, mod);
	PY_AKANTU_REGISTER_CLASS_ENUM(SolveConvergenceCriteria,
	AKANTU_SOLVE_CONVERGENCE_CRITERIA, mod);

	py::enum_<CohesiveMethod>(mod, "CohesiveMethod")
	.value("_intrinsic", _intrinsic)
	.value("_extrinsic", _extrinsic)
	.export_values();

	py::enum_<GhostType>(mod, "GhostType")
	.value("_not_ghost", _not_ghost)
	.value("_ghost", _ghost)
	.value("_casper", _casper)
	.export_values();

	py::enum_<MeshIOType>(mod, "MeshIOType")
	.value("_miot_auto", _miot_auto)
	.value("_miot_gmsh", _miot_gmsh)
	.value("_miot_gmsh_struct", _miot_gmsh_struct)
	.value("_miot_diana", _miot_diana)
	.value("_miot_abaqus", _miot_abaqus)
	.export_values();

	py::enum_<MatrixType>(mod, "MatrixType")
	.value("_unsymmetric", _unsymmetric)
	.value("_symmetric", _symmetric)
	.export_values();

	PY_AKANTU_REGISTER_ENUM(ElementType, AKANTU_ALL_ELEMENT_TYPE(_not_defined),
	mod);
	PY_AKANTU_REGISTER_ENUM(ElementKind, AKANTU_ELEMENT_KIND(_ek_not_defined),
	mod);
	}

	/* -------------------------------------------------------------------------- */
	#define AKANTU_PP_STR_TO_TYPE2(s, data, elem) ({BOOST_PP_STRINGIZE(elem), elem})

	void register_functions(py::module & mod) {

	mod.def("getElementTypes", []() {
	std::map<std::string, akantu::ElementType> element_types{
	BOOST_PP_SEQ_FOR_EACH_I(
	AKANTU_PP_ENUM, BOOST_PP_SEQ_SIZE(AKANTU_ek_regular_ELEMENT_TYPE),
	BOOST_PP_SEQ_TRANSFORM(AKANTU_PP_STR_TO_TYPE2, akantu,
	AKANTU_ek_regular_ELEMENT_TYPE))};

	return element_types;
	});
	}

	#undef AKANTU_PP_STR_TO_TYPE2

	} // namespace akantu
	diff --git a/python/py_aka_common.hh b/python/py_aka_common.hh
	index 2993bd566..568a6c2d3 100644
	--- a/python/py_aka_common.hh
	+++ b/python/py_aka_common.hh
	@@ -1,45 +1,45 @@
	/**
	* @file py_aka_common.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Fri May 03 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to aka_common.hh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_AKA_COMMON_HH_
	#define AKANTU_PY_AKA_COMMON_HH_

	namespace akantu {

	void register_enums(pybind11::module & mod);
	void register_initialize(pybind11::module & mod);
	void register_functions(pybind11::module & mod);

	} // namespace akantu

	#endif
	diff --git a/python/py_aka_error.cc b/python/py_aka_error.cc
	index 9e3e07caa..3a45390a9 100644
	--- a/python/py_aka_error.cc
	+++ b/python/py_aka_error.cc
	@@ -1,69 +1,70 @@
	/**
	* @file py_aka_error.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 07 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to aka_error
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_error.hh"
	/* -------------------------------------------------------------------------- */
	#include <aka_error.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */

	void register_error(py::module & mod) {

	mod.def("setDebugLevel", &debug::setDebugLevel);
	mod.def("getDebugLevel", &debug::getDebugLevel);
	- mod.def("printBacktrace", [](bool flag) { debug::debugger.printBacktrace(flag); });
	+ mod.def("printBacktrace",
	+ [](bool flag) { debug::debugger.printBacktrace(flag); });

	py::enum_<DebugLevel>(mod, "DebugLevel")
	.value("dblError", dblError)
	.value("dblException", dblException)
	.value("dblCritical", dblCritical)
	.value("dblMajor", dblMajor)
	.value("dblWarning", dblWarning)
	.value("dblInfo", dblInfo)
	.value("dblTrace", dblTrace)
	.value("dblAccessory", dblAccessory)
	.value("dblDebug", dblDebug)
	.value("dblDump", dblDump)
	.value("dblTest", dblTest)
	.export_values();
	}

	} // namespace akantu
	diff --git a/python/py_aka_error.hh b/python/py_aka_error.hh
	index 7f9296635..cc73c1e9c 100644
	--- a/python/py_aka_error.hh
	+++ b/python/py_aka_error.hh
	@@ -1,43 +1,43 @@
	/**
	* @file py_aka_error.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Tue May 07 2019
	* @date last modification: Mon Jan 18 2021
	*
	* @brief pybind11 interface to aka_error
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_AKA_ERROR_HH_
	#define AKANTU_PY_AKA_ERROR_HH_

	namespace akantu {

	void register_error(pybind11::module & mod);

	}

	#endif
	diff --git a/python/py_akantu.cc b/python/py_akantu.cc
	index 63db238f1..43958335b 100644
	--- a/python/py_akantu.cc
	+++ b/python/py_akantu.cc
	@@ -1,171 +1,171 @@
	/**
	* @file py_akantu.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Philip Mueller <philip.paul.mueller@bluemail.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 31 2018
	* @date last modification: Mon Mar 29 2021
	*
	* @brief pybind11 interface to akantu main's file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_config.hh"
	/* -------------------------------------------------------------------------- */
	#include "py_aka_common.hh"
	#include "py_aka_error.hh"
	#include "py_boundary_conditions.hh"
	#include "py_fe_engine.hh"
	#include "py_group_manager.hh"
	#include "py_mesh.hh"
	#include "py_model.hh"
	#include "py_parser.hh"
	#include "py_solver.hh"

	#if defined(AKANTU_USE_IOHELPER)
	#include "py_dumpable.hh"
	#endif

	#if defined(AKANTU_SOLID_MECHANICS)
	#include "py_material.hh"
	#include "py_material_selector.hh"
	#include "py_solid_mechanics_model.hh"
	#endif

	#if defined(AKANTU_HEAT_TRANSFER)
	#include "py_heat_transfer_model.hh"
	#endif

	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "py_fragment_manager.hh"
	#include "py_solid_mechanics_model_cohesive.hh"
	#endif

	#if defined(AKANTU_CONTACT_MECHANICS)
	#include "py_contact_mechanics_model.hh"
	#include "py_model_couplers.hh"
	#endif

	#if defined(AKANTU_PHASE_FIELD)
	#include "py_phase_field_model.hh"
	#endif

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	#include "py_structural_mechanics_model.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	#include <aka_error.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	namespace py = pybind11;

	namespace akantu {
	void register_all(pybind11::module & mod) {
	register_initialize(mod);
	register_enums(mod);
	register_error(mod);
	register_functions(mod);
	register_parser(mod);
	register_solvers(mod);

	register_group_manager(mod);
	#if defined(AKANTU_USE_IOHELPER)
	register_dumpable(mod);
	#endif
	register_mesh(mod);

	register_fe_engine(mod);

	register_boundary_conditions(mod);
	register_model(mod);
	#if defined(AKANTU_HEAT_TRANSFER)
	register_heat_transfer_model(mod);
	#endif

	#if defined(AKANTU_SOLID_MECHANICS)
	register_solid_mechanics_model(mod);
	register_material(mod);
	register_material_selector(mod);
	#endif

	#if defined(AKANTU_COHESIVE_ELEMENT)
	register_solid_mechanics_model_cohesive(mod);
	register_fragment_manager(mod);
	#endif

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	register_structural_mechanics_model(mod);
	#endif

	#if defined(AKANTU_CONTACT_MECHANICS)
	register_contact_mechanics_model(mod);
	register_model_couplers(mod);
	#endif

	#if defined(AKANTU_PHASE_FIELD)
	register_phase_field_model(mod);
	register_phase_field_coupler(mod);
	#endif
	}
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	PYBIND11_MODULE(py11_akantu, mod) {
	mod.doc() = "Akantu python interface";

	static py::exception<akantu::debug::Exception> akantu_exception(mod,
	"Exception");

	py::register_exception_translator([](std::exception_ptr ptr) {
	try {
	if (ptr) {
	std::rethrow_exception(ptr);
	}
	} catch (akantu::debug::Exception & e) {
	if (akantu::debug::debugger.printBacktrace()) {
	akantu::debug::printBacktrace();
	}
	akantu_exception(e.info().c_str());
	}
	});

	akantu::register_all(mod);

	mod.def("has_mpi", []() {
	#if defined(AKANTU_USE_MPI)
	return true;
	#else
	return false;
	#endif
	});

	} // Module akantu
	diff --git a/python/py_akantu.hh b/python/py_akantu.hh
	index b853b238c..d0d51cd53 100644
	--- a/python/py_akantu.hh
	+++ b/python/py_akantu.hh
	@@ -1,45 +1,45 @@
	/**
	* @file py_akantu.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to akantu main's file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */

	#ifndef PY_AKANTU_HH_
	#define PY_AKANTU_HH_

	namespace akantu {
	void register_all(pybind11::module & mod);
	}

	#endif /* PY_AKANTU_HH_ */
	diff --git a/python/py_akantu_pybind11_compatibility.hh b/python/py_akantu_pybind11_compatibility.hh
	index 83fa8619b..baa471a4b 100644
	--- a/python/py_akantu_pybind11_compatibility.hh
	+++ b/python/py_akantu_pybind11_compatibility.hh
	@@ -1,42 +1,42 @@
	/**
	* @file py_akantu_pybind11_compatibility.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 26 2021
	* @date last modification: Wed May 26 2021
	*
	* @brief Include for compatibility between pybind11 versions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef PY_AKANTU_PYBIND11_COMPATIBILITY_HH_
	#define PY_AKANTU_PYBIND11_COMPATIBILITY_HH_

	#if not defined(PYBIND11_OVERRIDE)
	#define PYBIND11_OVERRIDE PYBIND11_OVERLOAD
	#define PYBIND11_OVERRIDE_NAME PYBIND11_OVERLOAD_NAME
	#define PYBIND11_OVERRIDE_PURE PYBIND11_OVERLOAD_PURE
	#define PYBIND11_OVERRIDE_PURE_NAME PYBIND11_OVERLOAD_PURE_NAME
	#endif

	#endif // PY_AKANTU_PYBIND11_COMPATIBILITY_HH_
	diff --git a/python/py_boundary_conditions.cc b/python/py_boundary_conditions.cc
	index 05c50abe7..c33b40949 100644
	--- a/python/py_boundary_conditions.cc
	+++ b/python/py_boundary_conditions.cc
	@@ -1,129 +1,129 @@
	/**
	* @file py_boundary_conditions.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Mon Dec 02 2019
	* @date last modification: Mon Dec 02 2019
	*
	* @brief pybind11 interface to boundary conditions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_boundary_conditions.hh"
	#include "py_aka_array.hh"
	#include "py_akantu_pybind11_compatibility.hh"
	/* -------------------------------------------------------------------------- */
	#include <boundary_condition_functor.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;

	namespace akantu {

	namespace {
	/* ------------------------------------------------------------------------ */
	template <typename daughter = BC::Dirichlet::DirichletFunctor>
	class PyDirichletFunctor : public daughter {
	public:
	/* Inherit the constructors */
	using daughter::daughter;

	/* Trampoline (need one for each virtual function) */
	void operator()(UInt node, Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE_NAME(void, daughter, "__call__", operator(), node,
	flags, primal, coord);
	}
	};

	/* ------------------------------------------------------------------------ */
	template <typename daughter = BC::Neumann::NeumannFunctor>
	class PyNeumannFunctor : public daughter {
	public:
	/* Inherit the constructors */
	using daughter::daughter;

	/* Trampoline (need one for each virtual function) */
	void operator()(const IntegrationPoint & quad_point, Vector<Real> & dual,
	const Vector<Real> & coord,
	const Vector<Real> & normals) const override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE_PURE_NAME(void, daughter, "__call__", operator(),
	quad_point, dual, coord, normals);
	}
	};

	/* ------------------------------------------------------------------------ */
	template <typename Functor, typename Constructor>
	decltype(auto) register_dirichlet_functor(py::module mod, const char * name,
	Constructor && cons) {
	py::class_<Functor, PyDirichletFunctor<Functor>,
	BC::Dirichlet::DirichletFunctor>(mod, name)
	.def(cons);
	}

	/* ------------------------------------------------------------------------ */
	template <typename Functor, typename Constructor>
	decltype(auto) register_neumann_functor(py::module mod, const char * name,
	Constructor && cons) {
	py::class_<Functor, PyNeumannFunctor<Functor>, BC::Neumann::NeumannFunctor>(
	mod, name)
	.def(cons);
	}
	} // namespace

	/* -------------------------------------------------------------------------- */
	void register_boundary_conditions(py::module & mod) {

	py::class_<BC::Functor>(mod, "BCFunctor");
	py::class_<BC::Dirichlet::DirichletFunctor, PyDirichletFunctor<>,
	BC::Functor>(mod, "DirichletFunctor")
	.def(py::init())
	.def(py::init<SpatialDirection>());

	py::class_<BC::Neumann::NeumannFunctor, PyNeumannFunctor<>, BC::Functor>(
	mod, "NeumannFunctor")
	.def(py::init());

	register_dirichlet_functor<BC::Dirichlet::FixedValue>(
	mod, "FixedValue", py::init<Real, BC::Axis>());

	register_dirichlet_functor<BC::Dirichlet::IncrementValue>(
	mod, "IncrementValue", py::init<Real, BC::Axis>());

	register_dirichlet_functor<BC::Dirichlet::Increment>(
	mod, "Increment", py::init<Vector<Real> &>());

	register_neumann_functor<BC::Neumann::FromHigherDim>(
	mod, "FromHigherDim", py::init<Matrix<Real> &>());

	register_neumann_functor<BC::Neumann::FromSameDim>(
	mod, "FromSameDim", py::init<Vector<Real> &>());

	register_neumann_functor<BC::Neumann::FreeBoundary>(mod, "FreeBoundary",
	py::init());
	}
	} // namespace akantu
	diff --git a/python/py_boundary_conditions.hh b/python/py_boundary_conditions.hh
	index 03a774b91..e0600d77e 100644
	--- a/python/py_boundary_conditions.hh
	+++ b/python/py_boundary_conditions.hh
	@@ -1,43 +1,43 @@
	/**
	* @file py_boundary_conditions.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to boundary conditions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_BOUNDARY_CONDITIONS_HH_
	#define AKANTU_PY_BOUNDARY_CONDITIONS_HH_

	namespace akantu {

	void register_boundary_conditions(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_BOUNDARY_CONDITIONS_HH_
	diff --git a/python/py_contact_mechanics_model.cc b/python/py_contact_mechanics_model.cc
	index 1f2ed7dd2..22bf46504 100644
	--- a/python/py_contact_mechanics_model.cc
	+++ b/python/py_contact_mechanics_model.cc
	@@ -1,211 +1,211 @@
	/**
	* @file py_contact_mechanics_model.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Contact mechanics python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <contact_detector.hh>
	#include <contact_element.hh>
	#include <contact_mechanics_model.hh>
	#include <geometry_utils.hh>
	#include <mesh_events.hh>
	#include <parsable.hh>
	#include <surface_selector.hh>
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](ContactMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](ContactMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})

	namespace {
	class ContactElementsView {
	public:
	ContactElementsView(const Array<ContactElement> & contact_elements)
	: contact_elements(contact_elements) {}

	auto begin() const { return contact_elements.begin(); }
	auto end() const { return contact_elements.end(); }

	auto size() const { return contact_elements.size(); }
	auto operator[](size_t i) const { return contact_elements(i); }

	auto contains(const ContactElement & contact_element) const {
	return std::find(contact_elements.begin(), contact_elements.end(),
	contact_element) != contact_elements.end();
	}

	private:
	const Array<ContactElement> & contact_elements;
	};
	} // namespace

	/* -------------------------------------------------------------------------- */
	void register_contact_mechanics_model(py::module & mod) {
	py::class_<ContactDetector>(mod, "ContactDetector",
	py::multiple_inheritance())
	.def(py::init<Mesh &, const ID &>(), py::arg("mesh"),
	py::arg("id") = "contact_detector")
	.def(py::init<Mesh &, Array<Real>, const ID &>(), py::arg("mesh"),
	py::arg("positions"), py::arg("id") = "contact_detector")
	.def("setSurfaceSelector", &ContactDetector::setSurfaceSelector);

	py::class_<SurfaceSelector, std::shared_ptr<SurfaceSelector>>(
	mod, "SurfaceSelector", py::multiple_inheritance())
	.def(py::init<Mesh &>(), py::arg("mesh"));

	py::class_<PhysicalSurfaceSelector, SurfaceSelector,
	std::shared_ptr<PhysicalSurfaceSelector>>(
	mod, "PhysicalSurfaceSelector")
	.def(py::init<Mesh &>(), py::arg("mesh"));

	py::class_<CohesiveSurfaceSelector, SurfaceSelector,
	std::shared_ptr<CohesiveSurfaceSelector>>(
	mod, "CohesiveSurfaceSelector")
	.def(py::init<Mesh &>(), py::arg("mesh"));

	py::class_<AllSurfaceSelector, SurfaceSelector,
	std::shared_ptr<AllSurfaceSelector>>(mod, "AllSurfaceSelector")
	.def(py::init<Mesh &>(), py::arg("mesh"));

	py::class_<ContactMechanicsModelOptions>(mod, "ContactMechanicsModelOptions")
	.def(py::init<AnalysisMethod>(),
	py::arg("analysis_method") = _explicit_contact);

	/* ------------------------------------------------------------------------ */
	py::class_<ContactElementsView>(mod, "ContactElementsView")
	.def("__iter__",
	[](const ContactElementsView & self) {
	return py::make_iterator(self.begin(), self.end());
	})
	.def("__size__",
	[](const ContactElementsView & self) { return self.size(); })
	.def(
	"__contains__",
	[](const ContactElementsView & self, const ContactElement & element) {
	return self.contains(element);
	})
	.def("__getitem__",
	[](const ContactElementsView & self, size_t i) { return self[i]; });

	/* ------------------------------------------------------------------------ */
	py::class_<ContactMechanicsModel, Model>(mod, "ContactMechanicsModel",
	py::multiple_inheritance())
	.def(py::init<Mesh &, UInt, const ID &, std::shared_ptr<DOFManager>,
	const ModelType>(),
	py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "contact_mechanics_model",
	py::arg("dof_manager") = nullptr,
	py::arg("model_type") = ModelType::_contact_mechanics_model)
	.def(
	"initFull",
	[](ContactMechanicsModel & self,
	const ContactMechanicsModelOptions & options) {
	self.initFull(options);
	},
	py::arg("options") = ContactMechanicsModelOptions())
	.def(
	"initFull",
	[](ContactMechanicsModel & self,
	const AnalysisMethod & analysis_method) {
	self.initFull(_analysis_method = analysis_method);
	},
	py::arg("_analysis_method"))
	.def_function(search)
	.def_function(assembleStiffnessMatrix)
	.def_function(assembleInternalForces)
	.def_function_nocopy(getExternalForce)
	.def_function_nocopy(getNormalForce)
	.def_function_nocopy(getTangentialForce)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getGaps)
	.def_function_nocopy(getNormals)
	.def_function_nocopy(getNodalArea)
	.def_function_nocopy(getContactDetector)
	.def("getContactElements", [](ContactMechanicsModel & self) {
	return ContactElementsView(self.getContactElements());
	});

	py::class_<ContactElement>(mod, "ContactElement")
	.def(py::init<>())
	.def_readwrite("master", &ContactElement::master)
	.def_readwrite("slave", &ContactElement::slave)
	.def("__repr__", [](ContactElement & self) {
	return "{master: " + std::to_string(self.master) +
	", slave: " + std::to_string(self.slave) + "}";
	});

	py::class_<GeometryUtils>(mod, "GeometryUtils")
	.def_static(
	"normal",
	py::overload_cast<const Mesh &, const Array<Real> &, const Element &,
	Vector<Real> &, bool>(&GeometryUtils::normal),
	py::arg("mesh"), py::arg("positions"), py::arg("element"),
	py::arg("normal"), py::arg("outward") = true)
	.def_static(
	"covariantBasis",
	py::overload_cast<const Mesh &, const Array<Real> &, const Element &,
	const Vector<Real> &, Vector<Real> &,
	Matrix<Real> &>(&GeometryUtils::covariantBasis),
	py::arg("mesh"), py::arg("positions"), py::arg("element"),
	py::arg("normal"), py::arg("natural_projection"), py::arg("basis"))
	.def_static("curvature", &GeometryUtils::curvature)
	.def_static("contravariantBasis", &GeometryUtils::contravariantBasis,
	py::arg("covariant_basis"), py::arg("basis"))
	.def_static("realProjection",
	py::overload_cast<const Mesh &, const Array<Real> &,
	const Vector<Real> &, const Element &,
	const Vector<Real> &, Vector<Real> &>(
	&GeometryUtils::realProjection),
	py::arg("mesh"), py::arg("positions"), py::arg("slave"),
	py::arg("element"), py::arg("normal"), py::arg("projection"))
	.def_static("isBoundaryElement", &GeometryUtils::isBoundaryElement);
	}

	} // namespace akantu
	diff --git a/python/py_contact_mechanics_model.hh b/python/py_contact_mechanics_model.hh
	index 8856c8318..9fd1d521c 100644
	--- a/python/py_contact_mechanics_model.hh
	+++ b/python/py_contact_mechanics_model.hh
	@@ -1,41 +1,41 @@
	/**
	* @file py_contact_mechanics_model.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Sat Dec 12 2020
	*
	* @brief Contact mechanics python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef __AKANTU_PY_CONTACT_MECHANICS_MODEL_HH__
	#define __AKANTU_PY_CONTACT_MECHANICS_MODEL_HH__

	namespace akantu {
	void register_contact_mechanics_model(pybind11::module & mod);
	} // namespace akantu

	#endif // __AKANTU_PY_CONTACT_MECHANICS_MODEL_HH__
	diff --git a/python/py_dumpable.cc b/python/py_dumpable.cc
	index fb8233845..781f8a313 100644
	--- a/python/py_dumpable.cc
	+++ b/python/py_dumpable.cc
	@@ -1,135 +1,136 @@
	/**
	* @file py_dumpable.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Thu Nov 12 2020
	*
	* @brief pybind11 interface to Dumpers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <dumper_iohelper_paraview.hh>
	#include <mesh.hh>
	/* -------------------------------------------------------------------------- */
	#include <dumpable_inline_impl.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	std::vector<detail::ArrayProxy<Real>> tmp_array;

	void register_dumpable(py::module & mod) {
	/* ------------------------------------------------------------------------ */
	py::class_<Dumpable>(mod, "Dumpable")
	.def("registerDumperParaview", &Dumpable::registerDumper<DumperParaview>,
	py::arg("dumper_name"), py::arg("file_name"),
	py::arg("is_default") = false)
	.def("addDumpMeshToDumper", &Dumpable::addDumpMeshToDumper,
	py::arg("dumper_name"), py::arg("mesh"), py::arg("dimension"),
	py::arg("ghost_type") = _not_ghost,
	py::arg("element_kind") = _ek_regular)
	.def("addDumpMesh", &Dumpable::addDumpMesh, py::arg("mesh"),
	py::arg("dimension"), py::arg("ghost_type") = _not_ghost,
	py::arg("element_kind") = _ek_regular)
	.def("addDumpField", &Dumpable::addDumpField, py::arg("field_id"))
	.def("addDumpFieldToDumper", &Dumpable::addDumpFieldToDumper,
	py::arg("dumper_name"), py::arg("field_id"))
	.def(
	"addDumpFieldExternal",
	[](Dumpable & _this, const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	return _this.addDumpFieldExternal(field_id, field);
	},
	py::arg("field_id"), py::arg("field"))
	.def(
	"addDumpFieldExternal",
	[](Dumpable & _this, const std::string & field_id,
	Array<Real> & field) {
	auto & tmp = dynamic_cast<detail::ArrayProxy<Real> &>(field);
	tmp_array.push_back(tmp);
	return _this.addDumpFieldExternal(field_id, tmp_array.back());
	},
	py::arg("field_id"), py::arg("field"))
	.def(
	"addDumpFieldExternalToDumper",
	[](Dumpable & _this, const std::string & dumper_name,
	const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	return _this.addDumpFieldExternalToDumper(dumper_name, field_id,
	field);
	},
	py::arg("dumper_name"), py::arg("field_id"), py::arg("field"))

	.def("dump", [](Dumpable & self) { self.dump(); })
	.def(
	"dump", [](Dumpable & self, UInt step) { self.dump(step); },
	py::arg("step"))
	.def(
	"dump",
	[](Dumpable & self, Real time, UInt step) { self.dump(time, step); },
	py::arg("time"), py::arg("step"))
	.def(
	"dump",
	- [](Dumpable & self, const std::string & dumper) { self.dump(dumper); },
	+ [](Dumpable & self, const std::string & dumper) {
	+ self.dump(dumper);
	+ },
	py::arg("dumper_name"))
	.def(
	"dump",
	[](Dumpable & self, const std::string & dumper, UInt step) {
	self.dump(dumper, step);
	},
	py::arg("dumper_name"), py::arg("step"))
	.def(
	"dump",
	- [](Dumpable & self, const std::string & dumper, Real time, UInt step) {
	- self.dump(dumper, time, step);
	- },
	+ [](Dumpable & self, const std::string & dumper, Real time,
	+ UInt step) { self.dump(dumper, time, step); },
	py::arg("dumper_name"), py::arg("time"), py::arg("step"));
	}

	/* -------------------------------------------------------------------------- */
	PYBIND11_MODULE(dumper_module, mod) {
	mod.attr("__name__") = "py11_akantu.dumper";

	/* ------------------------------------------------------------------------ */
	py::class_<dumpers::Field, std::shared_ptr<dumpers::Field>>(mod, "Field");

	/* ------------------------------------------------------------------------ */
	py::class_<dumpers::ElementalField<UInt>, dumpers::Field,
	std::shared_ptr<dumpers::ElementalField<UInt>>>(
	mod, "ElementalFieldUInt", py::multiple_inheritance())
	.def(py::init<dumpers::ElementalField<UInt>::field_type &, UInt,
	GhostType, ElementKind>(),
	py::arg("field"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("ghost_type") = _not_ghost,
	py::arg("element_kind") = _ek_not_defined);
	}

	} // namespace akantu
	diff --git a/python/py_dumpable.hh b/python/py_dumpable.hh
	index a5d5fe386..86346c545 100644
	--- a/python/py_dumpable.hh
	+++ b/python/py_dumpable.hh
	@@ -1,43 +1,43 @@
	/**
	* @file py_dumpable.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to Dumpers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_DUMPABLE_HH_
	#define AKANTU_PY_DUMPABLE_HH_

	namespace akantu {

	void register_dumpable(pybind11::module & mod);

	} // namespace akantu

	#endif /* AKANTU_PY_DUMPABLE_HH_ */
	diff --git a/python/py_fe_engine.cc b/python/py_fe_engine.cc
	index c17e05a49..baa7e5225 100644
	--- a/python/py_fe_engine.cc
	+++ b/python/py_fe_engine.cc
	@@ -1,155 +1,155 @@
	/**
	* @file py_fe_engine.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 27 2019
	* @date last modification: Sat Dec 12 2020
	*
	* @brief pybind11 interface to FEEngine
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	#include "py_aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <element.hh>
	#include <fe_engine.hh>
	#include <integration_point.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/functional.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	void register_fe_engine(py::module & mod) {
	py::class_<Element>(mod, "Element")
	.def(py::init([](ElementType type, UInt id) {
	return new Element{type, id, _not_ghost};
	}))
	.def(py::init([](ElementType type, UInt id, GhostType ghost_type) {
	return new Element{type, id, ghost_type};
	}))
	.def("__lt__",
	[](Element & self, const Element & other) { return (self < other); })
	.def("__repr__", [](Element & self) { return std::to_string(self); });

	mod.attr("ElementNull") = ElementNull;

	py::class_<FEEngine>(mod, "FEEngine")
	.def(
	"getNbIntegrationPoints",
	[](FEEngine & fem, const ElementType & type,
	const GhostType & ghost_type) {
	return fem.getNbIntegrationPoints(type, ghost_type);
	},
	py::arg("type"), py::arg("ghost_type") = _not_ghost)
	.def(
	"gradientOnIntegrationPoints",
	[](FEEngine & fem, const Array<Real> & u, Array<Real> & nablauq,
	UInt nb_degree_of_freedom, ElementType type, GhostType ghost_type,
	const Array<UInt> * filter_elements) {
	if (filter_elements == nullptr) {
	// This is due to the ArrayProxy that looses the
	// empty_filter information
	filter_elements = &empty_filter;
	}
	fem.gradientOnIntegrationPoints(u, nablauq, nb_degree_of_freedom,
	type, ghost_type, *filter_elements);
	},
	py::arg("u"), py::arg("nablauq"), py::arg("nb_degree_of_freedom"),
	py::arg("type"), py::arg("ghost_type") = _not_ghost,
	py::arg("filter_elements") = nullptr)
	.def(
	"interpolateOnIntegrationPoints",
	[](FEEngine & self, const Array<Real> & u, Array<Real> & uq,
	UInt nb_degree_of_freedom, ElementType type, GhostType ghost_type,
	const Array<UInt> * filter_elements) {
	if (filter_elements == nullptr) {
	// This is due to the ArrayProxy that looses the
	// empty_filter information
	filter_elements = &empty_filter;
	}

	self.interpolateOnIntegrationPoints(u, uq, nb_degree_of_freedom,
	type, ghost_type,
	*filter_elements);
	},
	py::arg("u"), py::arg("uq"), py::arg("nb_degree_of_freedom"),
	py::arg("type"), py::arg("ghost_type") = _not_ghost,
	py::arg("filter_elements") = nullptr)
	.def(
	"interpolateOnIntegrationPoints",
	[](FEEngine & self, const Array<Real> & u,
	ElementTypeMapArray<Real> & uq,
	const ElementTypeMapArray<UInt> * filter_elements) {
	self.interpolateOnIntegrationPoints(u, uq, filter_elements);
	},
	py::arg("u"), py::arg("uq"), py::arg("filter_elements") = nullptr)
	.def(
	"computeIntegrationPointsCoordinates",
	[](FEEngine & self, ElementTypeMapArray<Real> & coordinates,
	const ElementTypeMapArray<UInt> * filter_elements)
	-> decltype(auto) {
	return self.computeIntegrationPointsCoordinates(coordinates,
	filter_elements);
	},
	py::arg("coordinates"), py::arg("filter_elements") = nullptr)
	.def(
	"assembleFieldLumped",
	[](FEEngine & fem,
	const std::function<void(Matrix<Real> &, const Element &)> &
	field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type) {
	fem.assembleFieldLumped(field_funct, matrix_id, dof_id, dof_manager,
	type, ghost_type);
	},
	py::arg("field_funct"), py::arg("matrix_id"), py::arg("dof_id"),
	py::arg("dof_manager"), py::arg("type"),
	py::arg("ghost_type") = _not_ghost)
	.def(
	"assembleFieldMatrix",
	[](FEEngine & fem,
	const std::function<void(Matrix<Real> &, const Element &)> &
	field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type = _not_ghost) {
	fem.assembleFieldMatrix(field_funct, matrix_id, dof_id, dof_manager,
	type, ghost_type);
	},
	py::arg("field_funct"), py::arg("matrix_id"), py::arg("dof_id"),
	py::arg("dof_manager"), py::arg("type"),
	py::arg("ghost_type") = _not_ghost)
	.def("getElementInradius", [](FEEngine & self, const Element & element) {
	return self.getElementInradius(element);
	});

	py::class_<IntegrationPoint>(mod, "IntegrationPoint");
	}
	} // namespace akantu
	diff --git a/python/py_fe_engine.hh b/python/py_fe_engine.hh
	index c65b4f1d7..b2b96774f 100644
	--- a/python/py_fe_engine.hh
	+++ b/python/py_fe_engine.hh
	@@ -1,45 +1,45 @@
	/**
	* @file py_fe_engine.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to FEEngine
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_FE_ENGINE_HH_
	#define AKANTU_PY_FE_ENGINE_HH_

	namespace akantu {

	void register_fe_engine(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_FE_ENGINE_HH_
	diff --git a/python/py_fragment_manager.cc b/python/py_fragment_manager.cc
	index a44b29b49..1af22f31f 100644
	--- a/python/py_fragment_manager.cc
	+++ b/python/py_fragment_manager.cc
	@@ -1,82 +1,82 @@
	/**
	* @file py_fragment_manager.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Mar 29 2021
	* @date last modification: Mon Mar 29 2021
	*
	* @brief pybind11 interface to FragmentManager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	#include <fragment_manager.hh>
	#include <solid_mechanics_model_cohesive.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](SolidMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](FragmentManager & self) -> decltype(auto) { \
	return self.func_name(); \
	})

	void register_fragment_manager(py::module & mod) {
	py::class_<FragmentManager, GroupManager>(mod, "FragmentManager")
	.def(py::init<SolidMechanicsModelCohesive &, bool, const ID &>(),
	py::arg("model"), py::arg("dump_data") = true,
	py::arg("ID") = "fragment_manager")
	.def("buildFragments", &FragmentManager::buildFragments,
	py::arg("damage_limit") = 1.)
	.def_function(computeCenterOfMass)
	.def_function(computeVelocity)
	.def_function(computeInertiaMoments)
	.def("computeAllData", &FragmentManager::computeAllData,
	py::arg("damage_limit") = 1.)
	.def_function(computeNbElementsPerFragment)
	.def_function(getNbFragment)
	.def_function(getMass)
	.def_function(getVelocity)
	.def_function(getMomentsOfInertia)
	.def_function(getPrincipalDirections)
	.def_function(getNbElementsPerFragment);
	}
	} // namespace akantu
	diff --git a/python/py_fragment_manager.hh b/python/py_fragment_manager.hh
	index d7cc6476f..fdb00f9fa 100644
	--- a/python/py_fragment_manager.hh
	+++ b/python/py_fragment_manager.hh
	@@ -1,46 +1,46 @@
	/**
	* @file py_fragment_manager.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Mar 29 2021
	* @date last modification: Mon Mar 29 2021
	*
	* @brief pybind11 interface to FragmentManager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_FRAGMENT_MANAGER_HH_
	#define AKANTU_PY_FRAGMENT_MANAGER_HH_

	namespace akantu {

	void register_fragment_manager(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_FRAGMENT_MANAGER_HH_
	diff --git a/python/py_group_manager.hh b/python/py_group_manager.hh
	index 8ad3edce0..7bb03acf5 100644
	--- a/python/py_group_manager.hh
	+++ b/python/py_group_manager.hh
	@@ -1,42 +1,42 @@
	/**
	* @file py_group_manager.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to GroupManager, ElementGroup and NodeGroup
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_GROUP_MANAGER_HH_
	#define AKANTU_PY_GROUP_MANAGER_HH_

	namespace akantu {
	void register_group_manager(pybind11::module & mod);
	} // namespace akantu

	#endif /* AKANTU_PY_GROUP_MANAGER_HH_ */
	diff --git a/python/py_heat_transfer_model.cc b/python/py_heat_transfer_model.cc
	index 44b2df682..fac0a0a6b 100644
	--- a/python/py_heat_transfer_model.cc
	+++ b/python/py_heat_transfer_model.cc
	@@ -1,99 +1,102 @@
	/**
	* @file py_heat_transfer_model.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Sun Jun 16 2019
	*
	* @brief pybind11 interface to HeatTransferModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <heat_transfer_model.hh>
	#include <non_linear_solver.hh>
	/* -------------------------------------------------------------------------- */
	//#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	//#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	- def(#func_name, \
	+ def( \
	+ #func_name, \
	[](HeatTransferModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](HeatTransferModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})
	/* -------------------------------------------------------------------------- */

	void register_heat_transfer_model(py::module & mod) {
	py::class_<HeatTransferModelOptions>(mod, "HeatTransferModelOptions")
	.def(py::init<AnalysisMethod>(),
	py::arg("analysis_method") = _explicit_lumped_mass);

	py::class_<HeatTransferModel, Model>(mod, "HeatTransferModel",
	py::multiple_inheritance())
	- .def(py::init<Mesh &, UInt, const ID &>(),
	- py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	+ .def(py::init<Mesh &, UInt, const ID &>(), py::arg("mesh"),
	+ py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "heat_transfer_model")
	- .def("initFull",
	- [](HeatTransferModel & self,
	- const HeatTransferModelOptions & options) {
	- self.initFull(options);
	- },
	- py::arg("_analysis_method") = HeatTransferModelOptions())
	- .def("initFull",
	- [](HeatTransferModel & self,
	- const AnalysisMethod & _analysis_method) {
	- self.initFull(HeatTransferModelOptions(_analysis_method));
	- },
	- py::arg("_analysis_method"))
	+ .def(
	+ "initFull",
	+ [](HeatTransferModel & self,
	+ const HeatTransferModelOptions & options) {
	+ self.initFull(options);
	+ },
	+ py::arg("_analysis_method") = HeatTransferModelOptions())
	+ .def(
	+ "initFull",
	+ [](HeatTransferModel & self,
	+ const AnalysisMethod & _analysis_method) {
	+ self.initFull(HeatTransferModelOptions(_analysis_method));
	+ },
	+ py::arg("_analysis_method"))
	.def("setTimeStep", &HeatTransferModel::setTimeStep, py::arg("time_step"),
	py::arg("solver_id") = "")
	.def_function(getStableTimeStep)
	.def_function_nocopy(getTemperature)
	.def_function_nocopy(getBlockedDOFs)
	.def("getTemperatureGradient", &HeatTransferModel::getTemperatureGradient,
	py::arg("el_type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def("getKgradT", &HeatTransferModel::getKgradT, py::arg("el_type"),
	py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference);
	}

	} // namespace akantu
	diff --git a/python/py_heat_transfer_model.hh b/python/py_heat_transfer_model.hh
	index e953101d5..d5be2ada4 100644
	--- a/python/py_heat_transfer_model.hh
	+++ b/python/py_heat_transfer_model.hh
	@@ -1,44 +1,44 @@
	/**
	* @file py_heat_transfer_model.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to HeatTransferModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_HEAT_TRANSFERT_MODEL_HH_
	#define AKANTU_PY_HEAT_TRANSFERT_MODEL_HH_

	namespace akantu {

	void register_heat_transfer_model(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_HEAT_TRANSFERT_MODEL_HH_
	diff --git a/python/py_material.cc b/python/py_material.cc
	index e07f137c6..a5beb568b 100644
	--- a/python/py_material.cc
	+++ b/python/py_material.cc
	@@ -1,213 +1,213 @@
	/**
	* @file py_material.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Fri Apr 09 2021
	*
	* @brief pybind11 interface to Material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	#include "py_akantu_pybind11_compatibility.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_selector.hh>
	#include <solid_mechanics_model.hh>
	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include <solid_mechanics_model_cohesive.hh>
	#endif
	-#include <material_elastic.cc>
	+#include <material_elastic.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace {
	template <typename _Material> class PyMaterial : public _Material {
	public:
	/* Inherit the constructors */
	using _Material::_Material;

	~PyMaterial() override = default;

	void initMaterial() override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE(void, _Material, initMaterial, );
	};
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE_PURE(void, _Material, computeStress, el_type,
	ghost_type);
	}
	void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE(void, _Material, computeTangentModuli, el_type,
	tangent_matrix, ghost_type);
	}

	void computePotentialEnergy(ElementType el_type) override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE(void, _Material, computePotentialEnergy, el_type);
	}

	Real getPushWaveSpeed(const Element & element) const override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE(Real, _Material, getPushWaveSpeed, element);
	}

	Real getShearWaveSpeed(const Element & element) const override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE(Real, _Material, getShearWaveSpeed, element);
	}

	template <typename T>
	void registerInternal(const std::string & name, UInt nb_component) {
	auto && internal = std::make_shared<InternalField<T>>(name, *this);
	AKANTU_DEBUG_INFO("alloc internal " << name << " "
	<< &this->internals[name]);

	internal->initialize(nb_component);
	this->internals[name] = internal;
	}

	protected:
	std::map<std::string, std::shared_ptr<ElementTypeMapBase>> internals;
	};

	/* ------------------------------------------------------------------------ */
	template <typename T>
	void register_internal_field(py::module & mod, const std::string & name) {
	py::class_<InternalField<T>, ElementTypeMapArray<T>,
	std::shared_ptr<InternalField<T>>>(
	mod, ("InternalField" + name).c_str());
	}

	/* ------------------------------------------------------------------------ */
	template <typename _Material>
	void register_material_classes(py::module & mod, const std::string & name) {
	py::class_<_Material, Material, Parsable, PyMaterial<_Material>>(
	mod, name.c_str(), py::multiple_inheritance())
	.def(py::init<SolidMechanicsModel &, const ID &>());
	}
	} // namespace

	/* -------------------------------------------------------------------------- */
	void register_material(py::module & mod) {
	py::class_<MaterialFactory>(mod, "MaterialFactory")
	.def_static(
	"getInstance",
	[]() -> MaterialFactory & { return Material::getFactory(); },
	py::return_value_policy::reference)
	.def("registerAllocator",
	[](MaterialFactory & self, const std::string id, py::function func) {
	self.registerAllocator(
	id,
	[func, id](UInt dim, const ID & /unused/,
	SolidMechanicsModel & model,
	const ID & option) -> std::unique_ptr<Material> {
	py::object obj = func(dim, id, model, option);
	auto & ptr = py::cast<Material &>(obj);

	obj.release();
	return std::unique_ptr<Material>(&ptr);
	});
	})
	.def("getPossibleAllocators", &MaterialFactory::getPossibleAllocators);

	register_internal_field<Real>(mod, "Real");
	register_internal_field<UInt>(mod, "UInt");

	py::class_<Material, Parsable, PyMaterial<Material>>(
	mod, "Material", py::multiple_inheritance())
	.def(py::init<SolidMechanicsModel &, const ID &>())
	.def(
	"getGradU",
	[](Material & self, ElementType el_type,
	GhostType ghost_type = _not_ghost) -> decltype(auto) {
	return self.getGradU(el_type, ghost_type);
	},
	py::arg("el_type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def(
	"getStress",
	[](Material & self, ElementType el_type,
	GhostType ghost_type = _not_ghost) -> decltype(auto) {
	return self.getStress(el_type, ghost_type);
	},
	py::arg("el_type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def(
	"getPotentialEnergy",
	[](Material & self, ElementType el_type) -> decltype(auto) {
	return self.getPotentialEnergy(el_type);
	},
	py::return_value_policy::reference)
	.def("initMaterial", &Material::initMaterial)
	.def("getModel", &Material::getModel)
	.def("registerInternalReal",
	[](Material & self, const std::string & name, UInt nb_component) {
	return dynamic_cast<PyMaterial<Material> &>(self)
	.registerInternal<Real>(name, nb_component);
	})
	.def("registerInternalUInt",
	[](Material & self, const std::string & name, UInt nb_component) {
	return dynamic_cast<PyMaterial<Material> &>(self)
	.registerInternal<UInt>(name, nb_component);
	})
	.def(
	"getInternalReal",
	[](Material & self, const ID & id) -> decltype(auto) {
	return self.getInternal<Real>(id);
	},
	py::arg("id"), py::return_value_policy::reference)
	.def(
	"getInternalUInt",
	[](Material & self, const ID & id) -> decltype(auto) {
	return self.getInternal<UInt>(id);
	},
	py::arg("id"), py::return_value_policy::reference)
	.def(
	"getElementFilter",
	[](Material & self) -> decltype(auto) {
	return self.getElementFilter();
	},
	py::return_value_policy::reference)
	.def("getPushWaveSpeed", &Material::getPushWaveSpeed)
	.def("getShearWaveSpeed", &Material::getShearWaveSpeed);

	register_material_classes<MaterialElastic<2>>(mod, "MaterialElastic2D");
	register_material_classes<MaterialElastic<3>>(mod, "MaterialElastic3D");
	}

	} // namespace akantu
	diff --git a/python/py_material.hh b/python/py_material.hh
	index ff6751264..55cf883b8 100644
	--- a/python/py_material.hh
	+++ b/python/py_material.hh
	@@ -1,44 +1,44 @@
	/**
	* @file py_material.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to Material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_MATERIAL_HH_
	#define AKANTU_PY_MATERIAL_HH_

	namespace akantu {

	void register_material(pybind11::module & mod);
	void register_material_selector(pybind11::module & mod);
	} // namespace akantu

	#endif // AKANTU_PY_MATERIAL_HH_
	diff --git a/python/py_material_selector.cc b/python/py_material_selector.cc
	index 1601109ce..375882aba 100644
	--- a/python/py_material_selector.cc
	+++ b/python/py_material_selector.cc
	@@ -1,117 +1,117 @@
	/**
	* @file py_material_selector.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 26 2021
	* @date last modification: Wed May 26 2021
	*
	* @brief Material selector python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_material_selector.hh"
	#include "py_akantu_pybind11_compatibility.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_selector.hh>
	#include <solid_mechanics_model.hh>
	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include <material_selector_cohesive.hh>
	#include <solid_mechanics_model_cohesive.hh>
	#endif
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace {
	template <class Base = MaterialSelector>
	class PyMaterialSelector : public Base {
	public:
	/* Inherit the constructors */
	using Base::Base;

	~PyMaterialSelector() override = default;

	UInt operator()(const Element & element) override {
	// NOLINTNEXTLINE
	PYBIND11_OVERRIDE_NAME(UInt, MaterialSelector, "__call__", operator(),
	element);
	}
	};

	template <class MaterialSelectorDaughter>
	decltype(auto) register_material_selectors(py::module & mod,
	const std::string & class_name) {
	return py::class_<MaterialSelectorDaughter, MaterialSelector,
	PyMaterialSelector<MaterialSelectorDaughter>,
	std::shared_ptr<MaterialSelectorDaughter>>(
	mod, class_name.c_str());
	}
	} // namespace

	void register_material_selector(py::module & mod) {
	py::class_<MaterialSelector, PyMaterialSelector<>,
	std::shared_ptr<MaterialSelector>>(mod, "MaterialSelector")
	.def(py::init())
	.def("setFallback",
	[](MaterialSelector & self, UInt f) { self.setFallback(f); })
	.def("setFallback",
	[](MaterialSelector & self,
	const std::shared_ptr<MaterialSelector> & fallback_selector) {
	self.setFallback(fallback_selector);
	})
	.def("__call__", &MaterialSelector::operator());

	register_material_selectors<DefaultMaterialSelector>(
	mod, "DefaultMaterialSelector")
	.def(py::init<const ElementTypeMapArray<UInt>>());

	register_material_selectors<MeshDataMaterialSelector<std::string>>(
	mod, "MeshDataMaterialSelectorString")
	.def(py::init<const std::string &, const SolidMechanicsModel &, UInt>(),
	py::arg("name"), py::arg("model"), py::arg("first_index") = 1);

	#if defined(AKANTU_COHESIVE_ELEMENT)
	register_material_selectors<DefaultMaterialCohesiveSelector>(
	mod, "DefaultMaterialCohesiveSelector")
	.def(py::init<const SolidMechanicsModelCohesive &>());

	register_material_selectors<MeshDataMaterialCohesiveSelector>(
	mod, "MeshDataMaterialCohesiveSelector")
	.def(py::init<const SolidMechanicsModelCohesive &>());

	register_material_selectors<MaterialCohesiveRulesSelector>(
	mod, "MaterialCohesiveRulesSelector")
	.def(py::init<const SolidMechanicsModelCohesive &,
	const MaterialCohesiveRules &, const ID &>(),
	py::arg("model"), py::arg("rules"),
	py::arg("mesh_data_id") = "physical_names");
	#endif
	}
	} // namespace akantu
	diff --git a/python/py_material_selector.hh b/python/py_material_selector.hh
	index a76575cba..baf3bc6da 100644
	--- a/python/py_material_selector.hh
	+++ b/python/py_material_selector.hh
	@@ -1,43 +1,43 @@
	/**
	* @file py_material_selector.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 26 2021
	* @date last modification: Wed May 26 2021
	*
	* @brief Material selector python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_MATERIAL_SELECTOR_HH_
	#define AKANTU_PY_MATERIAL_SELECTOR_HH_

	namespace akantu {

	void register_material_selector(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_MATERIAL_SELECTOR_HH_
	diff --git a/python/py_mesh.cc b/python/py_mesh.cc
	index b3b90270e..e3c6152f4 100644
	--- a/python/py_mesh.cc
	+++ b/python/py_mesh.cc
	@@ -1,194 +1,194 @@
	/**
	* @file py_mesh.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Philip Mueller <philip.paul.mueller@bluemail.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Mon Mar 15 2021
	*
	* @brief pybind11 interface to Mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_config.hh"
	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <mesh.hh>
	#include <mesh_accessor.hh>
	#include <mesh_utils.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace {
	/* ------------------------------------------------------------------------ */
	template <typename T>
	void register_element_type_map_array(py::module & mod,
	const std::string & name) {
	py::class_<ElementTypeMapArray<T>, std::shared_ptr<ElementTypeMapArray<T>>>(
	mod, ("ElementTypeMapArray" + name).c_str())
	.def(
	"__call__",
	[](ElementTypeMapArray<T> & self, ElementType type,
	GhostType ghost_type) -> decltype(auto) {
	return self(type, ghost_type);
	},
	py::arg("type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def(
	"elementTypes",
	[](ElementTypeMapArray<T> & self, UInt _dim, GhostType _ghost_type,
	ElementKind _kind) -> std::vector<ElementType> {
	auto types = self.elementTypes(_dim, _ghost_type, _kind);
	std::vector<ElementType> _types;
	for (auto && t : types) {
	_types.push_back(t);
	}
	return _types;
	},
	py::arg("dim") = _all_dimensions,
	py::arg("ghost_type") = _not_ghost, py::arg("kind") = _ek_regular);
	}
	} // namespace
	/* -------------------------------------------------------------------------- */
	void register_mesh(py::module & mod) {

	register_element_type_map_array<Real>(mod, "Real");
	register_element_type_map_array<UInt>(mod, "UInt");
	- //register_element_type_map_array<std::string>(mod, "String");
	+ // register_element_type_map_array<std::string>(mod, "String");

	py::class_<MeshData>(mod, "MeshData")
	.def(
	"getElementalDataUInt",
	[](MeshData & _this, const ID & name) -> decltype(auto) {
	return _this.getElementalData<UInt>(name);
	},
	py::return_value_policy::reference)
	.def(
	"getElementalDataReal",
	[](MeshData & _this, const ID & name) -> decltype(auto) {
	return _this.getElementalData<Real>(name);
	},
	py::return_value_policy::reference);

	py::class_<Mesh, GroupManager, Dumpable, MeshData>(mod, "Mesh",
	py::multiple_inheritance())
	.def(py::init<UInt, const ID &>(), py::arg("spatial_dimension"),
	py::arg("id") = "mesh")
	.def("read", &Mesh::read, py::arg("filename"),
	py::arg("mesh_io_type") = _miot_auto, "read the mesh from a file")
	.def(
	"getNodes",
	[](Mesh & self) -> decltype(auto) { return self.getNodes(); },
	py::return_value_policy::reference)
	.def("getNbNodes", &Mesh::getNbNodes)
	.def(
	"getConnectivity",
	[](Mesh & self, ElementType type) -> decltype(auto) {
	return self.getConnectivity(type);
	},
	py::return_value_policy::reference)
	.def(
	"addConnectivityType",
	[](Mesh & self, ElementType type, GhostType ghost_type) -> void {
	self.addConnectivityType(type, ghost_type);
	},
	py::arg("type"), py::arg("ghost_type") = _not_ghost)
	.def("distribute", [](Mesh & self) { self.distribute(); })
	.def("fillNodesToElements", &Mesh::fillNodesToElements,
	py::arg("dimension") = _all_dimensions)
	.def("getAssociatedElements",
	[](Mesh & self, const UInt & node, py::list list) {
	Array<Element> elements;
	self.getAssociatedElements(node, elements);
	for (auto && element : elements) {
	list.append(element);
	}
	})
	.def("makePeriodic",
	[](Mesh & self, const SpatialDirection & direction) {
	self.makePeriodic(direction);
	})
	.def(
	"getNbElement",
	[](Mesh & self, const UInt spatial_dimension, GhostType ghost_type,
	ElementKind kind) {
	return self.getNbElement(spatial_dimension, ghost_type, kind);
	},
	py::arg("spatial_dimension") = _all_dimensions,
	py::arg("ghost_type") = _not_ghost, py::arg("kind") = _ek_not_defined)
	.def(
	"getNbElement",
	[](Mesh & self, ElementType type, GhostType ghost_type) {
	return self.getNbElement(type, ghost_type);
	},
	py::arg("type"), py::arg("ghost_type") = _not_ghost)
	.def_static(
	"getSpatialDimension",
	[](ElementType & type) { return Mesh::getSpatialDimension(type); })
	.def(
	"getDataReal",
	[](Mesh & _this, const ID & name, ElementType type,
	GhostType ghost_type) -> decltype(auto) {
	return _this.getData<Real>(name, type, ghost_type);
	},
	py::arg("name"), py::arg("type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def(
	"hasDataReal",
	[](Mesh & _this, const ID & name, ElementType type,
	GhostType ghost_type) -> bool {
	return _this.hasData<Real>(name, type, ghost_type);
	},
	py::arg("name"), py::arg("type"), py::arg("ghost_type") = _not_ghost);

	/* ------------------------------------------------------------------------ */
	py::class_<MeshUtils>(mod, "MeshUtils")
	.def_static("buildFacets", &MeshUtils::buildFacets);

	py::class_<MeshAccessor>(mod, "MeshAccessor")
	.def(py::init<Mesh &>(), py::arg("mesh"))
	.def(
	"resizeConnectivity",
	[](MeshAccessor & self, UInt new_size, ElementType type, GhostType gt)
	-> void { self.resizeConnectivity(new_size, type, gt); },
	py::arg("new_size"), py::arg("type"),
	py::arg("ghost_type") = _not_ghost)
	.def(
	"resizeNodes",
	[](MeshAccessor & self, UInt new_size) -> void {
	self.resizeNodes(new_size);
	},
	py::arg("new_size"))
	.def("makeReady", &MeshAccessor::makeReady);
	}
	} // namespace akantu
	diff --git a/python/py_mesh.hh b/python/py_mesh.hh
	index ae7142252..17ff76b20 100644
	--- a/python/py_mesh.hh
	+++ b/python/py_mesh.hh
	@@ -1,42 +1,42 @@
	/**
	* @file py_mesh.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to Mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_MESH_HH_
	#define AKANTU_PY_MESH_HH_

	namespace akantu {
	void register_mesh(pybind11::module & mod);
	} // namespace akantu

	#endif // AKANTU_PY_MESH_HH_
	diff --git a/python/py_model.cc b/python/py_model.cc
	index 01c123893..7978dcc67 100644
	--- a/python/py_model.cc
	+++ b/python/py_model.cc
	@@ -1,159 +1,159 @@
	/**
	* @file py_model.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Philip Mueller <philip.paul.mueller@bluemail.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Sat Mar 13 2021
	*
	* @brief pybind11 interface to Model and parent classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <model.hh>
	#include <non_linear_solver.hh>
	#include <sparse_matrix_aij.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void register_model(py::module & mod) {
	py::class_<DOFManager>(mod, "DOFManager")
	.def("getMatrix", &DOFManager::getMatrix,
	py::return_value_policy::reference)
	.def(
	"getNewMatrix",
	[](DOFManager & self, const std::string & name,
	const std::string & matrix_to_copy_id) -> decltype(auto) {
	return self.getNewMatrix(name, matrix_to_copy_id);
	},
	py::return_value_policy::reference)
	.def(
	"getResidual",
	[](DOFManager & self) -> decltype(auto) {
	return self.getResidual();
	},
	py::return_value_policy::reference)
	.def("getArrayPerDOFs", &DOFManager::getArrayPerDOFs)
	.def(
	"hasMatrix",
	[](DOFManager & self, const ID & name) -> bool {
	return self.hasMatrix(name);
	},
	py::arg("name"))
	.def("assembleToResidual", &DOFManager::assembleToResidual);

	py::class_<NonLinearSolver>(mod, "NonLinearSolver")
	.def(
	"set",
	[](NonLinearSolver & self, const std::string & id, const Real & val) {
	if (id == "max_iterations") {
	self.set(id, int(val));
	} else {
	self.set(id, val);
	}
	})
	.def("set",
	[](NonLinearSolver & self, const std::string & id,
	const SolveConvergenceCriteria & val) { self.set(id, val); });

	py::class_<ModelSolver, Parsable>(mod, "ModelSolver",
	py::multiple_inheritance())
	.def("getNonLinearSolver",
	(NonLinearSolver & (ModelSolver::*)(const ID &)) &
	ModelSolver::getNonLinearSolver,
	py::arg("solver_id") = "", py::return_value_policy::reference)
	.def("solveStep", [](ModelSolver & self) { self.solveStep(); })
	.def("solveStep", [](ModelSolver & self, const ID & solver_id) {
	self.solveStep(solver_id);
	});

	py::class_<Model, ModelSolver>(mod, "Model", py::multiple_inheritance())
	.def("setBaseName", &Model::setBaseName)
	.def("setDirectory", &Model::setDirectory)
	.def("getFEEngine", &Model::getFEEngine, py::arg("name") = "",
	py::return_value_policy::reference)
	.def("getFEEngineBoundary", &Model::getFEEngine, py::arg("name") = "",
	py::return_value_policy::reference)
	.def("addDumpFieldVector", &Model::addDumpFieldVector)
	.def("addDumpField", &Model::addDumpField)
	.def("setBaseNameToDumper", &Model::setBaseNameToDumper)
	.def("addDumpFieldVectorToDumper", &Model::addDumpFieldVectorToDumper)
	.def("addDumpFieldToDumper", &Model::addDumpFieldToDumper)
	- .def("dump", [](Model & self) { self.dump(); })
	+ .def("dump", [](Model & self) { self.dump(); })
	.def(
	"dump", [](Model & self, UInt step) { self.dump(step); },
	py::arg("step"))
	.def(
	"dump",
	[](Model & self, Real time, UInt step) { self.dump(time, step); },
	py::arg("time"), py::arg("step"))
	.def(
	"dump",
	[](Model & self, const std::string & dumper) { self.dump(dumper); },
	py::arg("dumper_name"))
	.def(
	"dump",
	[](Model & self, const std::string & dumper, UInt step) {
	self.dump(dumper, step);
	},
	py::arg("dumper_name"), py::arg("step"))
	.def(
	"dump",
	[](Model & self, const std::string & dumper, Real time, UInt step) {
	self.dump(dumper, time, step);
	},
	py::arg("dumper_name"), py::arg("time"), py::arg("step"))
	.def("initNewSolver", &Model::initNewSolver)
	.def(
	"getNewSolver",
	[](Model & self, const std::string id,
	const TimeStepSolverType & time,
	const NonLinearSolverType & type) {
	self.getNewSolver(id, time, type);
	},
	py::return_value_policy::reference)
	.def("setIntegrationScheme",
	[](Model & self, const std::string id, const std::string primal,
	const IntegrationSchemeType & scheme) {
	self.setIntegrationScheme(id, primal, scheme);
	})
	.def("getDOFManager", &Model::getDOFManager,
	py::return_value_policy::reference)
	.def("assembleMatrix", &Model::assembleMatrix);
	}

	} // namespace akantu
	diff --git a/python/py_model.hh b/python/py_model.hh
	index 1f356847c..08cf7440e 100644
	--- a/python/py_model.hh
	+++ b/python/py_model.hh
	@@ -1,44 +1,44 @@
	/**
	* @file py_model.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to Model and parent classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_AKA_MODEL_HH_
	#define AKANTU_PY_AKA_MODEL_HH_

	namespace akantu {

	void register_model(pybind11::module & mod);

	}

	#endif
	diff --git a/python/py_model_couplers.cc b/python/py_model_couplers.cc
	index d5b250f71..7cc6f6424 100644
	--- a/python/py_model_couplers.cc
	+++ b/python/py_model_couplers.cc
	@@ -1,122 +1,122 @@
	/**
	* @file py_model_couplers.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Model Coupler python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <cohesive_contact_solvercallback.hh>
	#include <coupler_solid_cohesive_contact.hh>
	#include <coupler_solid_contact.hh>
	#include <non_linear_solver.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace {
	template <class CouplerSolidContact_>
	auto register_coupler_solid_contact(py::module & mod,
	const std::string & name)
	-> py::class_<CouplerSolidContact_, Model> {
	return py::class_<CouplerSolidContact_, Model>(mod, name.c_str(),
	py::multiple_inheritance())
	.def(py::init<Mesh &, UInt, const ID &, std::shared_ptr<DOFManager>,
	const ModelType>(),
	py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "coupler_solid_contact",
	py::arg("dof_manager") = nullptr,
	py::arg("model_type") = ModelType::_coupler_solid_contact)
	.def("applyBC",
	[](CouplerSolidContact_ & self,
	BC::Dirichlet::DirichletFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})
	.def("applyBC",
	[](CouplerSolidContact_ & self, BC::Neumann::NeumannFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})

	.def("setTimeStep", &CouplerSolidContact_::setTimeStep,
	py::arg("time_step"), py::arg("solver_id") = "")
	.def("getContactMechanicsModel",
	&CouplerSolidContact_::getContactMechanicsModel,
	py::return_value_policy::reference);
	}
	} // namespace

	/* -------------------------------------------------------------------------- */
	void register_model_couplers(py::module & mod) {
	register_coupler_solid_contact<CouplerSolidContact>(mod,
	"CouplerSolidContact")
	.def(
	"getSolidMechanicsModel",
	[](CouplerSolidContact & self) -> decltype(auto) {
	return self.getSolidMechanicsModel();
	},
	py::return_value_policy::reference)
	.def(
	"initFull",
	[](CouplerSolidContact & self,
	const AnalysisMethod & analysis_method) {
	self.initFull(_analysis_method = analysis_method);
	},
	py::arg("_analysis_method") = _explicit_lumped_mass);

	register_coupler_solid_contact<CouplerSolidCohesiveContact>(
	mod, "CouplerSolidCohesiveContact")
	.def(
	"initFull",
	[](CouplerSolidCohesiveContact & self,
	const AnalysisMethod & analysis_method, bool is_extrinsic) {
	self.initFull(_analysis_method = analysis_method,
	_is_extrinsic = is_extrinsic);
	},
	py::arg("_analysis_method") = _explicit_lumped_mass,
	py::arg("_is_extrinsic") = false)
	.def("checkCohesiveStress",
	[](CouplerSolidCohesiveContact & self) {
	return self.checkCohesiveStress();
	})
	.def(
	"getSolidMechanicsModelCohesive",
	[](CouplerSolidCohesiveContact & self) -> decltype(auto) {
	return self.getSolidMechanicsModelCohesive();
	},
	py::return_value_policy::reference);
	}

	} // namespace akantu
	diff --git a/python/py_model_couplers.hh b/python/py_model_couplers.hh
	index 1d4e67ed1..3884ec226 100644
	--- a/python/py_model_couplers.hh
	+++ b/python/py_model_couplers.hh
	@@ -1,41 +1,41 @@
	/**
	* @file py_model_couplers.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Jun 20 2019
	* @date last modification: Sat Dec 12 2020
	*
	* @brief Model Coupler python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef __AKANTU_PY_MODEL_COUPLERS_HH__
	#define __AKANTU_PY_MODEL_COUPLERS_HH__

	namespace akantu {
	void register_model_couplers(pybind11::module & mod);
	} // namespace akantu

	#endif // __AKANTU_PY_MODEL_COUPLERS_HH__
	diff --git a/python/py_parser.cc b/python/py_parser.cc
	index 1c9b7b496..dc66fade8 100644
	--- a/python/py_parser.cc
	+++ b/python/py_parser.cc
	@@ -1,102 +1,103 @@
	/**
	* @file py_parser.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Mon Mar 01 2021
	*
	* @brief pybind11 interface to Mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <aka_common.hh>
	#include <parameter_registry.hh>
	#include <parsable.hh>
	#include <parser.hh>
	/* -------------------------------------------------------------------------- */
	#include <map>
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	std::map<void , std::map<std::string, void >> map_params;

	void register_parser(py::module & mod) {
	py::enum_<ParameterAccessType>(mod, "ParameterAccessType", py::arithmetic())
	.value("_pat_internal", _pat_internal)
	.value("_pat_writable", _pat_writable)
	.value("_pat_readable", _pat_readable)
	.value("_pat_modifiable", _pat_modifiable)
	.value("_pat_parsable", _pat_parsable)
	.value("_pat_parsmod", _pat_parsmod)
	.export_values();

	py::class_<ParameterRegistry>(mod, "ParameterRegistry",
	py::multiple_inheritance())
	.def("registerParamReal",
	[](ParameterRegistry & self, const std::string & name, UInt type,
	const std::string & description) {
	Real * p = new Real;
	map_params[&self][name] = p;
	self.registerParam<Real>(name, *p, ParameterAccessType(type),
	description);
	})
	.def("registerParamReal",
	[](ParameterRegistry & self, const Real & _default,
	const std::string & name, UInt type,
	const std::string & description) {
	Real * p = new Real;
	map_params[&self][name] = p;
	self.registerParam<Real>(name, *p, _default,
	ParameterAccessType(type), description);
	})
	.def("getReal",
	[](ParameterRegistry & self, const std::string & name) {
	return Real(self.get(name));
	})
	- .def("getMatrix",
	- [](ParameterRegistry & self, const std::string & name) {
	- const Matrix<Real> & res =
	- static_cast<const Matrix<Real> &>(self.get(name));
	- return res;
	- },
	- py::return_value_policy::copy);
	+ .def(
	+ "getMatrix",
	+ [](ParameterRegistry & self, const std::string & name) {
	+ const Matrix<Real> & res =
	+ static_cast<const Matrix<Real> &>(self.get(name));
	+ return res;
	+ },
	+ py::return_value_policy::copy);

	py::class_<Parsable, ParameterRegistry>(mod, "Parsable",
	py::multiple_inheritance())
	.def(py::init<const ParserType &, const ID &>());

	- mod.def("parseInput",
	- [](const std::string & input_file) {
	- getStaticParser().parse(input_file);
	- },
	- "Parse an Akantu input file");
	-
	+ mod.def(
	+ "parseInput",
	+ [](const std::string & input_file) {
	+ getStaticParser().parse(input_file);
	+ },
	+ "Parse an Akantu input file");
	}
	} // namespace akantu
	diff --git a/python/py_parser.hh b/python/py_parser.hh
	index d7a6d60b0..e3f0d02e0 100644
	--- a/python/py_parser.hh
	+++ b/python/py_parser.hh
	@@ -1,44 +1,44 @@
	/**
	* @file py_parser.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to Mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_AKA_PARSER_HH_
	#define AKANTU_PY_AKA_PARSER_HH_

	namespace akantu {

	void register_parser(pybind11::module & mod);

	}

	#endif
	diff --git a/python/py_phase_field_model.cc b/python/py_phase_field_model.cc
	index 45e2ef393..960970144 100644
	--- a/python/py_phase_field_model.cc
	+++ b/python/py_phase_field_model.cc
	@@ -1,144 +1,144 @@
	/**
	* @file py_phase_field_model.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Fri Jun 25 2021
	*
	* @brief Phase field python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <coupler_solid_phasefield.hh>
	#include <non_linear_solver.hh>
	#include <phase_field_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](PhaseFieldModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](PhaseFieldModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})
	/* -------------------------------------------------------------------------- */

	[[gnu::visibility("default")]] void
	register_phase_field_model(py::module & mod) {

	py::class_<PhaseFieldModelOptions>(mod, "PhaseFieldModelOptions")
	.def(py::init<AnalysisMethod>(), py::arg("analysis_method") = _static);

	py::class_<PhaseFieldModel, Model>(mod, "PhaseFieldModel",
	py::multiple_inheritance())
	.def(py::init<Mesh &, UInt, const ID &, const ModelType>(),
	py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "phase_field_model",
	py::arg("model_type") = ModelType::_phase_field_model)
	.def(
	"initFull",
	[](PhaseFieldModel & self, const PhaseFieldModelOptions & options) {
	self.initFull(options);
	},
	py::arg("_analysis_method") = PhaseFieldModelOptions())
	.def(
	"initFull",
	[](PhaseFieldModel & self, const AnalysisMethod & analysis_method) {
	self.initFull(_analysis_method = analysis_method);
	},
	py::arg("_analysis_method"))
	.def_deprecated("applyDirichletBC", "Deprecated: use applyBC")
	.def("applyBC",
	[](PhaseFieldModel & self, BC::Dirichlet::DirichletFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})
	.def("applyBC",
	[](PhaseFieldModel & self, BC::Neumann::NeumannFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})
	.def("setTimeStep", &PhaseFieldModel::setTimeStep, py::arg("time_step"),
	py::arg("solver_id") = "")
	.def_function(assembleStiffnessMatrix)
	.def_function(assembleInternalForces)
	.def_function_nocopy(getDamage)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getBlockedDOFs)
	.def_function_nocopy(getMesh)
	.def(
	"getPhaseField",
	[](PhaseFieldModel & self, UInt phase_field_id) -> decltype(auto) {
	return self.getPhaseField(phase_field_id);
	},
	py::arg("phase_field_id"), py::return_value_policy::reference)
	.def(
	"getPhaseField",
	[](PhaseFieldModel & self,
	const ID & phase_field_name) -> decltype(auto) {
	return self.getPhaseField(phase_field_name);
	},
	py::arg("phase_field_name"), py::return_value_policy::reference)
	.def("getPhaseFieldIndex", &PhaseFieldModel::getPhaseFieldIndex)
	.def("setPhaseFieldSelector", &PhaseFieldModel::setPhaseFieldSelector);
	}

	[[gnu::visibility("default")]] void
	register_phase_field_coupler(py::module & mod) {

	py::class_<CouplerSolidPhaseField, Model>(mod, "CouplerSolidPhaseField")
	.def(py::init<Mesh &, UInt, const ID &, const ModelType>(),
	py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "coupler_solid_phasefield",
	py::arg("model_type") = ModelType::_coupler_solid_phasefield)
	.def("solve",
	[](CouplerSolidPhaseField & self, const ID & solid_solver_id,
	const ID & phase_solver_id) {
	self.solve(solid_solver_id, phase_solver_id);
	})
	.def("getSolidMechanicsModel",
	&CouplerSolidPhaseField::getSolidMechanicsModel,
	py::return_value_policy::reference)
	.def("getPhaseFieldModel", &CouplerSolidPhaseField::getPhaseFieldModel,
	py::return_value_policy::reference);
	}

	} // namespace akantu
	diff --git a/python/py_phase_field_model.hh b/python/py_phase_field_model.hh
	index 27aaea328..78e8c6add 100644
	--- a/python/py_phase_field_model.hh
	+++ b/python/py_phase_field_model.hh
	@@ -1,42 +1,42 @@
	/**
	* @file py_phase_field_model.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Feb 26 2021
	* @date last modification: Fri May 14 2021
	*
	* @brief Phase field python binding
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <pybind11/pybind11.h>

	#ifndef __AKANTU_PY_PHASE_FIELD_MODEL_HH__
	#define __AKANTU_PY_PHASE_FIELD_MODEL_HH__

	namespace akantu {
	- void register_phase_field_model(pybind11::module & mod);
	- void register_phase_field_coupler(pybind11::module & mod);
	+void register_phase_field_model(pybind11::module & mod);
	+void register_phase_field_coupler(pybind11::module & mod);
	} // namespace akantu

	#endif // __AKANTU_PY_PHASE_FIELD_MODEL_HH__
	diff --git a/python/py_solid_mechanics_model.cc b/python/py_solid_mechanics_model.cc
	index 26d35c75e..1f698389f 100644
	--- a/python/py_solid_mechanics_model.cc
	+++ b/python/py_solid_mechanics_model.cc
	@@ -1,166 +1,164 @@
	/**
	* @file py_solid_mechanics_model.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jun 16 2019
	* @date last modification: Sat Mar 13 2021
	*
	* @brief pybind11 interface to SolidMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <non_linear_solver.hh>
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](SolidMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](SolidMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})
	/* -------------------------------------------------------------------------- */
	void register_solid_mechanics_model(py::module & mod) {

	py::class_<SolidMechanicsModelOptions>(mod, "SolidMechanicsModelOptions")
	.def(py::init<AnalysisMethod>(),
	py::arg("_analysis_method") = _explicit_lumped_mass);

	py::class_<SolidMechanicsModel, Model>(mod, "SolidMechanicsModel",
	py::multiple_inheritance())
	.def(py::init<Mesh &, UInt, const ID &, std::shared_ptr<DOFManager>,
	const ModelType>(),
	py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "solid_mechanics_model",
	py::arg("dof_manager") = nullptr,
	py::arg("model_type") = ModelType::_solid_mechanics_model)
	.def(
	"initFull",
	[](SolidMechanicsModel & self,
	const SolidMechanicsModelOptions & options) {
	self.initFull(options);
	},
	py::arg("option") = SolidMechanicsModelOptions())
	.def(
	"initFull",
	[](SolidMechanicsModel & self,
	const AnalysisMethod & analysis_method) {
	self.initFull(_analysis_method = analysis_method);
	},
	py::arg("_analysis_method"))
	.def_deprecated("applyDirichletBC", "Deprecated: use applyBC")
	.def("applyBC",
	[](SolidMechanicsModel & self,
	BC::Dirichlet::DirichletFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})
	.def("applyBC",
	[](SolidMechanicsModel & self, BC::Neumann::NeumannFunctor & func,
	const std::string & element_group) {
	self.applyBC(func, element_group);
	})
	.def("setTimeStep", &SolidMechanicsModel::setTimeStep,
	py::arg("time_step"), py::arg("solver_id") = "")
	.def(
	"getEnergy",
	[](SolidMechanicsModel & self, const std::string & energy_id) {
	return self.getEnergy(energy_id);
	},
	py::arg("energy_id"))
	.def(
	"getEnergy",
	[](SolidMechanicsModel & self, const std::string & energy_id,
	const std::string & group_id) {
	return self.getEnergy(energy_id, group_id);
	},
	py::arg("energy_id"), py::arg("group_id"))

	.def_function(assembleStiffnessMatrix)
	.def_function(assembleInternalForces)
	.def_function(assembleMass)
	.def_function(assembleMassLumped)
	.def_function(getStableTimeStep)
	.def_function_nocopy(getExternalForce)
	.def_function_nocopy(getDisplacement)
	.def_function_nocopy(getPreviousDisplacement)
	.def_function_nocopy(getCurrentPosition)
	.def_function_nocopy(getIncrement)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getMass)
	.def_function_nocopy(getVelocity)
	.def_function_nocopy(getAcceleration)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getBlockedDOFs)
	.def_function_nocopy(getMesh)
	.def(
	"getMaterial",
	[](SolidMechanicsModel & self, UInt material_id) -> decltype(auto) {
	return self.getMaterial(material_id);
	},
	- py::arg("material_id"),
	- py::return_value_policy::reference)
	+ py::arg("material_id"), py::return_value_policy::reference)
	.def(
	"getMaterial",
	[](SolidMechanicsModel & self, const ID & material_name)
	- -> decltype(auto) { return self.getMaterial(material_name); },
	- py::arg("material_name"),
	- py::return_value_policy::reference)
	+ -> decltype(auto) { return self.getMaterial(material_name); },
	+ py::arg("material_name"), py::return_value_policy::reference)
	.def("getMaterialIndex", &SolidMechanicsModel::getMaterialIndex)
	// .def(
	// "setMaterialSelector",
	// [](SolidMechanicsModel & self, MaterialSelector &
	// material_selector) {
	// self.setMaterialSelector(material_selector.shared_from_this());
	// })
	.def("setMaterialSelector",
	[](SolidMechanicsModel & self,
	std::shared_ptr<MaterialSelector> material_selector) {
	std::cout << (*material_selector)(ElementNull) << std::endl;
	self.setMaterialSelector(material_selector);
	})
	.def("getMaterialSelector", &SolidMechanicsModel::getMaterialSelector);
	}

	} // namespace akantu
	diff --git a/python/py_solid_mechanics_model.hh b/python/py_solid_mechanics_model.hh
	index 95508fb39..5537d4726 100644
	--- a/python/py_solid_mechanics_model.hh
	+++ b/python/py_solid_mechanics_model.hh
	@@ -1,45 +1,44 @@
	/**
	* @file py_solid_mechanics_model.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to SolidMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_SOLID_MECHANICS_MODEL_HH_
	#define AKANTU_PY_SOLID_MECHANICS_MODEL_HH_

	-
	namespace akantu {

	void register_solid_mechanics_model(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_SOLID_MECHANICS_MODEL_HH_
	diff --git a/python/py_solid_mechanics_model_cohesive.cc b/python/py_solid_mechanics_model_cohesive.cc
	index 0d11e800c..6d4ce5f3e 100644
	--- a/python/py_solid_mechanics_model_cohesive.cc
	+++ b/python/py_solid_mechanics_model_cohesive.cc
	@@ -1,95 +1,95 @@
	/**
	* @file py_solid_mechanics_model_cohesive.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 21 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to SolidMechanicsModelCohesive
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <non_linear_solver.hh>
	#include <solid_mechanics_model_cohesive.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](SolidMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function(func_name) \
	def(#func_name, [](SolidMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})

	void register_solid_mechanics_model_cohesive(py::module & mod) {
	py::class_<CohesiveElementInserter>(mod, "CohesiveElementInserter")
	.def("setLimit", &CohesiveElementInserter::setLimit);

	py::class_<SolidMechanicsModelCohesiveOptions, SolidMechanicsModelOptions>(
	mod, "SolidMechanicsModelCohesiveOptions")
	.def(py::init<AnalysisMethod, bool>(),
	py::arg("analysis_method") = _explicit_lumped_mass,
	py::arg("is_extrinsic") = false);

	py::class_<SolidMechanicsModelCohesive, SolidMechanicsModel>(
	mod, "SolidMechanicsModelCohesive")
	- .def(py::init<Mesh &, UInt, const ID &>(),
	- py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	+ .def(py::init<Mesh &, UInt, const ID &>(), py::arg("mesh"),
	+ py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "solid_mechanics_model")
	.def(
	"initFull",
	[](SolidMechanicsModel & self, const AnalysisMethod & analysis_method,
	bool is_extrinsic) {
	self.initFull(_analysis_method = analysis_method,
	_is_extrinsic = is_extrinsic);
	},
	py::arg("_analysis_method"), py::arg("_is_extrinsic") = false)

	.def("checkCohesiveStress",
	&SolidMechanicsModelCohesive::checkCohesiveStress)
	.def("getElementInserter",
	&SolidMechanicsModelCohesive::getElementInserter,
	py::return_value_policy::reference)
	.def("updateAutomaticInsertion",
	- &SolidMechanicsModelCohesive::updateAutomaticInsertion);
	+ &SolidMechanicsModelCohesive::updateAutomaticInsertion);
	}

	} // namespace akantu
	diff --git a/python/py_solid_mechanics_model_cohesive.hh b/python/py_solid_mechanics_model_cohesive.hh
	index 42a94cfcc..af7c772d9 100644
	--- a/python/py_solid_mechanics_model_cohesive.hh
	+++ b/python/py_solid_mechanics_model_cohesive.hh
	@@ -1,45 +1,44 @@
	/**
	* @file py_solid_mechanics_model_cohesive.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Tue Sep 29 2020
	*
	* @brief pybind11 interface to SolidMechanicsModelCohesive
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_SOLID_MECHANICS_MODEL_COHESIVE_HH_
	#define AKANTU_PY_SOLID_MECHANICS_MODEL_COHESIVE_HH_

	-
	namespace akantu {

	void register_solid_mechanics_model_cohesive(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_SOLID_MECHANICS_MODEL_COHESIVE_HH_
	diff --git a/python/py_solver.cc b/python/py_solver.cc
	index 962445f78..e8dcd435f 100644
	--- a/python/py_solver.cc
	+++ b/python/py_solver.cc
	@@ -1,84 +1,84 @@
	/**
	* @file py_solver.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Sat Mar 06 2021
	*
	* @brief pybind11 interface to Solver and SparseMatrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_solver.hh"
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <model.hh>
	#include <non_linear_solver.hh>
	#include <sparse_matrix_aij.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/operators.h>
	#include <pybind11/pybind11.h>
	#include <pybind11/stl.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void register_solvers(py::module & mod) {
	py::class_<SparseMatrix>(mod, "SparseMatrix")
	.def("getMatrixType", &SparseMatrix::getMatrixType)
	.def("size", &SparseMatrix::size)
	.def("zero", &SparseMatrix::zero)
	.def("saveProfile", &SparseMatrix::saveProfile)
	.def("saveMatrix", &SparseMatrix::saveMatrix)
	.def(
	"add", [](SparseMatrix & self, UInt i, UInt j) { self.add(i, j); },
	"Add entry in the profile")
	.def(
	"add",
	[](SparseMatrix & self, UInt i, UInt j, Real value) {
	self.add(i, j, value);
	},
	"Add the value to the matrix")
	.def(
	"add",
	[](SparseMatrix & self, SparseMatrix & A, Real alpha) {
	self.add(A, alpha);
	},
	"Add a matrix to the matrix", py::arg("A"), py::arg("alpha") = 1.)
	.def("__call__", [](const SparseMatrix & self, UInt i, UInt j) {
	return self(i, j);
	});

	py::class_<SparseMatrixAIJ, SparseMatrix>(mod, "SparseMatrixAIJ")
	.def("getIRN", &SparseMatrixAIJ::getIRN)
	.def("getJCN", &SparseMatrixAIJ::getJCN)
	.def("getA", &SparseMatrixAIJ::getA);

	py::class_<SolverVector>(mod, "SolverVector");
	}

	} // namespace akantu
	diff --git a/python/py_solver.hh b/python/py_solver.hh
	index f28b18303..716b57cd5 100644
	--- a/python/py_solver.hh
	+++ b/python/py_solver.hh
	@@ -1,44 +1,44 @@
	/**
	* @file py_solver.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 29 2020
	* @date last modification: Wed Feb 24 2021
	*
	* @brief pybind11 interface to Solver and SparseMatrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_AKA_SOLVER_HH_
	#define AKANTU_PY_AKA_SOLVER_HH_

	namespace akantu {

	void register_solvers(pybind11::module & mod);

	}

	#endif
	diff --git a/python/py_structural_mechanics_model.cc b/python/py_structural_mechanics_model.cc
	index 8fbef76e5..a80b6a529 100644
	--- a/python/py_structural_mechanics_model.cc
	+++ b/python/py_structural_mechanics_model.cc
	@@ -1,162 +1,162 @@
	/**
	* @file py_structural_mechanics_model.cc
	*
	* @author Philip Mueller <philip.paul.mueller@bluemail.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Feb 03 2021
	* @date last modification: Thu Apr 01 2021
	*
	* @brief pybind11 interface to StructuralMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <structural_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	namespace py = pybind11;
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define def_deprecated(func_name, mesg) \
	def(func_name, [](py::args, py::kwargs) { AKANTU_ERROR(mesg); })

	#define def_function_nocopy(func_name) \
	def( \
	#func_name, \
	[](StructuralMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	}, \
	py::return_value_policy::reference)

	#define def_function_(func_name) \
	def(#func_name, [](StructuralMechanicsModel & self) -> decltype(auto) { \
	return self.func_name(); \
	})

	#define def_plainmember(M) def_readwrite(#M, &StructuralMaterial::M)
	/* -------------------------------------------------------------------------- */

	void register_structural_mechanics_model(pybind11::module & mod) {
	/* First we have to register the material class
	* The wrapper aims to mimic the behaviour of the real material.
	*/
	py::class_<StructuralMaterial>(mod, "StructuralMaterial")
	.def(py::init<>())
	.def(py::init<const StructuralMaterial &>())
	.def_plainmember(E)
	.def_plainmember(A)
	.def_plainmember(I)
	.def_plainmember(Iz)
	.def_plainmember(Iy)
	.def_plainmember(GJ)
	.def_plainmember(rho)
	.def_plainmember(t)
	.def_plainmember(nu);

	/* Now we create the structural model wrapper
	* Note that this is basically a port from the solid mechanic part.
	*/
	py::class_<StructuralMechanicsModel, Model>(mod, "StructuralMechanicsModel")
	- .def(py::init<Mesh &, UInt, const ID &>(),
	- py::arg("mesh"), py::arg("spatial_dimension") = _all_dimensions,
	+ .def(py::init<Mesh &, UInt, const ID &>(), py::arg("mesh"),
	+ py::arg("spatial_dimension") = _all_dimensions,
	py::arg("id") = "structural_mechanics_model")
	.def(
	"initFull",
	[](StructuralMechanicsModel & self,
	const AnalysisMethod & analysis_method) -> void {
	self.initFull(_analysis_method = analysis_method);
	},
	py::arg("_analysis_method"))
	.def("initFull",
	[](StructuralMechanicsModel & self) -> void { self.initFull(); })
	.def_function_nocopy(getExternalForce)
	.def_function_nocopy(getDisplacement)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getVelocity)
	.def_function_nocopy(getAcceleration)
	.def_function_nocopy(getInternalForce)
	.def_function_nocopy(getBlockedDOFs)
	.def_function_nocopy(getMesh)

	.def("setTimeStep", &StructuralMechanicsModel::setTimeStep,
	py::arg("time_step"), py::arg("solver_id") = "")
	.def(
	"getElementMaterial",
	[](StructuralMechanicsModel & self, const ElementType & type,
	GhostType ghost_type) -> decltype(auto) {
	return self.getElementMaterial(type, ghost_type);
	},
	"This function returns the map that maps elements to materials.",
	py::arg("type"), py::arg("ghost_type") = _not_ghost,
	py::return_value_policy::reference)
	.def(
	"getMaterialByElement",
	[](StructuralMechanicsModel & self, Element element)
	-> decltype(auto) { return self.getMaterialByElement(element); },
	"This function returns the `StructuralMaterial` instance that is "
	"associated with element `element`.",
	py::arg("element"), py::return_value_policy::reference)
	.def(
	"addMaterial",
	[](StructuralMechanicsModel & self, StructuralMaterial & mat,
	const ID & name) -> UInt { return self.addMaterial(mat, name); },
	"This function adds the `StructuralMaterial` `mat` to `self`."
	" The function returns the ID of the new material.",
	py::arg("mat"), py::arg("name") = "")
	.def(
	"getMaterial",
	[](StructuralMechanicsModel & self, UInt material_index)
	-> decltype(auto) { return self.getMaterial(material_index); },
	"This function returns the `i`th material of `self`."
	- " Note a reference is returned which allows to modify the material inside `self`.",
	- py::arg("i"),
	- py::return_value_policy::reference)
	+ " Note a reference is returned which allows to modify the material "
	+ "inside `self`.",
	+ py::arg("i"), py::return_value_policy::reference)
	.def(
	"getMaterial",
	[](StructuralMechanicsModel & self, const ID & name)
	-> decltype(auto) { return self.getMaterial(name); },
	"This function returns the material with name `i` of `self`."
	- " Note a reference is returned which allows to modify the material inside `self`.",
	- py::arg("i"),
	- py::return_value_policy::reference)
	+ " Note a reference is returned which allows to modify the material "
	+ "inside `self`.",
	+ py::arg("i"), py::return_value_policy::reference)
	.def(
	"getNbMaterials",
	[](StructuralMechanicsModel & self) { return self.getNbMaterials(); },
	"Returns the number of different materials inside `self`.")
	.def("getKineticEnergy", &StructuralMechanicsModel::getKineticEnergy,
	"Compute kinetic energy")
	.def("getPotentialEnergy", &StructuralMechanicsModel::getPotentialEnergy,
	"Compute potential energy")
	.def("getEnergy", &StructuralMechanicsModel::getEnergy,
	"Compute the specified energy");

	} // End: register structural mechanical model

	} // namespace akantu
	diff --git a/python/py_structural_mechanics_model.hh b/python/py_structural_mechanics_model.hh
	index 462f03f79..76357f5f4 100644
	--- a/python/py_structural_mechanics_model.hh
	+++ b/python/py_structural_mechanics_model.hh
	@@ -1,45 +1,45 @@
	/**
	* @file py_structural_mechanics_model.hh
	*
	* @author Philip Mueller <philip.paul.mueller@bluemail.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Feb 03 2021
	* @date last modification: Mon Feb 08 2021
	*
	* @brief pybind11 interface to StructuralMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>

	#ifndef AKANTU_PY_STRUCTURAL_MECHANICS_MODEL_HH_
	#define AKANTU_PY_STRUCTURAL_MECHANICS_MODEL_HH_

	namespace akantu {

	void register_structural_mechanics_model(pybind11::module & mod);

	} // namespace akantu

	#endif // AKANTU_PY_STRUCTURAL_MECHANICS_MODEL_HH_
	diff --git a/src/common/aka_array.cc b/src/common/aka_array.cc
	index 98a7cf9fb..cac1d33b9 100644
	--- a/src/common/aka_array.cc
	+++ b/src/common/aka_array.cc
	@@ -1,98 +1,98 @@
	/**
	* @file aka_array.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Implementation of akantu::Array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <memory>
	#include <utility>

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Functions ArrayBase */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <> UInt Array<Real>::find(const Real & elem) const {
	AKANTU_DEBUG_IN();

	Real epsilon = std::numeric_limits<Real>::epsilon();
	auto it = std::find_if(begin(), end(), [&elem, &epsilon](auto && a) {
	return std::abs(a - elem) <= epsilon;
	});

	AKANTU_DEBUG_OUT();
	return (it != end()) ? end() - it : UInt(-1);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	Array<ElementType> &
	-Array<ElementType>::operator=(const ElementType &/alpha*/) {
	+Array<ElementType>::operator=(const ElementType & /alpha*/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	template <>
	Array<ElementType> &
	Array<ElementType>::operator-=(const Array<ElementType> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	template <>
	Array<ElementType> &
	Array<ElementType>::operator+=(const Array<ElementType> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	template <> Array<char> & Array<char>::operator=(const char & /alpha*/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	template <>
	Array<char> & Array<char>::operator-=(const Array<char> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	template <>
	Array<char> & Array<char>::operator+=(const Array<char> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	return *this;
	}

	} // namespace akantu
	diff --git a/src/common/aka_array.hh b/src/common/aka_array.hh
	index 74a245513..3a346fc5d 100644
	--- a/src/common/aka_array.hh
	+++ b/src/common/aka_array.hh
	@@ -1,446 +1,445 @@
	/**
	* @file aka_array.hh
	*
	* @author Till Junge <till.junge@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Sun Nov 22 2020
	*
	- * @brief Array container for Akantu This container differs from the std::vector
	- * from the fact it as 2 dimensions a main dimension and the size stored per
	- * entries
	+ * @brief Array container for Akantu This container differs from the
	+ * std::vector from the fact it as 2 dimensions a main dimension and the size
	+ * stored per entries
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_types.hh"
	/* -------------------------------------------------------------------------- */
	#include <typeinfo>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_ARRAY_HH_
	#define AKANTU_ARRAY_HH_

	-
	namespace akantu {

	/// class that afford to store vectors in static memory
	// NOLINTNEXTLINE(cppcoreguidelines-special-member-functions)
	class ArrayBase {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	- explicit ArrayBase(const ID &id = "") : id(id) {}
	+ explicit ArrayBase(const ID & id = "") : id(id) {}
	ArrayBase(const ArrayBase & other, const ID & id = "") {
	this->id = (id.empty()) ? other.id : id;
	}

	ArrayBase(ArrayBase && other) = default;
	ArrayBase & operator=(const ArrayBase & other) = default;
	ArrayBase & operator=(ArrayBase && other) noexcept = default;

	virtual ~ArrayBase() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the amount of space allocated in bytes
	virtual UInt getMemorySize() const = 0;

	// changed empty to match std::vector empty
	inline bool empty() const __attribute__((warn_unused_result)) {
	return size_ == 0;
	}

	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Get the Size of the Array
	UInt size() const { return size_; }
	/// Get the number of components
	AKANTU_GET_MACRO(NbComponent, nb_component, UInt);
	/// Get the name of th array
	AKANTU_GET_MACRO(ID, id, const ID &);
	/// Set the name of th array
	AKANTU_SET_MACRO(ID, id, const ID &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// id of the vector
	ID id;

	/// the size used
	UInt size_{0};

	/// number of components
	UInt nb_component{1};
	};

	/* -------------------------------------------------------------------------- */
	namespace {
	template <std::size_t dim, typename T> struct IteratorHelper {};

	template <typename T> struct IteratorHelper<0, T> { using type = T; };
	template <typename T> struct IteratorHelper<1, T> { using type = Vector<T>; };
	template <typename T> struct IteratorHelper<2, T> { using type = Matrix<T>; };
	template <typename T> struct IteratorHelper<3, T> {
	using type = Tensor3<T>;
	};

	template <std::size_t dim, typename T>
	using IteratorHelper_t = typename IteratorHelper<dim, T>::type;
	} // namespace

	/* -------------------------------------------------------------------------- */
	/* Memory handling layer */
	/* -------------------------------------------------------------------------- */
	enum class ArrayAllocationType {
	_default,
	_pod,
	};

	template <typename T>
	struct ArrayAllocationTrait
	: public std::conditional_t<
	std::is_scalar<T>::value,
	std::integral_constant<ArrayAllocationType,
	ArrayAllocationType::_pod>,
	std::integral_constant<ArrayAllocationType,
	ArrayAllocationType::_default>> {};

	/* -------------------------------------------------------------------------- */
	template <typename T,
	ArrayAllocationType allocation_trait = ArrayAllocationTrait<T>::value>
	class ArrayDataLayer : public ArrayBase {
	public:
	using value_type = T;
	using reference = value_type &;
	using pointer_type = value_type *;
	using const_reference = const value_type &;

	public:
	- ~ArrayDataLayer() override = default;
	+ ~ArrayDataLayer() override = default;

	/// Allocation of a new vector
	explicit ArrayDataLayer(UInt size = 0, UInt nb_component = 1,
	const ID & id = "");

	/// Allocation of a new vector with a default value
	ArrayDataLayer(UInt size, UInt nb_component, const_reference value,
	const ID & id = "");

	/// Copy constructor (deep copy)
	ArrayDataLayer(const ArrayDataLayer & vect, const ID & id = "");

	/// Copy constructor (deep copy)
	explicit ArrayDataLayer(const std::vector<value_type> & vect);

	// copy operator
	ArrayDataLayer & operator=(const ArrayDataLayer & other);

	// move constructor
	ArrayDataLayer(ArrayDataLayer && other) noexcept = default;

	// move assign
	ArrayDataLayer & operator=(ArrayDataLayer && other) noexcept = default;

	protected:
	// deallocate the memory
	virtual void deallocate() {}

	// allocate the memory
	virtual void allocate(UInt size, UInt nb_component);

	// allocate and initialize the memory
	virtual void allocate(UInt size, UInt nb_component, const T & value);

	public:
	/// append a tuple of size nb_component containing value
	inline void push_back(const_reference value);
	/// append a vector
	// inline void push_back(const value_type new_elem[]);

	/// append a Vector or a Matrix
	template <template <typename> class C,
	typename = std::enable_if_t<aka::is_tensor<C<T>>::value or
	aka::is_tensor_proxy<C<T>>::value>>
	inline void push_back(const C<T> & new_elem);

	/// changes the allocated size but not the size, if new_size = 0, the size is
	/// set to min(current_size and reserve size)
	virtual void reserve(UInt size, UInt new_size = UInt(-1));

	/// change the size of the Array
	virtual void resize(UInt size);

	/// change the size of the Array and initialize the values
	virtual void resize(UInt size, const T & val);

	/// get the amount of space allocated in bytes
	inline UInt getMemorySize() const override;

	/// Get the real size allocated in memory
	inline UInt getAllocatedSize() const;

	/// give the address of the memory allocated for this vector
	T * storage() const { return values; };

	protected:
	/// allocation type agnostic data access
	T * values{nullptr};

	/// data storage
	std::vector<T> data_storage;
	};

	/* -------------------------------------------------------------------------- */
	/* Actual Array */
	/* -------------------------------------------------------------------------- */
	template <typename T, bool is_scal> class Array : public ArrayDataLayer<T> {
	private:
	using parent = ArrayDataLayer<T>;
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using value_type = typename parent::value_type;
	using reference = typename parent::reference;
	using pointer_type = typename parent::pointer_type;
	using const_reference = typename parent::const_reference;
	using array_type = Array<T>;

	~Array() override;

	Array() : Array(0){};

	/// Allocation of a new vector
	explicit Array(UInt size, UInt nb_component = 1, const ID & id = "");

	/// Allocation of a new vector with a default value
	explicit Array(UInt size, UInt nb_component, const_reference value,
	const ID & id = "");

	/// Copy constructor
	Array(const Array & vect, const ID & id = "");

	/// Copy constructor (deep copy)
	explicit Array(const std::vector<T> & vect);

	// copy operator
	Array & operator=(const Array & other);

	// move constructor
	Array(Array && other) noexcept = default;

	// move assign
	- Array & operator=(Array && other) noexcept = default;
	+ Array & operator=(Array && other) noexcept = default;

	/* ------------------------------------------------------------------------ */
	/* Iterator */
	/* ------------------------------------------------------------------------ */
	/// \todo protected: does not compile with intel check why
	public:
	template <class R, class it, class IR = R,
	bool is_tensor_ = aka::is_tensor<std::decay_t<R>>::value>
	class iterator_internal;

	public:
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	template <typename R = T> class const_iterator;
	template <typename R = T> class iterator;

	/* ------------------------------------------------------------------------ */

	/// iterator for Array of nb_component = 1
	using scalar_iterator = iterator<T>;
	/// const_iterator for Array of nb_component = 1
	using const_scalar_iterator = const_iterator<T>;

	/// iterator returning Vectors of size n on entries of Array with
	/// nb_component = n
	using vector_iterator = iterator<Vector<T>>;
	/// const_iterator returning Vectors of n size on entries of Array with
	/// nb_component = n
	using const_vector_iterator = const_iterator<Vector<T>>;

	/// iterator returning Matrices of size (m, n) on entries of Array with
	/// nb_component = m*n
	using matrix_iterator = iterator<Matrix<T>>;
	/// const iterator returning Matrices of size (m, n) on entries of Array with
	/// nb_component = m*n
	using const_matrix_iterator = const_iterator<Matrix<T>>;

	/// iterator returning Tensor3 of size (m, n, k) on entries of Array with
	/// nb_component = mnk
	using tensor3_iterator = iterator<Tensor3<T>>;
	/// const iterator returning Tensor3 of size (m, n, k) on entries of Array
	/// with nb_component = mnk
	using const_tensor3_iterator = const_iterator<Tensor3<T>>;

	/* ------------------------------------------------------------------------ */
	template <typename... Ns> inline decltype(auto) begin(Ns &&... n);
	template <typename... Ns> inline decltype(auto) end(Ns &&... n);

	template <typename... Ns> inline decltype(auto) begin(Ns &&... n) const;
	template <typename... Ns> inline decltype(auto) end(Ns &&... n) const;

	template <typename... Ns> inline decltype(auto) begin_reinterpret(Ns &&... n);
	template <typename... Ns> inline decltype(auto) end_reinterpret(Ns &&... n);

	template <typename... Ns>
	inline decltype(auto) begin_reinterpret(Ns &&... n) const;
	template <typename... Ns>
	inline decltype(auto) end_reinterpret(Ns &&... n) const;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// search elem in the vector, return the position of the first occurrence or
	/// -1 if not found
	UInt find(const_reference elem) const;

	/// @see Array::find(const_reference elem) const
	// UInt find(T elem[]) const;

	/// append a value to the end of the Array
	inline void push_back(const_reference value) { parent::push_back(value); }

	/// append a Vector or a Matrix
	template <template <typename> class C,
	typename = std::enable_if_t<aka::is_tensor<C<T>>::value or
	aka::is_tensor_proxy<C<T>>::value>>
	inline void push_back(const C<T> & new_elem) {
	parent::push_back(new_elem);
	}

	/// append the content of the iterator at the end of the Array
	template <typename Ret> inline void push_back(const iterator<Ret> & it) {
	push_back(*it);
	}

	/// erase the value at position i
	inline void erase(UInt i);
	/// ask Nico, clarify
	template <typename R> inline iterator<R> erase(const iterator<R> & it);

	/// @see Array::find(const_reference elem) const
	template <template <typename> class C,
	typename = std::enable_if_t<aka::is_tensor<C<T>>::value or
	aka::is_tensor_proxy<C<T>>::value>>
	inline UInt find(const C<T> & elem);

	/// set all entries of the array to the value t
	/// @param t value to fill the array with
	inline void set(T t) {
	std::fill_n(this->values, this->size_ * this->nb_component, t);
	}

	/// set the array to T{}
	inline void zero() { this->set({}); }

	/// resize the array to 0
	inline void clear() { this->resize(0); }

	/// set all tuples of the array to a given vector or matrix
	/// @param vm Matrix or Vector to fill the array with
	template <template <typename> class C,
	typename = std::enable_if_t<aka::is_tensor<C<T>>::value or
	aka::is_tensor_proxy<C<T>>::value>>
	inline void set(const C<T> & vm);

	/// Append the content of the other array to the current one
	void append(const Array<T> & other);

	/// copy another Array in the current Array, the no_sanity_check allows you to
	/// force the copy in cases where you know what you do with two non matching
	/// Arrays in terms of n
	void copy(const Array<T, is_scal> & other, bool no_sanity_check = false);

	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Operators */
	/* ------------------------------------------------------------------------ */
	public:
	/// substraction entry-wise
	Array<T, is_scal> & operator-=(const Array<T, is_scal> & other);
	/// addition entry-wise
	Array<T, is_scal> & operator+=(const Array<T, is_scal> & other);
	/// multiply evry entry by alpha
	Array<T, is_scal> & operator*=(const T & alpha);

	/// check if the array are identical entry-wise
	bool operator==(const Array<T, is_scal> & other) const;
	/// @see Array::operator==(const Array<T, is_scal> & other) const
	bool operator!=(const Array<T, is_scal> & other) const;

	/// return a reference to the j-th entry of the i-th tuple
	inline reference operator()(UInt i, UInt j = 0);
	/// return a const reference to the j-th entry of the i-th tuple
	inline const_reference operator()(UInt i, UInt j = 0) const;

	/// return a reference to the ith component of the 1D array
	inline reference operator[](UInt i);
	/// return a const reference to the ith component of the 1D array
	inline const_reference operator[](UInt i) const;
	};

	/* -------------------------------------------------------------------------- */
	/* Inline Functions Array<T, is_scal> */
	/* -------------------------------------------------------------------------- */
	template <typename T, bool is_scal>
	inline std::ostream & operator<<(std::ostream & stream,
	const Array<T, is_scal> & _this) {
	_this.printself(stream);
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	/* Inline Functions ArrayBase */
	/* -------------------------------------------------------------------------- */
	inline std::ostream & operator<<(std::ostream & stream,
	const ArrayBase & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "aka_array_tmpl.hh"

	#endif /* AKANTU_ARRAY_HH_ */
	diff --git a/src/common/aka_array_printer.hh b/src/common/aka_array_printer.hh
	index c9d5d53ec..eeaa1f327 100644
	--- a/src/common/aka_array_printer.hh
	+++ b/src/common/aka_array_printer.hh
	@@ -1,104 +1,104 @@
	/**
	* @file aka_array_printer.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jul 03 2019
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Helper to print arrays on screen
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_ARRAY_PRINTER_HH_
	#define AKANTU_AKA_ARRAY_PRINTER_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class container, bool no_explicit = true> class ArrayPrinter {
	public:
	ArrayPrinter(const container & cont) : cont(cont) {}

	void printself(std::ostream & stream, int indent = 0) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "{";
	for (UInt i = 0; i < this->cont.size(); ++i) {
	stream << this->cont[i];
	if (i != this->cont.size() - 1)
	stream << ", ";
	}
	stream << "}";
	}

	private:
	const container & cont;
	};

	/* -------------------------------------------------------------------------- */
	template <class T> class ArrayPrinter<Array<T>> {
	public:
	ArrayPrinter(const Array<T> & cont) : cont(cont) {}

	void printself(std::ostream & stream, int indent = 0) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "{";
	for (UInt i = 0; i < this->cont.size(); ++i) {
	stream << "{";
	for (UInt j = 0; j < this->cont.getNbComponent(); ++j) {
	stream << this->cont(i, j);
	if (j != this->cont.getNbComponent() - 1)
	stream << ", ";
	}
	stream << "}";
	if (i != this->cont.size() - 1)
	stream << ", ";
	}
	stream << "}";
	}

	private:
	const Array<T> & cont;
	};

	template <class container>
	decltype(auto) make_printer(const container & array) {
	return ArrayPrinter<container>(array);
	}

	/* -------------------------------------------------------------------------- */
	template <class T>
	inline std::ostream & operator<<(std::ostream & stream,
	const ArrayPrinter<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_ARRAY_PRINTER_HH_ */
	diff --git a/src/common/aka_array_tmpl.hh b/src/common/aka_array_tmpl.hh
	index 11994d8e8..6813a95d7 100644
	--- a/src/common/aka_array_tmpl.hh
	+++ b/src/common/aka_array_tmpl.hh
	@@ -1,1364 +1,1363 @@
	/**
	* @file aka_array_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jul 15 2010
	* @date last modification: Fri Feb 26 2021
	*
	* @brief Inline functions of the classes Array<T> and ArrayBase
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	/* Inline Functions Array<T> */
	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh" // NOLINT
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_ARRAY_TMPL_HH_
	#define AKANTU_AKA_ARRAY_TMPL_HH_

	namespace akantu {

	namespace debug {
	struct ArrayException : public Exception {};
	} // namespace debug

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	ArrayDataLayer<T, allocation_trait>::ArrayDataLayer(UInt size,
	UInt nb_component,
	const ID & id)
	: ArrayBase(id) {
	allocate(size, nb_component);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	ArrayDataLayer<T, allocation_trait>::ArrayDataLayer(UInt size,
	UInt nb_component,
	const_reference value,
	const ID & id)
	: ArrayBase(id) {
	allocate(size, nb_component, value);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	ArrayDataLayer<T, allocation_trait>::ArrayDataLayer(const ArrayDataLayer & vect,
	const ID & id)
	: ArrayBase(vect, id) {
	this->data_storage = vect.data_storage;
	this->size_ = vect.size_;
	this->nb_component = vect.nb_component;
	this->values = this->data_storage.data();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	ArrayDataLayer<T, allocation_trait>::ArrayDataLayer(
	const std::vector<value_type> & vect) {
	this->data_storage = vect;
	this->size_ = vect.size();
	this->nb_component = 1;
	this->values = this->data_storage.data();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	ArrayDataLayer<T, allocation_trait> &
	ArrayDataLayer<T, allocation_trait>::operator=(const ArrayDataLayer & other) {
	if (this != &other) {
	this->data_storage = other.data_storage;
	this->nb_component = other.nb_component;
	this->size_ = other.size_;
	this->values = this->data_storage.data();
	}
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	void ArrayDataLayer<T, allocation_trait>::allocate(UInt new_size,
	UInt nb_component) {
	this->nb_component = nb_component;
	this->resize(new_size);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	void ArrayDataLayer<T, allocation_trait>::allocate(UInt new_size,
	UInt nb_component,
	const T & val) {
	this->nb_component = nb_component;
	this->resize(new_size, val);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	void ArrayDataLayer<T, allocation_trait>::resize(UInt new_size) {
	this->data_storage.resize(new_size * this->nb_component);
	this->values = this->data_storage.data();
	this->size_ = new_size;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	void ArrayDataLayer<T, allocation_trait>::resize(UInt new_size,
	const T & value) {
	this->data_storage.resize(new_size * this->nb_component, value);
	this->values = this->data_storage.data();
	this->size_ = new_size;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	void ArrayDataLayer<T, allocation_trait>::reserve(UInt size, UInt new_size) {
	if (new_size != UInt(-1)) {
	this->data_storage.resize(new_size * this->nb_component);
	}

	this->data_storage.reserve(size * this->nb_component);
	this->values = this->data_storage.data();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* append a tuple to the array with the value value for all components
	* @param value the new last tuple or the array will contain nb_component copies
	* of value
	*/
	template <typename T, ArrayAllocationType allocation_trait>
	inline void ArrayDataLayer<T, allocation_trait>::push_back(const T & value) {
	this->data_storage.push_back(value);
	this->values = this->data_storage.data();
	this->size_ += 1;
	}

	/* -------------------------------------------------------------------------- */
	/**
	* append a matrix or a vector to the array
	* @param new_elem a reference to a Matrix<T> or Vector<T> */
	template <typename T, ArrayAllocationType allocation_trait>
	template <template <typename> class C, typename>
	inline void
	ArrayDataLayer<T, allocation_trait>::push_back(const C<T> & new_elem) {
	AKANTU_DEBUG_ASSERT(
	nb_component == new_elem.size(),
	"The vector("
	<< new_elem.size()
	<< ") as not a size compatible with the Array (nb_component="
	<< nb_component << ").");
	for (UInt i = 0; i < new_elem.size(); ++i) {
	this->data_storage.push_back(new_elem[i]);
	}
	this->values = this->data_storage.data();
	this->size_ += 1;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	inline UInt ArrayDataLayer<T, allocation_trait>::getAllocatedSize() const {
	return this->data_storage.capacity() / this->nb_component;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, ArrayAllocationType allocation_trait>
	inline UInt ArrayDataLayer<T, allocation_trait>::getMemorySize() const {
	return this->data_storage.capacity() * sizeof(T);
	}

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <typename T>
	class ArrayDataLayer<T, ArrayAllocationType::_pod> : public ArrayBase {
	public:
	using value_type = T;
	using reference = value_type &;
	using pointer_type = value_type *;
	using const_reference = const value_type &;

	public:
	~ArrayDataLayer() override { deallocate(); }

	/// Allocation of a new vector
	ArrayDataLayer(UInt size = 0, UInt nb_component = 1, const ID & id = "")
	: ArrayBase(id) {
	allocate(size, nb_component);
	}

	/// Allocation of a new vector with a default value
	ArrayDataLayer(UInt size, UInt nb_component, const_reference value,
	const ID & id = "")
	: ArrayBase(id) {
	allocate(size, nb_component, value);
	}

	/// Copy constructor (deep copy)
	ArrayDataLayer(const ArrayDataLayer & vect, const ID & id = "")
	: ArrayBase(vect, id) {
	allocate(vect.size(), vect.getNbComponent());
	std::copy_n(vect.storage(), this->size_ * this->nb_component, values);
	}

	/// Copy constructor (deep copy)
	explicit ArrayDataLayer(const std::vector<value_type> & vect) {
	allocate(vect.size(), 1);
	std::copy_n(vect.data(), this->size_ * this->nb_component, values);
	}

	// copy operator
	inline ArrayDataLayer & operator=(const ArrayDataLayer & other) {
	if (this != &other) {
	allocate(other.size(), other.getNbComponent());
	std::copy_n(other.storage(), this->size_ * this->nb_component, values);
	}
	return *this;
	}

	// move constructor
	inline ArrayDataLayer(ArrayDataLayer && other) noexcept = default;

	// move assign
	inline ArrayDataLayer & operator=(ArrayDataLayer && other) noexcept = default;

	protected:
	// deallocate the memory
	virtual void deallocate() {
	// NOLINTNEXTLINE(cppcoreguidelines-owning-memory,
	// cppcoreguidelines-no-malloc)
	free(this->values);
	}

	// allocate the memory
	virtual inline void allocate(UInt size, UInt nb_component) {
	if (size != 0) { // malloc can return a non NULL pointer in case size is 0
	this->values = static_cast<T *>( // NOLINT
	std::malloc(nb_component * size * sizeof(T))); // NOLINT
	}

	if (this->values == nullptr and size != 0) {
	throw std::bad_alloc();
	}
	this->nb_component = nb_component;
	this->allocated_size = this->size_ = size;
	}

	// allocate and initialize the memory
	virtual inline void allocate(UInt size, UInt nb_component, const T & value) {
	allocate(size, nb_component);
	std::fill_n(values, size * nb_component, value);
	}

	public:
	/// append a tuple of size nb_component containing value
	inline void push_back(const_reference value) {
	resize(this->size_ + 1, value);
	}

	/// append a Vector or a Matrix
	template <template <typename> class C,
	typename = std::enable_if_t<aka::is_tensor<C<T>>::value or
	aka::is_tensor_proxy<C<T>>::value>>
	inline void push_back(const C<T> & new_elem) {
	AKANTU_DEBUG_ASSERT(
	nb_component == new_elem.size(),
	"The vector("
	<< new_elem.size()
	<< ") as not a size compatible with the Array (nb_component="
	<< nb_component << ").");
	this->resize(this->size_ + 1);
	std::copy_n(new_elem.storage(), new_elem.size(),
	values + this->nb_component * (this->size_ - 1));
	}

	/// changes the allocated size but not the size
	virtual void reserve(UInt size, UInt new_size = UInt(-1)) {
	UInt tmp_size = this->size_;
	if (new_size != UInt(-1)) {
	tmp_size = new_size;
	}
	this->resize(size);
	this->size_ = std::min(this->size_, tmp_size);
	}

	/// change the size of the Array
	virtual void resize(UInt size) {
	if (size * this->nb_component == 0) {
	free(values); // NOLINT: cppcoreguidelines-no-malloc
	values = nullptr;
	this->allocated_size = 0;
	} else {
	if (this->values == nullptr) {
	this->allocate(size, this->nb_component);
	return;
	}

	Int diff = size - allocated_size;
	- UInt size_to_allocate = (std::abs(diff) > AKANTU_MIN_ALLOCATION)
	- ? size
	- : (diff > 0)
	- ? allocated_size + AKANTU_MIN_ALLOCATION
	- : allocated_size;
	+ UInt size_to_allocate = (std::abs(diff) > AKANTU_MIN_ALLOCATION) ? size
	+ : (diff > 0)
	+ ? allocated_size + AKANTU_MIN_ALLOCATION
	+ : allocated_size;

	if (size_to_allocate ==
	allocated_size) { // otherwhy the reserve + push_back might fail...
	this->size_ = size;
	return;
	}

	auto * tmp_ptr = reinterpret_cast<T *>( // NOLINT
	realloc(this->values,
	size_to_allocate * this->nb_component * sizeof(T)));

	if (tmp_ptr == nullptr) {
	throw std::bad_alloc();
	}

	this->values = tmp_ptr;
	this->allocated_size = size_to_allocate;
	}

	this->size_ = size;
	}

	/// change the size of the Array and initialize the values
	virtual void resize(UInt size, const T & val) {
	UInt tmp_size = this->size_;
	this->resize(size);
	if (size > tmp_size) {
	// NOLINTNEXTLINE(cppcoreguidelines-pro-bounds-pointer-arithmetic)
	std::fill_n(values + this->nb_component * tmp_size,
	(size - tmp_size) * this->nb_component, val);
	}
	}

	/// get the amount of space allocated in bytes
	inline UInt getMemorySize() const final {
	return this->allocated_size * this->nb_component * sizeof(T);
	}

	/// Get the real size allocated in memory
	inline UInt getAllocatedSize() const { return this->allocated_size; }

	/// give the address of the memory allocated for this vector
	T * storage() const { return values; };

	protected:
	/// allocation type agnostic data access
	T * values{nullptr};

	UInt allocated_size{0};
	};

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	inline auto Array<T, is_scal>::operator()(UInt i, UInt j) -> reference {
	AKANTU_DEBUG_ASSERT(this->size_ > 0,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT((i < this->size_) && (j < this->nb_component),
	"The value at position ["
	<< i << "," << j << "] is out of range in array \""
	<< this->id << "\"");
	return this->values[i * this->nb_component + j];
	}

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	inline auto Array<T, is_scal>::operator()(UInt i, UInt j) const
	-> const_reference {
	AKANTU_DEBUG_ASSERT(this->size_ > 0,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT((i < this->size_) && (j < this->nb_component),
	"The value at position ["
	<< i << "," << j << "] is out of range in array \""
	<< this->id << "\"");
	// NOLINTNEXTLINE(cppcoreguidelines-pro-bounds-pointer-arithmetic)
	return this->values[i * this->nb_component + j];
	}

	template <class T, bool is_scal>
	inline auto Array<T, is_scal>::operator[](UInt i) -> reference {
	AKANTU_DEBUG_ASSERT(this->size_ > 0,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT((i < this->size_ * this->nb_component),
	"The value at position ["
	<< i << "] is out of range in array \"" << this->id
	<< "\"");
	return this->values[i];
	}

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	inline auto Array<T, is_scal>::operator[](UInt i) const -> const_reference {
	AKANTU_DEBUG_ASSERT(this->size_ > 0,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT((i < this->size_ * this->nb_component),
	"The value at position ["
	<< i << "] is out of range in array \"" << this->id
	<< "\"");
	return this->values[i];
	}

	/* -------------------------------------------------------------------------- */
	/**
	* erase an element. If the erased element is not the last of the array, the
	* last element is moved into the hole in order to maintain contiguity. This
	* may invalidate existing iterators (For instance an iterator obtained by
	* Array::end() is no longer correct) and will change the order of the
	* elements.
	* @param i index of element to erase
	*/
	template <class T, bool is_scal> inline void Array<T, is_scal>::erase(UInt i) {
	AKANTU_DEBUG_IN();
	AKANTU_DEBUG_ASSERT((this->size_ > 0), "The array is empty");
	AKANTU_DEBUG_ASSERT((i < this->size_), "The element at position ["
	<< i << "] is out of range (" << i
	<< ">=" << this->size_ << ")");

	if (i != (this->size_ - 1)) {
	for (UInt j = 0; j < this->nb_component; ++j) {
	// NOLINTNEXTLINE(cppcoreguidelines-pro-bounds-pointer-arithmetic)
	this->values[i * this->nb_component + j] =
	this->values[(this->size_ - 1) * this->nb_component + j];
	}
	}

	this->resize(this->size_ - 1);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Subtract another array entry by entry from this array in place. Both arrays
	* must
	* have the same size and nb_component. If the arrays have different shapes,
	* code compiled in debug mode will throw an expeption and optimised code
	* will behave in an unpredicted manner
	* @param other array to subtract from this
	* @return reference to modified this
	*/
	template <class T, bool is_scal>
	Array<T, is_scal> &
	Array<T, is_scal>::operator-=(const Array<T, is_scal> & other) {
	AKANTU_DEBUG_ASSERT((this->size_ == other.size_) &&
	(this->nb_component == other.nb_component),
	"The too array don't have the same sizes");

	T * a = this->values;
	T * b = other.storage();
	for (UInt i = 0; i < this->size_ * this->nb_component; ++i) {
	a -= b;
	++a;
	++b;
	}

	return *this;
	}

	/* --------------------------------------------------------------------------
	*/
	/**
	* Add another array entry by entry to this array in
	* place. Both arrays must have the same size and
	* nb_component. If the arrays have different shapes, code
	* compiled in debug mode will throw an expeption and
	* optimised code will behave in an unpredicted manner
	* @param other array to add to this
	* @return reference to modified this
	*/
	template <class T, bool is_scal>
	Array<T, is_scal> &
	Array<T, is_scal>::operator+=(const Array<T, is_scal> & other) {
	AKANTU_DEBUG_ASSERT((this->size_ == other.size()) &&
	(this->nb_component == other.nb_component),
	"The too array don't have the same sizes");

	T * a = this->values;
	T * b = other.storage();
	for (UInt i = 0; i < this->size_ * this->nb_component; ++i) {
	a++ += b++;
	}

	return *this;
	}

	/* --------------------------------------------------------------------------
	*/
	/**
	* Multiply all entries of this array by a scalar in place
	* @param alpha scalar multiplicant
	* @return reference to modified this
	*/

	template <class T, bool is_scal>
	Array<T, is_scal> & Array<T, is_scal>::operator*=(const T & alpha) {
	T * a = this->values;
	for (UInt i = 0; i < this->size_ * this->nb_component; ++i) {
	a++ = alpha;
	}

	return *this;
	}

	/* --------------------------------------------------------------------------
	*/
	/**
	* Compare this array element by element to another.
	* @param other array to compare to
	* @return true it all element are equal and arrays have
	* the same shape, else false
	*/
	template <class T, bool is_scal>
	bool Array<T, is_scal>::operator==(const Array<T, is_scal> & other) const {
	bool equal = this->nb_component == other.nb_component &&
	this->size_ == other.size_ && this->id == other.id;
	if (not equal) {
	return false;
	}
	if (this->values == other.storage()) {
	return true;
	}

	// NOLINTNEXTLINE(cppcoreguidelines-pro-bounds-pointer-arithmetic)
	return std::equal(this->values,
	this->values + this->size_ * this->nb_component,
	other.storage());
	}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	bool Array<T, is_scal>::operator!=(const Array<T, is_scal> & other) const {
	return !operator==(other);
	}

	/* --------------------------------------------------------------------------
	*/
	/**
	* set all tuples of the array to a given vector or matrix
	* @param vm Matrix or Vector to fill the array with
	*/
	template <class T, bool is_scal>
	template <template <typename> class C, typename>
	inline void Array<T, is_scal>::set(const C<T> & vm) {
	AKANTU_DEBUG_ASSERT(this->nb_component == vm.size(),
	"The size of the object does not "
	"match the number of components");
	for (T * it = this->values;
	it < this->values + this->nb_component * this->size_;
	it += this->nb_component) {
	std::copy_n(vm.storage(), this->nb_component, it);
	}
	}
	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	void Array<T, is_scal>::append(const Array<T> & other) {
	AKANTU_DEBUG_ASSERT(this->nb_component == other.nb_component,
	"Cannot append an array with a "
	"different number of component");
	UInt old_size = this->size_;
	this->resize(this->size_ + other.size());

	T * tmp = this->values + this->nb_component * old_size;
	std::copy_n(other.storage(), other.size() * this->nb_component, tmp);
	}

	/* --------------------------------------------------------------------------
	*/
	/* Functions Array<T, is_scal> */
	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	Array<T, is_scal>::Array(UInt size, UInt nb_component, const ID & id)
	: parent(size, nb_component, id) {}

	template <>
	inline Array<std::string, false>::Array(UInt size, UInt nb_component,
	const ID & id)
	: parent(size, nb_component, "", id) {}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	Array<T, is_scal>::Array(UInt size, UInt nb_component, const_reference value,
	const ID & id)
	: parent(size, nb_component, value, id) {}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	Array<T, is_scal>::Array(const Array & vect, const ID & id)
	: parent(vect, id) {}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	Array<T, is_scal> &
	Array<T, is_scal>::operator=(const Array<T, is_scal> & other) {
	AKANTU_DEBUG_WARNING("You are copying the array "
	<< this->id << " are you sure it is on purpose");

	if (&other == this) {
	return *this;
	}

	parent::operator=(other);
	return *this;
	}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	Array<T, is_scal>::Array(const std::vector<T> & vect) : parent(vect) {}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal> Array<T, is_scal>::~Array() = default;

	/* --------------------------------------------------------------------------
	*/
	/**
	* search elem in the array, return the position of the
	* first occurrence or -1 if not found
	* @param elem the element to look for
	* @return index of the first occurrence of elem or -1 if
	* elem is not present
	*/
	template <class T, bool is_scal>
	UInt Array<T, is_scal>::find(const_reference elem) const {
	AKANTU_DEBUG_IN();

	auto begin = this->begin();
	auto end = this->end();
	auto it = std::find(begin, end, elem);

	AKANTU_DEBUG_OUT();
	return (it != end) ? it - begin : UInt(-1);
	}

	/* --------------------------------------------------------------------------
	*/
	// template <class T, bool is_scal> UInt Array<T,
	// is_scal>::find(T elem[]) const
	// {
	// AKANTU_DEBUG_IN();
	// T * it = this->values;
	// UInt i = 0;
	// for (; i < this->size_; ++i) {
	// if (*it == elem[0]) {
	// T * cit = it;
	// UInt c = 0;
	// for (; (c < this->nb_component) && (*cit ==
	// elem[c]); ++c, ++cit)
	// ;
	// if (c == this->nb_component) {
	// AKANTU_DEBUG_OUT();
	// return i;
	// }
	// }
	// it += this->nb_component;
	// }
	// return UInt(-1);
	// }

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	template <template <typename> class C, typename>
	inline UInt Array<T, is_scal>::find(const C<T> & elem) {
	AKANTU_DEBUG_ASSERT(elem.size() == this->nb_component,
	"Cannot find an element with a wrong size ("
	<< elem.size() << ") != " << this->nb_component);
	return this->find(*elem.storage());
	}

	/* --------------------------------------------------------------------------
	*/
	/**
	* copy the content of another array. This overwrites the
	* current content.
	* @param other Array to copy into this array. It has to
	* have the same nb_component as this. If compiled in
	* debug mode, an incorrect other will result in an
	* exception being thrown. Optimised code may result in
	* unpredicted behaviour.
	* @param no_sanity_check turns off all checkes
	*/
	template <class T, bool is_scal>
	void Array<T, is_scal>::copy(const Array<T, is_scal> & other,
	bool no_sanity_check) {
	AKANTU_DEBUG_IN();

	if (not no_sanity_check and (other.nb_component != this->nb_component)) {
	AKANTU_ERROR("The two arrays do not have the same "
	"number of components");
	}

	this->resize((other.size_ * other.nb_component) / this->nb_component);

	std::copy_n(other.storage(), this->size_ * this->nb_component, this->values);

	AKANTU_DEBUG_OUT();
	}

	/* --------------------------------------------------------------------------
	*/
	template <bool is_scal> class ArrayPrintHelper {
	public:
	template <typename T>
	static void print_content(const Array<T> & vect, std::ostream & stream,
	int indent) {
	std::string space(indent, AKANTU_INDENT);

	stream << space << " + values : {";
	for (UInt i = 0; i < vect.size(); ++i) {
	stream << "{";
	for (UInt j = 0; j < vect.getNbComponent(); ++j) {
	stream << vect(i, j);
	if (j != vect.getNbComponent() - 1) {
	stream << ", ";
	}
	}
	stream << "}";
	if (i != vect.size() - 1) {
	stream << ", ";
	}
	}
	stream << "}" << std::endl;
	}
	};

	template <> class ArrayPrintHelper<false> {
	public:
	template <typename T>
	static void print_content(__attribute__((unused)) const Array<T> & vect,
	__attribute__((unused)) std::ostream & stream,
	__attribute__((unused)) int indent) {}
	};

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	void Array<T, is_scal>::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	std::streamsize prec = stream.precision();
	std::ios_base::fmtflags ff = stream.flags();

	stream.setf(std::ios_base::showbase);
	stream.precision(2);

	stream << space << "Array<" << debug::demangle(typeid(T).name()) << "> ["
	<< std::endl;
	stream << space << " + id : " << this->id << std::endl;
	stream << space << " + size : " << this->size_ << std::endl;
	stream << space << " + nb_component : " << this->nb_component << std::endl;
	stream << space << " + allocated size : " << this->getAllocatedSize()
	<< std::endl;
	stream << space
	<< " + memory size : " << printMemorySize<T>(this->getMemorySize())
	<< std::endl;
	if (not AKANTU_DEBUG_LEVEL_IS_TEST()) {
	stream << space << " + address : " << std::hex << this->values
	<< std::dec << std::endl;
	}

	stream.precision(prec);
	stream.flags(ff);

	if (AKANTU_DEBUG_TEST(dblDump) \|\| AKANTU_DEBUG_LEVEL_IS_TEST()) {
	ArrayPrintHelper<is_scal or std::is_enum<T>::value>::print_content(
	*this, stream, indent);
	}

	stream << space << "]" << std::endl;
	}

	/* --------------------------------------------------------------------------
	*/
	/* Inline Functions ArrayBase */
	/* --------------------------------------------------------------------------
	*/

	// inline bool ArrayBase::empty() { return (this->size_ ==
	// 0); }

	/* --------------------------------------------------------------------------
	*/
	/* Iterators */
	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	template <class R, class daughter, class IR, bool is_tensor>
	class Array<T, is_scal>::iterator_internal {
	public:
	using value_type = R;
	using pointer = R *;
	using reference = R &;
	using const_reference = const R &;
	using internal_value_type = IR;
	using internal_pointer = IR *;
	using difference_type = std::ptrdiff_t;
	using iterator_category = std::random_access_iterator_tag;
	static_assert(not is_tensor, "Cannot handle tensors");

	public:
	iterator_internal(pointer data = nullptr) : ret(data), initial(data){};
	iterator_internal(const iterator_internal & it) = default;
	iterator_internal(iterator_internal && it) noexcept = default;

	virtual ~iterator_internal() = default;

	inline iterator_internal & operator=(const iterator_internal & it) = default;
	inline iterator_internal &
	operator=(iterator_internal && it) noexcept = default;

	UInt getCurrentIndex() { return (this->ret - this->initial); };

	inline reference operator() { return ret; };
	inline const_reference operator() const { return ret; };
	inline pointer operator->() { return ret; };
	inline daughter & operator++() {
	++ret;
	return static_cast<daughter &>(*this);
	};
	inline daughter & operator--() {
	--ret;
	return static_cast<daughter &>(*this);
	};

	inline daughter & operator+=(const UInt n) {
	ret += n;
	return static_cast<daughter &>(*this);
	}
	inline daughter & operator-=(const UInt n) {
	ret -= n;
	return static_cast<daughter &>(*this);
	}

	inline reference operator[](const UInt n) { return ret[n]; }

	inline bool operator==(const iterator_internal & other) const {
	return ret == other.ret;
	}
	inline bool operator!=(const iterator_internal & other) const {
	return ret != other.ret;
	}
	inline bool operator<(const iterator_internal & other) const {
	return ret < other.ret;
	}
	inline bool operator<=(const iterator_internal & other) const {
	return ret <= other.ret;
	}
	inline bool operator>(const iterator_internal & other) const {
	return ret > other.ret;
	}
	inline bool operator>=(const iterator_internal & other) const {
	return ret >= other.ret;
	}

	inline daughter operator-(difference_type n) { return daughter(ret - n); }
	inline daughter operator+(difference_type n) { return daughter(ret + n); }

	inline difference_type operator-(const iterator_internal & b) {
	return ret - b.ret;
	}

	inline pointer data() const { return ret; }

	protected:
	pointer ret{nullptr};
	pointer initial{nullptr};
	};

	/* --------------------------------------------------------------------------
	*/
	/**
	* Specialization for scalar types
	*/
	template <class T, bool is_scal>
	template <class R, class daughter, class IR>
	class Array<T, is_scal>::iterator_internal<R, daughter, IR, true> {
	public:
	using value_type = R;
	using pointer = R *;
	using pointer_type = typename Array<T, is_scal>::pointer_type;
	using reference = R &;
	using proxy = typename R::proxy;
	using const_proxy = const typename R::proxy;
	using const_reference = const R &;
	using internal_value_type = IR;
	using internal_pointer = IR *;
	using difference_type = std::ptrdiff_t;
	using iterator_category = std::random_access_iterator_tag;

	public:
	iterator_internal() = default;

	iterator_internal(pointer_type data, UInt _offset)
	: _offset(_offset), initial(data), ret(nullptr), ret_ptr(data) {
	AKANTU_ERROR("The constructor should never be called "
	"it is just an ugly trick...");
	}

	iterator_internal(std::unique_ptr<internal_value_type> && wrapped)
	: _offset(wrapped->size()), initial(wrapped->storage()),
	ret(std::move(wrapped)), ret_ptr(ret->storage()) {}

	iterator_internal(const iterator_internal & it) {
	if (this != &it) {
	this->_offset = it._offset;
	this->initial = it.initial;
	this->ret_ptr = it.ret_ptr;
	this->ret = std::make_unique<internal_value_type>(*it.ret, false);
	}
	}

	iterator_internal(iterator_internal && it) noexcept = default;

	virtual ~iterator_internal() = default;

	inline iterator_internal & operator=(const iterator_internal & it) {
	if (this != &it) {
	this->_offset = it._offset;
	this->initial = it.initial;
	this->ret_ptr = it.ret_ptr;
	if (this->ret) {
	this->ret->shallowCopy(*it.ret);
	} else {
	this->ret = std::make_unique<internal_value_type>(*it.ret, false);
	}
	}
	return *this;
	}

	inline iterator_internal &
	operator=(iterator_internal && it) noexcept = default;

	UInt getCurrentIndex() {
	return (this->ret_ptr - this->initial) / this->_offset;
	};

	inline reference operator*() {
	ret->values = ret_ptr;
	return *ret;
	};
	inline const_reference operator*() const {
	ret->values = ret_ptr;
	return *ret;
	};
	inline pointer operator->() {
	ret->values = ret_ptr;
	return ret.get();
	};
	inline daughter & operator++() {
	ret_ptr += _offset;
	return static_cast<daughter &>(*this);
	};
	inline daughter & operator--() {
	ret_ptr -= _offset;
	return static_cast<daughter &>(*this);
	};

	inline daughter & operator+=(const UInt n) {
	ret_ptr += _offset * n;
	return static_cast<daughter &>(*this);
	}
	inline daughter & operator-=(const UInt n) {
	ret_ptr -= _offset * n;
	return static_cast<daughter &>(*this);
	}

	inline proxy operator[](const UInt n) {
	ret->values = ret_ptr + n * _offset;
	return proxy(*ret);
	}
	inline const_proxy operator[](const UInt n) const { // NOLINT
	ret->values = ret_ptr + n * _offset;
	return const_proxy(*ret);
	}

	inline bool operator==(const iterator_internal & other) const {
	return this->ret_ptr == other.ret_ptr;
	}
	inline bool operator!=(const iterator_internal & other) const {
	return this->ret_ptr != other.ret_ptr;
	}
	inline bool operator<(const iterator_internal & other) const {
	return this->ret_ptr < other.ret_ptr;
	}
	inline bool operator<=(const iterator_internal & other) const {
	return this->ret_ptr <= other.ret_ptr;
	}
	inline bool operator>(const iterator_internal & other) const {
	return this->ret_ptr > other.ret_ptr;
	}
	inline bool operator>=(const iterator_internal & other) const {
	return this->ret_ptr >= other.ret_ptr;
	}

	inline daughter operator+(difference_type n) {
	daughter tmp(static_cast<daughter &>(*this));
	tmp += n;
	return tmp;
	}
	inline daughter operator-(difference_type n) {
	daughter tmp(static_cast<daughter &>(*this));
	tmp -= n;
	return tmp;
	}

	inline difference_type operator-(const iterator_internal & b) {
	return (this->ret_ptr - b.ret_ptr) / _offset;
	}

	inline pointer_type data() const { return ret_ptr; }
	inline difference_type offset() const { return _offset; }

	protected:
	UInt _offset{0};
	pointer_type initial{nullptr};
	std::unique_ptr<internal_value_type> ret{nullptr};
	pointer_type ret_ptr{nullptr};
	};

	/* -------------------------------------------------------------------------- */
	/* Iterators */
	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	template <typename R>
	class Array<T, is_scal>::const_iterator
	: public iterator_internal<const R, Array<T, is_scal>::const_iterator<R>,
	R> {
	public:
	using parent = iterator_internal<const R, const_iterator, R>;
	using value_type = typename parent::value_type;
	using pointer = typename parent::pointer;
	using reference = typename parent::reference;
	using difference_type = typename parent::difference_type;
	using iterator_category = typename parent::iterator_category;

	public:
	~const_iterator() override = default;

	const_iterator() = default;
	const_iterator(const const_iterator & it) = default;
	const_iterator(const_iterator && it) noexcept = default;

	const_iterator & operator=(const const_iterator & it) = default;
	const_iterator & operator=(const_iterator && it) noexcept = default;

	template <typename P,
	typename = std::enable_if_t<not aka::is_tensor<P>::value>>
	const_iterator(P * data) : parent(data) {}

	template <typename UP_P, typename = std::enable_if_t<aka::is_tensor<
	typename UP_P::element_type>::value>>
	const_iterator(UP_P && tensor) : parent(std::forward<UP_P>(tensor)) {}
	};

	/* -------------------------------------------------------------------------- */
	template <class T, class R, bool is_tensor_ = aka::is_tensor<R>::value>
	struct ConstConverterIteratorHelper {
	using const_iterator = typename Array<T>::template const_iterator<R>;
	using iterator = typename Array<T>::template iterator<R>;

	static inline const_iterator convert(const iterator & it) {
	return const_iterator(std::unique_ptr<R>(new R(*it, false)));
	}
	};

	template <class T, class R> struct ConstConverterIteratorHelper<T, R, false> {
	using const_iterator = typename Array<T>::template const_iterator<R>;
	using iterator = typename Array<T>::template iterator<R>;
	static inline const_iterator convert(const iterator & it) {
	return const_iterator(it.data());
	}
	};

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	template <typename R>
	class Array<T, is_scal>::iterator
	: public iterator_internal<R, Array<T, is_scal>::iterator<R>> {
	public:
	using parent = iterator_internal<R, iterator>;
	using value_type = typename parent::value_type;
	using pointer = typename parent::pointer;
	using reference = typename parent::reference;
	using difference_type = typename parent::difference_type;
	using iterator_category = typename parent::iterator_category;

	public:
	~iterator() override = default;
	iterator() = default;
	iterator(const iterator & it) = default;
	iterator(iterator && it) noexcept = default;
	iterator & operator=(const iterator & it) = default;
	iterator & operator=(iterator && it) noexcept = default;

	template <typename P,
	typename = std::enable_if_t<not aka::is_tensor<P>::value>>
	iterator(P * data) : parent(data) {}

	template <typename UP_P, typename = std::enable_if_t<aka::is_tensor<
	typename UP_P::element_type>::value>>
	iterator(UP_P && tensor) : parent(std::forward<UP_P>(tensor)) {}

	operator const_iterator<R>() {
	return ConstConverterIteratorHelper<T, R>::convert(*this);
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Begin/End functions implementation */
	/* -------------------------------------------------------------------------- */
	namespace detail {
	template <class Tuple, size_t... Is>
	constexpr auto take_front_impl(Tuple && t,
	std::index_sequence<Is...> /idxs/) {
	return std::make_tuple(std::get<Is>(std::forward<Tuple>(t))...);
	}

	template <size_t N, class Tuple> constexpr auto take_front(Tuple && t) {
	return take_front_impl(std::forward<Tuple>(t),
	std::make_index_sequence<N>{});
	}

	template <typename... V> constexpr auto product_all(V &&... v) {
	std::common_type_t<int, V...> result = 1;
	(void)std::initializer_list<int>{(result *= v, 0)...};
	return result;
	}

	template <typename... T> std::string to_string_all(T &&... t) {
	if (sizeof...(T) == 0) {
	return "";
	}

	std::stringstream ss;
	bool noComma = true;
	ss << "(";
	(void)std::initializer_list<bool>{
	(ss << (noComma ? "" : ", ") << t, noComma = false)...};
	ss << ")";
	return ss.str();
	}

	template <std::size_t N> struct InstantiationHelper {
	template <typename type, typename T, typename... Ns>
	static auto instantiate(T && data, Ns... ns) {
	return std::make_unique<type>(data, ns...);
	}
	};

	template <> struct InstantiationHelper<0> {
	template <typename type, typename T> static auto instantiate(T && data) {
	return data;
	}
	};

	template <typename Arr, typename T, typename... Ns>
	decltype(auto) get_iterator(Arr && array, T * data, Ns &&... ns) {
	using type = IteratorHelper_t<sizeof...(Ns) - 1, T>;
	using array_type = std::decay_t<Arr>;
	using iterator =
	std::conditional_t<std::is_const<std::remove_reference_t<Arr>>::value,
	typename array_type::template const_iterator<type>,
	typename array_type::template iterator<type>>;
	static_assert(sizeof...(Ns), "You should provide a least one size");

	if (array.getNbComponent() * array.size() !=
	product_all(std::forward<Ns>(ns)...)) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::ArrayException(),
	"The iterator on "
	<< debug::demangle(typeid(Arr).name())
	<< to_string_all(array.size(), array.getNbComponent())
	<< "is not compatible with the type "
	<< debug::demangle(typeid(type).name()) << to_string_all(ns...));
	}

	auto && wrapped = aka::apply(
	[&](auto... n) {
	return InstantiationHelper<sizeof...(n)>::template instantiate<type>(
	data, n...);
	},
	take_front<sizeof...(Ns) - 1>(std::make_tuple(ns...)));

	return iterator(std::move(wrapped));
	}
	} // namespace detail

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::begin(Ns &&... ns) {
	return detail::get_iterator(*this, this->values, std::forward<Ns>(ns)...,
	this->size_);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::end(Ns &&... ns) {
	return detail::get_iterator(*this,
	this->values + this->nb_component * this->size_,
	std::forward<Ns>(ns)..., this->size_);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::begin(Ns &&... ns) const {
	return detail::get_iterator(*this, this->values, std::forward<Ns>(ns)...,
	this->size_);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::end(Ns &&... ns) const {
	return detail::get_iterator(*this,
	this->values + this->nb_component * this->size_,
	std::forward<Ns>(ns)..., this->size_);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::begin_reinterpret(Ns &&... ns) {
	return detail::get_iterator(*this, this->values, std::forward<Ns>(ns)...);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::end_reinterpret(Ns &&... ns) {
	return detail::get_iterator(
	*this, this->values + detail::product_all(std::forward<Ns>(ns)...),
	std::forward<Ns>(ns)...);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::begin_reinterpret(Ns &&... ns) const {
	return detail::get_iterator(*this, this->values, std::forward<Ns>(ns)...);
	}

	template <class T, bool is_scal>
	template <typename... Ns>
	inline decltype(auto) Array<T, is_scal>::end_reinterpret(Ns &&... ns) const {
	return detail::get_iterator(
	*this, this->values + detail::product_all(std::forward<Ns>(ns)...),
	std::forward<Ns>(ns)...);
	}

	/* -------------------------------------------------------------------------- */
	/* Views */
	/* -------------------------------------------------------------------------- */
	namespace detail {
	template <typename Array, typename... Ns> class ArrayView {
	using tuple = std::tuple<Ns...>;

	public:
	~ArrayView() = default;
	ArrayView(Array && array, Ns... ns) noexcept
	: array(array), sizes(std::move(ns)...) {}

	ArrayView(const ArrayView & array_view) = default;
	ArrayView & operator=(const ArrayView & array_view) = default;

	ArrayView(ArrayView && array_view) noexcept = default;
	ArrayView & operator=(ArrayView && array_view) noexcept = default;

	decltype(auto) begin() {
	return aka::apply(
	[&](auto &&... ns) { return array.get().begin_reinterpret(ns...); },
	sizes);
	}

	decltype(auto) begin() const {
	return aka::apply(
	[&](auto &&... ns) { return array.get().begin_reinterpret(ns...); },
	sizes);
	}

	decltype(auto) end() {
	return aka::apply(
	[&](auto &&... ns) { return array.get().end_reinterpret(ns...); },
	sizes);
	}

	decltype(auto) end() const {
	return aka::apply(
	[&](auto &&... ns) { return array.get().end_reinterpret(ns...); },
	sizes);
	}

	decltype(auto) size() const {
	return std::get<std::tuple_size<tuple>::value - 1>(sizes);
	}

	decltype(auto) dims() const { return std::tuple_size<tuple>::value - 1; }

	private:
	std::reference_wrapper<std::remove_reference_t<Array>> array;
	tuple sizes;
	};
	} // namespace detail

	/* -------------------------------------------------------------------------- */
	template <typename Array, typename... Ns>
	decltype(auto) make_view(Array && array, const Ns... ns) {
	static_assert(aka::conjunction<std::is_integral<std::decay_t<Ns>>...>::value,
	"Ns should be integral types");
	AKANTU_DEBUG_ASSERT((detail::product_all(ns...) != 0),
	"You must specify non zero dimensions");
	auto size = std::forward<decltype(array)>(array).size() *
	std::forward<decltype(array)>(array).getNbComponent() /
	detail::product_all(ns...);

	return detail::ArrayView<Array, std::common_type_t<size_t, Ns>...,
	std::common_type_t<size_t, decltype(size)>>(
	std::forward<Array>(array), std::move(ns)..., size);
	}

	/* --------------------------------------------------------------------------
	*/
	template <class T, bool is_scal>
	template <typename R>
	inline typename Array<T, is_scal>::template iterator<R>
	Array<T, is_scal>::erase(const iterator<R> & it) {
	T * curr = it.data();
	UInt pos = (curr - this->values) / this->nb_component;
	erase(pos);
	iterator<R> rit = it;
	return --rit;
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_ARRAY_TMPL_HH_ */
	diff --git a/src/common/aka_bbox.hh b/src/common/aka_bbox.hh
	index 1d7424420..2d48b4122 100644
	--- a/src/common/aka_bbox.hh
	+++ b/src/common/aka_bbox.hh
	@@ -1,278 +1,279 @@
	/**
	* @file aka_bbox.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Feb 14 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief A simple bounding box class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "aka_types.hh"
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_BBOX_HH_
	#define AKANTU_AKA_BBOX_HH_

	namespace akantu {

	class BBox {
	public:
	BBox() = default;

	BBox(UInt spatial_dimension)
	: dim(spatial_dimension),
	lower_bounds(spatial_dimension, std::numeric_limits<Real>::max()),
	upper_bounds(spatial_dimension, std::numeric_limits<Real>::lowest()) {}

	BBox(const BBox & other)
	: dim(other.dim), empty{false}, lower_bounds(other.lower_bounds),
	upper_bounds(other.upper_bounds) {}

	BBox & operator=(const BBox & other) {
	if (this != &other) {
	this->dim = other.dim;
	this->lower_bounds = other.lower_bounds;
	this->upper_bounds = other.upper_bounds;
	this->empty = other.empty;
	}
	return *this;
	}

	inline BBox & operator+=(const Vector<Real> & position) {
	AKANTU_DEBUG_ASSERT(
	this->dim == position.size(),
	"You are adding a point of a wrong dimension to the bounding box");

	this->empty = false;

	for (auto s : arange(dim)) {
	lower_bounds(s) = std::min(lower_bounds(s), position(s));
	upper_bounds(s) = std::max(upper_bounds(s), position(s));
	}
	return *this;
	}

	/* ------------------------------------------------------------------------ */
	inline bool intersects(const BBox & other,
	const SpatialDirection & direction) const {
	AKANTU_DEBUG_ASSERT(
	this->dim == other.dim,
	"You are intersecting bounding boxes of different dimensions");
	return Math::intersects(lower_bounds(direction), upper_bounds(direction),
	other.lower_bounds(direction),
	other.upper_bounds(direction));
	}

	inline bool intersects(const BBox & other) const {
	if (this->empty or other.empty) {
	return false;
	}

	bool intersects_ = true;
	for (auto s : arange(this->dim)) {
	intersects_ &= this->intersects(other, SpatialDirection(s));
	}
	return intersects_;
	}

	/* ------------------------------------------------------------------------ */
	inline BBox intersection(const BBox & other) const {
	AKANTU_DEBUG_ASSERT(
	this->dim == other.dim,
	"You are intersecting bounding boxes of different dimensions");

	BBox intersection_(this->dim);
	intersection_.empty = not this->intersects(other);

	if (intersection_.empty) {
	return intersection_;
	}

	for (auto s : arange(this->dim)) {
	// is lower point in range ?
	bool point1 = Math::is_in_range(other.lower_bounds(s), lower_bounds(s),
	upper_bounds(s));

	// is upper point in range ?
	bool point2 = Math::is_in_range(other.upper_bounds(s), lower_bounds(s),
	upper_bounds(s));

	if (point1 and not point2) {
	// \|-----------\| this (i)
	// \|-----------\| other(i)
	// 1 2
	intersection_.lower_bounds(s) = other.lower_bounds(s);
	intersection_.upper_bounds(s) = upper_bounds(s);
	} else if (point1 && point2) {
	// \|-----------------\| this (i)
	// \|-----------\| other(i)
	// 1 2
	intersection_.lower_bounds(s) = other.lower_bounds(s);
	intersection_.upper_bounds(s) = other.upper_bounds(s);
	} else if (!point1 && point2) {
	// \|-----------\| this (i)
	// \|-----------\| other(i)
	// 1 2
	intersection_.lower_bounds(s) = this->lower_bounds(s);
	intersection_.upper_bounds(s) = other.upper_bounds(s);
	} else {
	// \|-----------\| this (i)
	// \|-----------------\| other(i)
	// 1 2
	intersection_.lower_bounds(s) = this->lower_bounds(s);
	intersection_.upper_bounds(s) = this->upper_bounds(s);
	}
	}

	return intersection_;
	}

	/* ------------------------------------------------------------------------ */
	inline bool contains(const Vector<Real> & point) const {
	return (point >= lower_bounds) and (point <= upper_bounds);
	}

	/* ------------------------------------------------------------------------ */
	inline void reset() {
	lower_bounds.set(std::numeric_limits<Real>::max());
	upper_bounds.set(std::numeric_limits<Real>::lowest());
	}

	- /* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */
	inline void getCenter(Vector<Real> & center) {
	- center = upper_bounds;
	+ center = upper_bounds;
	center += lower_bounds;
	center /= 2.;
	}

	/* ------------------------------------------------------------------------ */
	const Vector<Real> & getLowerBounds() const { return lower_bounds; }
	const Vector<Real> & getUpperBounds() const { return upper_bounds; }

	Vector<Real> & getLowerBounds() { return lower_bounds; }
	Vector<Real> & getUpperBounds() { return upper_bounds; }

	/* ------------------------------------------------------------------------ */
	inline Real size(const SpatialDirection & direction) const {
	return upper_bounds(direction) - lower_bounds(direction);
	}

	Vector<Real> size() const {
	Vector<Real> size_(dim);
	for (auto s : arange(this->dim)) {
	size_(s) = this->size(SpatialDirection(s));
	}
	return size_;
	}

	inline operator bool() const { return not empty; }

	/* ------------------------------------------------------------------------ */
	BBox allSum(const Communicator & communicator) const {
	Matrix<Real> reduce_bounds(dim, 2);

	Vector<Real>(reduce_bounds(0)) = lower_bounds;
	Vector<Real>(reduce_bounds(1)) = Real(-1.) * upper_bounds;

	communicator.allReduce(reduce_bounds, SynchronizerOperation::_min);

	BBox global(dim);
	global.lower_bounds = Vector<Real>(reduce_bounds(0));
	global.upper_bounds = Real(-1.) * Vector<Real>(reduce_bounds(1));
	global.empty = false;
	return global;
	}

	std::vector<BBox> allGather(const Communicator & communicator) const {
	auto prank = communicator.whoAmI();
	auto nb_proc = communicator.getNbProc();
	Array<Real> bboxes_data(nb_proc, dim * 2 + 1);

	auto * base = bboxes_data.storage() + prank * (2 * dim + 1);
	Vector<Real>(base + dim * 0, dim) = lower_bounds;
	Vector<Real>(base + dim * 1, dim) = upper_bounds;
	base[dim * 2] = empty ? 1. : 0.; // ugly trick

	communicator.allGather(bboxes_data);

	std::vector<BBox> bboxes;
	bboxes.reserve(nb_proc);

	for (auto p : arange(nb_proc)) {
	bboxes.emplace_back(dim);
	auto & bbox = bboxes.back();

	auto * base = bboxes_data.storage() + p * (2 * dim + 1);
	bbox.lower_bounds = Vector<Real>(base + dim * 0, dim);
	bbox.upper_bounds = Vector<Real>(base + dim * 1, dim);
	bbox.empty = (base[dim * 2] == 1.);
	}

	return bboxes;
	}

	std::map<UInt, BBox> intersection(const BBox & other,
	const Communicator & communicator) const {
	// todo: change for a custom reduction algorithm
	auto other_bboxes = other.allGather(communicator);
	std::map<UInt, BBox> intersections;
	for (const auto & bbox : enumerate(other_bboxes)) {
	auto && tmp = this->intersection(std::get<1>(bbox));
	if (tmp) {
	intersections[std::get<0>(bbox)] = tmp;
	}
	}
	return intersections;
	}

	void printself(std::ostream & stream) const {
	stream << "BBox[";
	if (not empty) {
	stream << lower_bounds << " - " << upper_bounds;
	}
	stream << "]";
	}

	protected:
	UInt dim{0};
	bool empty{true};
	Vector<Real> lower_bounds;
	Vector<Real> upper_bounds;
	};

	inline std::ostream & operator<<(std::ostream & stream, const BBox & bbox) {
	bbox.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_BBOX_HH_ */
	diff --git a/src/common/aka_blas_lapack.hh b/src/common/aka_blas_lapack.hh
	index cd077caa2..67cda6a0a 100644
	--- a/src/common/aka_blas_lapack.hh
	+++ b/src/common/aka_blas_lapack.hh
	@@ -1,346 +1,346 @@
	/**
	* @file aka_blas_lapack.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 06 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Interface of the Fortran BLAS/LAPACK libraries
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_error.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_BLAS_LAPACK_HH_
	#define AKANTU_AKA_BLAS_LAPACK_HH_

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_BLAS
	#include "aka_fortran_mangling.hh"
	extern "C" {

	/* ------------------------------------------------------------------------ */
	/* Double precision */
	/* ------------------------------------------------------------------------ */
	// LEVEL 1
	double AKA_FC_GLOBAL(ddot, DDOT)(int , double , int , double , int *);
	void AKA_FC_GLOBAL(daxpy, DAXPY)(int , double , double , int , double *,
	int *);

	// LEVEL 2
	void AKA_FC_GLOBAL(dgemv, DGEMV)(char , int , int , double , double *,
	int , double , int , double , double *,
	int *);
	// LEVEL 3
	void AKA_FC_GLOBAL(dgemm, DGEMM)(char , char , int , int , int , double ,
	double , int , double , int , double *,
	double , int );
	/* ------------------------------------------------------------------------ */
	/* Simple precision */
	/* ------------------------------------------------------------------------ */
	// LEVEL 1
	float AKA_FC_GLOBAL(sdot, SDOT)(int , float , int , float , int *);
	void AKA_FC_GLOBAL(saxpy, SAXPY)(int , float , float , int , float *,
	int *);

	// LEVEL 2
	void AKA_FC_GLOBAL(sgemv, SGEMV)(char , int , int , float , float , int ,
	float , int , float , float , int *);
	// LEVEL 3
	void AKA_FC_GLOBAL(sgemm, SGEMM)(char , char , int , int , int , float ,
	float , int , float , int , float *,
	float , int );
	}
	#endif

	namespace akantu {

	#define AKANTU_WARNING_IGNORE_UNUSED_PARAMETER
	#include "aka_warning.hh"

	/// Wrapper around the S/DDOT BLAS function that returns the dot product of two
	/// vectors
	template <typename T>
	inline T aka_dot(int * n, T * x, int * incx, T * y, int * incy) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"BLAS in the compilation options!");
	}

	/// Wrapper around the S/DAXPY BLAS function that computes \f$y := \alpha x +
	/// y\f$
	template <typename T>
	inline void aka_axpy(int * n, T * alpha, T * x, int * incx, T * y, int * incy) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"BLAS in the compilation options!");
	}

	/// Wrapper around the S/DGEMV BLAS function that computes matrix-vector product
	/// \f$y := \alpha A^{(T)}x + \beta y \f$
	template <typename T>
	inline void aka_gemv(char * trans, int * m, int * n, T * alpha, T * a,
	int * lda, T * x, int * incx, T * beta, T * y,
	int * incy) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"BLAS in the compilation options!");
	}

	/// Wrapper around the S/DGEMM BLAS function that computes the product of two
	/// matrices \f$C := \alpha A^{(T)} B^{(T)} + \beta C \f$
	template <typename T>
	inline void aka_gemm(char * transa, char * transb, int * m, int * n, int * k,
	T * alpha, T * a, int * lda, T * b, int * ldb, T * beta,
	T * c, int * ldc) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"BLAS in the compilation options!");
	}

	#if defined(AKANTU_USE_BLAS)
	template <>
	inline double aka_dot<double>(int * n, double * x, int * incx, double * y,
	int * incy) {
	return AKA_FC_GLOBAL(ddot, DDOT)(n, x, incx, y, incy);
	}

	template <>
	inline void aka_axpy(int * n, double * alpha, double * x, int * incx,
	double * y, int * incy) {
	return AKA_FC_GLOBAL(daxpy, DAXPY)(n, alpha, x, incx, y, incy);
	}

	template <>
	inline void aka_gemv<double>(char * trans, int * m, int * n, double * alpha,
	double * a, int * lda, double * x, int * incx,
	double * beta, double * y, int * incy) {
	return AKA_FC_GLOBAL(dgemv, DGEMV)(trans, m, n, alpha, a, lda, x, incx, beta,
	y, incy);
	}

	template <>
	inline void aka_gemm<double>(char * transa, char * transb, int * m, int * n,
	int * k, double * alpha, double * a, int * lda,
	double * b, int * ldb, double * beta, double * c,
	int * ldc) {
	AKA_FC_GLOBAL(dgemm, DGEMM)
	(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	template <>
	inline float aka_dot<float>(int * n, float * x, int * incx, float * y,
	int * incy) {
	return AKA_FC_GLOBAL(sdot, SDOT)(n, x, incx, y, incy);
	}

	template <>
	inline void aka_axpy(int * n, float * alpha, float * x, int * incx, float * y,
	int * incy) {
	return AKA_FC_GLOBAL(daxpy, DAXPY)(n, alpha, x, incx, y, incy);
	}

	template <>
	inline void aka_gemv<float>(char * trans, int * m, int * n, float * alpha,
	float * a, int * lda, float * x, int * incx,
	float * beta, float * y, int * incy) {
	AKA_FC_GLOBAL(sgemv, SGEMV)
	(trans, m, n, alpha, a, lda, x, incx, beta, y, incy);
	}

	template <>
	inline void aka_gemm<float>(char * transa, char * transb, int * m, int * n,
	int * k, float * alpha, float * a, int * lda,
	float * b, int * ldb, float * beta, float * c,
	int * ldc) {
	AKA_FC_GLOBAL(sgemm, SGEMM)
	(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
	}

	#endif

	} // namespace akantu

	#ifdef AKANTU_USE_LAPACK
	#include "aka_fortran_mangling.hh"
	extern "C" {
	/* ------------------------------------------------------------------------ */
	/* Double general matrix */
	/* ------------------------------------------------------------------------ */
	/// compute the eigenvalues/vectors
	void AKA_FC_GLOBAL(dgeev, DGEEV)(char * jobvl, char * jobvr, int * n,
	double * a, int * lda, double * wr,
	double * wi, double * vl, int * ldvl,
	double * vr, int * ldvr, double * work,
	int * lwork, int * info);

	/// LU decomposition of a general matrix
	void AKA_FC_GLOBAL(dgetrf, DGETRF)(int * m, int * n, double * a, int * lda,
	int * ipiv, int * info);

	/// generate inverse of a matrix given its LU decomposition
	void AKA_FC_GLOBAL(dgetri, DGETRI)(int * n, double * a, int * lda, int * ipiv,
	double * work, int * lwork, int * info);

	/// solving A x = b using a LU factorization
	void AKA_FC_GLOBAL(dgetrs, DGETRS)(char * trans, int * n, int * nrhs,
	double * A, int * lda, int * ipiv,
	double * b, int * ldb, int * info);

	/* ------------------------------------------------------------------------ */
	/* Simple general matrix */
	/* ------------------------------------------------------------------------ */
	/// compute the eigenvalues/vectors
	void AKA_FC_GLOBAL(sgeev, SGEEV)(char * jobvl, char * jobvr, int * n, float * a,
	int * lda, float * wr, float * wi, float * vl,
	int * ldvl, float * vr, int * ldvr,
	float * work, int * lwork, int * info);

	/// LU decomposition of a general matrix
	void AKA_FC_GLOBAL(sgetrf, SGETRF)(int * m, int * n, float * a, int * lda,
	int * ipiv, int * info);

	/// generate inverse of a matrix given its LU decomposition
	void AKA_FC_GLOBAL(sgetri, SGETRI)(int * n, float * a, int * lda, int * ipiv,
	float * work, int * lwork, int * info);

	/// solving A x = b using a LU factorization
	void AKA_FC_GLOBAL(sgetrs, SGETRS)(char * trans, int * n, int * nrhs, float * A,
	int * lda, int * ipiv, float * b, int * ldb,
	int * info);
	}
	#endif // AKANTU_USE_LAPACK

	namespace akantu {

	/// Wrapper around the S/DGEEV BLAS function that computes the eigenvalues and
	/// eigenvectors of a matrix
	template <typename T>
	inline void aka_geev(char * jobvl, char * jobvr, int * n, T * a, int * lda,
	T * wr, T * wi, T * vl, int * ldvl, T * vr, int * ldvr,
	T * work, int * lwork, int * info) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"LAPACK in the compilation options!");
	}

	/// Wrapper around the S/DGETRF BLAS function that computes the LU decomposition
	/// of a matrix
	template <typename T>
	inline void aka_getrf(int * m, int * n, T * a, int * lda, int * ipiv,
	int * info) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"LAPACK in the compilation options!");
	}

	/// Wrapper around the S/DGETRI BLAS function that computes the inverse of a
	/// matrix given its LU decomposition
	template <typename T>
	inline void aka_getri(int * n, T * a, int * lda, int * ipiv, T * work,
	int * lwork, int * info) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"LAPACK in the compilation options!");
	}

	/// Wrapper around the S/DGETRS BLAS function that solves \f$A^{(T)}x = b\f$
	/// using LU decomposition
	template <typename T>
	inline void aka_getrs(char * trans, int * n, int * nrhs, T * A, int * lda,
	int * ipiv, T * b, int * ldb, int * info) {
	AKANTU_ERROR(debug::demangle(typeid(T).name())
	<< "is not a type recognized, or you didn't activated "
	"LAPACK in the compilation options!");
	}

	#include "aka_warning_restore.hh"

	#ifdef AKANTU_USE_LAPACK
	template <>
	inline void aka_geev<double>(char * jobvl, char * jobvr, int * n, double * a,
	int * lda, double * wr, double * wi, double * vl,
	int * ldvl, double * vr, int * ldvr, double * work,
	int * lwork, int * info) {
	AKA_FC_GLOBAL(dgeev, DGEEV)
	(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info);
	}

	template <>
	inline void aka_getrf<double>(int * m, int * n, double * a, int * lda,
	int * ipiv, int * info) {
	AKA_FC_GLOBAL(dgetrf, DGETRF)(m, n, a, lda, ipiv, info);
	}

	template <>
	inline void aka_getri<double>(int * n, double * a, int * lda, int * ipiv,
	double * work, int * lwork, int * info) {
	AKA_FC_GLOBAL(dgetri, DGETRI)(n, a, lda, ipiv, work, lwork, info);
	}

	template <>
	inline void aka_getrs<double>(char * trans, int * n, int * nrhs, double * A,
	int * lda, int * ipiv, double * b, int * ldb,
	int * info) {
	AKA_FC_GLOBAL(dgetrs, DGETRS)(trans, n, nrhs, A, lda, ipiv, b, ldb, info);
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <>
	inline void aka_geev<float>(char * jobvl, char * jobvr, int * n, float * a,
	int * lda, float * wr, float * wi, float * vl,
	int * ldvl, float * vr, int * ldvr, float * work,
	int * lwork, int * info) {
	AKA_FC_GLOBAL(sgeev, SGEEV)
	(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info);
	}

	template <>
	inline void aka_getrf<float>(int * m, int * n, float * a, int * lda, int * ipiv,
	int * info) {
	AKA_FC_GLOBAL(sgetrf, SGETRF)(m, n, a, lda, ipiv, info);
	}

	template <>
	inline void aka_getri<float>(int * n, float * a, int * lda, int * ipiv,
	float * work, int * lwork, int * info) {
	AKA_FC_GLOBAL(sgetri, SGETRI)(n, a, lda, ipiv, work, lwork, info);
	}

	template <>
	inline void aka_getrs<float>(char * trans, int * n, int * nrhs, float * A,
	int * lda, int * ipiv, float * b, int * ldb,
	int * info) {
	AKA_FC_GLOBAL(sgetrs, SGETRS)(trans, n, nrhs, A, lda, ipiv, b, ldb, info);
	}
	#endif

	} // namespace akantu

	#endif /* AKANTU_AKA_BLAS_LAPACK_HH_ */
	diff --git a/src/common/aka_circular_array.hh b/src/common/aka_circular_array.hh
	index ae97900ee..db95bc240 100644
	--- a/src/common/aka_circular_array.hh
	+++ b/src/common/aka_circular_array.hh
	@@ -1,123 +1,123 @@
	/**
	* @file aka_circular_array.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief class of circular array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <typeinfo>
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_AKA_CIRCULAR_ARRAY_HH_
	#define AKANTU_AKA_CIRCULAR_ARRAY_HH_

	namespace akantu {

	template <class T> class CircularArray : protected Array<T> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	typedef typename Array<T>::value_type value_type;
	typedef typename Array<T>::reference reference;
	typedef typename Array<T>::pointer_type pointer_type;
	typedef typename Array<T>::const_reference const_reference;

	/// Allocation of a new array with a default value
	CircularArray(UInt size, UInt nb_component = 1,
	const_reference value = value_type(), const ID & id = "")
	: Array<T>(size, nb_component, value, id), start_position(0),
	end_position(size - 1) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	};

	virtual ~CircularArray() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/**
	advance start and end position by one:
	the first element is now at the end of the array
	**/
	inline void makeStep();

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	private:
	/* ------------------------------------------------------------------------ */
	/* Operators */
	/* ------------------------------------------------------------------------ */
	public:
	inline reference operator()(UInt i, UInt j = 0);
	inline const_reference operator()(UInt i, UInt j = 0) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	UInt size() const { return this->size_; };

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// indice of first element in this circular array
	UInt start_position;

	/// indice of last element in this circular array
	UInt end_position;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	/// standard output stream operator
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const CircularArray<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "aka_circular_array_inline_impl.hh"

	#endif /* AKANTU_AKA_CIRCULAR_ARRAY_HH_ */
	diff --git a/src/common/aka_circular_array_inline_impl.hh b/src/common/aka_circular_array_inline_impl.hh
	index 6651ec6a7..66f2f6bbc 100644
	--- a/src/common/aka_circular_array_inline_impl.hh
	+++ b/src/common/aka_circular_array_inline_impl.hh
	@@ -1,103 +1,103 @@
	/**
	* @file aka_circular_array_inline_impl.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Nov 11 2011
	* @date last modification: Fri Mar 16 2018
	*
	* @brief implementation of circular array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_circular_array.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class T>
	-inline typename CircularArray<T>::reference CircularArray<T>::
	-operator()(UInt i, UInt j) {
	+inline typename CircularArray<T>::reference
	+CircularArray<T>::operator()(UInt i, UInt j) {
	AKANTU_DEBUG_ASSERT(end_position != start_position,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT(
	(i < (end_position - start_position + this->allocated_size) %
	this->allocated_size +
	1) &&
	(j < this->nb_component),
	"The value at position [" << i << "," << j
	<< "] is out of range in array \"" << this->id
	<< "\"");
	return this->values[((i + start_position) % this->allocated_size) *
	this->nb_component +
	j];
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	-inline typename CircularArray<T>::const_reference CircularArray<T>::
	-operator()(UInt i, UInt j) const {
	+inline typename CircularArray<T>::const_reference
	+CircularArray<T>::operator()(UInt i, UInt j) const {
	AKANTU_DEBUG_ASSERT(end_position != start_position,
	"The array \"" << this->id << "\" is empty");
	AKANTU_DEBUG_ASSERT(
	(i < (end_position - start_position + this->allocated_size) %
	this->allocated_size +
	1) &&
	(j < this->nb_component),
	"The value at position [" << i << "," << j
	<< "] is out of range in array \"" << this->id
	<< "\"");
	return this->values[((i + start_position) % this->allocated_size) *
	this->nb_component +
	j];
	}

	/* -------------------------------------------------------------------------- */
	template <class T> inline void CircularArray<T>::makeStep() {
	AKANTU_DEBUG_IN();

	start_position = (start_position + 1) % this->allocated_size;
	end_position = (end_position + 1) % this->allocated_size;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class T>
	void CircularArray<T>::printself(std::ostream & stream, int indent) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	;

	stream << space << "CircularArray<" << debug::demangle(typeid(T).name())
	<< "> [" << std::endl;
	stream << space << " + start_position : " << this->start_position
	<< std::endl;
	stream << space << " + end_position : " << this->end_position << std::endl;
	Array<T>::printself(stream, indent + 1);

	stream << space << "]" << std::endl;
	}

	-}
	+} // namespace akantu
	diff --git a/src/common/aka_common.cc b/src/common/aka_common.cc
	index 530ce8df5..4dca7b03b 100644
	--- a/src/common/aka_common.cc
	+++ b/src/common/aka_common.cc
	@@ -1,155 +1,156 @@
	/**
	* @file aka_common.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Initialization of global variables
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_random_generator.hh"
	#include "communicator.hh"

	#include "cppargparse.hh"
	#include "parser.hh"

	#include "communication_tag.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <ctime>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void initialize(int & argc, char **& argv) {
	AKANTU_DEBUG_IN();

	initialize("", argc, argv);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void initialize(const std::string & input_file, int & argc, char **& argv) {
	AKANTU_DEBUG_IN();
	Communicator & comm = Communicator::getStaticCommunicator(argc, argv);

	Tag::setMaxTag(comm.getMaxTag());

	debug::debugger.setParallelContext(comm.whoAmI(), comm.getNbProc());
	debug::setDebugLevel(dblError);

	static_argparser.setParallelContext(comm.whoAmI(), comm.getNbProc());
	static_argparser.setExternalExitFunction(debug::exit);
	static_argparser.addArgument("--aka_input_file", "Akantu's input file", 1,
	cppargparse::_string, std::string());
	static_argparser.addArgument(
	"--aka_debug_level",
	std::string("Akantu's overall debug level") +
	std::string(" (0: error, 1: exceptions, 4: warnings, 5: info, ..., "
	"100: dump") +
	std::string(" more info on levels can be foind in aka_error.hh)"),
	1, cppargparse::_integer, (long int)(dblWarning));

	static_argparser.addArgument(
	"--aka_print_backtrace",
	"Should Akantu print a backtrace in case of error", 0,
	cppargparse::_boolean, false, true);

	static_argparser.addArgument("--aka_seed", "The seed to use on prank 0", 1,
	cppargparse::_integer);

	static_argparser.parse(argc, argv, cppargparse::_remove_parsed);

	std::string infile = static_argparser["aka_input_file"];
	if (infile.empty()) {
	infile = input_file;
	}
	debug::debugger.printBacktrace(static_argparser["aka_print_backtrace"]);

	if (not infile.empty()) {
	readInputFile(infile);
	}

	long int seed;
	if (static_argparser.has("aka_seed")) {
	seed = static_argparser["aka_seed"];
	} else {
	seed =
	static_parser.getParameter("seed", time(nullptr), _ppsc_current_scope);
	}

	seed *= (comm.whoAmI() + 1);
	RandomGenerator<UInt>::seed(seed);

	long int dbl_level = static_argparser["aka_debug_level"];
	debug::setDebugLevel(DebugLevel(dbl_level));

	AKANTU_DEBUG_INFO("Random seed set to " << seed);

	std::atexit(finalize);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	-void finalize() { }
	+void finalize() {}

	/* -------------------------------------------------------------------------- */
	void readInputFile(const std::string & input_file) {
	static_parser.parse(input_file);
	}

	/* -------------------------------------------------------------------------- */
	cppargparse::ArgumentParser & getStaticArgumentParser() {
	return static_argparser;
	}

	/* -------------------------------------------------------------------------- */
	Parser & getStaticParser() { return static_parser; }

	/* -------------------------------------------------------------------------- */
	const ParserSection & getUserParser() {
	return *(static_parser.getSubSections(ParserType::_user).first);
	}

	std::unique_ptr<Communicator> Communicator::static_communicator;

	std::ostream & operator<<(std::ostream & stream, NodeFlag flag) {
	using under = std::underlying_type_t<NodeFlag>;
	- auto digits = static_cast<int>(std::log(std::numeric_limits<under>::max() + 1) / std::log(16));
	+ auto digits = static_cast<int>(
	+ std::log(std::numeric_limits<under>::max() + 1) / std::log(16));
	std::ios_base::fmtflags ff;
	ff = stream.flags();
	auto value = static_cast<std::common_type_t<under, unsigned int>>(flag);
	stream << "0x" << std::hex << std::setw(digits) << std::setfill('0') << value;
	stream.flags(ff);
	return stream;
	}

	} // namespace akantu
	diff --git a/src/common/aka_common.hh b/src/common/aka_common.hh
	index 1492dbe02..d3a804c90 100644
	--- a/src/common/aka_common.hh
	+++ b/src/common/aka_common.hh
	@@ -1,713 +1,709 @@
	/**
	* @file aka_common.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Sat May 01 2021
	*
	* @brief common type descriptions for akantu
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMON_HH_
	#define AKANTU_COMMON_HH_

	#include "aka_compatibilty_with_cpp_standard.hh"

	/* -------------------------------------------------------------------------- */
	#if defined(WIN32)
	#define __attribute__(x)
	#endif

	/* -------------------------------------------------------------------------- */
	#include "aka_config.hh"
	#include "aka_error.hh"
	#include "aka_safe_enum.hh"
	/* -------------------------------------------------------------------------- */
	#include <boost/preprocessor.hpp>
	#include <limits>
	#include <list>
	#include <memory>
	#include <string>
	#include <type_traits>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Constants */
	/* -------------------------------------------------------------------------- */
	namespace {
	[[gnu::unused]] constexpr UInt _all_dimensions{
	std::numeric_limits<UInt>::max()};
	#ifdef AKANTU_NDEBUG
	[[gnu::unused]] constexpr Real REAL_INIT_VALUE{0.};
	#else
	[[gnu::unused]] constexpr Real REAL_INIT_VALUE{
	std::numeric_limits<Real>::quiet_NaN()};
	#endif
	} // namespace

	/* -------------------------------------------------------------------------- */
	/* Common types */
	/* -------------------------------------------------------------------------- */
	using ID = std::string;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "aka_enum_macros.hh"
	/* -------------------------------------------------------------------------- */
	#include "aka_element_classes_info.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* Mesh/FEM/Model types */
	/* -------------------------------------------------------------------------- */

	/// small help to use names for directions
	enum SpatialDirection { _x = 0, _y = 1, _z = 2 };

	/// enum MeshIOType type of mesh reader/writer
	enum MeshIOType {
	_miot_auto, ///< Auto guess of the reader to use based on the extension
	_miot_gmsh, ///< Gmsh files
	_miot_gmsh_struct, ///< Gsmh reader with reintpretation of elements has
	/// structures elements
	_miot_diana, ///< TNO Diana mesh format
	_miot_abaqus ///< Abaqus mesh format
	};

	/// enum MeshEventHandlerPriority defines relative order of execution of
	/// events
	enum EventHandlerPriority {
	_ehp_highest = 0,
	_ehp_mesh = 5,
	_ehp_fe_engine = 9,
	_ehp_synchronizer = 10,
	_ehp_dof_manager = 20,
	_ehp_model = 94,
	_ehp_non_local_manager = 100,
	_ehp_lowest = 100
	};

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_MODEL_TYPES \
	(model) \
	(solid_mechanics_model) \
	(solid_mechanics_model_cohesive) \
	(heat_transfer_model) \
	(structural_mechanics_model) \
	(embedded_model) \
	(contact_mechanics_model) \
	(coupler_solid_contact) \
	(coupler_solid_cohesive_contact) \
	(phase_field_model) \
	(coupler_solid_phasefield)
	// clang-format on

	/// enum ModelType defines which type of physics is solved
	AKANTU_CLASS_ENUM_DECLARE(ModelType, AKANTU_MODEL_TYPES)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(ModelType, AKANTU_MODEL_TYPES)
	AKANTU_CLASS_ENUM_INPUT_STREAM(ModelType, AKANTU_MODEL_TYPES)
	#else
	enum class ModelType {
	model,
	solid_mechanics_model,
	solid_mechanics_model_cohesive,
	heat_transfer_model,
	structural_mechanics_model,
	embedded_model,
	};
	#endif
	/// enum AnalysisMethod type of solving method used to solve the equation of
	/// motion
	enum AnalysisMethod {
	_static = 0,
	_implicit_dynamic = 1,
	_explicit_lumped_mass = 2,
	_explicit_lumped_capacity = 2,
	_explicit_consistent_mass = 3,
	_explicit_contact = 4,
	_implicit_contact = 5
	};

	/// enum DOFSupportType defines which kind of dof that can exists
	enum DOFSupportType { _dst_nodal, _dst_generic };

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_NON_LINEAR_SOLVER_TYPES \
	(linear) \
	(newton_raphson) \
	(newton_raphson_modified) \
	(lumped) \
	(gmres) \
	(bfgs) \
	(cg) \
	(newton_raphson_contact) \
	(auto)
	// clang-format on
	AKANTU_CLASS_ENUM_DECLARE(NonLinearSolverType, AKANTU_NON_LINEAR_SOLVER_TYPES)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(NonLinearSolverType,
	AKANTU_NON_LINEAR_SOLVER_TYPES)
	AKANTU_CLASS_ENUM_INPUT_STREAM(NonLinearSolverType,
	AKANTU_NON_LINEAR_SOLVER_TYPES)
	#else
	/// Type of non linear resolution available in akantu
	enum class NonLinearSolverType {
	_linear, ///< No non linear convergence loop
	_newton_raphson, ///< Regular Newton-Raphson
	_newton_raphson_modified, ///< Newton-Raphson with initial tangent
	_lumped, ///< Case of lumped mass or equivalent matrix
	_gmres,
	_bfgs,
	_cg,
	_newton_raphson_contact, ///< Regular Newton-Raphson modified
	/// for contact problem
	_auto, ///< This will take a default value that make sense in case of
	/// model::getNewSolver
	};
	#endif

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_TIME_STEP_SOLVER_TYPE \
	(static) \
	(dynamic) \
	(dynamic_lumped) \
	(not_defined)
	// clang-format on
	AKANTU_CLASS_ENUM_DECLARE(TimeStepSolverType, AKANTU_TIME_STEP_SOLVER_TYPE)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(TimeStepSolverType,
	AKANTU_TIME_STEP_SOLVER_TYPE)
	AKANTU_CLASS_ENUM_INPUT_STREAM(TimeStepSolverType, AKANTU_TIME_STEP_SOLVER_TYPE)
	#else
	/// Type of time stepping solver
	enum class TimeStepSolverType {
	_static, ///< Static solution
	_dynamic, ///< Dynamic solver
	_dynamic_lumped, ///< Dynamic solver with lumped mass
	_not_defined, ///< For not defined cases
	};
	#endif

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_INTEGRATION_SCHEME_TYPE \
	(pseudo_time) \
	(forward_euler) \
	(trapezoidal_rule_1) \
	(backward_euler) \
	(central_difference) \
	(fox_goodwin) \
	(trapezoidal_rule_2) \
	(linear_acceleration) \
	(newmark_beta) \
	(generalized_trapezoidal)
	// clang-format on
	AKANTU_CLASS_ENUM_DECLARE(IntegrationSchemeType, AKANTU_INTEGRATION_SCHEME_TYPE)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(IntegrationSchemeType,
	AKANTU_INTEGRATION_SCHEME_TYPE)
	AKANTU_CLASS_ENUM_INPUT_STREAM(IntegrationSchemeType,
	AKANTU_INTEGRATION_SCHEME_TYPE)
	#else
	/// Type of integration scheme
	enum class IntegrationSchemeType {
	_pseudo_time, ///< Pseudo Time
	_forward_euler, ///< GeneralizedTrapezoidal(0)
	_trapezoidal_rule_1, ///< GeneralizedTrapezoidal(1/2)
	_backward_euler, ///< GeneralizedTrapezoidal(1)
	_central_difference, ///< NewmarkBeta(0, 1/2)
	_fox_goodwin, ///< NewmarkBeta(1/6, 1/2)
	_trapezoidal_rule_2, ///< NewmarkBeta(1/2, 1/2)
	_linear_acceleration, ///< NewmarkBeta(1/3, 1/2)
	_newmark_beta, ///< generic NewmarkBeta with user defined
	/// alpha and beta
	_generalized_trapezoidal ///< generic GeneralizedTrapezoidal with user
	/// defined alpha
	};
	#endif

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_SOLVE_CONVERGENCE_CRITERIA \
	(residual) \
	(solution) \
	(residual_mass_wgh)
	// clang-format on
	AKANTU_CLASS_ENUM_DECLARE(SolveConvergenceCriteria,
	AKANTU_SOLVE_CONVERGENCE_CRITERIA)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(SolveConvergenceCriteria,
	AKANTU_SOLVE_CONVERGENCE_CRITERIA)
	AKANTU_CLASS_ENUM_INPUT_STREAM(SolveConvergenceCriteria,
	AKANTU_SOLVE_CONVERGENCE_CRITERIA)
	#else
	/// enum SolveConvergenceCriteria different convergence criteria
	enum class SolveConvergenceCriteria {
	_residual, ///< Use residual to test the convergence
	_solution, ///< Use solution to test the convergence
	_residual_mass_wgh ///< Use residual weighted by inv. nodal mass to
	///< testb
	};
	#endif

	/// enum CohesiveMethod type of insertion of cohesive elements
	enum CohesiveMethod { _intrinsic, _extrinsic };

	/// @enum MatrixType type of sparse matrix used
	enum MatrixType { _unsymmetric, _symmetric, _mt_not_defined };

	/// @enum Type of contact detection
	enum DetectionType { _explicit, _implicit };

	-
	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_CONTACT_STATE \
	(no_contact) \
	(stick) \
	(slip)
	// clang-format on
	-AKANTU_CLASS_ENUM_DECLARE(ContactState,
	- AKANTU_CONTACT_STATE)
	-AKANTU_CLASS_ENUM_OUTPUT_STREAM(ContactState,
	- AKANTU_CONTACT_STATE)
	-AKANTU_CLASS_ENUM_INPUT_STREAM(ContactState,
	- AKANTU_CONTACT_STATE)
	+AKANTU_CLASS_ENUM_DECLARE(ContactState, AKANTU_CONTACT_STATE)
	+AKANTU_CLASS_ENUM_OUTPUT_STREAM(ContactState, AKANTU_CONTACT_STATE)
	+AKANTU_CLASS_ENUM_INPUT_STREAM(ContactState, AKANTU_CONTACT_STATE)
	#else
	/// @enum no contact or stick or slip state
	enum class ContactState {
	_no_contact = 0,
	_stick = 1,
	_slip = 2,
	};
	#endif

	/* -------------------------------------------------------------------------- */
	/* Ghosts handling */
	/* -------------------------------------------------------------------------- */
	/// @enum CommunicatorType type of communication method to use
	enum CommunicatorType { _communicator_mpi, _communicator_dummy };

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_SYNCHRONIZATION_TAG \
	(whatever) \
	(update) \
	(ask_nodes) \
	(size) \
	(smm_mass) \
	(smm_for_gradu) \
	(smm_boundary) \
	(smm_uv) \
	(smm_res) \
	(smm_init_mat) \
	(smm_stress) \
	(smmc_facets) \
	(smmc_facets_conn) \
	(smmc_facets_stress) \
	(smmc_damage) \
	(giu_global_conn) \
	(ce_groups) \
	(ce_insertion_order) \
	(gm_clusters) \
	(htm_temperature) \
	(htm_gradient_temperature) \
	(htm_phi) \
	(htm_gradient_phi) \
	(pfm_damage) \
	(pfm_driving) \
	(pfm_history) \
	(pfm_energy) \
	(csp_damage) \
	(csp_strain) \
	(mnl_for_average) \
	(mnl_weight) \
	(nh_criterion) \
	(test) \
	(user_1) \
	(user_2) \
	(material_id) \
	(for_dump) \
	(cf_nodal) \
	(cf_incr) \
	(solver_solution)
	// clang-format on
	AKANTU_CLASS_ENUM_DECLARE(SynchronizationTag, AKANTU_SYNCHRONIZATION_TAG)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(SynchronizationTag, AKANTU_SYNCHRONIZATION_TAG)
	#else
	/// @enum SynchronizationTag type of synchronizations
	enum class SynchronizationTag {
	//--- Generic tags ---
	_whatever,
	_update,
	_ask_nodes,
	_size,

	//--- SolidMechanicsModel tags ---
	_smm_mass, ///< synchronization of the SolidMechanicsModel.mass
	_smm_for_gradu, ///< synchronization of the
	/// SolidMechanicsModel.displacement
	_smm_boundary, ///< synchronization of the boundary, forces, velocities
	/// and displacement
	_smm_uv, ///< synchronization of the nodal velocities and displacement
	_smm_res, ///< synchronization of the nodal residual
	_smm_init_mat, ///< synchronization of the data to initialize materials
	_smm_stress, ///< synchronization of the stresses to compute the
	///< internal
	/// forces
	_smmc_facets, ///< synchronization of facet data to setup facet synch
	_smmc_facets_conn, ///< synchronization of facet global connectivity
	_smmc_facets_stress, ///< synchronization of facets' stress to setup
	///< facet
	/// synch
	_smmc_damage, ///< synchronization of damage

	// --- GlobalIdsUpdater tags ---
	_giu_global_conn, ///< synchronization of global connectivities

	// --- CohesiveElementInserter tags ---
	_ce_groups, ///< synchronization of cohesive element insertion depending
	/// on facet groups
	_ce_insertion_order, ///< synchronization of the order of insertion of
	/// cohesive elements

	// --- GroupManager tags ---
	_gm_clusters, ///< synchronization of clusters

	// --- HeatTransfer tags ---
	_htm_temperature, ///< synchronization of the nodal temperature
	_htm_gradient_temperature, ///< synchronization of the element gradient
	/// temperature

	// --- PhaseFieldModel tags ---
	_pfm_damage, ///< synchronization of the nodal damage
	_pfm_driving, ///< synchronization of the driving forces to
	/// compute the internal
	_pfm_history, ///< synchronization of the damage history to
	/// compute the internal
	_pfm_energy, ///< synchronization of the damage energy
	/// density to compute the internal

	// --- CouplerSolidPhaseField tags ---
	_csp_damage, ///< synchronization of the damage from phase
	/// model to solid model
	_csp_strain, ///< synchronization of the strain from solid
	/// model to phase model

	// --- LevelSet tags ---
	_htm_phi, ///< synchronization of the nodal level set value phi
	_htm_gradient_phi, ///< synchronization of the element gradient phi

	//--- Material non local ---
	_mnl_for_average, ///< synchronization of data to average in non local
	/// material
	_mnl_weight, ///< synchronization of data for the weight computations

	// --- NeighborhoodSynchronization tags ---
	_nh_criterion,

	// --- General tags ---
	_test, ///< Test tag
	_user_1, ///< tag for user simulations
	_user_2, ///< tag for user simulations
	_material_id, ///< synchronization of the material ids
	_for_dump, ///< everything that needs to be synch before dump

	// --- Contact & Friction ---
	_cf_nodal, ///< synchronization of disp, velo, and current position
	_cf_incr, ///< synchronization of increment

	// --- Solver tags ---
	_solver_solution ///< synchronization of the solution obained with the
	/// PETSc solver
	};
	#endif

	/// @enum GhostType type of ghost
	enum GhostType {
	_not_ghost = 0,
	_ghost = 1,
	_casper // not used but a real cute ghost
	};

	/// Define the flag that can be set to a node
	enum class NodeFlag : std::uint8_t {
	_normal = 0x00,
	_distributed = 0x01,
	_master = 0x03,
	_slave = 0x05,
	_pure_ghost = 0x09,
	_shared_mask = 0x0F,
	_periodic = 0x10,
	_periodic_master = 0x30,
	_periodic_slave = 0x50,
	_periodic_mask = 0xF0,
	_local_master_mask = 0xCC, // ~(_master & _periodic_mask)
	};

	inline NodeFlag operator&(const NodeFlag & a, const NodeFlag & b) {
	using under = std::underlying_type_t<NodeFlag>;
	return NodeFlag(under(a) & under(b));
	}

	inline NodeFlag operator\|(const NodeFlag & a, const NodeFlag & b) {
	using under = std::underlying_type_t<NodeFlag>;
	return NodeFlag(under(a) \| under(b));
	}

	inline NodeFlag & operator\|=(NodeFlag & a, const NodeFlag & b) {
	a = a \| b;
	return a;
	}

	inline NodeFlag & operator&=(NodeFlag & a, const NodeFlag & b) {
	a = a & b;
	return a;
	}

	inline NodeFlag operator~(const NodeFlag & a) {
	using under = std::underlying_type_t<NodeFlag>;
	return NodeFlag(~under(a));
	}

	std::ostream & operator<<(std::ostream & stream, NodeFlag flag);

	} // namespace akantu

	AKANTU_ENUM_HASH(GhostType)

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	struct GhostType_def {
	using type = GhostType;
	static const type _begin_ = _not_ghost;
	static const type _end_ = _casper;
	};

	using ghost_type_t = safe_enum<GhostType_def>;
	namespace {
	constexpr ghost_type_t ghost_types{_casper};
	}

	/// standard output stream operator for GhostType
	// inline std::ostream & operator<<(std::ostream & stream, GhostType type);

	/* -------------------------------------------------------------------------- */
	/* Global defines */
	/* -------------------------------------------------------------------------- */
	#define AKANTU_MIN_ALLOCATION 2000

	#define AKANTU_INDENT ' '
	#define AKANTU_INCLUDE_INLINE_IMPL

	/* -------------------------------------------------------------------------- */
	#define AKANTU_SET_MACRO(name, variable, type) \
	inline void set##name(type variable) { this->variable = variable; }

	#define AKANTU_GET_MACRO(name, variable, type) \
	inline type get##name() const { return variable; }

	#define AKANTU_GET_MACRO_NOT_CONST(name, variable, type) \
	inline type get##name() { return variable; }

	#define AKANTU_GET_MACRO_DEREF_PTR(name, ptr) \
	inline const auto & get##name() const { \
	if (not(ptr)) { \
	AKANTU_EXCEPTION("The member " << #ptr << " is not initialized"); \
	} \
	return (*(ptr)); \
	}

	#define AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(name, ptr) \
	inline auto & get##name() { \
	if (not(ptr)) { \
	AKANTU_EXCEPTION("The member " << #ptr << " is not initialized"); \
	} \
	return (*(ptr)); \
	}

	#define AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, support, con) \
	inline con Array<type> & get##name(const support & el_type, \
	GhostType ghost_type = _not_ghost) \
	con { /* NOLINT */ \
	return variable(el_type, ghost_type); \
	} // NOLINT

	#define AKANTU_GET_MACRO_BY_ELEMENT_TYPE(name, variable, type) \
	AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, ElementType, )
	#define AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(name, variable, type) \
	AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, ElementType, const)

	#define AKANTU_GET_MACRO_BY_GEOMETRIE_TYPE(name, variable, type) \
	AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, GeometricalType, )
	#define AKANTU_GET_MACRO_BY_GEOMETRIE_TYPE_CONST(name, variable, type) \
	AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, GeometricalType, const)

	/* -------------------------------------------------------------------------- */
	/// initialize the static part of akantu
	void initialize(int & argc, char **& argv);
	/// initialize the static part of akantu and read the global input_file
	void initialize(const std::string & input_file, int & argc, char **& argv);
	/* -------------------------------------------------------------------------- */
	/// finilize correctly akantu and clean the memory
	void finalize();
	/* -------------------------------------------------------------------------- */
	/// Read an new input file
	void readInputFile(const std::string & input_file);
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/* string manipulation */
	/* -------------------------------------------------------------------------- */
	inline std::string to_lower(const std::string & str);
	/* -------------------------------------------------------------------------- */
	inline std::string trim(const std::string & to_trim);
	inline std::string trim(const std::string & to_trim, char c);
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/// give a string representation of the a human readable size in bit
	template <typename T> std::string printMemorySize(UInt size);
	/* -------------------------------------------------------------------------- */

	struct TensorTrait {};
	struct TensorProxyTrait {};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* Type traits */
	/* -------------------------------------------------------------------------- */
	namespace aka {

	/* ------------------------------------------------------------------------ */
	template <typename T> using is_tensor = std::is_base_of<akantu::TensorTrait, T>;
	template <typename T>
	using is_tensor_proxy = std::is_base_of<akantu::TensorProxyTrait, T>;
	/* ------------------------------------------------------------------------ */
	template <typename T> using is_scalar = std::is_arithmetic<T>;
	/* ------------------------------------------------------------------------ */
	template <typename R, typename T,
	std::enable_if_t<std::is_reference<T>::value> * = nullptr>
	bool is_of_type(T && t) {
	return (
	dynamic_cast<std::add_pointer_t<
	std::conditional_t<std::is_const<std::remove_reference_t<T>>::value,
	std::add_const_t<R>, R>>>(&t) != nullptr);
	}

	/* -------------------------------------------------------------------------- */
	template <typename R, typename T> bool is_of_type(std::unique_ptr<T> & t) {
	return (
	dynamic_cast<std::add_pointer_t<
	std::conditional_t<std::is_const<T>::value, std::add_const_t<R>, R>>>(
	t.get()) != nullptr);
	}

	/* ------------------------------------------------------------------------ */
	template <typename R, typename T,
	std::enable_if_t<std::is_reference<T>::value> * = nullptr>
	decltype(auto) as_type(T && t) {
	static_assert(
	disjunction<
	std::is_base_of<std::decay_t<T>, std::decay_t<R>>, // down-cast
	std::is_base_of<std::decay_t<R>, std::decay_t<T>> // up-cast
	>::value,
	"Type T and R are not valid for a as_type conversion");
	return dynamic_cast<std::add_lvalue_reference_t<
	std::conditional_t<std::is_const<std::remove_reference_t<T>>::value,
	std::add_const_t<R>, R>>>(t);
	}

	/* -------------------------------------------------------------------------- */
	template <typename R, typename T,
	std::enable_if_t<std::is_pointer<T>::value> * = nullptr>
	decltype(auto) as_type(T && t) {
	return &as_type<R>(*t);
	}

	/* -------------------------------------------------------------------------- */
	template <typename R, typename T>
	decltype(auto) as_type(const std::shared_ptr<T> & t) {
	return std::dynamic_pointer_cast<R>(t);
	}

	} // namespace aka

	#include "aka_common_inline_impl.hh"

	#include "aka_fwd.hh"

	namespace akantu {
	/// get access to the internal argument parser
	cppargparse::ArgumentParser & getStaticArgumentParser();

	/// get access to the internal input file parser
	Parser & getStaticParser();

	/// get access to the user part of the internal input file parser
	const ParserSection & getUserParser();

	#define AKANTU_CURRENT_FUNCTION \
	(std::string(__func__) + "():" + std::to_string(__LINE__))

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#if AKANTU_INTEGER_SIZE == 4
	#define AKANTU_HASH_COMBINE_MAGIC_NUMBER 0x9e3779b9
	#elif AKANTU_INTEGER_SIZE == 8
	#define AKANTU_HASH_COMBINE_MAGIC_NUMBER 0x9e3779b97f4a7c13LL
	#endif

	namespace std {
	/**
	* Hashing function for pairs based on hash_combine from boost The magic
	* number is coming from the golden number @f[\phi = \frac{1 + \sqrt5}{2}@f]
	* @f[\frac{2^32}{\phi} = 0x9e3779b9@f]
	* http://stackoverflow.com/questions/4948780/magic-number-in-boosthash-combine
	* http://burtleburtle.net/bob/hash/doobs.html
	*/
	template <typename a, typename b> struct hash<std::pair<a, b>> {
	hash() = default;
	size_t operator()(const std::pair<a, b> & p) const {
	size_t seed = ah(p.first);
	return bh(p.second) + AKANTU_HASH_COMBINE_MAGIC_NUMBER + (seed << 6) +
	(seed >> 2);
	}

	private:
	const hash<a> ah{};
	const hash<b> bh{};
	};

	} // namespace std

	#endif // AKANTU_COMMON_HH_
	diff --git a/src/common/aka_common_inline_impl.hh b/src/common/aka_common_inline_impl.hh
	index c50502cc3..360636207 100644
	--- a/src/common/aka_common_inline_impl.hh
	+++ b/src/common/aka_common_inline_impl.hh
	@@ -1,131 +1,131 @@
	/**
	* @file aka_common_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Feb 09 2021
	*
	* @brief inline implementations of common akantu type descriptions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	+#include <array>
	#include <cctype>
	#include <cmath>
	#include <iomanip>
	#include <iostream>
	-#include <array>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/// standard output stream operator for GhostType
	inline std::ostream & operator<<(std::ostream & stream, GhostType type) {
	switch (type) {
	case _not_ghost:
	stream << "not_ghost";
	break;
	case _ghost:
	stream << "ghost";
	break;
	case _casper:
	stream << "Casper the friendly ghost";
	break;
	}
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	inline std::string to_lower(const std::string & str) {
	std::string lstr = str;
	std::transform(lstr.begin(), lstr.end(), lstr.begin(), (int (*)(int))tolower);
	return lstr;
	}

	namespace {
	template <typename pred>
	inline std::string trim_p(const std::string & to_trim, pred && p) {
	std::string trimed = to_trim;
	auto && not_ = [&](auto && a) { return not p(a); };

	// left trim
	trimed.erase(trimed.begin(),
	std::find_if(trimed.begin(), trimed.end(), not_));
	// right trim
	trimed.erase(std::find_if(trimed.rbegin(), trimed.rend(), not_).base(),
	trimed.end());
	return trimed;
	}

	} // namespace

	/* -------------------------------------------------------------------------- */
	inline std::string trim(const std::string & to_trim) {
	return trim_p(to_trim, [&](auto && a) { return std::isspace(a); });
	}

	inline std::string trim(const std::string & to_trim, char c) {
	return trim_p(to_trim, [&c](auto && a) { return (a == c); });
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> std::string printMemorySize(UInt size) {
	Real real_size = size * sizeof(T);

	UInt mult = 0;
	if (real_size != 0) {
	mult = (std::log(real_size) / std::log(2)) / 10;
	}

	std::stringstream sstr;

	real_size /= Real(1 << (10 * mult));
	sstr << std::setprecision(2) << std::fixed << real_size;

	std::string size_prefix;
	std::array<std::string, 9> ratio = {
	"", "Ki", "Mi",
	"Gi", // I started on this type of machines (32bit computers) (Nicolas)
	"Ti", "Pi",
	"Ei", // theoritical limit of RAM of the current computers in 2014 (64bit
	// computers) (Nicolas)
	"Zi", "Yi"};

	if (mult >= ratio.size()) {
	AKANTU_ERROR(
	"The programmer in 2014 didn't thought so far (even wikipedia does not "
	"go further)."
	<< " You have at least 1024 times more than a yobibit of RAM!!!"
	<< " Just add the prefix corresponding in the ratio array.");
	}

	sstr << ratio[mult] << "Byte";

	return sstr.str();
	}

	} // namespace akantu
	diff --git a/src/common/aka_csr.hh b/src/common/aka_csr.hh
	index 4f7f9f163..0ed83138c 100644
	--- a/src/common/aka_csr.hh
	+++ b/src/common/aka_csr.hh
	@@ -1,287 +1,287 @@
	/**
	* @file aka_csr.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Apr 20 2011
	* @date last modification: Tue Sep 29 2020
	*
	* @brief A compresed sparse row structure based on akantu Arrays
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_CSR_HH_
	#define AKANTU_AKA_CSR_HH_

	namespace akantu {

	/**
	* This class can be used to store the structure of a sparse matrix or for
	* vectors with variable number of component per element
	*
	* @param nb_rows number of rows of a matrix or size of a vector.
	*/
	template <typename T> class CSR {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	explicit CSR(UInt nb_rows = 0)
	: nb_rows(nb_rows), rows_offsets(nb_rows + 1, 1, "rows_offsets"),
	rows(0, 1, "rows") {
	rows_offsets.zero();
	};

	virtual ~CSR() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// does nothing
	inline void beginInsertions(){};

	/// insert a new entry val in row row
	inline UInt insertInRow(UInt row, const T & val) {
	UInt pos = rows_offsets(row)++;
	rows(pos) = val;
	return pos;
	}

	/// access an element of the matrix
	inline const T & operator()(UInt row, UInt col) const {
	AKANTU_DEBUG_ASSERT(rows_offsets(row + 1) - rows_offsets(row) > col,
	"This element is not present in this CSR");
	return rows(rows_offsets(row) + col);
	}

	/// access an element of the matrix
	inline T & operator()(UInt row, UInt col) {
	AKANTU_DEBUG_ASSERT(rows_offsets(row + 1) - rows_offsets(row) > col,
	"This element is not present in this CSR");
	return rows(rows_offsets(row) + col);
	}

	inline void endInsertions() {
	for (UInt i = nb_rows; i > 0; --i) {
	rows_offsets(i) = rows_offsets(i - 1);
	}
	rows_offsets(0) = 0;
	}

	inline void countToCSR() {
	for (UInt i = 1; i < nb_rows; ++i) {
	rows_offsets(i) += rows_offsets(i - 1);
	}
	for (UInt i = nb_rows; i >= 1; --i) {
	rows_offsets(i) = rows_offsets(i - 1);
	}
	rows_offsets(0) = 0;
	}

	inline void clearRows() {
	rows_offsets.zero();
	rows.resize(0);
	};

	inline void resizeRows(UInt nb_rows) {
	this->nb_rows = nb_rows;
	rows_offsets.resize(nb_rows + 1);
	rows_offsets.zero();
	}

	inline void resizeCols() { rows.resize(rows_offsets(nb_rows)); }

	inline void copy(Array<UInt> & offsets, Array<T> & values) {
	offsets.copy(rows_offsets);
	values.copy(rows);
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// returns the number of rows
	inline UInt getNbRows() const { return rows_offsets.size() - 1; };

	/// returns the number of non-empty columns in a given row
	inline UInt getNbCols(UInt row) const {
	return rows_offsets(row + 1) - rows_offsets(row);
	};

	/// returns the offset (start of columns) for a given row
	inline UInt & rowOffset(UInt row) { return rows_offsets(row); };

	// /// iterator on a row
	// template <class array_iterator>
	// class iterator_internal
	// : public std::iterator<std::bidirectional_iterator_tag, typename
	// array_iterator::value_type> {
	// public:
	// using _parent = std::iterator<std::bidirectional_iterator_tag, R>;
	// using pointer = typename _parent::pointer;
	// using reference = typename _parent::reference;

	// explicit iterator_internal(array_iterator ait) : pos(std::move(ait)){};
	// iterator_internal(const iterator_internal & it) : pos(it.pos){};

	// iterator_internal & operator++() {
	// ++pos;
	// return *this;
	// };
	// iterator_internal operator++(int) {
	// iterator tmp(*this);
	// operator++();
	// return tmp;
	// };

	// iterator_internal & operator--() {
	// --pos;
	// return *this;
	// };
	// iterator_internal operator--(int) {
	// iterator_internal tmp(*this);
	// operator--();
	// return tmp;
	// };

	// bool operator==(const iterator_internal & rhs) { return pos == rhs.pos;
	// }; bool operator!=(const iterator_internal & rhs) { return pos !=
	// rhs.pos; }; reference operator() { return pos; }; pointer operator->()
	// const { return pos; };

	// private:
	// array_iterator pos;
	// };

	using iterator = typename Array<T>::scalar_iterator;
	using const_iterator = typename Array<T>::const_scalar_iterator;

	template <typename iterator_internal> class CSRRow {
	public:
	CSRRow(iterator_internal begin, iterator_internal end)
	: begin_(std::move(begin)), end_(std::move(end)) {}

	inline auto begin() const { return begin_; }
	inline auto end() const { return end_; }

	private:
	iterator_internal begin_, end_;
	};

	inline iterator begin(UInt row) { return rows.begin() + rows_offsets(row); };
	inline iterator end(UInt row) {
	return rows.begin() + rows_offsets(row + 1);
	};

	inline const_iterator begin(UInt row) const {
	return rows.begin() + rows_offsets(row);
	};
	inline const_iterator end(UInt row) const {
	return rows.begin() + rows_offsets(row + 1);
	};

	private:
	template <typename iterator_internal>
	decltype(auto) make_row(iterator_internal begin, iterator_internal end) {
	return CSRRow<iterator_internal>(std::move(begin), std::move(end));
	}

	public:
	inline decltype(auto) getRow(UInt row) {
	return make_row(begin(row), end(row));
	}
	inline decltype(auto) getRow(UInt row) const {
	return make_row(begin(row), end(row));
	}

	inline iterator rbegin(UInt row) {
	return rows.begin() + rows_offsets(row + 1) - 1;
	};
	inline iterator rend(UInt row) {
	return rows.begin() + rows_offsets(row) - 1;
	};

	inline const Array<UInt> & getRowsOffset() const { return rows_offsets; };
	inline const Array<T> & getRows() const { return rows; };
	inline Array<T> & getRows() { return rows; };
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	UInt nb_rows;

	/// array of size nb_rows containing the offset where the values are stored in
	Array<UInt> rows_offsets;

	/// compressed row values, values of row[i] are stored between rows_offsets[i]
	/// and rows_offsets[i+1]
	Array<T> rows;
	};

	/* -------------------------------------------------------------------------- */
	/* Data CSR */
	/* -------------------------------------------------------------------------- */

	/**
	* Inherits from CSR<UInt> and can contain information such as matrix values
	* where the mother class would be a CSR structure for row and cols
	*
	* @return nb_rows
	*/
	template <class T> class DataCSR : public CSR<UInt> {
	public:
	DataCSR(UInt nb_rows = 0) : CSR<UInt>(nb_rows), data(0, 1){};

	inline void resizeCols() {
	CSR<UInt>::resizeCols();
	data.resize(rows_offsets(nb_rows));
	}

	inline const Array<T> & getData() const { return data; };

	private:
	Array<T> data;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "aka_csr_inline_impl.hh"

	/// standard output stream operator
	// inline std::ostream & operator <<(std::ostream & stream, const CSR & _this)
	// {
	// _this.printself(stream);
	// return stream;
	// }

	} // namespace akantu

	#endif /* AKANTU_AKA_CSR_HH_ */
	diff --git a/src/common/aka_element_classes_info_inline_impl.hh b/src/common/aka_element_classes_info_inline_impl.hh
	index e5f889756..33d64d7ae 100644
	--- a/src/common/aka_element_classes_info_inline_impl.hh
	+++ b/src/common/aka_element_classes_info_inline_impl.hh
	@@ -1,55 +1,55 @@
	/**
	* @file aka_element_classes_info_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 18 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Implementation of the streaming fonction for the element classes
	* enums
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_ELEMENT_CLASSES_INFO_INLINE_IMPL_HH_
	#define AKANTU_AKA_ELEMENT_CLASSES_INFO_INLINE_IMPL_HH_

	namespace akantu {

	AKANTU_ENUM_OUTPUT_STREAM(
	ElementType, AKANTU_ALL_ELEMENT_TYPE(_not_defined)(_max_element_type))
	AKANTU_ENUM_INPUT_STREAM(ElementType, AKANTU_ALL_ELEMENT_TYPE)

	AKANTU_ENUM_OUTPUT_STREAM(InterpolationType, AKANTU_INTERPOLATION_TYPES)
	AKANTU_ENUM_INPUT_STREAM(InterpolationType, AKANTU_INTERPOLATION_TYPES)

	AKANTU_ENUM_OUTPUT_STREAM(ElementKind, AKANTU_ELEMENT_KIND)
	AKANTU_ENUM_INPUT_STREAM(ElementKind, AKANTU_ELEMENT_KIND)

	} // namespace akantu

	#endif /* AKANTU_AKA_ELEMENT_CLASSES_INFO_INLINE_IMPL_HH_ */
	diff --git a/src/common/aka_enum_macros.hh b/src/common/aka_enum_macros.hh
	index e96bd5046..1c9c6594e 100644
	--- a/src/common/aka_enum_macros.hh
	+++ b/src/common/aka_enum_macros.hh
	@@ -1,137 +1,137 @@
	/**
	* @file aka_enum_macros.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Nov 05 2018
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Macros to help declare enums
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <string>
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_AKA_ENUM_MACROS_HH_
	#define AKANTU_AKA_ENUM_MACROS_HH_

	#define AKANTU_PP_ENUM(s, data, i, elem) \
	BOOST_PP_TUPLE_REM() \
	elem BOOST_PP_COMMA_IF(BOOST_PP_NOT_EQUAL(i, BOOST_PP_DEC(data)))

	#if (defined(__GNUC__) \|\| defined(__GNUG__))
	#define AKA_GCC_VERSION \
	(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	#if AKA_GCC_VERSION < 60000
	#define AKANTU_ENUM_HASH(type_name) \
	namespace std { \
	template <> struct hash<::akantu::type_name> { \
	using argument_type = ::akantu::type_name; \
	size_t operator()(const argument_type & e) const noexcept { \
	auto ue = underlying_type_t<argument_type>(e); \
	return uh(ue); \
	} \
	\
	private: \
	const hash<underlying_type_t<argument_type>> uh{}; \
	}; \
	}
	#else
	#define AKANTU_ENUM_HASH(type_name)
	#endif // AKA_GCC_VERSION
	#endif // GNU

	#define AKANTU_PP_CAT(s, data, elem) BOOST_PP_CAT(data, elem)

	#define AKANTU_PP_TYPE_TO_STR(s, data, elem) \
	({BOOST_PP_CAT(data, elem), BOOST_PP_STRINGIZE(elem)})

	#define AKANTU_PP_STR_TO_TYPE(s, data, elem) \
	({BOOST_PP_STRINGIZE(elem), BOOST_PP_CAT(data, elem)})

	#define AKANTU_CLASS_ENUM_DECLARE(type_name, list) \
	enum class type_name { \
	BOOST_PP_SEQ_ENUM(BOOST_PP_SEQ_TRANSFORM(AKANTU_PP_CAT, _, list)) \
	};

	#define AKANTU_ENUM_OUTPUT_STREAM_(type_name, list, prefix) \
	} \
	AKANTU_ENUM_HASH(type_name) \
	namespace std { \
	inline string to_string(const ::akantu::type_name & type) { \
	using namespace akantu; \
	static unordered_map<::akantu::type_name, string> convert{ \
	BOOST_PP_SEQ_FOR_EACH_I( \
	AKANTU_PP_ENUM, BOOST_PP_SEQ_SIZE(list), \
	BOOST_PP_SEQ_TRANSFORM(AKANTU_PP_TYPE_TO_STR, prefix, list))}; \
	return convert.at(type); \
	} \
	} \
	namespace akantu { \
	inline std::ostream & operator<<(std::ostream & stream, \
	const type_name & type) { \
	stream << std::to_string(type); \
	return stream; \
	}

	#define AKANTU_ENUM_INPUT_STREAM_(type_name, list, prefix) \
	inline std::istream & operator>>(std::istream & stream, \
	type_name & type) { /* NOLINT */ \
	std::string str; \
	stream >> str; /* NOLINT */ \
	static std::unordered_map<std::string, type_name> convert{ \
	BOOST_PP_SEQ_FOR_EACH_I( \
	AKANTU_PP_ENUM, BOOST_PP_SEQ_SIZE(list), \
	BOOST_PP_SEQ_TRANSFORM(AKANTU_PP_STR_TO_TYPE, prefix, list))}; \
	try { \
	type = convert.at(str); \
	} catch (std::out_of_range &) { \
	std::ostringstream values; \
	std::for_each(convert.begin(), convert.end(), [&values](auto && pair) { \
	static bool first = true; \
	if (not first) \
	values << ", "; \
	values << "\"" << pair.first << "\""; \
	first = false; \
	}); \
	AKANTU_EXCEPTION("The value " << str << " is not a valid " \
	- << BOOST_PP_STRINGIZE(type_name) \
	- << " valid values are " << values.str()); \
	+ << BOOST_PP_STRINGIZE(type_name) << " valid values are " \
	+ << values.str()); \
	} \
	return stream; \
	}

	#define AKANTU_CLASS_ENUM_OUTPUT_STREAM(type_name, list) \
	AKANTU_ENUM_OUTPUT_STREAM_(type_name, list, type_name::_)

	#define AKANTU_ENUM_OUTPUT_STREAM(type_name, list) \
	AKANTU_ENUM_OUTPUT_STREAM_(type_name, list, )

	#define AKANTU_CLASS_ENUM_INPUT_STREAM(type_name, list) \
	AKANTU_ENUM_INPUT_STREAM_(type_name, list, type_name::_)

	#define AKANTU_ENUM_INPUT_STREAM(type_name, list) \
	AKANTU_ENUM_INPUT_STREAM_(type_name, list, )

	#endif /* AKANTU_AKA_ENUM_MACROS_HH_ */
	diff --git a/src/common/aka_error.cc b/src/common/aka_error.cc
	index c0a142fa9..176754b69 100644
	--- a/src/common/aka_error.cc
	+++ b/src/common/aka_error.cc
	@@ -1,370 +1,374 @@
	/**
	* @file aka_error.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Sep 06 2010
	* @date last modification: Wed Feb 24 2021
	*
	* @brief handling of errors
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_error.hh"
	#include "aka_common.hh"
	#include "aka_config.hh"
	#include "aka_iterators.hh"
	#include "aka_random_generator.hh"
	/* -------------------------------------------------------------------------- */
	#include <csignal>
	#include <iostream>
	#include <vector>

	#if (defined(READLINK_COMMAND) \|\| defined(ADDR2LINE_COMMAND)) && \
	(!defined(_WIN32))
	#include <execinfo.h>
	#include <sys/wait.h>
	#endif

	#include <chrono>
	#include <cmath>
	#include <cstring>
	#include <cxxabi.h>
	#include <fstream>
	#include <iomanip>
	#include <map>
	#include <sys/types.h>
	#include <unistd.h>

	#ifdef AKANTU_USE_MPI
	#include <mpi.h>
	#endif

	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace debug {

	// static void printBacktraceAndExit(int) { std::terminate(); }

	- // /* ------------------------------------------------------------------------ */
	- // void initSignalHandler() { std::signal(SIGSEGV, &printBacktraceAndExit); }
	+ // /* ------------------------------------------------------------------------
	+ // */ void initSignalHandler() { std::signal(SIGSEGV, &printBacktraceAndExit);
	+ // }

	/* ------------------------------------------------------------------------ */
	-std::string demangle(const char * symbol) {
	+ std::string demangle(const char * symbol) {
	int status;
	std::string result;
	char * demangled_name;

	if ((demangled_name = abi::__cxa_demangle(symbol, nullptr, nullptr,
	&status)) != nullptr) {
	result = demangled_name;
	free(demangled_name);
	} else {
	result = symbol;
	}

	return result;
	}

	/* ------------------------------------------------------------------------ */
	#if (defined(READLINK_COMMAND) \|\| defined(ADDR2LINK_COMMAND)) && \
	(!defined(_WIN32))
	std::string exec(const std::string & cmd) {
	FILE * pipe = popen(cmd.c_str(), "r");
	if (pipe == nullptr) {
	return "";
	}
	char buffer[1024];
	std::string result;
	while (feof(pipe) == 0) {
	if (fgets(buffer, 128, pipe) != nullptr) {
	result += buffer;
	}
	}

	result = result.substr(0, result.size() - 1);
	pclose(pipe);
	return result;
	}
	#endif

	auto getBacktrace() -> std::vector<std::string> {
	std::vector<std::string> backtrace_lines;
	#if not defined(_WIN32)
	#if defined(READLINK_COMMAND) && defined(ADDR2LINE_COMMAND)
	std::string me;
	char buf[1024];
	/* The manpage says it won't null terminate. Let's zero the buffer. */
	memset(buf, 0, sizeof(buf));
	/* Note we use sizeof(buf)-1 since we may need an extra char for NUL. */
	if (readlink("/proc/self/exe", buf, sizeof(buf) - 1) != 0) {
	me = std::string(buf);
	}

	std::ifstream inmaps;
	inmaps.open("/proc/self/maps");
	std::map<std::string, size_t> addr_map;
	std::string line;
	while (inmaps.good()) {
	std::getline(inmaps, line);
	std::stringstream sstr(line);

	size_t first = line.find('-');
	std::stringstream sstra(line.substr(0, first));
	size_t addr;
	sstra >> std::hex >> addr;

	std::string lib;
	sstr >> lib;
	sstr >> lib;
	sstr >> lib;
	sstr >> lib;
	sstr >> lib;
	sstr >> lib;
	if (not lib.empty() and (addr_map.find(lib) == addr_map.end())) {
	addr_map[lib] = addr;
	}
	}

	if (not me.empty()) {
	addr_map[me] = 0;
	}
	#endif

	/// \todo for windows this part could be coded using CaptureStackBackTrace
	/// and SymFromAddr
	const size_t max_depth = 100;
	size_t stack_depth;
	void * stack_addrs[max_depth];
	char ** stack_strings;

	size_t i;
	stack_depth = backtrace(stack_addrs, max_depth);
	stack_strings = backtrace_symbols(stack_addrs, stack_depth);

	/// -1 to remove the call to the printBacktrace function
	for (i = 1; i < stack_depth; i++) {
	std::string bt_line(stack_strings[i]);
	size_t first;
	size_t second;

	if ((first = bt_line.find('(')) != std::string::npos &&
	(second = bt_line.find('+')) != std::string::npos) {
	std::string location = bt_line.substr(0, first);
	#if defined(READLINK_COMMAND)
	std::string location_cmd =
	std::string(BOOST_PP_STRINGIZE(READLINK_COMMAND)) +
	- std::string(" -f ") + location;
	+ std::string(" -f ") + location;
	location = exec(location_cmd);
	#endif
	std::string call =
	demangle(bt_line.substr(first + 1, second - first - 1).c_str());
	size_t f = bt_line.find('[');
	size_t s = bt_line.find(']');
	std::string address = bt_line.substr(f + 1, s - f - 1);
	std::stringstream sstra(address);
	size_t addr;
	sstra >> std::hex >> addr;
	std::string trace = location + " [" + call + "]";
	#if defined(READLINK_COMMAND) && defined(ADDR2LINE_COMMAND)
	auto it = addr_map.find(location);
	if (it != addr_map.end()) {
	std::stringstream syscom;
	- syscom << BOOST_PP_STRINGIZE(ADDR2LINE_COMMAND) << " 0x" << std::hex
	- << (addr - it->second) << " -i -e " << location;
	+ syscom << BOOST_PP_STRINGIZE(ADDR2LINE_COMMAND)
	+ << " 0x" << std::hex
	+ << (addr - it->second) << " -i -e "
	+ << location;
	std::string line = exec(syscom.str());
	trace += " (" + line + ")";
	} else {
	#endif
	std::stringstream sstr_addr;
	sstr_addr << std::hex << addr;
	trace += " (0x" + sstr_addr.str() + ")";
	#if defined(READLINK_COMMAND) && defined(ADDR2LINE_COMMAND)
	}
	#endif
	backtrace_lines.push_back(trace);
	} else {
	backtrace_lines.push_back(bt_line);
	}
	}

	free(stack_strings);

	#endif
	return backtrace_lines;
	}
	/* ------------------------------------------------------------------------ */
	void printBacktrace(const std::vector<std::string> & backtrace) {
	auto w = size_t(std::floor(std::log10(double(backtrace.size()))) + 1);
	std::cerr << "BACKTRACE : " << backtrace.size() << " stack frames.\n";
	- for (auto && data : enumerate(backtrace))
	+ for (auto && data : enumerate(backtrace)) {
	std::cerr << " [" << std::setw(w) << (std::get<0>(data) + 1) << "] "
	<< std::get<1>(data) << "\n";
	+ }
	std::cerr << "END BACKTRACE" << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	namespace {
	void terminate_handler() {
	auto eptr = std::current_exception();
	- auto *t = abi::__cxa_current_exception_type();
	+ auto * t = abi::__cxa_current_exception_type();
	auto name = (t != nullptr) ? demangle(t->name()) : std::string("unknown");
	try {
	if (eptr) {
	std::rethrow_exception(eptr);
	} else {
	printBacktrace();
	std::cerr << AKANTU_LOCATION
	<< "!! Execution terminated for unknown reasons !!"
	<< std::endl;
	}
	} catch (Exception & e) {
	printBacktrace(e.backtrace());
	std::cerr << "!! Uncaught akantu::Exception of type " << name
	<< " !!\nwhat(): \"" << e.what() << "\"" << std::endl;
	} catch (std::exception & e) {
	std::cerr << "!! Uncaught exception of type " << name
	<< " !!\nwhat(): \"" << e.what() << "\"" << std::endl;
	} catch (...) {
	std::cerr << "!! Something strange of type \"" << name
	<< "\" was thrown.... !!" << std::endl;
	}

	if (debugger.printBacktrace()) {
	std::cerr << "Random generator seed: " << RandomGenerator<UInt>::seed()
	<< std::endl;
	printBacktrace();
	}
	}
	} // namespace

	/* ------------------------------------------------------------------------ */
	/* ------------------------------------------------------------------------ */
	Debugger::Debugger() noexcept {
	cout = &std::cerr;
	level = dblWarning;
	parallel_context = "";
	file_open = false;
	print_backtrace = false;

	- //initSignalHandler();
	+ // initSignalHandler();
	std::set_terminate(terminate_handler);
	}

	/* ------------------------------------------------------------------------ */
	Debugger::~Debugger() {
	if (file_open) {
	dynamic_cast<std::ofstream *>(cout)->close();
	delete cout;
	}
	}

	/* ------------------------------------------------------------------------ */
	void Debugger::exit(int status) {
	if (status != 0) {
	std::terminate();
	}

	std::exit(0);
	}

	/------------------------------------------------------------------------- /
	void Debugger::throwException(const std::string & info,
	const std::string & file, unsigned int line,
	__attribute__((unused)) bool silent,
	__attribute__((unused))
	const std::string & location,
	const std::string & module) const
	noexcept(false) {

	#if !defined(AKANTU_NDEBUG)
	if (not silent) {
	printMessage("###", dblWarning, info + " " + location, module);
	}
	#endif

	debug::Exception ex(info, file, line);
	ex.setModule(module);
	throw ex;
	}

	/* ------------------------------------------------------------------------ */
	void Debugger::printMessage(const std::string & prefix,
	const DebugLevel & level,
	const std::string & info,
	const std::string & module) const {
	if (testLevel(level, module)) {
	double timestamp =
	std::chrono::duration_cast<std::chrono::duration<double, std::micro>>(
	std::chrono::system_clock::now().time_since_epoch())
	.count();

	*(cout) << parallel_context << "{" << (size_t)timestamp << "} " << prefix
	<< " " << info << std::endl;
	}
	}

	/* ------------------------------------------------------------------------ */
	void Debugger::setDebugLevel(const DebugLevel & level) {
	this->level = level;
	}

	/* ------------------------------------------------------------------------ */
	const DebugLevel & Debugger::getDebugLevel() const { return this->level; }

	/* ------------------------------------------------------------------------ */
	void Debugger::setLogFile(const std::string & filename) {
	if (file_open) {
	dynamic_cast<std::ofstream *>(cout)->close();
	delete cout;
	}

	auto * fileout = new std::ofstream(filename.c_str());
	file_open = true;
	cout = fileout;
	}

	std::ostream & Debugger::getOutputStream() { return *cout; }

	/* ------------------------------------------------------------------------ */
	void Debugger::setParallelContext(int rank, int size) {
	std::stringstream sstr;
	UInt pad = std::ceil(std::log10(size));
	sstr << "<" << getpid() << ">[R" << std::setfill(' ') << std::right
	<< std::setw(pad) << rank << "\|S" << size << "] ";
	parallel_context = sstr.str();
	}

	void setDebugLevel(const DebugLevel & level) {
	debugger.setDebugLevel(level);
	}

	const DebugLevel & getDebugLevel() { return debugger.getDebugLevel(); }

	/* ------------------------------------------------------------------------ */
	void exit(int status) { Debugger::exit(status); }

	} // namespace debug
	} // namespace akantu
	diff --git a/src/common/aka_error.hh b/src/common/aka_error.hh
	index ef549d220..fd65dfacd 100644
	--- a/src/common/aka_error.hh
	+++ b/src/common/aka_error.hh
	@@ -1,422 +1,422 @@
	/**
	* @file aka_error.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Tue Feb 09 2021
	*
	* @brief error management and internal exceptions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <set>
	#include <sstream>
	#include <typeinfo>
	#include <utility>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_ERROR_HH_
	#define AKANTU_ERROR_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	enum DebugLevel {
	dbl0 = 0,
	dblError = 0,
	dblAssert = 0,
	dbl1 = 1,
	dblException = 1,
	dblCritical = 1,
	dbl2 = 2,
	dblMajor = 2,
	dbl3 = 3,
	dblCall = 3,
	dblSecondary = 3,
	dblHead = 3,
	dbl4 = 4,
	dblWarning = 4,
	dbl5 = 5,
	dblInfo = 5,
	dbl6 = 6,
	dblIn = 6,
	dblOut = 6,
	dbl7 = 7,
	dbl8 = 8,
	dblTrace = 8,
	dbl9 = 9,
	dblAccessory = 9,
	dbl10 = 10,
	dblDebug = 42,
	dbl100 = 100,
	dblDump = 100,
	dblTest = 1337
	};

	/* -------------------------------------------------------------------------- */
	#define AKANTU_LOCATION \
	"(" << std::string(__func__) << "(): " << std::string(__FILE__) << ":" \
	<< std::to_string(__LINE__) \
	<< ")" // NOLINT(cppcoreguidelines-pro-bounds-array-to-pointer-decay)

	/* -------------------------------------------------------------------------- */
	namespace debug {
	void setDebugLevel(const DebugLevel & level);
	const DebugLevel & getDebugLevel();

	void initSignalHandler();
	std::string demangle(const char * symbol);
	template <class T> std::string demangle() {
	return demangle(typeid(T).name());
	}

	template <class T> std::string demangle(const T & t) {
	return demangle(typeid(t).name());
	}

	auto exec(const std::string & cmd) -> std::string;
	auto getBacktrace() -> std::vector<std::string>;
	void
	printBacktrace(const std::vector<std::string> & backtrace = getBacktrace());

	void exit(int status) __attribute__((noreturn));
	/* ------------------------------------------------------------------------ */
	/// exception class that can be thrown by akantu
	class Exception : public std::exception {
	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	protected:
	explicit Exception(const std::string & info = "") : _info(info) {}

	public:
	//! full constructor
	Exception(const std::string & info, const std::string & file,
	unsigned int line)
	: _info(info), _file(file), _line(line) {}

	/* ---------------------------------------------------------------------- */
	/* Methods */
	/* ---------------------------------------------------------------------- */
	public:
	const char * what() const noexcept override { return _info.c_str(); }

	virtual std::string info() const noexcept {
	std::stringstream stream;
	stream << debug::demangle(typeid(*this).name()) << " : " << _info << " ["
	<< _file << ":" << _line << "]";
	return stream.str();
	}

	public:
	void setInfo(const std::string & info) { _info = info; }
	void setFile(const std::string & file) { _file = file; }
	void setLine(unsigned int line) { _line = line; }
	void setModule(const std::string & module) { _module = module; }

	void setBacktrace(const std::vector<std::string> & backtrace) {
	backtrace_ = backtrace;
	}

	decltype(auto) backtrace() const { return backtrace_; }
	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	protected:
	/// exception description and additionals
	std::string _info;

	private:
	/// file it is thrown from
	std::string _file;

	/// line it is thrown from
	unsigned int _line{0};

	/// module in which exception was raised
	std::string _module{"core"};

	std::vector<std::string> backtrace_;
	};

	class CriticalError : public Exception {};
	class AssertException : public Exception {};
	class NotImplementedException : public Exception {};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const Exception & _this) {
	stream << _this.what();
	return stream;
	}

	/* --------------------------------------------------------------------------
	*/
	class Debugger {
	public:
	Debugger() noexcept;
	virtual ~Debugger();
	Debugger(const Debugger &) = default;
	Debugger & operator=(const Debugger &) = default;
	Debugger(Debugger &&) noexcept = default;
	Debugger & operator=(Debugger &&) noexcept = default;

	static void exit(int status) __attribute__((noreturn));

	void throwException(const std::string & info, const std::string & file,
	unsigned int line, bool /silent/,
	const std::string & /location/,
	const std::string & module) const noexcept(false)
	__attribute__((noreturn));

	/----------------------------------------------------------------------- /
	template <class Except>
	void throwCustomException(Except ex, const std::string & info,
	const std::string & file, unsigned int line,
	const std::string & module) const noexcept(false)
	__attribute__((noreturn));
	/----------------------------------------------------------------------- /
	template <class Except>
	void throwCustomException(Except ex, const std::string & file,
	unsigned int line,
	const std::string & module_) const noexcept(false)
	__attribute__((noreturn));

	void printMessage(const std::string & prefix, const DebugLevel & level,
	const std::string & info,
	const std::string & module_) const;

	void setOutStream(std::ostream & out) { cout = &out; }
	std::ostream & getOutStream() { return *cout; }

	public:
	void setParallelContext(int rank, int size);

	void setDebugLevel(const DebugLevel & level);
	const DebugLevel & getDebugLevel() const;

	void setLogFile(const std::string & filename);
	std::ostream & getOutputStream();

	inline bool testLevel(const DebugLevel & level,
	const std::string & module = "core") const {
	auto level_reached = (this->level >= (level));
	auto correct_module =
	(level <= dblCritical) or (modules_to_debug.empty()) or
	(modules_to_debug.find(module) != modules_to_debug.end());
	return level_reached and correct_module;
	}

	void printBacktrace(bool on_off) { this->print_backtrace = on_off; }
	bool printBacktrace() const { return this->print_backtrace; }

	void addModuleToDebug(const std::string & id) {
	this->modules_to_debug.insert(id);
	}
	void removeModuleToDebug(const std::string & id) {
	auto it = this->modules_to_debug.find(id);
	if (it != this->modules_to_debug.end()) {
	this->modules_to_debug.erase(it);
	}
	}

	void listModules() {
	for (const auto & module_ : modules_to_debug) {
	(*cout) << module_ << std::endl;
	}
	}

	private:
	std::string parallel_context;
	std::ostream * cout;
	bool file_open;
	DebugLevel level;
	bool print_backtrace;
	std::set<std::string> modules_to_debug;
	};

	extern Debugger debugger; // NOLINT
	} // namespace debug

	/* -------------------------------------------------------------------------- */
	#define AKANTU_STRINGIZE_(str) #str
	#define AKANTU_STRINGIZE(str) AKANTU_STRINGIZE_(str)
	/* -------------------------------------------------------------------------- */
	#define AKANTU_DEBUG_MODULE AKANTU_STRINGIZE(AKANTU_MODULE)
	/* -------------------------------------------------------------------------- */
	#define AKANTU_STRINGSTREAM_IN(_str, _sstr) \
	; \
	do { \
	std::stringstream _dbg_s_info; \
	_dbg_s_info << _sstr; /* NOLINT */ \
	(_str) = _dbg_s_info.str(); \
	} while (false)

	/* -------------------------------------------------------------------------- */
	#define AKANTU_EXCEPTION(info) AKANTU_EXCEPTION_(info, false)

	#define AKANTU_SILENT_EXCEPTION(info) AKANTU_EXCEPTION_(info, true)

	#define AKANTU_EXCEPTION_(info, silent) \
	do { \
	std::stringstream _dbg_str; \
	_dbg_str << info; /* NOLINT */ \
	std::stringstream _dbg_loc; \
	_dbg_loc << AKANTU_LOCATION; \
	::akantu::debug::debugger.throwException(_dbg_str.str(), __FILE__, \
	__LINE__, silent, _dbg_loc.str(), \
	AKANTU_DEBUG_MODULE); \
	} while (false)

	#define AKANTU_CUSTOM_EXCEPTION_INFO(ex, info) \
	do { \
	std::stringstream _dbg_str; \
	_dbg_str << info; /* NOLINT */ \
	::akantu::debug::debugger.throwCustomException( \
	ex, _dbg_str.str(), __FILE__, __LINE__, AKANTU_DEBUG_MODULE); \
	} while (false)

	#define AKANTU_CUSTOM_EXCEPTION(ex) \
	do { \
	::akantu::debug::debugger.throwCustomException(ex, __FILE__, __LINE__, \
	AKANTU_DEBUG_MODULE); \
	} while (false)

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_NDEBUG
	#define AKANTU_DEBUG_TEST(level) (false)
	#define AKANTU_DEBUG_LEVEL_IS_TEST() \
	(::akantu::debug::debugger.testLevel(dblTest, AKANTU_DEBUG_MODULE))
	#define AKANTU_DEBUG(level, info)
	#define AKANTU_DEBUG_(pref, level, info)
	#define AKANTU_DEBUG_IN()
	#define AKANTU_DEBUG_OUT()
	#define AKANTU_DEBUG_INFO(info)
	#define AKANTU_DEBUG_WARNING(info)
	#define AKANTU_DEBUG_TRACE(info)
	#define AKANTU_DEBUG_ASSERT(test, info)
	#define AKANTU_ERROR(info) \
	AKANTU_CUSTOM_EXCEPTION_INFO(::akantu::debug::CriticalError(), info)
	/* -------------------------------------------------------------------------- */
	#else
	#define AKANTU_DEBUG(level, info) AKANTU_DEBUG_(" ", level, info)

	#define AKANTU_DEBUG_(pref, level, info) \
	do { \
	std::string _dbg_str; \
	AKANTU_STRINGSTREAM_IN(_dbg_str, \
	info << " " << AKANTU_LOCATION); /* NOLINT */ \
	::akantu::debug::debugger.printMessage(pref, level, _dbg_str, \
	AKANTU_DEBUG_MODULE); \
	} while (false)

	#define AKANTU_DEBUG_TEST(level) \
	(::akantu::debug::debugger.testLevel(level, AKANTU_DEBUG_MODULE))

	#define AKANTU_DEBUG_LEVEL_IS_TEST() \
	(::akantu::debug::debugger.testLevel(dblTest))

	#define AKANTU_DEBUG_IN() \
	AKANTU_DEBUG_( \
	"==>", ::akantu::dblIn, \
	__func__ \
	<< "()") // NOLINT(cppcoreguidelines-pro-bounds-array-to-pointer-decay,
	// bugprone-lambda-function-name)

	#define AKANTU_DEBUG_OUT() \
	AKANTU_DEBUG_( \
	"<==", ::akantu::dblOut, \
	__func__ \
	<< "()") // NOLINT(cppcoreguidelines-pro-bounds-array-to-pointer-decay,
	// bugprone-lambda-function-name)

	#define AKANTU_DEBUG_INFO(info) AKANTU_DEBUG_("---", ::akantu::dblInfo, info)

	#define AKANTU_DEBUG_WARNING(info) \
	AKANTU_DEBUG_("/!\\", ::akantu::dblWarning, info)

	#define AKANTU_DEBUG_TRACE(info) AKANTU_DEBUG_(">>>", ::akantu::dblTrace, info)

	#define AKANTU_DEBUG_ASSERT(test, info) \
	do { \
	if (not(test)) \
	AKANTU_CUSTOM_EXCEPTION_INFO(::akantu::debug::AssertException(), \
	"assert [" << #test << "] " \
	<< info); /* NOLINT */ \
	} while (false)

	#define AKANTU_ERROR(info) \
	do { \
	AKANTU_DEBUG_("!!! ", ::akantu::dblError, info); \
	AKANTU_CUSTOM_EXCEPTION_INFO(::akantu::debug::CriticalError(), \
	info); /* NOLINT */ \
	} while (false)
	#endif // AKANTU_NDEBUG

	#define AKANTU_TO_IMPLEMENT() \
	AKANTU_CUSTOM_EXCEPTION_INFO( \
	::akantu::debug::NotImplementedException(), \
	__func__ \
	<< " : not implemented yet !") // NOLINT(cppcoreguidelines-pro-bounds-array-to-pointer-decay,
	// bugprone-lambda-function-name)

	/* -------------------------------------------------------------------------- */

	namespace debug {
	/* ------------------------------------------------------------------------ */
	template <class Except>
	void Debugger::throwCustomException(Except ex, const std::string & info,
	const std::string & file,
	unsigned int line,
	const std::string & module_) const
	noexcept(false) {
	ex.setInfo(info);
	ex.setFile(file);
	ex.setLine(line);
	ex.setModule(module_);
	if (::akantu::debug::debugger.printBacktrace()) {
	ex.setBacktrace(::akantu::debug::getBacktrace());
	}
	throw ex;
	}
	/* ------------------------------------------------------------------------ */
	template <class Except>
	void Debugger::throwCustomException(Except ex, const std::string & file,
	unsigned int line,
	const std::string & module_) const
	noexcept(false) {
	ex.setFile(file);
	ex.setLine(line);
	ex.setModule(module_);
	if (::akantu::debug::debugger.printBacktrace()) {
	ex.setBacktrace(::akantu::debug::getBacktrace());
	}
	throw ex;
	}
	} // namespace debug
	} // namespace akantu

	#endif /* AKANTU_ERROR_HH_ */
	diff --git a/src/common/aka_event_handler_manager.hh b/src/common/aka_event_handler_manager.hh
	index 5cd7afee3..453353665 100644
	--- a/src/common/aka_event_handler_manager.hh
	+++ b/src/common/aka_event_handler_manager.hh
	@@ -1,128 +1,128 @@
	/**
	* @file aka_event_handler_manager.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Feb 09 2021
	*
	* @brief Base of Event Handler classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_EVENT_HANDLER_MANAGER_HH_
	#define AKANTU_AKA_EVENT_HANDLER_MANAGER_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <list>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <class EventHandler> class EventHandlerManager {
	private:
	using priority_value = std::pair<EventHandlerPriority, EventHandler *>;
	using priority_list = std::list<priority_value>;
	struct KeyComp {
	bool operator()(const priority_value & a, const priority_value & b) const {
	return (a.first < b.first);
	}
	bool operator()(const priority_value & a, UInt b) const {
	return (a.first < b);
	}
	};

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	virtual ~EventHandlerManager() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register a new EventHandler to the Manager. The register object
	/// will then be informed about the events the manager observes.
	void registerEventHandler(EventHandler & event_handler,
	EventHandlerPriority priority = _ehp_highest) {
	auto it = this->searchEventHandler(event_handler);

	if (it != this->event_handlers.end()) {
	AKANTU_EXCEPTION("This event handler was already registered (priority: "
	<< priority << ")");
	}

	auto pos =
	std::lower_bound(this->event_handlers.begin(),
	this->event_handlers.end(), priority, KeyComp());

	this->event_handlers.insert(pos, std::make_pair(priority, &event_handler));
	}

	/// unregister a EventHandler object. This object will not be
	/// notified anymore about the events this manager observes.
	void unregisterEventHandler(EventHandler & event_handler) {
	auto it = this->searchEventHandler(event_handler);

	if (it == this->event_handlers.end()) {
	AKANTU_EXCEPTION("This event handler is not registered");
	}

	this->event_handlers.erase(it);
	}

	/// Notify all the registered EventHandlers about the event that just occured.
	template <class Event> void sendEvent(const Event & event) {
	for (auto & pair : this->event_handlers) {
	pair.second->sendEvent(event);
	}
	}

	private:
	typename priority_list::iterator searchEventHandler(EventHandler & handler) {
	auto it = this->event_handlers.begin();
	auto end = this->event_handlers.end();

	for (; it != end && it->second != &handler; ++it) {
	;
	}

	return it;
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// list of the event handlers
	priority_list event_handlers;
	};

	} // namespace akantu

	#endif /* AKANTU_AKA_EVENT_HANDLER_MANAGER_HH_ */
	diff --git a/src/common/aka_extern.cc b/src/common/aka_extern.cc
	index cc58e8651..f1b930ddc 100644
	--- a/src/common/aka_extern.cc
	+++ b/src/common/aka_extern.cc
	@@ -1,98 +1,98 @@
	/**
	* @file aka_extern.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Tue Oct 27 2020
	*
	* @brief initialisation of all global variables
	* to insure the order of creation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "aka_math.hh"
	#include "aka_named_argument.hh"
	#include "aka_random_generator.hh"
	#include "communication_tag.hh"
	#include "cppargparse.hh"
	#include "parser.hh"
	#include "solid_mechanics_model.hh"
	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "solid_mechanics_model_cohesive.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	#include <limits>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* error.hpp variables */
	/* -------------------------------------------------------------------------- */
	namespace debug {
	/** \todo write function to get this
	* values from the environment or a config file
	*/
	/// standard output for debug messages
	std::ostream * _akantu_debug_cout = &std::cerr;

	/// standard output for normal messages
	std::ostream & _akantu_cout = std::cout;

	/// parallel context used in debug messages
	std::string _parallel_context;

	Debugger debugger;

	} // namespace debug

	/* -------------------------------------------------------------------------- */
	/// Paser for commandline arguments
	::cppargparse::ArgumentParser static_argparser;

	/// Parser containing the information parsed by the input file given to initFull
	Parser static_parser;

	bool Parser::permissive_parser = false;

	/* -------------------------------------------------------------------------- */
	Real Math::tolerance = 1e2 * std::numeric_limits<Real>::epsilon();

	/* -------------------------------------------------------------------------- */
	const UInt _all_dimensions [[gnu::unused]] = UInt(-1);

	/* -------------------------------------------------------------------------- */
	const Array<UInt> empty_filter(0, 1, "empty_filter");

	/* -------------------------------------------------------------------------- */
	template <> long int RandomGenerator<UInt>::_seed = 5489U;
	template <> std::default_random_engine RandomGenerator<UInt>::generator(5489U);
	/* -------------------------------------------------------------------------- */
	int Tag::max_tag = 0;

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/common/aka_factory.hh b/src/common/aka_factory.hh
	index 90fe7e603..0fe6eda3c 100644
	--- a/src/common/aka_factory.hh
	+++ b/src/common/aka_factory.hh
	@@ -1,97 +1,97 @@
	/**
	* @file aka_factory.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jul 09 2017
	* @date last modification: Tue Mar 30 2021
	*
	* @brief This is a generic factory
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	#include <map>
	#include <memory>
	#include <string>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_FACTORY_HH_
	#define AKANTU_AKA_FACTORY_HH_

	namespace akantu {

	template <class Base, class T = ID, class... Args> class Factory {
	using allocator_t = std::function<std::unique_ptr<Base>(Args...)>;

	private:
	Factory() = default;

	public:
	Factory(const Factory &) = delete;
	Factory & operator=(const Factory &) = delete;

	static Factory & getInstance() {
	static Factory instance;
	return instance;
	}
	/* ------------------------------------------------------------------------ */
	bool registerAllocator(const T & id, const allocator_t & allocator) {
	if (allocators.find(id) != allocators.end()) {
	- AKANTU_EXCEPTION("The id \"" << id
	- << "\" is already registered in the "
	- << debug::demangle(typeid(Base).name()) << " factory");
	+ AKANTU_EXCEPTION("The id \"" << id << "\" is already registered in the "
	+ << debug::demangle(typeid(Base).name())
	+ << " factory");
	}
	allocators[id] = allocator;
	return true;
	}

	template <typename... AArgs>
	std::unique_ptr<Base> allocate(const T & id, AArgs &&... args) const {
	if (allocators.find(id) == allocators.end()) {
	- AKANTU_EXCEPTION("The id \"" << id
	- << "\" is not registered in the "
	- << debug::demangle(typeid(Base).name()) << " factory.");
	+ AKANTU_EXCEPTION("The id \"" << id << "\" is not registered in the "
	+ << debug::demangle(typeid(Base).name())
	+ << " factory.");
	}
	return std::forward<std::unique_ptr<Base>>(
	allocators.at(id)(std::forward<AArgs>(args)...));
	}

	std::vector<T> getPossibleAllocators() {
	std::vector<T> keys;
	for (auto & e : allocators) {
	keys.push_back(e.first);
	}
	return keys;
	}

	private:
	std::map<T, allocator_t> allocators;
	};

	} // namespace akantu

	#endif /* AKANTU_AKA_FACTORY_HH_ */
	diff --git a/src/common/aka_fwd.hh b/src/common/aka_fwd.hh
	index fe3a78fdd..d4b7ba9a6 100644
	--- a/src/common/aka_fwd.hh
	+++ b/src/common/aka_fwd.hh
	@@ -1,73 +1,73 @@
	/**
	* @file aka_fwd.hh
	*
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Tue Sep 29 2020
	*
	* @brief File containing forward declarations in akantu.
	* This file helps if circular #include would be needed because two classes
	* refer both to each other. This file usually does not need any modification.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_FWD_HH_
	#define AKANTU_FWD_HH_

	namespace cppargparse {
	class ArgumentParser;
	}

	namespace akantu {
	// forward declaration
	template <int dim, class model_type> struct ContactData;

	template <typename T> class Matrix;
	template <typename T> class Vector;
	template <typename T> class Tensor3;

	template <typename T, bool is_scal = aka::is_scalar<T>::value> class Array;
	template <typename T, typename SupportType = ElementType>
	class ElementTypeMapArray;

	template <class T> class SpatialGrid;

	// Model element
	template <class ModelPolicy> class ModelElement;

	extern const Array<UInt> empty_filter;

	class Parser;
	class ParserSection;

	extern Parser static_parser; // NOLINT

	extern cppargparse::ArgumentParser static_argparser; // NOLINT

	class Mesh;
	class SparseMatrix;
	} // namespace akantu

	#endif /* AKANTU_FWD_HH_ */
	diff --git a/src/common/aka_grid_dynamic.hh b/src/common/aka_grid_dynamic.hh
	index 316f49f19..c0386aa45 100644
	--- a/src/common/aka_grid_dynamic.hh
	+++ b/src/common/aka_grid_dynamic.hh
	@@ -1,533 +1,532 @@
	/**
	* @file aka_grid_dynamic.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue Feb 09 2021
	*
	* @brief Grid that is auto balanced
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "aka_types.hh"
	#include "mesh_accessor.hh"

	#include <iostream>

	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_GRID_DYNAMIC_HH_
	#define AKANTU_AKA_GRID_DYNAMIC_HH_

	namespace akantu {

	class Mesh;

	template <typename T> class SpatialGrid {
	public:
	explicit SpatialGrid(UInt dimension)
	: dimension(dimension), spacing(dimension), center(dimension),
	lower(dimension), upper(dimension), empty_cell() {}

	SpatialGrid(UInt dimension, const Vector<Real> & spacing,
	const Vector<Real> & center)
	: dimension(dimension), spacing(spacing), center(center),
	lower(dimension), upper(dimension), empty_cell() {
	for (UInt i = 0; i < dimension; ++i) {
	lower(i) = std::numeric_limits<Real>::max();
	upper(i) = -std::numeric_limits<Real>::max();
	}
	}

	virtual ~SpatialGrid() = default;

	class neighbor_cells_iterator;
	class cells_iterator;

	class CellID {
	public:
	CellID() = default;
	explicit CellID(UInt dimention) : ids(dimention) {}
	void setID(UInt dir, Int id) { ids(dir) = id; }
	Int getID(UInt dir) const { return ids(dir); }

	bool operator<(const CellID & id) const {
	return std::lexicographical_compare(
	ids.storage(), ids.storage() + ids.size(), id.ids.storage(),
	id.ids.storage() + id.ids.size());
	}

	bool operator==(const CellID & id) const {
	return std::equal(ids.storage(), ids.storage() + ids.size(),
	id.ids.storage());
	}

	bool operator!=(const CellID & id) const { return !(operator==(id)); }

	class neighbor_cells_iterator
	: private std::iterator<std::forward_iterator_tag, UInt> {
	public:
	neighbor_cells_iterator(const CellID & cell_id, bool end)
	: cell_id(cell_id), position(cell_id.ids.size(), end ? 1 : -1) {

	this->updateIt();
	if (end) {
	this->it++;
	}
	}

	neighbor_cells_iterator & operator++() {
	UInt i = 0;
	for (; i < position.size() && position(i) == 1; ++i) {
	;
	}

	if (i == position.size()) {
	++it;
	return *this;
	}

	for (UInt j = 0; j < i; ++j) {
	position(j) = -1;
	}
	position(i)++;
	updateIt();

	return *this;
	}

	neighbor_cells_iterator operator++(int) {
	neighbor_cells_iterator tmp(*this);
	operator++();
	return tmp;
	};

	bool operator==(const neighbor_cells_iterator & rhs) const {
	return cell_id == rhs.cell_id && it == rhs.it;
	};
	bool operator!=(const neighbor_cells_iterator & rhs) const {
	return !operator==(rhs);
	};

	CellID operator*() const {
	CellID cur_cell_id(cell_id);
	cur_cell_id.ids += position;
	return cur_cell_id;
	};

	private:
	void updateIt() {
	it = 0;
	for (UInt i = 0; i < position.size(); ++i) {
	it = it * 3 + (position(i) + 1);
	}
	}

	private:
	/// central cell id
	const CellID & cell_id;
	// number representing the current neighbor in base 3;
	UInt it;
	// current cell shift
	Vector<Int> position;
	};

	class Neighbors {
	public:
	explicit Neighbors(const CellID & cell_id) : cell_id(cell_id) {}
	decltype(auto) begin() { return neighbor_cells_iterator(cell_id, false); }
	decltype(auto) end() { return neighbor_cells_iterator(cell_id, true); }

	private:
	const CellID & cell_id;
	};

	decltype(auto) neighbors() { return Neighbors(*this); }

	private:
	friend class cells_iterator;
	Vector<Int> ids;
	};

	/* ------------------------------------------------------------------------ */
	class Cell {
	public:
	using iterator = typename std::vector<T>::iterator;
	using const_iterator = typename std::vector<T>::const_iterator;

	Cell() : id(), data() {}

	explicit Cell(const CellID & cell_id) : id(cell_id), data() {}

	bool operator==(const Cell & cell) const { return id == cell.id; }
	bool operator!=(const Cell & cell) const { return id != cell.id; }

	Cell & add(const T & d) {
	data.push_back(d);
	return *this;
	}

	iterator begin() { return data.begin(); }
	const_iterator begin() const { return data.begin(); }

	iterator end() { return data.end(); }
	const_iterator end() const { return data.end(); }

	private:
	CellID id;
	std::vector<T> data;
	};

	private:
	using cells_container = std::map<CellID, Cell>;

	public:
	const Cell & getCell(const CellID & cell_id) const {
	auto it = cells.find(cell_id);
	if (it != cells.end()) {
	return it->second;
	}
	return empty_cell;
	}

	decltype(auto) beginCell(const CellID & cell_id) {
	auto it = cells.find(cell_id);
	if (it != cells.end()) {
	return it->second.begin();
	}
	return empty_cell.begin();
	}

	decltype(auto) endCell(const CellID & cell_id) {
	auto it = cells.find(cell_id);
	if (it != cells.end()) {
	return it->second.end();
	}
	return empty_cell.end();
	}

	decltype(auto) beginCell(const CellID & cell_id) const {
	auto it = cells.find(cell_id);
	if (it != cells.end()) {
	return it->second.begin();
	}
	return empty_cell.begin();
	}

	decltype(auto) endCell(const CellID & cell_id) const {
	auto it = cells.find(cell_id);
	if (it != cells.end()) {
	return it->second.end();
	}
	return empty_cell.end();
	}

	/* ------------------------------------------------------------------------ */
	class cells_iterator
	: private std::iterator<std::forward_iterator_tag, CellID> {
	public:
	explicit cells_iterator(typename std::map<CellID, Cell>::const_iterator it)
	: it(it) {}

	cells_iterator & operator++() {
	this->it++;
	return *this;
	}

	cells_iterator operator++(int /unused/) {
	cells_iterator tmp(*this);
	operator++();
	return tmp;
	};

	bool operator==(const cells_iterator & rhs) const { return it == rhs.it; };
	bool operator!=(const cells_iterator & rhs) const {
	return !operator==(rhs);
	};

	CellID operator*() const {
	CellID cur_cell_id(this->it->first);
	return cur_cell_id;
	};

	private:
	/// map iterator
	typename std::map<CellID, Cell>::const_iterator it;
	};

	public:
	template <class vector_type>
	Cell & insert(const T & d, const vector_type & position) {
	auto && cell_id = getCellID(position);
	auto && it = cells.find(cell_id);
	if (it == cells.end()) {
	Cell cell(cell_id);
	auto & tmp = (cells[cell_id] = cell).add(d);

	for (UInt i = 0; i < dimension; ++i) {
	Real posl = center(i) + cell_id.getID(i) * spacing(i);
	Real posu = posl + spacing(i);
	if (posl <= lower(i)) {
	lower(i) = posl;
	}
	if (posu > upper(i)) {
	upper(i) = posu;
	}
	}
	return tmp;
	}
	return it->second.add(d);
	}

	/* ------------------------------------------------------------------------ */
	inline decltype(auto) begin() const {
	auto begin = this->cells.begin();
	return cells_iterator(begin);
	}

	inline decltype(auto) end() const {
	auto end = this->cells.end();
	return cells_iterator(end);
	}

	template <class vector_type>
	CellID getCellID(const vector_type & position) const {
	CellID cell_id(dimension);
	for (UInt i = 0; i < dimension; ++i) {
	cell_id.setID(i, getCellID(position(i), i));
	}
	return cell_id;
	}

	void printself(std::ostream & stream, int indent = 0) const {
	std::string space(indent, AKANTU_INDENT);

	std::streamsize prec = stream.precision();
	std::ios_base::fmtflags ff = stream.flags();

	stream.setf(std::ios_base::showbase);
	stream.precision(5);

	stream << space << "SpatialGrid<" << debug::demangle(typeid(T).name())
	<< "> [" << std::endl;
	stream << space << " + dimension : " << this->dimension << std::endl;
	stream << space << " + lower bounds : {";
	for (UInt i = 0; i < lower.size(); ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << lower(i);
	};
	stream << "}" << std::endl;
	stream << space << " + upper bounds : {";
	for (UInt i = 0; i < upper.size(); ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << upper(i);
	};
	stream << "}" << std::endl;
	stream << space << " + spacing : {";
	for (UInt i = 0; i < spacing.size(); ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << spacing(i);
	};
	stream << "}" << std::endl;
	stream << space << " + center : {";
	for (UInt i = 0; i < center.size(); ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << center(i);
	};
	stream << "}" << std::endl;

	stream << space << " + nb_cells : " << this->cells.size() << "/";
	Vector<Real> dist(this->dimension);
	dist = upper;
	dist -= lower;
	for (UInt i = 0; i < this->dimension; ++i) {
	dist(i) /= spacing(i);
	}
	UInt nb_cells = std::ceil(dist(0));
	for (UInt i = 1; i < this->dimension; ++i) {
	nb_cells *= std::ceil(dist(i));
	}
	stream << nb_cells << std::endl;
	stream << space << "]" << std::endl;

	stream.precision(prec);
	stream.flags(ff);
	}

	void saveAsMesh(Mesh & mesh) const;

	private:
	/* --------------------------------------------------------------------------
	*/
	inline UInt getCellID(Real position, UInt direction) const {
	AKANTU_DEBUG_ASSERT(direction < center.size(), "The direction asked ("
	<< direction
	<< ") is out of range "
	<< center.size());
	Real dist_center = position - center(direction);
	Int id = std::floor(dist_center / spacing(direction));
	// if(dist_center < 0) id--;
	return id;
	}

	friend class GridSynchronizer;

	public:
	AKANTU_GET_MACRO(LowerBounds, lower, const Vector<Real> &);
	AKANTU_GET_MACRO(UpperBounds, upper, const Vector<Real> &);
	AKANTU_GET_MACRO(Spacing, spacing, const Vector<Real> &);
	AKANTU_SET_MACRO(Spacing, spacing, Vector<Real> &);
	AKANTU_GET_MACRO(Center, center, const Vector<Real> &);
	AKANTU_SET_MACRO(Center, center, Vector<Real> &);

	-
	protected:
	UInt dimension;

	cells_container cells;

	Vector<Real> spacing;
	Vector<Real> center;

	Vector<Real> lower;
	Vector<Real> upper;

	Cell empty_cell;
	};

	/// standard output stream operator
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const SpatialGrid<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu
	#include "mesh.hh"
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T> void SpatialGrid<T>::saveAsMesh(Mesh & mesh) const {

	ElementType type = _not_defined;
	switch (dimension) {
	case 1:
	type = _segment_2;
	break;
	case 2:
	type = _quadrangle_4;
	break;
	case 3:
	type = _hexahedron_8;
	break;
	}

	MeshAccessor mesh_accessor(mesh);
	auto & connectivity = mesh_accessor.getConnectivity(type);
	auto & nodes = mesh_accessor.getNodes();
	auto & uint_data = mesh.getDataPointer<UInt>("tag_1", type);

	Vector<Real> pos(dimension);

	UInt global_id = 0;
	for (auto & cell_pair : cells) {
	UInt cur_node = nodes.size();
	UInt cur_elem = connectivity.size();
	const CellID & cell_id = cell_pair.first;

	for (UInt i = 0; i < dimension; ++i) {
	pos(i) = center(i) + cell_id.getID(i) * spacing(i);
	}
	nodes.push_back(pos);
	for (UInt i = 0; i < dimension; ++i) {
	pos(i) += spacing(i);
	}
	nodes.push_back(pos);

	connectivity.push_back(cur_node);
	switch (dimension) {
	case 1:
	connectivity(cur_elem, 1) = cur_node + 1;
	break;
	case 2:
	pos(0) -= spacing(0);
	nodes.push_back(pos);
	pos(0) += spacing(0);
	pos(1) -= spacing(1);
	nodes.push_back(pos);
	connectivity(cur_elem, 1) = cur_node + 3;
	connectivity(cur_elem, 2) = cur_node + 1;
	connectivity(cur_elem, 3) = cur_node + 2;
	break;
	case 3:
	pos(1) -= spacing(1);
	pos(2) -= spacing(2);
	nodes.push_back(pos);
	pos(1) += spacing(1);
	nodes.push_back(pos);
	pos(0) -= spacing(0);
	nodes.push_back(pos);

	pos(1) -= spacing(1);
	pos(2) += spacing(2);
	nodes.push_back(pos);
	pos(0) += spacing(0);
	nodes.push_back(pos);
	pos(0) -= spacing(0);
	pos(1) += spacing(1);
	nodes.push_back(pos);

	connectivity(cur_elem, 1) = cur_node + 2;
	connectivity(cur_elem, 2) = cur_node + 3;
	connectivity(cur_elem, 3) = cur_node + 4;
	connectivity(cur_elem, 4) = cur_node + 5;
	connectivity(cur_elem, 5) = cur_node + 6;
	connectivity(cur_elem, 6) = cur_node + 1;
	connectivity(cur_elem, 7) = cur_node + 7;
	break;
	}
	uint_data.push_back(global_id);

	++global_id;
	}
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_GRID_DYNAMIC_HH_ */
	diff --git a/src/common/aka_math.cc b/src/common/aka_math.cc
	index 9a997f3cd..0d356c30d 100644
	--- a/src/common/aka_math.cc
	+++ b/src/common/aka_math.cc
	@@ -1,271 +1,271 @@
	/**
	* @file aka_math.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Implementation of the math toolbox
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_math.hh"
	#include "aka_array.hh"
	#include "aka_iterators.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace Math {
	/* --------------------------------------------------------------------------
	*/
	void matrix_vector(UInt m, UInt n, const Array<Real> & A,
	const Array<Real> & x, Array<Real> & y, Real alpha) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(A.size() == x.size(),
	"The vector A(" << A.getID() << ") and the vector x("
	<< x.getID()
	<< ") must have the same size");

	AKANTU_DEBUG_ASSERT(
	A.getNbComponent() == m * n,
	"The vector A(" << A.getID() << ") has the good number of component.");

	AKANTU_DEBUG_ASSERT(x.getNbComponent() == n,
	"The vector x("
	<< x.getID()
	<< ") do not the good number of component.");

	AKANTU_DEBUG_ASSERT(y.getNbComponent() == n,
	"The vector y("
	<< y.getID()
	<< ") do not the good number of component.");

	UInt nb_element = A.size();
	UInt offset_A = A.getNbComponent();
	UInt offset_x = x.getNbComponent();

	y.resize(nb_element);

	Real * A_val = A.storage();
	Real * x_val = x.storage();
	Real * y_val = y.storage();

	for (UInt el = 0; el < nb_element; ++el) {
	matrix_vector(m, n, A_val, x_val, y_val, alpha);

	A_val += offset_A;
	x_val += offset_x;
	y_val += offset_x;
	}

	AKANTU_DEBUG_OUT();
	}

	/* --------------------------------------------------------------------------
	*/
	void matrix_matrix(UInt m, UInt n, UInt k, const Array<Real> & A,
	const Array<Real> & B, Array<Real> & C, Real alpha) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(A.size() == B.size(),
	"The vector A(" << A.getID() << ") and the vector B("
	<< B.getID()
	<< ") must have the same size");

	AKANTU_DEBUG_ASSERT(
	A.getNbComponent() == m * k,
	"The vector A(" << A.getID() << ") has the good number of component.");

	AKANTU_DEBUG_ASSERT(B.getNbComponent() == k * n,
	"The vector B("
	<< B.getID()
	<< ") do not the good number of component.");

	AKANTU_DEBUG_ASSERT(C.getNbComponent() == m * n,
	"The vector C("
	<< C.getID()
	<< ") do not the good number of component.");

	UInt nb_element = A.size();
	UInt offset_A = A.getNbComponent();
	UInt offset_B = B.getNbComponent();
	UInt offset_C = C.getNbComponent();

	C.resize(nb_element);

	Real * A_val = A.storage();
	Real * B_val = B.storage();
	Real * C_val = C.storage();

	for (UInt el = 0; el < nb_element; ++el) {
	matrix_matrix(m, n, k, A_val, B_val, C_val, alpha);

	A_val += offset_A;
	B_val += offset_B;
	C_val += offset_C;
	}

	AKANTU_DEBUG_OUT();
	}

	/* --------------------------------------------------------------------------
	*/
	void matrix_matrixt(UInt m, UInt n, UInt k, const Array<Real> & A,
	const Array<Real> & B, Array<Real> & C, Real alpha) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(A.size() == B.size(),
	"The vector A(" << A.getID() << ") and the vector B("
	<< B.getID()
	<< ") must have the same size");

	AKANTU_DEBUG_ASSERT(
	A.getNbComponent() == m * k,
	"The vector A(" << A.getID() << ") has the good number of component.");

	AKANTU_DEBUG_ASSERT(B.getNbComponent() == k * n,
	"The vector B("
	<< B.getID()
	<< ") do not the good number of component.");

	AKANTU_DEBUG_ASSERT(C.getNbComponent() == m * n,
	"The vector C("
	<< C.getID()
	<< ") do not the good number of component.");

	UInt nb_element = A.size();
	UInt offset_A = A.getNbComponent();
	UInt offset_B = B.getNbComponent();
	UInt offset_C = C.getNbComponent();

	C.resize(nb_element);

	Real * A_val = A.storage();
	Real * B_val = B.storage();
	Real * C_val = C.storage();

	for (UInt el = 0; el < nb_element; ++el) {
	matrix_matrixt(m, n, k, A_val, B_val, C_val, alpha);

	A_val += offset_A;
	B_val += offset_B;
	C_val += offset_C;
	}

	AKANTU_DEBUG_OUT();
	}

	/* --------------------------------------------------------------------------
	*/
	void compute_tangents(const Array<Real> & normals, Array<Real> & tangents) {
	AKANTU_DEBUG_IN();

	if (normals.empty()) {
	return;
	}

	auto spatial_dimension = normals.getNbComponent();
	auto tangent_components = spatial_dimension * (spatial_dimension - 1);

	if (tangent_components == 0) {
	return;
	}

	AKANTU_DEBUG_ASSERT(
	tangent_components == tangents.getNbComponent(),
	"Cannot compute the tangents, the storage array for tangents"
	<< " does not have the good amount of components.");

	auto nb_normals = normals.size();
	tangents.resize(nb_normals);
	tangents.zero();

	/// compute first tangent
	for (auto && data : zip(make_view(normals, spatial_dimension),
	make_view(tangents, tangent_components))) {
	const auto & normal = std::get<0>(data);
	auto & tangent = std::get<1>(data);

	if (are_float_equal(norm2(normal.storage()), 0.)) {
	tangent(0) = 1.;
	} else {
	normal2(normal.storage(), tangent.storage());
	}
	}

	/// compute second tangent (3D case)
	if (spatial_dimension == 3) {
	for (auto && data : zip(make_view(normals, spatial_dimension),
	make_view(tangents, tangent_components))) {
	const auto & normal = std::get<0>(data);
	auto & tangent = std::get<1>(data);

	normal3(normal.storage(), tangent.storage(),
	tangent.storage() + spatial_dimension);
	}
	}

	AKANTU_DEBUG_OUT();
	} // namespace akantu

	/* --------------------------------------------------------------------------
	*/
	Real reduce(Array<Real> & array) {
	UInt nb_values = array.size();
	if (nb_values == 0) {
	return 0.;
	}

	UInt nb_values_to_sum = nb_values >> 1;

	std::sort(array.begin(), array.end());

	// as long as the half is not empty
	while (nb_values_to_sum != 0U) {
	UInt remaining = (nb_values - 2 * nb_values_to_sum);
	if (remaining != 0U) {
	array(nb_values - 2) += array(nb_values - 1);
	}

	// sum to consecutive values and store the sum in the first half
	for (UInt i = 0; i < nb_values_to_sum; ++i) {
	array(i) = array(2 * i) + array(2 * i + 1);
	}

	nb_values = nb_values_to_sum;
	nb_values_to_sum >>= 1;
	}

	return array(0);
	}

	} // namespace Math
	} // namespace akantu
	diff --git a/src/common/aka_math.hh b/src/common/aka_math.hh
	index 62eb756f4..5e399db67 100644
	--- a/src/common/aka_math.hh
	+++ b/src/common/aka_math.hh
	@@ -1,287 +1,287 @@
	/**
	* @file aka_math.hh
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Tue Feb 09 2021
	*
	* @brief mathematical operations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <utility>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_MATH_H_
	#define AKANTU_AKA_MATH_H_

	namespace akantu {
	/* -------------------------------------------------------------------------- */

	namespace Math {
	/// tolerance for functions that need one
	extern Real tolerance; // NOLINT

	/* ------------------------------------------------------------------------ */
	/* Matrix algebra */
	/* ------------------------------------------------------------------------ */
	/// @f$ y = A*x @f$
	void matrix_vector(UInt m, UInt n, const Array<Real> & A,
	const Array<Real> & x, Array<Real> & y, Real alpha = 1.);

	/// @f$ y = A*x @f$
	inline void matrix_vector(UInt m, UInt n, Real * A, Real * x, Real * y,
	Real alpha = 1.);

	/// @f$ y = A^t*x @f$
	inline void matrixt_vector(UInt m, UInt n, Real * A, Real * x, Real * y,
	Real alpha = 1.);

	/// @f$ C = A*B @f$
	void matrix_matrix(UInt m, UInt n, UInt k, const Array<Real> & A,
	const Array<Real> & B, Array<Real> & C, Real alpha = 1.);

	/// @f$ C = A*B^t @f$
	void matrix_matrixt(UInt m, UInt n, UInt k, const Array<Real> & A,
	const Array<Real> & B, Array<Real> & C, Real alpha = 1.);

	/// @f$ C = A*B @f$
	inline void matrix_matrix(UInt m, UInt n, UInt k, Real * A, Real * B,
	Real * C, Real alpha = 1.);

	/// @f$ C = A^t*B @f$
	inline void matrixt_matrix(UInt m, UInt n, UInt k, Real * A, Real * B,
	Real * C, Real alpha = 1.);

	/// @f$ C = A*B^t @f$
	inline void matrix_matrixt(UInt m, UInt n, UInt k, Real * A, Real * B,
	Real * C, Real alpha = 1.);

	/// @f$ C = A^t*B^t @f$
	inline void matrixt_matrixt(UInt m, UInt n, UInt k, Real * A, Real * B,
	Real * C, Real alpha = 1.);

	template <bool tr_A, bool tr_B>
	inline void matMul(UInt m, UInt n, UInt k, Real alpha, Real * A, Real * B,
	Real beta, Real * C);

	template <bool tr_A>
	inline void matVectMul(UInt m, UInt n, Real alpha, Real * A, Real * x,
	Real beta, Real * y);

	inline void aXplusY(UInt n, Real alpha, Real * x, Real * y);

	inline void matrix33_eigenvalues(Real * A, Real * Adiag);

	inline void matrix22_eigenvalues(Real * A, Real * Adiag);
	template <UInt dim> inline void eigenvalues(Real * A, Real * d);

	/// solve @f$ A x = \Lambda x @f$ and return d and V such as @f$ A V[i:] =
	/// d[i] V[i:]@f$
	template <typename T> void matrixEig(UInt n, T * A, T * d, T * V = nullptr);

	/// determinent of a 2x2 matrix
	Real det2(const Real * mat);
	/// determinent of a 3x3 matrix
	Real det3(const Real * mat);
	/// determinent of a nxn matrix
	template <UInt n> Real det(const Real * mat);
	/// determinent of a nxn matrix
	template <typename T> T det(UInt n, const T * A);

	/// inverse a nxn matrix
	template <UInt n> inline void inv(const Real * A, Real * inv);
	/// inverse a nxn matrix
	template <typename T> inline void inv(UInt n, const T * A, T * inv);
	/// inverse a 3x3 matrix
	inline void inv3(const Real * mat, Real * inv);
	/// inverse a 2x2 matrix
	inline void inv2(const Real * mat, Real * inv);

	/// solve A x = b using a LU factorization
	template <typename T>
	inline void solve(UInt n, const T * A, T * x, const T * b);

	/// return the double dot product between 2 tensors in 2d
	inline Real matrixDoubleDot22(Real * A, Real * B);

	/// return the double dot product between 2 tensors in 3d
	inline Real matrixDoubleDot33(Real * A, Real * B);

	/// extension of the double dot product to two 2nd order tensor in dimension n
	inline Real matrixDoubleDot(UInt n, Real * A, Real * B);

	/* ------------------------------------------------------------------------ */
	/* Array algebra */
	/* ------------------------------------------------------------------------ */
	/// vector cross product
	inline void vectorProduct3(const Real * v1, const Real * v2, Real * res);

	/// normalize a vector
	inline void normalize2(Real * v);

	/// normalize a vector
	inline void normalize3(Real * v);

	/// return norm of a 2-vector
	inline Real norm2(const Real * v);

	/// return norm of a 3-vector
	inline Real norm3(const Real * v);

	/// return norm of a vector
	inline Real norm(UInt n, const Real * v);

	/// return the dot product between 2 vectors in 2d
	inline Real vectorDot2(const Real * v1, const Real * v2);

	/// return the dot product between 2 vectors in 3d
	inline Real vectorDot3(const Real * v1, const Real * v2);

	/// return the dot product between 2 vectors
	inline Real vectorDot(Real * v1, Real * v2, UInt n);

	/* ------------------------------------------------------------------------ */
	/* Geometry */
	/* ------------------------------------------------------------------------ */
	/// compute normal a normal to a vector
	inline void normal2(const Real * vec, Real * normal);

	/// compute normal a normal to a vector
	inline void normal3(const Real * vec1, const Real * vec2, Real * normal);

	/// compute the tangents to an array of normal vectors
	void compute_tangents(const Array<Real> & normals, Array<Real> & tangents);

	/// distance in 2D between x and y
	inline Real distance_2d(const Real * x, const Real * y);

	/// distance in 3D between x and y
	inline Real distance_3d(const Real * x, const Real * y);

	/// radius of the in-circle of a triangle in 2d space
	static inline Real triangle_inradius(const Vector<Real> & coord1,
	const Vector<Real> & coord2,
	const Vector<Real> & coord3);

	/// radius of the in-circle of a tetrahedron
	inline Real tetrahedron_inradius(const Real * coord1, const Real * coord2,
	const Real * coord3, const Real * coord4);

	/// volume of a tetrahedron
	inline Real tetrahedron_volume(const Real * coord1, const Real * coord2,
	const Real * coord3, const Real * coord4);

	/// compute the barycenter of n points
	inline void barycenter(const Real * coord, UInt nb_points,
	UInt spatial_dimension, Real * barycenter);

	/// vector between x and y
	inline void vector_2d(const Real * x, const Real * y, Real * res);

	/// vector pointing from x to y in 3 spatial dimension
	inline void vector_3d(const Real * x, const Real * y, Real * res);

	/// test if two scalar are equal within a given tolerance
	inline bool are_float_equal(Real x, Real y);

	/// test if two vectors are equal within a given tolerance
	inline bool are_vector_equal(UInt n, Real * x, Real * y);

	#ifdef isnan
	#error \
	"You probably included <math.h> which is incompatible with aka_math please use\
	<cmath> or add a \"#undef isnan\" before akantu includes"
	#endif
	/// test if a real is a NaN
	inline bool isnan(Real x);

	/// test if the line x and y intersects each other
	inline bool intersects(Real x_min, Real x_max, Real y_min, Real y_max);

	/// test if a is in the range [x_min, x_max]
	inline bool is_in_range(Real a, Real x_min, Real x_max);

	inline Real getTolerance() { return Math::tolerance; }
	inline void setTolerance(Real tol) { Math::tolerance = tol; }

	template <UInt p, typename T> inline T pow(T x);

	template <class T1, class T2,
	std::enable_if_t<std::is_integral<T1>::value and
	std::is_integral<T2>::value> * = nullptr>
	inline Real kronecker(T1 i, T2 j) {
	return static_cast<Real>(i == j);
	}

	/// reduce all the values of an array, the summation is done in place and the
	/// array is modified
	Real reduce(Array<Real> & array);

	class NewtonRaphson {
	public:
	NewtonRaphson(Real tolerance, Real max_iteration)
	: tolerance(tolerance), max_iteration(max_iteration) {}

	template <class Functor> Real solve(const Functor & funct, Real x_0);

	private:
	Real tolerance;
	Real max_iteration;
	};

	struct NewtonRaphsonFunctor {
	explicit NewtonRaphsonFunctor(const std::string & name) : name(name) {}

	virtual ~NewtonRaphsonFunctor() = default;

	NewtonRaphsonFunctor(const NewtonRaphsonFunctor & other) = default;
	NewtonRaphsonFunctor(NewtonRaphsonFunctor && other) noexcept = default;
	NewtonRaphsonFunctor &
	operator=(const NewtonRaphsonFunctor & other) = default;
	NewtonRaphsonFunctor &
	operator=(NewtonRaphsonFunctor && other) noexcept = default;

	virtual Real f(Real x) const = 0;
	virtual Real f_prime(Real x) const = 0;
	std::string name;
	};
	} // namespace Math
	} // namespace akantu
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "aka_math_tmpl.hh"

	#endif /* AKANTU_AKA_MATH_H_ */
	diff --git a/src/common/aka_math_tmpl.hh b/src/common/aka_math_tmpl.hh
	index 50809863a..a27337a82 100644
	--- a/src/common/aka_math_tmpl.hh
	+++ b/src/common/aka_math_tmpl.hh
	@@ -1,843 +1,844 @@
	/**
	* @file aka_math_tmpl.hh
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Mathilde Radiguet <mathilde.radiguet@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Implementation of the inline functions of the math toolkit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_blas_lapack.hh"
	#include "aka_math.hh"
	#include "aka_types.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <typeinfo>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace Math {
	/* ------------------------------------------------------------------------ */
	inline void matrix_vector(UInt im, UInt in,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * x, // NOLINT(readability-non-const-parameter)
	Real * y, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// y = alphaop(A)x + beta*y
	char tran_A = 'N';
	int incx = 1;
	int incy = 1;
	double beta = 0.;
	int m = im;
	int n = in;

	aka_gemv(&tran_A, &m, &n, &alpha, A, &m, x, &incx, &beta, y, &incy);

	#else
	std::fill_n(y, im, 0.);
	for (UInt i = 0; i < im; ++i) {
	for (UInt j = 0; j < in; ++j) {
	y[i] += A[i + j * im] * x[j];
	}
	y[i] *= alpha;
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrixt_vector(UInt im, UInt in,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * x, // NOLINT(readability-non-const-parameter)
	Real * y, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// y = alphaop(A)x + beta*y
	char tran_A = 'T';
	int incx = 1;
	int incy = 1;
	double beta = 0.;
	int m = im;
	int n = in;

	aka_gemv(&tran_A, &m, &n, &alpha, A, &m, x, &incx, &beta, y, &incy);
	#else
	std::fill_n(y, in, 0.);
	for (UInt i = 0; i < im; ++i) {
	for (UInt j = 0; j < in; ++j) {
	y[j] += A[j * im + i] * x[i];
	}
	y[i] *= alpha;
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void matrix_matrix(UInt im, UInt in, UInt ik,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B, // NOLINT(readability-non-const-parameter)
	Real * C, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// C := alphaop(A)op(B) + beta*C
	char trans_a = 'N';
	char trans_b = 'N';
	double beta = 0.;
	int m = im, n = in, k = ik;

	aka_gemm(&trans_a, &trans_b, &m, &n, &k, &alpha, A, &m, B, &k, &beta, C,
	&m);
	#else
	std::fill_n(C, im * in, 0.);
	for (UInt j = 0; j < in; ++j) {
	UInt _jb = j * ik;
	UInt _jc = j * im;
	for (UInt i = 0; i < im; ++i) {
	for (UInt l = 0; l < ik; ++l) {
	UInt _la = l * im;
	C[i + _jc] += A[i + _la] * B[l + _jb];
	}
	C[i + _jc] *= alpha;
	}
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrixt_matrix(UInt im, UInt in, UInt ik,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B, // NOLINT(readability-non-const-parameter)
	Real * C, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// C := alphaop(A)op(B) + beta*C
	char trans_a = 'T';
	char trans_b = 'N';
	double beta = 0.;
	int m = im, n = in, k = ik;

	aka_gemm(&trans_a, &trans_b, &m, &n, &k, &alpha, A, &k, B, &k, &beta, C,
	&m);
	#else
	std::fill_n(C, im * in, 0.);
	for (UInt j = 0; j < in; ++j) {
	UInt _jc = j * im;
	UInt _jb = j * ik;
	for (UInt i = 0; i < im; ++i) {
	UInt _ia = i * ik;
	for (UInt l = 0; l < ik; ++l) {
	C[i + _jc] += A[l + _ia] * B[l + _jb];
	}
	C[i + _jc] *= alpha;
	}
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrix_matrixt(UInt im, UInt in, UInt ik,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B, // NOLINT(readability-non-const-parameter)
	Real * C, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// C := alphaop(A)op(B) + beta*C
	char trans_a = 'N';
	char trans_b = 'T';
	double beta = 0.;
	int m = im, n = in, k = ik;

	aka_gemm(&trans_a, &trans_b, &m, &n, &k, &alpha, A, &m, B, &n, &beta, C,
	&m);
	#else
	std::fill_n(C, im * in, 0.);
	for (UInt j = 0; j < in; ++j) {
	UInt _jc = j * im;
	for (UInt i = 0; i < im; ++i) {
	for (UInt l = 0; l < ik; ++l) {
	UInt _la = l * im;
	UInt _lb = l * in;
	C[i + _jc] += A[i + _la] * B[j + _lb];
	}
	C[i + _jc] *= alpha;
	}
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrixt_matrixt(UInt im, UInt in, UInt ik,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B, // NOLINT(readability-non-const-parameter)
	Real * C, Real alpha) {
	#ifdef AKANTU_USE_BLAS
	/// C := alphaop(A)op(B) + beta*C
	char trans_a = 'T';
	char trans_b = 'T';
	double beta = 0.;
	int m = im, n = in, k = ik;

	aka_gemm(&trans_a, &trans_b, &m, &n, &k, &alpha, A, &k, B, &n, &beta, C,
	&m);
	#else
	std::fill_n(C, im * in, 0.);
	for (UInt j = 0; j < in; ++j) {
	UInt _jc = j * im;
	for (UInt i = 0; i < im; ++i) {
	UInt _ia = i * ik;
	for (UInt l = 0; l < ik; ++l) {
	UInt _lb = l * in;
	C[i + _jc] += A[l + _ia] * B[j + _lb];
	}
	C[i + _jc] *= alpha;
	}
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline void aXplusY(UInt n, Real alpha,
	Real * x, // NOLINT(readability-non-const-parameter)
	Real * y) {
	#ifdef AKANTU_USE_BLAS
	/// y := alpha x + y
	int incx = 1, incy = 1;
	aka_axpy(&n, &alpha, x, &incx, y, &incy);
	#else
	for (UInt i = 0; i < n; ++i) {
	(y++) += alpha *(x++);
	}
	#endif
	}

	/* ------------------------------------------------------------------------ */
	inline Real vectorDot(Real * v1, // NOLINT(readability-non-const-parameter)
	Real * v2, // NOLINT(readability-non-const-parameter)
	UInt in) {
	#ifdef AKANTU_USE_BLAS
	/// d := v1 . v2
	int incx = 1, incy = 1, n = in;
	Real d = aka_dot(&n, v1, &incx, v2, &incy);
	#else
	Real d = 0;
	for (UInt i = 0; i < in; ++i) {
	d += v1[i] * v2[i];
	}
	#endif
	return d;
	}

	/* ------------------------------------------------------------------------ */
	template <bool tr_A, bool tr_B>
	inline void matMul(UInt m, UInt n, UInt k, Real alpha,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B, // NOLINT(readability-non-const-parameter)
	Real /beta/, Real * C) {
	if (tr_A) {
	if (tr_B) {
	matrixt_matrixt(m, n, k, A, B, C, alpha);
	} else {
	matrixt_matrix(m, n, k, A, B, C, alpha);
	}
	} else {
	if (tr_B) {
	matrix_matrixt(m, n, k, A, B, C, alpha);
	} else {
	matrix_matrix(m, n, k, A, B, C, alpha);
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	template <bool tr_A>
	inline void matVectMul(UInt m, UInt n, Real alpha,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * x, // NOLINT(readability-non-const-parameter)
	Real /beta/, Real * y) {
	if (tr_A) {
	matrixt_vector(m, n, A, x, y, alpha);
	} else {
	matrix_vector(m, n, A, x, y, alpha);
	}
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void matrixEig(UInt n,
	T * A, // NOLINT(readability-non-const-parameter)
	T * d, T * V) {

	// Matrix A is row major, so the lapack function in fortran will
	// process A^t. Asking for the left eigenvectors of A^t will give the
	// transposed right eigenvectors of A so in the C++ code the right
	// eigenvectors.
	char jobvr{'N'};
	if (V != nullptr) {
	jobvr = 'V'; // compute left eigenvectors
	}

	char jobvl{'N'}; // compute right eigenvectors

	auto * di = new T[n]; // imaginary part of the eigenvalues

	int info;
	int N = n;

	T wkopt;
	int lwork = -1;
	// query and allocate the optimal workspace
	aka_geev<T>(&jobvl, &jobvr, &N, A, &N, d, di, nullptr, &N, V, &N, &wkopt,
	&lwork, &info);

	lwork = int(wkopt);
	auto * work = new T[lwork];
	// solve the eigenproblem
	aka_geev<T>(&jobvl, &jobvr, &N, A, &N, d, di, nullptr, &N, V, &N, work,
	&lwork, &info);

	AKANTU_DEBUG_ASSERT(
	info == 0,
	"Problem computing eigenvalues/vectors. DGEEV exited with the value "
	<< info);

	delete[] work;
	delete[] di; // I hope for you that there was no complex eigenvalues !!!
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrix22_eigenvalues(Real * A, // NOLINT(readability-non-const-parameter)
	Real * Adiag) {
	/// d = determinant of Matrix A
	Real d = det2(A);
	/// b = trace of Matrix A
	Real b = A[0] + A[3];

	Real c = std::sqrt(b * b - 4 * d);
	Adiag[0] = .5 * (b + c);
	Adiag[1] = .5 * (b - c);
	}

	/* ------------------------------------------------------------------------ */
	inline void
	matrix33_eigenvalues(Real * A, // NOLINT(readability-non-const-parameter)
	Real * Adiag) {
	matrixEig(3, A, Adiag);
	}

	/* ------------------------------------------------------------------------ */
	template <UInt dim>
	inline void eigenvalues(Real * A, // NOLINT(readability-non-const-parameter)
	Real * d) {
	if (dim == 1) {
	d[0] = A[0];
	} else if (dim == 2) {
	matrix22_eigenvalues(A, d);
	}
	// else if(dim == 3) { matrix33_eigenvalues(A, d); }
	else {
	matrixEig(dim, A, d);
	}
	}

	/* ------------------------------------------------------------------------ */
	inline Real det2(const Real * mat) {
	return mat[0] * mat[3] - mat[1] * mat[2];
	}

	/* ------------------------------------------------------------------------ */
	inline Real det3(const Real * mat) {
	return mat[0] * (mat[4] * mat[8] - mat[7] * mat[5]) -
	mat[3] * (mat[1] * mat[8] - mat[7] * mat[2]) +
	mat[6] * (mat[1] * mat[5] - mat[4] * mat[2]);
	}

	/* ------------------------------------------------------------------------ */
	template <UInt n> inline Real det(const Real * mat) {
	if (n == 1) {
	return *mat;
	}
	if (n == 2) {
	return det2(mat);
	}
	if (n == 3) {
	return det3(mat);
	}
	return det(n, mat);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T> inline T det(UInt n, const T * A) {
	int N = n;
	int info;
	auto * ipiv = new int[N + 1];

	auto * LU = new T[N * N];
	std::copy(A, A + N * N, LU);

	// LU factorization of A
	aka_getrf(&N, &N, LU, &N, ipiv, &info);
	if (info > 0) {
	AKANTU_ERROR("Singular matrix - cannot factorize it (info: " << info
	<< " )");
	}

	// det(A) = det(L) * det(U) = 1 * det(U) = product_i U_{ii}
	T det = 1.;
	for (int i = 0; i < N; ++i) {
	det = (2 (ipiv[i] == i) - 1) * LU[i * n + i];
	}

	delete[] ipiv;
	delete[] LU;
	return det;
	}

	/* ------------------------------------------------------------------------ */
	inline void normal2(const Real * vec, Real * normal) {
	normal[0] = vec[1];
	normal[1] = -vec[0];
	normalize2(normal);
	}

	/* ------------------------------------------------------------------------ */
	inline void normal3(const Real * vec1, const Real * vec2, Real * normal) {
	vectorProduct3(vec1, vec2, normal);
	normalize3(normal);
	}

	/* ------------------------------------------------------------------------ */
	inline void normalize2(Real * vec) {
	Real norm = norm2(vec);
	vec[0] /= norm;
	vec[1] /= norm;
	}

	/* ------------------------------------------------------------------------ */
	inline void normalize3(Real * vec) {
	Real norm = norm3(vec);
	vec[0] /= norm;
	vec[1] /= norm;
	vec[2] /= norm;
	}

	/* ------------------------------------------------------------------------ */
	inline Real norm2(const Real * vec) {
	return sqrt(vec[0] * vec[0] + vec[1] * vec[1]);
	}

	/* ------------------------------------------------------------------------ */
	inline Real norm3(const Real * vec) {
	return sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]);
	}

	/* ------------------------------------------------------------------------ */
	inline Real norm(UInt n, const Real * vec) {
	Real norm = 0.;
	for (UInt i = 0; i < n; ++i) {
	norm += vec[i] * vec[i];
	}
	return sqrt(norm);
	}

	/* ------------------------------------------------------------------------ */
	inline void inv2(const Real * mat, Real * inv) {
	Real det_mat = det2(mat);

	inv[0] = mat[3] / det_mat;
	inv[1] = -mat[1] / det_mat;
	inv[2] = -mat[2] / det_mat;
	inv[3] = mat[0] / det_mat;
	}

	/* ------------------------------------------------------------------------ */
	inline void inv3(const Real * mat, Real * inv) {
	Real det_mat = det3(mat);

	inv[0] = (mat[4] * mat[8] - mat[7] * mat[5]) / det_mat;
	inv[1] = (mat[2] * mat[7] - mat[8] * mat[1]) / det_mat;
	inv[2] = (mat[1] * mat[5] - mat[4] * mat[2]) / det_mat;
	inv[3] = (mat[5] * mat[6] - mat[8] * mat[3]) / det_mat;
	inv[4] = (mat[0] * mat[8] - mat[6] * mat[2]) / det_mat;
	inv[5] = (mat[2] * mat[3] - mat[5] * mat[0]) / det_mat;
	inv[6] = (mat[3] * mat[7] - mat[6] * mat[4]) / det_mat;
	inv[7] = (mat[1] * mat[6] - mat[7] * mat[0]) / det_mat;
	inv[8] = (mat[0] * mat[4] - mat[3] * mat[1]) / det_mat;
	}

	/* ------------------------------------------------------------------------ */
	template <UInt n> inline void inv(const Real * A, Real * Ainv) {
	if (n == 1) {
	Ainv = 1. / A;
	} else if (n == 2) {
	inv2(A, Ainv);
	} else if (n == 3) {
	inv3(A, Ainv);
	} else {
	inv(n, A, Ainv);
	}
	}

	/* ------------------------------------------------------------------------ */
	template <typename T> inline void inv(UInt n, const T * A, T * invA) {
	int N = n;
	int info;
	auto * ipiv = new int[N + 1];
	int lwork = N * N;
	auto * work = new T[lwork];

	std::copy(A, A + n * n, invA);

	aka_getrf(&N, &N, invA, &N, ipiv, &info);
	if (info > 0) {
	AKANTU_ERROR("Singular matrix - cannot factorize it (info: " << info
	<< " )");
	}

	aka_getri(&N, invA, &N, ipiv, work, &lwork, &info);
	if (info != 0) {
	AKANTU_ERROR("Cannot invert the matrix (info: " << info << " )");
	}

	delete[] ipiv;
	delete[] work;
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void solve(UInt n, const T * A, T * x, const T * b) {
	int N = n;
	int info;
	auto * ipiv = new int[N];
	auto * lu_A = new T[N * N];

	std::copy(A, A + N * N, lu_A);

	aka_getrf(&N, &N, lu_A, &N, ipiv, &info);
	if (info > 0) {
	AKANTU_ERROR("Singular matrix - cannot factorize it (info: " << info
	<< " )");
	}

	char trans = 'N';
	int nrhs = 1;

	std::copy(b, b + N, x);

	aka_getrs(&trans, &N, &nrhs, lu_A, &N, ipiv, x, &N, &info);
	if (info != 0) {
	AKANTU_ERROR("Cannot solve the system (info: " << info << " )");
	}

	delete[] ipiv;
	delete[] lu_A;
	}

	/* ------------------------------------------------------------------------ */
	/* ------------------------------------------------------------------------ */
	inline Real
	matrixDoubleDot22(Real * A, // NOLINT(readability-non-const-parameter)
	Real * B // NOLINT(readability-non-const-parameter)
	) {
	Real d;
	d = A[0] * B[0] + A[1] * B[1] + A[2] * B[2] + A[3] * B[3];
	return d;
	}

	/* ------------------------------------------------------------------------ */
	inline Real
	matrixDoubleDot33(Real * A, // NOLINT(readability-non-const-parameter)
	Real * B // NOLINT(readability-non-const-parameter)
	) {
	Real d;
	d = A[0] * B[0] + A[1] * B[1] + A[2] * B[2] + A[3] * B[3] + A[4] * B[4] +
	A[5] * B[5] + A[6] * B[6] + A[7] * B[7] + A[8] * B[8];
	return d;
	}

	/* ------------------------------------------------------------------------ */
	inline Real
	matrixDoubleDot(UInt n,
	Real * A, // NOLINT(readability-non-const-parameter)
	Real * B // NOLINT(readability-non-const-parameter)
	) {
	Real d = 0.;
	for (UInt i = 0; i < n; ++i) {
	for (UInt j = 0; j < n; ++j) {
	d += A[i * n + j] * B[i * n + j];
	}
	}
	return d;
	}

	/* ------------------------------------------------------------------------ */
	inline void vectorProduct3(const Real * v1, const Real * v2, Real * res) {
	res[0] = v1[1] * v2[2] - v1[2] * v2[1];
	res[1] = v1[2] * v2[0] - v1[0] * v2[2];
	res[2] = v1[0] * v2[1] - v1[1] * v2[0];
	}

	/* ------------------------------------------------------------------------ */
	inline Real vectorDot2(const Real * v1, const Real * v2) {
	return (v1[0] * v2[0] + v1[1] * v2[1]);
	}

	/* ------------------------------------------------------------------------ */
	inline Real vectorDot3(const Real * v1, const Real * v2) {
	return (v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2]);
	}

	/* ------------------------------------------------------------------------ */
	inline Real distance_2d(const Real * x, const Real * y) {
	return std::sqrt((y[0] - x[0]) * (y[0] - x[0]) +
	(y[1] - x[1]) * (y[1] - x[1]));
	}

	/* ------------------------------------------------------------------------ */
	- inline Real triangle_inradius(const Vector<Real> & coord1, const Vector<Real> & coord2,
	+ inline Real triangle_inradius(const Vector<Real> & coord1,
	+ const Vector<Real> & coord2,
	const Vector<Real> & coord3) {
	/**
	* @f{eqnarray*}{
	* r &=& A / s \\
	* A &=& 1/4 * \sqrt{(a + b + c) * (a - b + c) * (a + b - c) (-a + b + c)}
	* \\ s &=& \frac{a + b + c}{2}
	* @f}
	*/

	Real a, b, c;

	a = coord1.distance(coord2);
	b = coord2.distance(coord3);
	c = coord1.distance(coord3);

	Real s;
	s = (a + b + c) * 0.5;

	return std::sqrt((s - a) * (s - b) * (s - c) / s);
	}

	/* ------------------------------------------------------------------------ */
	inline Real distance_3d(const Real * x, const Real * y) {
	return std::sqrt((y[0] - x[0]) * (y[0] - x[0]) +
	(y[1] - x[1]) * (y[1] - x[1]) +
	(y[2] - x[2]) * (y[2] - x[2]));
	}

	/* ------------------------------------------------------------------------ */
	inline Real tetrahedron_volume(const Real * coord1, const Real * coord2,
	const Real * coord3, const Real * coord4) {
	Real xx[9];

	xx[0] = coord2[0];
	xx[1] = coord2[1];
	xx[2] = coord2[2];
	xx[3] = coord3[0];
	xx[4] = coord3[1];
	xx[5] = coord3[2];
	xx[6] = coord4[0];
	xx[7] = coord4[1];
	xx[8] = coord4[2];
	auto vol = det3(xx);

	xx[0] = coord1[0];
	xx[1] = coord1[1];
	xx[2] = coord1[2];
	xx[3] = coord3[0];
	xx[4] = coord3[1];
	xx[5] = coord3[2];
	xx[6] = coord4[0];
	xx[7] = coord4[1];
	xx[8] = coord4[2];
	vol -= det3(xx);

	xx[0] = coord1[0];
	xx[1] = coord1[1];
	xx[2] = coord1[2];
	xx[3] = coord2[0];
	xx[4] = coord2[1];
	xx[5] = coord2[2];
	xx[6] = coord4[0];
	xx[7] = coord4[1];
	xx[8] = coord4[2];
	vol += det3(xx);

	xx[0] = coord1[0];
	xx[1] = coord1[1];
	xx[2] = coord1[2];
	xx[3] = coord2[0];
	xx[4] = coord2[1];
	xx[5] = coord2[2];
	xx[6] = coord3[0];
	xx[7] = coord3[1];
	xx[8] = coord3[2];
	vol -= det3(xx);

	vol /= 6;

	return vol;
	}

	/* ------------------------------------------------------------------------ */
	inline Real tetrahedron_inradius(const Real * coord1, const Real * coord2,
	const Real * coord3, const Real * coord4) {
	auto l12 = distance_3d(coord1, coord2);
	auto l13 = distance_3d(coord1, coord3);
	auto l14 = distance_3d(coord1, coord4);
	auto l23 = distance_3d(coord2, coord3);
	auto l24 = distance_3d(coord2, coord4);
	auto l34 = distance_3d(coord3, coord4);

	auto s1 = (l12 + l23 + l13) * 0.5;
	s1 = std::sqrt(s1 * (s1 - l12) * (s1 - l23) * (s1 - l13));

	auto s2 = (l12 + l24 + l14) * 0.5;
	s2 = std::sqrt(s2 * (s2 - l12) * (s2 - l24) * (s2 - l14));

	auto s3 = (l23 + l34 + l24) * 0.5;
	s3 = std::sqrt(s3 * (s3 - l23) * (s3 - l34) * (s3 - l24));

	auto s4 = (l13 + l34 + l14) * 0.5;
	s4 = std::sqrt(s4 * (s4 - l13) * (s4 - l34) * (s4 - l14));

	auto volume = tetrahedron_volume(coord1, coord2, coord3, coord4);

	return 3 * volume / (s1 + s2 + s3 + s4);
	}

	/* ------------------------------------------------------------------------ */
	inline void barycenter(const Real * coord, UInt nb_points,
	UInt spatial_dimension, Real * barycenter) {
	std::fill_n(barycenter, spatial_dimension, 0.);
	for (UInt n = 0; n < nb_points; ++n) {
	UInt offset = n * spatial_dimension;
	for (UInt i = 0; i < spatial_dimension; ++i) {
	barycenter[i] += coord[offset + i] / (Real)nb_points;
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	inline void vector_2d(const Real * x, const Real * y, Real * res) {
	res[0] = y[0] - x[0];
	res[1] = y[1] - x[1];
	}

	/* ------------------------------------------------------------------------ */
	inline void vector_3d(const Real * x, const Real * y, Real * res) {
	res[0] = y[0] - x[0];
	res[1] = y[1] - x[1];
	res[2] = y[2] - x[2];
	}

	/* ------------------------------------------------------------------------ */
	/// Combined absolute and relative tolerance test proposed in
	/// Real-time collision detection by C. Ericson (2004)
	inline bool are_float_equal(const Real x, const Real y) {
	Real abs_max = std::max(std::abs(x), std::abs(y));
	abs_max = std::max(abs_max, Real(1.));
	return std::abs(x - y) <= (tolerance * abs_max);
	}

	/* ------------------------------------------------------------------------ */
	inline bool isnan(Real x) {
	#if defined(__INTEL_COMPILER)
	#pragma warning(push)
	#pragma warning(disable : 1572)
	#endif // defined(__INTEL_COMPILER)

	// x = x return false means x = quiet_NaN
	return !(x == x);

	#if defined(__INTEL_COMPILER)
	#pragma warning(pop)
	#endif // defined(__INTEL_COMPILER)
	}

	/* ------------------------------------------------------------------------ */
	inline bool are_vector_equal(UInt n, Real * x, Real * y) {
	bool test = true;
	for (UInt i = 0; i < n; ++i) {
	test &= are_float_equal(x[i], y[i]);
	}

	return test;
	}

	/* ------------------------------------------------------------------------ */
	inline bool intersects(Real x_min, Real x_max, Real y_min, Real y_max) {
	return not((x_max < y_min) or (x_min > y_max));
	}

	/* ------------------------------------------------------------------------ */
	inline bool is_in_range(Real a, Real x_min, Real x_max) {
	return ((a >= x_min) and (a <= x_max));
	}

	/* ------------------------------------------------------------------------ */
	template <UInt p, typename T> inline T pow(T x) {
	return (pow<p - 1, T>(x) * x);
	}
	template <> inline UInt pow<0, UInt>(__attribute__((unused)) UInt x) {
	return (1);
	}
	template <> inline Real pow<0, Real>(__attribute__((unused)) Real x) {
	return (1.);
	}

	/* ------------------------------------------------------------------------ */

	template <class Functor>
	Real NewtonRaphson::solve(const Functor & funct, Real x_0) {
	Real x = x_0;
	Real f_x = funct.f(x);
	UInt iter = 0;
	while (std::abs(f_x) > this->tolerance && iter < this->max_iteration) {
	x -= f_x / funct.f_prime(x);
	f_x = funct.f(x);
	iter++;
	}

	AKANTU_DEBUG_ASSERT(iter < this->max_iteration,
	"Newton Raphson ("
	<< funct.name << ") solve did not converge in "
	<< this->max_iteration << " iterations (tolerance: "
	<< this->tolerance << ")");

	return x;
	}

	} // namespace Math
	} // namespace akantu
	diff --git a/src/common/aka_random_generator.hh b/src/common/aka_random_generator.hh
	index eaae6c1bb..0312f2bd8 100644
	--- a/src/common/aka_random_generator.hh
	+++ b/src/common/aka_random_generator.hh
	@@ -1,285 +1,285 @@
	/**
	* @file aka_random_generator.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief generic random generator
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	/* -------------------------------------------------------------------------- */
	#include <random>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_RANDOM_GENERATOR_HH_
	#define AKANTU_AKA_RANDOM_GENERATOR_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* List of available distributions */
	/* -------------------------------------------------------------------------- */
	// clang-format off
	#define AKANTU_RANDOM_DISTRIBUTION_TYPES \
	((uniform , std::uniform_real_distribution )) \
	((exponential , std::exponential_distribution )) \
	((gamma , std::gamma_distribution )) \
	((weibull , std::weibull_distribution )) \
	((extreme_value, std::extreme_value_distribution)) \
	((normal , std::normal_distribution )) \
	((lognormal , std::lognormal_distribution )) \
	((chi_squared , std::chi_squared_distribution )) \
	((cauchy , std::cauchy_distribution )) \
	((fisher_f , std::fisher_f_distribution )) \
	((student_t , std::student_t_distribution ))
	// clang-format on

	#define AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX(elem) BOOST_PP_CAT(_rdt_, elem)
	#define AKANTU_RANDOM_DISTRIBUTION_PREFIX(s, data, elem) \
	AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX(BOOST_PP_TUPLE_ELEM(2, 0, elem))

	enum RandomDistributionType {
	BOOST_PP_SEQ_ENUM(BOOST_PP_SEQ_TRANSFORM(AKANTU_RANDOM_DISTRIBUTION_PREFIX, _,
	AKANTU_RANDOM_DISTRIBUTION_TYPES)),
	_rdt_not_defined
	};

	/* -------------------------------------------------------------------------- */
	/* Generator */
	/* -------------------------------------------------------------------------- */
	template <typename T> class RandomGenerator {
	/* ------------------------------------------------------------------------ */
	private:
	static long int _seed; // NOLINT
	static std::default_random_engine generator; // NOLINT
	/* ------------------------------------------------------------------------ */
	public:
	inline T operator()() { return generator(); }

	/// function to print the contain of the class
	void printself(std::ostream & stream, int /* indent */) const {
	stream << "RandGenerator [seed=" << _seed << "]";
	}

	/* ------------------------------------------------------------------------ */
	public:
	static void seed(long int s) {
	_seed = s;
	generator.seed(_seed);
	}
	static long int seed() { return _seed; }

	static constexpr T min() { return std::default_random_engine::min(); }
	static constexpr T max() { return std::default_random_engine::max(); }
	};

	#if defined(__clang__)
	template <typename T> long int RandomGenerator<T>::_seed; // NOLINT
	template <typename T> std::default_random_engine RandomGenerator<T>::generator;
	#endif

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	#undef AKANTU_RANDOM_DISTRIBUTION_PREFIX

	#define AKANTU_RANDOM_DISTRIBUTION_TYPE_PRINT_CASE(r, data, elem) \
	case AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX( \
	BOOST_PP_TUPLE_ELEM(2, 0, elem)): { \
	stream << BOOST_PP_STRINGIZE(AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX( \
	BOOST_PP_TUPLE_ELEM(2, 0, elem))); \
	break; \
	}

	inline std::ostream & operator<<(std::ostream & stream,
	RandomDistributionType type) {
	switch (type) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_RANDOM_DISTRIBUTION_TYPE_PRINT_CASE, _,
	AKANTU_RANDOM_DISTRIBUTION_TYPES)
	default:
	stream << UInt(type) << " not a RandomDistributionType";
	break;
	}
	return stream;
	}
	#undef AKANTU_RANDOM_DISTRIBUTION_TYPE_PRINT_CASE

	/* -------------------------------------------------------------------------- */
	/* Some Helper */
	/* -------------------------------------------------------------------------- */
	template <typename T, class Distribution> class RandomDistributionTypeHelper {
	enum { value = _rdt_not_defined };
	};

	/* -------------------------------------------------------------------------- */
	#define AKANTU_RANDOM_DISTRIBUTION_TYPE_GET_TYPE(r, data, elem) \
	template <typename T> \
	struct RandomDistributionTypeHelper<T, BOOST_PP_TUPLE_ELEM(2, 1, elem) < \
	T> > { \
	enum { \
	value = AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX( \
	BOOST_PP_TUPLE_ELEM(2, 0, elem)) \
	}; \
	\
	static void printself(std::ostream & stream) { \
	stream << BOOST_PP_STRINGIZE(BOOST_PP_TUPLE_ELEM(2, 0, elem)); \
	} \
	};

	BOOST_PP_SEQ_FOR_EACH(AKANTU_RANDOM_DISTRIBUTION_TYPE_GET_TYPE, _,
	AKANTU_RANDOM_DISTRIBUTION_TYPES)

	#undef AKANTU_RANDOM_DISTRIBUTION_TYPE_GET_TYPE

	/* -------------------------------------------------------------------------- */
	template <class T> class RandomDistribution {
	public:
	virtual ~RandomDistribution() = default;

	RandomDistribution() = default;
	RandomDistribution(const RandomDistribution & other) = default;
	RandomDistribution(RandomDistribution && other) noexcept = default;
	RandomDistribution & operator=(const RandomDistribution & other) = default;
	RandomDistribution &
	operator=(RandomDistribution && other) noexcept = default;

	virtual T operator()(RandomGenerator<UInt> & gen) = 0;
	virtual std::unique_ptr<RandomDistribution<T>> make_unique() const = 0;
	virtual void printself(std::ostream & stream, int = 0) const = 0;
	};

	template <class T, class Distribution>
	class RandomDistributionProxy : public RandomDistribution<T> {
	public:
	explicit RandomDistributionProxy(Distribution dist)
	: distribution(std::move(dist)) {}

	T operator()(RandomGenerator<UInt> & gen) override {
	return distribution(gen);
	}

	std::unique_ptr<RandomDistribution<T>> make_unique() const override {
	return std::make_unique<RandomDistributionProxy<T, Distribution>>(
	distribution);
	}

	void printself(std::ostream & stream, int /* indent */ = 0) const override {
	RandomDistributionTypeHelper<T, Distribution>::printself(stream);
	stream << " [ " << distribution << " ]";
	}

	private:
	Distribution distribution;
	};

	/* -------------------------------------------------------------------------- */
	/* RandomParameter */
	/* -------------------------------------------------------------------------- */
	template <typename T> class RandomParameter {
	public:
	template <class Distribution>
	explicit RandomParameter(T base_value, Distribution dist)
	: base_value(base_value),
	type(RandomDistributionType(
	RandomDistributionTypeHelper<T, Distribution>::value)),
	distribution_proxy(
	std::make_unique<RandomDistributionProxy<T, Distribution>>(
	std::move(dist))) {}

	explicit RandomParameter(T base_value)
	: base_value(base_value),
	type(RandomDistributionType(
	RandomDistributionTypeHelper<
	T, std::uniform_real_distribution<T>>::value)),
	distribution_proxy(
	std::make_unique<
	RandomDistributionProxy<T, std::uniform_real_distribution<T>>>(
	std::uniform_real_distribution<T>(0., 0.))) {}

	RandomParameter(const RandomParameter & other)
	: base_value(other.base_value), type(other.type),
	distribution_proxy(other.distribution_proxy->make_unique()) {}

	RandomParameter & operator=(const RandomParameter & other) {
	distribution_proxy = other.distribution_proxy->make_unique();
	base_value = other.base_value;
	type = other.type;
	return *this;
	}

	RandomParameter(RandomParameter && other) noexcept = default;
	RandomParameter & operator=(RandomParameter && other) noexcept = default;

	virtual ~RandomParameter() = default;

	inline void setBaseValue(const T & value) { this->base_value = value; }
	inline T getBaseValue() const { return this->base_value; }

	template <template <typename> class Generator, class iterator>
	void setValues(iterator it, iterator end) {
	RandomGenerator<UInt> gen;
	for (; it != end; ++it) {
	it = this->base_value + (distribution_proxy)(gen);
	}
	}

	virtual void printself(std::ostream & stream,
	__attribute__((unused)) int indent = 0) const {
	stream << base_value;
	stream << " + " << *distribution_proxy;
	}

	private:
	/// Value with no random variations
	T base_value;

	/// Random distribution type
	RandomDistributionType type;

	/// Proxy to store a std random distribution
	std::unique_ptr<RandomDistribution<T>> distribution_proxy;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	RandomDistribution<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	RandomParameter<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_RANDOM_GENERATOR_HH_ */
	diff --git a/src/common/aka_safe_enum.hh b/src/common/aka_safe_enum.hh
	index 7bd757357..ad3157c57 100644
	--- a/src/common/aka_safe_enum.hh
	+++ b/src/common/aka_safe_enum.hh
	@@ -1,96 +1,98 @@
	/**
	* @file aka_safe_enum.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Safe enums type (see More C++ Idioms/Type Safe Enum on Wikibooks
	* http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Type_Safe_Enum)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_SAFE_ENUM_HH_
	#define AKANTU_AKA_SAFE_ENUM_HH_

	namespace akantu {

	/// Safe enumerated type
	template <typename def, typename inner = typename def::type>
	class safe_enum : public def {
	using type = typename def::type;

	public:
	constexpr explicit safe_enum(type v = def::_end_) : val(v) {}

	constexpr inner underlying() const { return val; }

	constexpr bool operator==(const safe_enum & s) const {
	return this->val == s.val;
	}
	constexpr bool operator!=(const safe_enum & s) const {
	return this->val != s.val;
	}
	constexpr bool operator<(const safe_enum & s) const {
	return this->val < s.val;
	}
	constexpr bool operator<=(const safe_enum & s) const {
	return this->val <= s.val;
	}
	constexpr bool operator>(const safe_enum & s) const {
	return this->val > s.val;
	}
	constexpr bool operator>=(const safe_enum & s) const {
	return this->val >= s.val;
	}

	constexpr operator inner() { return val; };

	public:
	// Works only if enumerations are contiguous.
	class const_iterator {
	public:
	constexpr explicit const_iterator(type v) : it(v) {}
	constexpr const_iterator & operator++() {
	++it;
	return *this;
	}
	constexpr safe_enum operator*() { return safe_enum(static_cast<type>(it)); }
	- constexpr bool operator!=(const_iterator const & it) { return it.it != this->it; }
	+ constexpr bool operator!=(const_iterator const & it) {
	+ return it.it != this->it;
	+ }

	private:
	int it;
	};

	constexpr auto begin() const { return const_iterator(def::_begin_); }
	constexpr auto end() const { return const_iterator(def::_end_); }

	private:
	inner val;
	};

	} // namespace akantu

	#endif /* AKANTU_AKA_SAFE_ENUM_HH_ */
	diff --git a/src/common/aka_types.hh b/src/common/aka_types.hh
	index 69a126bc4..3c55c2604 100644
	--- a/src/common/aka_types.hh
	+++ b/src/common/aka_types.hh
	@@ -1,1558 +1,1558 @@
	/**
	* @file aka_types.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 17 2011
	* @date last modification: Wed Dec 09 2020
	*
	* @brief description of the "simple" types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_math.hh"
	/* -------------------------------------------------------------------------- */
	#include <initializer_list>
	#include <iomanip>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_TYPES_HH_
	#define AKANTU_AKA_TYPES_HH_

	namespace akantu {

	enum NormType { L_1 = 1, L_2 = 2, L_inf = UInt(-1) };

	/**
	* DimHelper is a class to generalize the setup of a dim array from 3
	* values. This gives a common interface in the TensorStorage class
	* independently of its derived inheritance (Vector, Matrix, Tensor3)
	* @tparam dim
	*/
	template <UInt dim> struct DimHelper {
	static inline void setDims(UInt m, UInt n, UInt p,
	std::array<UInt, dim> & dims);
	};

	/* -------------------------------------------------------------------------- */
	template <> struct DimHelper<1> {
	static inline void setDims(UInt m, UInt /n/, UInt /p/,
	std::array<UInt, 1> & dims) {
	dims[0] = m;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <> struct DimHelper<2> {
	static inline void setDims(UInt m, UInt n, UInt /p/,
	std::array<UInt, 2> & dims) {
	dims[0] = m;
	dims[1] = n;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <> struct DimHelper<3> {
	static inline void setDims(UInt m, UInt n, UInt p,
	std::array<UInt, 3> & dims) {
	dims[0] = m;
	dims[1] = n;
	dims[2] = p;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <typename T, UInt ndim, class RetType> class TensorStorage;

	/* -------------------------------------------------------------------------- */
	/* Proxy classes */
	/* -------------------------------------------------------------------------- */
	namespace tensors {
	template <class A, class B> struct is_copyable {
	enum : bool { value = false };
	};

	template <class A> struct is_copyable<A, A> {
	enum : bool { value = true };
	};

	template <class A> struct is_copyable<A, typename A::RetType> {
	enum : bool { value = true };
	};

	template <class A> struct is_copyable<A, typename A::RetType::proxy> {
	enum : bool { value = true };
	};

	} // namespace tensors

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	namespace types {
	namespace details {
	template <typename reference_> class vector_iterator {
	public:
	using difference_type = std::ptrdiff_t;
	using value_type = std::decay_t<reference_>;
	using pointer = value_type *;
	using reference = reference_;
	using iterator_category = std::input_iterator_tag;

	vector_iterator(pointer ptr) : ptr(ptr) {}

	// input iterator ++it
	vector_iterator & operator++() {
	++ptr;
	return *this;
	}
	// input iterator it++
	vector_iterator operator++(int) {
	auto cpy = *this;
	++ptr;
	return cpy;
	}
	vector_iterator & operator+=(int n) {
	ptr += n;
	return *this;
	}

	vector_iterator operator+(int n) {
	vector_iterator cpy(*this);
	cpy += n;
	return cpy;
	}

	// input iterator it != other_it
	bool operator!=(const vector_iterator & other) const {
	return ptr != other.ptr;
	}
	bool operator==(const vector_iterator & other) const {
	return ptr == other.ptr;
	}

	difference_type operator-(const vector_iterator & other) const {
	return this->ptr - other.ptr;
	}

	// input iterator dereference *it
	reference operator() { return ptr; }
	pointer operator->() { return ptr; }

	private:
	pointer ptr;
	};
	} // namespace details
	} // namespace types

	/**
	* @class TensorProxy aka_types.hh
	* The TensorProxy class is a proxy class to the
	* TensorStorage it handles the wrapped case. That is to say if an accessor
	* should give access to a Tensor wrapped on some data, like the
	* Array<T>::iterator they can return a TensorProxy that will be automatically
	* transformed as a TensorStorage wrapped on the same data
	* @tparam T stored type
	* @tparam ndim order of the tensor
	* @tparam _RetType real derived type
	*/
	template <typename T, UInt ndim, class RetType_>
	class TensorProxy : public TensorProxyTrait {
	protected:
	using RetTypeProxy = typename RetType_::proxy;

	constexpr TensorProxy(T * data, UInt m, UInt n, UInt p) {
	DimHelper<ndim>::setDims(m, n, p, this->n);
	this->values = data;
	}

	template <class Other, typename = std::enable_if_t<
	tensors::is_copyable<TensorProxy, Other>::value>>
	explicit TensorProxy(const Other & other) {
	this->values = other.storage();
	for (UInt i = 0; i < ndim; ++i) {
	this->n[i] = other.size(i);
	}
	}

	public:
	using RetType = RetType_;

	UInt size(UInt i) const {
	AKANTU_DEBUG_ASSERT(i < ndim, "This tensor has only " << ndim
	<< " dimensions, not "
	<< (i + 1));
	return n[i];
	}

	inline UInt size() const {
	UInt _size = 1;
	for (UInt d = 0; d < ndim; ++d) {
	_size *= this->n[d];
	}
	return _size;
	}

	T * storage() const { return values; }

	template <class Other, typename = std::enable_if_t<
	tensors::is_copyable<TensorProxy, Other>::value>>
	inline TensorProxy & operator=(const Other & other) {
	AKANTU_DEBUG_ASSERT(
	other.size() == this->size(),
	"You are trying to copy two tensors with different sizes");
	std::copy_n(other.storage(), this->size(), this->values);
	return *this;
	}
	// template <class Other, typename = std::enable_if_t<
	// tensors::is_copyable<TensorProxy, Other>::value>>
	// inline TensorProxy & operator=(const Other && other) {
	// AKANTU_DEBUG_ASSERT(
	// other.size() == this->size(),
	// "You are trying to copy two tensors with different sizes");
	// memcpy(this->values, other.storage(), this->size() * sizeof(T));
	// return *this;
	// }

	template <typename O> inline RetTypeProxy & operator*=(const O & o) {
	RetType(this) = o;
	return static_cast<RetTypeProxy &>(*this);
	}

	template <typename O> inline RetTypeProxy & operator/=(const O & o) {
	RetType(*this) /= o;
	return static_cast<RetTypeProxy &>(*this);
	}

	protected:
	T * values;
	std::array<UInt, ndim> n;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T> class VectorProxy : public TensorProxy<T, 1, Vector<T>> {
	using parent = TensorProxy<T, 1, Vector<T>>;
	using type = Vector<T>;

	public:
	constexpr VectorProxy(T * data, UInt n) : parent(data, n, 0, 0) {}
	template <class Other> explicit VectorProxy(Other & src) : parent(src) {}

	/* ---------------------------------------------------------------------- */
	template <class Other>
	inline VectorProxy<T> & operator=(const Other & other) {
	parent::operator=(other);
	return *this;
	}

	// inline VectorProxy<T> & operator=(const VectorProxy && other) {
	// parent::operator=(other);
	// return *this;
	// }
	using iterator = types::details::vector_iterator<T &>;
	using const_iterator = types::details::vector_iterator<const T &>;

	iterator begin() { return iterator(this->storage()); }
	iterator end() { return iterator(this->storage() + this->size()); }

	const_iterator begin() const { return const_iterator(this->storage()); }
	const_iterator end() const {
	return const_iterator(this->storage() + this->size());
	}

	/* ------------------------------------------------------------------------ */
	T & operator()(UInt index) { return this->values[index]; };
	const T & operator()(UInt index) const { return this->values[index]; };
	};

	template <typename T> class MatrixProxy : public TensorProxy<T, 2, Matrix<T>> {
	using parent = TensorProxy<T, 2, Matrix<T>>;
	using type = Matrix<T>;

	public:
	MatrixProxy(T * data, UInt m, UInt n) : parent(data, m, n, 0) {}
	template <class Other> explicit MatrixProxy(Other & src) : parent(src) {}

	/* ---------------------------------------------------------------------- */
	template <class Other>
	inline MatrixProxy<T> & operator=(const Other & other) {
	parent::operator=(other);
	return *this;
	}
	};

	template <typename T>
	class Tensor3Proxy : public TensorProxy<T, 3, Tensor3<T>> {
	using parent = TensorProxy<T, 3, Tensor3<T>>;
	using type = Tensor3<T>;

	public:
	Tensor3Proxy(const T * data, UInt m, UInt n, UInt k)
	: parent(data, m, n, k) {}
	Tensor3Proxy(const Tensor3Proxy & src) : parent(src) {}
	Tensor3Proxy(const Tensor3<T> & src) : parent(src) {}

	/* ---------------------------------------------------------------------- */
	template <class Other>
	inline Tensor3Proxy<T> & operator=(const Other & other) {
	parent::operator=(other);
	return *this;
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Tensor base class */
	/* -------------------------------------------------------------------------- */
	template <typename T, UInt ndim, class RetType>
	class TensorStorage : public TensorTrait {
	public:
	using value_type = T;

	friend class Array<T>;

	protected:
	template <class TensorType> void copySize(const TensorType & src) {
	for (UInt d = 0; d < ndim; ++d) {
	this->n[d] = src.size(d); // NOLINT
	}
	this->_size = src.size();
	}

	TensorStorage() = default;
	TensorStorage(const TensorProxy<T, ndim, RetType> & proxy) {
	this->copySize(proxy);
	this->values = proxy.storage();
	this->wrapped = true;
	}

	public:
	TensorStorage(const TensorStorage & src) = delete;

	TensorStorage(const TensorStorage & src, bool deep_copy) : values(nullptr) {
	if (deep_copy) {
	this->deepCopy(src);
	} else {
	this->shallowCopy(src);
	}
	}

	protected:
	TensorStorage(UInt m, UInt n, UInt p, const T & def) {
	static_assert(std::is_trivially_constructible<T>{},
	"Cannot create a tensor on non trivial types");
	DimHelper<ndim>::setDims(m, n, p, this->n);

	this->computeSize();
	this->values = new T[this->_size]; // NOLINT
	this->set(def);
	this->wrapped = false;
	}

	TensorStorage(T * data, UInt m, UInt n, UInt p) {
	DimHelper<ndim>::setDims(m, n, p, this->n);

	this->computeSize();
	this->values = data;
	this->wrapped = true;
	}

	public:
	/* ------------------------------------------------------------------------ */
	template <class TensorType> inline void shallowCopy(const TensorType & src) {
	this->copySize(src);
	if (!this->wrapped) {
	delete[] this->values;
	}
	this->values = src.storage();
	this->wrapped = true;
	}

	/* ------------------------------------------------------------------------ */
	template <class TensorType> inline void deepCopy(const TensorType & src) {
	this->copySize(src);

	if (!this->wrapped) {
	delete[] this->values;
	}

	static_assert(std::is_trivially_constructible<T>{},
	"Cannot create a tensor on non trivial types");
	this->values = new T[this->_size]; // NOLINT

	static_assert(std::is_trivially_copyable<T>{},
	"Cannot copy a tensor on non trivial types");
	std::copy_n(src.storage(), this->_size, this->values);

	this->wrapped = false;
	}

	virtual ~TensorStorage() {
	if (!this->wrapped) {
	delete[] this->values;
	}
	}

	/* ------------------------------------------------------------------------ */
	inline TensorStorage & operator=(const TensorStorage & other) {
	if (this == &other) {
	return *this;
	}
	this->operator=(aka::as_type<RetType>(other));
	return *this;
	}

	// inline TensorStorage & operator=(TensorStorage && other) noexcept {
	// std::swap(n, other.n);
	// std::swap(_size, other._size);
	// std::swap(values, other.values);
	// std::swap(wrapped, other.wrapped);
	// return *this;
	// }

	/* ------------------------------------------------------------------------ */
	inline TensorStorage & operator=(const RetType & src) {
	if (this != &src) {
	if (this->wrapped) {
	static_assert(std::is_trivially_copyable<T>{},
	"Cannot copy a tensor on non trivial types");
	// this test is not sufficient for Tensor of order higher than 1
	AKANTU_DEBUG_ASSERT(this->_size == src.size(),
	"Tensors of different size ("
	<< this->_size << " != " << src.size() << ")");
	std::copy_n(src.storage(), this->_size, this->values);
	} else {
	deepCopy(src);
	}
	}
	return *this;
	}

	/* ------------------------------------------------------------------------ */
	template <class R>
	inline RetType & operator+=(const TensorStorage<T, ndim, R> & other) {
	T * a = this->storage();
	T * b = other.storage();
	AKANTU_DEBUG_ASSERT(
	_size == other.size(),
	"The two tensors do not have the same size, they cannot be subtracted");
	for (UInt i = 0; i < _size; ++i) {
	(a++) += (b++);
	}
	return (static_cast<RetType >(this));
	}

	/* ------------------------------------------------------------------------ */
	template <class R>
	inline RetType & operator-=(const TensorStorage<T, ndim, R> & other) {
	T * a = this->storage();
	T * b = other.storage();
	AKANTU_DEBUG_ASSERT(
	_size == other.size(),
	"The two tensors do not have the same size, they cannot be subtracted");
	for (UInt i = 0; i < _size; ++i) {
	(a++) -= (b++);
	}
	return (static_cast<RetType >(this));
	}

	/* ------------------------------------------------------------------------ */
	inline RetType & operator+=(const T & x) {
	T * a = this->values;
	for (UInt i = 0; i < _size; ++i) {
	*(a++) += x;
	}
	return (static_cast<RetType >(this));
	}

	/* ------------------------------------------------------------------------ */
	inline RetType & operator-=(const T & x) {
	T * a = this->values;
	for (UInt i = 0; i < _size; ++i) {
	*(a++) -= x;
	}
	return (static_cast<RetType >(this));
	}

	/* ------------------------------------------------------------------------ */
	inline RetType & operator*=(const T & x) {
	T * a = this->storage();
	for (UInt i = 0; i < _size; ++i) {
	(a++) = x;
	}
	return (static_cast<RetType >(this));
	}

	/* ---------------------------------------------------------------------- */
	inline RetType & operator/=(const T & x) {
	T * a = this->values;
	for (UInt i = 0; i < _size; ++i) {
	*(a++) /= x;
	}
	return (static_cast<RetType >(this));
	}

	/// \f[Y = \alpha X + Y\f]
	inline RetType & aXplusY(const TensorStorage & other, const T & alpha = 1.) {
	AKANTU_DEBUG_ASSERT(
	_size == other.size(),
	"The two tensors do not have the same size, they cannot be subtracted");

	Math::aXplusY(this->_size, alpha, other.storage(), this->storage());
	return (static_cast<RetType >(this));
	}

	/* ------------------------------------------------------------------------ */
	T * storage() const { return values; }
	UInt size() const { return _size; }
	UInt size(UInt i) const {
	AKANTU_DEBUG_ASSERT(i < ndim, "This tensor has only " << ndim
	<< " dimensions, not "
	<< (i + 1));
	return n[i];
	};
	/* ------------------------------------------------------------------------ */
	inline void set(const T & t) { std::fill_n(values, _size, t); };
	inline void zero() { this->set(0.); };

	template <class TensorType> inline void copy(const TensorType & other) {
	AKANTU_DEBUG_ASSERT(
	_size == other.size(),
	"The two tensors do not have the same size, they cannot be copied");
	std::copy_n(other.storage(), _size, values);
	}

	bool isWrapped() const { return this->wrapped; }

	protected:
	inline void computeSize() {
	_size = 1;
	for (UInt d = 0; d < ndim; ++d) {
	_size *= this->n[d];
	}
	}

	protected:
	template <typename R, NormType norm_type> struct NormHelper {
	template <class Ten> static R norm(const Ten & ten) {
	R _norm = 0.;
	R * it = ten.storage();
	R * end = ten.storage() + ten.size();
	for (; it < end; ++it) {
	_norm += std::pow(std::abs(*it), norm_type);
	}
	return std::pow(_norm, 1. / norm_type);
	}
	}; // namespace akantu

	template <typename R> struct NormHelper<R, L_1> {
	template <class Ten> static R norm(const Ten & ten) {
	R _norm = 0.;
	R * it = ten.storage();
	R * end = ten.storage() + ten.size();
	for (; it < end; ++it) {
	_norm += std::abs(*it);
	}
	return _norm;
	}
	};

	template <typename R> struct NormHelper<R, L_2> {
	template <class Ten> static R norm(const Ten & ten) {
	R _norm = 0.;
	R * it = ten.storage();
	R * end = ten.storage() + ten.size();
	for (; it < end; ++it) {
	_norm += it *it;
	}
	return sqrt(_norm);
	}
	};

	template <typename R> struct NormHelper<R, L_inf> {
	template <class Ten> static R norm(const Ten & ten) {
	R _norm = 0.;
	R * it = ten.storage();
	R * end = ten.storage() + ten.size();
	for (; it < end; ++it) {
	_norm = std::max(std::abs(*it), _norm);
	}
	return _norm;
	}
	};

	public:
	/----------------------------------------------------------------------- /
	/// "Entrywise" norm norm<L_p> @f[ \\|\boldsymbol{T}\\|_p = \left(
	/// \sum_i^{n[0]}\sum_j^{n[1]}\sum_k^{n[2]} \|T_{ijk}\|^p \right)^{\frac{1}{p}}
	/// @f]
	template <NormType norm_type> inline T norm() const {
	return NormHelper<T, norm_type>::norm(*this);
	}

	protected:
	std::array<UInt, ndim> n{};
	UInt _size{0};
	T * values{nullptr};
	bool wrapped{false};
	};

	/* -------------------------------------------------------------------------- */
	/* Vector */
	/* -------------------------------------------------------------------------- */
	template <typename T> class Vector : public TensorStorage<T, 1, Vector<T>> {
	using parent = TensorStorage<T, 1, Vector<T>>;

	public:
	using value_type = typename parent::value_type;
	using proxy = VectorProxy<T>;

	public:
	Vector() : parent() {}
	explicit Vector(UInt n, const T & def = T()) : parent(n, 0, 0, def) {}
	Vector(T * data, UInt n) : parent(data, n, 0, 0) {}
	Vector(const Vector & src, bool deep_copy = true) : parent(src, deep_copy) {}
	Vector(const TensorProxy<T, 1, Vector> & src) : parent(src) {}

	Vector(std::initializer_list<T> list) : parent(list.size(), 0, 0, T()) {
	UInt i = 0;
	for (auto val : list) {
	operator()(i++) = val;
	}
	}

	public:
	using iterator = types::details::vector_iterator<T &>;
	using const_iterator = types::details::vector_iterator<const T &>;

	iterator begin() { return iterator(this->storage()); }
	iterator end() { return iterator(this->storage() + this->size()); }

	const_iterator begin() const { return const_iterator(this->storage()); }
	const_iterator end() const {
	return const_iterator(this->storage() + this->size());
	}

	public:
	~Vector() override = default;

	/* ------------------------------------------------------------------------ */
	inline Vector & operator=(const Vector & src) {
	parent::operator=(src);
	return *this;
	}

	inline Vector & operator=(Vector && src) noexcept = default;

	/* ------------------------------------------------------------------------ */
	inline T & operator()(UInt i) {
	AKANTU_DEBUG_ASSERT((i < this->n[0]),
	"Access out of the vector! "
	<< "Index (" << i
	<< ") is out of the vector of size (" << this->n[0]
	<< ")");
	return *(this->values + i);
	}

	inline const T & operator()(UInt i) const {
	AKANTU_DEBUG_ASSERT((i < this->n[0]),
	"Access out of the vector! "
	<< "Index (" << i
	<< ") is out of the vector of size (" << this->n[0]
	<< ")");
	return *(this->values + i);
	}

	inline T & operator[](UInt i) { return this->operator()(i); }
	inline const T & operator[](UInt i) const { return this->operator()(i); }

	/* ------------------------------------------------------------------------ */
	inline Vector<T> & operator=(Real x) { return parent::operator=(x); }
	inline Vector<T> & operator/=(Real x) { return parent::operator/=(x); }
	/* ------------------------------------------------------------------------ */
	inline Vector<T> & operator*=(const Vector<T> & vect) {
	AKANTU_DEBUG_ASSERT(this->_size == vect._size,
	"The vectors have non matching sizes");
	T * a = this->storage();
	T * b = vect.storage();
	for (UInt i = 0; i < this->_size; ++i) {
	(a++) = *(b++);
	}
	return *this;
	}

	/* ------------------------------------------------------------------------ */
	inline Real dot(const Vector<T> & vect) const {
	return Math::vectorDot(this->values, vect.storage(), this->_size);
	}

	/* ------------------------------------------------------------------------ */
	inline Real mean() const {
	Real mean = 0;
	T * a = this->storage();
	for (UInt i = 0; i < this->_size; ++i) {
	mean += *(a++);
	}
	return mean / this->_size;
	}

	/* ------------------------------------------------------------------------ */
	inline Vector & crossProduct(const Vector<T> & v1, const Vector<T> & v2) {
	AKANTU_DEBUG_ASSERT(this->size() == 3,
	"crossProduct is only defined in 3D (n=" << this->size()
	<< ")");
	AKANTU_DEBUG_ASSERT(
	this->size() == v1.size() && this->size() == v2.size(),
	"crossProduct is not a valid operation non matching size vectors");
	Math::vectorProduct3(v1.storage(), v2.storage(), this->values);
	return *this;
	}

	inline Vector crossProduct(const Vector<T> & v) {
	Vector<T> tmp(this->size());
	tmp.crossProduct(*this, v);
	return tmp;
	}

	/* ------------------------------------------------------------------------ */
	inline void solve(const Matrix<T> & A, const Vector<T> & b) {
	AKANTU_DEBUG_ASSERT(
	this->size() == A.rows() && this->_size == A.cols(),
	"The size of the solution vector mismatches the size of the matrix");
	AKANTU_DEBUG_ASSERT(
	this->_size == b._size,
	"The rhs vector has a mismatch in size with the matrix");
	Math::solve(this->_size, A.storage(), this->values, b.storage());
	}

	/* ------------------------------------------------------------------------ */
	template <bool tr_A>
	inline void mul(const Matrix<T> & A, const Vector<T> & x, T alpha = T(1));
	/* ------------------------------------------------------------------------ */
	inline Real norm() const { return parent::template norm<L_2>(); }

	template <NormType nt> inline Real norm() const {
	return parent::template norm<nt>();
	}

	/* ------------------------------------------------------------------------ */
	inline Vector<Real> & normalize() {
	Real n = norm();
	operator/=(n);
	return *this;
	}

	/* ------------------------------------------------------------------------ */
	/// norm of (*this - x)
	inline Real distance(const Vector<T> & y) const {
	Real * vx = this->values;
	Real * vy = y.storage();
	Real sum_2 = 0;
	for (UInt i = 0; i < this->_size; ++i, ++vx, ++vy) { // NOLINT
	sum_2 += (vx - vy) * (vx - vy);
	}
	return sqrt(sum_2);
	}

	/* ------------------------------------------------------------------------ */
	inline bool equal(const Vector<T> & v,
	Real tolerance = Math::getTolerance()) const {
	T * a = this->storage();
	T * b = v.storage();
	UInt i = 0;
	while (i < this->_size && (std::abs((a++) - (b++)) < tolerance)) {
	++i;
	}
	return i == this->_size;
	}

	/* ------------------------------------------------------------------------ */
	inline short compare(const Vector<T> & v,
	Real tolerance = Math::getTolerance()) const {
	T * a = this->storage();
	T * b = v.storage();
	for (UInt i(0); i < this->_size; ++i, ++a, ++b) {
	if (std::abs(a - b) > tolerance) {
	return (((a - b) > tolerance) ? 1 : -1);
	}
	}
	return 0;
	}

	/* ------------------------------------------------------------------------ */
	inline bool operator==(const Vector<T> & v) const { return equal(v); }
	inline bool operator!=(const Vector<T> & v) const { return !operator==(v); }
	inline bool operator<(const Vector<T> & v) const { return compare(v) == -1; }
	inline bool operator>(const Vector<T> & v) const { return compare(v) == 1; }

	template <typename Func, typename Acc>
	decltype(auto) accumulate(const Vector<T> & v, Acc && accumulator,
	Func && func) const {
	T * a = this->storage();
	T * b = v.storage();
	for (UInt i(0); i < this->_size; ++i, ++a, ++b) {
	accumulator = func(a, b, std::forward<Acc>(accumulator));
	}
	return accumulator;
	}

	inline bool operator<=(const Vector<T> & v) const {
	bool res = true;
	return accumulate(v, res, [](auto && a, auto && b, auto && accumulator) {
	return accumulator & (a <= b);
	});
	}

	inline bool operator>=(const Vector<T> & v) const {
	bool res = true;
	return accumulate(v, res, [](auto && a, auto && b, auto && accumulator) {
	return accumulator & (a >= b);
	});
	}

	/* ------------------------------------------------------------------------ */
	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}

	stream << "[";
	for (UInt i = 0; i < this->_size; ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << this->values[i];
	}
	stream << "]";
	}

	/* ---------------------------------------------------------------------- */
	static inline Vector<T> zeros(UInt n) {
	Vector<T> tmp(n);
	tmp.set(T());
	return tmp;
	}
	};

	using RVector = Vector<Real>;

	/* ------------------------------------------------------------------------ */
	template <>
	inline bool Vector<UInt>::equal(const Vector<UInt> & v,
	__attribute__((unused)) Real tolerance) const {
	UInt * a = this->storage();
	UInt * b = v.storage();
	UInt i = 0;
	while (i < this->_size && ((a++) == (b++))) {
	++i;
	}
	return i == this->_size;
	}

	/* -------------------------------------------------------------------------- */
	namespace types {
	namespace details {
	template <typename Mat> class column_iterator {
	public:
	using difference_type = std::ptrdiff_t;
	using value_type = decltype(std::declval<Mat>().operator()(0));
	using pointer = value_type *;
	using reference = value_type &;
	using iterator_category = std::input_iterator_tag;

	column_iterator(Mat & mat, UInt col) : mat(mat), col(col) {}
	decltype(auto) operator*() { return mat(col); }
	decltype(auto) operator++() {
	++col;
	AKANTU_DEBUG_ASSERT(col <= mat.cols(), "The iterator is out of bound");
	return *this;
	}
	decltype(auto) operator++(int) {
	auto tmp = *this;
	++col;
	AKANTU_DEBUG_ASSERT(col <= mat.cols(), "The iterator is out of bound");
	return tmp;
	}
	bool operator!=(const column_iterator & other) const {
	return col != other.col;
	}

	bool operator==(const column_iterator & other) const {
	return not operator!=(other);
	}

	private:
	Mat & mat;
	UInt col;
	};
	} // namespace details
	} // namespace types

	/* ------------------------------------------------------------------------ */
	/* Matrix */
	/* ------------------------------------------------------------------------ */
	template <typename T> class Matrix : public TensorStorage<T, 2, Matrix<T>> {
	using parent = TensorStorage<T, 2, Matrix<T>>;

	public:
	using value_type = typename parent::value_type;
	using proxy = MatrixProxy<T>;

	public:
	Matrix() : parent() {}
	Matrix(UInt m, UInt n, const T & def = T()) : parent(m, n, 0, def) {}
	Matrix(T * data, UInt m, UInt n) : parent(data, m, n, 0) {}
	Matrix(const Matrix & src, bool deep_copy = true) : parent(src, deep_copy) {}
	Matrix(const MatrixProxy<T> & src) : parent(src) {}
	Matrix(std::initializer_list<std::initializer_list<T>> list) {
	static_assert(std::is_trivially_copyable<T>{},
	"Cannot create a tensor on non trivial types");
	std::size_t n = 0;
	std::size_t m = list.size();
	for (auto row : list) {
	n = std::max(n, row.size());
	}

	DimHelper<2>::setDims(m, n, 0, this->n);
	this->computeSize();
	this->values = new T[this->_size];
	this->set(0);

	UInt i{0};
	UInt j{0};
	for (auto & row : list) {
	for (auto & val : row) {
	at(i, j++) = val;
	}
	++i;
	j = 0;
	}
	}

	~Matrix() override = default;
	/* ------------------------------------------------------------------------ */
	inline Matrix & operator=(const Matrix & src) {
	parent::operator=(src);
	return *this;
	}

	inline Matrix & operator=(Matrix && src) noexcept = default;

	public:
	/* ---------------------------------------------------------------------- */
	UInt rows() const { return this->n[0]; }
	UInt cols() const { return this->n[1]; }

	/* ---------------------------------------------------------------------- */
	inline T & at(UInt i, UInt j) {
	AKANTU_DEBUG_ASSERT(((i < this->n[0]) && (j < this->n[1])),
	"Access out of the matrix! "
	<< "Index (" << i << ", " << j
	<< ") is out of the matrix of size (" << this->n[0]
	<< ", " << this->n[1] << ")");
	return (this->values + i + j this->n[0]);
	}

	inline const T & at(UInt i, UInt j) const {
	AKANTU_DEBUG_ASSERT(((i < this->n[0]) && (j < this->n[1])),
	"Access out of the matrix! "
	<< "Index (" << i << ", " << j
	<< ") is out of the matrix of size (" << this->n[0]
	<< ", " << this->n[1] << ")");
	return (this->values + i + j this->n[0]);
	}

	/* ------------------------------------------------------------------------ */
	inline T & operator()(UInt i, UInt j) { return this->at(i, j); }
	inline const T & operator()(UInt i, UInt j) const { return this->at(i, j); }

	/// give a line vector wrapped on the column i
	inline VectorProxy<T> operator()(UInt j) {
	AKANTU_DEBUG_ASSERT(j < this->n[1],
	"Access out of the matrix! "
	<< "You are trying to access the column vector "
	<< j << " in a matrix of size (" << this->n[0]
	<< ", " << this->n[1] << ")");
	return VectorProxy<T>(this->values + j * this->n[0], this->n[0]);
	}

	inline VectorProxy<T> operator()(UInt j) const {
	AKANTU_DEBUG_ASSERT(j < this->n[1],
	"Access out of the matrix! "
	<< "You are trying to access the column vector "
	<< j << " in a matrix of size (" << this->n[0]
	<< ", " << this->n[1] << ")");
	return VectorProxy<T>(this->values + j * this->n[0], this->n[0]);
	}

	public:
	decltype(auto) begin() {
	return types::details::column_iterator<Matrix<T>>(*this, 0);
	}
	decltype(auto) begin() const {
	return types::details::column_iterator<const Matrix<T>>(*this, 0);
	}

	decltype(auto) end() {
	return types::details::column_iterator<Matrix<T>>(*this, this->cols());
	}
	decltype(auto) end() const {
	return types::details::column_iterator<const Matrix<T>>(*this,
	this->cols());
	}

	/* ------------------------------------------------------------------------ */
	inline void block(const Matrix & block, UInt pos_i, UInt pos_j) {
	AKANTU_DEBUG_ASSERT(pos_i + block.rows() <= rows(),
	"The block size or position are not correct");
	AKANTU_DEBUG_ASSERT(pos_i + block.cols() <= cols(),
	"The block size or position are not correct");
	for (UInt i = 0; i < block.rows(); ++i) {
	for (UInt j = 0; j < block.cols(); ++j) {
	this->at(i + pos_i, j + pos_j) = block(i, j);
	}
	}
	}

	inline Matrix block(UInt pos_i, UInt pos_j, UInt block_rows,
	UInt block_cols) const {
	AKANTU_DEBUG_ASSERT(pos_i + block_rows <= rows(),
	"The block size or position are not correct");
	AKANTU_DEBUG_ASSERT(pos_i + block_cols <= cols(),
	"The block size or position are not correct");
	Matrix block(block_rows, block_cols);
	for (UInt i = 0; i < block_rows; ++i) {
	for (UInt j = 0; j < block_cols; ++j) {
	block(i, j) = this->at(i + pos_i, j + pos_j);
	}
	}
	return block;
	}

	inline T & operator[](UInt idx) { return *(this->values + idx); };
	inline const T & operator[](UInt idx) const { return *(this->values + idx); };

	/* ---------------------------------------------------------------------- */
	inline Matrix operator*(const Matrix & B) const {
	Matrix C(this->rows(), B.cols());
	C.mul<false, false>(*this, B);
	return C;
	}

	/* ----------------------------------------------------------------------- */
	inline Matrix & operator=(const T & x) { return parent::operator=(x); }

	inline Matrix & operator*=(const Matrix & B) {
	Matrix C(*this);
	this->mul<false, false>(C, B);
	return *this;
	}

	/* ---------------------------------------------------------------------- */
	template <bool tr_A, bool tr_B>
	inline void mul(const Matrix & A, const Matrix & B, T alpha = 1.0) {
	UInt k = A.cols();
	if (tr_A) {
	k = A.rows();
	}

	#ifndef AKANTU_NDEBUG
	if (tr_B) {
	AKANTU_DEBUG_ASSERT(k == B.cols(),
	"matrices to multiply have no fit dimensions");
	AKANTU_DEBUG_ASSERT(this->cols() == B.rows(),
	"matrices to multiply have no fit dimensions");
	} else {
	AKANTU_DEBUG_ASSERT(k == B.rows(),
	"matrices to multiply have no fit dimensions");
	AKANTU_DEBUG_ASSERT(this->cols() == B.cols(),
	"matrices to multiply have no fit dimensions");
	}
	if (tr_A) {
	AKANTU_DEBUG_ASSERT(this->rows() == A.cols(),
	"matrices to multiply have no fit dimensions");
	} else {
	AKANTU_DEBUG_ASSERT(this->rows() == A.rows(),
	"matrices to multiply have no fit dimensions");
	}
	#endif // AKANTU_NDEBUG

	Math::matMul<tr_A, tr_B>(this->rows(), this->cols(), k, alpha, A.storage(),
	B.storage(), 0., this->storage());
	}

	/* ---------------------------------------------------------------------- */
	inline void outerProduct(const Vector<T> & A, const Vector<T> & B) {
	AKANTU_DEBUG_ASSERT(
	A.size() == this->rows() && B.size() == this->cols(),
	"A and B are not compatible with the size of the matrix");
	for (UInt i = 0; i < this->rows(); ++i) {
	for (UInt j = 0; j < this->cols(); ++j) {
	this->values[i + j * this->rows()] += A[i] * B[j];
	}
	}
	}

	private:
	class EigenSorter {
	public:
	EigenSorter(const Vector<T> & eigs) : eigs(eigs) {}

	bool operator()(const UInt & a, const UInt & b) const {
	return (eigs(a) > eigs(b));
	}

	private:
	const Vector<T> & eigs;
	};

	public:
	/* ---------------------------------------------------------------------- */
	inline void eig(Vector<T> & eigenvalues, Matrix<T> & eigenvectors,
	bool sort = true) const {
	AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
	"eig is not a valid operation on a rectangular matrix");
	AKANTU_DEBUG_ASSERT(eigenvalues.size() == this->cols(),
	"eigenvalues should be of size " << this->cols()
	<< ".");
	#ifndef AKANTU_NDEBUG
	if (eigenvectors.storage() != nullptr) {
	AKANTU_DEBUG_ASSERT((eigenvectors.rows() == eigenvectors.cols()) &&
	(eigenvectors.rows() == this->cols()),
	"Eigenvectors needs to be a square matrix of size "
	<< this->cols() << " x " << this->cols() << ".");
	}
	#endif

	Matrix<T> tmp = *this;
	Vector<T> tmp_eigs(eigenvalues.size());
	Matrix<T> tmp_eig_vects(eigenvectors.rows(), eigenvectors.cols());

	if (tmp_eig_vects.rows() == 0 \|\| tmp_eig_vects.cols() == 0) {
	Math::matrixEig(tmp.cols(), tmp.storage(), tmp_eigs.storage());
	} else {
	Math::matrixEig(tmp.cols(), tmp.storage(), tmp_eigs.storage(),
	tmp_eig_vects.storage());
	}

	if (not sort) {
	eigenvalues = tmp_eigs;
	eigenvectors = tmp_eig_vects;
	return;
	}

	Vector<UInt> perm(eigenvalues.size());
	for (UInt i = 0; i < perm.size(); ++i) {
	perm(i) = i;
	}

	std::sort(perm.storage(), perm.storage() + perm.size(),
	EigenSorter(tmp_eigs));

	for (UInt i = 0; i < perm.size(); ++i) {
	eigenvalues(i) = tmp_eigs(perm(i));
	}

	if (tmp_eig_vects.rows() != 0 && tmp_eig_vects.cols() != 0) {
	for (UInt i = 0; i < perm.size(); ++i) {
	for (UInt j = 0; j < eigenvectors.rows(); ++j) {
	eigenvectors(j, i) = tmp_eig_vects(j, perm(i));
	}
	}
	}
	}

	/* ---------------------------------------------------------------------- */
	inline void eig(Vector<T> & eigenvalues) const {
	Matrix<T> empty;
	eig(eigenvalues, empty);
	}

	/* ---------------------------------------------------------------------- */
	inline void eye(T alpha = 1.) {
	AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
	"eye is not a valid operation on a rectangular matrix");
	this->zero();
	for (UInt i = 0; i < this->cols(); ++i) {
	this->values[i + i * this->rows()] = alpha;
	}
	}

	/* ---------------------------------------------------------------------- */
	static inline Matrix<T> eye(UInt m, T alpha = 1.) {
	Matrix<T> tmp(m, m);
	tmp.eye(alpha);
	return tmp;
	}

	/* ---------------------------------------------------------------------- */
	inline T trace() const {
	AKANTU_DEBUG_ASSERT(
	this->cols() == this->rows(),
	"trace is not a valid operation on a rectangular matrix");
	T trace = 0.;
	for (UInt i = 0; i < this->rows(); ++i) {
	trace += this->values[i + i * this->rows()];
	}
	return trace;
	}

	/* ---------------------------------------------------------------------- */
	inline Matrix transpose() const {
	Matrix tmp(this->cols(), this->rows());
	for (UInt i = 0; i < this->rows(); ++i) {
	for (UInt j = 0; j < this->cols(); ++j) {
	tmp(j, i) = operator()(i, j);
	}
	}
	return tmp;
	}

	/* ---------------------------------------------------------------------- */
	inline void inverse(const Matrix & A) {
	AKANTU_DEBUG_ASSERT(A.cols() == A.rows(),
	"inv is not a valid operation on a rectangular matrix");
	AKANTU_DEBUG_ASSERT(this->cols() == A.cols(),
	"the matrix should have the same size as its inverse");

	if (this->cols() == 1) {
	this->values = 1. / A.storage();
	} else if (this->cols() == 2) {
	Math::inv2(A.storage(), this->values);
	} else if (this->cols() == 3) {
	Math::inv3(A.storage(), this->values);
	} else {
	Math::inv(this->cols(), A.storage(), this->values);
	}
	}

	inline Matrix inverse() {
	Matrix inv(this->rows(), this->cols());
	inv.inverse(*this);
	return inv;
	}

	/* --------------------------------------------------------------------- */
	inline T det() const {
	AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
	"inv is not a valid operation on a rectangular matrix");
	if (this->cols() == 1) {
	return *(this->values);
	}
	if (this->cols() == 2) {
	return Math::det2(this->values);
	}
	if (this->cols() == 3) {
	return Math::det3(this->values);
	}
	return Math::det(this->cols(), this->values);
	}

	/* --------------------------------------------------------------------- */
	inline T doubleDot(const Matrix<T> & other) const {
	AKANTU_DEBUG_ASSERT(
	this->cols() == this->rows(),
	"doubleDot is not a valid operation on a rectangular matrix");
	if (this->cols() == 1) {
	return (this->values) *(other.storage());
	}
	if (this->cols() == 2) {
	return Math::matrixDoubleDot22(this->values, other.storage());
	}
	if (this->cols() == 3) {
	return Math::matrixDoubleDot33(this->values, other.storage());
	}

	AKANTU_ERROR("doubleDot is not defined for other spatial dimensions"
	<< " than 1, 2 or 3.");
	}

	/* ---------------------------------------------------------------------- */
	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}

	stream << "[";
	for (UInt i = 0; i < this->n[0]; ++i) {
	if (i != 0) {
	stream << ", ";
	}
	stream << "[";
	for (UInt j = 0; j < this->n[1]; ++j) {
	if (j != 0) {
	stream << ", ";
	}
	stream << operator()(i, j);
	}
	stream << "]";
	}
	stream << "]";
	};
	};

	/* ------------------------------------------------------------------------ */
	template <typename T>
	template <bool tr_A>
	inline void Vector<T>::mul(const Matrix<T> & A, const Vector<T> & x, T alpha) {
	#ifndef AKANTU_NDEBUG
	UInt n = x.size();
	if (tr_A) {
	AKANTU_DEBUG_ASSERT(n == A.rows(),
	"matrix and vector to multiply have no fit dimensions");
	AKANTU_DEBUG_ASSERT(this->size() == A.cols(),
	"matrix and vector to multiply have no fit dimensions");
	} else {
	AKANTU_DEBUG_ASSERT(n == A.cols(),
	"matrix and vector to multiply have no fit dimensions");
	AKANTU_DEBUG_ASSERT(this->size() == A.rows(),
	"matrix and vector to multiply have no fit dimensions");
	}
	#endif
	Math::matVectMul<tr_A>(A.rows(), A.cols(), alpha, A.storage(), x.storage(),
	0., this->storage());
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const Matrix<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const Vector<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	/* ------------------------------------------------------------------------ */
	/* Tensor3 */
	/* ------------------------------------------------------------------------ */
	template <typename T> class Tensor3 : public TensorStorage<T, 3, Tensor3<T>> {
	using parent = TensorStorage<T, 3, Tensor3<T>>;

	public:
	using value_type = typename parent::value_type;
	using proxy = Tensor3Proxy<T>;

	public:
	Tensor3() : parent(){};

	Tensor3(UInt m, UInt n, UInt p, const T & def = T()) : parent(m, n, p, def) {}

	Tensor3(T * data, UInt m, UInt n, UInt p) : parent(data, m, n, p) {}

	Tensor3(const Tensor3 & src, bool deep_copy = true)
	: parent(src, deep_copy) {}

	Tensor3(const proxy & src) : parent(src) {}

	public:
	/* ------------------------------------------------------------------------ */
	inline Tensor3 & operator=(const Tensor3 & src) {
	parent::operator=(src);
	return *this;
	}

	/* ---------------------------------------------------------------------- */
	inline T & operator()(UInt i, UInt j, UInt k) {
	AKANTU_DEBUG_ASSERT(
	(i < this->n[0]) && (j < this->n[1]) && (k < this->n[2]),
	"Access out of the tensor3! "
	<< "You are trying to access the element "
	<< "(" << i << ", " << j << ", " << k << ") in a tensor of size ("
	<< this->n[0] << ", " << this->n[1] << ", " << this->n[2] << ")");
	return (this->values + (k this->n[0] + i) * this->n[1] + j);
	}

	inline const T & operator()(UInt i, UInt j, UInt k) const {
	AKANTU_DEBUG_ASSERT(
	(i < this->n[0]) && (j < this->n[1]) && (k < this->n[2]),
	"Access out of the tensor3! "
	<< "You are trying to access the element "
	<< "(" << i << ", " << j << ", " << k << ") in a tensor of size ("
	<< this->n[0] << ", " << this->n[1] << ", " << this->n[2] << ")");
	return (this->values + (k this->n[0] + i) * this->n[1] + j);
	}

	inline MatrixProxy<T> operator()(UInt k) {
	AKANTU_DEBUG_ASSERT((k < this->n[2]),
	"Access out of the tensor3! "
	<< "You are trying to access the slice " << k
	<< " in a tensor3 of size (" << this->n[0] << ", "
	<< this->n[1] << ", " << this->n[2] << ")");
	return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
	this->n[0], this->n[1]);
	}

	inline MatrixProxy<T> operator()(UInt k) const {
	AKANTU_DEBUG_ASSERT((k < this->n[2]),
	"Access out of the tensor3! "
	<< "You are trying to access the slice " << k
	<< " in a tensor3 of size (" << this->n[0] << ", "
	<< this->n[1] << ", " << this->n[2] << ")");
	return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
	this->n[0], this->n[1]);
	}

	inline MatrixProxy<T> operator[](UInt k) {
	return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
	this->n[0], this->n[1]);
	}

	inline MatrixProxy<T> operator[](UInt k) const {
	return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
	this->n[0], this->n[1]);
	}
	};

	/* -------------------------------------------------------------------------- */
	// support operations for the creation of other vectors
	/* -------------------------------------------------------------------------- */
	template <typename T>
	Vector<T> operator*(const T & scalar, const Vector<T> & a) {
	Vector<T> r(a);
	r *= scalar;
	return r;
	}

	template <typename T>
	Vector<T> operator*(const Vector<T> & a, const T & scalar) {
	Vector<T> r(a);
	r *= scalar;
	return r;
	}

	template <typename T>
	Vector<T> operator/(const Vector<T> & a, const T & scalar) {
	Vector<T> r(a);
	r /= scalar;
	return r;
	}

	template <typename T>
	Vector<T> operator*(const Vector<T> & a, const Vector<T> & b) {
	Vector<T> r(a);
	r *= b;
	return r;
	}

	template <typename T>
	Vector<T> operator+(const Vector<T> & a, const Vector<T> & b) {
	Vector<T> r(a);
	r += b;
	return r;
	}

	template <typename T>
	Vector<T> operator-(const Vector<T> & a, const Vector<T> & b) {
	Vector<T> r(a);
	r -= b;
	return r;
	}

	template <typename T>
	Vector<T> operator*(const Matrix<T> & A, const Vector<T> & b) {
	Vector<T> r(b.size());
	r.template mul<false>(A, b);
	return r;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	Matrix<T> operator*(const T & scalar, const Matrix<T> & a) {
	Matrix<T> r(a);
	r *= scalar;
	return r;
	}

	template <typename T>
	Matrix<T> operator*(const Matrix<T> & a, const T & scalar) {
	Matrix<T> r(a);
	r *= scalar;
	return r;
	}

	template <typename T>
	Matrix<T> operator/(const Matrix<T> & a, const T & scalar) {
	Matrix<T> r(a);
	r /= scalar;
	return r;
	}

	template <typename T>
	Matrix<T> operator+(const Matrix<T> & a, const Matrix<T> & b) {
	Matrix<T> r(a);
	r += b;
	return r;
	}

	template <typename T>
	Matrix<T> operator-(const Matrix<T> & a, const Matrix<T> & b) {
	Matrix<T> r(a);
	r -= b;
	return r;
	}

	} // namespace akantu

	#include <iterator>

	namespace std {
	template <typename R>
	struct iterator_traits<::akantu::types::details::vector_iterator<R>> {
	protected:
	using iterator = ::akantu::types::details::vector_iterator<R>;

	public:
	using iterator_category = typename iterator::iterator_category;
	using value_type = typename iterator::value_type;
	using difference_type = typename iterator::difference_type;
	using pointer = typename iterator::pointer;
	using reference = typename iterator::reference;
	};

	template <typename Mat>
	struct iterator_traits<::akantu::types::details::column_iterator<Mat>> {
	protected:
	using iterator = ::akantu::types::details::column_iterator<Mat>;

	public:
	using iterator_category = typename iterator::iterator_category;
	using value_type = typename iterator::value_type;
	using difference_type = typename iterator::difference_type;
	using pointer = typename iterator::pointer;
	using reference = typename iterator::reference;
	};

	} // namespace std

	#endif /* AKANTU_AKA_TYPES_HH_ */
	diff --git a/src/common/aka_voigthelper.cc b/src/common/aka_voigthelper.cc
	index 95199c21b..efb6517b1 100644
	--- a/src/common/aka_voigthelper.cc
	+++ b/src/common/aka_voigthelper.cc
	@@ -1,69 +1,69 @@
	/**
	* @file aka_voigthelper.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Till Junge <till.junge@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 20 2013
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Voigt indices
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_voigthelper.hh"
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* clang-format off */
	template <> const UInt VoigtHelper<1>::mat[][1] = {{0}};
	template <> const UInt VoigtHelper<2>::mat[][2] = {{0, 2},
	{3, 1}};
	template <> const UInt VoigtHelper<3>::mat[][3] = {{0, 5, 4},
	{8, 1, 3},
	{7, 6, 2}};
	template <> const UInt VoigtHelper<1>::vec[][2] = {{0, 0}};
	template <> const UInt VoigtHelper<2>::vec[][2] = {{0, 0},
	{1, 1},
	{0, 1},
	{1, 0}};
	template <> const UInt VoigtHelper<3>::vec[][2] = {{0, 0},
	{1, 1},
	{2, 2},
	{1, 2},
	{0, 2},
	{0, 1},
	{2, 1},
	{2, 0},
	{1, 0}};
	template <> const Real VoigtHelper<1>::factors[] = {1.};
	template <> const Real VoigtHelper<2>::factors[] = {1., 1., 2.};
	template <> const Real VoigtHelper<3>::factors[] = {1., 1., 1.,
	2., 2., 2.};

	/* clang-format on */
	} // namespace akantu
	diff --git a/src/common/aka_voigthelper.hh b/src/common/aka_voigthelper.hh
	index c0bd499be..61021db3b 100644
	--- a/src/common/aka_voigthelper.hh
	+++ b/src/common/aka_voigthelper.hh
	@@ -1,103 +1,103 @@
	/**
	* @file aka_voigthelper.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Till Junge <till.junge@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 20 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Helper file for Voigt notation
	* Wikipedia convention: @f[2*\epsilon_{ij} (i!=j) = voigt_\epsilon_{I}@f]
	* http://en.wikipedia.org/wiki/Voigt_notation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_types.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKA_VOIGTHELPER_HH_
	#define AKA_VOIGTHELPER_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim> class VoigtHelper {
	static_assert(dim > 0U, "Cannot be < 1D");
	static_assert(dim < 4U, "Cannot be > 3D");

	public:
	/* ------------------------------------------------------------------------ */
	template <class M, class V>
	static inline void matrixToVoigt(M && matrix, V && vector);

	template <class M> static inline decltype(auto) matrixToVoigt(M && matrix);

	template <class M, class V>
	static inline void matrixToVoigtWithFactors(M && matrix, V && vector);

	template <class M>
	static inline decltype(auto) matrixToVoigtWithFactors(M && matrix);

	template <class M, class V>
	static inline void voigtToMatrix(V && vector, M && matrix);

	template <class V> static inline decltype(auto) voigtToMatrix(V && vector);
	/* ------------------------------------------------------------------------ */

	/// transfer the B matrix to a Voigt notation B matrix
	inline static void transferBMatrixToSymVoigtBMatrix(
	const Matrix<Real> & B, Matrix<Real> & Bvoigt, UInt nb_nodes_per_element);

	/// transfer the BNL matrix to a Voigt notation B matrix (See Bathe et al.
	/// IJNME vol 9, 1975)
	inline static void transferBMatrixToBNL(const Matrix<Real> & B,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element);

	/// transfer the BL2 matrix to a Voigt notation B matrix (See Bathe et al.
	/// IJNME vol 9, 1975)
	inline static void transferBMatrixToBL2(const Matrix<Real> & B,
	const Matrix<Real> & grad_u,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element);

	public:
	static constexpr UInt size{(dim * (dim - 1)) / 2 + dim};
	// matrix of vector index I as function of tensor indices i,j
	static const UInt mat[dim][dim];
	// array of matrix indices ij as function of vector index I
	static const UInt vec[dim * dim][2];
	// factors to multiply the strain by for voigt notation
	static const Real factors[size];
	};

	} // namespace akantu

	#include "aka_voigthelper_tmpl.hh"

	#endif
	diff --git a/src/common/aka_voigthelper_tmpl.hh b/src/common/aka_voigthelper_tmpl.hh
	index 2ba35a305..f15c12ad6 100644
	--- a/src/common/aka_voigthelper_tmpl.hh
	+++ b/src/common/aka_voigthelper_tmpl.hh
	@@ -1,243 +1,243 @@
	/**
	* @file aka_voigthelper_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 20 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of the voight helper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_voigthelper.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_VOIGTHELPER_TMPL_HH_
	#define AKANTU_AKA_VOIGTHELPER_TMPL_HH_

	namespace akantu {

	template <UInt dim> constexpr UInt VoigtHelper<dim>::size;

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class M, class V>
	inline void VoigtHelper<dim>::matrixToVoigt(M && matrix, V && vector) {
	for (UInt I = 0; I < size; ++I) {
	auto i = vec[I][0];
	auto j = vec[I][1];
	vector(I) = matrix(i, j);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class M>
	inline decltype(auto) VoigtHelper<dim>::matrixToVoigt(M && matrix) {
	Vector<Real> vector(size);
	matrixToVoigt(std::forward<M>(matrix), vector);
	return vector;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class M, class V>
	inline void VoigtHelper<dim>::matrixToVoigtWithFactors(M && matrix,
	V && vector) {
	for (UInt I = 0; I < size; ++I) {
	auto i = vec[I][0];
	auto j = vec[I][1];
	vector(I) = factors[I] * matrix(i, j);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class M>
	inline decltype(auto) VoigtHelper<dim>::matrixToVoigtWithFactors(M && matrix) {
	Vector<Real> vector(size);
	matrixToVoigtWithFactors(std::forward<M>(matrix), vector);
	return vector;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class M, class V>
	inline void VoigtHelper<dim>::voigtToMatrix(V && vector, M && matrix) {
	for (UInt I = 0; I < size; ++I) {
	auto i = vec[I][0];
	auto j = vec[I][1];
	matrix(i, j) = matrix(j, i) = vector(I);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	template <class V>
	inline decltype(auto) VoigtHelper<dim>::voigtToMatrix(V && vector) {
	Matrix<Real> matrix(dim, dim);
	voigtToMatrix(std::forward<V>(vector), matrix);
	return matrix;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
	const Matrix<Real> & B, Matrix<Real> & Bvoigt, UInt nb_nodes_per_element) {
	Bvoigt.zero();

	for (UInt i = 0; i < dim; ++i) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	Bvoigt(i, i + n * dim) = B(i, n);
	}
	}

	if (dim == 2) {
	/// in 2D, fill the @f$ [\frac{\partial N_i}{\partial x}, \frac{\partial
	/// N_i}{\partial y}]@f$ row
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	Bvoigt(2, 1 + n * 2) = B(0, n);
	Bvoigt(2, 0 + n * 2) = B(1, n);
	}
	}

	if (dim == 3) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	Real dndx = B(0, n);
	Real dndy = B(1, n);
	Real dndz = B(2, n);

	/// in 3D, fill the @f$ [0, \frac{\partial N_i}{\partial y},
	/// \frac{N_i}{\partial z}]@f$ row
	Bvoigt(3, 1 + n * 3) = dndz;
	Bvoigt(3, 2 + n * 3) = dndy;

	/// in 3D, fill the @f$ [\frac{\partial N_i}{\partial x}, 0,
	/// \frac{N_i}{\partial z}]@f$ row
	Bvoigt(4, 0 + n * 3) = dndz;
	Bvoigt(4, 2 + n * 3) = dndx;

	/// in 3D, fill the @f$ [\frac{\partial N_i}{\partial x},
	/// \frac{N_i}{\partial y}, 0]@f$ row
	Bvoigt(5, 0 + n * 3) = dndy;
	Bvoigt(5, 1 + n * 3) = dndx;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void VoigtHelper<dim>::transferBMatrixToBNL(const Matrix<Real> & B,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element) {
	Bvoigt.zero();

	// see Finite element formulations for large deformation dynamic analysis,
	// Bathe et al. IJNME vol 9, 1975, page 364 B_{NL}
	for (UInt i = 0; i < dim; ++i) {
	for (UInt m = 0; m < nb_nodes_per_element; ++m) {
	for (UInt n = 0; n < dim; ++n) {
	// std::cout << B(n, m) << std::endl;
	Bvoigt(i * dim + n, m * dim + i) = B(n, m);
	}
	}
	}
	// TODO: Verify the 2D and 1D case
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void VoigtHelper<1>::transferBMatrixToBL2(const Matrix<Real> & B,
	const Matrix<Real> & grad_u,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element) {
	Bvoigt.zero();
	for (UInt j = 0; j < nb_nodes_per_element; ++j) {
	Bvoigt(0, j) = grad_u(0, 0) * B(0, j);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void VoigtHelper<3>::transferBMatrixToBL2(const Matrix<Real> & dNdX,
	const Matrix<Real> & grad_u,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element) {
	Bvoigt.zero();

	for (UInt I = 0; I < 3; ++I) {
	for (UInt a = 0; a < nb_nodes_per_element; ++a) {
	for (UInt i = 0; i < 3; ++i) {
	Bvoigt(I, a * 3 + i) = grad_u(i, I) * dNdX(I, a);
	}
	}
	}

	for (UInt Iv = 3; Iv < 6; ++Iv) {
	for (UInt a = 0; a < nb_nodes_per_element; ++a) {
	for (UInt k = 0; k < 3; ++k) {
	UInt aux = Iv - 3;
	for (UInt m = 0; m < 3; ++m) {
	if (m != aux) {
	UInt index1 = m;
	UInt index2 = 3 - m - aux;
	Bvoigt(Iv, a * 3 + k) += grad_u(k, index1) * dNdX(index2, a);
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void VoigtHelper<2>::transferBMatrixToBL2(const Matrix<Real> & B,
	const Matrix<Real> & grad_u,
	Matrix<Real> & Bvoigt,
	UInt nb_nodes_per_element) {

	Bvoigt.zero();

	for (UInt i = 0; i < 2; ++i) {
	for (UInt j = 0; j < nb_nodes_per_element; ++j) {
	for (UInt k = 0; k < 2; ++k) {
	Bvoigt(i, j * 2 + k) = grad_u(k, i) * B(i, j);
	}
	}
	}

	for (UInt j = 0; j < nb_nodes_per_element; ++j) {
	for (UInt k = 0; k < 2; ++k) {
	for (UInt m = 0; m < 2; ++m) {
	UInt index1 = m;
	UInt index2 = (2 - 1) - m;
	Bvoigt(2, j * 2 + k) += grad_u(k, index1) * B(index2, j);
	}
	}
	}
	}

	} // namespace akantu

	#endif /* AKANTU_AKA_VOIGTHELPER_TMPL_HH_ */
	diff --git a/src/common/aka_warning.hh b/src/common/aka_warning.hh
	index 24a0225b9..3e13c380f 100644
	--- a/src/common/aka_warning.hh
	+++ b/src/common/aka_warning.hh
	@@ -1,69 +1,69 @@
	/**
	* @file aka_warning.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Tue Nov 17 2020
	*
	* @brief file to include to remove some warnings
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	AKANTU_WARNING_IGNORE_UNUSED_PARAMETER

	AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS
	**/

	// --- Intel warnings ----------------------------------------------------------
	#if defined(__INTEL_COMPILER)

	-# if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	-# endif
	+#if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	+#endif

	// --- Clang Warnings ----------------------------------------------------------
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	-# pragma clang diagnostic push
	-# if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	-# pragma clang diagnostic ignored "-Wunused-parameter"
	-# endif
	-# if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	-# pragma clang diagnostic ignored "-Wgnu-zero-variadic-macro-arguments"
	-# endif
	+#pragma clang diagnostic push
	+#if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	+#pragma clang diagnostic ignored "-Wunused-parameter"
	+#endif
	+#if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	+#pragma clang diagnostic ignored "-Wgnu-zero-variadic-macro-arguments"
	+#endif

	// --- GCC warnings ------------------------------------------------------------
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	-# define GCC_VERSION \
	- (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	-# if GCC_VERSION > 40600
	-# pragma GCC diagnostic push
	-# endif
	-# if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	-# pragma GCC diagnostic ignored "-Wunused-parameter"
	-# endif
	-# if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	-# pragma GCC diagnostic ignored "-Wvariadic-macros"
	-# pragma GCC diagnostic ignored "-Wpedantic"
	-# endif
	+#define GCC_VERSION \
	+ (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	+#if GCC_VERSION > 40600
	+#pragma GCC diagnostic push
	+#endif
	+#if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	+#pragma GCC diagnostic ignored "-Wunused-parameter"
	+#endif
	+#if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	+#pragma GCC diagnostic ignored "-Wvariadic-macros"
	+#pragma GCC diagnostic ignored "-Wpedantic"
	+#endif
	#endif
	diff --git a/src/common/aka_warning_restore.hh b/src/common/aka_warning_restore.hh
	index 67ac911c7..7fa0ae320 100644
	--- a/src/common/aka_warning_restore.hh
	+++ b/src/common/aka_warning_restore.hh
	@@ -1,56 +1,56 @@
	/**
	* @file aka_warning_restore.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Tue Nov 17 2020
	*
	* @brief file to include to reactivate the previously deactivatied warnings
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	// --- Intel -------------------------------------------------------------------
	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )

	// --- Clang -------------------------------------------------------------------
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	-# pragma clang diagnostic pop
	+#pragma clang diagnostic pop

	// --- GCC ---------------------------------------------------------------------
	#elif defined(__GNUG__)
	-# if GCC_VERSION > 40600
	-# pragma GCC diagnostic pop
	-# else
	-# if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	-# pragma GCC diagnostic warning "-Wunused-parameter"
	-# endif
	-# if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	-# pragma GCC diagnostic ignored "-Wpedantic"
	-# endif
	-# endif
	+#if GCC_VERSION > 40600
	+#pragma GCC diagnostic pop
	+#else
	+#if defined(AKANTU_WARNING_IGNORE_UNUSED_PARAMETER)
	+#pragma GCC diagnostic warning "-Wunused-parameter"
	+#endif
	+#if defined(AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS)
	+#pragma GCC diagnostic ignored "-Wpedantic"
	+#endif
	+#endif
	#endif

	#undef AKANTU_WARNING_IGNORE_UNUSED_PARAMETER
	#undef AKANTU_WARNING_IGNORE_VARIADIC_MACRO_ARGUMENTS
	diff --git a/src/fe_engine/cohesive_element.hh b/src/fe_engine/cohesive_element.hh
	index 4e473a201..2f3a7e9f9 100644
	--- a/src/fe_engine/cohesive_element.hh
	+++ b/src/fe_engine/cohesive_element.hh
	@@ -1,91 +1,91 @@
	/**
	* @file cohesive_element.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Generates the cohesive element structres (defined in
	* element_class.hh)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COHESIVE_ELEMENT_HH_
	#define AKANTU_COHESIVE_ELEMENT_HH_

	namespace akantu {

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_2d_4, _gt_cohesive_2d_4,
	_itp_lagrange_segment_2, _ek_cohesive, 2,
	_git_segment, 2);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_2d_6, _gt_cohesive_2d_6,
	_itp_lagrange_segment_3, _ek_cohesive, 2,
	_git_segment, 3);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_1d_2, _gt_cohesive_1d_2,
	_itp_lagrange_point_1, _ek_cohesive, 1,
	_git_point, 1);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_3d_6, _gt_cohesive_3d_6,
	_itp_lagrange_triangle_3, _ek_cohesive, 3,
	_git_triangle, 2);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_3d_12, _gt_cohesive_3d_12,
	_itp_lagrange_triangle_6, _ek_cohesive, 3,
	_git_triangle, 3);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_3d_8, _gt_cohesive_3d_8,
	_itp_lagrange_quadrangle_4, _ek_cohesive,
	3, _git_segment, 2);

	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_cohesive_3d_16, _gt_cohesive_3d_16,
	_itp_serendip_quadrangle_8, _ek_cohesive,
	3, _git_segment, 3);

	template <ElementType> struct CohesiveFacetProperty {
	static const ElementType cohesive_type = _not_defined;
	};

	#define AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(ftype, ctype) \
	template <> struct CohesiveFacetProperty<ftype> { \
	static const ElementType cohesive_type = ctype; \
	}

	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_point_1, _cohesive_1d_2);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_segment_2, _cohesive_2d_4);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_segment_3, _cohesive_2d_6);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_triangle_3, _cohesive_3d_6);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_triangle_6, _cohesive_3d_12);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_quadrangle_4, _cohesive_3d_8);
	AKANTU_DEFINE_COHESIVE_FACET_PROPERTY(_quadrangle_8, _cohesive_3d_16);

	} // namespace akantu

	#endif /* AKANTU_COHESIVE_ELEMENT_HH_ */
	diff --git a/src/fe_engine/element.hh b/src/fe_engine/element.hh
	index 3c5b29168..ccf5f8589 100644
	--- a/src/fe_engine/element.hh
	+++ b/src/fe_engine/element.hh
	@@ -1,129 +1,129 @@
	/**
	* @file element.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Element helper class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_HH_
	#define AKANTU_ELEMENT_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Element */
	/* -------------------------------------------------------------------------- */
	class Element {
	public:
	ElementType type;
	UInt element;
	GhostType ghost_type;

	// ElementKind kind;
	// ElementType type{_not_defined};
	// UInt element{0};
	// GhostType ghost_type{_not_ghost};
	// ElementKind kind{_ek_regular};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline ElementKind kind() const;

	inline bool operator==(const Element & elem) const {
	return std::tie(type, element, ghost_type) ==
	std::tie(elem.type, elem.element, elem.ghost_type);
	}

	inline bool operator!=(const Element & elem) const {
	return std::tie(type, element, ghost_type) !=
	std::tie(elem.type, elem.element, elem.ghost_type);
	}

	// inline bool operator==(const Element & elem) const {
	// return ((element == elem.element) && (type == elem.type) &&
	// (ghost_type == elem.ghost_type) && (kind == elem.kind));
	// }

	// inline bool operator!=(const Element & elem) const {
	// return ((element != elem.element) \|\| (type != elem.type) \|\|
	// (ghost_type != elem.ghost_type) \|\| (kind != elem.kind));
	// }

	inline bool operator<(const Element & rhs) const;
	};

	namespace {
	const Element ElementNull{_not_defined, UInt(-1), _casper};
	// Element{_not_defined, 0, _casper, _ek_not_defined};
	} // namespace

	/* -------------------------------------------------------------------------- */
	inline bool Element::operator<(const Element & rhs) const {
	// bool res =
	// (rhs == ElementNull) \|\|
	// ((this->kind < rhs.kind) \|\|
	// ((this->kind == rhs.kind) &&
	// ((this->ghost_type < rhs.ghost_type) \|\|
	// ((this->ghost_type == rhs.ghost_type) &&
	// ((this->type < rhs.type) \|\|
	// ((this->type == rhs.type) && (this->element < rhs.element)))))));
	return ((rhs == ElementNull) \|\|
	std::tie(ghost_type, type, element) <
	std::tie(rhs.ghost_type, rhs.type, rhs.element));
	}

	} // namespace akantu

	namespace std {
	inline string to_string(const akantu::Element & _this) {
	if (_this == akantu::ElementNull) {
	return "ElementNull";
	}

	string str = "Element [" + to_string(_this.type) + ", " +
	to_string(_this.element) + ", " + to_string(_this.ghost_type) +
	"]";
	return str;
	}
	} // namespace std

	namespace akantu {

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream, const Element & _this) {
	stream << std::to_string(_this);
	return stream;
	}
	} // namespace akantu

	#endif /* AKANTU_ELEMENT_HH_ */
	diff --git a/src/fe_engine/element_class.hh b/src/fe_engine/element_class.hh
	index 6df433c19..e13009524 100644
	--- a/src/fe_engine/element_class.hh
	+++ b/src/fe_engine/element_class.hh
	@@ -1,436 +1,436 @@
	/**
	* @file element_class.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Declaration of the ElementClass main class and the
	* Integration and Interpolation elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_types.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_HH_
	#define AKANTU_ELEMENT_CLASS_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/// default element class structure
	template <ElementType element_type> struct ElementClassProperty {
	static const GeometricalType geometrical_type{_gt_not_defined};
	static const InterpolationType interpolation_type{_itp_not_defined};
	static const ElementKind element_kind{_ek_regular};
	static const UInt spatial_dimension{0};
	static const GaussIntegrationType gauss_integration_type{_git_not_defined};
	static const UInt polynomial_degree{0};
	};

	#if !defined(DOXYGEN)
	/// Macro to generate the element class structures for different element types
	#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
	interp_type, elem_kind, sp, \
	gauss_int_type, min_int_order) \
	template <> struct ElementClassProperty<elem_type> { \
	static const GeometricalType geometrical_type{geom_type}; \
	static const InterpolationType interpolation_type{interp_type}; \
	static const ElementKind element_kind{elem_kind}; \
	static const UInt spatial_dimension{sp}; \
	static const GaussIntegrationType gauss_integration_type{gauss_int_type}; \
	static const UInt polynomial_degree{min_int_order}; \
	}
	#else
	#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
	interp_type, elem_kind, sp, \
	gauss_int_type, min_int_order)
	#endif

	/* -------------------------------------------------------------------------- */
	/* Geometry */
	/* -------------------------------------------------------------------------- */
	/// Default GeometricalShape structure
	template <GeometricalType geometrical_type> struct GeometricalShape {
	static const GeometricalShapeType shape{_gst_point};
	};

	/// Templated GeometricalShape with function contains
	template <GeometricalShapeType shape> struct GeometricalShapeContains {
	/// Check if the point (vector in 2 and 3D) at natural coordinate coor
	template <class vector_type>
	static inline bool contains(const vector_type & coord);
	};

	#if !defined(DOXYGEN)
	/// Macro to generate the GeometricalShape structures for different geometrical
	/// types
	#define AKANTU_DEFINE_SHAPE(geom_type, geom_shape) \
	template <> struct GeometricalShape<geom_type> { \
	static const GeometricalShapeType shape{geom_shape}; \
	}

	AKANTU_DEFINE_SHAPE(_gt_hexahedron_20, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_hexahedron_8, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_pentahedron_15, _gst_prism);
	AKANTU_DEFINE_SHAPE(_gt_pentahedron_6, _gst_prism);
	AKANTU_DEFINE_SHAPE(_gt_point, _gst_point);
	AKANTU_DEFINE_SHAPE(_gt_quadrangle_4, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_quadrangle_8, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_segment_2, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_segment_3, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_tetrahedron_10, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_tetrahedron_4, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_triangle_3, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_triangle_6, _gst_triangle);
	#endif
	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type>
	struct GeometricalElementProperty {};

	template <ElementType element_type>
	struct ElementClassExtraGeometryProperties {};

	/* -------------------------------------------------------------------------- */
	/// Templated GeometricalElement with function getInradius
	template <GeometricalType geometrical_type,
	GeometricalShapeType shape =
	GeometricalShape<geometrical_type>::shape>
	class GeometricalElement {
	using geometrical_property = GeometricalElementProperty<geometrical_type>;

	public:
	/// compute the in-radius: \todo should be renamed for characteristic length
	static inline Real getInradius(const Matrix<Real> & /coord/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// true if the natural coordinates are in the element
	template <class vector_type>
	static inline bool contains(const vector_type & coord);

	public:
	static AKANTU_GET_MACRO_NOT_CONST(SpatialDimension,
	geometrical_property::spatial_dimension,
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(NbNodesPerElement,
	geometrical_property::nb_nodes_per_element,
	UInt);
	static inline constexpr auto getNbFacetTypes() {
	return geometrical_property::nb_facet_types;
	};
	static inline UInt getNbFacetsPerElement(UInt t);
	static inline UInt getNbFacetsPerElement();
	static inline constexpr auto getFacetLocalConnectivityPerElement(UInt t = 0);
	};

	/* -------------------------------------------------------------------------- */
	/* Interpolation */
	/* -------------------------------------------------------------------------- */
	/// default InterpolationProperty structure
	template <InterpolationType interpolation_type> struct InterpolationProperty {};

	#if !defined(DOXYGEN)
	/// Macro to generate the InterpolationProperty structures for different
	/// interpolation types
	#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
	nb_nodes, ndim) \
	template <> struct InterpolationProperty<itp_type> { \
	static constexpr InterpolationKind kind{itp_kind}; \
	static constexpr UInt nb_nodes_per_element{nb_nodes}; \
	static constexpr UInt natural_space_dimension{ndim}; \
	}
	#else
	#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
	nb_nodes, ndim)
	#endif
	/* -------------------------------------------------------------------------- */
	/// Generic (templated by the enum InterpolationType which specifies the order
	/// and the dimension of the interpolation) class handling the elemental
	/// interpolation
	template <InterpolationType interpolation_type,
	InterpolationKind kind =
	InterpolationProperty<interpolation_type>::kind>
	class InterpolationElement {
	public:
	using interpolation_property = InterpolationProperty<interpolation_type>;

	/// compute the shape values for a given set of points in natural coordinates
	static inline void computeShapes(const Matrix<Real> & natural_coord,
	Matrix<Real> & N);

	/// compute the shape values for a given point in natural coordinates
	template <class vector_type>
	static inline void computeShapes(const vector_type & /unused/,
	vector_type & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
	* shape functions along with variation of natural coordinates on a given set
	* of points in natural coordinates
	*/
	static inline void computeDNDS(const Matrix<Real> & natural_coord,
	Tensor3<Real> & dnds);
	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
	* shape functions along with
	* variation of natural coordinates on a given point in natural
	* coordinates
	*/
	template <class vector_type, class matrix_type>
	static inline void computeDNDS(const vector_type & /unused/,
	matrix_type & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/**
	* compute @f$ @f$
	-
	+
	**/
	static inline void computeD2NDS2(const Matrix<Real> & natural_coord,
	- Tensor3<Real> & d2nds2);
	+ Tensor3<Real> & d2nds2);

	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the
	* second variation of
	* shape functions along with
	* variation of natural coordinates on a given point in natural
	* coordinates
	*/
	template <class vector_type, class matrix_type>
	- static inline void computeD2NDS2(const vector_type &, matrix_type &) {
	+ static inline void computeD2NDS2(const vector_type & /unused/,
	+ matrix_type & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	-
	/// compute jacobian (or integration variable change factor) for a given point
	/// in the case of spatial_dimension != natural_space_dimension
	static inline void computeSpecialJacobian(const Matrix<Real> & /unused/,
	Real & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// interpolate a field given (arbitrary) natural coordinates
	static inline void
	interpolateOnNaturalCoordinates(const Vector<Real> & natural_coords,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated);

	/// interpolate a field given the shape functions on the interpolation point
	static inline void interpolate(const Matrix<Real> & nodal_values,
	const Vector<Real> & shapes,
	Vector<Real> & interpolated);

	/// interpolate a field given the shape functions on the interpolations points
	static inline void interpolate(const Matrix<Real> & nodal_values,
	const Matrix<Real> & shapes,
	Matrix<Real> & interpolated);

	/// compute the gradient of a given field on the given natural coordinates
	static inline void
	gradientOnNaturalCoordinates(const Vector<Real> & natural_coords,
	const Matrix<Real> & f, Matrix<Real> & gradient);

	public:
	static AKANTU_GET_MACRO_NOT_CONST(
	ShapeSize,
	InterpolationProperty<interpolation_type>::nb_nodes_per_element, UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	ShapeDerivativesSize,
	(InterpolationProperty<interpolation_type>::nb_nodes_per_element *
	InterpolationProperty<interpolation_type>::natural_space_dimension),
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NaturalSpaceDimension,
	InterpolationProperty<interpolation_type>::natural_space_dimension, UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NbNodesPerInterpolationElement,
	InterpolationProperty<interpolation_type>::nb_nodes_per_element, UInt);
	};

	/* -------------------------------------------------------------------------- */
	/* Integration */
	/* -------------------------------------------------------------------------- */
	template <GaussIntegrationType git_class, UInt nb_points>
	struct GaussIntegrationTypeData {
	/// quadrature points in natural coordinates
	static Real quad_positions[];
	/// weights for the Gauss integration
	static Real quad_weights[];
	};

	template <ElementType type,
	UInt n = ElementClassProperty<type>::polynomial_degree>
	class GaussIntegrationElement {
	public:
	static UInt getNbQuadraturePoints();
	static Matrix<Real> getQuadraturePoints();
	static Vector<Real> getWeights();
	};

	/* -------------------------------------------------------------------------- */
	/* ElementClass */
	/* -------------------------------------------------------------------------- */
	template <ElementType element_type,
	ElementKind element_kind =
	ElementClassProperty<element_type>::element_kind>
	class ElementClass
	: public GeometricalElement<
	ElementClassProperty<element_type>::geometrical_type>,
	public InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type> {
	protected:
	using geometrical_element =
	GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
	using interpolation_element = InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type>;

	using element_property = ElementClassProperty<element_type>;
	using interpolation_property =
	typename interpolation_element::interpolation_property;

	public:
	/**
	* compute @f$ J = \frac{\partial x_j}{\partial s_i} @f$ the variation of real
	* coordinates along with variation of natural coordinates on a given point in
	* natural coordinates
	*/
	static inline void computeJMat(const Matrix<Real> & dnds,
	const Matrix<Real> & node_coords,
	Matrix<Real> & J);

	/**
	* compute the Jacobian matrix by computing the variation of real coordinates
	* along with variation of natural coordinates on a given set of points in
	* natural coordinates
	*/
	static inline void computeJMat(const Tensor3<Real> & dnds,
	const Matrix<Real> & node_coords,
	Tensor3<Real> & J);

	/// compute the jacobians of a serie of natural coordinates
	static inline void computeJacobian(const Matrix<Real> & natural_coords,
	const Matrix<Real> & node_coords,
	Vector<Real> & jacobians);

	/// compute jacobian (or integration variable change factor) for a set of
	/// points
	static inline void computeJacobian(const Tensor3<Real> & J,
	Vector<Real> & jacobians);

	/// compute jacobian (or integration variable change factor) for a given point
	static inline void computeJacobian(const Matrix<Real> & J, Real & jacobians);

	/// compute shape derivatives (input is dxds) for a set of points
	static inline void computeShapeDerivatives(const Tensor3<Real> & J,
	const Tensor3<Real> & dnds,
	Tensor3<Real> & shape_deriv);

	/// compute shape derivatives (input is dxds) for a given point
	static inline void computeShapeDerivatives(const Matrix<Real> & J,
	const Matrix<Real> & dnds,
	Matrix<Real> & shape_deriv);

	/// compute the normal of a surface defined by the function f
	static inline void
	computeNormalsOnNaturalCoordinates(const Matrix<Real> & coord,
	Matrix<Real> & f, Matrix<Real> & normals);

	/// get natural coordinates from real coordinates
	static inline void inverseMap(const Vector<Real> & real_coords,
	const Matrix<Real> & node_coords,
	Vector<Real> & natural_coords,
	UInt max_iterations = 100,
	Real tolerance = 1e-10);

	/// get natural coordinates from real coordinates
	static inline void inverseMap(const Matrix<Real> & real_coords,
	const Matrix<Real> & node_coords,
	Matrix<Real> & natural_coords,
	UInt max_iterations = 100,
	Real tolerance = 1e-10);

	public:
	static AKANTU_GET_MACRO_NOT_CONST(Kind, element_kind, ElementKind);
	static constexpr AKANTU_GET_MACRO_NOT_CONST(
	SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
	UInt);

	using element_class_extra_geom_property =
	ElementClassExtraGeometryProperties<element_type>;

	static constexpr auto getP1ElementType() {
	return element_class_extra_geom_property::p1_type;
	}
	static constexpr auto getFacetType(UInt t = 0) {
	return element_class_extra_geom_property::facet_type[t];
	}
	static constexpr auto getFacetTypes();
	};

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "geometrical_element_property.hh"
	#include "interpolation_element_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_class_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_class_hexahedron_8_inline_impl.hh"
	#include "element_class_pentahedron_6_inline_impl.hh"
	/* keep order */
	#include "element_class_hexahedron_20_inline_impl.hh"
	#include "element_class_pentahedron_15_inline_impl.hh"
	#include "element_class_point_1_inline_impl.hh"
	#include "element_class_quadrangle_4_inline_impl.hh"
	#include "element_class_quadrangle_8_inline_impl.hh"
	#include "element_class_segment_2_inline_impl.hh"
	#include "element_class_segment_3_inline_impl.hh"
	#include "element_class_tetrahedron_10_inline_impl.hh"
	#include "element_class_tetrahedron_4_inline_impl.hh"
	#include "element_class_triangle_3_inline_impl.hh"
	#include "element_class_triangle_6_inline_impl.hh"

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	#include "element_class_structural.hh"
	#endif

	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "cohesive_element.hh"
	#endif

	#if defined(AKANTU_IGFEM)
	#include "element_class_igfem.hh"
	#endif

	#endif /* AKANTU_ELEMENT_CLASS_HH_ */
	diff --git a/src/fe_engine/element_class_helper.hh b/src/fe_engine/element_class_helper.hh
	index 379a82433..ed04ebaf7 100644
	--- a/src/fe_engine/element_class_helper.hh
	+++ b/src/fe_engine/element_class_helper.hh
	@@ -1,75 +1,75 @@
	#ifndef ELEMENT_CLASS_HELPER_HH
	#define ELEMENT_CLASS_HELPER_HH

	#include "element_class.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind> class ElementClassHelper {};

	/* -------------------------------------------------------------------------- */
	template <> class ElementClassHelper<_ek_regular> {
	public:
	static inline Vector<Real> getN(const Vector<Real> & natural_coords,
	ElementType type) {
	#define GET_SHAPE_NATURAL(type) \
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement(); \
	Vector<Real> shapes(nb_nodes_per_element); \
	ElementClass<type>::computeShapes(natural_coords, shapes); \
	return shapes
	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(GET_SHAPE_NATURAL);
	#undef GET_SHAPE_NATURAL

	return Vector<Real>(0);
	}

	/* ------------------------------------------------------------------------ */
	static inline Matrix<Real> getDNDS(const Vector<Real> & natural_coords,
	ElementType type) {
	#define GET_DNDS_NATURAL(type) \
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement(); \
	Matrix<Real> dnds(natural_coords.size(), nb_nodes_per_element); \
	ElementClass<type>::computeDNDS(natural_coords, dnds); \
	return dnds
	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(GET_DNDS_NATURAL);
	#undef GET_DNDS_NATURAL

	return Matrix<Real>(0, 0);
	}

	/* ------------------------------------------------------------------------ */
	static inline Matrix<Real> getD2NDS2(const Vector<Real> & natural_coords,
	ElementType type) {
	#define GET_D2ND2S_NATURAL(type) \
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement(); \
	auto dim = natural_coords.size(); \
	Matrix<Real> d2nds2(dim * dim, nb_nodes_per_element); \
	ElementClass<type>::computeD2NDS2(natural_coords, d2nds2); \
	return d2nds2
	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(GET_D2ND2S_NATURAL);
	#undef GET_D2NDS2_NATURAL

	return Matrix<Real>(0, 0);
	}

	/* ------------------------------------------------------------------------ */
	static inline Matrix<Real> getJMat(const Vector<Real> & natural_coords,
	const Matrix<Real> & positions,
	ElementType type) {
	#define GET_JMAT_NATURAL(type) \
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement(); \
	Matrix<Real> dnds(natural_coords.size(), nb_nodes_per_element); \
	Matrix<Real> jmat(dnds.rows(), positions.rows()); \
	ElementClass<type>::computeDNDS(natural_coords, dnds); \
	- ElementClass<type>::computeJMat(dnds, positions, jmat); \
	+ ElementClass<type>::computeJMat(dnds, positions, jmat); \
	return jmat
	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(GET_JMAT_NATURAL);
	#undef GET_JMAT_NATURAL

	return Matrix<Real>(0, 0);
	}
	};

	} // namespace akantu
	#endif // ELEMENT_CLASS_HELPER_H
	diff --git a/src/fe_engine/element_class_structural.hh b/src/fe_engine/element_class_structural.hh
	index 72ea08316..c9d6c569c 100644
	--- a/src/fe_engine/element_class_structural.hh
	+++ b/src/fe_engine/element_class_structural.hh
	@@ -1,276 +1,276 @@
	/**
	* @file element_class_structural.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Mon Feb 01 2021
	*
	* @brief Specialization of the element classes for structural elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_
	#define AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_

	namespace akantu {

	/// Macro to generate the InterpolationProperty structures for different
	/// interpolation types
	#define AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY( \
	itp_type, itp_geom_type, ndof, nb_stress, nb_dnds_cols) \
	template <> struct InterpolationProperty<itp_type> { \
	static const InterpolationKind kind{_itk_structural}; \
	static const UInt nb_nodes_per_element{ \
	InterpolationProperty<itp_geom_type>::nb_nodes_per_element}; \
	static const InterpolationType itp_geometry_type{itp_geom_type}; \
	static const UInt natural_space_dimension{ \
	InterpolationProperty<itp_geom_type>::natural_space_dimension}; \
	static const UInt nb_degree_of_freedom{ndof}; \
	static const UInt nb_stress_components{nb_stress}; \
	static const UInt dnds_columns{nb_dnds_cols}; \
	}

	/* -------------------------------------------------------------------------- */
	template <InterpolationType interpolation_type>
	class InterpolationElement<interpolation_type, _itk_structural> {
	public:
	using interpolation_property = InterpolationProperty<interpolation_type>;

	/// compute the shape values for a given set of points in natural coordinates
	static inline void computeShapes(const Matrix<Real> & natural_coord,
	const Matrix<Real> & real_coord,
	const Matrix<Real> & T, Tensor3<Real> & Ns) {
	for (UInt i = 0; i < natural_coord.cols(); ++i) {
	Matrix<Real> N_T = Ns(i);
	Matrix<Real> N(N_T.rows(), N_T.cols());
	computeShapes(natural_coord(i), real_coord, N);
	N_T.mul<false, false>(N, T);
	}
	}

	/// compute the shape values for a given point in natural coordinates
	static inline void computeShapes(const Vector<Real> & natural_coord,
	const Matrix<Real> & real_coord,
	Matrix<Real> & N);

	static inline void computeShapesMass(const Matrix<Real> & natural_coords,
	const Matrix<Real> & xs,
	const Matrix<Real> & T,
	Tensor3<Real> & Ns) {
	for (UInt i = 0; i < natural_coords.cols(); ++i) {
	Matrix<Real> N_T = Ns(i);
	Vector<Real> X = natural_coords(i);
	Matrix<Real> N(interpolation_property::nb_degree_of_freedom, N_T.cols());

	computeShapes(X, xs, N);
	N_T.mul<false, false>(N.block(0, 0, N_T.rows(), N_T.cols()), T);
	}
	}

	/// compute shape derivatives (input is dxds) for a set of points
	static inline void computeShapeDerivatives(const Tensor3<Real> & Js,
	const Tensor3<Real> & DNDSs,
	const Matrix<Real> & R,
	Tensor3<Real> & Bs) {
	for (UInt i = 0; i < Js.size(2); ++i) {
	Matrix<Real> J = Js(i);
	Matrix<Real> DNDS = DNDSs(i);
	Matrix<Real> DNDX(DNDS.rows(), DNDS.cols());
	auto inv_J = J.inverse();
	DNDX.mul<false, false>(inv_J, DNDS);
	Matrix<Real> B_R = Bs(i);
	Matrix<Real> B(B_R.rows(), B_R.cols());
	arrangeInVoigt(DNDX, B);
	B_R.mul<false, false>(B, R);
	}
	}

	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
	* shape functions along with variation of natural coordinates on a given set
	* of points in natural coordinates
	*/
	static inline void computeDNDS(const Matrix<Real> & natural_coord,
	const Matrix<Real> & real_coord,
	Tensor3<Real> & dnds) {
	for (UInt i = 0; i < natural_coord.cols(); ++i) {
	Matrix<Real> dnds_t = dnds(i);
	computeDNDS(natural_coord(i), real_coord, dnds_t);
	}
	}

	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
	* shape functions along with
	* variation of natural coordinates on a given point in natural
	* coordinates
	*/
	static inline void computeDNDS(const Vector<Real> & natural_coord,
	const Matrix<Real> & real_coord,
	Matrix<Real> & dnds);

	/**
	* arrange B in Voigt notation from DNDS
	*/
	static inline void arrangeInVoigt(const Matrix<Real> & dnds,
	Matrix<Real> & B) {
	// Default implementation assumes dnds is already in Voigt notation
	B.deepCopy(dnds);
	}

	public:
	static inline constexpr auto getNbNodesPerInterpolationElement() {
	return interpolation_property::nb_nodes_per_element;
	}

	static inline constexpr auto getShapeSize() {
	return interpolation_property::nb_nodes_per_element *
	interpolation_property::nb_degree_of_freedom *
	interpolation_property::nb_degree_of_freedom;
	}
	static inline constexpr auto getShapeIndependantSize() {
	return interpolation_property::nb_nodes_per_element *
	interpolation_property::nb_degree_of_freedom *
	interpolation_property::nb_stress_components;
	}
	static inline constexpr auto getShapeDerivativesSize() {
	return interpolation_property::nb_nodes_per_element *
	interpolation_property::nb_degree_of_freedom *
	interpolation_property::nb_stress_components;
	}
	static inline constexpr auto getNaturalSpaceDimension() {
	return interpolation_property::natural_space_dimension;
	}
	static inline constexpr auto getNbDegreeOfFreedom() {
	return interpolation_property::nb_degree_of_freedom;
	}
	static inline constexpr auto getNbStressComponents() {
	return interpolation_property::nb_stress_components;
	}
	};

	/// Macro to generate the element class structures for different structural
	/// element types
	/* -------------------------------------------------------------------------- */
	#define AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY( \
	elem_type, geom_type, interp_type, parent_el_type, elem_kind, sp, \
	gauss_int_type, min_int_order) \
	template <> struct ElementClassProperty<elem_type> { \
	static const GeometricalType geometrical_type{geom_type}; \
	static const InterpolationType interpolation_type{interp_type}; \
	static const ElementType parent_element_type{parent_el_type}; \
	static const ElementKind element_kind{elem_kind}; \
	static const UInt spatial_dimension{sp}; \
	static const GaussIntegrationType gauss_integration_type{gauss_int_type}; \
	static const UInt polynomial_degree{min_int_order}; \
	}

	/* -------------------------------------------------------------------------- */
	/* ElementClass for structural elements */
	/* -------------------------------------------------------------------------- */
	template <ElementType element_type>
	class ElementClass<element_type, _ek_structural>
	: public GeometricalElement<
	ElementClassProperty<element_type>::geometrical_type>,
	public InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type> {
	protected:
	using geometrical_element =
	GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
	using interpolation_element = InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type>;
	using parent_element =
	ElementClass<ElementClassProperty<element_type>::parent_element_type>;

	public:
	static inline void
	computeRotationMatrix(Matrix<Real> & /R/, const Matrix<Real> & /X/,
	const Vector<Real> & /extra_normal/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute jacobian (or integration variable change factor) for a given point
	static inline void computeJMat(const Vector<Real> & natural_coords,
	const Matrix<Real> & Xs, Matrix<Real> & J) {
	Matrix<Real> dnds(Xs.rows(), Xs.cols());
	parent_element::computeDNDS(natural_coords, dnds);
	J.mul<false, true>(dnds, Xs);
	}

	static inline void computeJMat(const Matrix<Real> & natural_coords,
	const Matrix<Real> & Xs, Tensor3<Real> & Js) {
	for (UInt i = 0; i < natural_coords.cols(); ++i) {
	// because non-const l-value reference does not bind to r-value
	Matrix<Real> J = Js(i);
	computeJMat(Vector<Real>(natural_coords(i)), Xs, J);
	}
	}

	static inline void computeJacobian(const Matrix<Real> & natural_coords,
	const Matrix<Real> & node_coords,
	Vector<Real> & jacobians) {
	using itp = typename interpolation_element::interpolation_property;
	Tensor3<Real> Js(itp::natural_space_dimension, itp::natural_space_dimension,
	natural_coords.cols());
	computeJMat(natural_coords, node_coords, Js);
	for (UInt i = 0; i < natural_coords.cols(); ++i) {
	Matrix<Real> J = Js(i);
	jacobians(i) = J.det();
	}
	}

	static inline void computeRotation(const Matrix<Real> & node_coords,
	Matrix<Real> & rotation);

	public:
	static AKANTU_GET_MACRO_NOT_CONST(Kind, _ek_structural, ElementKind);
	static AKANTU_GET_MACRO_NOT_CONST(P1ElementType, _not_defined, ElementType);
	static AKANTU_GET_MACRO_NOT_CONST(FacetType, _not_defined, ElementType);
	static constexpr auto getFacetType(__attribute__((unused)) UInt t = 0) {
	return _not_defined;
	}
	static constexpr AKANTU_GET_MACRO_NOT_CONST(
	SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
	UInt);
	static constexpr auto getFacetTypes() {
	return ElementClass<_not_defined>::getFacetTypes();
	}
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "element_class_hermite_inline_impl.hh"
	/* keep order */
	#include "element_class_bernoulli_beam_inline_impl.hh"
	#include "element_class_kirchhoff_shell_inline_impl.hh"
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_ */
	diff --git a/src/fe_engine/element_class_tmpl.hh b/src/fe_engine/element_class_tmpl.hh
	index 03007b1bb..a66857002 100644
	--- a/src/fe_engine/element_class_tmpl.hh
	+++ b/src/fe_engine/element_class_tmpl.hh
	@@ -1,541 +1,541 @@
	/**
	* @file element_class_tmpl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Thomas Menouillard <tmenouillard@stucky.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Implementation of the inline templated function of the element class
	* descriptions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	#include "gauss_integration_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_TMPL_HH_
	#define AKANTU_ELEMENT_CLASS_TMPL_HH_

	namespace akantu {

	template <ElementType element_type, ElementKind element_kind>
	inline constexpr auto
	ElementClass<element_type, element_kind>::getFacetTypes() {
	return VectorProxy<const ElementType>(
	element_class_extra_geom_property::facet_type.data(),
	geometrical_element::getNbFacetTypes());
	}

	/* -------------------------------------------------------------------------- */
	/* GeometricalElement */
	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type, GeometricalShapeType shape>
	inline constexpr auto
	GeometricalElement<geometrical_type,
	shape>::getFacetLocalConnectivityPerElement(UInt t) {
	int pos = 0;
	for (UInt i = 0; i < t; ++i) {
	pos += geometrical_property::nb_facets[i] *
	geometrical_property::nb_nodes_per_facet[i];
	}

	return MatrixProxy<const UInt>(
	geometrical_property::facet_connectivity_vect.data() + pos,
	geometrical_property::nb_facets[t],
	geometrical_property::nb_nodes_per_facet[t]);
	}

	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type, GeometricalShapeType shape>
	inline UInt
	GeometricalElement<geometrical_type, shape>::getNbFacetsPerElement() {
	UInt total_nb_facets = 0;
	for (UInt n = 0; n < geometrical_property::nb_facet_types; ++n) {
	total_nb_facets += geometrical_property::nb_facets[n];
	}

	return total_nb_facets;
	}

	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type, GeometricalShapeType shape>
	inline UInt
	GeometricalElement<geometrical_type, shape>::getNbFacetsPerElement(UInt t) {
	return geometrical_property::nb_facets[t];
	}

	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type, GeometricalShapeType shape>
	template <class vector_type>
	inline bool GeometricalElement<geometrical_type, shape>::contains(
	const vector_type & coords) {
	return GeometricalShapeContains<shape>::contains(coords);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline bool
	GeometricalShapeContains<_gst_point>::contains(const vector_type & coords) {
	return (coords(0) < std::numeric_limits<Real>::epsilon());
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline bool
	GeometricalShapeContains<_gst_square>::contains(const vector_type & coords) {
	bool in = true;
	for (UInt i = 0; i < coords.size() && in; ++i) {
	in &= ((coords(i) >= -(1. + std::numeric_limits<Real>::epsilon())) &&
	(coords(i) <= (1. + std::numeric_limits<Real>::epsilon())));
	}
	return in;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline bool
	GeometricalShapeContains<_gst_triangle>::contains(const vector_type & coords) {
	bool in = true;
	Real sum = 0;
	for (UInt i = 0; (i < coords.size()) && in; ++i) {
	in &= ((coords(i) >= -(Math::getTolerance())) &&
	(coords(i) <= (1. + Math::getTolerance())));
	sum += coords(i);
	}
	if (in) {
	return (in && (sum <= (1. + Math::getTolerance())));
	}
	return in;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline bool
	GeometricalShapeContains<_gst_prism>::contains(const vector_type & coords) {
	bool in = ((coords(0) >= -1.) && (coords(0) <= 1.)); // x in segment [-1, 1]

	// y and z in triangle
	in &= ((coords(1) >= 0) && (coords(1) <= 1.));
	in &= ((coords(2) >= 0) && (coords(2) <= 1.));
	Real sum = coords(1) + coords(2);

	return (in && (sum <= 1));
	}

	/* -------------------------------------------------------------------------- */
	/* InterpolationElement */
	/* -------------------------------------------------------------------------- */
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void InterpolationElement<interpolation_type, kind>::computeShapes(
	const Matrix<Real> & natural_coord, Matrix<Real> & N) {
	UInt nb_points = natural_coord.cols();
	for (UInt p = 0; p < nb_points; ++p) {
	Vector<Real> Np(N(p));
	Vector<Real> ncoord_p(natural_coord(p));
	computeShapes(ncoord_p, Np);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void InterpolationElement<interpolation_type, kind>::computeDNDS(
	const Matrix<Real> & natural_coord, Tensor3<Real> & dnds) {
	UInt nb_points = natural_coord.cols();
	for (UInt p = 0; p < nb_points; ++p) {
	Matrix<Real> dnds_p(dnds(p));
	Vector<Real> ncoord_p(natural_coord(p));
	computeDNDS(ncoord_p, dnds_p);
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* interpolate on a point a field for which values are given on the
	* node of the element using the shape functions at this interpolation point
	*
	* @param nodal_values values of the function per node @f$ f_{ij} = f_{n_i j}
	*@f$ so it should be a matrix of size nb_nodes_per_element @f$\times@f$
	*nb_degree_of_freedom
	* @param shapes value of shape functions at the interpolation point
	* @param interpolated interpolated value of f @f$ f_j(\xi) = \sum_i f_{n_i j}
	*N_i @f$
	*/
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void InterpolationElement<interpolation_type, kind>::interpolate(
	const Matrix<Real> & nodal_values, const Vector<Real> & shapes,
	Vector<Real> & interpolated) {
	Matrix<Real> interpm(interpolated.storage(), nodal_values.rows(), 1);
	Matrix<Real> shapesm(
	shapes.storage(),
	InterpolationProperty<interpolation_type>::nb_nodes_per_element, 1);
	interpm.mul<false, false>(nodal_values, shapesm);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* interpolate on several points a field for which values are given on the
	* node of the element using the shape functions at the interpolation point
	*
	* @param nodal_values values of the function per node @f$ f_{ij} = f_{n_i j}
	*@f$ so it should be a matrix of size nb_nodes_per_element @f$\times@f$
	*nb_degree_of_freedom
	* @param shapes value of shape functions at the interpolation point
	* @param interpolated interpolated values of f @f$ f_j(\xi) = \sum_i f_{n_i j}
	*N_i @f$
	*/
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void InterpolationElement<interpolation_type, kind>::interpolate(
	const Matrix<Real> & nodal_values, const Matrix<Real> & shapes,
	Matrix<Real> & interpolated) {
	UInt nb_points = shapes.cols();
	for (UInt p = 0; p < nb_points; ++p) {
	Vector<Real> Np(shapes(p));
	Vector<Real> interpolated_p(interpolated(p));
	interpolate(nodal_values, Np, interpolated_p);
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* interpolate the field on a point given in natural coordinates the field which
	* values are given on the node of the element
	*
	* @param natural_coords natural coordinates of point where to interpolate \xi
	* @param nodal_values values of the function per node @f$ f_{ij} = f_{n_i j}
	*@f$ so it should be a matrix of size nb_nodes_per_element @f$\times@f$
	*nb_degree_of_freedom
	* @param interpolated interpolated value of f @f$ f_j(\xi) = \sum_i f_{n_i j}
	*N_i @f$
	*/
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void
	InterpolationElement<interpolation_type, kind>::interpolateOnNaturalCoordinates(
	const Vector<Real> & natural_coords, const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated) {
	Vector<Real> shapes(
	InterpolationProperty<interpolation_type>::nb_nodes_per_element);
	computeShapes(natural_coords, shapes);

	interpolate(nodal_values, shapes, interpolated);
	}

	/* -------------------------------------------------------------------------- */
	/// @f$ gradient_{ij} = \frac{\partial f_j}{\partial s_i} = \sum_k
	/// \frac{\partial N_k}{\partial s_i}f_{j n_k} @f$
	template <InterpolationType interpolation_type, InterpolationKind kind>
	inline void
	InterpolationElement<interpolation_type, kind>::gradientOnNaturalCoordinates(
	const Vector<Real> & natural_coords, const Matrix<Real> & f,
	Matrix<Real> & gradient) {
	Matrix<Real> dnds(
	InterpolationProperty<interpolation_type>::natural_space_dimension,
	InterpolationProperty<interpolation_type>::nb_nodes_per_element);
	computeDNDS(natural_coords, dnds);
	gradient.mul<false, true>(f, dnds);
	}

	/* -------------------------------------------------------------------------- */
	/* ElementClass */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeJMat(const Tensor3<Real> & dnds,
	const Matrix<Real> & node_coords,
	Tensor3<Real> & J) {
	UInt nb_points = dnds.size(2);
	for (UInt p = 0; p < nb_points; ++p) {
	Matrix<Real> J_p(J(p));
	Matrix<Real> dnds_p(dnds(p));
	computeJMat(dnds_p, node_coords, J_p);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeJMat(const Matrix<Real> & dnds,
	const Matrix<Real> & node_coords,
	Matrix<Real> & J) {
	/// @f$ J = dxds = dnds * x @f$
	J.mul<false, true>(dnds, node_coords);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeJacobian(const Matrix<Real> & natural_coords,
	const Matrix<Real> & node_coords,
	Vector<Real> & jacobians) {
	UInt nb_points = natural_coords.cols();
	Matrix<Real> dnds(interpolation_property::natural_space_dimension,
	interpolation_property::nb_nodes_per_element);
	Matrix<Real> J(natural_coords.rows(), node_coords.rows());

	for (UInt p = 0; p < nb_points; ++p) {
	Vector<Real> ncoord_p(natural_coords(p));
	interpolation_element::computeDNDS(ncoord_p, dnds);
	computeJMat(dnds, node_coords, J);
	computeJacobian(J, jacobians(p));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeJacobian(const Tensor3<Real> & J,
	Vector<Real> & jacobians) {
	UInt nb_points = J.size(2);
	for (UInt p = 0; p < nb_points; ++p) {
	computeJacobian(J(p), jacobians(p));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void ElementClass<type, kind>::computeJacobian(const Matrix<Real> & J,
	Real & jacobians) {
	if (J.rows() == J.cols()) {
	jacobians = Math::det<element_property::spatial_dimension>(J.storage());
	} else {
	interpolation_element::computeSpecialJacobian(J, jacobians);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeShapeDerivatives(const Tensor3<Real> & J,
	const Tensor3<Real> & dnds,
	Tensor3<Real> & shape_deriv) {
	UInt nb_points = J.size(2);
	for (UInt p = 0; p < nb_points; ++p) {
	Matrix<Real> shape_deriv_p(shape_deriv(p));
	computeShapeDerivatives(J(p), dnds(p), shape_deriv_p);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void
	ElementClass<type, kind>::computeShapeDerivatives(const Matrix<Real> & J,
	const Matrix<Real> & dnds,
	Matrix<Real> & shape_deriv) {
	Matrix<Real> inv_J(J.rows(), J.cols());
	Math::inv<element_property::spatial_dimension>(J.storage(), inv_J.storage());

	shape_deriv.mul<false, false>(inv_J, dnds);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void ElementClass<type, kind>::computeNormalsOnNaturalCoordinates(
	const Matrix<Real> & coord, Matrix<Real> & f, Matrix<Real> & normals) {
	UInt dimension = normals.rows();
	UInt nb_points = coord.cols();

	AKANTU_DEBUG_ASSERT((dimension - 1) ==
	interpolation_property::natural_space_dimension,
	"cannot extract a normal because of dimension mismatch "
	<< dimension - 1 << " "
	<< interpolation_property::natural_space_dimension);

	Matrix<Real> J(dimension, interpolation_property::natural_space_dimension);
	for (UInt p = 0; p < nb_points; ++p) {
	interpolation_element::gradientOnNaturalCoordinates(coord(p), f, J);
	if (dimension == 2) {
	Math::normal2(J.storage(), normals(p).storage());
	}
	if (dimension == 3) {
	Math::normal3(J(0).storage(), J(1).storage(), normals(p).storage());
	}
	}
	}

	/* ------------------------------------------------------------------------- */
	/**
	* In the non linear cases we need to iterate to find the natural coordinates
	*@f$\xi@f$
	* provided real coordinates @f$x@f$.
	*
	* We want to solve: @f$ x- \phi(\xi) = 0@f$ with @f$\phi(\xi) = \sum_I N_I(\xi)
	*x_I@f$
	* the mapping function which uses the nodal coordinates @f$x_I@f$.
	*
	* To that end we use the Newton method and the following series:
	*
	* @f$ \frac{\partial \phi(x_k)}{\partial \xi} \left( \xi_{k+1} - \xi_k \right)
	*= x - \phi(x_k)@f$
	*
	* When we consider elements embedded in a dimension higher than them (2D
	*triangle in a 3D space for example)
	* @f$ J = \frac{\partial \phi(\xi_k)}{\partial \xi}@f$ is of dimension
	*@f$dim_{space} \times dim_{elem}@f$ which
	* is not invertible in most cases. Rather we can solve the problem:
	*
	* @f$ J^T J \left( \xi_{k+1} - \xi_k \right) = J^T \left( x - \phi(\xi_k)
	*\right) @f$
	*
	* So that
	*
	* @f$ d\xi = \xi_{k+1} - \xi_k = (J^T J)^{-1} J^T \left( x - \phi(\xi_k)
	*\right) @f$
	*
	* So that if the series converges we have:
	*
	* @f$ 0 = J^T \left( \phi(\xi_\infty) - x \right) @f$
	*
	* And we see that this is ill-posed only if @f$ J^T x = 0@f$ which means that
	*the vector provided
	* is normal to any tangent which means it is outside of the element itself.
	*
	* @param real_coords: the real coordinates the natural coordinates are sought
	*for
	* @param node_coords: the coordinates of the nodes forming the element
	* @param natural_coords: output->the sought natural coordinates
	* @param spatial_dimension: spatial dimension of the problem
	*
	**/
	template <ElementType type, ElementKind kind>
	inline void ElementClass<type, kind>::inverseMap(
	const Vector<Real> & real_coords, const Matrix<Real> & node_coords,
	Vector<Real> & natural_coords, UInt max_iterations, Real tolerance) {
	UInt spatial_dimension = real_coords.size();
	UInt dimension = natural_coords.size();

	// matrix copy of the real_coords
	Matrix<Real> mreal_coords(real_coords.storage(), spatial_dimension, 1);

	// initial guess
	natural_coords.zero();

	// real space coordinates provided by initial guess
	Matrix<Real> physical_guess(spatial_dimension, 1);

	// objective function f = real_coords - physical_guess
	Matrix<Real> f(spatial_dimension, 1);

	// J Jacobian matrix computed on the natural_guess
	Matrix<Real> J(dimension, spatial_dimension);

	// J^t
	Matrix<Real> Jt(spatial_dimension, dimension);

	// G = J^t * J
	Matrix<Real> G(dimension, dimension);

	// Ginv = G^{-1}
	Matrix<Real> Ginv(dimension, dimension);

	// J = Ginv * J^t
	Matrix<Real> F(spatial_dimension, dimension);

	// dxi = \xi_{k+1} - \xi in the iterative process
	Matrix<Real> dxi(dimension, 1);

	Matrix<Real> dxit(1, dimension);

	/* --------------------------- */
	/* init before iteration loop */
	/* --------------------------- */
	// do interpolation
	auto update_f = [&f, &physical_guess, &natural_coords, &node_coords,
	&mreal_coords, spatial_dimension]() {
	Vector<Real> physical_guess_v(physical_guess.storage(), spatial_dimension);
	interpolation_element::interpolateOnNaturalCoordinates(
	natural_coords, node_coords, physical_guess_v);

	// compute initial objective function value f = real_coords - physical_guess
	f = mreal_coords;
	f -= physical_guess;

	// compute initial error
	auto error = f.norm<L_2>();
	return error;
	};

	auto inverse_map_error = update_f();
	/* --------------------------- */
	/* iteration loop */
	/* --------------------------- */
	UInt iterations{0};
	while (tolerance < inverse_map_error and iterations < max_iterations) {
	// compute J^t
	interpolation_element::gradientOnNaturalCoordinates(natural_coords,
	node_coords, Jt);
	J = Jt.transpose();

	// compute G
	G.mul<false, true>(J, J);

	// inverse G
	Ginv.inverse(G);

	// compute F
	F.mul<true, false>(J, Ginv);

	// compute increment
	dxit.mul<true, false>(f, F);

	dxi = dxit.transpose();

	// update our guess
	natural_coords += Vector<Real>(dxi(0));

	inverse_map_error = update_f();
	iterations++;
	}

	- if(iterations >= max_iterations) {
	+ if (iterations >= max_iterations) {
	AKANTU_EXCEPTION("The solver in inverse map did not converge");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, ElementKind kind>
	inline void ElementClass<type, kind>::inverseMap(
	const Matrix<Real> & real_coords, const Matrix<Real> & node_coords,
	Matrix<Real> & natural_coords, UInt max_iterations, Real tolerance) {
	UInt nb_points = real_coords.cols();
	for (UInt p = 0; p < nb_points; ++p) {
	Vector<Real> X(real_coords(p));
	Vector<Real> ncoord_p(natural_coords(p));
	inverseMap(X, node_coords, ncoord_p, max_iterations, tolerance);
	}
	}

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_CLASS_TMPL_HH_ */
	diff --git a/src/fe_engine/element_classes/element_class_bernoulli_beam_inline_impl.hh b/src/fe_engine/element_classes/element_class_bernoulli_beam_inline_impl.hh
	index b611e910b..7adc2af0d 100644
	--- a/src/fe_engine/element_classes/element_class_bernoulli_beam_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_bernoulli_beam_inline_impl.hh
	@@ -1,239 +1,238 @@
	/**
	* @file element_class_bernoulli_beam_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 15 2011
	* @date last modification: Fri Feb 05 2021
	*
	* @brief Specialization of the element_class class for the type
	* _bernoulli_beam_2
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	-
	/**
	* @verbatim
	--x-----q1----\|----q2-----x---> x
	-1 0 1
	@endverbatim
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_static_if.hh"
	#include "element_class_structural.hh"
	//#include "aka_element_classes_info.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_
	#define AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(_itp_bernoulli_beam_2,
	_itp_lagrange_segment_2, 3,
	2, 6);

	AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(_itp_bernoulli_beam_3,
	_itp_lagrange_segment_2, 6,
	4, 6);

	AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_bernoulli_beam_2,
	_gt_segment_2,
	_itp_bernoulli_beam_2,
	_segment_2, _ek_structural, 2,
	_git_segment, 3);

	AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_bernoulli_beam_3,
	_gt_segment_2,
	_itp_bernoulli_beam_3,
	_segment_2, _ek_structural, 3,
	_git_segment, 3);

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeShapes(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & N) {
	Vector<Real> L(2);
	InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
	natural_coords, L);
	Matrix<Real> H(2, 4);
	InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
	natural_coords, real_coord, H);

	// clang-format off
	// u1 v1 t1 u2 v2 t2
	N = {{L(0), 0 , 0 , L(1), 0 , 0 }, // u
	{0 , H(0, 0), H(0, 1), 0 , H(0, 2), H(0, 3)}, // v
	{0 , H(1, 0), H(1, 1), 0 , H(1, 2), H(1, 3)}}; // theta
	// clang-format on
	}

	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapes(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & N) {
	Vector<Real> L(2);
	InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
	natural_coords, L);
	Matrix<Real> H(2, 4);
	InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
	natural_coords, real_coord, H);

	// clang-format off
	// u1 v1 w1 tx1 ty1 tz1 u2 v2 w2 tx2 ty2 tz2
	N = {{L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 , 0 , 0 , 0 }, // u
	{0 , H(0, 0), 0 , 0 , 0 , H(0, 1), 0 , H(0, 2), 0 , 0 , 0 , H(0, 3)}, // v
	{0 , 0 , H(0, 0), 0 , -H(0, 1), 0 , 0 , 0 , H(0, 2), 0 , -H(0, 3), 0 }, // w
	{0 , 0 , 0 , L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 }, // thetax
	{0 , 0 , H(1, 0), 0 , -H(1, 1), 0 , 0 , 0 , H(1, 2), 0 , -H(1, 3), 0 }, // thetay
	{0 , H(1, 0), 0 , 0 , 0 , H(1, 1), 0 , H(1, 2), 0 , 0 , 0 , H(1, 3)}}; // thetaz
	// clang-format on
	}

	/* -------------------------------------------------------------------------- */
	#if 0
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapesDisplacements(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & N) {
	}
	#endif

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & dnds) {
	Matrix<Real> L(1, 2);
	InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeDNDS(
	natural_coords, L);
	Matrix<Real> H(1, 4);
	InterpolationElement<_itp_hermite_2, _itk_structural>::computeDNDS(
	natural_coords, real_coord, H);

	// Storing the derivatives in dnds
	dnds.block(L, 0, 0);
	dnds.block(H, 0, 2);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::arrangeInVoigt(
	const Matrix<Real> & dnds, Matrix<Real> & B) {
	auto L = dnds.block(0, 0, 1, 2); // Lagrange shape derivatives
	auto H = dnds.block(0, 2, 1, 4); // Hermite shape derivatives
	// clang-format off
	// u1 v1 t1 u2 v2 t2
	B = {{L(0, 0), 0, 0, L(0, 1), 0, 0 },
	{0, -H(0, 0), -H(0, 1), 0, -H(0, 2), -H(0, 3)}};
	// clang-format on
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeDNDS(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & dnds) {
	InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
	natural_coords, real_coord, dnds);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::arrangeInVoigt(
	const Matrix<Real> & dnds, Matrix<Real> & B) {
	auto L = dnds.block(0, 0, 1, 2); // Lagrange shape derivatives
	auto H = dnds.block(0, 2, 1, 4); // Hermite shape derivatives

	// clang-format off
	// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
	B = {{L(0, 0), 0 , 0 , 0 , 0 , 0 , L(0, 1), 0 , 0 , 0 , 0 , 0 }, // eps
	{0 , -H(0, 0), 0 , 0 , 0 , -H(0, 1), 0 , -H(0, 2), 0 , 0 , 0 ,-H(0, 3)}, // chi strong axis
	{0 , 0 , -H(0, 0), 0 , H(0, 1) , 0 , 0 , 0 , -H(0, 2) , 0 , H(0, 3) , 0 }, // chi weak axis
	{0 , 0 , 0 , L(0, 0), 0 , 0 , 0 , 0 , 0 , L(0, 1), 0 , 0 }}; // chi torsion
	// clang-format on
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ElementClass<_bernoulli_beam_2>::computeRotationMatrix(
	Matrix<Real> & R, const Matrix<Real> & X, const Vector<Real> & /n/) {
	Vector<Real> x2 = X(1); // X2
	Vector<Real> x1 = X(0); // X1

	auto cs = (x2 - x1);
	cs.normalize();

	auto c = cs(0);
	auto s = cs(1);

	// clang-format off
	/// Definition of the rotation matrix
	R = {{ c, s, 0.},
	{-s, c, 0.},
	{ 0., 0., 1.}};
	// clang-format on
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ElementClass<_bernoulli_beam_3>::computeRotationMatrix(
	Matrix<Real> & R, const Matrix<Real> & X, const Vector<Real> & n) {
	Vector<Real> x2 = X(1); // X2
	Vector<Real> x1 = X(0); // X1
	auto dim = X.rows();
	auto x = (x2 - x1);
	x.normalize();
	auto x_n = x.crossProduct(n);

	Matrix<Real> Pe = {{1., 0., 0.}, {0., -1., 0.}, {0., 0., 1.}};

	Matrix<Real> Pg(dim, dim);
	Pg(0) = x;
	Pg(1) = x_n;
	Pg(2) = n;

	Pe *= Pg.inverse();

	R.zero();
	/// Definition of the rotation matrix
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	R(i + dim, j + dim) = R(i, j) = Pe(i, j);
	}
	}
	}

	} // namespace akantu
	#endif /* AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/element_classes/element_class_hermite_inline_impl.hh b/src/fe_engine/element_classes/element_class_hermite_inline_impl.hh
	index f744254cb..cd4dfd565 100644
	--- a/src/fe_engine/element_classes/element_class_hermite_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_hermite_inline_impl.hh
	@@ -1,181 +1,182 @@
	/**
	* @file element_class_hermite_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Nov 10 2017
	* @date last modification: Tue Feb 09 2021
	*
	* @brief Specialization of the element_class class for the type
	* _hermite
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	--x-----q1----\|----q2-----x---> x
	-1 0 1
	@endverbatim
	*
	* @f[
	* \begin{array}{ll}
	* M_1(\xi) &= 1/4(\xi^{3}/-3\xi+2)\\
	* M_2(\xi) &= -1/4(\xi^{3}-3\xi-2)
	* \end{array}
	*
	* \begin{array}{ll}
	* L_1(\xi) &= 1/4(\xi^{3}-\xi^{2}-\xi+1)\\
	* L_2(\xi) &= 1/4(\xi^{3}+\xi^{2}-\xi-1)
	* \end{array}
	*
	* \begin{array}{ll}
	* M'_1(\xi) &= 3/4(\xi^{2}-1)\\
	* M'_2(\xi) &= -3/4(\xi^{2}-1)
	* \end{array}
	*
	* \begin{array}{ll}
	* L'_1(\xi) &= 1/4(3\xi^{2}-2\xi-1)\\
	* L'_2(\xi) &= 1/4(3\xi^{2}+2\xi-1)
	* \end{array}
	*@f]
	*
	*
	*@f[
	* \begin{array}{ll}
	* N'_1(\xi) &= -1/2\\
	* N'_2(\xi) &= 1/2
	* \end{array}]
	*
	* \begin{array}{ll}
	* -M''_1(\xi) &= -3\xi/2\\
	* -M''_2(\xi) &= 3\xi/2\\
	* \end{array}
	*
	* \begin{array}{ll}
	* -L''_1(\xi) &= -1/2a(3\xi/a-1)\\
	* -L''_2(\xi) &= -1/2a(3\xi/a+1)
	* \end{array}
	*@f]
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_static_if.hh"
	#include "element_class_structural.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_HERMITE_INLINE_IMPL_HH_
	#define AKANTU_ELEMENT_CLASS_HERMITE_INLINE_IMPL_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */

	AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(_itp_hermite_2,
	_itp_lagrange_segment_2, 2,
	1, 4);

	/* -------------------------------------------------------------------------- */

	namespace {
	namespace details {
	inline Real computeLength(const Matrix<Real> & real_coord) {
	Vector<Real> x1 = real_coord(0);
	Vector<Real> x2 = real_coord(1);
	return x1.distance(x2);
	}

	inline void computeShapes(const Vector<Real> & natural_coords, Real a,
	Matrix<Real> & N) {
	/// natural coordinate
	Real xi = natural_coords(0);
	auto xi2 = xi * xi;
	auto xi3 = xi * xi * xi;
	// Cubic Hermite splines interpolating displacement
	auto M1 = 1. / 4. * (2. - 3. * xi + xi3);
	auto M2 = 1. / 4. * (2. + 3. * xi - xi3);
	auto L1 = a / 4. * (1 - xi - xi2 + xi3);
	- auto L2 = a / 4. * (-1 - xi + xi2 + xi3);;
	+ auto L2 = a / 4. * (-1 - xi + xi2 + xi3);
	+ ;

	#if 1 // Version where we also interpolate the rotations
	// Derivatives (with respect to x) of previous functions interpolating
	// rotations
	auto M1_ = 3. / (4. * a) * (xi2 - 1);
	auto M2_ = 3. / (4. * a) * (1 - xi2);
	auto L1_ = 1 / 4. * (3 * xi2 - 2 * xi - 1);
	auto L2_ = 1 / 4. * (3 * xi2 + 2 * xi - 1);

	// clang-format off
	// v1 t1 v2 t2
	N = {{M1 , L1 , M2 , L2}, // displacement interpolation
	{M1_, L1_, M2_, L2_}}; // rotation interpolation
	// clang-format on

	#else // Version where we only interpolate displacements
	// clang-format off
	// v1 t1 v2 t2
	N = {{M1, L1, M2, L2}};
	// clang-format on
	#endif
	}

	/* ---------------------------------------------------------------------- */

	inline void computeDNDS(const Vector<Real> & natural_coords, Real a,
	Matrix<Real> & B) {
	// natural coordinate
	Real xi = natural_coords(0);
	// Derivatives with respect to xi for rotations
	auto M1 = 3. / 2. * xi;
	auto M2 = 3. / 2. * (-xi);
	auto L1 = 1. * a / 2. * (3 * xi - 1);
	auto L2 = 1. * a / 2. * (3 * xi + 1);

	// v1 t1 v2 t2
	B = {{M1, L1, M2, L2}}; // computing curvature : {chi} = [B]{d}
	- B /= a; // to account for first order deriv w/r to x
	+ B /= a; // to account for first order deriv w/r to x
	}
	} // namespace details
	} // namespace

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & N) {
	auto L = details::computeLength(real_coord);
	details::computeShapes(natural_coords, L / 2, N);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void InterpolationElement<_itp_hermite_2, _itk_structural>::computeDNDS(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
	Matrix<Real> & B) {
	auto L = details::computeLength(real_coord);
	details::computeDNDS(natural_coords, L / 2, B);
	}

	} // namespace akantu
	#endif /* AKANTU_ELEMENT_CLASS_HERMITE_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.hh b/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.hh
	index fd6f06b11..8e364fced 100644
	--- a/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.hh
	@@ -1,231 +1,231 @@
	/**
	* @file element_class_hexahedron_20_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Sacha Laffely <sacha.laffely@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
	*
	* @date creation: Tue Mar 31 2015
	* @date last modification: Fri Feb 07 2020
	*
	* @brief Specialization of the element_class class for the type _hexahedron_20
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\y
	\z /
	\| /
	7-----\|18--------6
	/\| \| / /\|
	/ \| \| / / \|
	19 \| \| / 17 \|
	/ 15 \| / / 14
	/ \| \| / / \|
	4-------16---/---5 \|
	\| \| +----\|------------\x
	\| 3-------10-\|-----2
	\| / \| /
	12 / 13 /
	\| 11 \| 9
	\| / \| /
	\|/ \|/
	0--------8-------1
	x y z
	* N0 -1 -1 -1
	* N1 1 -1 -1
	* N2 1 1 -1
	* N3 -1 1 -1
	* N4 -1 -1 1
	* N5 1 -1 1
	* N6 1 1 1
	* N7 -1 1 1
	* N8 0 -1 -1
	* N9 1 0 -1
	* N10 0 1 -1
	* N11 -1 0 -1
	* N12 -1 -1 0
	* N13 1 -1 0
	* N14 1 1 0
	* N15 -1 1 0
	* N16 0 -1 1
	* N17 1 0 1
	* N18 0 1 1
	* N19 -1 0 1
	* \endverbatim
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_hexahedron_20, _gt_hexahedron_20,
	_itp_serendip_hexahedron_20, _ek_regular,
	3, _git_segment, 3);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_serendip_hexahedron_20>::computeShapes(
	const vector_type & c, vector_type & N) {

	// Shape function , Natural coordinates
	N(0) =
	0.125 * (1 - c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 - c(0) - c(1) - c(2));
	N(1) =
	0.125 * (1 + c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 + c(0) - c(1) - c(2));
	N(2) =
	0.125 * (1 + c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 + c(0) + c(1) - c(2));
	N(3) =
	0.125 * (1 - c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 - c(0) + c(1) - c(2));
	N(4) =
	0.125 * (1 - c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 - c(0) - c(1) + c(2));
	N(5) =
	0.125 * (1 + c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 + c(0) - c(1) + c(2));
	N(6) =
	0.125 * (1 + c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 + c(0) + c(1) + c(2));
	N(7) =
	0.125 * (1 - c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 - c(0) + c(1) + c(2));
	N(8) = 0.25 * (1 - c(0) * c(0)) * (1 - c(1)) * (1 - c(2));
	N(9) = 0.25 * (1 - c(1) * c(1)) * (1 + c(0)) * (1 - c(2));
	N(10) = 0.25 * (1 - c(0) * c(0)) * (1 + c(1)) * (1 - c(2));
	N(11) = 0.25 * (1 - c(1) * c(1)) * (1 - c(0)) * (1 - c(2));
	N(12) = 0.25 * (1 - c(2) * c(2)) * (1 - c(0)) * (1 - c(1));
	N(13) = 0.25 * (1 - c(2) * c(2)) * (1 + c(0)) * (1 - c(1));
	N(14) = 0.25 * (1 - c(2) * c(2)) * (1 + c(0)) * (1 + c(1));
	N(15) = 0.25 * (1 - c(2) * c(2)) * (1 - c(0)) * (1 + c(1));
	N(16) = 0.25 * (1 - c(0) * c(0)) * (1 - c(1)) * (1 + c(2));
	N(17) = 0.25 * (1 - c(1) * c(1)) * (1 + c(0)) * (1 + c(2));
	N(18) = 0.25 * (1 - c(0) * c(0)) * (1 + c(1)) * (1 + c(2));
	N(19) = 0.25 * (1 - c(1) * c(1)) * (1 - c(0)) * (1 + c(2));
	}
	/* -------------------------------------------------------------------------- */

	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_serendip_hexahedron_20>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {
	// derivatives
	// ddx
	dnds(0, 0) =
	0.25 * (c(0) + 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
	dnds(0, 1) =
	0.25 * (c(0) - 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
	dnds(0, 2) =
	-0.25 * (c(0) + 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
	dnds(0, 3) =
	-0.25 * (c(0) - 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
	dnds(0, 4) =
	-0.25 * (c(0) + 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
	dnds(0, 5) =
	-0.25 * (c(0) - 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
	dnds(0, 6) =
	0.25 * (c(0) + 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
	dnds(0, 7) =
	0.25 * (c(0) - 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
	dnds(0, 8) = -0.5 * c(0) * (c(1) - 1) * (c(2) - 1);
	dnds(0, 9) = 0.25 * (c(1) * c(1) - 1) * (c(2) - 1);
	dnds(0, 10) = 0.5 * c(0) * (c(1) + 1) * (c(2) - 1);
	dnds(0, 11) = -0.25 * (c(1) * c(1) - 1) * (c(2) - 1);
	dnds(0, 12) = -0.25 * (c(2) * c(2) - 1) * (c(1) - 1);
	dnds(0, 13) = 0.25 * (c(1) - 1) * (c(2) * c(2) - 1);
	dnds(0, 14) = -0.25 * (c(1) + 1) * (c(2) * c(2) - 1);
	dnds(0, 15) = 0.25 * (c(1) + 1) * (c(2) * c(2) - 1);
	dnds(0, 16) = 0.5 * c(0) * (c(1) - 1) * (c(2) + 1);
	dnds(0, 17) = -0.25 * (c(2) + 1) * (c(1) * c(1) - 1);
	dnds(0, 18) = -0.5 * c(0) * (c(1) + 1) * (c(2) + 1);
	dnds(0, 19) = 0.25 * (c(2) + 1) * (c(1) * c(1) - 1);

	// ddy
	dnds(1, 0) =
	0.25 * (c(1) + 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
	dnds(1, 1) =
	-0.25 * (c(1) - 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
	dnds(1, 2) =
	-0.25 * (c(1) + 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
	dnds(1, 3) =
	0.25 * (c(1) - 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
	dnds(1, 4) =
	-0.25 * (c(1) + 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
	dnds(1, 5) =
	0.25 * (c(1) - 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
	dnds(1, 6) =
	0.25 * (c(1) + 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
	dnds(1, 7) =
	-0.25 * (c(1) - 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
	dnds(1, 8) = -0.25 * (c(0) * c(0) - 1) * (c(2) - 1);
	dnds(1, 9) = 0.5 * c(1) * (c(0) + 1) * (c(2) - 1);
	dnds(1, 10) = 0.25 * (c(0) * c(0) - 1) * (c(2) - 1);
	dnds(1, 11) = -0.5 * c(1) * (c(0) - 1) * (c(2) - 1);
	dnds(1, 12) = -0.25 * (c(2) * c(2) - 1) * (c(0) - 1);
	dnds(1, 13) = 0.25 * (c(0) + 1) * (c(2) * c(2) - 1);
	dnds(1, 14) = -0.25 * (c(0) + 1) * (c(2) * c(2) - 1);
	dnds(1, 15) = 0.25 * (c(0) - 1) * (c(2) * c(2) - 1);
	dnds(1, 16) = 0.25 * (c(2) + 1) * (c(0) * c(0) - 1);
	dnds(1, 17) = -0.5 * c(1) * (c(0) + 1) * (c(2) + 1);
	dnds(1, 18) = -0.25 * (c(2) + 1) * (c(0) * c(0) - 1);
	dnds(1, 19) = 0.5 * c(1) * (c(0) - 1) * (c(2) + 1);

	// ddz
	dnds(2, 0) =
	0.25 * (c(2) + 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
	dnds(2, 1) =
	-0.25 * (c(2) - 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
	dnds(2, 2) =
	0.25 * (c(2) - 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
	dnds(2, 3) =
	-0.25 * (c(2) + 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
	dnds(2, 4) =
	0.25 * (c(2) - 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
	dnds(2, 5) =
	-0.25 * (c(2) + 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
	dnds(2, 6) =
	0.25 * (c(2) + 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
	dnds(2, 7) =
	-0.25 * (c(2) - 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
	dnds(2, 8) = -0.25 * (c(0) * c(0) - 1) * (c(1) - 1);
	dnds(2, 9) = 0.25 * (c(1) * c(1) - 1) * (c(0) + 1);
	dnds(2, 10) = 0.25 * (c(0) * c(0) - 1) * (c(1) + 1);
	dnds(2, 11) = -0.25 * (c(1) * c(1) - 1) * (c(0) - 1);
	dnds(2, 12) = -0.5 * c(2) * (c(1) - 1) * (c(0) - 1);
	dnds(2, 13) = 0.5 * c(2) * (c(0) + 1) * (c(1) - 1);
	dnds(2, 14) = -0.5 * c(2) * (c(0) + 1) * (c(1) + 1);
	dnds(2, 15) = 0.5 * c(2) * (c(0) - 1) * (c(1) + 1);
	dnds(2, 16) = 0.25 * (c(1) - 1) * (c(0) * c(0) - 1);
	dnds(2, 17) = -0.25 * (c(0) + 1) * (c(1) * c(1) - 1);
	dnds(2, 18) = -0.25 * (c(1) + 1) * (c(0) * c(0) - 1);
	dnds(2, 19) = 0.25 * (c(0) - 1) * (c(1) * c(1) - 1);
	}

	/* -------------------------------------------------------------------------- */

	template <>
	inline Real
	GeometricalElement<_gt_hexahedron_20>::getInradius(const Matrix<Real> & coord) {
	return GeometricalElement<_gt_hexahedron_8>::getInradius(coord) * 0.5;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_hexahedron_8_inline_impl.hh b/src/fe_engine/element_classes/element_class_hexahedron_8_inline_impl.hh
	index 1ed0e2a36..67bb4b099 100644
	--- a/src/fe_engine/element_classes/element_class_hexahedron_8_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_hexahedron_8_inline_impl.hh
	@@ -1,253 +1,253 @@
	/**
	* @file element_class_hexahedron_8_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	*
	* @date creation: Mon Mar 14 2011
	* @date last modification: Fri Feb 07 2020
	*
	* @brief Specialization of the element_class class for the type _hexahedron_8
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\zeta
	^
	(-1,1,1) \| (1,1,1)
	7---\|------6
	/\| \| /\|
	/ \| \| / \|
	(-1,-1,1) 4----------5 \| (1,-1,1)
	\| \| \| \| \|
	\| \| \| \| \|
	\| \| +---\|-------> \xi
	\| \| / \| \|
	(-1,1,-1) \| 3-/-----\|--2 (1,1,-1)
	\| / / \| /
	\|/ / \|/
	0-/--------1
	(-1,-1,-1) / (1,-1,-1)
	/
	\eta
	@endverbatim
	*
	* \f[
	* \begin{array}{llll}
	* N1 = (1 - \xi) (1 - \eta) (1 - \zeta) / 8
	* & \frac{\partial N1}{\partial \xi} = - (1 - \eta) (1 - \zeta) / 8
	* & \frac{\partial N1}{\partial \eta} = - (1 - \xi) (1 - \zeta) / 8
	* & \frac{\partial N1}{\partial \zeta} = - (1 - \xi) (1 - \eta) / 8 \\
	* N2 = (1 + \xi) (1 - \eta) (1 - \zeta) / 8
	* & \frac{\partial N2}{\partial \xi} = (1 - \eta) (1 - \zeta) / 8
	* & \frac{\partial N2}{\partial \eta} = - (1 + \xi) (1 - \zeta) / 8
	* & \frac{\partial N2}{\partial \zeta} = - (1 + \xi) (1 - \eta) / 8 \\
	* N3 = (1 + \xi) (1 + \eta) (1 - \zeta) / 8
	* & \frac{\partial N3}{\partial \xi} = (1 + \eta) (1 - \zeta) / 8
	* & \frac{\partial N3}{\partial \eta} = (1 + \xi) (1 - \zeta) / 8
	* & \frac{\partial N3}{\partial \zeta} = - (1 + \xi) (1 + \eta) / 8 \\
	* N4 = (1 - \xi) (1 + \eta) (1 - \zeta) / 8
	* & \frac{\partial N4}{\partial \xi} = - (1 + \eta) (1 - \zeta) / 8
	* & \frac{\partial N4}{\partial \eta} = (1 - \xi) (1 - \zeta) / 8
	* & \frac{\partial N4}{\partial \zeta} = - (1 - \xi) (1 + \eta) / 8 \\
	* N5 = (1 - \xi) (1 - \eta) (1 + \zeta) / 8
	* & \frac{\partial N5}{\partial \xi} = - (1 - \eta) (1 + \zeta) / 8
	* & \frac{\partial N5}{\partial \eta} = - (1 - \xi) (1 + \zeta) / 8
	* & \frac{\partial N5}{\partial \zeta} = (1 - \xi) (1 - \eta) / 8 \\
	* N6 = (1 + \xi) (1 - \eta) (1 + \zeta) / 8
	* & \frac{\partial N6}{\partial \xi} = (1 - \eta) (1 + \zeta) / 8
	* & \frac{\partial N6}{\partial \eta} = - (1 + \xi) (1 + \zeta) / 8
	* & \frac{\partial N6}{\partial \zeta} = (1 + \xi) (1 - \eta) / 8 \\
	* N7 = (1 + \xi) (1 + \eta) (1 + \zeta) / 8
	* & \frac{\partial N7}{\partial \xi} = (1 + \eta) (1 + \zeta) / 8
	* & \frac{\partial N7}{\partial \eta} = (1 + \xi) (1 + \zeta) / 8
	* & \frac{\partial N7}{\partial \zeta} = (1 + \xi) (1 + \eta) / 8 \\
	* N8 = (1 - \xi) (1 + \eta) (1 + \zeta) / 8
	* & \frac{\partial N8}{\partial \xi} = - (1 + \eta) (1 + \zeta) / 8
	* & \frac{\partial N8}{\partial \eta} = (1 - \xi) (1 + \zeta) / 8
	* & \frac{\partial N8}{\partial \zeta} = (1 - \xi) (1 + \eta) / 8 \\
	* \end{array}
	* \f]
	*
	* @f{eqnarray*}{
	* \xi_{q0} &=& -1/\sqrt{3} \qquad \eta_{q0} = -1/\sqrt{3} \qquad \zeta_{q0} =
	-1/\sqrt{3} \\
	* \xi_{q1} &=& 1/\sqrt{3} \qquad \eta_{q1} = -1/\sqrt{3} \qquad \zeta_{q1} =
	-1/\sqrt{3} \\
	* \xi_{q2} &=& 1/\sqrt{3} \qquad \eta_{q2} = 1/\sqrt{3} \qquad \zeta_{q2} =
	-1/\sqrt{3} \\
	* \xi_{q3} &=& -1/\sqrt{3} \qquad \eta_{q3} = 1/\sqrt{3} \qquad \zeta_{q3} =
	-1/\sqrt{3} \\
	* \xi_{q4} &=& -1/\sqrt{3} \qquad \eta_{q4} = -1/\sqrt{3} \qquad \zeta_{q4} =
	1/\sqrt{3} \\
	* \xi_{q5} &=& 1/\sqrt{3} \qquad \eta_{q5} = -1/\sqrt{3} \qquad \zeta_{q5} =
	1/\sqrt{3} \\
	* \xi_{q6} &=& 1/\sqrt{3} \qquad \eta_{q6} = 1/\sqrt{3} \qquad \zeta_{q6} =
	1/\sqrt{3} \\
	* \xi_{q7} &=& -1/\sqrt{3} \qquad \eta_{q7} = 1/\sqrt{3} \qquad \zeta_{q7} =
	1/\sqrt{3} \\
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_hexahedron_8, _gt_hexahedron_8,
	_itp_lagrange_hexahedron_8, _ek_regular, 3,
	_git_segment, 2);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_hexahedron_8>::computeShapes(
	const vector_type & c, vector_type & N) {
	/// Natural coordinates
	N(0) = .125 * (1 - c(0)) * (1 - c(1)) * (1 - c(2)); /// N1(q_0)
	N(1) = .125 * (1 + c(0)) * (1 - c(1)) * (1 - c(2)); /// N2(q_0)
	N(2) = .125 * (1 + c(0)) * (1 + c(1)) * (1 - c(2)); /// N3(q_0)
	N(3) = .125 * (1 - c(0)) * (1 + c(1)) * (1 - c(2)); /// N4(q_0)
	N(4) = .125 * (1 - c(0)) * (1 - c(1)) * (1 + c(2)); /// N5(q_0)
	N(5) = .125 * (1 + c(0)) * (1 - c(1)) * (1 + c(2)); /// N6(q_0)
	N(6) = .125 * (1 + c(0)) * (1 + c(1)) * (1 + c(2)); /// N7(q_0)
	N(7) = .125 * (1 - c(0)) * (1 + c(1)) * (1 + c(2)); /// N8(q_0)
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_hexahedron_8>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {
	/**
	* @f[
	* dnds = \left(
	* \begin{array}{cccccccc}
	* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
	* \xi}
	* & \frac{\partial N3}{\partial \xi} & \frac{\partial
	* N4}{\partial \xi}
	* & \frac{\partial N5}{\partial \xi} & \frac{\partial
	* N6}{\partial \xi}
	* & \frac{\partial N7}{\partial \xi} & \frac{\partial
	* N8}{\partial \xi}\\
	* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
	* \eta}
	* & \frac{\partial N3}{\partial \eta} & \frac{\partial
	* N4}{\partial \eta}
	* & \frac{\partial N5}{\partial \eta} & \frac{\partial
	* N6}{\partial \eta}
	* & \frac{\partial N7}{\partial \eta} & \frac{\partial
	* N8}{\partial \eta}\\
	* \frac{\partial N1}{\partial \zeta} & \frac{\partial N2}{\partial
	* \zeta}
	* & \frac{\partial N3}{\partial \zeta} & \frac{\partial
	* N4}{\partial \zeta}
	* & \frac{\partial N5}{\partial \zeta} & \frac{\partial
	* N6}{\partial \zeta}
	* & \frac{\partial N7}{\partial \zeta} & \frac{\partial
	* N8}{\partial \zeta}
	* \end{array}
	* \right)
	* @f]
	*/
	dnds(0, 0) = -.125 * (1 - c(1)) * (1 - c(2));
	dnds(0, 1) = .125 * (1 - c(1)) * (1 - c(2));
	dnds(0, 2) = .125 * (1 + c(1)) * (1 - c(2));
	dnds(0, 3) = -.125 * (1 + c(1)) * (1 - c(2));
	dnds(0, 4) = -.125 * (1 - c(1)) * (1 + c(2));
	;
	dnds(0, 5) = .125 * (1 - c(1)) * (1 + c(2));
	;
	dnds(0, 6) = .125 * (1 + c(1)) * (1 + c(2));
	;
	dnds(0, 7) = -.125 * (1 + c(1)) * (1 + c(2));
	;

	dnds(1, 0) = -.125 * (1 - c(0)) * (1 - c(2));
	;
	dnds(1, 1) = -.125 * (1 + c(0)) * (1 - c(2));
	;
	dnds(1, 2) = .125 * (1 + c(0)) * (1 - c(2));
	;
	dnds(1, 3) = .125 * (1 - c(0)) * (1 - c(2));
	;
	dnds(1, 4) = -.125 * (1 - c(0)) * (1 + c(2));
	;
	dnds(1, 5) = -.125 * (1 + c(0)) * (1 + c(2));
	;
	dnds(1, 6) = .125 * (1 + c(0)) * (1 + c(2));
	;
	dnds(1, 7) = .125 * (1 - c(0)) * (1 + c(2));
	;

	dnds(2, 0) = -.125 * (1 - c(0)) * (1 - c(1));
	;
	dnds(2, 1) = -.125 * (1 + c(0)) * (1 - c(1));
	;
	dnds(2, 2) = -.125 * (1 + c(0)) * (1 + c(1));
	;
	dnds(2, 3) = -.125 * (1 - c(0)) * (1 + c(1));
	;
	dnds(2, 4) = .125 * (1 - c(0)) * (1 - c(1));
	;
	dnds(2, 5) = .125 * (1 + c(0)) * (1 - c(1));
	;
	dnds(2, 6) = .125 * (1 + c(0)) * (1 + c(1));
	;
	dnds(2, 7) = .125 * (1 - c(0)) * (1 + c(1));
	;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_hexahedron_8>::getInradius(const Matrix<Real> & coord) {
	Vector<Real> u0 = coord(0);
	Vector<Real> u1 = coord(1);
	Vector<Real> u2 = coord(2);
	Vector<Real> u3 = coord(3);
	Vector<Real> u4 = coord(4);
	Vector<Real> u5 = coord(5);
	Vector<Real> u6 = coord(6);
	Vector<Real> u7 = coord(7);

	Real a = u0.distance(u1);
	Real b = u1.distance(u2);
	Real c = u2.distance(u3);
	Real d = u3.distance(u0);
	Real e = u0.distance(u4);
	Real f = u1.distance(u5);
	Real g = u2.distance(u6);
	Real h = u3.distance(u7);
	Real i = u4.distance(u5);
	Real j = u5.distance(u6);
	Real k = u6.distance(u7);
	Real l = u7.distance(u4);

	Real p = std::min({a, b, c, d, e, f, g, h, i, j, k, l});

	return p;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_kirchhoff_shell_inline_impl.hh b/src/fe_engine/element_classes/element_class_kirchhoff_shell_inline_impl.hh
	index 520b6f31d..804dce975 100644
	--- a/src/fe_engine/element_classes/element_class_kirchhoff_shell_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_kirchhoff_shell_inline_impl.hh
	@@ -1,226 +1,226 @@
	/**
	* @file element_class_kirchhoff_shell_inline_impl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Fri Jul 04 2014
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Element class Kirchhoff Shell
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class_structural.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_CLASS_KIRCHHOFF_SHELL_INLINE_IMPL_HH_
	#define AKANTU_ELEMENT_CLASS_KIRCHHOFF_SHELL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(
	_itp_discrete_kirchhoff_triangle_18, _itp_lagrange_triangle_3, 6, 6, 21);
	AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(
	_discrete_kirchhoff_triangle_18, _gt_triangle_3,
	_itp_discrete_kirchhoff_triangle_18, _triangle_3, _ek_structural, 3,
	_git_triangle, 2);

	/* -------------------------------------------------------------------------- */
	namespace detail {
	inline void computeBasisChangeMatrix(Matrix<Real> & P,
	const Matrix<Real> & X) {
	Vector<Real> X1 = X(0);
	Vector<Real> X2 = X(1);
	Vector<Real> X3 = X(2);

	Vector<Real> a1 = X2 - X1;
	Vector<Real> a2 = X3 - X1;

	a1.normalize();
	Vector<Real> e3 = a1.crossProduct(a2);
	e3.normalize();
	Vector<Real> e2 = e3.crossProduct(a1);

	P(0) = a1;
	P(1) = e2;
	P(2) = e3;
	P = P.transpose();
	}
	} // namespace detail

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ElementClass<_discrete_kirchhoff_triangle_18>::computeRotationMatrix(
	Matrix<Real> & R, const Matrix<Real> & X, const Vector<Real> & /n/) {
	auto dim = X.rows();
	Matrix<Real> P(dim, dim);
	detail::computeBasisChangeMatrix(P, X);

	R.zero();
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	R(i + dim, j + dim) = R(i, j) = P(i, j);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_discrete_kirchhoff_triangle_18>::computeShapes(
	const Vector<Real> & /natural_coords/,
	const Matrix<Real> & /real_coord/, Matrix<Real> & /N/) {}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_discrete_kirchhoff_triangle_18>::computeDNDS(
	const Vector<Real> & natural_coords, const Matrix<Real> & real_coordinates,
	Matrix<Real> & B) {

	auto dim = real_coordinates.cols();
	Matrix<Real> P(dim, dim);
	detail::computeBasisChangeMatrix(P, real_coordinates);
	auto X = P * real_coordinates;
	Vector<Real> X1 = X(0);
	Vector<Real> X2 = X(1);
	Vector<Real> X3 = X(2);

	std::array<Vector<Real>, 3> A = {X2 - X1, X3 - X2, X1 - X3};
	std::array<Real, 3> L;
	std::array<Real, 3> C;
	std::array<Real, 3> S;

	// Setting all last coordinates to 0
	std::for_each(A.begin(), A.end(), [](auto & a) { a(2) = 0; });
	// Computing lengths
	std::transform(A.begin(), A.end(), L.begin(),
	[](auto & a) { return a.template norm<L_2>(); });
	// Computing cosines
	std::transform(A.begin(), A.end(), L.begin(), C.begin(),
	[](auto & a, auto & l) { return a(0) / l; });
	// Computing sines
	std::transform(A.begin(), A.end(), L.begin(), S.begin(),
	[](auto & a, auto & l) { return a(1) / l; });

	// Natural coordinates
	Real xi = natural_coords(0);
	Real eta = natural_coords(1);

	// Derivative of quadratic interpolation functions
	Matrix<Real> dP = {{4 * (1 - 2 * xi - eta), 4 * eta, -4 * eta},
	{-4 * xi, 4 * xi, 4 * (1 - xi - 2 * eta)}};

	Matrix<Real> dNx1 = {
	{3. / 2 * (dP(0, 0) * C[0] / L[0] - dP(0, 2) * C[2] / L[2]),
	3. / 2 * (dP(0, 1) * C[1] / L[1] - dP(0, 0) * C[0] / L[0]),
	3. / 2 * (dP(0, 2) * C[2] / L[2] - dP(0, 1) * C[1] / L[1])},
	{3. / 2 * (dP(1, 0) * C[0] / L[0] - dP(1, 2) * C[2] / L[2]),
	3. / 2 * (dP(1, 1) * C[1] / L[1] - dP(1, 0) * C[0] / L[0]),
	3. / 2 * (dP(1, 2) * C[2] / L[2] - dP(1, 1) * C[1] / L[1])}};
	Matrix<Real> dNx2 = {
	// clang-format off
	{-1 - 3. / 4 * (dP(0, 0) * C[0] * C[0] + dP(0, 2) * C[2] * C[2]),
	1 - 3. / 4 * (dP(0, 1) * C[1] * C[1] + dP(0, 0) * C[0] * C[0]),
	- 3. / 4 * (dP(0, 2) * C[2] * C[2] + dP(0, 1) * C[1] * C[1])},
	{-1 - 3. / 4 * (dP(1, 0) * C[0] * C[0] + dP(1, 2) * C[2] * C[2]),
	- 3. / 4 * (dP(1, 1) * C[1] * C[1] + dP(1, 0) * C[0] * C[0]),
	1 - 3. / 4 * (dP(1, 2) * C[2] * C[2] + dP(1, 1) * C[1] * C[1])}};
	// clang-format on
	Matrix<Real> dNx3 = {
	{-3. / 4 * (dP(0, 0) * C[0] * S[0] + dP(0, 2) * C[2] * S[2]),
	-3. / 4 * (dP(0, 1) * C[1] * S[1] + dP(0, 0) * C[0] * S[0]),
	-3. / 4 * (dP(0, 2) * C[2] * S[2] + dP(0, 1) * C[1] * S[1])},
	{-3. / 4 * (dP(1, 0) * C[0] * S[0] + dP(1, 2) * C[2] * S[2]),
	-3. / 4 * (dP(1, 1) * C[1] * S[1] + dP(1, 0) * C[0] * S[0]),
	-3. / 4 * (dP(1, 2) * C[2] * S[2] + dP(1, 1) * C[1] * S[1])}};
	Matrix<Real> dNy1 = {
	{3. / 2 * (dP(0, 0) * S[0] / L[0] - dP(0, 2) * S[2] / L[2]),
	3. / 2 * (dP(0, 1) * S[1] / L[1] - dP(0, 0) * S[0] / L[0]),
	3. / 2 * (dP(0, 2) * S[2] / L[2] - dP(0, 1) * S[1] / L[1])},
	{3. / 2 * (dP(1, 0) * S[0] / L[0] - dP(1, 2) * S[2] / L[2]),
	3. / 2 * (dP(1, 1) * S[1] / L[1] - dP(1, 0) * S[0] / L[0]),
	3. / 2 * (dP(1, 2) * S[2] / L[2] - dP(1, 1) * S[1] / L[1])}};
	const Matrix<Real> & dNy2 = dNx3;
	Matrix<Real> dNy3 = {
	// clang-format off
	{-1 - 3. / 4 * (dP(0, 0) * S[0] * S[0] + dP(0, 2) * S[2] * S[2]),
	1 - 3. / 4 * (dP(0, 1) * S[1] * S[1] + dP(0, 0) * S[0] * S[0]),
	- 3. / 4 * (dP(0, 2) * S[2] * S[2] + dP(0, 1) * S[1] * S[1])},
	{-1 - 3. / 4 * (dP(1, 0) * S[0] * S[0] + dP(1, 2) * S[2] * S[2]),
	- 3. / 4 * (dP(1, 1) * S[1] * S[1] + dP(1, 0) * S[0] * S[0]),
	1 - 3. / 4 * (dP(1, 2) * S[2] * S[2] + dP(1, 1) * S[1] * S[1])}};
	// clang-format on

	// Derivative of linear (membrane mode) functions
	Matrix<Real> dNm(2, 3);
	InterpolationElement<_itp_lagrange_triangle_3, _itk_lagrangian>::computeDNDS(
	natural_coords, dNm);

	UInt i = 0;
	for (const Matrix<Real> & mat : {dNm, dNx1, dNx2, dNx3, dNy1, dNy2, dNy3}) {
	B.block(mat, 0, i);
	i += mat.cols();
	}
	}
	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_discrete_kirchhoff_triangle_18,
	_itk_structural>::arrangeInVoigt(const Matrix<Real> & dnds,
	Matrix<Real> & B) {
	Matrix<Real> dNm(2, 3);
	Matrix<Real> dNx1(2, 3);
	Matrix<Real> dNx2(2, 3);
	Matrix<Real> dNx3(2, 3);
	Matrix<Real> dNy1(2, 3);
	Matrix<Real> dNy2(2, 3);
	Matrix<Real> dNy3(2, 3);
	UInt i = 0;

	for (Matrix<Real> * mat : {&dNm, &dNx1, &dNx2, &dNx3, &dNy1, &dNy2, &dNy3}) {
	*mat = dnds.block(0, i, 2, 3);
	i += mat->cols();
	}

	for (UInt i = 0; i < 3; ++i) {
	// clang-format off
	Matrix<Real> Bm = {{dNm(0, i), 0, 0, 0, 0, 0},
	{0, dNm(1, i), 0, 0, 0, 0},
	{dNm(1, i), dNm(0, i), 0, 0, 0, 0}};
	Matrix<Real> Bf = {{0, 0, dNx1(0, i), -dNx3(0, i), dNx2(0, i), 0},
	{0, 0, dNy1(1, i), -dNy3(1, i), dNy2(1, i), 0},
	{0, 0, dNx1(1, i) + dNy1(0, i), -dNx3(1, i) - dNy3(0, i), dNx2(1, i) + dNy2(0, i), 0}};
	// clang-format on
	B.block(Bm, 0, i * 6);
	B.block(Bf, 3, i * 6);
	}
	}

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_CLASS_KIRCHHOFF_SHELL_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/element_classes/element_class_pentahedron_15_inline_impl.hh b/src/fe_engine/element_classes/element_class_pentahedron_15_inline_impl.hh
	index e02d0ae16..01362e6eb 100644
	--- a/src/fe_engine/element_classes/element_class_pentahedron_15_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_pentahedron_15_inline_impl.hh
	@@ -1,184 +1,184 @@
	/**
	* @file element_class_pentahedron_15_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Sacha Laffely <sacha.laffely@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
	*
	* @date creation: Tue Mar 31 2015
	* @date last modification: Fri Feb 07 2020
	*
	* @brief Specialization of the element_class class for the type
	* _pentahedron_15
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* \verbatim
	z
	^
	\|
	\|
	\| 1
	\| /\|\
	\|/ \| \
	10 7 6
	/ \| \
	/ \| \
	4 2--8--0
	\| \ / /
	\| \11 /
	13 12 9---------->y
	\| / \ /
	\|/ \ /
	5--14--3
	/
	/
	/
	v
	x
	\endverbatim
	x y z
	* N0 -1 1 0
	* N1 -1 0 1
	* N2 -1 0 0
	* N3 1 1 0
	* N4 1 0 1
	* N5 1 0 0
	* N6 -1 0.5 0.5
	* N7 -1 0 0.5
	* N8 -1 0.5 0
	* N9 0 1 0
	* N10 0 0 1
	* N11 0 0 0
	* N12 1 0.5 0.5
	* N13 1 0 0.5
	* N14 1 0.5 0
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_pentahedron_15, _gt_pentahedron_15,
	_itp_lagrange_pentahedron_15, _ek_regular,
	3, _git_pentahedron, 2);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_pentahedron_15>::computeShapes(
	const vector_type & c, vector_type & N) {
	auto & x = c(0);
	auto & y = c(1);
	auto & z = c(2);

	// Shape Functions, Natural coordinates
	N(0) = 0.5 * y * (1 - x) * (2 * y - 2 - x);
	N(1) = 0.5 * z * (1 - x) * (2 * z - 2 - x);
	N(2) = 0.5 * (x - 1) * (1 - y - z) * (x + 2 * y + 2 * z);
	N(3) = 0.5 * y * (1 + x) * (2 * y - 2 + x);
	N(4) = 0.5 * z * (1 + x) * (2 * z - 2 + x);
	N(5) = 0.5 * (-x - 1) * (1 - y - z) * (-x + 2 * y + 2 * z);
	N(6) = 2.0 * y * z * (1 - x);
	N(7) = 2.0 * z * (1 - y - z) * (1 - x);
	N(8) = 2.0 * y * (1 - x) * (1 - y - z);
	N(9) = y * (1 - x * x);
	N(10) = z * (1 - x * x);
	N(11) = (1 - y - z) * (1 - x * x);
	N(12) = 2.0 * y * z * (1 + x);
	N(13) = 2.0 * z * (1 - y - z) * (1 + x);
	N(14) = 2.0 * y * (1 - y - z) * (1 + x);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_pentahedron_15>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {
	auto & x = c(0);
	auto & y = c(1);
	auto & z = c(2);

	// ddx
	dnds(0, 0) = 0.5 * y * (2 * x - 2 * y + 1);
	dnds(0, 1) = 0.5 * z * (2 * x - 2 * z + 1);
	dnds(0, 2) = -0.5 * (2 * x + 2 * y + 2 * z - 1) * (y + z - 1);
	dnds(0, 3) = 0.5 * y * (2 * x + 2 * y - 1);
	dnds(0, 4) = 0.5 * z * (2 * x + 2 * z - 1);
	dnds(0, 5) = -0.5 * (y + z - 1) * (2 * x - 2 * y - 2 * z + 1);
	dnds(0, 6) = -2.0 * y * z;
	dnds(0, 7) = 2.0 * z * (y + z - 1);
	dnds(0, 8) = 2.0 * y * (y + z - 1);
	dnds(0, 9) = -2.0 * x * y;
	dnds(0, 10) = -2.0 * x * z;
	dnds(0, 11) = 2.0 * x * (y + z - 1);
	dnds(0, 12) = 2.0 * y * z;
	dnds(0, 13) = -2.0 * z * (y + z - 1);
	dnds(0, 14) = -2.0 * y * (y + z - 1);

	// ddy
	dnds(1, 0) = -0.5 * (x - 1) * (4 * y - x - 2);
	dnds(1, 1) = 0.0;
	dnds(1, 2) = -0.5 * (x - 1) * (4 * y + x + 2 * (2 * z - 1));
	dnds(1, 3) = 0.5 * (x + 1) * (4 * y + x - 2);
	dnds(1, 4) = 0.0;
	dnds(1, 5) = 0.5 * (x + 1) * (4 * y - x + 2 * (2 * z - 1));
	dnds(1, 6) = -2.0 * (x - 1) * z;
	dnds(1, 7) = 2.0 * z * (x - 1);
	dnds(1, 8) = 2.0 * (2 * y + z - 1) * (x - 1);
	dnds(1, 9) = -(x * x - 1);
	dnds(1, 10) = 0.0;
	dnds(1, 11) = (x * x - 1);
	dnds(1, 12) = 2.0 * z * (x + 1);
	dnds(1, 13) = -2.0 * z * (x + 1);
	dnds(1, 14) = -2.0 * (2 * y + z - 1) * (x + 1);

	// ddz
	dnds(2, 0) = 0.0;
	dnds(2, 1) = -0.5 * (x - 1) * (4 * z - x - 2);
	dnds(2, 2) = -0.5 * (x - 1) * (4 * z + x + 2 * (2 * y - 1));
	dnds(2, 3) = 0.0;
	dnds(2, 4) = 0.5 * (x + 1) * (4 * z + x - 2);
	dnds(2, 5) = 0.5 * (x + 1) * (4 * z - x + 2 * (2 * y - 1));
	dnds(2, 6) = -2.0 * (x - 1) * y;
	dnds(2, 7) = 2.0 * (x - 1) * (2 * z + y - 1);
	dnds(2, 8) = 2.0 * y * (x - 1);
	dnds(2, 9) = 0.0;
	dnds(2, 10) = -(x * x - 1);
	dnds(2, 11) = (x * x - 1);
	dnds(2, 12) = 2.0 * (x + 1) * y;
	dnds(2, 13) = -2.0 * (x + 1) * (2 * z + y - 1);
	dnds(2, 14) = -2.0 * (x + 1) * y;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real GeometricalElement<_gt_pentahedron_15>::getInradius(
	const Matrix<Real> & coord) {
	return GeometricalElement<_gt_pentahedron_6>::getInradius(coord) * 0.5;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_pentahedron_6_inline_impl.hh b/src/fe_engine/element_classes/element_class_pentahedron_6_inline_impl.hh
	index 5c0122b5f..290904cb0 100644
	--- a/src/fe_engine/element_classes/element_class_pentahedron_6_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_pentahedron_6_inline_impl.hh
	@@ -1,168 +1,168 @@
	/**
	* @file element_class_pentahedron_6_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <mchambart@stucky.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Thomas Menouillard <tmenouillard@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Mar 14 2011
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Specialization of the element_class class for the type _pentahedron_6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	/z
	\|
	\|
	\| 1
	\| /\|\
	\|/ \| \
	/ \| \
	/ \| \
	/ \| \
	4 2-----0
	\| \ / /
	\| \/ /
	\| \ /----------/y
	\| / \ /
	\|/ \ /
	5---.--3
	/
	/
	/
	\x
	x y z
	* N0 -1 1 0
	* N1 -1 0 1
	* N2 -1 0 0
	* N3 1 1 0
	* N4 1 0 1
	* N5 1 0 0
	\endverbatim
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_pentahedron_6, _gt_pentahedron_6,
	_itp_lagrange_pentahedron_6, _ek_regular,
	3, _git_pentahedron, 1);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeShapes(
	const vector_type & c, vector_type & N) {
	/// Natural coordinates
	N(0) = 0.5 * c(1) * (1 - c(0)); // N1(q)
	N(1) = 0.5 * c(2) * (1 - c(0)); // N2(q)
	N(2) = 0.5 * (1 - c(1) - c(2)) * (1 - c(0)); // N3(q)
	N(3) = 0.5 * c(1) * (1 + c(0)); // N4(q)
	N(4) = 0.5 * c(2) * (1 + c(0)); // N5(q)
	N(5) = 0.5 * (1 - c(1) - c(2)) * (1 + c(0)); // N6(q)
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {
	dnds(0, 0) = -0.5 * c(1);
	dnds(0, 1) = -0.5 * c(2);
	dnds(0, 2) = -0.5 * (1 - c(1) - c(2));
	- dnds(0, 3) = 0.5 * c(1);
	- dnds(0, 4) = 0.5 * c(2);
	- dnds(0, 5) = 0.5 * (1 - c(1) - c(2));
	+ dnds(0, 3) = 0.5 * c(1);
	+ dnds(0, 4) = 0.5 * c(2);
	+ dnds(0, 5) = 0.5 * (1 - c(1) - c(2));

	dnds(1, 0) = 0.5 * (1 - c(0));
	dnds(1, 1) = 0.0;
	dnds(1, 2) = -0.5 * (1 - c(0));
	dnds(1, 3) = 0.5 * (1 + c(0));
	dnds(1, 4) = 0.0;
	dnds(1, 5) = -0.5 * (1 + c(0));

	dnds(2, 0) = 0.0;
	dnds(2, 1) = 0.5 * (1 - c(0));
	dnds(2, 2) = -0.5 * (1 - c(0));
	dnds(2, 3) = 0.0;
	dnds(2, 4) = 0.5 * (1 + c(0));
	dnds(2, 5) = -0.5 * (1 + c(0));
	}

	/* -------------------------------------------------------------------------- */
	// I have to duplicate this code since the Real * coords do not know their size
	// in the Math module.
	// If later we use eigen or Vector to implement this function
	// there should be only one function in akantu::Math
	// -> this is temporary for the release deadline which was so extended

	inline Real triangle_inradius(const Real * coord1, const Real * coord2,
	const Real * coord3) {
	/**
	* @f{eqnarray*}{
	* r &=& A / s \\
	* A &=& 1/4 * \sqrt{(a + b + c) * (a - b + c) * (a + b - c) (-a + b + c)} \\
	* s &=& \frac{a + b + c}{2}
	* @f}
	*/

	auto a = Math::distance_3d(coord1, coord2);
	auto b = Math::distance_3d(coord2, coord3);
	auto c = Math::distance_3d(coord1, coord3);

	auto s = (a + b + c) * 0.5;

	return std::sqrt((s - a) * (s - b) * (s - c) / s);
	}
	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_pentahedron_6>::getInradius(const Matrix<Real> & coord) {
	Vector<Real> u0 = coord(0);
	Vector<Real> u1 = coord(1);
	Vector<Real> u2 = coord(2);
	Vector<Real> u3 = coord(3);
	Vector<Real> u4 = coord(4);
	Vector<Real> u5 = coord(5);

	auto inradius_triangle_1 =
	triangle_inradius(u0.storage(), u1.storage(), u2.storage());

	auto inradius_triangle_2 =
	triangle_inradius(u3.storage(), u4.storage(), u5.storage());

	auto d1 = u3.distance(u0) * 0.5;
	auto d2 = u5.distance(u2) * 0.5;
	auto d3 = u4.distance(u1) * 0.5;
	auto p =
	2. * std::min({inradius_triangle_1, inradius_triangle_2, d1, d2, d3});

	return p;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_point_1_inline_impl.hh b/src/fe_engine/element_classes/element_class_point_1_inline_impl.hh
	index 188dacccd..0bd4f81a1 100644
	--- a/src/fe_engine/element_classes/element_class_point_1_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_point_1_inline_impl.hh
	@@ -1,86 +1,86 @@
	/**
	* @file element_class_point_1_inline_impl.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Specialization of the element_class class for the type _point_1
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	x
	(0)
	@endverbatim
	*
	* @f{eqnarray*}{
	* N1 &=& 1
	* @f}
	*
	* @f{eqnarray*}{
	* q_0 &=& 0
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_point_1, _gt_point, _itp_lagrange_point_1,
	_ek_regular, 0, _git_point, 1);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_point_1>::computeShapes(
	__attribute__((unused)) const vector_type & natural_coords,
	vector_type & N) {
	N(0) = 1; /// N1(q_0)
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_point_1>::computeDNDS(
	__attribute__((unused)) const vector_type & natural_coords,
	__attribute__((unused)) matrix_type & dnds) {}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void InterpolationElement<_itp_lagrange_point_1>::computeSpecialJacobian(
	__attribute__((unused)) const Matrix<Real> & J, Real & jac) {
	jac = 0.;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_point>::getInradius(__attribute__((unused))
	const Matrix<Real> & coord) {
	return 0.;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_quadrangle_4_inline_impl.hh b/src/fe_engine/element_classes/element_class_quadrangle_4_inline_impl.hh
	index b64037202..e1a537410 100644
	--- a/src/fe_engine/element_classes/element_class_quadrangle_4_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_quadrangle_4_inline_impl.hh
	@@ -1,179 +1,179 @@
	/**
	* @file element_class_quadrangle_4_inline_impl.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Specialization of the element_class class for the type _quadrangle_4
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\eta
	^
	(-1,1) \| (1,1)
	x---------x
	\| \| \|
	\| \| \|
	--\|---------\|-----> \xi
	\| \| \|
	\| \| \|
	x---------x
	(-1,-1) \| (1,-1)
	@endverbatim
	*
	* @f[
	* \begin{array}{lll}
	* N1 = (1 - \xi) (1 - \eta) / 4
	* & \frac{\partial N1}{\partial \xi} = - (1 - \eta) / 4
	* & \frac{\partial N1}{\partial \eta} = - (1 - \xi) / 4 \\
	* N2 = (1 + \xi) (1 - \eta) / 4 \\
	* & \frac{\partial N2}{\partial \xi} = (1 - \eta) / 4
	* & \frac{\partial N2}{\partial \eta} = - (1 + \xi) / 4 \\
	* N3 = (1 + \xi) (1 + \eta) / 4 \\
	* & \frac{\partial N3}{\partial \xi} = (1 + \eta) / 4
	* & \frac{\partial N3}{\partial \eta} = (1 + \xi) / 4 \\
	* N4 = (1 - \xi) (1 + \eta) / 4
	* & \frac{\partial N4}{\partial \xi} = - (1 + \eta) / 4
	* & \frac{\partial N4}{\partial \eta} = (1 - \xi) / 4 \\
	* \end{array}
	* @f]
	*
	* @f{eqnarray*}{
	* \xi_{q0} &=& 0 \qquad \eta_{q0} = 0
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_quadrangle_4, _gt_quadrangle_4,
	_itp_lagrange_quadrangle_4, _ek_regular, 2,
	_git_segment, 2);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_quadrangle_4>::computeShapes(
	const vector_type & c, vector_type & N) {
	N(0) = 1. / 4. * (1. - c(0)) * (1. - c(1)); /// N1(q_0)
	N(1) = 1. / 4. * (1. + c(0)) * (1. - c(1)); /// N2(q_0)
	N(2) = 1. / 4. * (1. + c(0)) * (1. + c(1)); /// N3(q_0)
	N(3) = 1. / 4. * (1. - c(0)) * (1. + c(1)); /// N4(q_0)
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_quadrangle_4>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {
	/**
	* @f[
	* dnds = \left(
	* \begin{array}{cccc}
	* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
	* \xi}
	* & \frac{\partial N3}{\partial \xi} & \frac{\partial
	* N4}{\partial \xi}\\
	* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
	* \eta}
	* & \frac{\partial N3}{\partial \eta} & \frac{\partial
	* N4}{\partial \eta}
	* \end{array}
	* \right)
	* @f]
	*/

	dnds(0, 0) = -1. / 4. * (1. - c(1));
	dnds(0, 1) = 1. / 4. * (1. - c(1));
	dnds(0, 2) = 1. / 4. * (1. + c(1));
	dnds(0, 3) = -1. / 4. * (1. + c(1));

	dnds(1, 0) = -1. / 4. * (1. - c(0));
	dnds(1, 1) = -1. / 4. * (1. + c(0));
	dnds(1, 2) = 1. / 4. * (1. + c(0));
	dnds(1, 3) = 1. / 4. * (1. - c(0));
	}

	/* -------------------------------------------------------------------------- */
	-template<>
	+template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_quadrangle_4>::computeD2NDS2(
	const vector_type & /c/, matrix_type & d2nds2) {
	d2nds2.zero();

	- d2nds2(1, 0) = 1./4.;
	- d2nds2(1, 1) = -1./4.;
	- d2nds2(1, 2) = 1./4.;
	- d2nds2(1, 3) = -1./4.;
	+ d2nds2(1, 0) = 1. / 4.;
	+ d2nds2(1, 1) = -1. / 4.;
	+ d2nds2(1, 2) = 1. / 4.;
	+ d2nds2(1, 3) = -1. / 4.;

	- d2nds2(2, 0) = 1./4.;
	- d2nds2(2, 1) = -1./4.;
	- d2nds2(2, 2) = 1./4.;
	- d2nds2(2, 3) = -1./4.;
	+ d2nds2(2, 0) = 1. / 4.;
	+ d2nds2(2, 1) = -1. / 4.;
	+ d2nds2(2, 2) = 1. / 4.;
	+ d2nds2(2, 3) = -1. / 4.;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_lagrange_quadrangle_4>::computeSpecialJacobian(
	const Matrix<Real> & J, Real & jac) {
	Vector<Real> vprod(J.cols());
	Matrix<Real> Jt(J.transpose(), true);
	vprod.crossProduct(Jt(0), Jt(1));
	jac = vprod.norm();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_quadrangle_4>::getInradius(const Matrix<Real> & coord) {
	Vector<Real> u0 = coord(0);
	Vector<Real> u1 = coord(1);
	Vector<Real> u2 = coord(2);
	Vector<Real> u3 = coord(3);
	Real a = u0.distance(u1);
	Real b = u1.distance(u2);
	Real c = u2.distance(u3);
	Real d = u3.distance(u0);

	// Real septimetre = (a + b + c + d) / 2.;

	// Real p = Math::distance_2d(coord + 0, coord + 4);
	// Real q = Math::distance_2d(coord + 2, coord + 6);

	// Real area = sqrt(4(pp * qq) - (aa + bb + cc + dd)(aa + cc - b*b -
	// d*d)) / 4.;
	// Real h = sqrt(area); // to get a length
	// Real h = area / septimetre; // formula of inradius for circumscritable
	// quadrelateral
	Real h = std::min({a, b, c, d});

	return h;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_quadrangle_8_inline_impl.hh b/src/fe_engine/element_classes/element_class_quadrangle_8_inline_impl.hh
	index cb6f34429..6944b42b1 100644
	--- a/src/fe_engine/element_classes/element_class_quadrangle_8_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_quadrangle_8_inline_impl.hh
	@@ -1,189 +1,189 @@
	/**
	* @file element_class_quadrangle_8_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 18 2011
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Specialization of the ElementClass for the _quadrangle_8
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\eta
	^
	\|
	(-1,1) (0,1) (1,1)
	x-------x-------x
	\| \| \|
	\| \| \|
	\| \| \|
	(-1,0)\| \| \|(1,0)
	----x---------------X-----> \xi
	\| \| \|
	\| \| \|
	\| \| \|
	\| \| \|
	x-------x-------x
	(-1,-1) (0,-1) (1,-1)
	\|
	@endverbatim
	*
	* @f[
	* \begin{array}{lll}
	* N1 = (1 - \xi) (1 - \eta)(- 1 - \xi - \eta) / 4
	* & \frac{\partial N1}{\partial \xi} = (1 - \eta)(2 \xi + \eta) / 4
	* & \frac{\partial N1}{\partial \eta} = (1 - \xi)(\xi + 2 \eta) / 4 \\
	* N2 = (1 + \xi) (1 - \eta)(- 1 + \xi - \eta) / 4 \\
	* & \frac{\partial N2}{\partial \xi} = (1 - \eta)(2 \xi - \eta) / 4
	* & \frac{\partial N2}{\partial \eta} = - (1 + \xi)(\xi - 2 \eta) / 4 \\
	* N3 = (1 + \xi) (1 + \eta)(- 1 + \xi + \eta) / 4 \\
	* & \frac{\partial N3}{\partial \xi} = (1 + \eta)(2 \xi + \eta) / 4
	* & \frac{\partial N3}{\partial \eta} = (1 + \xi)(\xi + 2 \eta) / 4 \\
	* N4 = (1 - \xi) (1 + \eta)(- 1 - \xi + \eta) / 4
	* & \frac{\partial N4}{\partial \xi} = (1 + \eta)(2 \xi - \eta) / 4
	* & \frac{\partial N4}{\partial \eta} = - (1 - \xi)(\xi - 2 \eta) / 4 \\
	* N5 = (1 - \xi^2) (1 - \eta) / 2
	* & \frac{\partial N1}{\partial \xi} = - \xi (1 - \eta)
	* & \frac{\partial N1}{\partial \eta} = - (1 - \xi^2) / 2 \\
	* N6 = (1 + \xi) (1 - \eta^2) / 2 \\
	* & \frac{\partial N2}{\partial \xi} = (1 - \eta^2) / 2
	* & \frac{\partial N2}{\partial \eta} = - \eta (1 + \xi) \\
	* N7 = (1 - \xi^2) (1 + \eta) / 2 \\
	* & \frac{\partial N3}{\partial \xi} = - \xi (1 + \eta)
	* & \frac{\partial N3}{\partial \eta} = (1 - \xi^2) / 2 \\
	* N8 = (1 - \xi) (1 - \eta^2) / 2
	* & \frac{\partial N4}{\partial \xi} = - (1 - \eta^2) / 2
	* & \frac{\partial N4}{\partial \eta} = - \eta (1 - \xi) \\
	* \end{array}
	* @f]
	*
	* @f{eqnarray*}{
	* \xi_{q0} &=& 0 \qquad \eta_{q0} = 0
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_quadrangle_8, _gt_quadrangle_8,
	_itp_serendip_quadrangle_8, _ek_regular, 2,
	_git_segment, 3);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_serendip_quadrangle_8>::computeShapes(
	const vector_type & c, vector_type & N) {

	/// Natural coordinates
	const Real xi = c(0);
	const Real eta = c(1);

	N(0) = .25 * (1 - xi) * (1 - eta) * (-1 - xi - eta);
	N(1) = .25 * (1 + xi) * (1 - eta) * (-1 + xi - eta);
	N(2) = .25 * (1 + xi) * (1 + eta) * (-1 + xi + eta);
	N(3) = .25 * (1 - xi) * (1 + eta) * (-1 - xi + eta);
	N(4) = .5 * (1 - xi * xi) * (1 - eta);
	N(5) = .5 * (1 + xi) * (1 - eta * eta);
	N(6) = .5 * (1 - xi * xi) * (1 + eta);
	N(7) = .5 * (1 - xi) * (1 - eta * eta);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_serendip_quadrangle_8>::computeDNDS(
	const vector_type & c, matrix_type & dnds) {

	const Real xi = c(0);
	const Real eta = c(1);

	/// dN/dxi
	dnds(0, 0) = .25 * (1 - eta) * (2 * xi + eta);
	dnds(0, 1) = .25 * (1 - eta) * (2 * xi - eta);
	dnds(0, 2) = .25 * (1 + eta) * (2 * xi + eta);
	dnds(0, 3) = .25 * (1 + eta) * (2 * xi - eta);
	dnds(0, 4) = -xi * (1 - eta);
	dnds(0, 5) = .5 * (1 - eta * eta);
	dnds(0, 6) = -xi * (1 + eta);
	dnds(0, 7) = -.5 * (1 - eta * eta);

	/// dN/deta
	dnds(1, 0) = .25 * (1 - xi) * (2 * eta + xi);
	dnds(1, 1) = .25 * (1 + xi) * (2 * eta - xi);
	dnds(1, 2) = .25 * (1 + xi) * (2 * eta + xi);
	dnds(1, 3) = .25 * (1 - xi) * (2 * eta - xi);
	dnds(1, 4) = -.5 * (1 - xi * xi);
	dnds(1, 5) = -eta * (1 + xi);
	dnds(1, 6) = .5 * (1 - xi * xi);
	dnds(1, 7) = -eta * (1 - xi);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_quadrangle_8>::getInradius(const Matrix<Real> & coord) {
	Vector<Real> u0 = coord(0);
	Vector<Real> u1 = coord(1);
	Vector<Real> u2 = coord(2);
	Vector<Real> u3 = coord(3);
	Vector<Real> u4 = coord(4);
	Vector<Real> u5 = coord(5);
	Vector<Real> u6 = coord(6);
	Vector<Real> u7 = coord(7);

	auto a = u0.distance(u4);
	auto b = u4.distance(u1);
	auto h = std::min(a, b);

	a = u1.distance(u5);
	b = u5.distance(u2);
	h = std::min(h, std::min(a, b));

	a = u2.distance(u6);
	b = u6.distance(u3);
	h = std::min(h, std::min(a, b));

	a = u3.distance(u7);
	b = u7.distance(u0);
	h = std::min(h, std::min(a, b));

	return h;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_serendip_quadrangle_8>::computeSpecialJacobian(
	const Matrix<Real> & J, Real & jac) {
	Vector<Real> vprod(J.cols());
	Matrix<Real> Jt(J.transpose(), true);
	vprod.crossProduct(Jt(0), Jt(1));
	jac = vprod.norm();
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_segment_2_inline_impl.hh b/src/fe_engine/element_classes/element_class_segment_2_inline_impl.hh
	index 9f0d2252e..9ebd87b41 100644
	--- a/src/fe_engine/element_classes/element_class_segment_2_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_segment_2_inline_impl.hh
	@@ -1,123 +1,122 @@
	/**
	* @file element_class_segment_2_inline_impl.hh
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Specialization of the element_class class for the type _segment_2
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	q
	--x--------\|--------x---> x
	-1 0 1
	@endverbatim
	*
	* @f{eqnarray*}{
	* w_1(x) &=& 1/2(1 - x) \\
	* w_2(x) &=& 1/2(1 + x)
	* @f}
	*
	* @f{eqnarray*}{
	* x_{q} &=& 0
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_segment_2, _gt_segment_2,
	_itp_lagrange_segment_2, _ek_regular, 1,
	_git_segment, 1);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_segment_2>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {

	/// natural coordinate
	Real c = natural_coords(0);
	/// shape functions
	N(0) = 0.5 * (1 - c);
	N(1) = 0.5 * (1 + c);
	}
	/* -------------------------------------------------------------------------- */

	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_segment_2>::computeDNDS(
	__attribute__((unused)) const vector_type & natural_coords,
	matrix_type & dnds) {

	/// dN1/de
	dnds(0, 0) = -.5;
	/// dN2/de
	dnds(0, 1) = .5;
	}

	-
	/* -------------------------------------------------------------------------- */
	-template<>
	+template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_segment_2>::computeD2NDS2(
	const vector_type & /natural_coords/, matrix_type & d2nds2) {
	d2nds2.zero();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_lagrange_segment_2>::computeSpecialJacobian(
	const Matrix<Real> & dxds, Real & jac) {
	jac = dxds.norm<L_2>();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_segment_2>::getInradius(const Matrix<Real> & coord) {
	Vector<Real> a(coord(0));
	Vector<Real> b(coord(1));
	return a.distance(b);
	}

	// /* --------------------------------------------------------------------------
	// */
	// template<> inline bool ElementClass<_segment_2>::contains(const Vector<Real>
	// & natural_coords) {
	// if (natural_coords(0) < -1.) return false;
	// if (natural_coords(0) > 1.) return false;
	// return true;
	// }

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_segment_3_inline_impl.hh b/src/fe_engine/element_classes/element_class_segment_3_inline_impl.hh
	index 42e13e196..19d3f1b19 100644
	--- a/src/fe_engine/element_classes/element_class_segment_3_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_segment_3_inline_impl.hh
	@@ -1,111 +1,111 @@
	/**
	* @file element_class_segment_3_inline_impl.hh
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Specialization of the element_class class for the type _segment_3
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	-1 0 1
	-----x---------x---------x-----> x
	1 3 2
	@endverbatim
	*
	*
	* @f[
	* \begin{array}{lll}
	* x_{1} = -1 & x_{2} = 1 & x_{3} = 0
	* \end{array}
	* @f]
	*
	* @f[
	* \begin{array}{ll}
	* w_1(x) = \frac{x}{2}(x - 1) & w'_1(x) = x - \frac{1}{2}\\
	* w_2(x) = \frac{x}{2}(x + 1) & w'_2(x) = x + \frac{1}{2}\\
	* w_3(x) = 1-x^2 & w'_3(x) = -2x
	* \end{array}
	* @f]
	*
	* @f[
	* \begin{array}{ll}
	* x_{q1} = -1/\sqrt{3} & x_{q2} = 1/\sqrt{3}
	* \end{array}
	* @f]
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_segment_3, _gt_segment_3,
	_itp_lagrange_segment_3, _ek_regular, 1,
	_git_segment, 2);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_segment_3>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {

	Real c = natural_coords(0);
	N(0) = (c - 1) * c / 2;
	N(1) = (c + 1) * c / 2;
	N(2) = 1 - c * c;
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_segment_3>::computeDNDS(
	const vector_type & natural_coords, matrix_type & dnds) {

	Real c = natural_coords(0);
	dnds(0, 0) = c - .5;
	dnds(0, 1) = c + .5;
	dnds(0, 2) = -2 * c;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_lagrange_segment_3>::computeSpecialJacobian(
	const Matrix<Real> & dxds, Real & jac) {
	jac = Math::norm2(dxds.storage());
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_segment_3>::getInradius(const Matrix<Real> & coord) {
	Real dist1 = std::abs(coord(0, 0) - coord(0, 1));
	Real dist2 = std::abs(coord(0, 1) - coord(0, 2));
	return std::min(dist1, dist2);
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_tetrahedron_10_inline_impl.hh b/src/fe_engine/element_classes/element_class_tetrahedron_10_inline_impl.hh
	index aa2dd82c4..98b7eec10 100644
	--- a/src/fe_engine/element_classes/element_class_tetrahedron_10_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_tetrahedron_10_inline_impl.hh
	@@ -1,284 +1,284 @@
	/**
	* @file element_class_tetrahedron_10_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Fri Feb 07 2020
	*
	* @brief Specialization of the element_class class for the type
	* _tetrahedron_10
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\zeta
	^
	\|
	(0,0,1)
	x
	\|` .
	\| ` .
	\| ` .
	\| ` . (0,0.5,0.5)
	\| ` x.
	\| q4 o ` . \eta
	\| ` . -,
	(0,0,0.5) x ` x (0.5,0,0.5) -
	\| ` x-(0,1,0)
	\| q3 o` - '
	\| (0,0.5,0) - ` '
	\| x- ` x (0.5,0.5,0)
	\| q1 o - o q2` '
	\| - ` '
	\| - ` '
	x---------------x--------------` x-----> \xi
	(0,0,0) (0.5,0,0) (1,0,0)
	@endverbatim
	*
	*
	* @f[
	* \begin{array}{lll}
	* \xi_{0} = 0 & \eta_{0} = 0 & \zeta_{0} = 0 \\
	* \xi_{1} = 1 & \eta_{1} = 0 & \zeta_{1} = 0 \\
	* \xi_{2} = 0 & \eta_{2} = 1 & \zeta_{2} = 0 \\
	* \xi_{3} = 0 & \eta_{3} = 0 & \zeta_{3} = 1 \\
	* \xi_{4} = 1/2 & \eta_{4} = 0 & \zeta_{4} = 0 \\
	* \xi_{5} = 1/2 & \eta_{5} = 1/2 & \zeta_{5} = 0 \\
	* \xi_{6} = 0 & \eta_{6} = 1/2 & \zeta_{6} = 0 \\
	* \xi_{7} = 0 & \eta_{7} = 0 & \zeta_{7} = 1/2 \\
	* \xi_{8} = 1/2 & \eta_{8} = 0 & \zeta_{8} = 1/2 \\
	* \xi_{9} = 0 & \eta_{9} = 1/2 & \zeta_{9} = 1/2
	* \end{array}
	* @f]
	*
	* @f[
	* \begin{array}{llll}
	* N1 = (1 - \xi - \eta - \zeta) (1 - 2 \xi - 2 \eta - 2 \zeta)
	* & \frac{\partial N1}{\partial \xi} = 4 \xi + 4 \eta + 4 \zeta -
	3
	* & \frac{\partial N1}{\partial \eta} = 4 \xi + 4 \eta + 4 \zeta -
	3
	* & \frac{\partial N1}{\partial \zeta} = 4 \xi + 4 \eta + 4 \zeta -
	3 \\
	* N2 = \xi (2 \xi - 1)
	* & \frac{\partial N2}{\partial \xi} = 4 \xi - 1
	* & \frac{\partial N2}{\partial \eta} = 0
	* & \frac{\partial N2}{\partial \zeta} = 0 \\
	* N3 = \eta (2 \eta - 1)
	* & \frac{\partial N3}{\partial \xi} = 0
	* & \frac{\partial N3}{\partial \eta} = 4 \eta - 1
	* & \frac{\partial N3}{\partial \zeta} = 0 \\
	* N4 = \zeta (2 \zeta - 1)
	* & \frac{\partial N4}{\partial \xi} = 0
	* & \frac{\partial N4}{\partial \eta} = 0
	* & \frac{\partial N4}{\partial \zeta} = 4 \zeta - 1 \\
	* N5 = 4 \xi (1 - \xi - \eta - \zeta)
	* & \frac{\partial N5}{\partial \xi} = 4 - 8 \xi - 4 \eta - 4
	\zeta
	* & \frac{\partial N5}{\partial \eta} = -4 \xi
	* & \frac{\partial N5}{\partial \zeta} = -4 \xi \\
	* N6 = 4 \xi \eta
	* & \frac{\partial N6}{\partial \xi} = 4 \eta
	* & \frac{\partial N6}{\partial \eta} = 4 \xi
	* & \frac{\partial N6}{\partial \zeta} = 0 \\
	* N7 = 4 \eta (1 - \xi - \eta - \zeta)
	* & \frac{\partial N7}{\partial \xi} = -4 \eta
	* & \frac{\partial N7}{\partial \eta} = 4 - 4 \xi - 8 \eta - 4
	\zeta
	* & \frac{\partial N7}{\partial \zeta} = -4 \eta \\
	* N8 = 4 \zeta (1 - \xi - \eta - \zeta)
	* & \frac{\partial N8}{\partial \xi} = -4 \zeta
	* & \frac{\partial N8}{\partial \eta} = -4 \zeta
	* & \frac{\partial N8}{\partial \zeta} = 4 - 4 \xi - 4 \eta - 8
	\zeta \\
	* N9 = 4 \zeta \xi
	* & \frac{\partial N9}{\partial \xi} = 4 \zeta
	* & \frac{\partial N9}{\partial \eta} = 0
	* & \frac{\partial N9}{\partial \zeta} = 4 \xi \\
	* N10 = 4 \eta \zeta
	* & \frac{\partial N10}{\partial \xi} = 0
	* & \frac{\partial N10}{\partial \eta} = 4 \zeta
	* & \frac{\partial N10}{\partial \zeta} = 4 \eta \\
	* \end{array}
	* @f]
	*
	* @f[
	* a = \frac{5 - \sqrt{5}}{20}\\
	* b = \frac{5 + 3 \sqrt{5}}{20}
	* \begin{array}{lll}
	* \xi_{q_0} = a & \eta_{q_0} = a & \zeta_{q_0} = a \\
	* \xi_{q_1} = b & \eta_{q_1} = a & \zeta_{q_1} = a \\
	* \xi_{q_2} = a & \eta_{q_2} = b & \zeta_{q_2} = a \\
	* \xi_{q_3} = a & \eta_{q_3} = a & \zeta_{q_3} = b
	* \end{array}
	* @f]
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_tetrahedron_10, _gt_tetrahedron_10,
	_itp_lagrange_tetrahedron_10, _ek_regular,
	3, _git_tetrahedron, 2);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_tetrahedron_10>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {
	/// Natural coordinates
	Real xi = natural_coords(0);
	Real eta = natural_coords(1);
	Real zeta = natural_coords(2);
	Real sum = xi + eta + zeta;
	Real c0 = 1 - sum;
	Real c1 = 1 - 2 * sum;
	Real c2 = 2 * xi - 1;
	Real c3 = 2 * eta - 1;
	Real c4 = 2 * zeta - 1;

	/// Shape functions
	N(0) = c0 * c1;
	N(1) = xi * c2;
	N(2) = eta * c3;
	N(3) = zeta * c4;
	N(4) = 4 * xi * c0;
	N(5) = 4 * xi * eta;
	N(6) = 4 * eta * c0;
	N(7) = 4 * zeta * c0;
	N(8) = 4 * xi * zeta;
	N(9) = 4 * eta * zeta;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_tetrahedron_10>::computeDNDS(
	const vector_type & natural_coords, matrix_type & dnds) {
	/**
	* \f[
	* dnds = \left(
	* \begin{array}{cccccccccc}
	* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
	* \xi}
	* & \frac{\partial N3}{\partial \xi} & \frac{\partial N4}{\partial
	* \xi}
	* & \frac{\partial N5}{\partial \xi} & \frac{\partial N6}{\partial
	* \xi}
	* & \frac{\partial N7}{\partial \xi} & \frac{\partial N8}{\partial
	* \xi}
	* & \frac{\partial N9}{\partial \xi} & \frac{\partial
	* N10}{\partial \xi} \\
	* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
	* \eta}
	* & \frac{\partial N3}{\partial \eta} & \frac{\partial N4}{\partial
	* \eta}
	* & \frac{\partial N5}{\partial \eta} & \frac{\partial N6}{\partial
	* \eta}
	* & \frac{\partial N7}{\partial \eta} & \frac{\partial N8}{\partial
	* \eta}
	* & \frac{\partial N9}{\partial \eta} & \frac{\partial
	* N10}{\partial \eta} \\
	* \frac{\partial N1}{\partial \zeta} & \frac{\partial N2}{\partial
	* \zeta}
	* & \frac{\partial N3}{\partial \zeta} & \frac{\partial N4}{\partial
	* \zeta}
	* & \frac{\partial N5}{\partial \zeta} & \frac{\partial N6}{\partial
	* \zeta}
	* & \frac{\partial N7}{\partial \zeta} & \frac{\partial N8}{\partial
	* \zeta}
	* & \frac{\partial N9}{\partial \zeta} & \frac{\partial
	* N10}{\partial \zeta}
	* \end{array}
	* \right)
	* \f]
	*/

	/// Natural coordinates
	Real xi = natural_coords(0);
	Real eta = natural_coords(1);
	Real zeta = natural_coords(2);
	Real sum = xi + eta + zeta;

	/// \frac{\partial N_i}{\partial \xi}
	dnds(0, 0) = 4 * sum - 3;
	dnds(0, 1) = 4 * xi - 1;
	dnds(0, 2) = 0;
	dnds(0, 3) = 0;
	dnds(0, 4) = 4 * (1 - sum - xi);
	dnds(0, 5) = 4 * eta;
	dnds(0, 6) = -4 * eta;
	dnds(0, 7) = -4 * zeta;
	dnds(0, 8) = 4 * zeta;
	dnds(0, 9) = 0;

	/// \frac{\partial N_i}{\partial \eta}
	dnds(1, 0) = 4 * sum - 3;
	dnds(1, 1) = 0;
	dnds(1, 2) = 4 * eta - 1;
	dnds(1, 3) = 0;
	dnds(1, 4) = -4 * xi;
	dnds(1, 5) = 4 * xi;
	dnds(1, 6) = 4 * (1 - sum - eta);
	dnds(1, 7) = -4 * zeta;
	dnds(1, 8) = 0;
	dnds(1, 9) = 4 * zeta;

	/// \frac{\partial N_i}{\partial \zeta}
	dnds(2, 0) = 4 * sum - 3;
	dnds(2, 1) = 0;
	dnds(2, 2) = 0;
	dnds(2, 3) = 4 * zeta - 1;
	dnds(2, 4) = -4 * xi;
	dnds(2, 5) = 0;
	dnds(2, 6) = -4 * eta;
	dnds(2, 7) = 4 * (1 - sum - zeta);
	dnds(2, 8) = 4 * xi;
	dnds(2, 9) = 4 * eta;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real GeometricalElement<_gt_tetrahedron_10>::getInradius(
	const Matrix<Real> & coord) {
	// Only take the four corner tetrahedra
	UInt tetrahedra[4][4] = {
	{0, 4, 6, 7}, {4, 1, 5, 8}, {6, 5, 2, 9}, {7, 8, 9, 3}};

	Real inradius = std::numeric_limits<Real>::max();
	for (UInt t = 0; t < 4; t++) {
	Real ir = Math::tetrahedron_inradius(
	coord(tetrahedra[t][0]).storage(), coord(tetrahedra[t][1]).storage(),
	coord(tetrahedra[t][2]).storage(), coord(tetrahedra[t][3]).storage());
	inradius = std::min(ir, inradius);
	}

	return 2. * inradius;
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_tetrahedron_4_inline_impl.hh b/src/fe_engine/element_classes/element_class_tetrahedron_4_inline_impl.hh
	index 8daebbd39..8d3e732a7 100644
	--- a/src/fe_engine/element_classes/element_class_tetrahedron_4_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_tetrahedron_4_inline_impl.hh
	@@ -1,143 +1,143 @@
	/**
	* @file element_class_tetrahedron_4_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Wed Jun 17 2020
	*
	* @brief Specialization of the element_class class for the type _tetrahedron_4
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\eta
	^
	\|
	x (0,0,1,0)
	\|`
	\| ` ° \zeta
	\| ` ° -
	\| ` x (0,0,0,1)
	\| q.` - '
	\| -` '
	\| - ` '
	\| - ` '
	x------------------x-----> \xi
	(1,0,0,0) (0,1,0,0)
	@endverbatim
	*
	* @f{eqnarray*}{
	* N1 &=& 1 - \xi - \eta - \zeta \\
	* N2 &=& \xi \\
	* N3 &=& \eta \\
	* N4 &=& \zeta
	* @f}
	*
	* @f[
	* \xi_{q0} = 1/4 \qquad \eta_{q0} = 1/4 \qquad \zeta_{q0} = 1/4
	* @f]
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_tetrahedron_4, _gt_tetrahedron_4,
	_itp_lagrange_tetrahedron_4, _ek_regular,
	3, _git_tetrahedron, 1);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_tetrahedron_4>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {

	Real c0 = 1 - natural_coords(0) - natural_coords(1) -
	natural_coords(2); /// @f$ c0 = 1 - \xi - \eta - \zeta @f$
	Real c1 = natural_coords(1); /// @f$ c1 = \xi @f$
	Real c2 = natural_coords(2); /// @f$ c2 = \eta @f$
	Real c3 = natural_coords(0); /// @f$ c3 = \zeta @f$

	N(0) = c0;
	N(1) = c1;
	N(2) = c2;
	N(3) = c3;
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_tetrahedron_4>::computeDNDS(
	__attribute__((unused)) const vector_type & natural_coords,
	matrix_type & dnds) {

	/**
	* @f[
	* dnds = \left(
	* \begin{array}{cccccc}
	* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
	* \xi}
	* & \frac{\partial N3}{\partial \xi} & \frac{\partial N4}{\partial
	* \xi} \\
	* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
	* \eta}
	* & \frac{\partial N3}{\partial \eta} & \frac{\partial N4}{\partial
	* \eta} \\
	* \frac{\partial N1}{\partial \zeta} & \frac{\partial N2}{\partial
	* \zeta}
	* & \frac{\partial N3}{\partial \zeta} & \frac{\partial N4}{\partial
	* \zeta}
	* \end{array}
	* \right)
	* @f]
	*/

	dnds(0, 0) = -1.;
	dnds(1, 0) = -1.;
	dnds(2, 0) = -1.;

	dnds(0, 1) = 0.;
	dnds(1, 1) = 1.;
	dnds(2, 1) = 0.;

	dnds(0, 2) = 0.;
	dnds(1, 2) = 0.;
	dnds(2, 2) = 1.;

	dnds(0, 3) = 1.;
	dnds(1, 3) = 0.;
	dnds(2, 3) = 0.;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_tetrahedron_4>::getInradius(const Matrix<Real> & coord) {
	return 2. * Math::tetrahedron_inradius(coord(0).storage(), coord(1).storage(),
	coord(2).storage(),
	coord(3).storage());
	}
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_triangle_3_inline_impl.hh b/src/fe_engine/element_classes/element_class_triangle_3_inline_impl.hh
	index 32ae9db2b..450a57810 100644
	--- a/src/fe_engine/element_classes/element_class_triangle_3_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_triangle_3_inline_impl.hh
	@@ -1,148 +1,148 @@
	/**
	* @file element_class_triangle_3_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Specialization of the element_class class for the type _triangle_3
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\eta
	^
	\|
	x (0,0,1)
	\|`
	\| `
	\| q `
	\| ° `
	x--------x-----> \xi
	(1,0,0) (0,1,0)
	@endverbatim
	*
	* @f{eqnarray*}{
	* N1 &=& 1 - \xi - \eta \\
	* N2 &=& \xi \\
	* N3 &=& \eta
	* @f}
	*
	* @f{eqnarray*}{
	* \xi_{q0} &=& 1/3 \qquad \eta_{q0} = 1/3
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_triangle_3, _gt_triangle_3,
	_itp_lagrange_triangle_3, _ek_regular, 2,
	_git_triangle, 1);

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_triangle_3>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {

	/// Natural coordinates
	Real c0 =
	1 - natural_coords(0) - natural_coords(1); /// @f$ c0 = 1 - \xi - \eta @f$
	Real c1 = natural_coords(0); /// @f$ c1 = \xi @f$
	Real c2 = natural_coords(1); /// @f$ c2 = \eta @f$

	N(0) = c0; /// N1(q_0)
	N(1) = c1; /// N2(q_0)
	N(2) = c2; /// N3(q_0)
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_triangle_3>::computeDNDS(
	__attribute__((unused)) const vector_type & natural_coords,
	matrix_type & dnds) {
	/**
	* @f[
	* dnds = \left(
	* \begin{array}{cccccc}
	* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
	* \xi} & \frac{\partial N3}{\partial \xi} \\
	* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
	* \eta} & \frac{\partial N3}{\partial \eta}
	* \end{array}
	* \right)
	* @f]
	*/
	dnds(0, 0) = -1.;
	dnds(0, 1) = 1.;
	dnds(0, 2) = 0.;
	dnds(1, 0) = -1.;
	dnds(1, 1) = 0.;
	dnds(1, 2) = 1.;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_triangle_3>::computeD2NDS2(
	const vector_type & /natural_coords/, matrix_type & d2nds2) {
	d2nds2.zero();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_lagrange_triangle_3>::computeSpecialJacobian(
	const Matrix<Real> & J, Real & jac) {
	Vector<Real> vprod(J.cols());
	Matrix<Real> Jt(J.transpose(), true);
	vprod.crossProduct(Jt(0), Jt(1));
	jac = vprod.norm();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_triangle_3>::getInradius(const Matrix<Real> & coord) {
	- return 2. * Math::triangle_inradius(coord(0), coord(1), coord(2));
	+ return 2. * Math::triangle_inradius(coord(0), coord(1), coord(2));
	}

	/* -------------------------------------------------------------------------- */
	// template<> inline bool ElementClass<_triangle_3>::contains(const Vector<Real>
	// & natural_coords) {
	// if (natural_coords[0] < 0.) return false;
	// if (natural_coords[0] > 1.) return false;
	// if (natural_coords[1] < 0.) return false;
	// if (natural_coords[1] > 1.) return false;
	// if (natural_coords[0]+natural_coords[1] > 1.) return false;
	// return true;
	// }
	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/fe_engine/element_classes/element_class_triangle_6_inline_impl.hh b/src/fe_engine/element_classes/element_class_triangle_6_inline_impl.hh
	index db4245376..961d66a37 100644
	--- a/src/fe_engine/element_classes/element_class_triangle_6_inline_impl.hh
	+++ b/src/fe_engine/element_classes/element_class_triangle_6_inline_impl.hh
	@@ -1,206 +1,205 @@
	/**
	* @file element_class_triangle_6_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 16 2010
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Specialization of the element_class class for the type _triangle_6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/**
	* @verbatim
	\eta
	^
	\|
	x 2
	\| `
	\| `
	\| . `
	\| q2 `
	5 x x 4
	\| `
	\| `
	\| .q0 q1. `
	\| `
	x---------x---------x-----> \xi
	0 3 1
	@endverbatim
	*
	*
	* @f[
	* \begin{array}{ll}
	* \xi_{0} = 0 & \eta_{0} = 0 \\
	* \xi_{1} = 1 & \eta_{1} = 0 \\
	* \xi_{2} = 0 & \eta_{2} = 1 \\
	* \xi_{3} = 1/2 & \eta_{3} = 0 \\
	* \xi_{4} = 1/2 & \eta_{4} = 1/2 \\
	* \xi_{5} = 0 & \eta_{5} = 1/2
	* \end{array}
	* @f]
	*
	* @f[
	* \begin{array}{lll}
	* N1 = -(1 - \xi - \eta) (1 - 2 (1 - \xi - \eta))
	* & \frac{\partial N1}{\partial \xi} = 1 - 4(1 - \xi - \eta)
	* & \frac{\partial N1}{\partial \eta} = 1 - 4(1 - \xi - \eta) \\
	* N2 = - \xi (1 - 2 \xi)
	* & \frac{\partial N2}{\partial \xi} = - 1 + 4 \xi
	* & \frac{\partial N2}{\partial \eta} = 0 \\
	* N3 = - \eta (1 - 2 \eta)
	* & \frac{\partial N3}{\partial \xi} = 0
	* & \frac{\partial N3}{\partial \eta} = - 1 + 4 \eta \\
	* N4 = 4 \xi (1 - \xi - \eta)
	* & \frac{\partial N4}{\partial \xi} = 4 (1 - 2 \xi - \eta)
	* & \frac{\partial N4}{\partial \eta} = - 4 \xi \\
	* N5 = 4 \xi \eta
	* & \frac{\partial N5}{\partial \xi} = 4 \eta
	* & \frac{\partial N5}{\partial \eta} = 4 \xi \\
	* N6 = 4 \eta (1 - \xi - \eta)
	* & \frac{\partial N6}{\partial \xi} = - 4 \eta
	* & \frac{\partial N6}{\partial \eta} = 4 (1 - \xi - 2 \eta)
	* \end{array}
	* @f]
	*
	* @f{eqnarray*}{
	* \xi_{q0} &=& 1/6 \qquad \eta_{q0} = 1/6 \\
	* \xi_{q1} &=& 2/3 \qquad \eta_{q1} = 1/6 \\
	* \xi_{q2} &=& 1/6 \qquad \eta_{q2} = 2/3
	* @f}
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_triangle_6, _gt_triangle_6,
	_itp_lagrange_triangle_6, _ek_regular, 2,
	_git_triangle, 2);

	/* -------------------------------------------------------------------------- */

	template <>
	template <class vector_type>
	inline void InterpolationElement<_itp_lagrange_triangle_6>::computeShapes(
	const vector_type & natural_coords, vector_type & N) {
	/// Natural coordinates
	Real c0 =
	1 - natural_coords(0) - natural_coords(1); /// @f$ c0 = 1 - \xi - \eta @f$
	Real c1 = natural_coords(0); /// @f$ c1 = \xi @f$
	Real c2 = natural_coords(1); /// @f$ c2 = \eta @f$

	N(0) = c0 * (2 * c0 - 1.);
	N(1) = c1 * (2 * c1 - 1.);
	N(2) = c2 * (2 * c2 - 1.);
	N(3) = 4 * c0 * c1;
	N(4) = 4 * c1 * c2;
	N(5) = 4 * c2 * c0;
	}
	/* -------------------------------------------------------------------------- */
	template <>
	template <class vector_type, class matrix_type>
	inline void InterpolationElement<_itp_lagrange_triangle_6>::computeDNDS(
	const vector_type & natural_coords, matrix_type & dnds) {

	/**
	* @f[
	* dnds = \left(
	* \begin{array}{cccccc}
	* \frac{\partial N1}{\partial \xi}
	* & \frac{\partial N2}{\partial \xi}
	* & \frac{\partial N3}{\partial \xi}
	* & \frac{\partial N4}{\partial \xi}
	* & \frac{\partial N5}{\partial \xi}
	* & \frac{\partial N6}{\partial \xi} \\
	*
	* \frac{\partial N1}{\partial \eta}
	* & \frac{\partial N2}{\partial \eta}
	* & \frac{\partial N3}{\partial \eta}
	* & \frac{\partial N4}{\partial \eta}
	* & \frac{\partial N5}{\partial \eta}
	* & \frac{\partial N6}{\partial \eta}
	* \end{array}
	* \right)
	* @f]
	*/

	/// Natural coordinates
	Real c0 =
	1 - natural_coords(0) - natural_coords(1); /// @f$ c0 = 1 - \xi - \eta @f$
	Real c1 = natural_coords(0); /// @f$ c1 = \xi @f$
	Real c2 = natural_coords(1); /// @f$ c2 = \eta @f$

	dnds(0, 0) = 1 - 4 * c0;
	dnds(0, 1) = 4 * c1 - 1.;
	dnds(0, 2) = 0.;
	dnds(0, 3) = 4 * (c0 - c1);
	dnds(0, 4) = 4 * c2;
	dnds(0, 5) = -4 * c2;

	dnds(1, 0) = 1 - 4 * c0;
	dnds(1, 1) = 0.;
	dnds(1, 2) = 4 * c2 - 1.;
	dnds(1, 3) = -4 * c1;
	dnds(1, 4) = 4 * c1;
	dnds(1, 5) = 4 * (c0 - c2);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	InterpolationElement<_itp_lagrange_triangle_6>::computeSpecialJacobian(
	const Matrix<Real> & J, Real & jac) {
	Vector<Real> vprod(J.cols());
	Matrix<Real> Jt(J.transpose(), true);
	vprod.crossProduct(Jt(0), Jt(1));
	jac = vprod.norm();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline Real
	GeometricalElement<_gt_triangle_6>::getInradius(const Matrix<Real> & coord) {
	UInt triangles[4][3] = {{0, 3, 5}, {3, 1, 4}, {3, 4, 5}, {5, 4, 2}};

	Real inradius = std::numeric_limits<Real>::max();
	for (UInt t = 0; t < 4; t++) {
	- auto ir = Math::triangle_inradius(coord(triangles[t][0]),
	- coord(triangles[t][1]),
	- coord(triangles[t][2]));
	+ auto ir = Math::triangle_inradius(
	+ coord(triangles[t][0]), coord(triangles[t][1]), coord(triangles[t][2]));
	inradius = std::min(ir, inradius);
	}

	return 2. * inradius;
	}

	/* -------------------------------------------------------------------------- */
	// template<> inline bool ElementClass<_triangle_6>::contains(const Vector<Real>
	// & natural_coords) {
	// return ElementClass<_triangle_3>::contains(natural_coords);
	// }
	} // namespace akantu
	diff --git a/src/fe_engine/element_type_conversion.hh b/src/fe_engine/element_type_conversion.hh
	index 8b3e817ad..1bd56c58f 100644
	--- a/src/fe_engine/element_type_conversion.hh
	+++ b/src/fe_engine/element_type_conversion.hh
	@@ -1,59 +1,58 @@
	/**
	* @file element_type_conversion.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief conversion between different types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_TYPE_CONVERSION_HH_
	#define AKANTU_ELEMENT_TYPE_CONVERSION_HH_

	namespace akantu {

	-template <class InType, class OutType>
	-OutType convertType(InType /unused/) {
	+template <class InType, class OutType> OutType convertType(InType /unused/) {
	return OutType();
	}

	template <>
	inline InterpolationType
	convertType<ElementType, InterpolationType>(ElementType type) {
	InterpolationType itp_type = _itp_not_defined;
	#define GET_ITP(type) itp_type = ElementClassProperty<type>::interpolation_type;

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_ITP);
	#undef GET_ITP
	return itp_type;
	}

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_TYPE_CONVERSION_HH_ */
	diff --git a/src/fe_engine/fe_engine.cc b/src/fe_engine/fe_engine.cc
	index cb8ed6117..060a7f68e 100644
	--- a/src/fe_engine/fe_engine.cc
	+++ b/src/fe_engine/fe_engine.cc
	@@ -1,91 +1,90 @@
	/**
	* @file fe_engine.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 20 2010
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Implementation of the FEEngine class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	FEEngine::FEEngine(Mesh & mesh, UInt element_dimension, const ID & id)
	- : mesh(mesh),
	- normals_on_integration_points("normals_on_quad_points", id) {
	+ : mesh(mesh), normals_on_integration_points("normals_on_quad_points", id) {
	AKANTU_DEBUG_IN();
	this->element_dimension = (element_dimension != _all_dimensions)
	? element_dimension
	: mesh.getSpatialDimension();

	this->mesh.registerEventHandler(*this, _ehp_fe_engine);

	init();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FEEngine::init() {}

	/* -------------------------------------------------------------------------- */
	FEEngine::~FEEngine() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	typename FEEngine::ElementTypesIteratorHelper
	FEEngine::elementTypes(UInt dim, GhostType ghost_type, ElementKind kind) const {
	return this->getIntegratorInterface().getJacobians().elementTypes(
	dim, ghost_type, kind);
	}

	/* -------------------------------------------------------------------------- */
	void FEEngine::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "FEEngine [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + element dimension : " << element_dimension
	<< std::endl;

	stream << space << " + mesh [" << std::endl;
	mesh.printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/fe_engine/fe_engine.hh b/src/fe_engine/fe_engine.hh
	index 7a1739b8c..111aa45f3 100644
	--- a/src/fe_engine/fe_engine.hh
	+++ b/src/fe_engine/fe_engine.hh
	@@ -1,385 +1,371 @@
	/**
	* @file fe_engine.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri May 14 2021
	*
	* @brief FEM class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_type_map.hh"
	#include "mesh_events.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FE_ENGINE_HH_
	#define AKANTU_FE_ENGINE_HH_

	namespace akantu {
	class Mesh;
	class Integrator;
	class ShapeFunctions;
	class DOFManager;
	class Element;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	/* -------------------------------------------------------------------------- */

	/**
	* The generic FEEngine class derived in a FEEngineTemplate class
	* containing the
	* shape functions and the integration method
	*/
	class FEEngine : public MeshEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	FEEngine(Mesh & mesh, UInt element_dimension = _all_dimensions,
	const ID & id = "fem");

	~FEEngine() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// pre-compute all the shape functions, their derivatives and the jacobians
	- virtual void
	- initShapeFunctions(GhostType ghost_type = _not_ghost) = 0;
	+ virtual void initShapeFunctions(GhostType ghost_type = _not_ghost) = 0;

	/// extract the nodal values and store them per element
	template <typename T>
	static void extractNodalToElementField(
	const Mesh & mesh, const Array<T> & nodal_f, Array<T> & elemental_f,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter);

	/// filter a field
	template <typename T>
	static void
	filterElementalData(const Mesh & mesh, const Array<T> & elem_f,
	Array<T> & filtered_f, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter);

	/* ------------------------------------------------------------------------ */
	/* Integration method bridges */
	/* ------------------------------------------------------------------------ */
	/// integrate f for all elements of type "type"
	virtual void
	integrate(const Array<Real> & f, Array<Real> & intf,
	UInt nb_degree_of_freedom, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// integrate a scalar value f on all elements of type "type"
	virtual Real
	integrate(const Array<Real> & f, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// integrate f for all integration points of type "type" but don't sum over
	/// all integration points
	virtual void integrateOnIntegrationPoints(
	const Array<Real> & f, Array<Real> & intf, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// integrate one element scalar value on all elements of type "type"
	- virtual Real integrate(const Vector<Real> & f, ElementType type,
	- UInt index,
	+ virtual Real integrate(const Vector<Real> & f, ElementType type, UInt index,
	GhostType ghost_type = _not_ghost) const = 0;

	/* ------------------------------------------------------------------------ */
	/* compatibility with old FEEngine fashion */
	/* ------------------------------------------------------------------------ */
	/// get the number of integration points
	virtual UInt
	getNbIntegrationPoints(ElementType type,
	GhostType ghost_type = _not_ghost) const = 0;

	/// get the precomputed shapes
	- const virtual Array<Real> &
	- getShapes(ElementType type, GhostType ghost_type = _not_ghost,
	- UInt id = 0) const = 0;
	+ const virtual Array<Real> & getShapes(ElementType type,
	+ GhostType ghost_type = _not_ghost,
	+ UInt id = 0) const = 0;

	/// get the derivatives of shapes
	const virtual Array<Real> &
	- getShapesDerivatives(ElementType type,
	- GhostType ghost_type = _not_ghost,
	+ getShapesDerivatives(ElementType type, GhostType ghost_type = _not_ghost,
	UInt id = 0) const = 0;

	/// get integration points
	const virtual Matrix<Real> &
	getIntegrationPoints(ElementType type,
	GhostType ghost_type = _not_ghost) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Shape method bridges */
	/* ------------------------------------------------------------------------ */
	/// Compute the gradient nablauq on the integration points of an element type
	/// from nodal values u
	virtual void gradientOnIntegrationPoints(
	- const Array<Real> & u, Array<Real> & nablauq,
	- UInt nb_degree_of_freedom, ElementType type,
	- GhostType ghost_type = _not_ghost,
	+ const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	+ ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// Interpolate a nodal field u at the integration points of an element type
	/// -> uq
	virtual void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// Interpolate a nodal field u at the integration points of many element
	/// types -> uq
	virtual void interpolateOnIntegrationPoints(
	const Array<Real> & u, ElementTypeMapArray<Real> & uq,
	const ElementTypeMapArray<UInt> * filter_elements = nullptr) const = 0;

	/// pre multiplies a tensor by the shapes derivaties
	virtual void
	- computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
	- ElementType type,
	+ computeBtD(const Array<Real> & Ds, Array<Real> & BtDs, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// left and right multiplies a tensor by the shapes derivaties
	virtual void
	computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d,
	- ElementType type,
	- GhostType ghost_type = _not_ghost,
	+ ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// left multiples a vector by the shape functions
	virtual void
	- computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
	- ElementType type,
	+ computeNtb(const Array<Real> & bs, Array<Real> & Ntbs, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// left and right multiplies a tensor by the shapes
	virtual void
	- computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs,
	- ElementType type, GhostType ghost_type = _not_ghost,
	+ computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs, ElementType type,
	+ GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	-
	/// Compute the interpolation point position in the global coordinates for
	/// many element types
	virtual void computeIntegrationPointsCoordinates(
	ElementTypeMapArray<Real> & integration_points_coordinates,
	const ElementTypeMapArray<UInt> * filter_elements = nullptr) const = 0;

	/// Compute the interpolation point position in the global coordinates for an
	/// element type
	virtual void computeIntegrationPointsCoordinates(
	Array<Real> & integration_points_coordinates, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// Build pre-computed matrices for interpolation of field form integration
	/// points at other given positions (interpolation_points)
	virtual void initElementalFieldInterpolationFromIntegrationPoints(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & integration_points_coordinates_inv_matrices,
	const ElementTypeMapArray<UInt> * element_filter) const = 0;

	/// interpolate field at given position (interpolation_points) from given
	/// values of this field at integration points (field)
	virtual void interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const = 0;

	/// Interpolate field at given position from given values of this field at
	/// integration points (field)
	/// using matrices precomputed with
	/// initElementalFieldInterplationFromIntegrationPoints
	virtual void interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> &
	interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> &
	integration_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const = 0;

	/// interpolate on a phyiscal point inside an element
	virtual void interpolate(const Vector<Real> & real_coords,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated,
	const Element & element) const = 0;

	/// compute the shape on a provided point
	- virtual void
	- computeShapes(const Vector<Real> & real_coords, UInt elem,
	- ElementType type, Vector<Real> & shapes,
	- GhostType ghost_type = _not_ghost) const = 0;
	+ virtual void computeShapes(const Vector<Real> & real_coords, UInt elem,
	+ ElementType type, Vector<Real> & shapes,
	+ GhostType ghost_type = _not_ghost) const = 0;

	/// compute the shape derivatives on a provided point
	virtual void
	computeShapeDerivatives(const Vector<Real> & real_coords, UInt element,
	- ElementType type,
	- Matrix<Real> & shape_derivatives,
	+ ElementType type, Matrix<Real> & shape_derivatives,
	GhostType ghost_type = _not_ghost) const = 0;

	/// assembles the lumped version of @f[ \int N^t rho N @f]
	virtual void assembleFieldLumped(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type = _not_ghost) const = 0;

	/// assembles the matrix @f[ \int N^t rho N @f]
	virtual void assembleFieldMatrix(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type = _not_ghost) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Other methods */
	/* ------------------------------------------------------------------------ */

	/// pre-compute normals on integration points
	- virtual void computeNormalsOnIntegrationPoints(
	- GhostType ghost_type = _not_ghost) = 0;
	+ virtual void
	+ computeNormalsOnIntegrationPoints(GhostType ghost_type = _not_ghost) = 0;

	/// pre-compute normals on integration points
	- virtual void computeNormalsOnIntegrationPoints(
	- const Array<Real> & /field/,
	- GhostType /ghost_type/ = _not_ghost) {
	+ virtual void
	+ computeNormalsOnIntegrationPoints(const Array<Real> & /field/,
	+ GhostType /ghost_type/ = _not_ghost) {
	AKANTU_TO_IMPLEMENT();
	}

	/// pre-compute normals on integration points
	virtual void computeNormalsOnIntegrationPoints(
	const Array<Real> & /field/, Array<Real> & /normal/,
	- ElementType /type/,
	- GhostType /ghost_type/ = _not_ghost) const {
	+ ElementType /type/, GhostType /ghost_type/ = _not_ghost) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	private:
	/// initialise the class
	void init();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	using ElementTypesIteratorHelper =
	ElementTypeMapArray<Real, ElementType>::ElementTypesIteratorHelper;

	ElementTypesIteratorHelper elementTypes(UInt dim = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_regular) const;

	/// get the dimension of the element handeled by this fe_engine object
	AKANTU_GET_MACRO(ElementDimension, element_dimension, UInt);

	/// get the mesh contained in the fem object
	AKANTU_GET_MACRO(Mesh, mesh, const Mesh &);
	/// get the mesh contained in the fem object
	AKANTU_GET_MACRO_NOT_CONST(Mesh, mesh, Mesh &);

	/// get the in-radius of an element
	static inline Real getElementInradius(const Matrix<Real> & coord,
	ElementType type);

	inline Real getElementInradius(const Element & element) const;

	/// get the normals on integration points
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(NormalsOnIntegrationPoints,
	normals_on_integration_points, Real);

	/// get cohesive element type for a given facet type
	- static inline ElementType
	- getCohesiveElementType(ElementType type_facet);
	+ static inline ElementType getCohesiveElementType(ElementType type_facet);

	/// get igfem element type for a given regular type
	- static inline Vector<ElementType>
	- getIGFEMElementTypes(ElementType type);
	+ static inline Vector<ElementType> getIGFEMElementTypes(ElementType type);

	/// get the interpolation element associated to an element type
	- static inline InterpolationType
	- getInterpolationType(ElementType el_type);
	+ static inline InterpolationType getInterpolationType(ElementType el_type);

	/// get the shape function class (probably useless: see getShapeFunction in
	/// fe_engine_template.hh)
	virtual const ShapeFunctions & getShapeFunctionsInterface() const = 0;
	/// get the integrator class (probably useless: see getIntegrator in
	/// fe_engine_template.hh)
	virtual const Integrator & getIntegratorInterface() const = 0;

	AKANTU_GET_MACRO(ID, id, ID);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	/// spatial dimension of the problem
	UInt element_dimension;

	/// the mesh on which all computation are made
	Mesh & mesh;

	/// normals at integration points
	ElementTypeMapArray<Real> normals_on_integration_points;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const FEEngine & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "fe_engine_inline_impl.hh"
	#include "fe_engine_template.hh"

	#endif /* AKANTU_FE_ENGINE_HH_ */
	diff --git a/src/fe_engine/fe_engine_inline_impl.hh b/src/fe_engine/fe_engine_inline_impl.hh
	index 763c4ba1e..bb3f72b2e 100644
	--- a/src/fe_engine/fe_engine_inline_impl.hh
	+++ b/src/fe_engine/fe_engine_inline_impl.hh
	@@ -1,208 +1,207 @@
	/**
	* @file fe_engine_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 20 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Implementation of the inline functions of the FEEngine Class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_type_conversion.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FE_ENGINE_INLINE_IMPL_HH_
	#define AKANTU_FE_ENGINE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline Real FEEngine::getElementInradius(const Matrix<Real> & coord,
	ElementType type) {
	Real inradius = 0;

	#define GET_INRADIUS(type) inradius = ElementClass<type>::getInradius(coord);

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_INRADIUS);
	#undef GET_INRADIUS

	return inradius;
	}

	/* -------------------------------------------------------------------------- */
	inline Real FEEngine::getElementInradius(const Element & element) const {
	auto spatial_dimension = mesh.getSpatialDimension();
	auto positions = make_view(mesh.getNodes(), spatial_dimension).begin();
	auto connectivity = mesh.getConnectivities().get(element);

	Matrix<Real> coords(spatial_dimension, connectivity.size());

	- for(auto && data : zip(connectivity, coords)) {
	+ for (auto && data : zip(connectivity, coords)) {
	std::get<1>(data) = positions[std::get<0>(data)];
	}

	return getElementInradius(coords, element.type);
	}

	-
	/* -------------------------------------------------------------------------- */
	inline InterpolationType FEEngine::getInterpolationType(ElementType type) {
	return convertType<ElementType, InterpolationType>(type);
	}

	/* -------------------------------------------------------------------------- */
	/// @todo rewrite this function in order to get the cohesive element
	/// type directly from the facet
	#if defined(AKANTU_COHESIVE_ELEMENT)
	inline ElementType FEEngine::getCohesiveElementType(ElementType type) {
	ElementType ctype;
	#define GET_COHESIVE_TYPE(type) \
	ctype = CohesiveFacetProperty<type>::cohesive_type;

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_COHESIVE_TYPE);
	#undef GET_COHESIVE_TYPE

	return ctype;
	}
	#else
	inline ElementType FEEngine::getCohesiveElementType(__attribute__((unused))
	ElementType type_facet) {
	return _not_defined;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_IGFEM)
	} // akantu
	#include "igfem_helper.hh"
	namespace akantu {

	inline Vector<ElementType> FEEngine::getIGFEMElementTypes(ElementType type) {

	#define GET_IGFEM_ELEMENT_TYPES(type) \
	return IGFEMHelper::getIGFEMElementTypes<type>();

	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(GET_IGFEM_ELEMENT_TYPES);

	#undef GET_IGFEM_ELEMENT_TYPES
	}
	#endif

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void FEEngine::extractNodalToElementField(const Mesh & mesh,
	const Array<T> & nodal_f,
	Array<T> & elemental_f,
	ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_degree_of_freedom = nodal_f.getNbComponent();
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt * conn_val = mesh.getConnectivity(type, ghost_type).storage();

	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	elemental_f.resize(nb_element);

	T * nodal_f_val = nodal_f.storage();
	T * f_val = elemental_f.storage();

	UInt * el_conn;
	for (UInt el = 0; el < nb_element; ++el) {
	if (filter_elements != empty_filter) {
	el_conn = conn_val + filter_elements(el) * nb_nodes_per_element;
	} else {
	el_conn = conn_val + el * nb_nodes_per_element;
	}

	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = *(el_conn + n);
	std::copy(nodal_f_val + node * nb_degree_of_freedom,
	nodal_f_val + (node + 1) * nb_degree_of_freedom, f_val);
	f_val += nb_degree_of_freedom;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void FEEngine::filterElementalData(const Mesh & mesh, const Array<T> & elem_f,
	Array<T> & filtered_f, ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (nb_element == 0) {
	filtered_f.resize(0);
	return;
	}

	UInt nb_degree_of_freedom = elem_f.getNbComponent();
	UInt nb_data_per_element = elem_f.size() / nb_element;

	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	filtered_f.resize(nb_element * nb_data_per_element);

	T * elem_f_val = elem_f.storage();
	T * f_val = filtered_f.storage();

	UInt el_offset;
	for (UInt el = 0; el < nb_element; ++el) {
	if (filter_elements != empty_filter) {
	el_offset = filter_elements(el);
	} else {
	el_offset = el;
	}

	std::copy(elem_f_val +
	el_offset * nb_data_per_element * nb_degree_of_freedom,
	elem_f_val +
	(el_offset + 1) * nb_data_per_element * nb_degree_of_freedom,
	f_val);
	f_val += nb_degree_of_freedom * nb_data_per_element;
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_FE_ENGINE_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/fe_engine_template.hh b/src/fe_engine/fe_engine_template.hh
	index 68c288f61..296ca2117 100644
	--- a/src/fe_engine/fe_engine_template.hh
	+++ b/src/fe_engine/fe_engine_template.hh
	@@ -1,431 +1,431 @@
	/**
	* @file fe_engine_template.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri May 14 2021
	*
	* @brief templated class that calls integration and shape objects
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "integrator.hh"
	#include "shape_functions.hh"
	/* -------------------------------------------------------------------------- */
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_FE_ENGINE_TEMPLATE_HH_
	#define AKANTU_FE_ENGINE_TEMPLATE_HH_

	namespace akantu {
	class DOFManager;
	namespace fe_engine {
	namespace details {
	template <ElementKind> struct AssembleLumpedTemplateHelper;
	template <ElementKind> struct AssembleFieldMatrixHelper;
	} // namespace details
	} // namespace fe_engine

	template <ElementKind, typename> struct AssembleFieldMatrixStructHelper;

	struct DefaultIntegrationOrderFunctor {
	template <ElementType type> static inline constexpr int getOrder() {
	return ElementClassProperty<type>::polynomial_degree;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind = _ek_regular,
	class IntegrationOrderFunctor = DefaultIntegrationOrderFunctor>
	class FEEngineTemplate : public FEEngine {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using Integ = I<kind, IntegrationOrderFunctor>;
	using Shape = S<kind>;

	FEEngineTemplate(Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	const ID & id = "fem");

	~FEEngineTemplate() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// pre-compute all the shape functions, their derivatives and the jacobians
	void initShapeFunctions(GhostType ghost_type = _not_ghost) override;
	void initShapeFunctions(const Array<Real> & nodes,
	GhostType ghost_type = _not_ghost);

	/* ------------------------------------------------------------------------ */
	/* Integration method bridges */
	/* ------------------------------------------------------------------------ */
	/// integrate f for all elements of type "type"
	void
	integrate(const Array<Real> & f, Array<Real> & intf,
	UInt nb_degree_of_freedom, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// integrate a scalar value on all elements of type "type"
	Real
	integrate(const Array<Real> & f, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// integrate one element scalar value on all elements of type "type"
	Real integrate(const Vector<Real> & f, ElementType type, UInt index,
	GhostType ghost_type = _not_ghost) const override;

	/// integrate partially around an integration point (@f$ intf_q = f_q * J_q *
	/// w_q @f$)
	void integrateOnIntegrationPoints(
	const Array<Real> & f, Array<Real> & intf, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// interpolate on a phyiscal point inside an element
	void interpolate(const Vector<Real> & real_coords,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated,
	const Element & element) const override;

	/// get the number of integration points
	UInt getNbIntegrationPoints(ElementType type,
	GhostType ghost_type = _not_ghost) const override;

	/// get shapes precomputed
	const Array<Real> & getShapes(ElementType type,
	GhostType ghost_type = _not_ghost,
	UInt id = 0) const override;

	/// get the derivatives of shapes
	const Array<Real> & getShapesDerivatives(ElementType type,
	GhostType ghost_type = _not_ghost,
	UInt id = 0) const override;

	/// get integration points
	const inline Matrix<Real> &
	getIntegrationPoints(ElementType type,
	GhostType ghost_type = _not_ghost) const override;

	/* ------------------------------------------------------------------------ */
	/* Shape method bridges */
	/* ------------------------------------------------------------------------ */

	/// compute the gradient of a nodal field on the integration points
	void gradientOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// interpolate a nodal field on the integration points
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// interpolate a nodal field on the integration points given a
	/// by_element_type
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, ElementTypeMapArray<Real> & uq,
	const ElementTypeMapArray<UInt> * filter_elements =
	nullptr) const override;

	/// pre multiplies a tensor by the shapes derivaties
	void
	computeBtD(const Array<Real> & Ds, Array<Real> & BtDs, ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// left and right multiplies a tensor by the shapes derivaties
	void computeBtDB(
	const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d,
	ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// left multiples a vector by the shape functions
	void
	computeNtb(const Array<Real> & bs, Array<Real> & Ntbs, ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// left and right multiplies a tensor by the shapes
	void computeNtbN(
	const Array<Real> & bs, Array<Real> & NtbNs, ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// compute the position of integration points given by an element_type_map
	/// from nodes position
	inline void computeIntegrationPointsCoordinates(
	ElementTypeMapArray<Real> & quadrature_points_coordinates,
	const ElementTypeMapArray<UInt> * filter_elements =
	nullptr) const override;

	/// compute the position of integration points from nodes position
	inline void computeIntegrationPointsCoordinates(
	Array<Real> & quadrature_points_coordinates, ElementType type,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const override;

	/// interpolate field at given position (interpolation_points) from given
	/// values of this field at integration points (field)
	inline void interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const override;

	/// Interpolate field at given position from given values of this field at
	/// integration points (field)
	/// using matrices precomputed with
	/// initElementalFieldInterplationFromIntegrationPoints
	inline void interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> &
	interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const override;

	/// Build pre-computed matrices for interpolation of field form integration
	/// points at other given positions (interpolation_points)
	inline void initElementalFieldInterpolationFromIntegrationPoints(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	const ElementTypeMapArray<UInt> * element_filter =
	nullptr) const override;

	/// find natural coords from real coords provided an element
	void inverseMap(const Vector<Real> & real_coords, UInt element,
	ElementType type, Vector<Real> & natural_coords,
	GhostType ghost_type = _not_ghost) const;

	/// return true if the coordinates provided are inside the element, false
	/// otherwise
	inline bool contains(const Vector<Real> & real_coords, UInt element,
	ElementType type,
	GhostType ghost_type = _not_ghost) const;

	/// compute the shape on a provided point
	inline void computeShapes(const Vector<Real> & real_coords, UInt element,
	ElementType type, Vector<Real> & shapes,
	GhostType ghost_type = _not_ghost) const override;

	/// compute the shape derivatives on a provided point
	inline void
	computeShapeDerivatives(const Vector<Real> & real_coords, UInt element,
	ElementType type, Matrix<Real> & shape_derivatives,
	GhostType ghost_type = _not_ghost) const override;

	/* ------------------------------------------------------------------------ */
	/* Other methods */
	/* ------------------------------------------------------------------------ */
	/// pre-compute normals on integration points
	void
	computeNormalsOnIntegrationPoints(GhostType ghost_type = _not_ghost) override;
	void
	computeNormalsOnIntegrationPoints(const Array<Real> & field,
	GhostType ghost_type = _not_ghost) override;
	void computeNormalsOnIntegrationPoints(
	const Array<Real> & field, Array<Real> & normal, ElementType type,
	GhostType ghost_type = _not_ghost) const override;
	template <ElementType type>
	void computeNormalsOnIntegrationPoints(const Array<Real> & field,
	Array<Real> & normal,
	GhostType ghost_type) const;

	private:
	// To avoid a weird full specialization of a method in a non specalized class
	void computeNormalsOnIntegrationPointsPoint1(const Array<Real> & /unused/,
	Array<Real> & normal,
	GhostType ghost_type) const;

	public:
	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	void assembleFieldLumped(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type) const override;

	/// assemble a field as a matrix (ex. rho to mass matrix)
	void assembleFieldMatrix(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type) const override;

	/// assemble a field as a lumped matrix (ex. rho in lumped mass)
	// template <class Functor>
	// void assembleFieldLumped(const Functor & field_funct, const ID & matrix_id,
	// const ID & dof_id, DOFManager & dof_manager,
	// ElementType type,
	// GhostType ghost_type) const;

	// /// assemble a field as a matrix (ex. rho to mass matrix)
	// template <class Functor>
	// void assembleFieldMatrix(const Functor & field_funct, const ID & matrix_id,
	// const ID & dof_id, DOFManager & dof_manager,
	// ElementType type,
	// GhostType ghost_type) const;

	// #ifdef AKANTU_STRUCTURAL_MECHANICS
	// /// assemble a field as a matrix (ex. rho to mass matrix)
	// void assembleFieldMatrix(const Array<Real> & field_1,
	// UInt nb_degree_of_freedom, SparseMatrix & M,
	// Array<Real> * n,
	// ElementTypeMapArray<Real> & rotation_mat,
	// ElementType type,
	// GhostType ghost_type = _not_ghost)
	// const;

	// /// compute shapes function in a matrix for structural elements
	// void
	// computeShapesMatrix(ElementType type, UInt nb_degree_of_freedom,
	// UInt nb_nodes_per_element, Array<Real> * n, UInt id,
	// UInt degree_to_interpolate, UInt degree_interpolated,
	// const bool sign,
	// GhostType ghost_type = _not_ghost) const
	// override;
	// #endif

	private:
	friend struct fe_engine::details::AssembleLumpedTemplateHelper<kind>;
	friend struct fe_engine::details::AssembleFieldMatrixHelper<kind>;
	friend struct AssembleFieldMatrixStructHelper<kind, void>;

	/// templated function to compute the scaling to assemble a lumped matrix
	template <ElementType type>
	void assembleFieldLumped(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const;

	/// @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j
	/// dV = \int \rho \varphi_i dV @f$
	template <ElementType type>
	void assembleLumpedRowSum(const Array<Real> & field, const ID & matrix_id,
	const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const;

	/// @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
	template <ElementType type>
	void assembleLumpedDiagonalScaling(const Array<Real> & field,
	const ID & matrix_id, const ID & dof_id,
	DOFManager & dof_manager,
	GhostType ghost_type) const;

	/// assemble a field as a matrix (ex. rho to mass matrix)
	template <ElementType type>
	void assembleFieldMatrix(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const;

	#ifdef AKANTU_STRUCTURAL_MECHANICS

	/// assemble a field as a matrix for structural elements (ex. rho to mass
	/// matrix)
	template <ElementType type>
	void assembleFieldMatrix(const Array<Real> & field_1,
	UInt nb_degree_of_freedom, SparseMatrix & M,
	Array<Real> * n,
	ElementTypeMapArray<Real> & rotation_mat,
	__attribute__((unused)) GhostType ghost_type) const;

	#endif

	/* ------------------------------------------------------------------------ */
	/* Mesh Event Handler interface */
	/* ------------------------------------------------------------------------ */
	public:
	void onElementsAdded(const Array<Element> & /new_elements/,
	const NewElementsEvent & /unused/) override;
	void onElementsRemoved(const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const RemovedElementsEvent & /unused/) override;
	void onElementsChanged(const Array<Element> & /unused/,
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the shape class (probably useless: see getShapeFunction)
	const ShapeFunctions & getShapeFunctionsInterface() const override {
	return shape_functions;
	};
	/// get the shape class
	const Shape & getShapeFunctions() const { return shape_functions; };

	/// get the integrator class (probably useless: see getIntegrator)
	const Integrator & getIntegratorInterface() const override {
	return integrator;
	};
	/// get the integrator class
	const Integ & getIntegrator() const { return integrator; };

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	Integ integrator;
	Shape shape_functions;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "fe_engine_template_tmpl.hh"
	#include "fe_engine_template_tmpl_field.hh"
	/* -------------------------------------------------------------------------- */
	/* Shape Linked specialization */
	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	#include "fe_engine_template_tmpl_struct.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	/* Shape IGFEM specialization */
	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_IGFEM)
	#include "fe_engine_template_tmpl_igfem.hh"
	#endif

	#endif /* AKANTU_FE_ENGINE_TEMPLATE_HH_ */
	diff --git a/src/fe_engine/fe_engine_template_cohesive.cc b/src/fe_engine/fe_engine_template_cohesive.cc
	index 617ff433b..0ad4f6bd3 100644
	--- a/src/fe_engine/fe_engine_template_cohesive.cc
	+++ b/src/fe_engine/fe_engine_template_cohesive.cc
	@@ -1,137 +1,135 @@
	/**
	* @file fe_engine_template_cohesive.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Oct 31 2012
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Specialization of the FEEngineTemplate for cohesive element
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine_template.hh"
	#include "integrator_gauss.hh"
	#include "shape_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* compatibility functions */
	/* -------------------------------------------------------------------------- */
	template <>
	Real FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_cohesive,
	DefaultIntegrationOrderFunctor>::
	- integrate(const Array<Real> & f, ElementType type,
	- GhostType ghost_type,
	+ integrate(const Array<Real> & f, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	#ifndef AKANTU_NDEBUG
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	UInt nb_quadrature_points = getNbIntegrationPoints(type);

	AKANTU_DEBUG_ASSERT(f.size() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID()
	<< ") has not the good size.");
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == 1,
	"The vector f("
	<< f.getID()
	<< ") has not the good number of component.");
	#endif

	Real integral = 0.;

	#define INTEGRATE(type) \
	integral = integrator.integrate<type>(f, ghost_type, filter_elements);

	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
	#undef INTEGRATE

	AKANTU_DEBUG_OUT();
	return integral;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_cohesive,
	DefaultIntegrationOrderFunctor>::
	integrate(const Array<Real> & f, Array<Real> & intf,
	- UInt nb_degree_of_freedom, ElementType type,
	- GhostType ghost_type,
	+ UInt nb_degree_of_freedom, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {

	#ifndef AKANTU_NDEBUG
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	UInt nb_quadrature_points = getNbIntegrationPoints(type);

	AKANTU_DEBUG_ASSERT(f.size() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << " size " << f.size()
	<< ") has not the good size ("
	<< nb_element << ").");
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f("
	<< f.getID()
	<< ") has not the good number of component.");
	AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
	"The vector intf("
	<< intf.getID()
	<< ") has not the good number of component.");
	AKANTU_DEBUG_ASSERT(intf.size() == nb_element,
	"The vector intf(" << intf.getID()
	<< ") has not the good size.");
	#endif

	#define INTEGRATE(type) \
	integrator.integrate<type>(f, intf, nb_degree_of_freedom, ghost_type, \
	filter_elements);

	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
	#undef INTEGRATE
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_cohesive,
	DefaultIntegrationOrderFunctor>::
	gradientOnIntegrationPoints(
	const Array<Real> & /* u /, Array<Real> & / nablauq */,
	UInt /* nb_degree_of_freedom /, ElementType / type */,
	GhostType /* ghost_type */,
	const Array<UInt> & /* filter_elements */) const {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/fe_engine/fe_engine_template_tmpl.hh b/src/fe_engine/fe_engine_template_tmpl.hh
	index a7feec5b0..5cf4758ce 100644
	--- a/src/fe_engine/fe_engine_template_tmpl.hh
	+++ b/src/fe_engine/fe_engine_template_tmpl.hh
	@@ -1,1449 +1,1449 @@
	/**
	* @file fe_engine_template_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Fri May 14 2021
	*
	* @brief Template implementation of FEEngineTemplate
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dof_manager.hh"
	#include "fe_engine_template.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::FEEngineTemplate(
	Mesh & mesh, UInt spatial_dimension, const ID & id)
	: FEEngine(mesh, spatial_dimension, id),
	integrator(mesh, spatial_dimension, id),
	shape_functions(mesh, spatial_dimension, id) {}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::~FEEngineTemplate() =
	default;

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct GradientOnIntegrationPointsHelper {
	template <class S>
	static void call(const S & /unused/, Mesh & /unused/,
	const Array<Real> & /unused/, Array<Real> & /unused/,
	const UInt /unused/, ElementType /unused/,
	GhostType /unused/, const Array<UInt> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define COMPUTE_GRADIENT(type) \
	if (element_dimension == ElementClass<type>::getSpatialDimension()) \
	shape_functions.template gradientOnIntegrationPoints<type>( \
	u, nablauq, nb_degree_of_freedom, ghost_type, filter_elements);

	#define AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER(kind) \
	template <> struct GradientOnIntegrationPointsHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, Mesh & mesh, \
	const Array<Real> & u, Array<Real> & nablauq, \
	const UInt nb_degree_of_freedom, ElementType type, \
	GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	UInt element_dimension = mesh.getSpatialDimension(type); \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_GRADIENT, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(
	AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER,
	AKANTU_FE_ENGINE_LIST_GRADIENT_ON_INTEGRATION_POINTS)

	#undef AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER
	#undef COMPUTE_GRADIENT
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	gradientOnIntegrationPoints(const Array<Real> & u, Array<Real> & nablauq,
	const UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}
	UInt nb_points =
	shape_functions.getIntegrationPoints(type, ghost_type).cols();

	#ifndef AKANTU_NDEBUG

	UInt element_dimension = mesh.getSpatialDimension(type);

	AKANTU_DEBUG_ASSERT(u.size() == mesh.getNbNodes(),
	"The vector u(" << u.getID()
	<< ") has not the good size.");
	AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom,
	"The vector u("
	<< u.getID()
	<< ") has not the good number of component.");

	AKANTU_DEBUG_ASSERT(
	nablauq.getNbComponent() == nb_degree_of_freedom * element_dimension,
	"The vector nablauq(" << nablauq.getID()
	<< ") has not the good number of component.");

	// AKANTU_DEBUG_ASSERT(nablauq.size() == nb_element * nb_points,
	// "The vector nablauq(" << nablauq.getID()
	// << ") has not the good size.");
	#endif

	nablauq.resize(nb_element * nb_points);

	fe_engine::details::GradientOnIntegrationPointsHelper<kind>::call(
	shape_functions, mesh, u, nablauq, nb_degree_of_freedom, type, ghost_type,
	filter_elements);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::initShapeFunctions(
	GhostType ghost_type) {
	initShapeFunctions(mesh.getNodes(), ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::initShapeFunctions(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	for (auto & type : mesh.elementTypes(element_dimension, ghost_type, kind)) {
	integrator.initIntegrator(nodes, type, ghost_type);
	const auto & control_points = getIntegrationPoints(type, ghost_type);
	shape_functions.initShapeFunctions(nodes, control_points, type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct IntegrateHelper {};

	#define INTEGRATE(type) \
	integrator.template integrate<type>(f, intf, nb_degree_of_freedom, \
	ghost_type, filter_elements);

	#define AKANTU_SPECIALIZE_INTEGRATE_HELPER(kind) \
	template <> struct IntegrateHelper<kind> { \
	template <class I> \
	static void call(const I & integrator, const Array<Real> & f, \
	Array<Real> & intf, UInt nb_degree_of_freedom, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_INTEGRATE_HELPER)

	#undef AKANTU_SPECIALIZE_INTEGRATE_HELPER
	#undef INTEGRATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & f, Array<Real> & intf, UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}
	#ifndef AKANTU_NDEBUG

	UInt nb_quadrature_points = getNbIntegrationPoints(type);

	AKANTU_DEBUG_ASSERT(f.size() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << " size " << f.size()
	<< ") has not the good size ("
	<< nb_element << ").");
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f("
	<< f.getID()
	<< ") has not the good number of component.");
	AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
	"The vector intf("
	<< intf.getID()
	<< ") has not the good number of component.");
	#endif

	intf.resize(nb_element);

	fe_engine::details::IntegrateHelper<kind>::call(integrator, f, intf,
	nb_degree_of_freedom, type,
	ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct IntegrateScalarHelper {};

	#define INTEGRATE(type) \
	integral = \
	integrator.template integrate<type>(f, ghost_type, filter_elements);

	#define AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER(kind) \
	template <> struct IntegrateScalarHelper<kind> { \
	template <class I> \
	static Real call(const I & integrator, const Array<Real> & f, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	Real integral = 0.; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
	return integral; \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER)

	#undef AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER
	#undef INTEGRATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	Real FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & f, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	#ifndef AKANTU_NDEBUG
	// std::stringstream sstr; sstr << ghost_type;
	// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
	// "The vector " << nablauq.getID() << " is not taged " <<
	// ghost_type);
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	UInt nb_quadrature_points = getNbIntegrationPoints(type, ghost_type);

	AKANTU_DEBUG_ASSERT(
	f.size() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << ") has not the good size. (" << f.size()
	<< "!=" << nb_quadrature_points * nb_element << ")");
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == 1,
	"The vector f("
	<< f.getID()
	<< ") has not the good number of component.");
	#endif

	Real integral = fe_engine::details::IntegrateScalarHelper<kind>::call(
	integrator, f, type, ghost_type, filter_elements);
	AKANTU_DEBUG_OUT();
	return integral;
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct IntegrateScalarOnOneElementHelper {};

	#define INTEGRATE(type) \
	res = integrator.template integrate<type>(f, index, ghost_type);

	#define AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER(kind) \
	template <> struct IntegrateScalarOnOneElementHelper<kind> { \
	template <class I> \
	static Real call(const I & integrator, const Vector<Real> & f, \
	ElementType type, UInt index, GhostType ghost_type) { \
	Real res = 0.; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
	return res; \
	} \
	};

	AKANTU_BOOST_ALL_KIND(
	AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER)

	#undef AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER
	#undef INTEGRATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	Real FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
	const Vector<Real> & f, ElementType type, UInt index,
	GhostType ghost_type) const {

	Real res = fe_engine::details::IntegrateScalarOnOneElementHelper<kind>::call(
	integrator, f, type, index, ghost_type);
	return res;
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct IntegrateOnIntegrationPointsHelper {};

	#define INTEGRATE(type) \
	integrator.template integrateOnIntegrationPoints<type>( \
	f, intf, nb_degree_of_freedom, ghost_type, filter_elements);

	#define AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER(kind) \
	template <> struct IntegrateOnIntegrationPointsHelper<kind> { \
	template <class I> \
	static void call(const I & integrator, const Array<Real> & f, \
	Array<Real> & intf, UInt nb_degree_of_freedom, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(
	AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER)

	#undef AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER
	#undef INTEGRATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	integrateOnIntegrationPoints(const Array<Real> & f, Array<Real> & intf,
	UInt nb_degree_of_freedom, ElementType type,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const {

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}
	UInt nb_quadrature_points = getNbIntegrationPoints(type);
	#ifndef AKANTU_NDEBUG
	// std::stringstream sstr; sstr << ghost_type;
	// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
	// "The vector " << nablauq.getID() << " is not taged " <<
	// ghost_type);

	AKANTU_DEBUG_ASSERT(f.size() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << " size " << f.size()
	<< ") has not the good size ("
	<< nb_element << ").");
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f("
	<< f.getID()
	<< ") has not the good number of component.");
	AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
	"The vector intf("
	<< intf.getID()
	<< ") has not the good number of component.");
	#endif

	intf.resize(nb_element * nb_quadrature_points);
	fe_engine::details::IntegrateOnIntegrationPointsHelper<kind>::call(
	integrator, f, intf, nb_degree_of_freedom, type, ghost_type,
	filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct InterpolateOnIntegrationPointsHelper {
	template <class S>
	static void call(const S & /unused/, const Array<Real> & /unused/,
	Array<Real> & /unused/, const UInt /unused/,
	ElementType /unused/, GhostType /unused/,
	const Array<UInt> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define INTERPOLATE(type) \
	shape_functions.template interpolateOnIntegrationPoints<type>( \
	u, uq, nb_degree_of_freedom, ghost_type, filter_elements);

	#define AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER(kind) \
	template <> struct InterpolateOnIntegrationPointsHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, const Array<Real> & u, \
	Array<Real> & uq, const UInt nb_degree_of_freedom, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTERPOLATE, kind); \
	} \
	};
	AKANTU_BOOST_ALL_KIND_LIST(
	AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER,
	AKANTU_FE_ENGINE_LIST_INTERPOLATE_ON_INTEGRATION_POINTS)

	#undef AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER
	#undef INTERPOLATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	interpolateOnIntegrationPoints(const Array<Real> & u, Array<Real> & uq,
	const UInt nb_degree_of_freedom,
	ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_points =
	shape_functions.getIntegrationPoints(type, ghost_type).cols();
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}
	#ifndef AKANTU_NDEBUG

	AKANTU_DEBUG_ASSERT(u.size() == mesh.getNbNodes(),
	"The vector u(" << u.getID()
	<< ") has not the good size.");
	AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom,
	"The vector u("
	<< u.getID()
	<< ") has not the good number of component.");
	AKANTU_DEBUG_ASSERT(uq.getNbComponent() == nb_degree_of_freedom,
	"The vector uq("
	<< uq.getID()
	<< ") has not the good number of component.");
	#endif

	uq.resize(nb_element * nb_points);

	fe_engine::details::InterpolateOnIntegrationPointsHelper<kind>::call(
	shape_functions, u, uq, nb_degree_of_freedom, type, ghost_type,
	filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	interpolateOnIntegrationPoints(
	const Array<Real> & u, ElementTypeMapArray<Real> & uq,
	const ElementTypeMapArray<UInt> * filter_elements) const {
	AKANTU_DEBUG_IN();

	const Array<UInt> * filter = nullptr;

	for (auto ghost_type : ghost_types) {
	for (auto && type : uq.elementTypes(_all_dimensions, ghost_type, kind)) {
	UInt nb_quad_per_element = getNbIntegrationPoints(type, ghost_type);

	UInt nb_element = 0;

	if (filter_elements != nullptr) {
	filter = &((*filter_elements)(type, ghost_type));
	nb_element = filter->size();
	} else {
	filter = &empty_filter;
	nb_element = mesh.getNbElement(type, ghost_type);
	}

	UInt nb_tot_quad = nb_quad_per_element * nb_element;

	Array<Real> & quad = uq(type, ghost_type);
	quad.resize(nb_tot_quad);

	interpolateOnIntegrationPoints(u, quad, quad.getNbComponent(), type,
	ghost_type, *filter);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeBtDHelper {};

	#define COMPUTE_BTD(type) \
	shape_functions.template computeBtD<type>(Ds, BtDs, ghost_type, \
	filter_elements);

	#define AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER(kind) \
	template <> struct ComputeBtDHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, const Array<Real> & Ds, \
	Array<Real> & BtDs, ElementType type, \
	GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_BTD, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER)

	#undef AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER
	#undef COMPUTE_BTD
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeBtD(
	const Array<Real> & Ds, Array<Real> & BtDs, ElementType type,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	fe_engine::details::ComputeBtDHelper<kind>::call(
	shape_functions, Ds, BtDs, type, ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeBtDBHelper {};

	#define COMPUTE_BTDB(type) \
	shape_functions.template computeBtDB<type>(Ds, BtDBs, order_d, ghost_type, \
	filter_elements);

	#define AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER(kind) \
	template <> struct ComputeBtDBHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, const Array<Real> & Ds, \
	Array<Real> & BtDBs, UInt order_d, ElementType type, \
	GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_BTDB, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER)

	#undef AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER
	#undef COMPUTE_BTDB
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeBtDB(
	const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d, ElementType type,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	fe_engine::details::ComputeBtDBHelper<kind>::call(
	shape_functions, Ds, BtDBs, order_d, type, ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeNtbNHelper {};

	#define COMPUTE_NtbN(type) \
	shape_functions.template computeNtbN<type>(bs, NtbNs, ghost_type, \
	filter_elements);

	#define AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER(kind) \
	template <> struct ComputeNtbNHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, const Array<Real> & bs, \
	Array<Real> & NtbNs, ElementType type, \
	GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_NtbN, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER)

	#undef AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER
	#undef COMPUTE_NtbN
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeNtbN(
	const Array<Real> & bs, Array<Real> & NtbNs, ElementType type,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	fe_engine::details::ComputeNtbNHelper<kind>::call(
	shape_functions, bs, NtbNs, type, ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeNtbHelper {};

	#define COMPUTE_Ntb(type) \
	shape_functions.template computeNtb<type>(bs, Ntbs, ghost_type, \
	filter_elements);

	#define AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER(kind) \
	template <> struct ComputeNtbHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, const Array<Real> & bs, \
	Array<Real> & Ntbs, ElementType type, \
	GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_Ntb, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER)

	#undef AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER
	#undef COMPUTE_Ntb
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeNtb(
	const Array<Real> & bs, Array<Real> & Ntbs, ElementType type,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	fe_engine::details::ComputeNtbHelper<kind>::call(
	shape_functions, bs, Ntbs, type, ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeIntegrationPointsCoordinates(
	ElementTypeMapArray<Real> & quadrature_points_coordinates,
	const ElementTypeMapArray<UInt> * filter_elements) const {

	const Array<Real> & nodes_coordinates = mesh.getNodes();

	interpolateOnIntegrationPoints(
	nodes_coordinates, quadrature_points_coordinates, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeIntegrationPointsCoordinates(
	Array<Real> & quadrature_points_coordinates, ElementType type,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {

	const Array<Real> & nodes_coordinates = mesh.getNodes();

	UInt spatial_dimension = mesh.getSpatialDimension();

	interpolateOnIntegrationPoints(
	nodes_coordinates, quadrature_points_coordinates, spatial_dimension, type,
	ghost_type, filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	initElementalFieldInterpolationFromIntegrationPoints(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	const ElementTypeMapArray<UInt> * element_filter) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = this->mesh.getSpatialDimension();

	ElementTypeMapArray<Real> quadrature_points_coordinates(
	"quadrature_points_coordinates_for_interpolation", getID());

	quadrature_points_coordinates.initialize(*this,
	_nb_component = spatial_dimension);

	computeIntegrationPointsCoordinates(quadrature_points_coordinates,
	element_filter);
	shape_functions.initElementalFieldInterpolationFromIntegrationPoints(
	interpolation_points_coordinates,
	interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, quadrature_points_coordinates,
	element_filter);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const {

	ElementTypeMapArray<Real> interpolation_points_coordinates_matrices(
	"interpolation_points_coordinates_matrices", id);
	ElementTypeMapArray<Real> quad_points_coordinates_inv_matrices(
	"quad_points_coordinates_inv_matrices", id);

	initElementalFieldInterpolationFromIntegrationPoints(
	interpolation_points_coordinates,
	interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, element_filter);

	interpolateElementalFieldFromIntegrationPoints(
	field, interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, result, ghost_type, element_filter);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> &
	interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const {

	shape_functions.interpolateElementalFieldFromIntegrationPoints(
	field, interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, result, ghost_type, element_filter);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct InterpolateHelper {
	template <class S>
	static void call(const S & /unused/, const Vector<Real> & /unused/,
	UInt /unused/, const Matrix<Real> & /unused/,
	Vector<Real> & /unused/, ElementType /unused/,
	GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define INTERPOLATE(type) \
	shape_functions.template interpolate<type>( \
	real_coords, element, nodal_values, interpolated, ghost_type);

	#define AKANTU_SPECIALIZE_INTERPOLATE_HELPER(kind) \
	template <> struct InterpolateHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, \
	const Vector<Real> & real_coords, UInt element, \
	const Matrix<Real> & nodal_values, \
	Vector<Real> & interpolated, ElementType type, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTERPOLATE, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_INTERPOLATE_HELPER,
	AKANTU_FE_ENGINE_LIST_INTERPOLATE)

	#undef AKANTU_SPECIALIZE_INTERPOLATE_HELPER
	#undef INTERPOLATE
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::interpolate(
	const Vector<Real> & real_coords, const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated, const Element & element) const {

	AKANTU_DEBUG_IN();

	fe_engine::details::InterpolateHelper<kind>::call(
	shape_functions, real_coords, element.element, nodal_values, interpolated,
	element.type, element.ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeNormalsOnIntegrationPoints(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	computeNormalsOnIntegrationPoints(mesh.getNodes(), ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeNormalsOnIntegrationPoints(const Array<Real> & field,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// Real * coord = mesh.getNodes().storage();
	UInt spatial_dimension = mesh.getSpatialDimension();

	// allocate the normal arrays
	normals_on_integration_points.initialize(
	*this, _nb_component = spatial_dimension,
	_spatial_dimension = element_dimension, _ghost_type = ghost_type,
	_element_kind = kind);

	// loop over the type to build the normals
	for (auto & type : mesh.elementTypes(element_dimension, ghost_type, kind)) {
	auto & normals_on_quad = normals_on_integration_points(type, ghost_type);
	computeNormalsOnIntegrationPoints(field, normals_on_quad, type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeNormalsOnIntegrationPoints {
	template <template <ElementKind, class> class I,
	template <ElementKind> class S, ElementKind k, class IOF>
	static void call(const FEEngineTemplate<I, S, k, IOF> & /unused/,
	const Array<Real> & /unused/, Array<Real> & /unused/,
	ElementType /unused/, GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define COMPUTE_NORMALS_ON_INTEGRATION_POINTS(type) \
	fem.template computeNormalsOnIntegrationPoints<type>(field, normal, \
	ghost_type);

	#define AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS(kind) \
	template <> struct ComputeNormalsOnIntegrationPoints<kind> { \
	template <template <ElementKind, class> class I, \
	template <ElementKind> class S, ElementKind k, class IOF> \
	static void call(const FEEngineTemplate<I, S, k, IOF> & fem, \
	const Array<Real> & field, Array<Real> & normal, \
	ElementType type, GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_NORMALS_ON_INTEGRATION_POINTS, \
	kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(
	AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS,
	AKANTU_FE_ENGINE_LIST_COMPUTE_NORMALS_ON_INTEGRATION_POINTS)

	#undef AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS
	#undef COMPUTE_NORMALS_ON_INTEGRATION_POINTS
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeNormalsOnIntegrationPoints(const Array<Real> & field,
	Array<Real> & normal, ElementType type,
	GhostType ghost_type) const {
	fe_engine::details::ComputeNormalsOnIntegrationPoints<kind>::call(
	*this, field, normal, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeNormalsOnIntegrationPoints(const Array<Real> & field,
	Array<Real> & normal,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	if (type == _point_1) {
	computeNormalsOnIntegrationPointsPoint1(field, normal, ghost_type);
	return;
	}

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_points = getNbIntegrationPoints(type, ghost_type);

	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();
	normal.resize(nb_element * nb_points);
	Array<Real>::matrix_iterator normals_on_quad =
	normal.begin_reinterpret(spatial_dimension, nb_points, nb_element);
	Array<Real> f_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, field, f_el, type, ghost_type);

	const Matrix<Real> & quads =
	integrator.template getIntegrationPoints<type>(ghost_type);

	Array<Real>::matrix_iterator f_it =
	f_el.begin(spatial_dimension, nb_nodes_per_element);

	for (UInt elem = 0; elem < nb_element; ++elem) {
	ElementClass<type>::computeNormalsOnNaturalCoordinates(quads, *f_it,
	*normals_on_quad);
	++normals_on_quad;
	++f_it;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	template <ElementKind kind> struct InverseMapHelper {
	template <class S>
	static void call(const S & /shape_functions/,
	const Vector<Real> & /real_coords/, UInt /element/,
	ElementType /type/, Vector<Real> & /natural_coords/,
	GhostType /ghost_type/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define INVERSE_MAP(type) \
	shape_functions.template inverseMap<type>(real_coords, element, \
	natural_coords, ghost_type);

	#define AKANTU_SPECIALIZE_INVERSE_MAP_HELPER(kind) \
	template <> struct InverseMapHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, \
	const Vector<Real> & real_coords, UInt element, \
	ElementType type, Vector<Real> & natural_coords, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INVERSE_MAP, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_INVERSE_MAP_HELPER,
	AKANTU_FE_ENGINE_LIST_INVERSE_MAP)

	#undef AKANTU_SPECIALIZE_INVERSE_MAP_HELPER
	#undef INVERSE_MAP

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::inverseMap(
	const Vector<Real> & real_coords, UInt element, ElementType type,
	Vector<Real> & natural_coords, GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	InverseMapHelper<kind>::call(shape_functions, real_coords, element, type,
	natural_coords, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ContainsHelper {
	template <class S>
	static void call(const S & /unused/, const Vector<Real> & /unused/,
	UInt /unused/, ElementType /unused/,
	GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define CONTAINS(type) \
	contain = shape_functions.template contains<type>(real_coords, element, \
	ghost_type);

	#define AKANTU_SPECIALIZE_CONTAINS_HELPER(kind) \
	template <> struct ContainsHelper<kind> { \
	template <template <ElementKind> class S, ElementKind k> \
	static bool call(const S<k> & shape_functions, \
	const Vector<Real> & real_coords, UInt element, \
	ElementType type, GhostType ghost_type) { \
	bool contain = false; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(CONTAINS, kind); \
	return contain; \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_CONTAINS_HELPER,
	AKANTU_FE_ENGINE_LIST_CONTAINS)

	#undef AKANTU_SPECIALIZE_CONTAINS_HELPER
	#undef CONTAINS
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline bool FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::contains(
	const Vector<Real> & real_coords, UInt element, ElementType type,
	GhostType ghost_type) const {
	return fe_engine::details::ContainsHelper<kind>::call(
	shape_functions, real_coords, element, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeShapesHelper {
	template <class S>
	static void call(const S & /unused/, const Vector<Real> & /unused/,
	UInt /unused/, const ElementType /unused/,
	Vector<Real> & /unused/, GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define COMPUTE_SHAPES(type) \
	shape_functions.template computeShapes<type>(real_coords, element, shapes, \
	ghost_type);

	#define AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER(kind) \
	template <> struct ComputeShapesHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, \
	const Vector<Real> & real_coords, UInt element, \
	const ElementType type, Vector<Real> & shapes, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_SHAPES, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER,
	AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES)

	#undef AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER
	#undef COMPUTE_SHAPES
	} // namespace details
	} // namespace fe_engine
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapes(
	const Vector<Real> & real_coords, UInt element, ElementType type,
	Vector<Real> & shapes, GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	fe_engine::details::ComputeShapesHelper<kind>::call(
	shape_functions, real_coords, element, type, shapes, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ComputeShapeDerivativesHelper {
	template <class S>
	static void call(__attribute__((unused)) const S & shape_functions,
	__attribute__((unused)) const Vector<Real> & real_coords,
	__attribute__((unused)) UInt element,
	__attribute__((unused)) const ElementType type,
	__attribute__((unused)) Matrix<Real> & shape_derivatives,
	__attribute__((unused)) GhostType ghost_type) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define COMPUTE_SHAPE_DERIVATIVES(type) \
	Matrix<Real> coords_mat(real_coords.storage(), shape_derivatives.rows(), 1); \
	Tensor3<Real> shapesd_tensor(shape_derivatives.storage(), \
	shape_derivatives.rows(), \
	shape_derivatives.cols(), 1); \
	shape_functions.template computeShapeDerivatives<type>( \
	coords_mat, element, shapesd_tensor, ghost_type);

	#define AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER(kind) \
	template <> struct ComputeShapeDerivativesHelper<kind> { \
	template <class S> \
	static void call(const S & shape_functions, \
	const Vector<Real> & real_coords, UInt element, \
	const ElementType type, Matrix<Real> & shape_derivatives, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_SHAPE_DERIVATIVES, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(
	AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER,
	AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES_DERIVATIVES)

	#undef AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER
	#undef COMPUTE_SHAPE_DERIVATIVES
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapeDerivatives(
	const Vector<Real> & real_coords, UInt element, ElementType type,
	Matrix<Real> & shape_derivatives, GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	fe_engine::details::ComputeShapeDerivativesHelper<kind>::call(
	shape_functions, real_coords, element, type, shape_derivatives,
	ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct GetNbIntegrationPointsHelper {};

	#define GET_NB_INTEGRATION_POINTS(type) \
	nb_quad_points = integrator.template getNbIntegrationPoints<type>(ghost_type);

	#define AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER(kind) \
	template <> struct GetNbIntegrationPointsHelper<kind> { \
	template <template <ElementKind, class> class I, ElementKind k, class IOF> \
	static UInt call(const I<k, IOF> & integrator, const ElementType type, \
	GhostType ghost_type) { \
	UInt nb_quad_points = 0; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_NB_INTEGRATION_POINTS, kind); \
	return nb_quad_points; \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER)

	#undef AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER
	#undef GET_NB_INTEGRATION
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline UInt
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
	ElementType type, GhostType ghost_type) const {
	return fe_engine::details::GetNbIntegrationPointsHelper<kind>::call(
	integrator, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct GetShapesHelper {};

	#define GET_SHAPES(type) ret = &(shape_functions.getShapes(type, ghost_type));

	#define AKANTU_SPECIALIZE_GET_SHAPES_HELPER(kind) \
	template <> struct GetShapesHelper<kind> { \
	template <class S> \
	static const Array<Real> & call(const S & shape_functions, \
	const ElementType type, \
	GhostType ghost_type) { \
	const Array<Real> * ret = NULL; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_SHAPES, kind); \
	return *ret; \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_SHAPES_HELPER)

	#undef AKANTU_SPECIALIZE_GET_SHAPES_HELPER
	#undef GET_SHAPES
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Array<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapes(
	ElementType type, GhostType ghost_type,
	__attribute__((unused)) UInt id) const {
	return fe_engine::details::GetShapesHelper<kind>::call(shape_functions, type,
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct GetShapesDerivativesHelper {
	template <template <ElementKind> class S, ElementKind k>
	static const Array<Real> & call(const S<k> & /unused/,
	ElementType /unused/,
	GhostType /unused/, UInt /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define GET_SHAPES_DERIVATIVES(type) \
	ret = &(shape_functions.getShapesDerivatives(type, ghost_type));

	#define AKANTU_SPECIALIZE_GET_SHAPES_DERIVATIVES_HELPER(kind) \
	template <> struct GetShapesDerivativesHelper<kind> { \
	template <template <ElementKind> class S, ElementKind k> \
	static const Array<Real> & \
	call(const S<k> & shape_functions, const ElementType type, \
	GhostType ghost_type, __attribute__((unused)) UInt id) { \
	const Array<Real> * ret = NULL; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_SHAPES_DERIVATIVES, kind); \
	return *ret; \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_GET_SHAPES_DERIVATIVES_HELPER,
	AKANTU_FE_ENGINE_LIST_GET_SHAPES_DERIVATIVES)

	#undef AKANTU_SPECIALIZE_GET_SHAPE_DERIVATIVES_HELPER
	#undef GET_SHAPES_DERIVATIVES
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Array<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapesDerivatives(
	ElementType type, GhostType ghost_type,
	__attribute__((unused)) UInt id) const {
	return fe_engine::details::GetShapesDerivativesHelper<kind>::call(
	shape_functions, type, ghost_type, id);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct GetIntegrationPointsHelper {};

	#define GET_INTEGRATION_POINTS(type) \
	ret = &(integrator.template getIntegrationPoints<type>(ghost_type));

	#define AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER(kind) \
	template <> struct GetIntegrationPointsHelper<kind> { \
	template <template <ElementKind, class> class I, ElementKind k, class IOF> \
	static const Matrix<Real> & call(const I<k, IOF> & integrator, \
	const ElementType type, \
	GhostType ghost_type) { \
	const Matrix<Real> * ret = NULL; \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_INTEGRATION_POINTS, kind); \
	return *ret; \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER)

	#undef AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER
	#undef GET_INTEGRATION_POINTS
	} // namespace details
	} // namespace fe_engine

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Matrix<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getIntegrationPoints(
	ElementType type, GhostType ghost_type) const {
	return fe_engine::details::GetIntegrationPointsHelper<kind>::call(
	integrator, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::printself(
	std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "FEEngineTemplate [" << std::endl;
	stream << space << " + parent [" << std::endl;
	FEEngine::printself(stream, indent + 3);
	stream << space << " ]" << std::endl;
	stream << space << " + shape functions [" << std::endl;
	shape_functions.printself(stream, indent + 3);
	stream << space << " ]" << std::endl;
	stream << space << " + integrator [" << std::endl;
	integrator.printself(stream, indent + 3);
	stream << space << " ]" << std::endl;
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsAdded(
	const Array<Element> & new_elements, const NewElementsEvent & /unused/) {
	integrator.onElementsAdded(new_elements);
	shape_functions.onElementsAdded(new_elements);
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsRemoved(
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const RemovedElementsEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsChanged(
	const Array<Element> & /unused/, const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	computeNormalsOnIntegrationPointsPoint1(const Array<Real> & /unused/,
	Array<Real> & normal,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == 1,
	"Mesh dimension must be 1 to compute normals on points!");
	const auto type = _point_1;
	auto spatial_dimension = mesh.getSpatialDimension();
	// UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_points = getNbIntegrationPoints(type, ghost_type);
	const auto & connectivity = mesh.getConnectivity(type, ghost_type);
	auto nb_element = connectivity.size();

	normal.resize(nb_element * nb_points);
	auto normals_on_quad =
	normal.begin_reinterpret(spatial_dimension, nb_points, nb_element);
	const auto & segments = mesh.getElementToSubelement(type, ghost_type);
	const auto & coords = mesh.getNodes();

	const Mesh * mesh_segment;
	if (mesh.isMeshFacets()) {
	mesh_segment = &(mesh.getMeshParent());
	} else {
	mesh_segment = &mesh;
	}

	for (UInt elem = 0; elem < nb_element; ++elem) {
	UInt nb_segment = segments(elem).size();
	AKANTU_DEBUG_ASSERT(
	nb_segment > 0,
	"Impossible to compute a normal on a point connected to 0 segments");

	Real normal_value = 1;
	if (nb_segment == 1) {
	auto point = connectivity(elem);
	const auto segment = segments(elem)[0];
	const auto & segment_connectivity =
	mesh_segment->getConnectivity(segment.type, segment.ghost_type);
	Vector<UInt> segment_points = segment_connectivity.begin(
	Mesh::getNbNodesPerElement(segment.type))[segment.element];
	Real difference;
	if (segment_points(0) == point) {
	difference = coords(elem) - coords(segment_points(1));
	} else {
	difference = coords(elem) - coords(segment_points(0));
	}

	normal_value = difference / std::abs(difference);
	}

	for (UInt n(0); n < nb_points; ++n) {
	(*normals_on_quad)(0, n) = normal_value;
	}
	++normals_on_quad;
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/fe_engine/fe_engine_template_tmpl_field.hh b/src/fe_engine/fe_engine_template_tmpl_field.hh
	index 83abf6100..e30fbc7c2 100644
	--- a/src/fe_engine/fe_engine_template_tmpl_field.hh
	+++ b/src/fe_engine/fe_engine_template_tmpl_field.hh
	@@ -1,507 +1,507 @@
	/**
	* @file fe_engine_template_tmpl_field.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 09 2017
	* @date last modification: Sat Mar 13 2021
	*
	* @brief implementation of the assemble field s functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine_template.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_
	#define AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Matrix lumping functions */
	/* -------------------------------------------------------------------------- */
	namespace fe_engine {
	namespace details {
	namespace {
	template <class Functor>
	void fillField(const Functor & field_funct, Array<Real> & field,
	UInt nb_element, UInt nb_integration_points,
	ElementType type, GhostType ghost_type) {
	UInt nb_degree_of_freedom = field.getNbComponent();
	field.resize(nb_integration_points * nb_element);

	auto field_it = field.begin_reinterpret(
	nb_degree_of_freedom, nb_integration_points, nb_element);

	Element el{type, 0, ghost_type};
	for (; el.element < nb_element; ++el.element, ++field_it) {
	field_funct(*field_it, el);
	}
	}
	} // namespace
	} // namespace details
	} // namespace fe_engine

	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct AssembleLumpedTemplateHelper {
	template <template <ElementKind, class> class I,
	template <ElementKind> class S, ElementKind k, class IOF>
	static void call(const FEEngineTemplate<I, S, k, IOF> & /unused/,
	const std::function<void(Matrix<Real> &,
	const Element &)> & /unused/,
	const ID & /unused/, const ID & /unused/,
	DOFManager & /unused/, ElementType /unused/,
	GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define ASSEMBLE_LUMPED(type) \
	fem.template assembleFieldLumped<type>(field_funct, lumped, dof_id, \
	dof_manager, ghost_type)

	#define AKANTU_SPECIALIZE_ASSEMBLE_HELPER(kind) \
	template <> struct AssembleLumpedTemplateHelper<kind> { \
	template <template <ElementKind, class> class I, \
	template <ElementKind> class S, ElementKind k, class IOF> \
	static void \
	call(const FEEngineTemplate<I, S, k, IOF> & fem, \
	const std::function<void(Matrix<Real> &, const Element &)> & \
	field_funct, \
	const ID & lumped, const ID & dof_id, DOFManager & dof_manager, \
	ElementType type, GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ASSEMBLE_LUMPED, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_ASSEMBLE_HELPER,
	AKANTU_FE_ENGINE_LIST_ASSEMBLE_FIELDS)

	#undef AKANTU_SPECIALIZE_ASSEMBLE_HELPER
	#undef AKANTU_SPECIALIZE_ASSEMBLE_HELPER_LIST_KIND
	#undef ASSEMBLE_LUMPED
	} // namespace details
	} // namespace fe_engine

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IOF>
	void FEEngineTemplate<I, S, kind, IOF>::assembleFieldLumped(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	fe_engine::details::AssembleLumpedTemplateHelper<kind>::call(
	*this, field_funct, matrix_id, dof_id, dof_manager, type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldLumped(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt nb_degree_of_freedom = dof_manager.getDOFs(dof_id).getNbComponent();
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt nb_integration_points = this->getNbIntegrationPoints(type);

	Array<Real> field(0, nb_degree_of_freedom);
	fe_engine::details::fillField(field_funct, field, nb_element,
	nb_integration_points, type, ghost_type);

	switch (type) {
	case _triangle_6:
	case _quadrangle_8:
	case _tetrahedron_10:
	case _hexahedron_20:
	case _pentahedron_15:
	this->template assembleLumpedDiagonalScaling<type>(field, matrix_id, dof_id,
	dof_manager, ghost_type);
	break;
	default:
	this->template assembleLumpedRowSum<type>(field, matrix_id, dof_id,
	dof_manager, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV =
	* \int \rho \varphi_i dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	assembleLumpedRowSum(const Array<Real> & field, const ID & matrix_id,
	const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt shapes_size = ElementClass<type>::getShapeSize();
	UInt nb_degree_of_freedom = field.getNbComponent();

	auto * field_times_shapes =
	new Array<Real>(0, shapes_size * nb_degree_of_freedom);

	shape_functions.template computeNtb<type>(field, *field_times_shapes,
	ghost_type);

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	auto * int_field_times_shapes = new Array<Real>(
	nb_element, shapes_size * nb_degree_of_freedom, "inte_rho_x_shapes");

	integrator.template integrate<type>(
	field_times_shapes, int_field_times_shapes,
	nb_degree_of_freedom * shapes_size, ghost_type, empty_filter);

	delete field_times_shapes;

	dof_manager.assembleElementalArrayToLumpedMatrix(
	dof_id, *int_field_times_shapes, matrix_id, type, ghost_type);

	delete int_field_times_shapes;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	assembleLumpedDiagonalScaling(const Array<Real> & field,
	const ID & matrix_id, const ID & dof_id,
	DOFManager & dof_manager,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	ElementType type_p1 = ElementClass<type>::getP1ElementType();
	UInt nb_nodes_per_element_p1 = Mesh::getNbNodesPerElement(type_p1);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_degree_of_freedom = field.getNbComponent();
	UInt nb_element = mesh.getNbElement(type, ghost_type);

	Vector<Real> nodal_factor(nb_nodes_per_element);

	#define ASSIGN_WEIGHT_TO_NODES(corner, mid) \
	{ \
	for (UInt n = 0; n < nb_nodes_per_element_p1; n++) \
	nodal_factor(n) = corner; \
	for (UInt n = nb_nodes_per_element_p1; n < nb_nodes_per_element; n++) \
	nodal_factor(n) = mid; \
	}

	if (type == _triangle_6)
	ASSIGN_WEIGHT_TO_NODES(1. / 12., 1. / 4.);
	if (type == _tetrahedron_10)
	ASSIGN_WEIGHT_TO_NODES(1. / 32., 7. / 48.);
	if (type == _quadrangle_8)
	ASSIGN_WEIGHT_TO_NODES(
	3. / 76.,
	16. / 76.); /** coeff. derived by scaling
	* the diagonal terms of the corresponding
	* consistent mass computed with 3x3 gauss points;
	* coeff. are (1./36., 8./36.) for 2x2 gauss points */
	if (type == _hexahedron_20)
	ASSIGN_WEIGHT_TO_NODES(
	7. / 248., 16. / 248.); /** coeff. derived by scaling
	* the diagonal terms of the corresponding
	* consistent mass computed with 3x3x3 gauss
	* points; coeff. are (1./40.,
	* 1./15.) for 2x2x2 gauss points */
	if (type == _pentahedron_15) {
	// coefficients derived by scaling the diagonal terms of the corresponding
	// consistent mass computed with 8 gauss points;
	for (UInt n = 0; n < nb_nodes_per_element_p1; n++) {
	nodal_factor(n) = 51. / 2358.;
	}

	Real mid_triangle = 192. / 2358.;
	Real mid_quadrangle = 300. / 2358.;

	nodal_factor(6) = mid_triangle;
	nodal_factor(7) = mid_triangle;
	nodal_factor(8) = mid_triangle;
	nodal_factor(9) = mid_quadrangle;
	nodal_factor(10) = mid_quadrangle;
	nodal_factor(11) = mid_quadrangle;
	nodal_factor(12) = mid_triangle;
	nodal_factor(13) = mid_triangle;
	nodal_factor(14) = mid_triangle;
	}

	if (nb_element == 0) {
	AKANTU_DEBUG_OUT();
	return;
	}

	#undef ASSIGN_WEIGHT_TO_NODES
	/// compute @f$ \int \rho dV = \rho V @f$ for each element
	auto int_field = std::make_unique<Array<Real>>(
	field.size(), nb_degree_of_freedom, "inte_rho_x");
	integrator.template integrate<type>(field, *int_field, nb_degree_of_freedom,
	ghost_type, empty_filter);

	/// distribute the mass of the element to the nodes
	auto lumped_per_node = std::make_unique<Array<Real>>(
	nb_element, nb_degree_of_freedom * nb_nodes_per_element, "mass_per_node");
	auto int_field_it = int_field->begin(nb_degree_of_freedom);
	auto lumped_per_node_it =
	lumped_per_node->begin(nb_degree_of_freedom, nb_nodes_per_element);

	for (UInt e = 0; e < nb_element; ++e) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	Vector<Real> l = (*lumped_per_node_it)(n);
	l = *int_field_it;
	l *= nodal_factor(n);
	}
	++int_field_it;
	++lumped_per_node_it;
	}

	dof_manager.assembleElementalArrayToLumpedMatrix(dof_id, *lumped_per_node,
	matrix_id, type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct AssembleFieldMatrixHelper {
	template <template <ElementKind, class> class I,
	template <ElementKind> class S, ElementKind k, class IOF>
	static void call(const FEEngineTemplate<I, S, k, IOF> & /unused/,
	const std::function<void(Matrix<Real> &,
	const Element &)> & /unused/,
	const ID & /unused/, const ID & /unused/,
	DOFManager & /unused/, ElementType /unused/,
	GhostType /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#define ASSEMBLE_MATRIX(type) \
	fem.template assembleFieldMatrix<type>(field_funct, matrix_id, dof_id, \
	dof_manager, ghost_type)

	#define AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER(kind) \
	template <> struct AssembleFieldMatrixHelper<kind> { \
	template <template <ElementKind, class> class I, \
	template <ElementKind> class S, ElementKind k, class IOF> \
	static void \
	call(const FEEngineTemplate<I, S, k, IOF> & fem, \
	const std::function<void(Matrix<Real> &, const Element &)> & \
	field_funct, \
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager, \
	ElementType type, GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ASSEMBLE_MATRIX, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER,
	AKANTU_FE_ENGINE_LIST_ASSEMBLE_FIELDS)

	#undef AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER
	#undef ASSEMBLE_MATRIX
	} // namespace details
	} // namespace fe_engine

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IOF>
	void FEEngineTemplate<I, S, kind, IOF>::assembleFieldMatrix(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	ElementType type, GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	fe_engine::details::AssembleFieldMatrixHelper<kind>::template call(
	*this, field_funct, matrix_id, dof_id, dof_manager, type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	namespace fe_engine {
	namespace details {
	template <ElementKind kind> struct ShapesForMassHelper {
	template <ElementType type, class ShapeFunctions>
	static auto getShapes(ShapeFunctions & shape_functions,
	const Matrix<Real> & integration_points,
	const Array<Real> & nodes,
	UInt & nb_degree_of_freedom, UInt nb_element,
	GhostType ghost_type) {

	UInt shapes_size = ElementClass<type>::getShapeSize();
	Array<Real> shapes(0, shapes_size);

	shape_functions.template computeShapesOnIntegrationPoints<type>(
	nodes, integration_points, shapes, ghost_type);

	UInt nb_integration_points = integration_points.cols();
	UInt vect_size = nb_integration_points * nb_element;
	UInt lmat_size = nb_degree_of_freedom * shapes_size;

	// Extending the shape functions
	/// \todo move this in the shape functions as Voigt format shapes to
	/// have the code in common with the structural elements
	auto shapes_voigt = std::make_unique<Array<Real>>(
	vect_size, lmat_size * nb_degree_of_freedom, 0.);
	auto mshapes_it = shapes_voigt->begin(nb_degree_of_freedom, lmat_size);
	auto shapes_it = shapes.begin(shapes_size);

	for (UInt q = 0; q < vect_size; ++q, ++mshapes_it, ++shapes_it) {
	for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
	for (UInt s = 0; s < shapes_size; ++s) {
	(mshapes_it)(d, s nb_degree_of_freedom + d) = (*shapes_it)(s);
	}
	}
	}

	return shapes_voigt;
	}
	};

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	template <> struct ShapesForMassHelper<_ek_structural> {
	template <ElementType type, class ShapeFunctions>
	static auto getShapes(ShapeFunctions & shape_functions,
	const Matrix<Real> & integration_points,
	const Array<Real> & nodes,
	UInt & nb_degree_of_freedom, UInt /nb_element/,
	GhostType ghost_type) {

	auto nb_unknown = ElementClass<type>::getNbStressComponents();
	auto nb_degree_of_freedom_ = ElementClass<type>::getNbDegreeOfFreedom();
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();
	auto shapes = std::make_unique<Array<Real>>(
	0, nb_unknown * nb_nodes_per_element * nb_degree_of_freedom_);
	nb_degree_of_freedom = nb_unknown;
	shape_functions.template computeShapesMassOnIntegrationPoints<type>(
	nodes, integration_points, *shapes, ghost_type);

	return shapes;
	}
	};
	#endif
	} // namespace details
	} // namespace fe_engine
	//
	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV =
	* \int \rho \varphi_i dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
	const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
	const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	// \int N * N so degree 2 * degree of N
	const UInt polynomial_degree =
	2 * ElementClassProperty<type>::polynomial_degree;

	// getting the integration points
	Matrix<Real> integration_points =
	integrator.template getIntegrationPoints<type, polynomial_degree>();

	UInt nb_degree_of_freedom = dof_manager.getDOFs(dof_id).getNbComponent();
	UInt nb_element = mesh.getNbElement(type, ghost_type);

	// getting the shapes on the integration points
	auto shapes_voigt =
	fe_engine::details::ShapesForMassHelper<kind>::template getShapes<type>(
	shape_functions, integration_points, mesh.getNodes(),
	nb_degree_of_freedom, nb_element, ghost_type);

	auto vect_size = shapes_voigt->size();

	// getting the value to assemble on the integration points
	Array<Real> field(vect_size, nb_degree_of_freedom);
	fe_engine::details::fillField(field_funct, field, nb_element,
	integration_points.cols(), type, ghost_type);

	auto lmat_size = shapes_voigt->getNbComponent() / nb_degree_of_freedom;

	// computing \rho * N
	Array<Real> local_mat(vect_size, lmat_size * lmat_size);
	auto N_it = shapes_voigt->begin(nb_degree_of_freedom, lmat_size);
	auto lmat_it = local_mat.begin(lmat_size, lmat_size);
	auto field_it = field.begin_reinterpret(nb_degree_of_freedom, field.size());

	for (UInt q = 0; q < vect_size; ++q, ++lmat_it, ++N_it, ++field_it) {
	const auto & rho = *field_it;
	const auto & N = *N_it;
	auto & mat = *lmat_it;

	Matrix<Real> Nt = N.transpose();
	for (UInt d = 0; d < Nt.cols(); ++d) {
	Nt(d) *= rho(d);
	}

	mat.template mul<false, false>(Nt, N);
	}

	// integrate the elemental values
	Array<Real> int_field_times_shapes(nb_element, lmat_size * lmat_size,
	"inte_rho_x_shapes");
	this->integrator.template integrate<type, polynomial_degree>(
	local_mat, int_field_times_shapes, lmat_size * lmat_size, ghost_type);

	// assemble the elemental values to the matrix
	dof_manager.assembleElementalMatricesToMatrix(
	matrix_id, dof_id, int_field_times_shapes, type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_ */
	diff --git a/src/fe_engine/fe_engine_template_tmpl_struct.hh b/src/fe_engine/fe_engine_template_tmpl_struct.hh
	index d6d80f772..0ac7aa332 100644
	--- a/src/fe_engine/fe_engine_template_tmpl_struct.hh
	+++ b/src/fe_engine/fe_engine_template_tmpl_struct.hh
	@@ -1,103 +1,103 @@
	/**
	* @file fe_engine_template_tmpl_struct.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jul 07 2014
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Template implementation of FEEngineTemplate for Structural Element
	* Kinds
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_structural.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, typename = void>
	struct AssembleFieldMatrixStructHelper {};

	template <ElementKind kind>
	struct AssembleFieldMatrixStructHelper<
	kind, typename std::enable_if<kind == _ek_structural>::type> {
	template <template <ElementKind, class> class I,
	template <ElementKind> class S, ElementKind k, class IOF>
	static void call(const FEEngineTemplate<I, S, k, IOF> & fem,
	const Array<Real> & field_1, UInt nb_degree_of_freedom,
	SparseMatrix & M, Array<Real> * n,
	ElementTypeMapArray<Real> & rotation_mat, ElementType type,
	GhostType ghost_type) {
	#define ASSEMBLE_MATRIX(type) \
	fem.template assembleFieldMatrix<type>(field_1, nb_degree_of_freedom, M, n, \
	rotation_mat, ghost_type)

	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ASSEMBLE_MATRIX, _ek_structural);
	#undef ASSEMBLE_MATRIX
	}
	};

	// template <template <ElementKind, class> class I, template <ElementKind> class
	// S,
	// ElementKind kind, class IntegrationOrderFunctor>
	// inline void
	// FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
	// const Array<Real> & field_1, UInt nb_degree_of_freedom, SparseMatrix & M,
	// Array<Real> * n, ElementTypeMapArray<Real> & rotation_mat,
	// ElementType type, GhostType ghost_type) const {
	// AKANTU_DEBUG_IN();

	// AssembleFieldMatrixStructHelper<kind>::template call(
	// *this, field_1, nb_degree_of_freedom, M, n, rotation_mat, type,
	// ghost_type);

	// AKANTU_DEBUG_OUT();
	// }
	// /* --------------------------------------------------------------------------
	// */ template <template <ElementKind, class> class I, template <ElementKind>
	// class S,
	// ElementKind kind, class IntegrationOrderFunctor>
	// inline void
	// FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapesMatrix(
	// ElementType, UInt, UInt, Array<Real> *, UInt, UInt, UInt,
	// const bool, GhostType) const {

	// AKANTU_TO_IMPLEMENT();
	// }

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
	const Array<Real> & /unused/, UInt /unused/, SparseMatrix & /unused/,
	Array<Real> * /unused/, ElementTypeMapArray<Real> & /unused/,
	GhostType /unused/) const {
	AKANTU_TO_IMPLEMENT();
	}

	} // namespace akantu
	diff --git a/src/fe_engine/gauss_integration.cc b/src/fe_engine/gauss_integration.cc
	index 422114a5b..4755d106c 100644
	--- a/src/fe_engine/gauss_integration.cc
	+++ b/src/fe_engine/gauss_integration.cc
	@@ -1,239 +1,239 @@
	/**
	* @file gauss_integration.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Thomas Menouillard <tmenouillard@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Definition of the integration constants, some of the value are taken
	* from r3.01.01 doc from Code Aster
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "element_class.hh"

	using std::sqrt;

	namespace akantu {

	/* clang-format off */
	/* -------------------------------------------------------------------------- */
	/* Points */
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_point, 1>::quad_positions[] = {0};
	template<> Real GaussIntegrationTypeData<_git_point, 1>::quad_weights[] = {1.};

	/* -------------------------------------------------------------------------- */
	/* Segments */
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_segment, 1>::quad_positions[] = {0.};
	template<> Real GaussIntegrationTypeData<_git_segment, 1>::quad_weights[] = {2.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_segment, 2>::quad_positions[] = {-1./sqrt(3.), 1./sqrt(3.)};
	template<> Real GaussIntegrationTypeData<_git_segment, 2>::quad_weights[] = {1., 1.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_segment, 3>::quad_positions[] = {-sqrt(3./5.), 0., sqrt(3./5.)};
	template<> Real GaussIntegrationTypeData<_git_segment, 3>::quad_weights[] = {5./9., 8./9., 5./9.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_segment, 4>::quad_positions[] = {-sqrt((3. + 2.*sqrt(6./5.))/7.),
	-sqrt((3. - 2.*sqrt(6./5.))/7.),
	sqrt((3. - 2.*sqrt(6./5.))/7.),
	sqrt((3. + 2.*sqrt(6./5.))/7.)};
	template<> Real GaussIntegrationTypeData<_git_segment, 4>::quad_weights[] = {(18. - sqrt(30.))/36.,
	(18. + sqrt(30.))/36.,
	(18. + sqrt(30.))/36.,
	(18. - sqrt(30.))/36.};
	/* -------------------------------------------------------------------------- */
	/* Triangles */
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_triangle, 1>::quad_positions[] = {1./3., 1./3.};
	template<> Real GaussIntegrationTypeData<_git_triangle, 1>::quad_weights[] = {1./2.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_triangle, 3>::quad_positions[] = {1./6., 1./6.,
	2./3., 1./6.,
	1./6., 2./3.};
	template<> Real GaussIntegrationTypeData<_git_triangle, 3>::quad_weights[] = {1./6., 1./6., 1./6.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_triangle, 4>::quad_positions[] = {1./5., 1./5.,
	3./5., 1./5.,
	1./5., 3./5.,
	1./3., 1./3.};
	template<> Real GaussIntegrationTypeData<_git_triangle, 4>::quad_weights[] = {25./(24.4.), 25./(24.4.), 25./(24.4.), -27/(24.4.)};
	/* -------------------------------------------------------------------------- */
	/// Found those one in the TrigGaussRuleInfo from mathematica and matched them to the code aster values
	/// http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/AFEM.AppI.d/AFEM.AppI.pdf
	static const Real tri_6_a = (8. - std::sqrt(10.) + std::sqrt(38.-44.*std::sqrt(2./5.)))/18.;
	static const Real tri_6_b = (8. - std::sqrt(10.) - std::sqrt(38.-44.*std::sqrt(2./5.)))/18.;
	static const Real tri_6_w1 = (620. - std::sqrt(213125. - 53320.*std::sqrt(10.)))/7440.;
	static const Real tri_6_w2 = (620. + std::sqrt(213125. - 53320.*std::sqrt(10.)))/7440.;
	template<> Real GaussIntegrationTypeData<_git_triangle, 6>::quad_positions[] = {tri_6_b, tri_6_b,
	1. - 2. * tri_6_b, tri_6_b,
	tri_6_b, 1. - 2. * tri_6_b,
	tri_6_a, 1. - 2. * tri_6_a,
	tri_6_a, tri_6_a,
	1. - 2. * tri_6_a, tri_6_a};
	template<> Real GaussIntegrationTypeData<_git_triangle, 6>::quad_weights[] = {tri_6_w1, tri_6_w1, tri_6_w1,
	tri_6_w2, tri_6_w2, tri_6_w2};
	/* -------------------------------------------------------------------------- */
	static const Real tri_7_a = (6. + std::sqrt(15.)) / 21.;
	static const Real tri_7_b = (6. - std::sqrt(15.)) / 21.;
	static const Real tri_7_w1 = (155. + std::sqrt(15.))/2400.;
	static const Real tri_7_w2 = (155. - std::sqrt(15.))/2400.;
	template<> Real GaussIntegrationTypeData<_git_triangle, 7>::quad_positions[] = { 1./3., 1./3.,
	tri_7_a, tri_7_a,
	1. - 2.*tri_7_a, tri_7_a,
	tri_7_a, 1. - 2.*tri_7_a,
	tri_7_b, tri_7_b,
	1. - 2.*tri_7_b, tri_7_b,
	tri_7_b, 1. - 2.*tri_7_b};
	template<> Real GaussIntegrationTypeData<_git_triangle, 7>::quad_weights[] = {9./80.,
	tri_7_w1, tri_7_w1, tri_7_w1,
	tri_7_w2, tri_7_w2, tri_7_w2};

	/* -------------------------------------------------------------------------- */


	/* -------------------------------------------------------------------------- */
	/* Tetrahedrons */
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 1>::quad_positions[] = {1./4., 1./4., 1./4.};
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 1>::quad_weights[] = {1./6.};
	/* -------------------------------------------------------------------------- */
	static const Real tet_4_a = (5. - std::sqrt(5.))/20.;
	static const Real tet_4_b = (5. + 3.*std::sqrt(5.))/20.;
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 4>::quad_positions[] = {tet_4_a, tet_4_a, tet_4_a,
	tet_4_b, tet_4_a, tet_4_a,
	tet_4_a, tet_4_b, tet_4_a,
	tet_4_a, tet_4_a, tet_4_b};
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 4>::quad_weights[] = {1./24., 1./24., 1./24., 1./24.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 5>::quad_positions[] = {1./4., 1./4., 1./4.,
	1./6., 1./6., 1./6.,
	1./6., 1./6., 1./2.,
	1./6., 1./2., 1./6.,
	1./2., 1./6., 1./6.,};
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 5>::quad_weights[] = {-2./15., 3./40.,
	3./40., 3./40.,
	3./40.};
	/* -------------------------------------------------------------------------- */
	static const Real tet_15_a = (7. + std::sqrt(15.))/34.;
	static const Real tet_15_b = (13. - 3. * std::sqrt(15.))/34.;
	static const Real tet_15_c = (7. - std::sqrt(15.))/34.;
	static const Real tet_15_d = (13. + 3. * std::sqrt(15.))/34.;
	static const Real tet_15_e = (5. - std::sqrt(15.))/20.;
	static const Real tet_15_f = (5. + std::sqrt(15.))/20.;
	static const Real tet_15_w1 = (2665. - 14. * std::sqrt(15.))/226800.;
	static const Real tet_15_w2 = (2665. + 14. * std::sqrt(15.))/226800.;
	static const Real tet_15_w3 = 5./567.;
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 15>::quad_positions[] = {1./4., 1./4., 1./4.,
	tet_15_a, tet_15_a, tet_15_a,
	tet_15_a, tet_15_a, tet_15_b,
	tet_15_a, tet_15_b, tet_15_a,
	tet_15_b, tet_15_a, tet_15_a,

	tet_15_c, tet_15_c, tet_15_c,
	tet_15_c, tet_15_c, tet_15_d,
	tet_15_c, tet_15_d, tet_15_c,
	tet_15_d, tet_15_c, tet_15_c,

	tet_15_e, tet_15_e, tet_15_f,
	tet_15_e, tet_15_f, tet_15_e,
	tet_15_f, tet_15_e, tet_15_e,

	tet_15_e, tet_15_f, tet_15_f,
	tet_15_f, tet_15_e, tet_15_f,
	tet_15_f, tet_15_f, tet_15_e};
	template<> Real GaussIntegrationTypeData<_git_tetrahedron, 15>::quad_weights[] = {8./405.,
	tet_15_w1, tet_15_w1, tet_15_w1, tet_15_w1,
	tet_15_w2, tet_15_w2, tet_15_w2, tet_15_w2,
	tet_15_w3, tet_15_w3, tet_15_w3, tet_15_w3, tet_15_w3, tet_15_w3};

	/* -------------------------------------------------------------------------- */
	/* Pentahedrons */
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 6>::quad_positions[] = {-1./sqrt(3.), 0.5, 0.5,
	-1./sqrt(3.), 0. , 0.5,
	-1./sqrt(3.), 0.5, 0.,
	1./sqrt(3.), 0.5, 0.5,
	1./sqrt(3.), 0. , 0.5,
	1./sqrt(3.), 0.5 ,0.};
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 6>::quad_weights[] = {1./6., 1./6., 1./6.,
	1./6., 1./6., 1./6.};
	/* -------------------------------------------------------------------------- */
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 8>::quad_positions[] = {-sqrt(3.)/3., 1./3., 1./3.,
	-sqrt(3.)/3., 0.6, 0.2,
	-sqrt(3.)/3., 0.2, 0.6,
	-sqrt(3.)/3., 0.2, 0.2,
	sqrt(3.)/3., 1./3., 1./3.,
	sqrt(3.)/3., 0.6, 0.2,
	sqrt(3.)/3., 0.2, 0.6,
	sqrt(3.)/3., 0.2, 0.2};
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 8>::quad_weights[] = {-27./96., 25./96., 25./96., 25./96.,
	-27./96., 25./96., 25./96., 25./96.};
	/* -------------------------------------------------------------------------- */
	static const Real pent_21_x = std::sqrt(3./5.);
	static const Real pent_21_a = (6. + std::sqrt(15.)) / 21.;
	static const Real pent_21_b = (6. - std::sqrt(15.)) / 21.;

	static const Real pent_21_w1_1 = 5./9.;
	static const Real pent_21_w2_1 = 8./9.;
	static const Real pent_21_w1_2 = (155. + std::sqrt(15.))/2400.;
	static const Real pent_21_w2_2 = (155. - std::sqrt(15.))/2400.;
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 21>::quad_positions[] = {- pent_21_x, 1./3., 1./3.,
	- pent_21_x, pent_21_a, pent_21_a,
	- pent_21_x, 1. - 2.*pent_21_a, pent_21_a,
	- pent_21_x, pent_21_a, 1. - 2.*pent_21_a,
	- pent_21_x, pent_21_b, pent_21_b,
	- pent_21_x, 1. - 2.*pent_21_b, pent_21_b,
	- pent_21_x, pent_21_b, 1. - 2.*pent_21_b,
	0., 1./3., 1./3.,
	0., pent_21_a, pent_21_a,
	0., 1. - 2.*pent_21_a, pent_21_a,
	0., pent_21_a, 1. - 2.*pent_21_a,
	0., pent_21_b, pent_21_b,
	0., 1. - 2.*pent_21_b, pent_21_b,
	0., pent_21_b, 1. - 2.*pent_21_b,
	pent_21_x, 1./3., 1./3.,
	pent_21_x, pent_21_a, pent_21_a,
	pent_21_x, 1. - 2.*pent_21_a, pent_21_a,
	pent_21_x, pent_21_a, 1. - 2.*pent_21_a,
	pent_21_x, pent_21_b, pent_21_b,
	pent_21_x, 1. - 2.*pent_21_b, pent_21_b,
	pent_21_x, pent_21_b, 1. - 2.*pent_21_b};
	template<> Real GaussIntegrationTypeData<_git_pentahedron, 21>::quad_weights[] = {pent_21_w1_1 * 9. / 80.,
	pent_21_w1_1pent_21_w1_2, pent_21_w1_1pent_21_w1_2, pent_21_w1_1*pent_21_w1_2,
	pent_21_w1_1pent_21_w2_2, pent_21_w1_1pent_21_w2_2, pent_21_w1_1*pent_21_w2_2,
	pent_21_w2_1 * 9. / 80.,
	pent_21_w1_2pent_21_w1_2, pent_21_w1_2pent_21_w1_2, pent_21_w1_2*pent_21_w1_2,
	pent_21_w1_2pent_21_w2_2, pent_21_w1_2pent_21_w2_2, pent_21_w1_2*pent_21_w2_2,
	pent_21_w1_1 * 9. / 80.,
	pent_21_w1_1pent_21_w1_2, pent_21_w1_1pent_21_w1_2, pent_21_w1_1*pent_21_w1_2,
	pent_21_w1_1pent_21_w2_2, pent_21_w1_1pent_21_w2_2, pent_21_w1_1*pent_21_w2_2};


	} // akantu
	diff --git a/src/fe_engine/gauss_integration_tmpl.hh b/src/fe_engine/gauss_integration_tmpl.hh
	index a759333eb..5874b69f9 100644
	--- a/src/fe_engine/gauss_integration_tmpl.hh
	+++ b/src/fe_engine/gauss_integration_tmpl.hh
	@@ -1,280 +1,278 @@
	/**
	* @file gauss_integration_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 10 2016
	* @date last modification: Tue Sep 29 2020
	*
	* @brief implementation of the gauss integration helpers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_GAUSS_INTEGRATION_TMPL_HH_
	#define AKANTU_GAUSS_INTEGRATION_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* GaussIntegrationElement */
	/* -------------------------------------------------------------------------- */
	namespace _aka_gauss_helpers {
	- template <GaussIntegrationType type, UInt n>
	- struct GaussIntegrationNbPoints {
	+ template <GaussIntegrationType type, UInt n> struct GaussIntegrationNbPoints {
	static const UInt nb_points = 0;
	};

	#if !defined(DOXYGEN)
	template <UInt n> struct GaussIntegrationNbPoints<_git_not_defined, n> {
	static const UInt nb_points = 0;
	};

	template <UInt n> struct GaussIntegrationNbPoints<_git_point, n> {
	static const UInt nb_points = 1;
	};

	template <UInt n> struct GaussIntegrationNbPoints<_git_segment, n> {
	static const UInt nb_points = (n + 1) / 2 + (bool((n + 1) % 2) ? 1 : 0);
	};

	#define DECLARE_GAUSS_NB_POINTS(type, order, points) \
	template <> struct GaussIntegrationNbPoints<type, order> { \
	static const UInt nb_points = points; \
	}

	#define DECLARE_GAUSS_NB_POINTS_PENT(type, order, xo, yo) \
	template <> struct GaussIntegrationNbPoints<type, order> { \
	static const UInt x_order = xo; \
	static const UInt yz_order = yo; \
	static const UInt nb_points = 1; \
	}

	DECLARE_GAUSS_NB_POINTS(_git_triangle, 1, 1);
	DECLARE_GAUSS_NB_POINTS(_git_triangle, 2, 3);
	DECLARE_GAUSS_NB_POINTS(_git_triangle, 3, 4);
	DECLARE_GAUSS_NB_POINTS(_git_triangle, 4, 6);
	DECLARE_GAUSS_NB_POINTS(_git_triangle, 5, 7);
	DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 1, 1);
	DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 2, 4);
	DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 3, 5);
	DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 4, 15);
	DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 5, 15);
	DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 1, 3,
	2); // order 3 in x, order 2 in y and z
	DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 2, 3,
	2); // order 3 in x, order 2 in y and z
	DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 3, 3,
	3); // order 3 in x, order 3 in y and z
	DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 4, 5,
	5); // order 5 in x, order 5 in y and z
	DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 5, 5,
	5); // order 5 in x, order 5 in y and z

	template <GaussIntegrationType type, UInt n, UInt on = n,
	bool end_recurse = false>
	struct GaussIntegrationNbPointsHelper {
	static const UInt pnp = GaussIntegrationNbPoints<type, n>::nb_points;
	static const UInt order = n;
	static const UInt nb_points = pnp;
	};

	template <GaussIntegrationType type, UInt n, UInt on>
	struct GaussIntegrationNbPointsHelper<type, n, on, true> {
	static const UInt nb_points = 0;
	};
	#endif

	/* ------------------------------------------------------------------------ */
	/* Generic helper */
	/* ------------------------------------------------------------------------ */
	template <GaussIntegrationType type, UInt dimension, UInt n>
	struct GaussIntegrationTypeDataHelper {
	using git_np = GaussIntegrationNbPoints<type, n>;
	using git_data = GaussIntegrationTypeData<type, git_np::nb_points>;

	static UInt getNbQuadraturePoints() { return git_np::nb_points; }

	static Matrix<Real> getQuadraturePoints() {
	return Matrix<Real>(git_data::quad_positions, dimension,
	git_np::nb_points);
	}

	static Vector<Real> getWeights() {
	return Vector<Real>(git_data::quad_weights, git_np::nb_points);
	}
	};

	#if !defined(DOXYGEN)
	/* ------------------------------------------------------------------------ */
	/* helper for _segment _quadrangle _hexahedron */
	/* ------------------------------------------------------------------------ */
	template <UInt dimension, UInt dp>
	struct GaussIntegrationTypeDataHelper<_git_segment, dimension, dp> {
	using git_np = GaussIntegrationNbPoints<_git_segment, dp>;
	using git_data = GaussIntegrationTypeData<_git_segment, git_np::nb_points>;

	static UInt getNbQuadraturePoints() {
	return Math::pow<dimension>(git_np::nb_points);
	}

	static Matrix<Real> getQuadraturePoints() {
	UInt tot_nquad = getNbQuadraturePoints();
	UInt nquad = git_np::nb_points;

	Matrix<Real> quads(dimension, tot_nquad);
	Vector<Real> pos(git_data::quad_positions, nquad);

	UInt offset = 1;
	for (UInt d = 0; d < dimension; ++d) {
	for (UInt n = 0, q = 0; n < tot_nquad; ++n, q += offset) {
	UInt rq = q % tot_nquad + q / tot_nquad;
	quads(d, rq) = pos(n % nquad);
	}
	offset *= nquad;
	}
	return quads;
	}

	static Vector<Real> getWeights() {
	UInt tot_nquad = getNbQuadraturePoints();
	UInt nquad = git_np::nb_points;

	Vector<Real> quads_weights(tot_nquad, 1.);
	Vector<Real> weights(git_data::quad_weights, nquad);

	UInt offset = 1;
	for (UInt d = 0; d < dimension; ++d) {
	for (UInt n = 0, q = 0; n < tot_nquad; ++n, q += offset) {
	UInt rq = q % tot_nquad + q / tot_nquad;
	quads_weights(rq) *= weights(n % nquad);
	}
	offset *= nquad;
	}
	return quads_weights;
	}
	};

	/* ------------------------------------------------------------------------ */
	/* helper for _pentahedron */
	/* ------------------------------------------------------------------------ */
	template <UInt dimension, UInt dp>
	struct GaussIntegrationTypeDataHelper<_git_pentahedron, dimension, dp> {
	using git_info = GaussIntegrationNbPoints<_git_pentahedron, dp>;
	using git_np_seg =
	GaussIntegrationNbPoints<_git_segment, git_info::x_order>;
	using git_np_tri =
	GaussIntegrationNbPoints<_git_triangle, git_info::yz_order>;
	using git_data_seg =
	GaussIntegrationTypeData<_git_segment, git_np_seg::nb_points>;
	using git_data_tri =
	GaussIntegrationTypeData<_git_triangle, git_np_tri::nb_points>;

	static UInt getNbQuadraturePoints() {
	return git_np_seg::nb_points * git_np_tri::nb_points;
	}

	static Matrix<Real> getQuadraturePoints() {
	UInt tot_nquad = getNbQuadraturePoints();
	UInt nquad_seg = git_np_seg::nb_points;
	UInt nquad_tri = git_np_tri::nb_points;

	Matrix<Real> quads(dimension, tot_nquad);
	Matrix<Real> pos_seg_w(git_data_seg::quad_positions, 1, nquad_seg);
	Matrix<Real> pos_tri_w(git_data_tri::quad_positions, 2, nquad_tri);

	for (UInt ns = 0, q = 0; ns < nquad_seg; ++ns) {
	Vector<Real> pos_seg = pos_seg_w(ns);
	for (UInt nt = 0; nt < nquad_tri; ++nt, ++q) {
	Vector<Real> pos_tri = pos_tri_w(nt);
	Vector<Real> quad = quads(q);
	quad(_x) = pos_seg(_x);
	quad(_y) = pos_tri(_x);
	quad(_z) = pos_tri(_y);
	}
	}
	return quads;
	}

	static Vector<Real> getWeights() {
	UInt tot_nquad = getNbQuadraturePoints();
	UInt nquad_seg = git_np_seg::nb_points;
	UInt nquad_tri = git_np_tri::nb_points;

	Vector<Real> quads_weights(tot_nquad);

	Vector<Real> weight_seg(git_data_seg::quad_weights, nquad_seg);
	Vector<Real> weight_tri(git_data_tri::quad_weights, nquad_tri);

	for (UInt ns = 0, q = 0; ns < nquad_seg; ++ns) {
	for (UInt nt = 0; nt < nquad_tri; ++nt, ++q) {
	quads_weights(q) = weight_seg(ns) * weight_tri(nt);
	}
	}
	return quads_weights;
	}
	};
	#endif
	} // namespace _aka_gauss_helpers

	template <ElementType element_type, UInt n>
	-Matrix<Real>
	-GaussIntegrationElement<element_type, n>::getQuadraturePoints() {
	+Matrix<Real> GaussIntegrationElement<element_type, n>::getQuadraturePoints() {
	const InterpolationType itp_type =
	ElementClassProperty<element_type>::interpolation_type;
	using interpolation_property = InterpolationProperty<itp_type>;
	using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
	ElementClassProperty<element_type>::gauss_integration_type,
	interpolation_property::natural_space_dimension, n>;
	Matrix<Real> tmp(data_helper::getQuadraturePoints());
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType element_type, UInt n>
	Vector<Real> GaussIntegrationElement<element_type, n>::getWeights() {
	const InterpolationType itp_type =
	ElementClassProperty<element_type>::interpolation_type;
	using interpolation_property = InterpolationProperty<itp_type>;
	using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
	ElementClassProperty<element_type>::gauss_integration_type,
	interpolation_property::natural_space_dimension, n>;
	Vector<Real> tmp(data_helper::getWeights());
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType element_type, UInt n>
	UInt GaussIntegrationElement<element_type, n>::getNbQuadraturePoints() {
	const InterpolationType itp_type =
	ElementClassProperty<element_type>::interpolation_type;
	using interpolation_property = InterpolationProperty<itp_type>;
	using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
	ElementClassProperty<element_type>::gauss_integration_type,
	interpolation_property::natural_space_dimension, n>;
	return data_helper::getNbQuadraturePoints();
	}

	} // namespace akantu

	#endif /* AKANTU_GAUSS_INTEGRATION_TMPL_HH_ */
	diff --git a/src/fe_engine/geometrical_element_property.cc b/src/fe_engine/geometrical_element_property.cc
	index 07807498b..3a279cad3 100644
	--- a/src/fe_engine/geometrical_element_property.cc
	+++ b/src/fe_engine/geometrical_element_property.cc
	@@ -1,63 +1,63 @@
	/**
	* @file geometrical_element_property.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 29 2017
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Specialization of the geometrical types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */
	#include <boost/preprocessor.hpp>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	#define AKANTU_INSTANTIATE_TYPES(r, data, type) \
	constexpr std::array<UInt, ElementClass<type>::getNbFacetTypes()> \
	GeometricalElementProperty< \
	ElementClassProperty<type>::geometrical_type>::nb_facets; \
	constexpr std::array<UInt, ElementClass<type>::getNbFacetTypes()> \
	GeometricalElementProperty< \
	ElementClassProperty<type>::geometrical_type>::nb_nodes_per_facet; \
	constexpr std::array< \
	UInt, detail::sizeFacetConnectivity<GeometricalElementProperty< \
	ElementClassProperty<type>::geometrical_type>>()> \
	GeometricalElementProperty<ElementClassProperty< \
	type>::geometrical_type>::facet_connectivity_vect; \
	constexpr std::array<ElementType, ElementClass<type>::getNbFacetTypes()> \
	ElementClassExtraGeometryProperties<type>::facet_type;

	BOOST_PP_SEQ_FOR_EACH(AKANTU_INSTANTIATE_TYPES, _,
	(_not_defined)AKANTU_ek_regular_ELEMENT_TYPE)

	#if defined(AKANTU_COHESIVE_ELEMENT)
	BOOST_PP_SEQ_FOR_EACH(AKANTU_INSTANTIATE_TYPES, _,
	AKANTU_ek_cohesive_ELEMENT_TYPE)
	#endif

	} // namespace akantu
	diff --git a/src/fe_engine/geometrical_element_property.hh b/src/fe_engine/geometrical_element_property.hh
	index a2b7c09dc..aea6ef7f6 100644
	--- a/src/fe_engine/geometrical_element_property.hh
	+++ b/src/fe_engine/geometrical_element_property.hh
	@@ -1,481 +1,481 @@
	/**
	* @file geometrical_element_property.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Thomas Menouillard <tmenouillard@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 29 2017
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Specialization of the geometrical types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */
	#include <array>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace detail {
	template <typename properties> constexpr size_t sizeFacetConnectivity() {
	size_t s = 0;
	for (size_t n = 0; n < properties::nb_facet_types; ++n) {
	s += properties::nb_facets[n] * properties::nb_nodes_per_facet[n];
	}
	return s == 0 ? 1 : s;
	}
	} // namespace detail

	#if !defined(DOXYGEN)
	template <> struct GeometricalElementProperty<_gt_not_defined> {
	static constexpr UInt spatial_dimension{0};
	static constexpr UInt nb_nodes_per_element{0};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{0}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{0}};
	static constexpr std::array<UInt, 1> facet_connectivity_vect{{0}};
	};

	template <> struct GeometricalElementProperty<_gt_point> {
	static constexpr UInt spatial_dimension{0};
	static constexpr UInt nb_nodes_per_element{1};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{1}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{1}};
	static constexpr std::array<UInt, 1> facet_connectivity_vect{{0}};
	};

	template <> struct GeometricalElementProperty<_gt_segment_2> {
	static constexpr UInt spatial_dimension{1};
	static constexpr UInt nb_nodes_per_element{2};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{1}};
	static constexpr std::array<UInt, 2> facet_connectivity_vect{{0, 1}};
	};

	template <> struct GeometricalElementProperty<_gt_segment_3> {
	static constexpr UInt spatial_dimension{1};
	static constexpr UInt nb_nodes_per_element{3};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{1}};
	// clang-format off
	static constexpr std::array<UInt, 2> facet_connectivity_vect{{0, 1}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_triangle_3> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{3};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{3}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{2}};
	// clang-format off
	static constexpr std::array<UInt, 6> facet_connectivity_vect{{
	0, 1, 2,
	1, 2, 0}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_triangle_6> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{6};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{3}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3}};
	// clang-format off
	static constexpr std::array<UInt, 9> facet_connectivity_vect{{
	0, 1, 2,
	1, 2, 0,
	3, 4, 5}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_tetrahedron_4> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{4};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{4}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3}};
	// clang-format off
	static constexpr std::array<UInt, 12> facet_connectivity_vect{{
	0, 1, 2, 0,
	2, 2, 0, 1,
	1, 3, 3, 3}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_tetrahedron_10> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{10};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{4}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{6}};
	// clang-format off
	static constexpr std::array<UInt, 6*4> facet_connectivity_vect{{
	0, 1, 2, 0,
	2, 2, 0, 1,
	1, 3, 3, 3,
	6, 5, 6, 4,
	5, 9, 7, 8,
	4, 8, 9, 7}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_quadrangle_4> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{4};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{4}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{2}};
	// clang-format off
	static constexpr std::array<UInt, 2*4> facet_connectivity_vect{{
	0, 1, 2, 3,
	1, 2, 3, 0}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_quadrangle_8> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{8};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{4}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3}};
	// clang-format off
	static constexpr std::array<UInt, 4*3> facet_connectivity_vect{{
	0, 1, 2, 3,
	1, 2, 3, 0,
	4, 5, 6, 7}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_hexahedron_8> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{8};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{6}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{4}};
	// clang-format off
	static constexpr std::array<UInt, 4*6> facet_connectivity_vect{{
	0, 0, 1, 2, 3, 4,
	3, 1, 2, 3, 0, 5,
	2, 5, 6, 7, 4, 6,
	1, 4, 5, 6, 7, 7}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_hexahedron_20> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{20};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{6}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{8}};
	// clang-format off
	static constexpr std::array<UInt, 8*6> facet_connectivity_vect{{
	0, 1, 2, 3, 0, 4,
	1, 2, 3, 0, 3, 5,
	5, 6, 7, 4, 2, 6,
	4, 5, 6, 7, 1, 7,
	8, 9, 10, 11, 11, 16,
	13, 14, 15, 12, 10, 17,
	16, 17, 18, 19, 9, 18,
	12, 13, 14, 15, 8, 19}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_pentahedron_6> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{6};
	static constexpr UInt nb_facet_types{2};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2, 3}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3, 4}};
	// clang-format off
	static constexpr std::array<UInt, 32 + 43> facet_connectivity_vect{{
	// first type
	0, 3,
	2, 4,
	1, 5,
	// second type
	0, 0, 1,
	1, 3, 2,
	4, 5, 5,
	3, 2, 4}};
	// clang-format on
	};

	template <> struct GeometricalElementProperty<_gt_pentahedron_15> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{15};
	static constexpr UInt nb_facet_types{2};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2, 3}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{6, 8}};
	// clang-format off
	static constexpr std::array<UInt, 62 + 83> facet_connectivity_vect{{
	// first type
	0, 3,
	2, 4,
	1, 5,
	8, 12,
	7, 13,
	6, 14,
	// second type
	0, 0, 1,
	1, 3, 2,
	4, 5, 5,
	3, 2, 4,
	6, 9, 7,
	10, 14, 11,
	12, 11, 13,
	9, 8, 10}};
	// clang-format on
	};

	#if defined(AKANTU_COHESIVE_ELEMENT)
	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_2d_4> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{4};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{2}};
	// clang-format off
	static constexpr std::array<UInt, 2 * 2> facet_connectivity_vect{{
	0, 2,
	1, 3}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_2d_6> {
	static constexpr UInt spatial_dimension{2};
	static constexpr UInt nb_nodes_per_element{6};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3}};
	// clang-format off
	static constexpr std::array<UInt, 3*2> facet_connectivity_vect{{
	0, 3,
	1, 4,
	2, 5}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_1d_2> {
	static constexpr UInt spatial_dimension{1};
	static constexpr UInt nb_nodes_per_element{2};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{1}};
	// clang-format off
	static constexpr std::array<UInt, 2> facet_connectivity_vect{{0, 1}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_3d_6> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{6};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{3}};
	// clang-format off
	static constexpr std::array<UInt, 3*2> facet_connectivity_vect{{
	0, 3,
	1, 4,
	2, 5}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_3d_12> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{12};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{6}};
	// clang-format off
	static constexpr std::array<UInt, 6*2> facet_connectivity_vect{{
	0, 6,
	1, 7,
	2, 8,
	3, 9,
	4, 10,
	5, 11}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_3d_8> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{8};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{4}};
	// clang-format off
	static constexpr std::array<UInt, 4*2> facet_connectivity_vect{{
	0, 4,
	1, 5,
	2, 6,
	3, 7}};
	// clang-format on
	};

	/* -------------------------------------------------------------------------- */
	template <> struct GeometricalElementProperty<_gt_cohesive_3d_16> {
	static constexpr UInt spatial_dimension{3};
	static constexpr UInt nb_nodes_per_element{16};
	static constexpr UInt nb_facet_types{1};
	static constexpr std::array<UInt, nb_facet_types> nb_facets{{2}};
	static constexpr std::array<UInt, nb_facet_types> nb_nodes_per_facet{{8}};
	// clang-format off
	static constexpr std::array<UInt, 8*2> facet_connectivity_vect{{
	0, 8,
	1, 9,
	2, 10,
	3, 11,
	4, 12,
	5, 13,
	6, 14,
	7, 15}};
	// clang-format on
	};
	#endif // AKANTU_COHESIVE_ELEMENT

	/* -------------------------------------------------------------------------- */
	template <> struct ElementClassExtraGeometryProperties<_not_defined> {
	static constexpr ElementType p1_type{_not_defined};
	static constexpr std::array<ElementType, 1> facet_type{{_not_defined}};
	};

	template <> struct ElementClassExtraGeometryProperties<_point_1> {
	static constexpr ElementType p1_type{_point_1};
	static constexpr std::array<ElementType, 1> facet_type{{_point_1}};
	};

	template <> struct ElementClassExtraGeometryProperties<_segment_2> {
	static constexpr ElementType p1_type{_segment_2};
	static constexpr std::array<ElementType, 1> facet_type{{_point_1}};
	};

	template <> struct ElementClassExtraGeometryProperties<_segment_3> {
	static constexpr ElementType p1_type{_segment_2};
	static constexpr std::array<ElementType, 1> facet_type{{_point_1}};
	};

	template <> struct ElementClassExtraGeometryProperties<_triangle_3> {
	static constexpr ElementType p1_type{_triangle_3};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_2}};
	};

	template <> struct ElementClassExtraGeometryProperties<_triangle_6> {
	static constexpr ElementType p1_type{_triangle_3};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_3}};
	};

	template <> struct ElementClassExtraGeometryProperties<_tetrahedron_4> {
	static constexpr ElementType p1_type{_tetrahedron_4};
	static constexpr std::array<ElementType, 1> facet_type{{_triangle_3}};
	};

	template <> struct ElementClassExtraGeometryProperties<_tetrahedron_10> {
	static constexpr ElementType p1_type{_tetrahedron_4};
	static constexpr std::array<ElementType, 1> facet_type{{_triangle_6}};
	};

	template <> struct ElementClassExtraGeometryProperties<_quadrangle_4> {
	static constexpr ElementType p1_type{_quadrangle_4};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_2}};
	};

	template <> struct ElementClassExtraGeometryProperties<_quadrangle_8> {
	static constexpr ElementType p1_type{_quadrangle_4};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_3}};
	};

	template <> struct ElementClassExtraGeometryProperties<_hexahedron_8> {
	static constexpr ElementType p1_type{_hexahedron_8};
	static constexpr std::array<ElementType, 1> facet_type{{_quadrangle_4}};
	};

	template <> struct ElementClassExtraGeometryProperties<_hexahedron_20> {
	static constexpr ElementType p1_type{_hexahedron_8};
	static constexpr std::array<ElementType, 1> facet_type{{_quadrangle_8}};
	};

	template <> struct ElementClassExtraGeometryProperties<_pentahedron_6> {
	static constexpr ElementType p1_type{_pentahedron_6};
	static constexpr std::array<ElementType, 2> facet_type{
	{_triangle_3, _quadrangle_4}};
	};

	template <> struct ElementClassExtraGeometryProperties<_pentahedron_15> {
	static constexpr ElementType p1_type{_pentahedron_6};
	static constexpr std::array<ElementType, 2> facet_type{
	{_triangle_6, _quadrangle_8}};
	};

	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <> struct ElementClassExtraGeometryProperties<_cohesive_2d_4> {
	static constexpr ElementType p1_type{_cohesive_2d_4};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_2}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_2d_6> {
	static constexpr ElementType p1_type{_cohesive_2d_4};
	static constexpr std::array<ElementType, 1> facet_type{{_segment_3}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_1d_2> {
	static constexpr ElementType p1_type{_cohesive_1d_2};
	static constexpr std::array<ElementType, 1> facet_type{{_point_1}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_3d_6> {
	static constexpr ElementType p1_type{_cohesive_3d_6};
	static constexpr std::array<ElementType, 1> facet_type{{_triangle_3}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_3d_12> {
	static constexpr ElementType p1_type{_cohesive_3d_6};
	static constexpr std::array<ElementType, 1> facet_type{{_triangle_6}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_3d_8> {
	static constexpr ElementType p1_type{_cohesive_3d_8};
	static constexpr std::array<ElementType, 1> facet_type{{_quadrangle_4}};
	};

	template <> struct ElementClassExtraGeometryProperties<_cohesive_3d_16> {
	static constexpr ElementType p1_type{_cohesive_3d_8};
	static constexpr std::array<ElementType, 1> facet_type{{_quadrangle_8}};
	};
	#endif // AKANTU_COHESIVE_ELEMENT

	#endif // !defined(DOXYGEN)

	} // namespace akantu
	diff --git a/src/fe_engine/integration_point.hh b/src/fe_engine/integration_point.hh
	index cefbfc1ba..5e82c2e69 100644
	--- a/src/fe_engine/integration_point.hh
	+++ b/src/fe_engine/integration_point.hh
	@@ -1,172 +1,172 @@
	/**
	* @file integration_point.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jun 17 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief definition of the class IntegrationPoint
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_types.hh"
	#include "element.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_QUADRATURE_POINT_H
	#define AKANTU_QUADRATURE_POINT_H

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class IntegrationPoint;
	extern const IntegrationPoint IntegrationPointNull;
	/* -------------------------------------------------------------------------- */

	class IntegrationPoint : public Element {

	/* ------------------------------------------------------------------------ */
	/* Typedefs */
	/* ------------------------------------------------------------------------ */

	public:
	using position_type = Vector<Real>;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */

	public:
	IntegrationPoint(const Element & element, UInt num_point = 0,
	UInt nb_quad_per_element = 0)
	: Element(element), num_point(num_point),
	global_num(element.element * nb_quad_per_element + num_point),
	position(nullptr, 0){};

	IntegrationPoint(ElementType type = _not_defined, UInt element = 0,
	UInt num_point = 0, GhostType ghost_type = _not_ghost)
	: Element{type, element, ghost_type}, num_point(num_point),
	position(nullptr, 0){};

	IntegrationPoint(UInt element, UInt num_point, UInt global_num,
	const position_type & position, ElementType type,
	GhostType ghost_type = _not_ghost)
	: Element{type, element, ghost_type}, num_point(num_point),
	global_num(global_num), position(nullptr, 0) {
	this->position.shallowCopy(position);
	};

	IntegrationPoint(const IntegrationPoint & quad)
	: Element(quad), num_point(quad.num_point), global_num(quad.global_num),
	position(nullptr, 0) {
	position.shallowCopy(quad.position);
	};

	virtual ~IntegrationPoint() = default;
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */

	inline bool operator==(const IntegrationPoint & quad) const {
	return Element::operator==(quad) && this->num_point == quad.num_point;
	}

	inline bool operator!=(const IntegrationPoint & quad) const {
	return Element::operator!=(quad) \|\| (num_point != quad.num_point) \|\|
	(global_num != quad.global_num);
	}

	bool operator<(const IntegrationPoint & rhs) const {
	bool res = Element::operator<(rhs) \|\|
	(Element::operator==(rhs) && this->num_point < rhs.num_point);
	return res;
	}

	inline IntegrationPoint & operator=(const IntegrationPoint & q) {
	if (this != &q) {
	element = q.element;
	type = q.type;
	ghost_type = q.ghost_type;
	num_point = q.num_point;
	global_num = q.global_num;
	position.shallowCopy(q.position);
	}

	return *this;
	}

	/// get the position of the integration point
	AKANTU_GET_MACRO(Position, position, const position_type &);

	/// set the position of the integration point
	void setPosition(const position_type & position) {
	this->position.shallowCopy(position);
	}

	/// deep copy of the position of the integration point
	void copyPosition(const position_type & position) {
	this->position.deepCopy(position);
	}

	/// function to print the containt of the class
	virtual void printself(std::ostream & stream, int indent = 0) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}
	stream << space << "IntegrationPoint [";
	stream << static_cast<const Element >(this);
	stream << ", " << num_point << "(" << global_num << ")"
	<< "]";
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */

	public:
	/// number of quadrature point in the element
	UInt num_point;
	/// global number of the quadrature point
	UInt global_num{0};
	// TODO might be temporary: however this class should be tought maybe...
	std::string material_id;

	private:
	/// position of the quadrature point
	position_type position;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const IntegrationPoint & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_QUADRATURE_POINT_H */
	diff --git a/src/fe_engine/integrator.hh b/src/fe_engine/integrator.hh
	index c034272a0..123acf8d3 100644
	--- a/src/fe_engine/integrator.hh
	+++ b/src/fe_engine/integrator.hh
	@@ -1,138 +1,138 @@
	/**
	* @file integrator.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief interface for integrator classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_INTEGRATOR_HH_
	#define AKANTU_INTEGRATOR_HH_

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class Integrator {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Integrator(const Mesh & mesh, UInt spatial_dimension,
	const ID & id = "integrator")
	: mesh(mesh), _spatial_dimension(spatial_dimension),
	jacobians("jacobians", id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	};

	virtual ~Integrator() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// empty method
	template <ElementType type>
	inline void precomputeJacobiansOnQuadraturePoints(__attribute__((unused))
	GhostType ghost_type) {}

	/// empty method
	void integrateOnElement(const Array<Real> & /f/, Real * /intf/,
	UInt /nb_degree_of_freedom/,
	const Element & /elem/,
	GhostType /ghost_type/) const {};

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}
	stream << space << "Integrator [" << std::endl;
	jacobians.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	};

	/* ------------------------------------------------------------------------ */
	public:
	virtual void onElementsAdded(const Array<Element> & /unused/) {}
	virtual void
	onElementsRemoved(const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & new_numbering) {
	jacobians.onElementsRemoved(new_numbering);
	}
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// access to the jacobians
	Array<Real> & getJacobians(ElementType type,
	GhostType ghost_type = _not_ghost) {
	return jacobians(type, ghost_type);
	};

	/// access to the jacobians const
	const Array<Real> & getJacobians(ElementType type,
	GhostType ghost_type = _not_ghost) const {
	return jacobians(type, ghost_type);
	};

	AKANTU_GET_MACRO(Jacobians, jacobians, const ElementTypeMapArray<Real> &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// mesh associated to the integrator
	const Mesh & mesh;

	// spatial dimension of the elements to consider
	UInt _spatial_dimension;

	/// jacobians for all elements
	ElementTypeMapArray<Real> jacobians;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "integrator_inline_impl.hh"

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const Integrator & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_INTEGRATOR_HH_ */
	diff --git a/src/fe_engine/integrator_gauss.hh b/src/fe_engine/integrator_gauss.hh
	index ec7dabd37..7dfe4745c 100644
	--- a/src/fe_engine/integrator_gauss.hh
	+++ b/src/fe_engine/integrator_gauss.hh
	@@ -1,205 +1,201 @@
	/**
	* @file integrator_gauss.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Gauss integration facilities
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTEGRATOR_GAUSS_HH_
	#define AKANTU_INTEGRATOR_GAUSS_HH_

	namespace akantu {
	namespace integrator {
	namespace details {
	template <ElementKind> struct GaussIntegratorComputeJacobiansHelper;
	} // namespace details
	} // namespace integrator

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	class IntegratorGauss : public Integrator {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	IntegratorGauss(const Mesh & mesh, UInt spatial_dimension,
	const ID & id = "integrator_gauss");

	~IntegratorGauss() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initIntegrator(const Array<Real> & nodes, ElementType type,
	GhostType ghost_type);

	template <ElementType type>
	- inline void initIntegrator(const Array<Real> & nodes,
	- GhostType ghost_type);
	+ inline void initIntegrator(const Array<Real> & nodes, GhostType ghost_type);

	/// integrate f on the element "elem" of type "type"
	template <ElementType type>
	inline void integrateOnElement(const Array<Real> & f, Real * intf,
	UInt nb_degree_of_freedom, UInt elem,
	GhostType ghost_type) const;

	/// integrate f for all elements of type "type"
	template <ElementType type>
	void integrate(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom, GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// integrate scalar field in_f
	template <ElementType type, UInt polynomial_degree>
	Real integrate(const Array<Real> & in_f,
	GhostType ghost_type = _not_ghost) const;

	/// integrate partially around a quadrature point (@f$ intf_q = f_q * J_q *
	/// w_q @f$)
	template <ElementType type>
	Real integrate(const Vector<Real> & in_f, UInt index,
	GhostType ghost_type) const;

	/// integrate scalar field in_f
	template <ElementType type>
	Real integrate(const Array<Real> & in_f, GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// integrate a field without using the pre-computed values
	template <ElementType type, UInt polynomial_degree>
	void integrate(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom, GhostType ghost_type) const;

	/// integrate partially around a quadrature point (@f$ intf_q = f_q * J_q *
	/// w_q @f$)
	template <ElementType type>
	- void integrateOnIntegrationPoints(const Array<Real> & in_f,
	- Array<Real> & intf,
	- UInt nb_degree_of_freedom,
	- GhostType ghost_type,
	- const Array<UInt> & filter_elements) const;
	+ void
	+ integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	+ UInt nb_degree_of_freedom, GhostType ghost_type,
	+ const Array<UInt> & filter_elements) const;

	/// return a matrix with quadrature points natural coordinates
	template <ElementType type>
	const Matrix<Real> & getIntegrationPoints(GhostType ghost_type) const;

	/// return number of quadrature points
	template <ElementType type>
	UInt getNbIntegrationPoints(GhostType ghost_type) const;

	template <ElementType type, UInt n> Matrix<Real> getIntegrationPoints() const;
	template <ElementType type, UInt n>
	Vector<Real> getIntegrationWeights() const;

	protected:
	friend struct integrator::details::GaussIntegratorComputeJacobiansHelper<
	kind>;

	template <ElementType type>
	void computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	void computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	- Array<Real> & jacobians, ElementType type,
	- GhostType ghost_type,
	+ Array<Real> & jacobians, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// precompute jacobians on elements of type "type"
	template <ElementType type>
	void precomputeJacobiansOnQuadraturePoints(const Array<Real> & nodes,
	GhostType ghost_type);

	// multiply the jacobians by the integration weights and stores the results in
	// jacobians
	template <ElementType type, UInt polynomial_degree>
	void multiplyJacobiansByWeights(
	Array<Real> & jacobians,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// compute the vector of quadrature points natural coordinates
	template <ElementType type>
	void computeQuadraturePoints(GhostType ghost_type);

	/// check that the jacobians are not negative
	- template <ElementType type>
	- void checkJacobians(GhostType ghost_type) const;
	+ template <ElementType type> void checkJacobians(GhostType ghost_type) const;

	/// internal integrate partially around a quadrature point (@f$ intf_q = f_q *
	/// J_q *
	/// w_q @f$)
	void integrateOnIntegrationPoints(const Array<Real> & in_f,
	Array<Real> & intf,
	UInt nb_degree_of_freedom,
	const Array<Real> & jacobians,
	UInt nb_element) const;

	void integrate(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom, const Array<Real> & jacobians,
	UInt nb_element) const;

	public:
	/// compute the jacobians on quad points for a given element
	template <ElementType type>
	void computeJacobianOnQuadPointsByElement(const Matrix<Real> & node_coords,
	const Matrix<Real> & quad,
	Vector<Real> & jacobians) const;

	public:
	void onElementsAdded(const Array<Element> & elements) override;

	template <ElementType type>
	void onElementsAddedByType(const Array<UInt> & new_elements,
	GhostType ghost_type);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// integrate the field f with the jacobian jac -> inte
	inline void integrate(Real * f, Real * jac, Real * inte,
	UInt nb_degree_of_freedom,
	UInt nb_quadrature_points) const;

	private:
	/// ElementTypeMap of the quadrature points
	ElementTypeMap<Matrix<Real>> quadrature_points;
	};

	} // namespace akantu

	#include "integrator_gauss_inline_impl.hh"

	#endif /* AKANTU_INTEGRATOR_GAUSS_HH_ */
	diff --git a/src/fe_engine/integrator_gauss_inline_impl.hh b/src/fe_engine/integrator_gauss_inline_impl.hh
	index e743f55a9..dc3787092 100644
	--- a/src/fe_engine/integrator_gauss_inline_impl.hh
	+++ b/src/fe_engine/integrator_gauss_inline_impl.hh
	@@ -1,765 +1,765 @@
	/**
	* @file integrator_gauss_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Tue Oct 27 2020
	*
	* @brief inline function of gauss integrator
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "mesh_iterators.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace debug {
	struct IntegratorGaussException : public Exception {};
	} // namespace debug
	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrateOnElement(
	const Array<Real> & f, Real * intf, UInt nb_degree_of_freedom,
	const UInt elem, GhostType ghost_type) const {
	Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points = ElementClass<type>::getNbQuadraturePoints();
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f do not have the good number of component.");

	Real * f_val = f.storage() + elem * f.getNbComponent();
	Real * jac_val = jac_loc.storage() + elem * nb_quadrature_points;

	integrate(f_val, jac_val, intf, nb_degree_of_freedom, nb_quadrature_points);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Vector<Real> & in_f, UInt index, GhostType ghost_type) const {
	const Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points =
	GaussIntegrationElement<type>::getNbQuadraturePoints();
	AKANTU_DEBUG_ASSERT(in_f.size() == nb_quadrature_points,
	"The vector f do not have nb_quadrature_points entries.");

	Real * jac_val = jac_loc.storage() + index * nb_quadrature_points;
	Real intf;

	integrate(in_f.storage(), jac_val, &intf, 1, nb_quadrature_points);

	return intf;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	Real * f, Real * jac, Real * inte, UInt nb_degree_of_freedom,
	UInt nb_quadrature_points) const {
	std::fill_n(inte, nb_degree_of_freedom, 0.);

	Real * cjac = jac;
	for (UInt q = 0; q < nb_quadrature_points; ++q) {
	for (UInt dof = 0; dof < nb_degree_of_freedom; ++dof) {
	inte[dof] += f *cjac;
	++f;
	}
	++cjac;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline const Matrix<Real> &
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints(
	GhostType ghost_type) const {
	AKANTU_DEBUG_ASSERT(
	quadrature_points.exists(type, ghost_type),
	"Quadrature points for type "
	<< quadrature_points.printType(type, ghost_type)
	<< " have not been initialized."
	<< " Did you use 'computeQuadraturePoints' function ?");
	return quadrature_points(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline UInt
	IntegratorGauss<kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
	GhostType ghost_type) const {
	AKANTU_DEBUG_ASSERT(
	quadrature_points.exists(type, ghost_type),
	"Quadrature points for type "
	<< quadrature_points.printType(type, ghost_type)
	<< " have not been initialized."
	<< " Did you use 'computeQuadraturePoints' function ?");
	return quadrature_points(type, ghost_type).cols();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	inline Matrix<Real>
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints() const {
	return GaussIntegrationElement<type,
	polynomial_degree>::getQuadraturePoints();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	inline Vector<Real>
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationWeights() const {
	return GaussIntegrationElement<type, polynomial_degree>::getWeights();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void
	IntegratorGauss<kind, IntegrationOrderFunctor>::computeQuadraturePoints(
	GhostType ghost_type) {
	Matrix<Real> & quads = quadrature_points(type, ghost_type);
	const UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();
	quads =
	GaussIntegrationElement<type, polynomial_degree>::getQuadraturePoints();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobianOnQuadPointsByElement(const Matrix<Real> & node_coords,
	const Matrix<Real> & quad,
	Vector<Real> & jacobians) const {
	// jacobian
	ElementClass<type>::computeJacobian(quad, node_coords, jacobians);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	IntegratorGauss<kind, IntegrationOrderFunctor>::IntegratorGauss(
	const Mesh & mesh, UInt spatial_dimension, const ID & id)
	: Integrator(mesh, spatial_dimension, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::checkJacobians(
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->quadrature_points(type, ghost_type).cols();

	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	Real * jacobians_val = jacobians(type, ghost_type).storage();

	for (UInt i = 0; i < nb_element * nb_quadrature_points;
	++i, ++jacobians_val) {
	if (*jacobians_val < 0) {
	AKANTU_CUSTOM_EXCEPTION_INFO(debug::IntegratorGaussException{},
	"Negative jacobian computed,"
	<< " possible problem in the element "
	"node ordering (Quadrature Point "
	<< i % nb_quadrature_points << ":"
	<< i / nb_quadrature_points << ":"
	<< type << ":" << ghost_type << ")");
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points = quad_points.cols();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_it =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);
	auto jacobians_begin = jacobians_it;

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	nb_element = x_el.size();

	// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
	const Matrix<Real> & x = *x_it;

	if (filter_elements != empty_filter) {
	jacobians_it = jacobians_begin + filter_elements(elem);
	}

	Vector<Real> & J = *jacobians_it;
	computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);

	if (filter_elements == empty_filter) {
	++jacobians_it;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	template <>
	template <ElementType type>
	void IntegratorGauss<_ek_structural, DefaultIntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	const UInt spatial_dimension = mesh.getSpatialDimension();
	const UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const UInt nb_quadrature_points = quad_points.cols();
	const UInt nb_dofs = ElementClass<type>::getNbDegreeOfFreedom();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_it =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);
	auto jacobians_begin = jacobians_it;

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	nb_element = x_el.size();

	const bool has_extra_normal =
	mesh.hasData<Real>("extra_normal", type, ghost_type);
	Array<Real>::const_vector_iterator extra_normal;
	Array<Real>::const_vector_iterator extra_normal_begin;
	if (has_extra_normal) {
	extra_normal = mesh.getData<Real>("extra_normal", type, ghost_type)
	.begin(spatial_dimension);
	extra_normal_begin = extra_normal;
	}

	// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
	if (filter_elements != empty_filter) {
	jacobians_it = jacobians_begin + filter_elements(elem);
	extra_normal = extra_normal_begin + filter_elements(elem);
	}

	const Matrix<Real> & X = *x_it;
	Vector<Real> & J = *jacobians_it;
	Matrix<Real> R(nb_dofs, nb_dofs);

	if (has_extra_normal) {
	ElementClass<type>::computeRotationMatrix(R, X, *extra_normal);
	} else {
	ElementClass<type>::computeRotationMatrix(R, X, Vector<Real>(X.rows()));
	}
	// Extracting relevant lines
	auto x = (R.block(0, 0, spatial_dimension, spatial_dimension) * X)
	.block(0, 0, ElementClass<type>::getNaturalSpaceDimension(),
	ElementClass<type>::getNbNodesPerElement());

	computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);

	if (filter_elements == empty_filter) {
	++jacobians_it;
	++extra_normal;
	}
	}

	AKANTU_DEBUG_OUT();
	}
	#endif

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <>
	template <ElementType type>
	void IntegratorGauss<_ek_cohesive, DefaultIntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points = quad_points.cols();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_begin =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	UInt nb_nodes_per_subelement = nb_nodes_per_element / 2;
	Matrix<Real> x(spatial_dimension, nb_nodes_per_subelement);

	nb_element = x_el.size();
	UInt l_el = 0;
	auto compute = [&](const auto & el) {
	Vector<Real> J(jacobians_begin[el]);
	Matrix<Real> X(x_it[l_el]);
	++l_el;

	for (UInt n = 0; n < nb_nodes_per_subelement; ++n) {
	Vector<Real>(x(n)) =
	(Vector<Real>(X(n)) + Vector<Real>(X(n + nb_nodes_per_subelement))) /
	2.;
	}

	if (type == _cohesive_1d_2) {
	J(0) = 1;
	} else {
	this->computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);
	}
	};

	for_each_element(nb_element, filter_elements, compute);

	AKANTU_DEBUG_OUT();
	}
	#endif
	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	precomputeJacobiansOnQuadraturePoints(const Array<Real> & nodes,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Array<Real> & jacobians_tmp = jacobians.alloc(0, 1, type, ghost_type);

	this->computeJacobiansOnIntegrationPoints<type>(
	nodes, quadrature_points(type, ghost_type), jacobians_tmp, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::multiplyJacobiansByWeights(
	Array<Real> & jacobians, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points =
	GaussIntegrationElement<type, polynomial_degree>::getNbQuadraturePoints();

	Vector<Real> weights =
	GaussIntegrationElement<type, polynomial_degree>::getWeights();

	auto && view = make_view(jacobians, nb_quadrature_points);

	if (filter_elements != empty_filter) {
	auto J_it = view.begin();
	for (auto el : filter_elements) {
	Vector<Real> J(J_it[el]);
	J *= weights;
	}
	} else {
	for (auto & J : make_view(jacobians, nb_quadrature_points)) {
	J *= weights;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	const Array<Real> & jacobians, UInt nb_element) const {
	AKANTU_DEBUG_IN();

	intf.resize(nb_element);
	if (nb_element == 0) {
	return;
	}

	UInt nb_points = jacobians.size() / nb_element;

	Array<Real>::const_matrix_iterator J_it;
	Array<Real>::matrix_iterator inte_it;
	Array<Real>::const_matrix_iterator f_it;

	f_it = in_f.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);
	inte_it = intf.begin_reinterpret(nb_degree_of_freedom, 1, nb_element);
	J_it = jacobians.begin_reinterpret(nb_points, 1, nb_element);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Matrix<Real> & f = *f_it;
	const Matrix<Real> & J = *J_it;
	Matrix<Real> & inte_f = *inte_it;

	inte_f.mul<false, false>(f, J);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	const Array<Real> & jac_loc = jacobians(type, ghost_type);
	if (filter_elements != empty_filter) {
	UInt nb_element = filter_elements.size();
	auto * filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);
	this->integrate(in_f, intf, nb_degree_of_freedom, *filtered_J, nb_element);
	delete filtered_J;
	} else {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	this->integrate(in_f, intf, nb_degree_of_freedom, jac_loc, nb_element);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	Matrix<Real> quads = this->getIntegrationPoints<type, polynomial_degree>();

	Array<Real> jacobians;
	this->computeJacobiansOnIntegrationPoints<type>(mesh.getNodes(), quads,
	jacobians, ghost_type);
	this->multiplyJacobiansByWeights<type, polynomial_degree>(jacobians);

	this->integrate(in_f, intf, nb_degree_of_freedom, jacobians,
	mesh.getNbElement(type, ghost_type));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	Array<Real> intfv(0, 1);
	integrate<type, polynomial_degree>(in_f, intfv, 1, ghost_type);

	Real res = Math::reduce(intfv);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	Array<Real> intfv(0, 1);
	integrate<type>(in_f, intfv, 1, ghost_type, filter_elements);

	Real res = Math::reduce(intfv);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom,
	const Array<Real> & jacobians,
	UInt nb_element) const {
	AKANTU_DEBUG_IN();

	UInt nb_points = jacobians.size() / nb_element;

	intf.resize(nb_element * nb_points);

	auto J_it = jacobians.begin();
	auto f_it = in_f.begin(nb_degree_of_freedom);
	auto inte_it = intf.begin(nb_degree_of_freedom);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Real & J = *J_it;
	const Vector<Real> & f = *f_it;
	Vector<Real> & inte_f = *inte_it;

	inte_f = f;
	inte_f *= J;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	const Array<Real> & jac_loc = this->jacobians(type, ghost_type);

	if (filter_elements != empty_filter) {

	UInt nb_element = filter_elements.size();
	auto * filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);

	this->integrateOnIntegrationPoints(in_f, intf, nb_degree_of_freedom,
	*filtered_J, nb_element);
	} else {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	this->integrateOnIntegrationPoints(in_f, intf, nb_degree_of_freedom,
	jac_loc, nb_element);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void
	IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAddedByType(
	const Array<UInt> & elements, GhostType ghost_type) {
	const auto & nodes = mesh.getNodes();

	if (not quadrature_points.exists(type, ghost_type)) {
	computeQuadraturePoints<type>(ghost_type);
	}

	if (not jacobians.exists(type, ghost_type)) {
	jacobians.alloc(0, 1, type, ghost_type);
	}

	this->computeJacobiansOnIntegrationPoints(
	nodes, quadrature_points(type, ghost_type), jacobians(type, ghost_type),
	type, ghost_type, elements);

	constexpr UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();

	multiplyJacobiansByWeights<type, polynomial_degree>(
	this->jacobians(type, ghost_type), elements);
	}

	/* -------------------------------------------------------------------------- */
	namespace integrator {
	namespace details {
	template <ElementKind kind> struct IntegratorOnElementsAddedHelper {};

	#define ON_ELEMENT_ADDED(type) \
	integrator.template onElementsAddedByType<type>(elements, ghost_type);

	#define AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER(kind) \
	template <> struct IntegratorOnElementsAddedHelper<kind> { \
	template <class I> \
	static void call(I & integrator, const Array<UInt> & elements, \
	ElementType type, GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ON_ELEMENT_ADDED, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER)

	#undef AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER
	#undef ON_ELEMENT_ADDED
	} // namespace details
	} // namespace integrator

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAdded(
	const Array<Element> & new_elements) {
	for (auto elements_range : MeshElementsByTypes(new_elements)) {
	auto type = elements_range.getType();
	auto ghost_type = elements_range.getGhostType();

	if (mesh.getSpatialDimension(type) != _spatial_dimension) {
	continue;
	}

	if (mesh.getKind(type) != kind) {
	continue;
	}

	integrator::details::IntegratorOnElementsAddedHelper<kind>::call(
	*this, elements_range.getElements(), type, ghost_type);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
	const Array<Real> & nodes, GhostType ghost_type) {
	computeQuadraturePoints<type>(ghost_type);
	precomputeJacobiansOnQuadraturePoints<type>(nodes, ghost_type);
	checkJacobians<type>(ghost_type);
	constexpr UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();
	multiplyJacobiansByWeights<type, polynomial_degree>(
	this->jacobians(type, ghost_type));
	}

	namespace integrator {
	namespace details {
	template <ElementKind kind> struct GaussIntegratorInitHelper {};

	#define INIT_INTEGRATOR(type) \
	_int.template initIntegrator<type>(nodes, ghost_type)

	#define AKANTU_GAUSS_INTERGRATOR_INIT_HELPER(kind) \
	template <> struct GaussIntegratorInitHelper<kind> { \
	template <ElementKind k, class IOF> \
	static void call(IntegratorGauss<k, IOF> & _int, \
	const Array<Real> & nodes, ElementType type, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INIT_INTEGRATOR, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_GAUSS_INTERGRATOR_INIT_HELPER)

	#undef AKANTU_GAUSS_INTERGRATOR_INIT_HELPER
	#undef INIT_INTEGRATOR
	} // namespace details
	} // namespace integrator

	template <ElementKind kind, class IntegrationOrderFunctor>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
	const Array<Real> & nodes, ElementType type, GhostType ghost_type) {
	integrator::details::GaussIntegratorInitHelper<kind>::call(*this, nodes, type,
	ghost_type);
	}

	namespace integrator {
	namespace details {
	template <ElementKind kind> struct GaussIntegratorComputeJacobiansHelper {};

	#define AKANTU_COMPUTE_JACOBIANS(type) \
	_int.template computeJacobiansOnIntegrationPoints<type>( \
	nodes, quad_points, jacobians, ghost_type, filter_elements);

	#define AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS(kind) \
	template <> struct GaussIntegratorComputeJacobiansHelper<kind> { \
	template <ElementKind k, class IOF> \
	static void \
	call(const IntegratorGauss<k, IOF> & _int, const Array<Real> & nodes, \
	const Matrix<Real> & quad_points, Array<Real> & jacobians, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(AKANTU_COMPUTE_JACOBIANS, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS)

	#undef AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS
	#undef AKANTU_COMPUTE_JACOBIANS
	} // namespace details
	} // namespace integrator

	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	integrator::details::GaussIntegratorComputeJacobiansHelper<kind>::call(
	*this, nodes, quad_points, jacobians, type, ghost_type, filter_elements);
	}

	} // namespace akantu
	diff --git a/src/fe_engine/interpolation_element_tmpl.hh b/src/fe_engine/interpolation_element_tmpl.hh
	index 13ce075a3..74afdfeeb 100644
	--- a/src/fe_engine/interpolation_element_tmpl.hh
	+++ b/src/fe_engine/interpolation_element_tmpl.hh
	@@ -1,74 +1,74 @@
	/**
	* @file interpolation_element_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 06 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief interpolation property description
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTERPOLATION_ELEMENT_TMPL_HH_
	#define AKANTU_INTERPOLATION_ELEMENT_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Regular Elements */
	/* -------------------------------------------------------------------------- */
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_not_defined, _itk_not_defined, 0,
	0);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_point_1,
	_itk_lagrangian, 1, 0);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_segment_2,
	_itk_lagrangian, 2, 1);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_segment_3,
	_itk_lagrangian, 3, 1);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_triangle_3,
	_itk_lagrangian, 3, 2);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_triangle_6,
	_itk_lagrangian, 6, 2);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_tetrahedron_4,
	_itk_lagrangian, 4, 3);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_tetrahedron_10,
	_itk_lagrangian, 10, 3);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_quadrangle_4,
	_itk_lagrangian, 4, 2);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_serendip_quadrangle_8,
	_itk_lagrangian, 8, 2);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_hexahedron_8,
	_itk_lagrangian, 8, 3);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_serendip_hexahedron_20,
	_itk_lagrangian, 20, 3);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_pentahedron_6,
	_itk_lagrangian, 6, 3);
	AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(_itp_lagrange_pentahedron_15,
	_itk_lagrangian, 15, 3);

	} // namespace akantu
	#endif /* AKANTU_INTERPOLATION_ELEMENT_TMPL_HH_ */
	diff --git a/src/fe_engine/shape_cohesive.hh b/src/fe_engine/shape_cohesive.hh
	index e5dab2beb..570c179cd 100644
	--- a/src/fe_engine/shape_cohesive.hh
	+++ b/src/fe_engine/shape_cohesive.hh
	@@ -1,191 +1,191 @@
	/**
	* @file shape_cohesive.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Fri May 14 2021
	*
	* @brief shape functions for cohesive elements description
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "shape_lagrange.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_COHESIVE_HH_
	#define AKANTU_SHAPE_COHESIVE_HH_

	namespace akantu {

	struct CohesiveReduceFunctionMean {
	inline Real operator()(Real u_plus, Real u_minus) {
	return .5 * (u_plus + u_minus);
	}
	};

	struct CohesiveReduceFunctionOpening {
	inline Real operator()(Real u_plus, Real u_minus) {
	return (u_plus - u_minus);
	}
	};

	template <> class ShapeLagrange<_ek_cohesive> : public ShapeLagrangeBase {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ShapeLagrange(const Mesh & mesh, UInt spatial_dimension,
	const ID & id = "shape_cohesive");

	~ShapeLagrange() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline void initShapeFunctions(const Array<Real> & nodes,
	const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type);

	/// extract the nodal values and store them per element
	template <ElementType type, class ReduceFunction>
	void extractNodalToElementField(
	const Array<Real> & nodal_f, Array<Real> & elemental_f,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// computes the shape functions derivatives for given interpolation points
	template <ElementType type>
	void computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	void computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const override;

	/// pre compute all shapes on the element integration points from natural
	/// coordinates
	template <ElementType type>
	void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// pre compute all shape derivatives on the element integration points from
	/// natural coordinates
	template <ElementType type>
	void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// interpolate nodal values on the integration points
	template <ElementType type, class ReduceFunction>
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	template <ElementType type>
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const {
	interpolateOnIntegrationPoints<type, CohesiveReduceFunctionMean>(
	u, uq, nb_degree_of_freedom, ghost_type, filter_elements);
	}

	/// compute the gradient of u on the integration points in the natural
	/// coordinates
	template <ElementType type>
	void gradientOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const {
	variationOnIntegrationPoints<type, CohesiveReduceFunctionMean>(
	u, nablauq, nb_degree_of_freedom, ghost_type, filter_elements);
	}

	/* ------------------------------------------------------------------------ */
	template <ElementType type>
	void computeBtD(const Array<Real> & /Ds/, Array<Real> & /BtDs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <ElementType type>
	void computeBtDB(const Array<Real> & /Ds/, Array<Real> & /BtDBs/,
	UInt /order_d/, GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// multiply a field by shape functions
	template <ElementType type>
	void
	computeNtb(const Array<Real> & /bs/, Array<Real> & /Ntbs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/ = empty_filter) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <ElementType type>
	void computeNtbN(const Array<Real> & /bs/, Array<Real> & /NtbNs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/* ------------------------------------------------------------------------ */
	/// compute the gradient of u on the integration points
	template <ElementType type, class ReduceFunction>
	void variationOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// compute the normals to the field u on integration points
	template <ElementType type, class ReduceFunction>
	void computeNormalsOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & normals_u,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;
	};

	/// standard output stream operator
	template <class ShapeFunction>
	inline std::ostream & operator<<(std::ostream & stream,
	const ShapeCohesive<ShapeFunction> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "shape_cohesive_inline_impl.hh"

	#endif /* AKANTU_SHAPE_COHESIVE_HH_ */
	diff --git a/src/fe_engine/shape_cohesive_inline_impl.hh b/src/fe_engine/shape_cohesive_inline_impl.hh
	index b4ad63c0f..4373a08a0 100644
	--- a/src/fe_engine/shape_cohesive_inline_impl.hh
	+++ b/src/fe_engine/shape_cohesive_inline_impl.hh
	@@ -1,333 +1,333 @@
	/**
	* @file shape_cohesive_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Feb 03 2012
	* @date last modification: Tue Sep 29 2020
	*
	* @brief ShapeCohesive inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_iterators.hh"
	#include "shape_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_COHESIVE_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_COHESIVE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline ShapeLagrange<_ek_cohesive>::ShapeLagrange(const Mesh & mesh,
	UInt spatial_dimension,
	const ID & id)
	: ShapeLagrangeBase(mesh, spatial_dimension, _ek_cohesive, id) {}

	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type);

	/* -------------------------------------------------------------------------- */
	inline void ShapeLagrange<_ek_cohesive>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type) {
	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_cohesive>::computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & /unused/, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();
	UInt spatial_dimension = ElementClass<type>::getNaturalSpaceDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt nb_points = integration_points.cols();
	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	AKANTU_DEBUG_ASSERT(shape_derivatives.getNbComponent() == size_of_shapesd,
	"The shapes_derivatives array does not have the correct "
	<< "number of component");

	shape_derivatives.resize(nb_element * nb_points);
	Real * shapesd_val = shape_derivatives.storage();

	auto compute = [&](const auto & el) {
	auto ptr = shapesd_val + el * nb_points * size_of_shapesd;
	Tensor3<Real> B(ptr, spatial_dimension, nb_nodes_per_element, nb_points);
	ElementClass<type>::computeDNDS(integration_points, B);
	};

	for_each_element(nb_element, filter_elements, compute);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline void
	ShapeLagrange<_ek_cohesive>::computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	- Array<Real> & shape_derivatives, ElementType type,
	- GhostType ghost_type, const Array<UInt> & filter_elements) const {
	+ Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
	+ const Array<UInt> & filter_elements) const {
	#define AKANTU_COMPUTE_SHAPES(type) \
	computeShapeDerivativesOnIntegrationPoints<type>( \
	nodes, integration_points, shape_derivatives, ghost_type, \
	filter_elements);

	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(AKANTU_COMPUTE_SHAPES);

	#undef AKANTU_COMPUTE_SHAPES
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_cohesive>::precomputeShapesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	Matrix<Real> & natural_coords = integration_points(type, ghost_type);
	UInt size_of_shapes = ElementClass<type>::getShapeSize();

	Array<Real> & shapes_tmp =
	shapes.alloc(0, size_of_shapes, itp_type, ghost_type);

	this->computeShapesOnIntegrationPoints<type>(nodes, natural_coords,
	shapes_tmp, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_cohesive>::precomputeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	Matrix<Real> & natural_coords = integration_points(type, ghost_type);
	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();

	Array<Real> & shapes_derivatives_tmp =
	shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);

	this->computeShapeDerivativesOnIntegrationPoints<type>(
	nodes, natural_coords, shapes_derivatives_tmp, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, class ReduceFunction>
	void ShapeLagrange<_ek_cohesive>::extractNodalToElementField(
	const Array<Real> & nodal_f, Array<Real> & elemental_f,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_itp_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	UInt nb_degree_of_freedom = nodal_f.getNbComponent();
	UInt nb_element = this->mesh.getNbElement(type, ghost_type);

	const auto & conn_array = this->mesh.getConnectivity(type, ghost_type);
	auto conn = conn_array.begin(conn_array.getNbComponent() / 2, 2);

	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	elemental_f.resize(nb_element);

	Array<Real>::matrix_iterator u_it =
	elemental_f.begin(nb_degree_of_freedom, nb_nodes_per_itp_element);

	ReduceFunction reduce_function;

	auto compute = [&](const auto & el) {
	Matrix<Real> & u = *u_it;
	Matrix<UInt> el_conn(conn[el]);

	// compute the average/difference of the nodal field loaded from cohesive
	// element
	for (UInt n = 0; n < el_conn.rows(); ++n) {
	UInt node_plus = el_conn(n, 0);
	UInt node_minus = el_conn(n, 1);
	for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
	Real u_plus = nodal_f(node_plus, d);
	Real u_minus = nodal_f(node_minus, d);
	u(d, n) = reduce_function(u_plus, u_minus);
	}
	}

	++u_it;
	};

	for_each_element(nb_element, filter_elements, compute);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, class ReduceFunction>
	void ShapeLagrange<_ek_cohesive>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	AKANTU_DEBUG_ASSERT(this->shapes.exists(itp_type, ghost_type),
	"No shapes for the type "
	<< this->shapes.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	this->extractNodalToElementField<type, ReduceFunction>(in_u, u_el, ghost_type,
	filter_elements);

	this->template interpolateElementalFieldOnIntegrationPoints<type>(
	u_el, out_uq, ghost_type, shapes(itp_type, ghost_type), filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, class ReduceFunction>
	void ShapeLagrange<_ek_cohesive>::variationOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	AKANTU_DEBUG_ASSERT(
	this->shapes_derivatives.exists(itp_type, ghost_type),
	"No shapes for the type "
	<< this->shapes_derivatives.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	this->extractNodalToElementField<type, ReduceFunction>(in_u, u_el, ghost_type,
	filter_elements);

	this->template gradientElementalFieldOnIntegrationPoints<type>(
	u_el, nablauq, ghost_type, shapes_derivatives(itp_type, ghost_type),
	filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type, class ReduceFunction>
	void ShapeLagrange<_ek_cohesive>::computeNormalsOnIntegrationPoints(
	- const Array<Real> & u, Array<Real> & normals_u,
	- GhostType ghost_type, const Array<UInt> & filter_elements) const {
	+ const Array<Real> & u, Array<Real> & normals_u, GhostType ghost_type,
	+ const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_element = this->mesh.getNbElement(type, ghost_type);
	UInt nb_points = this->integration_points(type, ghost_type).cols();
	UInt spatial_dimension = this->mesh.getSpatialDimension();

	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	normals_u.resize(nb_points * nb_element);

	Array<Real> tangents_u(0, (spatial_dimension * (spatial_dimension - 1)));

	if (spatial_dimension > 1) {
	tangents_u.resize(nb_element * nb_points);
	this->template variationOnIntegrationPoints<type, ReduceFunction>(
	u, tangents_u, spatial_dimension, ghost_type, filter_elements);
	}

	Real * tangent = tangents_u.storage();

	if (spatial_dimension == 3) {
	for (auto & normal : make_view(normals_u, spatial_dimension)) {
	Math::vectorProduct3(tangent, tangent + spatial_dimension,
	normal.storage());

	normal /= normal.norm();
	tangent += spatial_dimension * 2;
	}
	} else if (spatial_dimension == 2) {
	for (auto & normal : make_view(normals_u, spatial_dimension)) {
	Vector<Real> a1(tangent, spatial_dimension);

	normal(0) = -a1(1);
	normal(1) = a1(0);
	normal.normalize();

	tangent += spatial_dimension;
	}
	} else if (spatial_dimension == 1) {
	const auto facet_type = Mesh::getFacetType(type);
	const auto & mesh_facets = mesh.getMeshFacets();
	const auto & facets = mesh_facets.getSubelementToElement(type, ghost_type);
	const auto & segments =
	mesh_facets.getElementToSubelement(facet_type, ghost_type);

	Real values[2];

	for (auto el : arange(nb_element)) {
	if (filter_elements != empty_filter) {
	el = filter_elements(el);
	}

	for (UInt p = 0; p < 2; ++p) {
	Element facet = facets(el, p);
	Element segment = segments(facet.element)[0];
	Vector<Real> barycenter(values + p, 1);
	mesh.getBarycenter(segment, barycenter);
	}

	Real difference = values[0] - values[1];

	AKANTU_DEBUG_ASSERT(difference != 0.,
	"Error in normal computation for cohesive elements");

	normals_u(el) = difference / std::abs(difference);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_SHAPE_COHESIVE_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/shape_functions.cc b/src/fe_engine/shape_functions.cc
	index b09fcafc6..9d64c58bb 100644
	--- a/src/fe_engine/shape_functions.cc
	+++ b/src/fe_engine/shape_functions.cc
	@@ -1,243 +1,243 @@
	/**
	* @file shape_functions.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 09 2017
	* @date last modification: Tue Feb 09 2021
	*
	* @brief implementation of th shape functions interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_functions.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ShapeFunctions::ShapeFunctions(const Mesh & mesh, UInt spatial_dimension,
	const ID & id)
	: shapes("shapes_generic", id),
	- shapes_derivatives("shapes_derivatives_generic", id),
	- mesh(mesh), _spatial_dimension(spatial_dimension) {}
	+ shapes_derivatives("shapes_derivatives_generic", id), mesh(mesh),
	+ _spatial_dimension(spatial_dimension) {}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void
	ShapeFunctions::initElementalFieldInterpolationFromIntegrationPoints(
	const Array<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	- const Array<Real> & quadrature_points_coordinates,
	- GhostType ghost_type, const Array<UInt> & element_filter) const {
	+ const Array<Real> & quadrature_points_coordinates, GhostType ghost_type,
	+ const Array<UInt> & element_filter) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = this->mesh.getSpatialDimension();
	UInt nb_element = this->mesh.getNbElement(type, ghost_type);
	UInt nb_element_filter;

	if (element_filter == empty_filter) {
	nb_element_filter = nb_element;
	} else {
	nb_element_filter = element_filter.size();
	}

	auto nb_quad_per_element =
	GaussIntegrationElement<type>::getNbQuadraturePoints();
	auto nb_interpolation_points_per_elem =
	interpolation_points_coordinates.size() / nb_element;

	AKANTU_DEBUG_ASSERT(interpolation_points_coordinates.size() % nb_element == 0,
	"Number of interpolation points should be a multiple of "
	"total number of elements");

	if (not quad_points_coordinates_inv_matrices.exists(type, ghost_type)) {
	quad_points_coordinates_inv_matrices.alloc(
	nb_element_filter, nb_quad_per_element * nb_quad_per_element, type,
	ghost_type);
	} else {
	quad_points_coordinates_inv_matrices(type, ghost_type)
	.resize(nb_element_filter);
	}

	if (!interpolation_points_coordinates_matrices.exists(type, ghost_type)) {
	interpolation_points_coordinates_matrices.alloc(
	nb_element_filter,
	nb_interpolation_points_per_elem * nb_quad_per_element, type,
	ghost_type);
	} else {
	interpolation_points_coordinates_matrices(type, ghost_type)
	.resize(nb_element_filter);
	}

	Array<Real> & quad_inv_mat =
	quad_points_coordinates_inv_matrices(type, ghost_type);
	Array<Real> & interp_points_mat =
	interpolation_points_coordinates_matrices(type, ghost_type);

	Matrix<Real> quad_coord_matrix(nb_quad_per_element, nb_quad_per_element);

	Array<Real>::const_matrix_iterator quad_coords_it =
	quadrature_points_coordinates.begin_reinterpret(
	spatial_dimension, nb_quad_per_element, nb_element_filter);

	Array<Real>::const_matrix_iterator points_coords_begin =
	interpolation_points_coordinates.begin_reinterpret(
	spatial_dimension, nb_interpolation_points_per_elem, nb_element);

	Array<Real>::matrix_iterator inv_quad_coord_it =
	quad_inv_mat.begin(nb_quad_per_element, nb_quad_per_element);

	Array<Real>::matrix_iterator int_points_mat_it = interp_points_mat.begin(
	nb_interpolation_points_per_elem, nb_quad_per_element);

	/// loop over the elements of the current material and element type
	for (UInt el = 0; el < nb_element_filter;
	++el, ++inv_quad_coord_it, ++int_points_mat_it, ++quad_coords_it) {
	/// matrix containing the quadrature points coordinates
	const Matrix<Real> & quad_coords = *quad_coords_it;
	/// matrix to store the matrix inversion result
	Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

	/// insert the quad coordinates in a matrix compatible with the
	/// interpolation
	buildElementalFieldInterpolationMatrix<type>(quad_coords,
	quad_coord_matrix);

	/// invert the interpolation matrix
	inv_quad_coord_matrix.inverse(quad_coord_matrix);

	/// matrix containing the interpolation points coordinates
	const Matrix<Real> & points_coords =
	points_coords_begin[element_filter(el)];
	/// matrix to store the interpolation points coordinates
	/// compatible with these functions
	Matrix<Real> & inv_points_coord_matrix = *int_points_mat_it;

	/// insert the quad coordinates in a matrix compatible with the
	/// interpolation
	buildElementalFieldInterpolationMatrix<type>(points_coords,
	inv_points_coord_matrix);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ShapeFunctions::initElementalFieldInterpolationFromIntegrationPoints(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	const ElementTypeMapArray<Real> & quadrature_points_coordinates,
	const ElementTypeMapArray<UInt> * element_filter) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = this->mesh.getSpatialDimension();

	for (auto ghost_type : ghost_types) {
	auto types_iterable = mesh.elementTypes(spatial_dimension, ghost_type);
	if (element_filter != nullptr) {
	types_iterable =
	element_filter->elementTypes(spatial_dimension, ghost_type);
	}

	for (auto type : types_iterable) {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (nb_element == 0) {
	continue;
	}

	const Array<UInt> * elem_filter;
	if (element_filter != nullptr) {
	elem_filter = &((*element_filter)(type, ghost_type));
	} else {
	elem_filter = &(empty_filter);
	}

	#define AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS(type) \
	this->initElementalFieldInterpolationFromIntegrationPoints<type>( \
	interpolation_points_coordinates(type, ghost_type), \
	interpolation_points_coordinates_matrices, \
	quad_points_coordinates_inv_matrices, \
	quadrature_points_coordinates(type, ghost_type), ghost_type, \
	*elem_filter)

	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(
	AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS);
	#undef AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ShapeFunctions::interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = this->mesh.getSpatialDimension();

	auto types_iterable = mesh.elementTypes(spatial_dimension, ghost_type);
	if (element_filter != nullptr) {
	types_iterable =
	element_filter->elementTypes(spatial_dimension, ghost_type);
	}

	for (auto type : types_iterable) {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	if (nb_element == 0) {
	continue;
	}
	-
	+
	const Array<UInt> * elem_filter;
	if (element_filter != nullptr) {
	elem_filter = &((*element_filter)(type, ghost_type));
	} else {
	elem_filter = &(empty_filter);
	}

	#define AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS(type) \
	interpolateElementalFieldFromIntegrationPoints<type>( \
	field(type, ghost_type), \
	interpolation_points_coordinates_matrices(type, ghost_type), \
	quad_points_coordinates_inv_matrices(type, ghost_type), result, \
	ghost_type, *elem_filter)

	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(
	AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS);
	#undef AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/fe_engine/shape_functions.hh b/src/fe_engine/shape_functions.hh
	index b4ce221c1..66429fd4a 100644
	--- a/src/fe_engine/shape_functions.hh
	+++ b/src/fe_engine/shape_functions.hh
	@@ -1,216 +1,214 @@
	/**
	* @file shape_functions.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 29 2020
	*
	* @brief shape function class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_FUNCTIONS_HH_
	#define AKANTU_SHAPE_FUNCTIONS_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-class ShapeFunctions {
	+class ShapeFunctions {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ShapeFunctions(const Mesh & mesh, UInt spatial_dimension,
	const ID & id = "shape");
	virtual ~ShapeFunctions() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}
	stream << space << "Shapes [" << std::endl;
	integration_points.printself(stream, indent + 1);
	// shapes.printself(stream, indent + 1);
	// shapes_derivatives.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	/// set the integration points for a given element
	template <ElementType type>
	void setIntegrationPointsByType(const Matrix<Real> & integration_points,
	GhostType ghost_type);

	/// Build pre-computed matrices for interpolation of field form integration
	/// points at other given positions (interpolation_points)
	void initElementalFieldInterpolationFromIntegrationPoints(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	const ElementTypeMapArray<Real> & quadrature_points_coordinates,
	const ElementTypeMapArray<UInt> * element_filter) const;

	/// Interpolate field at given position from given values of this field at
	/// integration points (field)
	/// using matrices precomputed with
	/// initElementalFieldInterplationFromIntegrationPoints
	void interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> &
	interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const ElementTypeMapArray<UInt> * element_filter) const;

	protected:
	/// interpolate nodal values stored by element on the integration points
	template <ElementType type>
	void interpolateElementalFieldOnIntegrationPoints(
	const Array<Real> & u_el, Array<Real> & uq, GhostType ghost_type,
	const Array<Real> & shapes,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// gradient of nodal values stored by element on the control points
	template <ElementType type>
	void gradientElementalFieldOnIntegrationPoints(
	- const Array<Real> & u_el, Array<Real> & out_nablauq,
	- GhostType ghost_type, const Array<Real> & shapes_derivatives,
	+ const Array<Real> & u_el, Array<Real> & out_nablauq, GhostType ghost_type,
	+ const Array<Real> & shapes_derivatives,
	const Array<UInt> & filter_elements) const;

	protected:
	/// By element versions of non-templated eponym methods
	template <ElementType type>
	inline void interpolateElementalFieldFromIntegrationPoints(
	const Array<Real> & field,
	const Array<Real> & interpolation_points_coordinates_matrices,
	const Array<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const Array<UInt> & element_filter) const;

	/// Interpolate field at given position from given values of this field at
	/// integration points (field)
	/// using matrices precomputed with
	/// initElementalFieldInterplationFromIntegrationPoints
	template <ElementType type>
	inline void initElementalFieldInterpolationFromIntegrationPoints(
	const Array<Real> & interpolation_points_coordinates,
	ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
	ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	- const Array<Real> & quadrature_points_coordinates,
	- GhostType ghost_type, const Array<UInt> & element_filter) const;
	+ const Array<Real> & quadrature_points_coordinates, GhostType ghost_type,
	+ const Array<UInt> & element_filter) const;

	/// build matrix for the interpolation of field form integration points
	template <ElementType type>
	inline void buildElementalFieldInterpolationMatrix(
	const Matrix<Real> & coordinates, Matrix<Real> & coordMatrix,
	UInt integration_order =
	ElementClassProperty<type>::polynomial_degree) const;

	/// build the so called interpolation matrix (first collumn is 1, then the
	/// other collumns are the traansposed coordinates)
	static inline void buildInterpolationMatrix(const Matrix<Real> & coordinates,
	- Matrix<Real> & coordMatrix,
	- UInt integration_order);
	+ Matrix<Real> & coordMatrix,
	+ UInt integration_order);

	public:
	virtual void onElementsAdded(const Array<Element> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	virtual void onElementsRemoved(const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the size of the shapes returned by the element class
	static inline UInt getShapeSize(ElementType type);

	/// get the size of the shapes derivatives returned by the element class
	static inline UInt getShapeDerivativesSize(ElementType type);

	- inline const Matrix<Real> &
	- getIntegrationPoints(ElementType type,
	- GhostType ghost_type) const {
	+ inline const Matrix<Real> & getIntegrationPoints(ElementType type,
	+ GhostType ghost_type) const {
	return integration_points(type, ghost_type);
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get a the shapes vector
	- inline const Array<Real> &
	- getShapes(ElementType el_type,
	- GhostType ghost_type = _not_ghost) const;
	+ inline const Array<Real> & getShapes(ElementType el_type,
	+ GhostType ghost_type = _not_ghost) const;

	/// get a the shapes derivatives vector
	inline const Array<Real> &
	getShapesDerivatives(ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// shape functions for all elements
	ElementTypeMapArray<Real, InterpolationType> shapes;

	/// shape functions derivatives for all elements
	ElementTypeMapArray<Real, InterpolationType> shapes_derivatives;

	/// associated mesh
	const Mesh & mesh;

	// spatial dimension of the elements to consider
	UInt _spatial_dimension;

	/// shape functions for all elements
	ElementTypeMap<Matrix<Real>> integration_points;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const ShapeFunctions & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu
	#include "shape_functions_inline_impl.hh"

	#endif /* AKANTU_SHAPE_FUNCTIONS_HH_ */
	diff --git a/src/fe_engine/shape_functions_inline_impl.hh b/src/fe_engine/shape_functions_inline_impl.hh
	index 5c8a09164..26e313d94 100644
	--- a/src/fe_engine/shape_functions_inline_impl.hh
	+++ b/src/fe_engine/shape_functions_inline_impl.hh
	@@ -1,416 +1,415 @@
	/**
	* @file shape_functions_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Oct 27 2010
	* @date last modification: Sat Dec 19 2020
	*
	* @brief ShapeFunctions inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "shape_functions.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> &
	-ShapeFunctions::getShapes(ElementType el_type,
	- GhostType ghost_type) const {
	+ShapeFunctions::getShapes(ElementType el_type, GhostType ghost_type) const {
	return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> &
	ShapeFunctions::getShapesDerivatives(ElementType el_type,
	GhostType ghost_type) const {
	return shapes_derivatives(FEEngine::getInterpolationType(el_type),
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt ShapeFunctions::getShapeSize(ElementType type) {
	AKANTU_DEBUG_IN();

	UInt shape_size = 0;
	#define GET_SHAPE_SIZE(type) shape_size = ElementClass<type>::getShapeSize()

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_SIZE); // ,

	#undef GET_SHAPE_SIZE

	AKANTU_DEBUG_OUT();
	return shape_size;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt ShapeFunctions::getShapeDerivativesSize(ElementType type) {
	AKANTU_DEBUG_IN();

	UInt shape_derivatives_size = 0;
	#define GET_SHAPE_DERIVATIVES_SIZE(type) \
	shape_derivatives_size = ElementClass<type>::getShapeDerivativesSize()

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_DERIVATIVES_SIZE); // ,

	#undef GET_SHAPE_DERIVATIVES_SIZE

	AKANTU_DEBUG_OUT();
	return shape_derivatives_size;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeFunctions::setIntegrationPointsByType(const Matrix<Real> & points,
	GhostType ghost_type) {
	if (not this->integration_points.exists(type, ghost_type)) {
	this->integration_points(type, ghost_type).shallowCopy(points);
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	ShapeFunctions::buildInterpolationMatrix(const Matrix<Real> & coordinates,
	Matrix<Real> & coordMatrix,
	UInt integration_order) {
	switch (integration_order) {
	case 1: {
	for (UInt i = 0; i < coordinates.cols(); ++i) {
	coordMatrix(i, 0) = 1;
	}
	break;
	}
	case 2: {
	UInt nb_quadrature_points = coordMatrix.cols();

	for (UInt i = 0; i < coordinates.cols(); ++i) {
	coordMatrix(i, 0) = 1;
	for (UInt j = 1; j < nb_quadrature_points; ++j) {
	coordMatrix(i, j) = coordinates(j - 1, i);
	}
	}
	break;
	}
	default: {
	AKANTU_TO_IMPLEMENT();
	break;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void ShapeFunctions::buildElementalFieldInterpolationMatrix(
	const Matrix<Real> & /unused/, Matrix<Real> & /unused/,
	UInt /unused/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_2>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_3>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_3>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_6>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_4>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_10>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {
	buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
	}

	/**
	* @todo Write a more efficient interpolation for quadrangles by
	* dropping unnecessary quadrature points
	*
	*/

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_4>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {

	if (integration_order !=
	ElementClassProperty<_quadrangle_4>::polynomial_degree) {
	AKANTU_TO_IMPLEMENT();
	} else {
	for (UInt i = 0; i < coordinates.cols(); ++i) {
	Real x = coordinates(0, i);
	Real y = coordinates(1, i);

	coordMatrix(i, 0) = 1;
	coordMatrix(i, 1) = x;
	coordMatrix(i, 2) = y;
	coordMatrix(i, 3) = x * y;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_8>(
	const Matrix<Real> & /unused/ coordinates,
	Matrix<Real> & /unused/ coordMatrix,
	UInt /unused/ integration_order) const {

	if (integration_order !=
	ElementClassProperty<_quadrangle_8>::polynomial_degree) {
	AKANTU_TO_IMPLEMENT();
	} else {
	for (UInt i = 0; i < coordinates.cols(); ++i) {
	// UInt j = 0;
	Real x = coordinates(0, i);
	Real y = coordinates(1, i);

	coordMatrix(i, 0) = 1;
	coordMatrix(i, 1) = x;
	coordMatrix(i, 2) = y;
	coordMatrix(i, 3) = x * y;
	// for (UInt e = 0; e <= 2; ++e) {
	// for (UInt n = 0; n <= 2; ++n) {
	// coordMatrix(i, j) = std::pow(x, e) * std::pow(y, n);
	// ++j;
	// }
	// }
	}
	}
	}
	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void ShapeFunctions::interpolateElementalFieldFromIntegrationPoints(
	const Array<Real> & field,
	const Array<Real> & interpolation_points_coordinates_matrices,
	const Array<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, GhostType ghost_type,
	const Array<UInt> & element_filter) const {
	AKANTU_DEBUG_IN();

	auto nb_element = this->mesh.getNbElement(type, ghost_type);

	auto nb_quad_per_element =
	GaussIntegrationElement<type>::getNbQuadraturePoints();
	auto nb_interpolation_points_per_elem =
	interpolation_points_coordinates_matrices.getNbComponent() /
	nb_quad_per_element;

	if (not result.exists(type, ghost_type)) {
	result.alloc(nb_element * nb_interpolation_points_per_elem,
	field.getNbComponent(), type, ghost_type);
	}

	if (element_filter != empty_filter) {
	nb_element = element_filter.size();
	}

	Matrix<Real> coefficients(nb_quad_per_element, field.getNbComponent());

	auto & result_vec = result(type, ghost_type);

	auto field_it = field.begin_reinterpret(field.getNbComponent(),
	nb_quad_per_element, nb_element);

	auto interpolation_points_coordinates_it =
	interpolation_points_coordinates_matrices.begin(
	nb_interpolation_points_per_elem, nb_quad_per_element);

	auto result_begin = result_vec.begin_reinterpret(
	field.getNbComponent(), nb_interpolation_points_per_elem,
	result_vec.size() / nb_interpolation_points_per_elem);

	auto inv_quad_coord_it = quad_points_coordinates_inv_matrices.begin(
	nb_quad_per_element, nb_quad_per_element);

	/// loop over the elements of the current filter and element type
	for (UInt el = 0; el < nb_element; ++el, ++field_it, ++inv_quad_coord_it,
	++interpolation_points_coordinates_it) {
	/**
	* matrix containing the inversion of the quadrature points'
	* coordinates
	*/
	const auto & inv_quad_coord_matrix = *inv_quad_coord_it;

	/**
	* multiply it by the field values over quadrature points to get
	* the interpolation coefficients
	*/
	coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);

	/// matrix containing the points' coordinates
	const auto & coord = *interpolation_points_coordinates_it;

	/// multiply the coordinates matrix by the coefficients matrix and store the
	/// result
	Matrix<Real> res(result_begin[element_filter(el)]);
	res.mul<true, true>(coefficients, coord);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void ShapeFunctions::interpolateElementalFieldOnIntegrationPoints(
	const Array<Real> & u_el, Array<Real> & uq, GhostType ghost_type,
	const Array<Real> & shapes, const Array<UInt> & filter_elements) const {
	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_nodes_per_element = ElementClass<type>::getShapeSize();
	auto nb_points = shapes.size() / mesh.getNbElement(type, ghost_type);
	auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;

	Array<Real>::const_matrix_iterator N_it;
	Array<Real> * filtered_N = nullptr;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	filtered_N = new Array<Real>(0, shapes.getNbComponent());
	FEEngine::filterElementalData(mesh, shapes, *filtered_N, type, ghost_type,
	filter_elements);
	N_it = filtered_N->begin_reinterpret(nb_nodes_per_element, nb_points,
	nb_element);
	} else {
	N_it =
	shapes.begin_reinterpret(nb_nodes_per_element, nb_points, nb_element);
	}

	uq.resize(nb_element * nb_points);

	auto u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
	auto inter_u_it =
	uq.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);

	for (UInt el = 0; el < nb_element; ++el, ++N_it, ++u_it, ++inter_u_it) {
	const auto & u = *u_it;
	const auto & N = *N_it;
	auto & inter_u = *inter_u_it;

	inter_u.template mul<false, false>(u, N);
	}

	delete filtered_N;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeFunctions::gradientElementalFieldOnIntegrationPoints(
	- const Array<Real> & u_el, Array<Real> & out_nablauq,
	- GhostType ghost_type, const Array<Real> & shapes_derivatives,
	+ const Array<Real> & u_el, Array<Real> & out_nablauq, GhostType ghost_type,
	+ const Array<Real> & shapes_derivatives,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	auto nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	auto nb_points = integration_points(type, ghost_type).cols();
	auto element_dimension = ElementClass<type>::getNaturalSpaceDimension();
	auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
	auto nb_element = mesh.getNbElement(type, ghost_type);

	Array<Real>::const_matrix_iterator B_it;

	Array<Real> * filtered_B = nullptr;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	filtered_B = new Array<Real>(0, shapes_derivatives.getNbComponent());
	FEEngine::filterElementalData(mesh, shapes_derivatives, *filtered_B, type,
	ghost_type, filter_elements);
	B_it = filtered_B->begin(element_dimension, nb_nodes_per_element);
	} else {
	B_it = shapes_derivatives.begin(element_dimension, nb_nodes_per_element);
	}

	out_nablauq.resize(nb_element * nb_points);
	auto u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
	auto nabla_u_it = out_nablauq.begin(nb_degree_of_freedom, element_dimension);

	for (UInt el = 0; el < nb_element; ++el, ++u_it) {
	const auto & u = *u_it;
	for (UInt q = 0; q < nb_points; ++q, ++B_it, ++nabla_u_it) {
	const auto & B = *B_it;
	auto & nabla_u = *nabla_u_it;
	nabla_u.template mul<false, true>(u, B);
	}
	}

	delete filtered_B;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/shape_lagrange.hh b/src/fe_engine/shape_lagrange.hh
	index 81f4a47c9..7d3877dcc 100644
	--- a/src/fe_engine/shape_lagrange.hh
	+++ b/src/fe_engine/shape_lagrange.hh
	@@ -1,180 +1,176 @@
	/**
	* @file shape_lagrange.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Fri May 14 2021
	*
	* @brief lagrangian shape functions class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_lagrange_base.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_LAGRANGE_HH_
	#define AKANTU_SHAPE_LAGRANGE_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Shape> class ShapeCohesive;
	class ShapeIGFEM;

	template <ElementKind kind> class ShapeLagrange : public ShapeLagrangeBase {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ShapeLagrange(const Mesh & mesh, UInt spatial_dimension,
	const ID & id = "shape_lagrange");
	~ShapeLagrange() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialization function for structural elements not yet implemented
	inline void initShapeFunctions(const Array<Real> & nodes,
	const Matrix<Real> & integration_points,
	- ElementType type,
	- GhostType ghost_type);
	+ ElementType type, GhostType ghost_type);

	/// computes the shape functions derivatives for given interpolation points
	template <ElementType type>
	void computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	void computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	- Array<Real> & shape_derivatives, ElementType type,
	- GhostType ghost_type,
	+ Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const override;

	/// pre compute all shapes on the element integration points from natural
	/// coordinates
	template <ElementType type>
	void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// pre compute all shape derivatives on the element integration points from
	/// natural coordinates
	template <ElementType type>
	- void
	- precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
	- GhostType ghost_type);
	+ void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
	+ GhostType ghost_type);

	/// interpolate nodal values on the integration points
	template <ElementType type>
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	template <ElementType type>
	void interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	const Array<Real> & shapes, GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// interpolate on physical point
	template <ElementType type>
	void interpolate(const Vector<Real> & real_coords, UInt elem,
	const Matrix<Real> & nodal_values,
	- Vector<Real> & interpolated,
	- GhostType ghost_type) const;
	+ Vector<Real> & interpolated, GhostType ghost_type) const;

	/// compute the gradient of u on the integration points
	template <ElementType type>
	void gradientOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	template <ElementType type>
	void computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	template <ElementType type>
	void computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// multiply a field by shape functions @f$ fts_{ij} = f_i * \varphi_j @f$
	template <ElementType type>
	void computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
	GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	template <ElementType type>
	void computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const;

	/// find natural coords from real coords provided an element
	template <ElementType type>
	void inverseMap(const Vector<Real> & real_coords, UInt element,
	Vector<Real> & natural_coords,
	GhostType ghost_type = _not_ghost) const;

	/// return true if the coordinates provided are inside the element, false
	/// otherwise
	template <ElementType type>
	bool contains(const Vector<Real> & real_coords, UInt elem,
	GhostType ghost_type) const;

	/// compute the shape on a provided point
	template <ElementType type>
	void computeShapes(const Vector<Real> & real_coords, UInt elem,
	Vector<Real> & shapes, GhostType ghost_type) const;

	/// compute the shape derivatives on a provided point
	template <ElementType type>
	void computeShapeDerivatives(const Matrix<Real> & real_coords, UInt elem,
	Tensor3<Real> & shapes,
	GhostType ghost_type) const;

	protected:
	/// compute the shape derivatives on integration points for a given element
	template <ElementType type>
	inline void
	computeShapeDerivativesOnCPointsByElement(const Matrix<Real> & node_coords,
	const Matrix<Real> & natural_coords,
	Tensor3<Real> & shapesd) const;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "shape_lagrange_inline_impl.hh"

	#endif /* AKANTU_SHAPE_LAGRANGE_HH_ */
	diff --git a/src/fe_engine/shape_lagrange_base.cc b/src/fe_engine/shape_lagrange_base.cc
	index c30cd5d1f..eea7946b5 100644
	--- a/src/fe_engine/shape_lagrange_base.cc
	+++ b/src/fe_engine/shape_lagrange_base.cc
	@@ -1,174 +1,173 @@
	/**
	* @file shape_lagrange_base.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 09 2017
	* @date last modification: Wed Dec 09 2020
	*
	* @brief common part for the shape lagrange
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_lagrange_base.hh"
	#include "mesh_iterators.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	ShapeLagrangeBase::ShapeLagrangeBase(const Mesh & mesh, UInt spatial_dimension,
	ElementKind kind, const ID & id)
	: ShapeFunctions(mesh, spatial_dimension, id), _kind(kind) {}

	/* -------------------------------------------------------------------------- */
	ShapeLagrangeBase::~ShapeLagrangeBase() = default;

	/* -------------------------------------------------------------------------- */
	#define AKANTU_COMPUTE_SHAPES(type) \
	_this.template computeShapesOnIntegrationPoints<type>( \
	nodes, integration_points, shapes, ghost_type, filter_elements)

	namespace shape_lagrange {
	namespace details {
	template <ElementKind kind> struct Helper {
	template <class S>
	static void call(const S & /unused/, const Array<Real> & /unused/,
	const Matrix<Real> & /unused/,
	Array<Real> & /unused/, ElementType /unused/,
	- GhostType /unused/,
	- const Array<UInt> & /unused/) {
	+ GhostType /unused/, const Array<UInt> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	#if !defined(DOXYGEN)
	#define AKANTU_COMPUTE_SHAPES_KIND(kind) \
	template <> struct Helper<kind> { \
	template <class S> \
	static void call(const S & _this, const Array<Real> & nodes, \
	const Matrix<Real> & integration_points, \
	- Array<Real> & shapes, ElementType type, \
	- GhostType ghost_type, \
	+ Array<Real> & shapes, ElementType type, \
	+ GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(AKANTU_COMPUTE_SHAPES, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND_LIST(AKANTU_COMPUTE_SHAPES_KIND,
	AKANTU_FE_ENGINE_LIST_LAGRANGE_BASE)

	} // namespace details
	} // namespace shape_lagrange
	#endif

	/* -------------------------------------------------------------------------- */
	void ShapeLagrangeBase::computeShapesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	- Array<Real> & shapes, ElementType type,
	- GhostType ghost_type, const Array<UInt> & filter_elements) const {
	+ Array<Real> & shapes, ElementType type, GhostType ghost_type,
	+ const Array<UInt> & filter_elements) const {

	auto kind = Mesh::getKind(type);

	#define AKANTU_COMPUTE_SHAPES_KIND_SWITCH(kind) \
	shape_lagrange::details::Helper<kind>::call( \
	*this, nodes, integration_points, shapes, type, ghost_type, \
	filter_elements);

	AKANTU_BOOST_LIST_SWITCH(
	AKANTU_COMPUTE_SHAPES_KIND_SWITCH,
	BOOST_PP_LIST_TO_SEQ(AKANTU_FE_ENGINE_LIST_LAGRANGE_BASE), kind);

	#undef AKANTU_COMPUTE_SHAPES
	#undef AKANTU_COMPUTE_SHAPES_KIND
	#undef AKANTU_COMPUTE_SHAPES_KIND_SWITCH
	}

	/* -------------------------------------------------------------------------- */
	void ShapeLagrangeBase::onElementsAdded(const Array<Element> & new_elements) {
	AKANTU_DEBUG_IN();
	const auto & nodes = mesh.getNodes();

	for (auto elements_range : MeshElementsByTypes(new_elements)) {
	auto type = elements_range.getType();
	auto ghost_type = elements_range.getGhostType();

	if (mesh.getSpatialDimension(type) != _spatial_dimension) {
	continue;
	}

	if (mesh.getKind(type) != _kind) {
	continue;
	}

	const auto & elements = elements_range.getElements();

	auto itp_type = FEEngine::getInterpolationType(type);

	if (not shapes.exists(itp_type, ghost_type)) {
	auto size_of_shapes = this->getShapeSize(type);
	this->shapes.alloc(0, size_of_shapes, itp_type, ghost_type);
	}

	const auto & natural_coords = integration_points(type, ghost_type);
	computeShapesOnIntegrationPoints(nodes, natural_coords,
	shapes(itp_type, ghost_type), type,
	ghost_type, elements);

	if (_spatial_dimension != mesh.getSpatialDimension()) {
	continue;
	}

	if (not this->shapes_derivatives.exists(itp_type, ghost_type)) {
	auto size_of_shapesd = this->getShapeDerivativesSize(type);
	this->shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);
	}
	-
	+
	computeShapeDerivativesOnIntegrationPoints(
	nodes, natural_coords, shapes_derivatives(itp_type, ghost_type), type,
	ghost_type, elements);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ShapeLagrangeBase::onElementsRemoved(
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & new_numbering) {
	this->shapes.onElementsRemoved(new_numbering);
	this->shapes_derivatives.onElementsRemoved(new_numbering);
	}

	/* -------------------------------------------------------------------------- */
	void ShapeLagrangeBase::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "Shapes Lagrange [" << std::endl;
	ShapeFunctions::printself(stream, indent + 1);
	shapes.printself(stream, indent + 1);
	shapes_derivatives.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	} // namespace akantu
	diff --git a/src/fe_engine/shape_lagrange_base.hh b/src/fe_engine/shape_lagrange_base.hh
	index 2770dfe4f..f6515b983 100644
	--- a/src/fe_engine/shape_lagrange_base.hh
	+++ b/src/fe_engine/shape_lagrange_base.hh
	@@ -1,90 +1,90 @@
	/**
	* @file shape_lagrange_base.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 09 2017
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Base class for the shape lagrange
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_functions.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_LAGRANGE_BASE_HH_
	#define AKANTU_SHAPE_LAGRANGE_BASE_HH_

	namespace akantu {

	class ShapeLagrangeBase : public ShapeFunctions {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ShapeLagrangeBase(const Mesh & mesh, UInt spatial_dimension, ElementKind kind,
	const ID & id = "shape_lagrange");
	~ShapeLagrangeBase() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// computes the shape functions for given interpolation points
	virtual void computeShapesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// computes the shape functions derivatives for given interpolation points
	virtual void computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const = 0;

	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	template <ElementType type>
	void computeShapesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const;

	public:
	void onElementsAdded(const Array<Element> & elements) override;
	void
	onElementsRemoved(const Array<Element> & elements,
	const ElementTypeMapArray<UInt> & new_numbering) override;

	protected:
	/// The kind to consider
	ElementKind _kind;
	};

	} // namespace akantu

	#include "shape_lagrange_base_inline_impl.hh"

	#endif /* AKANTU_SHAPE_LAGRANGE_BASE_HH_ */
	diff --git a/src/fe_engine/shape_lagrange_base_inline_impl.hh b/src/fe_engine/shape_lagrange_base_inline_impl.hh
	index e799f8280..7eab6e3ab 100644
	--- a/src/fe_engine/shape_lagrange_base_inline_impl.hh
	+++ b/src/fe_engine/shape_lagrange_base_inline_impl.hh
	@@ -1,87 +1,87 @@
	/**
	* @file shape_lagrange_base_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 09 2017
	* @date last modification: Tue Sep 29 2020
	*
	* @brief common part for the shape lagrange
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_lagrange_base.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_LAGRANGE_BASE_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_LAGRANGE_BASE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrangeBase::computeShapesOnIntegrationPoints(
	const Array<Real> & /unused/, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_points = integration_points.cols();
	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	shapes.resize(nb_element * nb_points);

	#if !defined(AKANTU_NDEBUG)
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	AKANTU_DEBUG_ASSERT(shapes.getNbComponent() == size_of_shapes,
	"The shapes array does not have the correct "
	<< "number of component");
	#endif

	auto shapes_it = shapes.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(), nb_points,
	nb_element);
	auto shapes_begin = shapes_it;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	for (UInt elem = 0; elem < nb_element; ++elem) {
	if (filter_elements != empty_filter) {
	shapes_it = shapes_begin + filter_elements(elem);
	}

	Matrix<Real> & N = *shapes_it;
	ElementClass<type>::computeShapes(integration_points, N);

	if (filter_elements == empty_filter) {
	++shapes_it;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_SHAPE_LAGRANGE_BASE_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/shape_lagrange_inline_impl.hh b/src/fe_engine/shape_lagrange_inline_impl.hh
	index c25921523..199ce5c70 100644
	--- a/src/fe_engine/shape_lagrange_inline_impl.hh
	+++ b/src/fe_engine/shape_lagrange_inline_impl.hh
	@@ -1,582 +1,582 @@
	/**
	* @file shape_lagrange_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 27 2010
	* @date last modification: Fri May 14 2021
	*
	* @brief ShapeLagrange inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "aka_voigthelper.hh"
	#include "fe_engine.hh"
	#include "shape_lagrange.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	if (ElementClass<type>::getNaturalSpaceDimension() == \
	mesh.getSpatialDimension() \|\| \
	kind != _ek_regular) \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type);

	template <ElementKind kind>
	inline void ShapeLagrange<kind>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type) {
	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}

	#undef INIT_SHAPE_FUNCTIONS

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	inline void ShapeLagrange<kind>::computeShapeDerivativesOnCPointsByElement(
	const Matrix<Real> & node_coords, const Matrix<Real> & natural_coords,
	Tensor3<Real> & shapesd) const {
	AKANTU_DEBUG_IN();

	// compute dnds
	Tensor3<Real> dnds(node_coords.rows(), node_coords.cols(),
	natural_coords.cols());
	ElementClass<type>::computeDNDS(natural_coords, dnds);
	// compute jacobian
	Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
	natural_coords.cols());
	ElementClass<type>::computeJMat(dnds, node_coords, J);

	// compute dndx
	ElementClass<type>::computeShapeDerivatives(J, dnds, shapesd);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::inverseMap(const Vector<Real> & real_coords,
	UInt elem, Vector<Real> & natural_coords,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	ElementClass<type>::inverseMap(real_coords, nodes_coord, natural_coords);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	bool ShapeLagrange<kind>::contains(const Vector<Real> & real_coords, UInt elem,
	GhostType ghost_type) const {

	UInt spatial_dimension = mesh.getSpatialDimension();
	Vector<Real> natural_coords(spatial_dimension);

	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	return ElementClass<type>::contains(natural_coords);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::interpolate(const Vector<Real> & real_coords,
	UInt elem,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated,
	GhostType ghost_type) const {
	UInt nb_shapes = ElementClass<type>::getShapeSize();
	Vector<Real> shapes(nb_shapes);
	computeShapes<type>(real_coords, elem, shapes, ghost_type);
	ElementClass<type>::interpolate(nodal_values, shapes, interpolated);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeShapes(const Vector<Real> & real_coords,
	UInt elem, Vector<Real> & shapes,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	Vector<Real> natural_coords(spatial_dimension);

	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	ElementClass<type>::computeShapes(natural_coords, shapes);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeShapeDerivatives(
	const Matrix<Real> & real_coords, UInt elem, Tensor3<Real> & shapesd,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_points = real_coords.cols();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == shapesd.size(0) &&
	nb_nodes_per_element == shapesd.size(1),
	"Shape size doesn't match");
	AKANTU_DEBUG_ASSERT(nb_points == shapesd.size(2),
	"Number of points doesn't match shapes size");

	Matrix<Real> natural_coords(spatial_dimension, nb_points);

	// Creates the matrix of natural coordinates
	for (UInt i = 0; i < nb_points; i++) {
	Vector<Real> real_point = real_coords(i);
	Vector<Real> natural_point = natural_coords(i);

	inverseMap<type>(real_point, elem, natural_point, ghost_type);
	}

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	computeShapeDerivativesOnCPointsByElement<type>(nodes_coord, natural_coords,
	shapesd);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	ShapeLagrange<kind>::ShapeLagrange(const Mesh & mesh, UInt spatial_dimension,
	const ID & id)
	: ShapeLagrangeBase(mesh, spatial_dimension, kind, id) {}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt nb_points = integration_points.cols();
	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();
	AKANTU_DEBUG_ASSERT(shape_derivatives.getNbComponent() == size_of_shapesd,
	"The shapes_derivatives array does not have the correct "
	<< "number of component");
	shape_derivatives.resize(nb_element * nb_points);

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	Real * shapesd_val = shape_derivatives.storage();
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
	if (filter_elements != empty_filter) {
	shapesd_val = shape_derivatives.storage() +
	filter_elements(elem) * size_of_shapesd * nb_points;
	}

	Matrix<Real> & X = *x_it;
	Tensor3<Real> B(shapesd_val, spatial_dimension, nb_nodes_per_element,
	nb_points);
	computeShapeDerivativesOnCPointsByElement<type>(X, integration_points, B);

	if (filter_elements == empty_filter) {
	shapesd_val += size_of_shapesd * nb_points;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	void ShapeLagrange<kind>::computeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	#define AKANTU_COMPUTE_SHAPES(type) \
	computeShapeDerivativesOnIntegrationPoints<type>( \
	nodes, integration_points, shape_derivatives, ghost_type, \
	filter_elements);

	AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_COMPUTE_SHAPES);

	#undef AKANTU_COMPUTE_SHAPES
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::precomputeShapesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	Matrix<Real> & natural_coords = integration_points(type, ghost_type);
	UInt size_of_shapes = ElementClass<type>::getShapeSize();

	Array<Real> & shapes_tmp =
	shapes.alloc(0, size_of_shapes, itp_type, ghost_type);

	this->computeShapesOnIntegrationPoints<type>(nodes, natural_coords,
	shapes_tmp, ghost_type);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::precomputeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	Matrix<Real> & natural_coords = integration_points(type, ghost_type);
	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();

	Array<Real> & shapes_derivatives_tmp =
	shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);

	this->computeShapeDerivativesOnIntegrationPoints<type>(
	nodes, natural_coords, shapes_derivatives_tmp, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	const Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->interpolateElementalFieldOnIntegrationPoints<type>(
	u_el, out_uq, ghost_type, shapes, filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(shapes.exists(itp_type, ghost_type),
	"No shapes for the type "
	<< shapes.printType(itp_type, ghost_type));

	this->interpolateOnIntegrationPoints<type>(in_u, out_uq, nb_degree_of_freedom,
	shapes(itp_type, ghost_type),
	ghost_type, filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::gradientOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_nablauq,
	UInt nb_degree_of_freedom, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(
	shapes_derivatives.exists(itp_type, ghost_type),
	"No shapes derivatives for the type "
	<< shapes_derivatives.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->gradientElementalFieldOnIntegrationPoints<type>(
	u_el, out_nablauq, ghost_type, shapes_derivatives(itp_type, ghost_type),
	filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeBtD(
	const Array<Real> & Ds, Array<Real> & BtDs, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	auto itp_type = ElementClassProperty<type>::interpolation_type;
	const auto & shapes_derivatives =
	this->shapes_derivatives(itp_type, ghost_type);

	auto spatial_dimension = mesh.getSpatialDimension();
	auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	Array<Real> shapes_derivatives_filtered(0,
	shapes_derivatives.getNbComponent());
	auto && view =
	make_view(shapes_derivatives, spatial_dimension, nb_nodes_per_element);
	auto B_it = view.begin();
	auto B_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes_derivatives,
	shapes_derivatives_filtered, type, ghost_type,
	filter_elements);
	auto && view = make_view(shapes_derivatives_filtered, spatial_dimension,
	nb_nodes_per_element);
	B_it = view.begin();
	B_end = view.end();
	}

	for (auto && values :
	zip(range(B_it, B_end),
	make_view(Ds, Ds.getNbComponent() / spatial_dimension,
	spatial_dimension),
	make_view(BtDs, BtDs.getNbComponent() / nb_nodes_per_element,
	nb_nodes_per_element))) {
	const auto & B = std::get<0>(values);
	const auto & D = std::get<1>(values);
	auto & Bt_D = std::get<2>(values);
	// transposed due to the storage layout of B
	Bt_D.template mul<false, false>(D, B);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeBtDB(
	const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	auto itp_type = ElementClassProperty<type>::interpolation_type;
	const auto & shapes_derivatives =
	this->shapes_derivatives(itp_type, ghost_type);

	constexpr auto dim = ElementClass<type>::getSpatialDimension();
	auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	Array<Real> shapes_derivatives_filtered(0,
	shapes_derivatives.getNbComponent());
	auto && view = make_view(shapes_derivatives, dim, nb_nodes_per_element);
	auto B_it = view.begin();
	auto B_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes_derivatives,
	shapes_derivatives_filtered, type, ghost_type,
	filter_elements);
	auto && view =
	make_view(shapes_derivatives_filtered, dim, nb_nodes_per_element);
	B_it = view.begin();
	B_end = view.end();
	}

	if (order_d == 4) {
	UInt tangent_size = VoigtHelper<dim>::size;
	Matrix<Real> B(tangent_size, dim * nb_nodes_per_element);
	Matrix<Real> Bt_D(dim * nb_nodes_per_element, tangent_size);

	for (auto && values :
	zip(range(B_it, B_end), make_view(Ds, tangent_size, tangent_size),
	make_view(BtDBs, dim * nb_nodes_per_element,
	dim * nb_nodes_per_element))) {
	const auto & Bfull = std::get<0>(values);
	const auto & D = std::get<1>(values);
	auto & Bt_D_B = std::get<2>(values);

	VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(Bfull, B,
	nb_nodes_per_element);
	Bt_D.template mul<true, false>(B, D);
	Bt_D_B.template mul<false, false>(Bt_D, B);
	}
	} else if (order_d == 2) {
	Matrix<Real> Bt_D(nb_nodes_per_element, dim);
	for (auto && values :
	zip(range(B_it, B_end), make_view(Ds, dim, dim),
	make_view(BtDBs, nb_nodes_per_element, nb_nodes_per_element))) {
	const auto & B = std::get<0>(values);
	const auto & D = std::get<1>(values);
	auto & Bt_D_B = std::get<2>(values);
	Bt_D.template mul<true, false>(B, D);
	Bt_D_B.template mul<false, false>(Bt_D, B);
	}
	}
	}

	template <>
	template <>
	inline void ShapeLagrange<_ek_regular>::computeBtDB<_point_1>(
	const Array<Real> & /Ds/, Array<Real> & /BtDBs/, UInt /order_d/,
	GhostType /ghost_type/, const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeNtbN(
	const Array<Real> & bs, Array<Real> & NtbNs, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {

	auto itp_type = ElementClassProperty<type>::interpolation_type;
	auto size_of_shapes = ElementClass<type>::getShapeSize();
	auto nb_degree_of_freedom = bs.getNbComponent();

	auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Array<Real> shapes_filtered(0, size_of_shapes);

	auto && view = make_view(shapes(itp_type, ghost_type), 1, size_of_shapes);
	auto N_it = view.begin();
	auto N_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes(itp_type, ghost_type),
	shapes_filtered, type, ghost_type,
	filter_elements);
	auto && view = make_view(shapes_filtered, 1, size_of_shapes);
	N_it = view.begin();
	N_end = view.end();
	}

	Matrix<Real> Nt_b(nb_nodes_per_element, nb_degree_of_freedom);
	for (auto && values :
	zip(range(N_it, N_end), make_view(bs, nb_degree_of_freedom, 1),
	make_view(NtbNs, nb_nodes_per_element, nb_nodes_per_element))) {
	const auto & N = std::get<0>(values);
	const auto & b = std::get<1>(values);
	auto & Nt_b_N = std::get<2>(values);
	Nt_b.template mul<true, false>(N, b);
	Nt_b_N.template mul<false, false>(Nt_b, N);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeLagrange<kind>::computeNtb(
	const Array<Real> & bs, Array<Real> & Ntbs, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	Ntbs.resize(bs.size());

	auto size_of_shapes = ElementClass<type>::getShapeSize();
	auto itp_type = ElementClassProperty<type>::interpolation_type;
	auto nb_degree_of_freedom = bs.getNbComponent();

	Array<Real> shapes_filtered(0, size_of_shapes);
	auto && view = make_view(shapes(itp_type, ghost_type), 1, size_of_shapes);
	auto N_it = view.begin();
	auto N_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes(itp_type, ghost_type),
	shapes_filtered, type, ghost_type,
	filter_elements);
	auto && view = make_view(shapes_filtered, 1, size_of_shapes);
	N_it = view.begin();
	N_end = view.end();
	}

	for (auto && values :
	zip(make_view(bs, nb_degree_of_freedom, 1), range(N_it, N_end),
	make_view(Ntbs, nb_degree_of_freedom, size_of_shapes))) {
	const auto & b = std::get<0>(values);
	const auto & N = std::get<1>(values);
	auto & Ntb = std::get<2>(values);

	Ntb.template mul<false, false>(b, N);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_ */
	diff --git a/src/fe_engine/shape_structural.cc b/src/fe_engine/shape_structural.cc
	index 698854eae..7eb5af079 100644
	--- a/src/fe_engine/shape_structural.cc
	+++ b/src/fe_engine/shape_structural.cc
	@@ -1,54 +1,54 @@
	/**
	* @file shape_structural.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue Aug 27 2019
	*
	* @brief ShapeStructural implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_structural.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	ShapeStructural<_ek_structural>::ShapeStructural(Mesh & mesh,
	UInt spatial_dimension,
	const ID & id)
	: ShapeFunctions(mesh, spatial_dimension, id),
	rotation_matrices("rotation_matrices", id) {}

	/* -------------------------------------------------------------------------- */
	template <> ShapeStructural<_ek_structural>::~ShapeStructural() = default;

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/fe_engine/shape_structural.hh b/src/fe_engine/shape_structural.hh
	index e2668d85e..d2fd99cea 100644
	--- a/src/fe_engine/shape_structural.hh
	+++ b/src/fe_engine/shape_structural.hh
	@@ -1,201 +1,201 @@
	/**
	* @file shape_structural.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Fri May 14 2021
	*
	* @brief shape class for element with different set of shapes functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "shape_functions.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_STRUCTURAL_HH_
	#define AKANTU_SHAPE_STRUCTURAL_HH_

	namespace akantu {

	template <ElementKind kind> class ShapeStructural : public ShapeFunctions {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	// Ctors/Dtors should be explicitely implemented for _ek_structural
	public:
	ShapeStructural(Mesh & mesh, UInt spatial_dimension,
	const ID & id = "shape_structural");
	~ShapeStructural() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "ShapesStructural [" << std::endl;
	rotation_matrices.printself(stream, indent + 1);
	ShapeFunctions::printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	private:
	template <ElementType type>
	void computeShapesOnIntegrationPointsInternal(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter,
	bool mass = false) const;

	public:
	/// compute shape functions on given integration points
	template <ElementType type>
	void computeShapesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const {
	this->template computeShapesOnIntegrationPointsInternal<type>(
	nodes, integration_points, shapes, ghost_type, filter_elements, false);
	}

	template <ElementType type>
	void computeShapesMassOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements = empty_filter) const {
	this->template computeShapesOnIntegrationPointsInternal<type>(
	nodes, integration_points, shapes, ghost_type, filter_elements, true);
	}

	/// initialization function for structural elements
	inline void initShapeFunctions(const Array<Real> & nodes,
	const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type);

	/// precompute the rotation matrices for the elements dofs
	template <ElementType type>
	void precomputeRotationMatrices(const Array<Real> & nodes,
	GhostType ghost_type);

	/// pre compute all shapes on the element integration points from natural
	/// coordinates
	template <ElementType type>
	void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// pre compute all shapes on the element integration points from natural
	/// coordinates
	template <ElementType type>
	void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
	GhostType ghost_type);

	/// interpolate nodal values on the integration points
	template <ElementType type>
	void interpolateOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & uq, UInt nb_dof,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// compute the gradient of u on the integration points
	template <ElementType type>
	void gradientOnIntegrationPoints(
	const Array<Real> & u, Array<Real> & nablauq, UInt nb_dof,
	GhostType ghost_type = _not_ghost,
	const Array<UInt> & filter_elements = empty_filter) const;

	/// interpolate on physical point
	template <ElementType type>
	void interpolate(const Vector<Real> & /real_coords/, UInt /elem/,
	const Matrix<Real> & /nodal_values/,
	Vector<Real> & /interpolated/,
	GhostType /ghost_type/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the shapes on a provided point
	template <ElementType type>
	void computeShapes(const Vector<Real> & /real_coords/, UInt /elem/,
	Vector<Real> & /shapes/,
	GhostType /ghost_type/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the shape derivatives on a provided point
	template <ElementType type>
	void computeShapeDerivatives(const Matrix<Real> & /real_coords/,
	UInt /elem/, Tensor3<Real> & /shapes/,
	GhostType /ghost_type/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// get the rotations vector
	inline const Array<Real> &
	- getRotations(ElementType el_type, __attribute__((unused))
	- GhostType ghost_type = _not_ghost) const {
	+ getRotations(ElementType el_type,
	+ GhostType /ghost_type/ = _not_ghost) const {
	return rotation_matrices(el_type);
	}

	/* ------------------------------------------------------------------------ */
	template <ElementType type>
	void computeBtD(const Array<Real> & /Ds/, Array<Real> & /BtDs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <ElementType type>
	void computeBtDB(const Array<Real> & /Ds/, Array<Real> & /BtDBs/,
	UInt /order_d/, GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <ElementType type>
	void computeNtbN(const Array<Real> & /bs/, Array<Real> & /NtbNs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// multiply a field by shape functions
	template <ElementType type>
	void
	computeNtb(const Array<Real> & /bs/, Array<Real> & /Ntbs/,
	GhostType /ghost_type/,
	const Array<UInt> & /filter_elements/ = empty_filter) const {
	AKANTU_TO_IMPLEMENT();
	}

	protected:
	ElementTypeMapArray<Real> rotation_matrices;
	};

	} // namespace akantu

	#include "shape_structural_inline_impl.hh"

	#endif /* AKANTU_SHAPE_STRUCTURAL_HH_ */
	diff --git a/src/fe_engine/shape_structural_inline_impl.hh b/src/fe_engine/shape_structural_inline_impl.hh
	index 6005cb75a..d43c18e10 100644
	--- a/src/fe_engine/shape_structural_inline_impl.hh
	+++ b/src/fe_engine/shape_structural_inline_impl.hh
	@@ -1,511 +1,511 @@
	/**
	* @file shape_structural_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 11 2017
	* @date last modification: Mon Feb 01 2021
	*
	* @brief ShapeStructural inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_iterators.hh"
	#include "shape_structural.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_

	namespace akantu {

	namespace {
	/// Extract nodal coordinates per elements
	template <ElementType type>
	std::unique_ptr<Array<Real>> getNodesPerElement(const Mesh & mesh,
	const Array<Real> & nodes,
	GhostType ghost_type) {
	const auto dim = ElementClass<type>::getSpatialDimension();
	const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto nodes_per_element =
	std::make_unique<Array<Real>>(0, dim * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, *nodes_per_element, type,
	ghost_type);
	return nodes_per_element;
	}
	} // namespace

	template <ElementKind kind>
	inline void ShapeStructural<kind>::initShapeFunctions(
	const Array<Real> & /* unused /, const Matrix<Real> & / unused */,
	ElementType /* unused /, GhostType / unused */) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	precomputeRotationMatrices<type>(nodes, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type);

	template <>
	inline void ShapeStructural<_ek_structural>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type) {
	AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}

	#undef INIT_SHAPE_FUNCTIONS

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::computeShapesOnIntegrationPointsInternal(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements, bool mass) const {

	auto nb_points = integration_points.cols();
	auto nb_element = mesh.getConnectivity(type, ghost_type).size();
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();

	shapes.resize(nb_element * nb_points);

	auto nb_dofs = ElementClass<type>::getNbDegreeOfFreedom();
	auto nb_rows = nb_dofs;
	if (mass) {
	nb_rows = ElementClass<type>::getNbStressComponents();
	}

	#if !defined(AKANTU_NDEBUG)
	UInt size_of_shapes = nb_rows * nb_dofs * nb_nodes_per_element;
	AKANTU_DEBUG_ASSERT(shapes.getNbComponent() == size_of_shapes,
	"The shapes array does not have the correct "
	<< "number of component");
	#endif

	-
	auto shapes_it = shapes.begin_reinterpret(
	- nb_rows, ElementClass<type>::getNbNodesPerInterpolationElement() * nb_dofs,
	+ nb_rows,
	+ ElementClass<type>::getNbNodesPerInterpolationElement() * nb_dofs,
	nb_points, nb_element);
	auto shapes_begin = shapes_it;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	auto nodes_per_element = getNodesPerElement<type>(mesh, nodes, ghost_type);
	auto nodes_it = nodes_per_element->begin(mesh.getSpatialDimension(),
	Mesh::getNbNodesPerElement(type));
	auto nodes_begin = nodes_it;
	auto rot_matrix_it =
	make_view(rotation_matrices(type, ghost_type), nb_dofs, nb_dofs).begin();
	auto rot_matrix_begin = rot_matrix_it;

	for (UInt elem = 0; elem < nb_element; ++elem) {
	if (filter_elements != empty_filter) {
	shapes_it = shapes_begin + filter_elements(elem);
	nodes_it = nodes_begin + filter_elements(elem);
	rot_matrix_it = rot_matrix_begin + filter_elements(elem);
	}

	Tensor3<Real> & N = *shapes_it;
	auto & real_coord = *nodes_it;

	auto & RDOFs = *rot_matrix_it;

	Matrix<Real> T(N.size(1), N.size(1), 0);

	for (UInt i = 0; i < nb_nodes_per_element; ++i) {
	T.block(RDOFs, i * RDOFs.rows(), i * RDOFs.rows());
	}

	if (not mass) {
	ElementClass<type>::computeShapes(integration_points, real_coord, T, N);
	} else {
	ElementClass<type>::computeShapesMass(integration_points, real_coord, T,
	N);
	}
	if (filter_elements == empty_filter) {
	++shapes_it;
	++nodes_it;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::precomputeRotationMatrices(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	const auto spatial_dimension = mesh.getSpatialDimension();
	const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const auto nb_element = mesh.getNbElement(type, ghost_type);
	const auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();

	if (not this->rotation_matrices.exists(type, ghost_type)) {
	this->rotation_matrices.alloc(0, nb_dof * nb_dof, type, ghost_type);
	}

	auto & rot_matrices = this->rotation_matrices(type, ghost_type);
	rot_matrices.resize(nb_element);

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

	bool has_extra_normal = mesh.hasData<Real>("extra_normal", type, ghost_type);
	Array<Real>::const_vector_iterator extra_normal;
	if (has_extra_normal) {
	extra_normal = mesh.getData<Real>("extra_normal", type, ghost_type)
	.begin(spatial_dimension);
	}

	for (auto && tuple :
	zip(make_view(x_el, spatial_dimension, nb_nodes_per_element),
	make_view(rot_matrices, nb_dof, nb_dof))) {
	// compute shape derivatives
	auto & X = std::get<0>(tuple);
	auto & R = std::get<1>(tuple);

	if (has_extra_normal) {
	ElementClass<type>::computeRotationMatrix(R, X, *extra_normal);
	++extra_normal;
	} else {
	ElementClass<type>::computeRotationMatrix(
	R, X, Vector<Real>(spatial_dimension));
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::precomputeShapesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	const auto & natural_coords = integration_points(type, ghost_type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_points = integration_points(type, ghost_type).cols();
	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
	const auto dim = ElementClass<type>::getSpatialDimension();
	const auto spatial_dimension = mesh.getSpatialDimension();
	const auto natural_spatial_dimension =
	ElementClass<type>::getNaturalSpaceDimension();

	auto itp_type = FEEngine::getInterpolationType(type);
	if (not shapes.exists(itp_type, ghost_type)) {
	auto size_of_shapes = this->getShapeSize(type);
	this->shapes.alloc(0, size_of_shapes, itp_type, ghost_type);
	}

	auto & rot_matrices = this->rotation_matrices(type, ghost_type);
	auto & shapes_ = this->shapes(itp_type, ghost_type);
	shapes_.resize(nb_element * nb_points);

	auto nodes_per_element = getNodesPerElement<type>(mesh, nodes, ghost_type);

	for (auto && tuple :
	zip(make_view(shapes_, nb_dof, nb_dof * nb_nodes_per_element, nb_points),
	make_view(*nodes_per_element, dim, nb_nodes_per_element),
	make_view(rot_matrices, nb_dof, nb_dof))) {
	auto & N = std::get<0>(tuple);
	auto & X = std::get<1>(tuple);
	auto & RDOFs = std::get<2>(tuple);

	Matrix<Real> T(N.size(1), N.size(1), 0);

	for (UInt i = 0; i < nb_nodes_per_element; ++i) {
	T.block(RDOFs, i * RDOFs.rows(), i * RDOFs.rows());
	}

	auto R = RDOFs.block(0, 0, spatial_dimension, spatial_dimension);
	// Rotate to local basis
	auto x =
	(R * X).block(0, 0, natural_spatial_dimension, nb_nodes_per_element);

	ElementClass<type>::computeShapes(natural_coords, x, T, N);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::precomputeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	const auto & natural_coords = integration_points(type, ghost_type);
	const auto spatial_dimension = mesh.getSpatialDimension();
	const auto natural_spatial_dimension =
	ElementClass<type>::getNaturalSpaceDimension();
	const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const auto nb_points = natural_coords.cols();
	const auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
	const auto nb_element = mesh.getNbElement(type, ghost_type);
	const auto nb_stress_components = ElementClass<type>::getNbStressComponents();

	auto itp_type = FEEngine::getInterpolationType(type);
	if (not this->shapes_derivatives.exists(itp_type, ghost_type)) {
	auto size_of_shapesd = this->getShapeDerivativesSize(type);
	this->shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);
	}

	auto & rot_matrices = this->rotation_matrices(type, ghost_type);

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

	auto & shapesd = this->shapes_derivatives(itp_type, ghost_type);
	shapesd.resize(nb_element * nb_points);

	for (auto && tuple :
	zip(make_view(x_el, spatial_dimension, nb_nodes_per_element),
	make_view(shapesd, nb_stress_components,
	nb_nodes_per_element * nb_dof, nb_points),
	make_view(rot_matrices, nb_dof, nb_dof))) {
	// compute shape derivatives
	auto & X = std::get<0>(tuple);
	auto & B = std::get<1>(tuple);
	auto & RDOFs = std::get<2>(tuple);

	Tensor3<Real> dnds(natural_spatial_dimension,
	ElementClass<type>::interpolation_property::dnds_columns,
	B.size(2));
	ElementClass<type>::computeDNDS(natural_coords, X, dnds);

	Tensor3<Real> J(natural_spatial_dimension, natural_spatial_dimension,
	natural_coords.cols());

	// Computing the coordinates of the element in the natural space
	auto R = RDOFs.block(0, 0, spatial_dimension, spatial_dimension);
	Matrix<Real> T(B.size(1), B.size(1), 0);

	for (UInt i = 0; i < nb_nodes_per_element; ++i) {
	T.block(RDOFs, i * RDOFs.rows(), i * RDOFs.rows());
	}

	// Rotate to local basis
	auto x =
	(R * X).block(0, 0, natural_spatial_dimension, nb_nodes_per_element);

	ElementClass<type>::computeJMat(natural_coords, x, J);
	ElementClass<type>::computeShapeDerivatives(J, dnds, T, B);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_dof,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(out_uq.getNbComponent() == nb_dof,
	"The output array shape is not correct");

	auto itp_type = FEEngine::getInterpolationType(type);
	const auto & shapes_ = shapes(itp_type, ghost_type);

	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();
	auto nb_quad_points_per_element = integration_points(type, ghost_type).cols();

	Array<Real> u_el(0, nb_nodes_per_element * nb_dof);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	auto nb_quad_points = nb_quad_points_per_element * u_el.size();
	out_uq.resize(nb_quad_points);

	auto out_it = out_uq.begin_reinterpret(nb_dof, 1, nb_quad_points_per_element,
	u_el.size());
	auto shapes_it =
	shapes_.begin_reinterpret(nb_dof, nb_dof * nb_nodes_per_element,
	nb_quad_points_per_element, nb_element);
	auto u_it = u_el.begin_reinterpret(nb_dof * nb_nodes_per_element, 1,
	nb_quad_points_per_element, u_el.size());

	for_each_element(nb_element, filter_elements, [&](auto && el) {
	auto & uq = *out_it;
	const auto & u = *u_it;
	auto N = Tensor3<Real>(shapes_it[el]);

	for (auto && q : arange(uq.size(2))) {
	auto uq_q = Matrix<Real>(uq(q));
	auto u_q = Matrix<Real>(u(q));
	auto N_q = Matrix<Real>(N(q));

	uq_q.mul<false, false>(N_q, u_q);
	}

	++out_it;
	++u_it;
	});
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind>
	template <ElementType type>
	void ShapeStructural<kind>::gradientOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_nablauq, UInt nb_dof,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	auto itp_type = FEEngine::getInterpolationType(type);
	const auto & shapesd = shapes_derivatives(itp_type, ghost_type);

	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto element_dimension = ElementClass<type>::getSpatialDimension();
	auto nb_quad_points_per_element = integration_points(type, ghost_type).cols();
	auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();

	Array<Real> u_el(0, nb_nodes_per_element * nb_dof);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	auto nb_quad_points = nb_quad_points_per_element * u_el.size();
	out_nablauq.resize(nb_quad_points);

	auto out_it = out_nablauq.begin_reinterpret(
	element_dimension, 1, nb_quad_points_per_element, u_el.size());
	auto shapesd_it = shapesd.begin_reinterpret(
	element_dimension, nb_dof * nb_nodes_per_element,
	nb_quad_points_per_element, nb_element);
	auto u_it = u_el.begin_reinterpret(nb_dof * nb_nodes_per_element, 1,
	nb_quad_points_per_element, u_el.size());

	for_each_element(nb_element, filter_elements, [&](auto && el) {
	auto & nablau = *out_it;
	const auto & u = *u_it;
	auto B = Tensor3<Real>(shapesd_it[el]);

	for (auto && q : arange(nablau.size(2))) {
	auto nablau_q = Matrix<Real>(nablau(q));
	auto u_q = Matrix<Real>(u(q));
	auto B_q = Matrix<Real>(B(q));

	nablau_q.mul<false, false>(B_q, u_q);
	}

	++out_it;
	++u_it;
	});

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <ElementType type>
	void ShapeStructural<_ek_structural>::computeBtD(
	const Array<Real> & Ds, Array<Real> & BtDs, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	auto itp_type = ElementClassProperty<type>::interpolation_type;

	auto nb_stress = ElementClass<type>::getNbStressComponents();
	auto nb_dof_per_element = ElementClass<type>::getNbDegreeOfFreedom() *
	mesh.getNbNodesPerElement(type);

	const auto & shapes_derivatives =
	this->shapes_derivatives(itp_type, ghost_type);

	Array<Real> shapes_derivatives_filtered(0,
	shapes_derivatives.getNbComponent());
	auto && view = make_view(shapes_derivatives, nb_stress, nb_dof_per_element);
	auto B_it = view.begin();
	auto B_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes_derivatives,
	shapes_derivatives_filtered, type, ghost_type,
	filter_elements);
	auto && view =
	make_view(shapes_derivatives_filtered, nb_stress, nb_dof_per_element);
	B_it = view.begin();
	B_end = view.end();
	}

	for (auto && values : zip(range(B_it, B_end), make_view(Ds, nb_stress),
	make_view(BtDs, BtDs.getNbComponent()))) {
	const auto & B = std::get<0>(values);
	const auto & D = std::get<1>(values);
	auto & Bt_D = std::get<2>(values);
	Bt_D.template mul<true>(B, D);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <ElementType type>
	void ShapeStructural<_ek_structural>::computeNtb(
	const Array<Real> & bs, Array<Real> & Ntbs, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	auto itp_type = ElementClassProperty<type>::interpolation_type;

	auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
	auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	const auto & shapes = this->shapes(itp_type, ghost_type);

	Array<Real> shapes_filtered(0, shapes.getNbComponent());
	auto && view = make_view(shapes, nb_dof, nb_dof * nb_nodes_per_element);
	auto N_it = view.begin();
	auto N_end = view.end();

	if (filter_elements != empty_filter) {
	FEEngine::filterElementalData(this->mesh, shapes, shapes_filtered, type,
	ghost_type, filter_elements);
	auto && view =
	make_view(shapes_filtered, nb_dof, nb_dof * nb_nodes_per_element);
	N_it = view.begin();
	N_end = view.end();
	}

	for (auto && values : zip(range(N_it, N_end), make_view(bs, nb_dof),
	make_view(Ntbs, nb_dof * nb_nodes_per_element))) {
	const auto & N = std::get<0>(values);
	const auto & b = std::get<1>(values);
	auto & Nt_b = std::get<2>(values);
	Nt_b.template mul<true>(N, b);
	}
	}

	} // namespace akantu

	#endif /* AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_ */
	diff --git a/src/geometry/aabb_primitives/aabb_primitive.cc b/src/geometry/aabb_primitives/aabb_primitive.cc
	index 55a0c1e37..6cebf3062 100644
	--- a/src/geometry/aabb_primitives/aabb_primitive.cc
	+++ b/src/geometry/aabb_primitives/aabb_primitive.cc
	@@ -1,50 +1,50 @@
	/**
	* @file aabb_primitive.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Fri Mar 16 2018
	*
	* @brief Macro classe (primitive) for AABB CGAL algos
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aabb_primitive.hh"

	namespace akantu {

	Triangle_primitive::Point Triangle_primitive::reference_point() const {
	return primitive.vertex(0);
	}

	Line_arc_primitive::Point Line_arc_primitive::reference_point() const {
	Real x = to_double(primitive.source().x());
	Real y = to_double(primitive.source().y());
	Real z = to_double(primitive.source().z());
	return cgal::Spherical::Point_3(x, y, z);
	}

	} // namespace akantu
	diff --git a/src/geometry/aabb_primitives/aabb_primitive.hh b/src/geometry/aabb_primitives/aabb_primitive.hh
	index 576bb71cb..f12311f6a 100644
	--- a/src/geometry/aabb_primitives/aabb_primitive.hh
	+++ b/src/geometry/aabb_primitives/aabb_primitive.hh
	@@ -1,90 +1,90 @@
	/**
	* @file aabb_primitive.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Mar 13 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Macro classe (primitive) for AABB CGAL algos
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AABB_PRIMITIVE_HH_
	#define AKANTU_AABB_PRIMITIVE_HH_

	#include "aka_common.hh"
	#include "line_arc.hh"
	#include "tetrahedron.hh"
	#include "triangle.hh"

	#include "mesh_geom_common.hh"

	namespace akantu {

	/**
	* This macro defines a class that is used in the CGAL AABB tree algorithm.
	* All the `typedef`s and methods are required by the AABB module.
	*
	* The member variables are
	* - the id of the element associated to the primitive
	* - the geometric primitive of the element
	*
	* @param name the name of the primitive type
	* @param kernel the name of the kernel used
	*/
	#define AKANTU_AABB_CLASS(name, kernel) \
	class name##_primitive { \
	using Iterator = std::list<name<kernel>>::iterator; /* NOLINT */ \
	\
	public: \
	using Id = UInt; \
	using Point = kernel::Point_3; \
	using Datum = kernel::name##_3; \
	\
	public: \
	name##_primitive() = default; \
	name##_primitive(Iterator it) : meshId(it->id()), primitive(*it) {} \
	\
	public: \
	const Datum & datum() const { return primitive; } \
	Point reference_point() const; \
	const Id & id() const { return meshId; } \
	\
	protected: \
	Id meshId{0}; \
	name<kernel> primitive; /* NOLINT */ \
	}

	// If the primitive is supported by CGAL::intersection() then the
	// implementation process is really easy with this macro
	AKANTU_AABB_CLASS(Triangle, cgal::Cartesian);
	AKANTU_AABB_CLASS(Line_arc, cgal::Spherical);

	#undef AKANTU_AABB_CLASS

	} // namespace akantu

	#endif // AKANTU_AABB_PRIMITIVE_HH_
	diff --git a/src/geometry/aabb_primitives/line_arc.hh b/src/geometry/aabb_primitives/line_arc.hh
	index 21661d917..efae0fd3e 100644
	--- a/src/geometry/aabb_primitives/line_arc.hh
	+++ b/src/geometry/aabb_primitives/line_arc.hh
	@@ -1,76 +1,76 @@
	/**
	* @file line_arc.hh
	*
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Segment classe (geometry) for AABB CGAL algos
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_geom_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_LINE_ARC_HH_
	#define AKANTU_LINE_ARC_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	/// Class used for substitution of CGAL::Triangle_3 primitive
	template <typename K> class Line_arc : public CGAL::Line_arc_3<K> {
	public:
	/// Default constructor
	Line_arc() : CGAL::Line_arc_3<K>() {}

	/// Copy constructor
	Line_arc(const Line_arc & other)
	: CGAL::Line_arc_3<K>(other), mesh_id(other.mesh_id),
	seg_id(other.seg_id) {}

	/// Construct from 3 points
	// "CGAL-4.5/doc_html/Circular_kernel_3/classCGAL_1_1Line__arc__3.html"
	Line_arc(const CGAL::Line_3<K> & l, const CGAL::Circular_arc_point_3<K> & a,
	const CGAL::Circular_arc_point_3<K> & b)
	: CGAL::Line_arc_3<K>(l, a, b) {}

	public:
	UInt id() const { return mesh_id; }
	UInt segId() const { return seg_id; }
	void setId(UInt newId) { mesh_id = newId; }
	void setSegId(UInt newId) { seg_id = newId; }

	protected:
	/// Id of the element represented by the primitive
	UInt mesh_id{0};

	/// Id of the segment represented by the primitive
	UInt seg_id{0};
	};

	} // namespace akantu

	#endif // AKANTU_LINE_ARC_HH_
	diff --git a/src/geometry/aabb_primitives/tetrahedron.hh b/src/geometry/aabb_primitives/tetrahedron.hh
	index 72f07025d..3700894ac 100644
	--- a/src/geometry/aabb_primitives/tetrahedron.hh
	+++ b/src/geometry/aabb_primitives/tetrahedron.hh
	@@ -1,71 +1,71 @@
	/**
	* @file tetrahedron.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Tetrahedron classe (geometry) for AABB CGAL algos
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TETRAHEDRON_HH_
	#define AKANTU_TETRAHEDRON_HH_

	#include "aka_common.hh"

	#include "mesh_geom_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	/// Class used for substitution of CGAL::Tetrahedron_3 primitive
	template <typename K> class Tetrahedron : public CGAL::Tetrahedron_3<K> {
	public:
	/// Default constructor
	Tetrahedron() : CGAL::Tetrahedron_3<K>() {}

	/// Copy constructor
	Tetrahedron(const Tetrahedron & other)
	: CGAL::Tetrahedron_3<K>(other), meshId(other.meshId) {}

	/// Construct from 4 points
	Tetrahedron(const CGAL::Point_3<K> & a, const CGAL::Point_3<K> & b,
	const CGAL::Point_3<K> & c, const CGAL::Point_3<K> & d)
	: CGAL::Tetrahedron_3<K>(a, b, c, d) {}

	public:
	UInt id() const { return meshId; }
	void setId(UInt newId) { meshId = newId; }

	protected:
	/// Id of the element represented by the primitive
	UInt meshId{0};
	};

	} // namespace akantu

	#endif
	diff --git a/src/geometry/aabb_primitives/triangle.hh b/src/geometry/aabb_primitives/triangle.hh
	index abcb60af6..2d7be645c 100644
	--- a/src/geometry/aabb_primitives/triangle.hh
	+++ b/src/geometry/aabb_primitives/triangle.hh
	@@ -1,76 +1,76 @@
	/**
	* @file triangle.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Tue Sep 29 2020
	*
	* @brief Triangle classe (geometry) for AABB CGAL algos
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TRIANGLE_HH_
	#define AKANTU_TRIANGLE_HH_

	#include "aka_common.hh"

	#include "mesh_geom_common.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	/// Class used for substitution of CGAL::Triangle_3 primitive
	template <typename K> class Triangle : public CGAL::Triangle_3<K> {
	using parent = CGAL::Triangle_3<K>;

	public:
	/// Default constructor
	Triangle() = default;

	/// Copy constructor
	Triangle(const Triangle & other) = default;
	Triangle(Triangle && other) noexcept = default;

	Triangle & operator=(const Triangle & other) = default;
	Triangle & operator=(Triangle && other) noexcept = default;

	/// Construct from 3 points
	Triangle(const CGAL::Point_3<K> & a, const CGAL::Point_3<K> & b,
	const CGAL::Point_3<K> & c)
	: parent(a, b, c) {}

	public:
	UInt id() const { return meshId; }
	void setId(UInt newId) { meshId = newId; }

	protected:
	/// Id of the element represented by the primitive
	UInt meshId{0};
	};

	} // namespace akantu

	#endif // AKANTU_TRIANGLE_HH_
	diff --git a/src/geometry/geom_helper_functions.hh b/src/geometry/geom_helper_functions.hh
	index d4689b388..955bee773 100644
	--- a/src/geometry/geom_helper_functions.hh
	+++ b/src/geometry/geom_helper_functions.hh
	@@ -1,115 +1,115 @@
	/**
	* @file geom_helper_functions.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Helper functions for the computational geometry algorithms
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_GEOM_HELPER_FUNCTIONS_HH_
	#define AKANTU_GEOM_HELPER_FUNCTIONS_HH_

	#include "aka_common.hh"
	#include "aka_math.hh"
	#include "tree_type_helper.hh"

	#include "mesh_geom_common.hh"

	namespace akantu {

	/// Fuzzy compare of two points
	template <class Point>
	inline bool comparePoints(const Point & a, const Point & b) {
	return Math::are_float_equal(a.x(), b.x()) &&
	Math::are_float_equal(a.y(), b.y()) &&
	Math::are_float_equal(a.z(), b.z());
	}

	template <>
	inline bool comparePoints(const cgal::Spherical::Circular_arc_point_3 & a,
	const cgal::Spherical::Circular_arc_point_3 & b) {
	return Math::are_float_equal(CGAL::to_double(a.x()),
	CGAL::to_double(b.x())) &&
	Math::are_float_equal(CGAL::to_double(a.y()),
	CGAL::to_double(b.y())) &&
	Math::are_float_equal(CGAL::to_double(a.z()), CGAL::to_double(b.z()));
	}

	/// Fuzzy compare of two segments
	template <class K>
	inline bool compareSegments(const CGAL::Segment_3<K> & a,
	const CGAL::Segment_3<K> & b) {
	return (comparePoints(a.source(), b.source()) &&
	comparePoints(a.target(), b.target())) \|\|
	(comparePoints(a.source(), b.target()) &&
	comparePoints(a.target(), b.source()));
	}

	/// Compare segment pairs
	inline bool
	compareSegmentPairs(const std::pair<cgal::Cartesian::Segment_3, UInt> & a,
	const std::pair<cgal::Cartesian::Segment_3, UInt> & b) {
	return compareSegments(a.first, b.first);
	}

	/// Pair ordering operator based on first member
	struct segmentPairsLess {
	inline bool
	operator()(const std::pair<cgal::Cartesian::Segment_3, UInt> & a,
	const std::pair<cgal::Cartesian::Segment_3, UInt> & b) {
	return static_cast<bool>(
	CGAL::compare_lexicographically(a.first.min(), b.first.min())) or
	static_cast<bool>(
	CGAL::compare_lexicographically(a.first.max(), b.first.max()));
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Predicates */
	/* -------------------------------------------------------------------------- */

	/// Predicate used to determine if two segments are equal
	class IsSameSegment {

	public:
	IsSameSegment(const cgal::Cartesian::Segment_3 & segment)
	: segment(segment) {}

	bool
	operator()(const std::pair<cgal::Cartesian::Segment_3, UInt> & test_pair) {
	return compareSegments(segment, test_pair.first);
	}

	protected:
	const cgal::Cartesian::Segment_3 segment;
	};

	} // namespace akantu

	#endif // AKANTU_GEOM_HELPER_FUNCTIONS_HH_
	diff --git a/src/geometry/mesh_abstract_intersector.hh b/src/geometry/mesh_abstract_intersector.hh
	index 580a229f1..88db3e062 100644
	--- a/src/geometry/mesh_abstract_intersector.hh
	+++ b/src/geometry/mesh_abstract_intersector.hh
	@@ -1,122 +1,122 @@
	/**
	* @file mesh_abstract_intersector.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Sat Apr 02 2016
	*
	* @brief Abstract class for intersection computations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_ABSTRACT_INTERSECTOR_HH_
	#define AKANTU_MESH_ABSTRACT_INTERSECTOR_HH_

	#include "aka_common.hh"
	#include "mesh_geom_abstract.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* @brief Class used to perform intersections on a mesh and construct output
	* data
	*/
	template <class Query> class MeshAbstractIntersector : public MeshGeomAbstract {

	public:
	/// Construct from mesh
	explicit MeshAbstractIntersector(Mesh & mesh);

	/// Destructor
	~MeshAbstractIntersector() override = default;

	public:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the new_node_per_elem array
	AKANTU_GET_MACRO(NewNodePerElem, *new_node_per_elem, const Array<UInt> &);
	/// get the intersection_points array
	AKANTU_GET_MACRO(IntersectionPoints, intersection_points,
	const Array<Real> *);
	/// get the nb_seg_by_el UInt
	AKANTU_GET_MACRO(NbSegByEl, nb_seg_by_el, UInt);

	/**
	* @brief Compute the intersection with a query object
	*
	* This function needs to be implemented for every subclass. It computes the
	* intersections
	* with the tree of primitives and creates the data for the user.
	*
	* @param query the CGAL primitive of the query object
	*/
	virtual void computeIntersectionQuery(const Query & query) = 0;

	/// Compute intersection points between the mesh primitives (segments) and a
	/// query (surface in 3D or a curve in 2D), double intersection points for the
	/// same primitives are not considered. A maximum intersection node per
	/// element is set : 2 in 2D and 4 in 3D
	virtual void computeMeshQueryIntersectionPoint(const Query & query,
	UInt nb_old_nodes) = 0;

	/// Compute intersection between the mesh and a list of queries
	virtual void
	computeIntersectionQueryList(const std::list<Query> & query_list);

	/// Compute intersection points between the mesh and a list of queries
	virtual void
	computeMeshQueryListIntersectionPoint(const std::list<Query> & query_list,
	UInt nb_old_nodes);

	/// Compute whatever result is needed from the user (should be move to the
	/// appropriate specific classe for genericity)
	virtual void
	buildResultFromQueryList(const std::list<Query> & query_list) = 0;

	protected:
	/// new node per element (column 0: number of new nodes, then odd is the
	/// intersection node number and even the ID of the intersected segment)
	Array<UInt> * new_node_per_elem{nullptr};

	/// intersection output: new intersection points
	/// (computeMeshQueryListIntersectionPoint)
	Array<Real> * intersection_points{nullptr};

	/// number of segment in a considered element of the templated type of element
	/// specialized intersector
	const UInt nb_seg_by_el{0};
	};

	} // namespace akantu

	#include "mesh_abstract_intersector_tmpl.hh"

	#endif // AKANTU_MESH_ABSTRACT_INTERSECTOR_HH_
	diff --git a/src/geometry/mesh_abstract_intersector_tmpl.hh b/src/geometry/mesh_abstract_intersector_tmpl.hh
	index 536d3f778..6733566a9 100644
	--- a/src/geometry/mesh_abstract_intersector_tmpl.hh
	+++ b/src/geometry/mesh_abstract_intersector_tmpl.hh
	@@ -1,80 +1,80 @@
	/**
	* @file mesh_abstract_intersector_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Sat Jan 23 2016
	*
	* @brief General class for intersection computations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_ABSTRACT_INTERSECTOR_TMPL_HH_
	#define AKANTU_MESH_ABSTRACT_INTERSECTOR_TMPL_HH_

	#include "aka_common.hh"
	#include "mesh_abstract_intersector.hh"

	namespace akantu {

	template <class Query>
	MeshAbstractIntersector<Query>::MeshAbstractIntersector(Mesh & mesh)
	: MeshGeomAbstract(mesh) {}

	template <class Query>
	void MeshAbstractIntersector<Query>::computeIntersectionQueryList(
	const std::list<Query> & query_list) {
	AKANTU_DEBUG_IN();

	auto query_it = query_list.begin();
	auto query_end = query_list.end();

	for (; query_it != query_end; ++query_it) {
	computeIntersectionQuery(*query_it);
	}

	AKANTU_DEBUG_OUT();
	}

	template <class Query>
	void MeshAbstractIntersector<Query>::computeMeshQueryListIntersectionPoint(
	const std::list<Query> & query_list, UInt nb_old_nodes) {
	AKANTU_DEBUG_IN();

	auto query_it = query_list.begin();
	auto query_end = query_list.end();

	for (; query_it != query_end; ++query_it) {
	computeMeshQueryIntersectionPoint(*query_it, nb_old_nodes);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif // AKANTU_MESH_ABSTRACT_INTERSECTOR_TMPL_HH_
	diff --git a/src/geometry/mesh_geom_abstract.hh b/src/geometry/mesh_geom_abstract.hh
	index 1c90c911b..a025fd17e 100644
	--- a/src/geometry/mesh_geom_abstract.hh
	+++ b/src/geometry/mesh_geom_abstract.hh
	@@ -1,64 +1,65 @@
	/**
	* @file mesh_geom_abstract.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Sat Jan 23 2016
	*
	* @brief Class for constructing the CGAL primitives of a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_GEOM_ABSTRACT_HH_
	#define AKANTU_MESH_GEOM_ABSTRACT_HH_

	#include "aka_common.hh"
	#include "mesh.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/// Abstract class for mesh geometry operations
	class MeshGeomAbstract {

	public:
	/// Construct from mesh
	explicit MeshGeomAbstract(Mesh & mesh) : mesh(mesh){};

	virtual ~MeshGeomAbstract() = default;
	+
	public:
	/// Construct geometric data for computational geometry algorithms
	virtual void constructData(GhostType ghost_type = _not_ghost) = 0;

	protected:
	/// Mesh used to construct the primitives
	Mesh & mesh;
	};

	} // namespace akantu

	#endif // AKANTU_MESH_GEOM_ABSTRACT_HH_
	diff --git a/src/geometry/mesh_geom_common.hh b/src/geometry/mesh_geom_common.hh
	index 309bf3645..fe22bd63f 100644
	--- a/src/geometry/mesh_geom_common.hh
	+++ b/src/geometry/mesh_geom_common.hh
	@@ -1,60 +1,60 @@
	/**
	* @file mesh_geom_common.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Common file for MeshGeom module
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_MESH_GEOM_COMMON_HH_
	#define AKANTU_MESH_GEOM_COMMON_HH_

	#include "aka_common.hh"

	/* -------------------------------------------------------------------------- */
	#include <CGAL/MP_Float.h>
	#include <CGAL/Quotient.h>
	/* -------------------------------------------------------------------------- */
	#include <CGAL/Algebraic_kernel_for_spheres_2_3.h>
	#include <CGAL/Cartesian.h>
	#include <CGAL/Simple_cartesian.h>
	#include <CGAL/Spherical_kernel_3.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace cgal {
	using Cartesian = CGAL::Simple_cartesian<Real>;

	using Spherical = CGAL::Spherical_kernel_3<
	CGAL::Simple_cartesian<CGAL::Quotient<CGAL::MP_Float>>,
	CGAL::Algebraic_kernel_for_spheres_2_3<CGAL::Quotient<CGAL::MP_Float>>>;
	} // namespace cgal

	} // namespace akantu

	#endif // AKANTU_MESH_GEOM_COMMON_HH_
	diff --git a/src/geometry/mesh_geom_factory.hh b/src/geometry/mesh_geom_factory.hh
	index 7ae2c4d99..d9d0a4b07 100644
	--- a/src/geometry/mesh_geom_factory.hh
	+++ b/src/geometry/mesh_geom_factory.hh
	@@ -1,107 +1,107 @@
	/**
	* @file mesh_geom_factory.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Class for constructing the CGAL primitives of a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */
	#include "geom_helper_functions.hh"
	#include "mesh.hh"
	#include "mesh_geom_abstract.hh"
	#include "tree_type_helper.hh"
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_GEOM_FACTORY_HH_
	#define AKANTU_MESH_GEOM_FACTORY_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* @brief Class used to construct AABB tree for intersection computations
	*
	* This class constructs a CGAL AABB tree of one type of element in a mesh
	* for fast intersection computations.
	*/
	template <UInt dim, ElementType el_type, class Primitive, class Kernel>
	class MeshGeomFactory : public MeshGeomAbstract {
	public:
	/// Construct from mesh
	explicit MeshGeomFactory(Mesh & mesh);

	/// Desctructor
	~MeshGeomFactory() override;

	using TreeTypeHelper_ = TreeTypeHelper<Primitive, Kernel>;
	using TreeType = typename TreeTypeHelper_::tree;
	using ContainerType = typename TreeTypeHelper_::container_type;

	public:
	/// Construct AABB tree for fast intersection computing
	void constructData(GhostType ghost_type = _not_ghost) override;

	/**
	* @brief Construct a primitive and add it to a list of primitives
	*
	* This function needs to be specialized for every type that is wished to be
	* supported.
	* @param node_coordinates coordinates of the nodes making up the element
	* @param id element number
	* @param list the primitive list (not used inside MeshGeomFactory)
	*/
	inline void addPrimitive(const Matrix<Real> & /node_coordinates/,
	UInt /id/, ContainerType & /list/);

	inline void addPrimitive(const Matrix<Real> & node_coordinates, UInt id);

	/// Getter for the AABB tree
	auto getTree() const -> const TreeType & { return *data_tree; }

	/// Getter for primitive list
	auto getPrimitiveList() const -> const ContainerType & {
	return primitive_list;
	}

	protected:
	/// AABB data tree
	TreeType * data_tree{nullptr};

	/// Primitive list
	ContainerType primitive_list;
	};

	} // namespace akantu

	#include "mesh_geom_factory_tmpl.hh"

	#endif // AKANTU_MESH_GEOM_FACTORY_HH_
	diff --git a/src/geometry/mesh_geom_factory_tmpl.hh b/src/geometry/mesh_geom_factory_tmpl.hh
	index 3ef885d1d..ea87cb406 100644
	--- a/src/geometry/mesh_geom_factory_tmpl.hh
	+++ b/src/geometry/mesh_geom_factory_tmpl.hh
	@@ -1,245 +1,245 @@
	/**
	* @file mesh_geom_factory_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Class for constructing the CGAL primitives of a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_geom_common.hh"
	#include "mesh_geom_factory.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_GEOM_FACTORY_TMPL_HH_
	#define AKANTU_MESH_GEOM_FACTORY_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim, ElementType type, class Primitive, class Kernel>
	MeshGeomFactory<dim, type, Primitive, Kernel>::MeshGeomFactory(Mesh & mesh)
	: MeshGeomAbstract(mesh) {}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, ElementType type, class Primitive, class Kernel>
	MeshGeomFactory<dim, type, Primitive, Kernel>::~MeshGeomFactory() {
	delete data_tree;
	}

	/* -------------------------------------------------------------------------- */
	/**
	* This function loops over the elements of `type` in the mesh and creates the
	* AABB tree of geometrical primitves (`data_tree`).
	*/
	template <UInt dim, ElementType type, class Primitive, class Kernel>
	void MeshGeomFactory<dim, type, Primitive, Kernel>::constructData(
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	primitive_list.clear();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	const Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);
	const Array<Real> & nodes = mesh.getNodes();

	UInt el_index = 0;
	auto it = connectivity.begin(nb_nodes_per_element);
	auto end = connectivity.end(nb_nodes_per_element);

	Matrix<Real> node_coordinates(dim, nb_nodes_per_element);

	// This loop builds the list of primitives
	for (; it != end; ++it, ++el_index) {
	const Vector<UInt> & el_connectivity = *it;

	for (UInt i = 0; i < nb_nodes_per_element; i++) {
	for (UInt j = 0; j < dim; j++) {
	node_coordinates(j, i) = nodes(el_connectivity(i), j);
	}
	}

	// the unique elemental id assigned to the primitive is the
	// linearized element index over ghost type
	addPrimitive(node_coordinates, el_index);
	}

	delete data_tree;

	// This condition allows the use of the mesh geom module
	// even if types are not compatible with AABB tree algorithm
	if (TreeTypeHelper_::is_valid) {
	data_tree = new TreeType(primitive_list.begin(), primitive_list.end());
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	namespace {
	namespace details {
	enum class GeometricalType {
	_triangle,
	_tetrahedron,
	};
	template <ElementType element_type> struct GeometricalTypeHelper {};

	template <> struct GeometricalTypeHelper<_triangle_3> {
	static const GeometricalType type{GeometricalType::_triangle};
	};

	template <> struct GeometricalTypeHelper<_triangle_6> {
	static const GeometricalType type{GeometricalType::_triangle};
	};

	template <> struct GeometricalTypeHelper<_tetrahedron_4> {
	static const GeometricalType type{GeometricalType::_triangle};
	};

	#if defined(AKANTU_IGFEM)
	template <> struct GeometricalTypeHelper<_igfem_triangle_4> {
	static const GeometricalType type{GeometricalType::_triangle};
	};
	template <> struct GeometricalTypeHelper<_igfem_triangle_5> {
	static const GeometricalType type{GeometricalType::_triangle};
	};
	#endif

	template <details::GeometricalType geom_type, class Primitive, class Kernel>
	struct AddPrimitiveHelper {};

	template <class Primitive>
	struct AddPrimitiveHelper<GeometricalType::_triangle, Primitive,
	cgal::Cartesian> {
	using TreeTypeHelper_ = TreeTypeHelper<Primitive, cgal::Cartesian>;
	using ContainerType = typename TreeTypeHelper_::container_type;
	static void addPrimitive(const Matrix<Real> & node_coordinates, UInt id,
	ContainerType & list) {
	using Point = typename TreeTypeHelper_::point_type;
	Point a(node_coordinates(0, 0), node_coordinates(1, 0), 0.);
	Point b(node_coordinates(0, 1), node_coordinates(1, 1), 0.);
	Point c(node_coordinates(0, 2), node_coordinates(1, 2), 0.);

	Triangle<cgal::Cartesian> t(a, b, c);
	t.setId(id);
	list.push_back(t);
	}
	};

	template <class Primitive>
	struct AddPrimitiveHelper<GeometricalType::_triangle, Primitive,
	cgal::Spherical> {
	using TreeTypeHelper_ = TreeTypeHelper<Primitive, cgal::Spherical>;
	using ContainerType = typename TreeTypeHelper_::container_type;
	static void addPrimitive(const Matrix<Real> & node_coordinates, UInt id,
	ContainerType & list) {
	using Point = typename TreeTypeHelper_::point_type;
	Point a(node_coordinates(0, 0), node_coordinates(1, 0), 0.);
	Point b(node_coordinates(0, 1), node_coordinates(1, 1), 0.);
	Point c(node_coordinates(0, 2), node_coordinates(1, 2), 0.);

	using Line = CGAL::Line_3<cgal::Spherical>;
	Line l1(a, b);
	Line l2(b, c);
	Line l3(c, a);

	using Arc = Line_arc<cgal::Spherical>;
	Arc s1(l1, a, b);
	Arc s2(l2, b, c);
	Arc s3(l3, c, a);

	s1.setId(id);
	s1.setSegId(0);
	s2.setId(id);
	s2.setSegId(1);
	s3.setId(id);
	s3.setSegId(2);

	list.push_back(s1);
	list.push_back(s2);
	list.push_back(s3);
	}
	};

	template <class Primitive>
	struct AddPrimitiveHelper<GeometricalType::_tetrahedron, Primitive,
	cgal::Cartesian> {
	using TreeTypeHelper_ = TreeTypeHelper<Primitive, cgal::Cartesian>;
	using ContainerType = typename TreeTypeHelper_::container_type;
	static void addPrimitive(const Matrix<Real> & node_coordinates, UInt id,
	ContainerType & list) {
	using Point = typename TreeTypeHelper_::point_type;
	Point a(node_coordinates(0, 0), node_coordinates(1, 0),
	node_coordinates(2, 0));
	Point b(node_coordinates(0, 1), node_coordinates(1, 1),
	node_coordinates(2, 1));
	Point c(node_coordinates(0, 2), node_coordinates(1, 2),
	node_coordinates(2, 2));
	Point d(node_coordinates(0, 3), node_coordinates(1, 3),
	node_coordinates(2, 3));

	Triangle<cgal::Cartesian> t1(a, b, c);
	Triangle<cgal::Cartesian> t2(b, c, d);
	Triangle<cgal::Cartesian> t3(c, d, a);
	Triangle<cgal::Cartesian> t4(d, a, b);

	t1.setId(id);
	t2.setId(id);
	t3.setId(id);
	t4.setId(id);

	list.push_back(t1);
	list.push_back(t2);
	list.push_back(t3);
	list.push_back(t4);
	}
	};
	} // namespace details
	} // namespace

	/* -------------------------------------------------------------------------- */
	template <UInt dim, ElementType type, class Primitive, class Kernel>
	void MeshGeomFactory<dim, type, Primitive, Kernel>::addPrimitive(
	const Matrix<Real> & node_coordinates, UInt id, ContainerType & list) {
	details::AddPrimitiveHelper<details::GeometricalTypeHelper<type>::type,
	Primitive, Kernel>::addPrimitive(node_coordinates,
	id, list);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, ElementType type, class Primitive, class Kernel>
	void MeshGeomFactory<dim, type, Primitive, Kernel>::addPrimitive(
	const Matrix<Real> & node_coordinates, UInt id) {
	this->addPrimitive(node_coordinates, id, this->primitive_list);
	}

	} // namespace akantu

	#endif // AKANTU_MESH_GEOM_FACTORY_TMPL_HH_
	diff --git a/src/geometry/mesh_geom_intersector.hh b/src/geometry/mesh_geom_intersector.hh
	index 760576441..4b88a49a9 100644
	--- a/src/geometry/mesh_geom_intersector.hh
	+++ b/src/geometry/mesh_geom_intersector.hh
	@@ -1,75 +1,75 @@
	/**
	* @file mesh_geom_intersector.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Sat Jan 23 2016
	*
	* @brief General class for intersection computations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_GEOM_INTERSECTOR_HH_
	#define AKANTU_MESH_GEOM_INTERSECTOR_HH_

	#include "aka_common.hh"
	#include "mesh_abstract_intersector.hh"
	#include "mesh_geom_factory.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* @brief Class used to perform intersections on a mesh and construct output
	* data
	*/
	template <UInt dim, ElementType type, class Primitive, class Query,
	class Kernel>
	class MeshGeomIntersector : public MeshAbstractIntersector<Query> {

	public:
	/// Construct from mesh
	explicit MeshGeomIntersector(Mesh & mesh);

	/// Destructor
	~MeshGeomIntersector() override = default;

	public:
	/// Construct the primitive tree object
	void constructData(GhostType ghost_type = _not_ghost) override;

	protected:
	/// Factory object containing the primitive tree
	MeshGeomFactory<dim, type, Primitive, Kernel> factory;
	};

	} // namespace akantu

	#include "mesh_geom_intersector_tmpl.hh"

	#endif // AKANTU_MESH_GEOM_INTERSECTOR_HH_
	diff --git a/src/geometry/mesh_geom_intersector_tmpl.hh b/src/geometry/mesh_geom_intersector_tmpl.hh
	index 8cd6d487b..40bdd45a5 100644
	--- a/src/geometry/mesh_geom_intersector_tmpl.hh
	+++ b/src/geometry/mesh_geom_intersector_tmpl.hh
	@@ -1,60 +1,60 @@
	/**
	* @file mesh_geom_intersector_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Sat Jan 23 2016
	*
	* @brief General class for intersection computations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_GEOM_INTERSECTOR_TMPL_HH_
	#define AKANTU_MESH_GEOM_INTERSECTOR_TMPL_HH_

	#include "aka_common.hh"
	#include "mesh_geom_intersector.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <UInt dim, ElementType type, class Primitive, class Query,
	class Kernel>
	MeshGeomIntersector<dim, type, Primitive, Query, Kernel>::MeshGeomIntersector(
	Mesh & mesh)
	: MeshAbstractIntersector<Query>(mesh), factory(mesh) {}

	template <UInt dim, ElementType type, class Primitive, class Query,
	class Kernel>
	void MeshGeomIntersector<dim, type, Primitive, Query, Kernel>::constructData(
	GhostType ghost_type) {
	this->intersection_points->resize(0);
	factory.constructData(ghost_type);
	}

	} // namespace akantu

	#endif // AKANTU_MESH_GEOM_INTERSECTOR_TMPL_HH_
	diff --git a/src/geometry/mesh_segment_intersector.hh b/src/geometry/mesh_segment_intersector.hh
	index 8e36a1e82..96a00d68b 100644
	--- a/src/geometry/mesh_segment_intersector.hh
	+++ b/src/geometry/mesh_segment_intersector.hh
	@@ -1,110 +1,110 @@
	/**
	* @file mesh_segment_intersector.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Computation of mesh intersection with segments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_SEGMENT_INTERSECTOR_HH_
	#define AKANTU_MESH_SEGMENT_INTERSECTOR_HH_

	#include "aka_common.hh"
	#include "mesh_geom_intersector.hh"

	#include "mesh_geom_common.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <UInt dim, ElementType type>
	class MeshSegmentIntersector
	: public MeshGeomIntersector<dim, type, Triangle<cgal::Cartesian>,
	cgal::Cartesian::Segment_3, cgal::Cartesian> {
	using K = cgal::Cartesian;
	/// Parent class type
	using parent_type =
	MeshGeomIntersector<dim, type, Triangle<K>, K::Segment_3, K>;

	/// Result of intersection function type
	using result_type =
	typename IntersectionTypeHelper<TreeTypeHelper<Triangle<K>, K>,
	K::Segment_3>::intersection_type;

	/// Pair of segments and element id
	using pair_type = std::pair<K::Segment_3, UInt>;

	public:
	/// Construct from mesh
	explicit MeshSegmentIntersector(Mesh & mesh, Mesh & result_mesh);

	/// Destructor
	~MeshSegmentIntersector() override = default;

	public:
	/**
	* @brief Computes the intersection of the mesh with a segment
	*
	* @param query the segment to compute the intersections with the mesh
	*/
	void computeIntersectionQuery(const K::Segment_3 & query) override;

	/// Compute intersection points between the mesh and a query
	void computeMeshQueryIntersectionPoint(const K::Segment_3 & query,
	- UInt nb_old_nodes) override;
	+ UInt nb_old_nodes) override;

	/// Compute the embedded mesh
	void
	buildResultFromQueryList(const std::list<K::Segment_3> & query_list) override;

	void setPhysicalName(const std::string & other) {
	current_physical_name = other;
	}

	protected:
	/// Compute segments from intersection list
	void computeSegments(const std::list<result_type> & intersections,
	std::set<pair_type, segmentPairsLess> & segments,
	const K::Segment_3 & query);

	protected:
	/// Result mesh
	Mesh & result_mesh;

	/// Physical name of the current batch of queries
	std::string current_physical_name;
	};

	} // namespace akantu

	#include "mesh_segment_intersector_tmpl.hh"

	#endif // AKANTU_MESH_SEGMENT_INTERSECTOR_HH_
	diff --git a/src/geometry/mesh_segment_intersector_tmpl.hh b/src/geometry/mesh_segment_intersector_tmpl.hh
	index eb4eb7792..f6646e591 100644
	--- a/src/geometry/mesh_segment_intersector_tmpl.hh
	+++ b/src/geometry/mesh_segment_intersector_tmpl.hh
	@@ -1,285 +1,284 @@
	/**
	* @file mesh_segment_intersector_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 29 2015
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Computation of mesh intersection with segments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_SEGMENT_INTERSECTOR_TMPL_HH_
	#define AKANTU_MESH_SEGMENT_INTERSECTOR_TMPL_HH_

	#include "aka_common.hh"
	#include "mesh_geom_common.hh"
	#include "tree_type_helper.hh"

	namespace akantu {

	template <UInt dim, ElementType type>
	MeshSegmentIntersector<dim, type>::MeshSegmentIntersector(Mesh & mesh,
	Mesh & result_mesh)
	: parent_type(mesh), result_mesh(result_mesh) {
	this->intersection_points = new Array<Real>(0, dim);
	this->constructData();
	}

	template <UInt dim, ElementType type>
	void MeshSegmentIntersector<dim, type>::computeIntersectionQuery(
	const K::Segment_3 & query) {
	AKANTU_DEBUG_IN();

	result_mesh.addConnectivityType(_segment_2, _not_ghost);
	result_mesh.addConnectivityType(_segment_2, _ghost);

	std::list<result_type> result_list;
	std::set<std::pair<K::Segment_3, UInt>, segmentPairsLess> segment_set;

	this->factory.getTree().all_intersections(query,
	std::back_inserter(result_list));
	this->computeSegments(result_list, segment_set, query);

	// Arrays for storing nodes and connectivity
	Array<Real> & nodes = result_mesh.getNodes();
	Array<UInt> & connectivity = result_mesh.getConnectivity(_segment_2);

	// Arrays for storing associated element and physical name
	bool valid_elemental_data = true;
	Array<Element> * associated_element = nullptr;
	Array<std::string> * associated_physical_name = nullptr;

	try {
	associated_element =
	&result_mesh.getData<Element>("associated_element", _segment_2);
	associated_physical_name =
	&result_mesh.getData<std::string>("physical_names", _segment_2);
	} catch (debug::Exception & e) {
	valid_elemental_data = false;
	}

	auto it = segment_set.begin();
	auto end = segment_set.end();

	// Loop over the segment pairs
	for (; it != end; ++it) {
	if (!it->first.is_degenerate()) {
	Vector<UInt> segment_connectivity(2);
	segment_connectivity(0) = result_mesh.getNbNodes();
	segment_connectivity(1) = result_mesh.getNbNodes() + 1;
	connectivity.push_back(segment_connectivity);

	// Copy nodes
	Vector<Real> source(dim);
	Vector<Real> target(dim);
	for (UInt j = 0; j < dim; j++) {
	source(j) = it->first.source()[j];
	target(j) = it->first.target()[j];
	}

	nodes.push_back(source);
	nodes.push_back(target);

	// Copy associated element info
	if (valid_elemental_data) {
	associated_element->push_back(Element{type, it->second, _not_ghost});
	associated_physical_name->push_back(current_physical_name);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	template <UInt dim, ElementType type>
	void MeshSegmentIntersector<dim, type>::computeMeshQueryIntersectionPoint(
	const K::Segment_3 & /query/, UInt /nb_old_nodes/) {
	AKANTU_ERROR("The method: computeMeshQueryIntersectionPoint has not "
	"been implemented in class MeshSegmentIntersector!");
	}

	template <UInt dim, ElementType type>
	void MeshSegmentIntersector<dim, type>::buildResultFromQueryList(
	const std::list<K::Segment_3> & query_list) {
	AKANTU_DEBUG_IN();

	this->computeIntersectionQueryList(query_list);

	AKANTU_DEBUG_OUT();
	}

	template <UInt dim, ElementType type>
	void MeshSegmentIntersector<dim, type>::computeSegments(
	const std::list<result_type> & intersections,
	std::set<pair_type, segmentPairsLess> & segments,
	const K::Segment_3 & query) {
	AKANTU_DEBUG_IN();

	/*
	* Number of intersections = 0 means
	*
	* - query is completely outside mesh
	* - query is completely inside primitive
	*
	* We try to determine the case and still construct the segment list
	*/
	if (intersections.empty()) {
	// We look at all the primitives intersected by two rays
	// If there is one primitive in common, then query is inside
	// that primitive
	K::Ray_3 ray1(query.source(), query.target());
	K::Ray_3 ray2(query.target(), query.source());

	std::set<UInt> ray1_results;
	std::set<UInt> ray2_results;

	this->factory.getTree().all_intersected_primitives(
	ray1, std::inserter(ray1_results, ray1_results.begin()));
	this->factory.getTree().all_intersected_primitives(
	ray2, std::inserter(ray2_results, ray2_results.begin()));

	bool inside_primitive = false;
	UInt primitive_id = 0;

	auto ray2_it = ray2_results.begin();
	auto ray2_end = ray2_results.end();

	// Test if first list contains an element of second list
	for (; ray2_it != ray2_end && !inside_primitive; ++ray2_it) {
	if (ray1_results.find(*ray2_it) != ray1_results.end()) {
	inside_primitive = true;
	primitive_id = *ray2_it;
	}
	}

	if (inside_primitive) {
	segments.insert(std::make_pair(query, primitive_id));
	}
	}

	else {
	auto it = intersections.begin();
	auto end = intersections.end();

	for (; it != end; ++it) {
	UInt el = (*it)->second;

	// Result of intersection is a segment
	if (const K::Segment_3 * segment =
	boost::get<K::Segment_3>(&((*it)->first))) {
	// Check if the segment was alread created
	segments.insert(std::make_pair(*segment, el));
	}

	// Result of intersection is a point
	else if (const K::Point_3 * point =
	boost::get<K::Point_3>(&((*it)->first))) {
	// We only want to treat points differently if we're in 3D with Tetra4
	// elements This should be optimized by compilator
	if (dim == 3 && type == _tetrahedron_4) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	TreeTypeHelper<Triangle<K>, K>::container_type facets;

	const Array<Real> & nodes = this->mesh.getNodes();
	Array<UInt>::const_vector_iterator connectivity_vec =
	this->mesh.getConnectivity(type).begin(nb_nodes_per_element);

	const Vector<UInt> & el_connectivity = connectivity_vec[el];

	Matrix<Real> node_coordinates(dim, nb_nodes_per_element);
	for (UInt i = 0; i < nb_nodes_per_element; i++) {
	for (UInt j = 0; j < dim; j++) {
	node_coordinates(j, i) = nodes(el_connectivity(i), j);
	}
	}

	this->factory.addPrimitive(node_coordinates, el, facets);

	// Local tree
	- auto * local_tree =
	- new TreeTypeHelper<Triangle<K>, K>::tree(facets.begin(),
	- facets.end());
	+ auto * local_tree = new TreeTypeHelper<Triangle<K>, K>::tree(
	+ facets.begin(), facets.end());

	// Compute local intersections (with current element)
	std::list<result_type> local_intersections;
	local_tree->all_intersections(
	query, std::back_inserter(local_intersections));

	bool out_point_found = false;
	auto local_it = local_intersections.begin();
	auto local_end = local_intersections.end();

	for (; local_it != local_end; ++local_it) {
	if (const auto * local_point =
	boost::get<K::Point_3>(&((*local_it)->first))) {
	if (!comparePoints(point, local_point)) {
	K::Segment_3 seg(point, local_point);
	segments.insert(std::make_pair(seg, el));
	out_point_found = true;
	}
	}
	}

	if (!out_point_found) {
	using Point = TreeTypeHelper<Triangle<K>, K>::point_type;
	Point a(node_coordinates(0, 0), node_coordinates(1, 0),
	node_coordinates(2, 0));
	Point b(node_coordinates(0, 1), node_coordinates(1, 1),
	node_coordinates(2, 1));
	Point c(node_coordinates(0, 2), node_coordinates(1, 2),
	node_coordinates(2, 2));
	Point d(node_coordinates(0, 3), node_coordinates(1, 3),
	node_coordinates(2, 3));
	K::Tetrahedron_3 tetra(a, b, c, d);
	const K::Point_3 * inside_point = nullptr;
	if (tetra.has_on_bounded_side(query.source()) &&
	!tetra.has_on_boundary(query.source())) {
	inside_point = &query.source();
	} else if (tetra.has_on_bounded_side(query.target()) &&
	!tetra.has_on_boundary(query.target())) {
	inside_point = &query.target();
	}

	if (inside_point != nullptr) {
	K::Segment_3 seg(inside_point, point);
	segments.insert(std::make_pair(seg, el));
	}
	}

	delete local_tree;
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif // AKANTU_MESH_SEGMENT_INTERSECTOR_TMPL_HH_
	diff --git a/src/geometry/mesh_sphere_intersector.hh b/src/geometry/mesh_sphere_intersector.hh
	index 4de042f1f..cba002d25 100644
	--- a/src/geometry/mesh_sphere_intersector.hh
	+++ b/src/geometry/mesh_sphere_intersector.hh
	@@ -1,120 +1,120 @@
	/**
	* @file mesh_sphere_intersector.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Jun 23 2015
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Computation of mesh intersection with sphere(s)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_SPHERE_INTERSECTOR_HH_
	#define AKANTU_MESH_SPHERE_INTERSECTOR_HH_

	#include "aka_common.hh"
	#include "mesh_geom_intersector.hh"

	#include "mesh_geom_common.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <UInt dim, ElementType type>
	class MeshSphereIntersector
	: public MeshGeomIntersector<dim, type, Line_arc<cgal::Spherical>,
	cgal::Spherical::Sphere_3, cgal::Spherical> {
	using SK = cgal::Spherical;
	using K = cgal::Cartesian;

	/// Parent class type
	typedef MeshGeomIntersector<dim, type, Line_arc<SK>, SK::Sphere_3, SK>
	parent_type;

	/// Result of intersection function type
	typedef typename IntersectionTypeHelper<TreeTypeHelper<Triangle<K>, K>,
	K::Segment_3>::intersection_type
	result_type;

	/// Pair of intersection points and element id
	typedef std::pair<SK::Circular_arc_point_3, UInt> pair_type;

	public:
	/// Construct from mesh
	explicit MeshSphereIntersector(Mesh & mesh);

	/// Destructor
	virtual ~MeshSphereIntersector();

	public:
	/// Construct the primitive tree object
	virtual void constructData(GhostType ghost_type = _not_ghost);

	/**
	* @brief Computes the intersection of the mesh with a sphere
	*/
	virtual void computeIntersectionQuery(const SK::Sphere_3 & /* query */) {
	AKANTU_ERROR("This function is not implemented for spheres (It was "
	"to generic and has been replaced by "
	"computeMeshQueryIntersectionPoint");
	}

	/**
	* Compute intersection points between the mesh primitives (segments) and a
	* query (surface in 3D or a curve in 2D), double intersection points for the
	* same primitives are not considered. A maximum is set to the number of
	* intersection nodes per element: 2 in 2D and 4 in 3D
	*/
	virtual void computeMeshQueryIntersectionPoint(const SK::Sphere_3 & query,
	UInt nb_old_nodes);

	/// Build the IGFEM mesh
	virtual void
	buildResultFromQueryList(const std::list<SK::Sphere_3> & /query/) {
	AKANTU_ERROR("This function is no longer implemented to split "
	"geometrical operations and dedicated result "
	"construction");
	}

	/// Set the tolerance
	void setToleranceIntersectionOnNode(UInt tol) {
	this->tol_intersection_on_node = tol;
	}

	protected:
	/// tolerance for which the intersection is considered on the mesh node
	/// (relative to the segment lenght)
	Real tol_intersection_on_node;
	};

	} // namespace akantu

	#include "mesh_sphere_intersector_tmpl.hh"

	#endif // AKANTU_MESH_SPHERE_INTERSECTOR_HH_
	diff --git a/src/geometry/mesh_sphere_intersector_tmpl.hh b/src/geometry/mesh_sphere_intersector_tmpl.hh
	index f5460850d..3a327264d 100644
	--- a/src/geometry/mesh_sphere_intersector_tmpl.hh
	+++ b/src/geometry/mesh_sphere_intersector_tmpl.hh
	@@ -1,216 +1,216 @@
	/**
	* @file mesh_sphere_intersector_tmpl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Jun 23 2015
	* @date last modification: Tue Dec 04 2018
	*
	* @brief Computation of mesh intersection with spheres
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_SPHERE_INTERSECTOR_TMPL_HH_
	#define AKANTU_MESH_SPHERE_INTERSECTOR_TMPL_HH_

	#include "aka_common.hh"
	#include "mesh_geom_common.hh"
	#include "mesh_sphere_intersector.hh"
	#include "tree_type_helper.hh"

	namespace akantu {

	template <UInt dim, ElementType type>
	MeshSphereIntersector<dim, type>::MeshSphereIntersector(Mesh & mesh)
	: parent_type(mesh), tol_intersection_on_node(1e-10) {
	#if defined(AKANTU_IGFEM)
	if ((type == _triangle_3) \|\| (type == _igfem_triangle_4) \|\|
	(type == _igfem_triangle_5)) {
	const_cast<UInt &>(this->nb_seg_by_el) = 3;
	} else {
	AKANTU_ERROR("Not ready for mesh type " << type);
	}
	#else
	if ((type != _triangle_3))
	AKANTU_ERROR("Not ready for mesh type " << type);
	#endif

	// initialize the intersection pointsss array with the spatial dimension
	this->intersection_points = new Array<Real>(0, dim);
	// A maximum is set to the number of intersection nodes per element to limit
	// the size of new_node_per_elem: 2 in 2D and 4 in 3D
	this->new_node_per_elem = new Array<UInt>(0, 1 + 4 * (dim - 1));
	}

	template <UInt dim, ElementType type>
	MeshSphereIntersector<dim, type>::~MeshSphereIntersector() {
	delete this->new_node_per_elem;
	delete this->intersection_points;
	}

	template <UInt dim, ElementType type>
	void MeshSphereIntersector<dim, type>::constructData(GhostType ghost_type) {

	this->new_node_per_elem->resize(this->mesh.getNbElement(type, ghost_type));
	this->new_node_per_elem->clear();

	MeshGeomIntersector<dim, type, Line_arc<SK>, SK::Sphere_3, SK>::constructData(
	ghost_type);
	}

	template <UInt dim, ElementType type>
	void MeshSphereIntersector<dim, type>::computeMeshQueryIntersectionPoint(
	const SK::Sphere_3 & query, UInt nb_old_nodes) {
	/// function to replace computeIntersectionQuery in a more generic geometry
	/// module version
	// The newNodeEvent is not send from this method who only compute the
	// intersection points
	AKANTU_DEBUG_IN();

	Array<Real> & nodes = this->mesh.getNodes();
	UInt nb_node = nodes.size() + this->intersection_points->size();

	// Tolerance for proximity checks should be defined by user
	Real global_tolerance = Math::getTolerance();
	Math::setTolerance(tol_intersection_on_node);
	typedef boost::variant<pair_type> sk_inter_res;

	TreeTypeHelper<Line_arc<cgal::Spherical>, cgal::Spherical>::const_iterator
	it = this->factory.getPrimitiveList().begin(),
	end = this->factory.getPrimitiveList().end();

	for (; it != end; ++it) { // loop on the primitives (segments)
	std::list<sk_inter_res> s_results;
	CGAL::intersection(*it, query, std::back_inserter(s_results));

	if (s_results.size() == 1) { // just one point
	if (pair_type * pair = boost::get<pair_type>(&s_results.front())) {
	if (pair->second == 1) { // not a point tangent to the sphere
	// the intersection point written as a vector
	Vector<Real> new_node(dim, 0.0);
	cgal::Cartesian::Point_3 point(CGAL::to_double(pair->first.x()),
	CGAL::to_double(pair->first.y()),
	CGAL::to_double(pair->first.z()));
	for (UInt i = 0; i < dim; i++) {
	new_node(i) = point[i];
	}

	/// boolean to decide wheter intersection point is on a standard node
	/// of the mesh or not
	bool is_on_mesh = false;
	/// boolean to decide if this intersection point has been already
	/// computed for a neighbor element
	bool is_new = true;

	/// check if intersection point has already been computed
	UInt n = nb_old_nodes;

	// check if we already compute this intersection and add it as a node
	// for a neighboor element of another type
	auto existing_node = nodes.begin(dim);

	for (; n < nodes.size(); ++n) { // loop on the nodes from nb_old_nodes
	if (Math::are_vector_equal(dim, new_node.storage(),
	existing_node[n].storage())) {
	is_new = false;
	break;
	}
	}
	if (is_new) {
	auto intersection_points_it = this->intersection_points->begin(dim);
	auto intersection_points_end = this->intersection_points->end(dim);
	for (; intersection_points_it != intersection_points_end;
	++intersection_points_it, ++n) {
	if (Math::are_vector_equal(dim, new_node.storage(),
	intersection_points_it->storage())) {
	is_new = false;
	break;
	}
	}
	}

	// get the initial and final points of the primitive (segment) and
	// write them as vectors
	cgal::Cartesian::Point_3 source_cgal(
	CGAL::to_double(it->source().x()),
	CGAL::to_double(it->source().y()),
	CGAL::to_double(it->source().z()));
	cgal::Cartesian::Point_3 target_cgal(
	CGAL::to_double(it->target().x()),
	CGAL::to_double(it->target().y()),
	CGAL::to_double(it->target().z()));
	Vector<Real> source(dim), target(dim);
	for (UInt i = 0; i < dim; i++) {
	source(i) = source_cgal[i];
	target(i) = target_cgal[i];
	}

	// Check if we are close from a node of the primitive (segment)
	if (Math::are_vector_equal(dim, source.storage(),
	new_node.storage()) \|\|
	Math::are_vector_equal(dim, target.storage(),
	new_node.storage())) {
	is_on_mesh = true;
	is_new = false;
	}

	if (is_new) { // if the intersection point is a new one add it to the
	// list
	this->intersection_points->push_back(new_node);
	nb_node++;
	}

	// deduce the element id
	UInt element_id = it->id();

	// fill the new_node_per_elem array
	if (!is_on_mesh) { // if the node is not on a mesh node
	UInt & nb_new_nodes_per_el =
	(*this->new_node_per_elem)(element_id, 0);
	nb_new_nodes_per_el += 1;
	AKANTU_DEBUG_ASSERT(
	2 * nb_new_nodes_per_el <
	this->new_node_per_elem->getNbComponent(),
	"You might have to interface crossing the same material");
	(*this->new_node_per_elem)(element_id,
	(2 * nb_new_nodes_per_el) - 1) = n;
	(this->new_node_per_elem)(element_id, 2 nb_new_nodes_per_el) =
	it->segId();
	}
	}
	}
	}
	}

	Math::setTolerance(global_tolerance);

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif // AKANTU_MESH_SPHERE_INTERSECTOR_TMPL_HH_
	diff --git a/src/geometry/tree_type_helper.hh b/src/geometry/tree_type_helper.hh
	index 9f4d0dd66..cf021feb2 100644
	--- a/src/geometry/tree_type_helper.hh
	+++ b/src/geometry/tree_type_helper.hh
	@@ -1,111 +1,111 @@
	/**
	* @file tree_type_helper.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Thu Feb 01 2018
	*
	* @brief Converts element types of a mesh to CGAL primitive types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TREE_TYPE_HELPER_HH_
	#define AKANTU_TREE_TYPE_HELPER_HH_

	#include "aka_common.hh"

	#include "line_arc.hh"
	#include "tetrahedron.hh"
	#include "triangle.hh"

	#include "aabb_primitive.hh"

	#include "mesh_geom_common.hh"
	#include <CGAL/AABB_traits.h>
	#include <CGAL/AABB_tree.h>

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	/// Replacement class for algorithm that can't use the AABB tree types
	template <typename iterator> struct VoidTree {
	VoidTree(const iterator & /begin/, const iterator & /end/) {}
	};

	/// Helper class used to ease the use of CGAL AABB tree algorithm
	template <class Primitive, class Kernel> struct TreeTypeHelper {
	static const bool is_valid = false;

	using primitive_type = Primitive;
	using container_type = typename std::list<primitive_type>;
	using iterator = typename container_type::iterator;
	using const_iterator = typename container_type::const_iterator;
	using point_type = typename CGAL::Point_3<Kernel>;
	using tree = VoidTree<iterator>;
	};

	/// Helper class used to ease the use of intersections
	template <class TTHelper, class Query> struct IntersectionTypeHelper;

	/**
	* Macro used to specialize TreeTypeHelper
	* @param my_primitive associated primitive type
	* @param my_query query_type
	* @param my_kernel kernel type
	*/
	#define TREE_TYPE_HELPER_MACRO(my_primitive, my_query, my_kernel) \
	template <> \
	struct TreeTypeHelper<my_primitive<my_kernel> /NOLINT/, my_kernel> { \
	static const bool is_valid = true; \
	using primitive_type = my_primitive<my_kernel>; /NOLINT/ \
	using aabb_primitive_type = my_primitive##_primitive; \
	using point_type = CGAL::Point_3<my_kernel>; \
	using container_type = std::list<primitive_type>; \
	using iterator = container_type::iterator; \
	using aabb_traits_type = \
	CGAL::AABB_traits<my_kernel, aabb_primitive_type>; \
	using tree = CGAL::AABB_tree<aabb_traits_type>; \
	using id_type = tree::Primitive_id; \
	}; \
	\
	template <> \
	struct IntersectionTypeHelper< \
	TreeTypeHelper<my_primitive<my_kernel>, /NOLINT/ my_kernel>, \
	my_query> { \
	typedef boost::optional<TreeTypeHelper< \
	my_primitive<my_kernel>, /NOLINT/ \
	my_kernel>::tree::Intersection_and_primitive_id<my_query>::Type> \
	intersection_type; \
	}

	TREE_TYPE_HELPER_MACRO(Triangle, cgal::Cartesian::Segment_3, cgal::Cartesian);
	// TREE_TYPE_HELPER_MACRO(Line_arc, cgal::Spherical::Sphere_3, cgal::Spherical);

	#undef TREE_TYPE_HELPER_MACRO

	} // namespace akantu

	#endif // AKANTU_TREE_TYPE_HELPER_HH_
	diff --git a/src/io/dumper/dumpable.cc b/src/io/dumper/dumpable.cc
	index 8ae9559a8..36a184a3a 100644
	--- a/src/io/dumper/dumpable.cc
	+++ b/src/io/dumper/dumpable.cc
	@@ -1,279 +1,279 @@
	/**
	* @file dumpable.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Implementation of the dumpable interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumpable.hh"
	/* -------------------------------------------------------------------------- */

	#ifdef AKANTU_USE_IOHELPER

	#include <io_helper.hh>
	#include <utility>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Dumpable::Dumpable() = default;

	/* -------------------------------------------------------------------------- */
	Dumpable::~Dumpable() = default;

	/* -------------------------------------------------------------------------- */
	void Dumpable::registerExternalDumper(std::shared_ptr<DumperIOHelper> dumper,
	const std::string & dumper_name,
	const bool is_default) {
	this->dumpers[dumper_name] = std::move(dumper);
	if (is_default) {
	this->default_dumper = dumper_name;
	}
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpMesh(const Mesh & mesh, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind) {

	this->addDumpMeshToDumper(this->default_dumper, mesh, spatial_dimension,
	ghost_type, element_kind);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpMeshToDumper(const std::string & dumper_name,
	const Mesh & mesh, UInt spatial_dimension,
	GhostType ghost_type,
	ElementKind element_kind) {

	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerMesh(mesh, spatial_dimension, ghost_type, element_kind);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFilteredMesh(
	const Mesh & mesh, const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind) {
	this->addDumpFilteredMeshToDumper(this->default_dumper, mesh, elements_filter,
	nodes_filter, spatial_dimension, ghost_type,
	element_kind);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFilteredMeshToDumper(
	const std::string & dumper_name, const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind) {

	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerFilteredMesh(mesh, elements_filter, nodes_filter,
	spatial_dimension, ghost_type, element_kind);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpField(const std::string & field_id) {
	this->addDumpFieldToDumper(this->default_dumper, field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldToDumper(__attribute__((unused))
	const std::string & dumper_name,
	__attribute__((unused))
	const std::string & field_id) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldExternal(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	this->addDumpFieldExternalToDumper(this->default_dumper, field_id,
	std::move(field));
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldExternalToDumper(
	const std::string & dumper_name, const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerField(field_id, std::move(field));
	}

	/* -------------------------------------------------------------------------- */

	void Dumpable::removeDumpField(const std::string & field_id) {
	this->removeDumpFieldFromDumper(this->default_dumper, field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::removeDumpFieldFromDumper(const std::string & dumper_name,
	const std::string & field_id) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.unRegisterField(field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldVector(const std::string & field_id) {
	this->addDumpFieldVectorToDumper(this->default_dumper, field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldVectorToDumper(const std::string & /dumper_name/,
	const std::string & /field_id/) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldTensor(const std::string & field_id) {
	this->addDumpFieldTensorToDumper(this->default_dumper, field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::addDumpFieldTensorToDumper(__attribute__((unused))
	const std::string & dumper_name,
	__attribute__((unused))
	const std::string & field_id) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setDirectory(const std::string & directory) {
	this->setDirectoryToDumper(this->default_dumper, directory);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setDirectoryToDumper(const std::string & dumper_name,
	const std::string & directory) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.setDirectory(directory);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setBaseName(const std::string & basename) {
	this->setBaseNameToDumper(this->default_dumper, basename);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setBaseNameToDumper(const std::string & dumper_name,
	const std::string & basename) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.setBaseName(basename);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setTimeStepToDumper(Real time_step) {
	this->setTimeStepToDumper(this->default_dumper, time_step);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setTimeStepToDumper(const std::string & dumper_name,
	Real time_step) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.setTimeStep(time_step);
	}

	/* -------------------------------------------------------------------------- */

	void Dumpable::setTextModeToDumper(const std::string & dumper_name) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.getDumper().setMode(iohelper::TEXT);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::setTextModeToDumper() {
	DumperIOHelper & dumper = this->getDumper(this->default_dumper);
	dumper.getDumper().setMode(iohelper::TEXT);
	}

	/* -------------------------------------------------------------------------- */

	void Dumpable::dump(const std::string & dumper_name) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.dump();
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::dump() { this->dump(this->default_dumper); }

	/* -------------------------------------------------------------------------- */
	void Dumpable::dump(const std::string & dumper_name, UInt step) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.dump(step);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::dump(UInt step) { this->dump(this->default_dumper, step); }

	/* -------------------------------------------------------------------------- */
	void Dumpable::dump(const std::string & dumper_name, Real time, UInt step) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.dump(time, step);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::dump(Real time, UInt step) {
	this->dump(this->default_dumper, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void Dumpable::internalAddDumpFieldToDumper(
	const std::string & dumper_name, const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerField(field_id, std::move(field));
	}

	/* -------------------------------------------------------------------------- */
	DumperIOHelper & Dumpable::getDumper() {
	return this->getDumper(this->default_dumper);
	}

	/* -------------------------------------------------------------------------- */
	DumperIOHelper & Dumpable::getDumper(const std::string & dumper_name) {

	auto it = this->dumpers.find(dumper_name);
	auto end = this->dumpers.end();

	if (it == end) {
	AKANTU_EXCEPTION("Dumper " << dumper_name
	<< "has not been registered, yet.");
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */

	std::string Dumpable::getDefaultDumperName() const {
	return this->default_dumper;
	}

	} // namespace akantu

	#endif
	diff --git a/src/io/dumper/dumpable.hh b/src/io/dumper/dumpable.hh
	index a5f5840d2..cc09253b4 100644
	--- a/src/io/dumper/dumpable.hh
	+++ b/src/io/dumper/dumpable.hh
	@@ -1,48 +1,48 @@
	/**
	* @file dumpable.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 26 2012
	* @date last modification: Tue Oct 01 2019
	*
	* @brief Interface for object who wants to dump themselves
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DUMPABLE_HH_
	#define AKANTU_DUMPABLE_HH_

	#ifdef AKANTU_USE_IOHELPER
	#include "dumpable_iohelper.hh"
	#else
	#include "dumpable_dummy.hh"
	#endif // AKANTU_USE_IOHELPER

	#endif /* AKANTU_DUMPABLE_HH_ */
	diff --git a/src/io/dumper/dumpable_dummy.hh b/src/io/dumper/dumpable_dummy.hh
	index 8faf9f80c..d5c754532 100644
	--- a/src/io/dumper/dumpable_dummy.hh
	+++ b/src/io/dumper/dumpable_dummy.hh
	@@ -1,270 +1,269 @@
	/**
	* @file dumpable_dummy.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 26 2012
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Interface for object who wants to dump themselves
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#if !defined(DOXYGEN)
	#ifndef AKANTU_DUMPABLE_DUMMY_HH_
	#define AKANTU_DUMPABLE_DUMMY_HH_
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wunused"

	namespace dumpers {
	class Field;
	}

	class DumperIOHelper;
	class Mesh;

	/* -------------------------------------------------------------------------- */
	class Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Dumpable(){};
	virtual ~Dumpable(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	template <class T>
	inline void registerDumper(const std::string & dumper_name,
	const std::string & file_name = "",
	const bool is_default = false) {}

	void registerExternalDumper(std::shared_ptr<DumperIOHelper> dumper,
	const std::string & dumper_name,
	const bool is_default = false) {}

	void addDumpMesh(const Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined) {}

	void addDumpMeshToDumper(const std::string & dumper_name, const Mesh & mesh,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) {
	- }
	+ ElementKind element_kind = _ek_not_defined) {}

	void addDumpFilteredMesh(const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) {
	- }
	+ ElementKind element_kind = _ek_not_defined) {}

	- void addDumpFilteredMeshToDumper(
	- const std::string & dumper_name, const Mesh & mesh,
	- const ElementTypeMapArray<UInt> & elements_filter,
	- const Array<UInt> & nodes_filter,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) {}
	+ void
	+ addDumpFilteredMeshToDumper(const std::string & dumper_name,
	+ const Mesh & mesh,
	+ const ElementTypeMapArray<UInt> & elements_filter,
	+ const Array<UInt> & nodes_filter,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined) {}

	virtual void addDumpField(const std::string & field_id) {
	AKANTU_TO_IMPLEMENT();
	}
	virtual void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_TO_IMPLEMENT();
	}

	virtual void addDumpFieldExternal(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	virtual void
	addDumpFieldExternalToDumper(const std::string & dumper_name,
	const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	template <typename T>
	void addDumpFieldExternal(const std::string & field_id,
	const Array<T> & field) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	template <typename T>
	void addDumpFieldExternalToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const Array<T> & field) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	template <typename T>
	- void
	- addDumpFieldExternal(const std::string & field_id,
	- const ElementTypeMapArray<T> & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) {
	+ void addDumpFieldExternal(const std::string & field_id,
	+ const ElementTypeMapArray<T> & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	template <typename T>
	- void addDumpFieldExternalToDumper(
	- const std::string & dumper_name, const std::string & field_id,
	- const ElementTypeMapArray<T> & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) {
	+ void
	+ addDumpFieldExternalToDumper(const std::string & dumper_name,
	+ const std::string & field_id,
	+ const ElementTypeMapArray<T> & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void removeDumpField(const std::string & field_id) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void removeDumpFieldFromDumper(const std::string & dumper_name,
	const std::string & field_id) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void setDirecory(const std::string & directory) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void setDirectoryToDumper(const std::string & dumper_name,
	const std::string & directory) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void setBaseName(const std::string & basename) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void setBaseNameToDumper(const std::string & dumper_name,
	const std::string & basename) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void setTextModeToDumper(const std::string & dumper_name) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void setTextModeToDumper() {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void dump() {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void dump(const std::string & dumper_name) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void dump(UInt step) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void dump(const std::string & dumper_name, UInt step) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	void dump(Real current_time, UInt step) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}
	void dump(const std::string & dumper_name, Real current_time, UInt step) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	protected:
	void internalAddDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	std::shared_ptr<dumpers::Field> field) {
	AKANTU_DEBUG_WARNING("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	protected:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperIOHelper & getDumper() {
	AKANTU_ERROR("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	DumperIOHelper & getDumper(const std::string & dumper_name) {
	AKANTU_ERROR("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	template <class T> T & getDumper(const std::string & dumper_name) {
	AKANTU_ERROR("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	std::string getDefaultDumperName() {
	AKANTU_ERROR("No dumper activated at compilation, turn on "
	"AKANTU_USE_IOHELPER in cmake.");
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	#pragma GCC diagnostic pop

	} // namespace akantu

	#endif /* AKANTU_DUMPABLE_DUMMY_HH_ */
	#endif // DOXYGEN
	diff --git a/src/io/dumper/dumpable_inline_impl.hh b/src/io/dumper/dumpable_inline_impl.hh
	index 0fd69200c..3f36c0a0e 100644
	--- a/src/io/dumper/dumpable_inline_impl.hh
	+++ b/src/io/dumper/dumpable_inline_impl.hh
	@@ -1,137 +1,137 @@
	/**
	* @file dumpable_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the Dumpable class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPABLE_INLINE_IMPL_HH_
	#define AKANTU_DUMPABLE_INLINE_IMPL_HH_

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_elemental_field.hh"
	#include "dumper_nodal_field.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class T>
	inline void Dumpable::registerDumper(const std::string & dumper_name,
	const std::string & file_name,
	const bool is_default) {

	if (this->dumpers.find(dumper_name) != this->dumpers.end()) {
	AKANTU_DEBUG_INFO("Dumper " + dumper_name + "is already registered.");
	}

	std::string name = file_name;
	if (name.empty()) {
	name = dumper_name;
	}

	this->dumpers[dumper_name] = std::make_shared<T>(name);

	if (is_default) {
	this->default_dumper = dumper_name;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Dumpable::addDumpFieldExternal(const std::string & field_id,
	const Array<T> & field) {
	this->addDumpFieldExternalToDumper<T>(this->default_dumper, field_id, field);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void
	Dumpable::addDumpFieldExternalToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const Array<T> & field) {
	auto field_cont = std::make_shared<dumpers::NodalField<T>>(field);
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerField(field_id, field_cont);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Dumpable::addDumpFieldExternal(const std::string & field_id,
	const ElementTypeMapArray<T> & field,
	UInt spatial_dimension,
	GhostType ghost_type,
	ElementKind element_kind) {
	this->addDumpFieldExternalToDumper(this->default_dumper, field_id, field,
	spatial_dimension, ghost_type,
	element_kind);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Dumpable::addDumpFieldExternalToDumper(
	const std::string & dumper_name, const std::string & field_id,
	const ElementTypeMapArray<T> & field, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind) {

	std::shared_ptr<dumpers::Field> field_cont;
	#if defined(AKANTU_IGFEM)
	if (element_kind == _ek_igfem) {
	field_cont = std::make_shared<dumpers::IGFEMElementalField<T>>(
	field, spatial_dimension, ghost_type, element_kind);
	} else
	#endif
	field_cont = std::make_shared<dumpers::ElementalField<T>>(
	field, spatial_dimension, ghost_type, element_kind);
	DumperIOHelper & dumper = this->getDumper(dumper_name);
	dumper.registerField(field_id, field_cont);
	}

	/* -------------------------------------------------------------------------- */
	template <class T>
	inline T & Dumpable::getDumper(const std::string & dumper_name) {
	DumperIOHelper & dumper = this->getDumper(dumper_name);

	try {
	auto & templated_dumper = aka::as_type<T>(dumper);
	return templated_dumper;
	} catch (std::bad_cast &) {
	AKANTU_EXCEPTION("Dumper " << dumper_name << " is not of type: "
	<< debug::demangle(typeid(T).name()));
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif

	#endif /* AKANTU_DUMPABLE_INLINE_IMPL_HH_ */
	diff --git a/src/io/dumper/dumpable_iohelper.hh b/src/io/dumper/dumpable_iohelper.hh
	index 381044d06..d9b1b4318 100644
	--- a/src/io/dumper/dumpable_iohelper.hh
	+++ b/src/io/dumper/dumpable_iohelper.hh
	@@ -1,194 +1,195 @@
	/**
	* @file dumpable_iohelper.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 06 2015
	* @date last modification: Fri Feb 28 2020
	*
	* @brief Interface for object who wants to dump themselves
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper.hh"
	/* -------------------------------------------------------------------------- */
	#include <set>
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DUMPABLE_IOHELPER_HH_
	#define AKANTU_DUMPABLE_IOHELPER_HH_
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Dumpable();
	virtual ~Dumpable();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// create a new dumper (of templated type T) and register it under
	/// dumper_name. file_name is used for construction of T. is default states if
	/// this dumper is the default dumper.
	template <class T>
	inline void registerDumper(const std::string & dumper_name,
	const std::string & file_name = "",
	bool is_default = false);

	/// register an externally created dumper
	void registerExternalDumper(std::shared_ptr<DumperIOHelper> dumper,
	const std::string & dumper_name,
	bool is_default = false);

	/// register a mesh to the default dumper
	void addDumpMesh(const Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	/// register a mesh to the default identified by its name
	void addDumpMeshToDumper(const std::string & dumper_name, const Mesh & mesh,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	/// register a filtered mesh as the default dumper
	void addDumpFilteredMesh(const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	/// register a filtered mesh and provides a name
	- void addDumpFilteredMeshToDumper(
	- const std::string & dumper_name, const Mesh & mesh,
	- const ElementTypeMapArray<UInt> & elements_filter,
	- const Array<UInt> & nodes_filter,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined);
	+ void
	+ addDumpFilteredMeshToDumper(const std::string & dumper_name,
	+ const Mesh & mesh,
	+ const ElementTypeMapArray<UInt> & elements_filter,
	+ const Array<UInt> & nodes_filter,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined);

	/// to implement
	virtual void addDumpField(const std::string & field_id);
	/// to implement
	virtual void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id);
	/// add a field
	virtual void addDumpFieldExternal(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field);
	virtual void
	addDumpFieldExternalToDumper(const std::string & dumper_name,
	const std::string & field_id,
	std::shared_ptr<dumpers::Field> field);

	template <typename T>
	inline void addDumpFieldExternal(const std::string & field_id,
	const Array<T> & field);
	template <typename T>
	inline void addDumpFieldExternalToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const Array<T> & field);
	template <typename T>
	- inline void
	- addDumpFieldExternal(const std::string & field_id,
	- const ElementTypeMapArray<T> & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined);
	+ inline void addDumpFieldExternal(const std::string & field_id,
	+ const ElementTypeMapArray<T> & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined);
	template <typename T>
	- inline void addDumpFieldExternalToDumper(
	- const std::string & dumper_name, const std::string & field_id,
	- const ElementTypeMapArray<T> & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined);
	+ inline void
	+ addDumpFieldExternalToDumper(const std::string & dumper_name,
	+ const std::string & field_id,
	+ const ElementTypeMapArray<T> & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined);

	void removeDumpField(const std::string & field_id);
	void removeDumpFieldFromDumper(const std::string & dumper_name,
	const std::string & field_id);

	virtual void addDumpFieldVector(const std::string & field_id);
	virtual void addDumpFieldVectorToDumper(const std::string & dumper_name,
	const std::string & field_id);

	virtual void addDumpFieldTensor(const std::string & field_id);
	virtual void addDumpFieldTensorToDumper(const std::string & dumper_name,
	const std::string & field_id);

	void setDirectory(const std::string & directory);
	void setDirectoryToDumper(const std::string & dumper_name,
	const std::string & directory);

	void setBaseName(const std::string & basename);

	void setBaseNameToDumper(const std::string & dumper_name,
	const std::string & basename);
	void setTimeStepToDumper(Real time_step);
	void setTimeStepToDumper(const std::string & dumper_name, Real time_step);

	void setTextModeToDumper(const std::string & dumper_name);
	void setTextModeToDumper();

	virtual void dump();
	virtual void dump(UInt step);
	virtual void dump(Real time, UInt step);
	virtual void dump(const std::string & dumper_name);
	virtual void dump(const std::string & dumper_name, UInt step);
	virtual void dump(const std::string & dumper_name, Real time, UInt step);

	public:
	void internalAddDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	std::shared_ptr<dumpers::Field> field);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperIOHelper & getDumper();
	DumperIOHelper & getDumper(const std::string & dumper_name);

	template <class T> T & getDumper(const std::string & dumper_name);
	std::string getDefaultDumperName() const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	using DumperMap = std::map<std::string, std::shared_ptr<DumperIOHelper>>;
	using DumperSet = std::set<std::string>;

	DumperMap dumpers;
	std::string default_dumper;
	};

	} // namespace akantu

	#endif /* AKANTU_DUMPABLE_IOHELPER_HH_ */
	diff --git a/src/io/dumper/dumper_compute.hh b/src/io/dumper/dumper_compute.hh
	index a45832117..c67168973 100644
	--- a/src/io/dumper/dumper_compute.hh
	+++ b/src/io/dumper/dumper_compute.hh
	@@ -1,411 +1,411 @@
	/**
	* @file dumper_compute.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Field that map a function to another field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_COMPUTE_HH_
	#define AKANTU_DUMPER_COMPUTE_HH_
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dumper_field.hh"
	#include "dumper_iohelper.hh"
	#include "dumper_type_traits.hh"
	/* -------------------------------------------------------------------------- */
	#include <aka_iterators.hh>
	/* -------------------------------------------------------------------------- */
	#include <io_helper.hh>
	/* -------------------------------------------------------------------------- */
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {
	/* ------------------------------------------------------------------------ */
	class ComputeFunctorInterface {
	public:
	virtual ~ComputeFunctorInterface() = default;

	virtual UInt getDim() = 0;
	virtual UInt getNbComponent(UInt old_nb_comp) = 0;
	};

	/* ------------------------------------------------------------------------ */

	template <typename return_type>
	class ComputeFunctorOutput : public ComputeFunctorInterface {
	public:
	ComputeFunctorOutput() = default;
	~ComputeFunctorOutput() override = default;
	};

	/* ------------------------------------------------------------------------ */
	template <typename input_type, typename return_type>
	class ComputeFunctor : public ComputeFunctorOutput<return_type> {
	public:
	ComputeFunctor() = default;
	~ComputeFunctor() override = default;

	virtual return_type func(const input_type & /d/,
	Element /global_index/) {
	AKANTU_TO_IMPLEMENT();
	}
	virtual return_type func(const input_type & /d/) {
	AKANTU_TO_IMPLEMENT();
	}
	};

	/* ------------------------------------------------------------------------ */
	template <class EnumType>
	class ComputeUIntFromEnum
	: public ComputeFunctor<Vector<EnumType>, Vector<UInt>> {
	public:
	ComputeUIntFromEnum() = default;

	inline Vector<UInt> func(const Vector<EnumType> & in) override {
	Vector<UInt> out(in.size());
	for (auto && data : zip(in, out)) {
	std::get<1>(data) =
	static_cast<std::underlying_type_t<EnumType>>(std::get<0>(data));
	}

	return out;
	}

	UInt getDim() override { return 1; };
	UInt getNbComponent(UInt old_nb_comp) override { return old_nb_comp; };
	};

	/* ------------------------------------------------------------------------ */
	template <typename SubFieldCompute, typename _return_type,
	class support_type_ = typename SubFieldCompute::support_type>
	class FieldCompute : public Field {
	/* ---------------------------------------------------------------------- */
	/* Typedefs */
	/* ---------------------------------------------------------------------- */
	public:
	using return_type = _return_type;
	using support_type = support_type_;

	using sub_iterator = typename SubFieldCompute::iterator;
	using sub_types = typename SubFieldCompute::types;
	using sub_return_type = typename sub_types::return_type;
	using data_type = typename return_type::value_type;
	using functor_type = ComputeFunctor<sub_return_type, return_type>;

	using types = TypeTraits<data_type, return_type, Array<data_type>>;

	public:
	class iterator {
	public:
	iterator(const sub_iterator & it, functor_type & func)
	: it(it), func(func) {}

	bool operator!=(const iterator & it) const { return it.it != this->it; }

	iterator operator++() {
	++this->it;
	return *this;
	}

	return_type operator() { return func.func(it); }

	/// Do to IOHelper the needs it...
	UInt element_type() { return this->it.element_type(); }

	protected:
	sub_iterator it;
	functor_type & func;
	};

	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	FieldCompute(SubFieldCompute & cont,
	std::unique_ptr<ComputeFunctorInterface> func)
	: sub_field(aka::as_type<SubFieldCompute>(cont.shared_from_this())),
	func(aka::as_type<functor_type>(func.release())) {
	this->checkHomogeneity();
	};

	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addNodeDataField(id, *this);
	}

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	public:
	iterator begin() { return iterator(sub_field->begin(), *func); }
	iterator end() { return iterator(sub_field->end(), *func); }

	UInt getDim() { return func->getDim(); }

	UInt size() {
	throw;
	// return Functor::size();
	return 0;
	}

	void checkHomogeneity() override { this->homogeneous = true; };

	iohelper::DataType getDataType() {
	return iohelper::getDataType<data_type>();
	}

	/// for connection to a FieldCompute
	inline std::shared_ptr<Field> connect(FieldComputeProxy & proxy) override;

	/// for connection to a FieldCompute
	std::unique_ptr<ComputeFunctorInterface>
	connect(HomogenizerProxy & proxy) override;

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	public:
	std::shared_ptr<SubFieldCompute> sub_field;
	std::unique_ptr<functor_type> func;
	};

	/* ------------------------------------------------------------------------ */
	template <typename SubFieldCompute, typename _return_type>
	class FieldCompute<SubFieldCompute, _return_type, Element> : public Field {
	/* ---------------------------------------------------------------------- */
	/* Typedefs */
	/* ---------------------------------------------------------------------- */
	public:
	using return_type = _return_type;
	using support_type = Element;

	using sub_iterator = typename SubFieldCompute::iterator;
	using sub_types = typename SubFieldCompute::types;
	using sub_return_type = typename sub_types::return_type;
	using data_type = typename sub_types::data_type;
	using functor_type = ComputeFunctor<sub_return_type, return_type>;

	using types =
	TypeTraits<data_type, return_type, ElementTypeMapArray<data_type>>;

	public:
	class iterator {
	public:
	iterator(const sub_iterator & it, functor_type & func)
	: it(it), func(func) {}

	bool operator!=(const iterator & it) const { return it.it != this->it; }
	iterator operator++() {
	++this->it;
	return *this;
	}

	UInt currentGlobalIndex() { return this->it.currentGlobalIndex(); }

	return_type operator() { return func.func(it, it.getCurrentElement()); }

	Element getCurrentElement() { return this->it.getCurrentElement(); }

	UInt element_type() { return this->it.element_type(); }

	protected:
	sub_iterator it;
	functor_type & func;
	};

	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	FieldCompute(SubFieldCompute & cont,
	std::unique_ptr<ComputeFunctorInterface> func)
	: sub_field(aka::as_type<SubFieldCompute>(cont.shared_from_this())),
	func(aka::as_type<functor_type>(func.release())) {
	this->checkHomogeneity();
	};

	~FieldCompute() override = default;

	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addElemDataField(id, *this);
	}

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	public:
	iterator begin() { return iterator(sub_field->begin(), *func); }
	iterator end() { return iterator(sub_field->end(), *func); }

	UInt getDim() { return func->getDim(); }

	UInt size() {
	throw;
	// return Functor::size();
	return 0;
	}

	void checkHomogeneity() override { this->homogeneous = true; };

	template <class T1 = data_type,
	std::enable_if_t<std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<UInt>();
	}

	template <class T1 = data_type,
	std::enable_if_t<not std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<data_type>();
	}

	/// get the number of components of the hosted field
	ElementTypeMap<UInt>
	getNbComponents(UInt dim = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) override {
	ElementTypeMap<UInt> nb_components;
	const auto & old_nb_components =
	this->sub_field->getNbComponents(dim, ghost_type, kind);

	for (auto type : old_nb_components.elementTypes(dim, ghost_type, kind)) {
	UInt nb_comp = old_nb_components(type, ghost_type);
	nb_components(type, ghost_type) = func->getNbComponent(nb_comp);
	}
	return nb_components;
	};

	/// for connection to a FieldCompute
	inline std::shared_ptr<Field> connect(FieldComputeProxy & proxy) override;

	/// for connection to a FieldCompute
	std::unique_ptr<ComputeFunctorInterface>
	connect(HomogenizerProxy & proxy) override;

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	public:
	std::shared_ptr<SubFieldCompute> sub_field;
	std::unique_ptr<functor_type> func;
	};

	/* ------------------------------------------------------------------------ */
	class FieldComputeProxy {
	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	FieldComputeProxy(std::unique_ptr<ComputeFunctorInterface> func)
	: func(std::move(func)){};

	inline static std::shared_ptr<Field>
	createFieldCompute(std::shared_ptr<Field> & field,
	std::unique_ptr<ComputeFunctorInterface> func) {
	FieldComputeProxy compute_proxy(std::move(func));
	return field->connect(compute_proxy);
	}

	template <typename T> std::shared_ptr<Field> connectToField(T * ptr) {
	if (aka::is_of_type<ComputeFunctorOutput<Vector<Real>>>(func)) {
	return this->connectToFunctor<Vector<Real>>(ptr);
	}

	if (aka::is_of_type<ComputeFunctorOutput<Vector<UInt>>>(func)) {
	return this->connectToFunctor<Vector<UInt>>(ptr);
	}

	if (aka::is_of_type<ComputeFunctorOutput<Matrix<UInt>>>(func)) {
	return this->connectToFunctor<Matrix<UInt>>(ptr);
	}

	if (aka::is_of_type<ComputeFunctorOutput<Matrix<Real>>>(func)) {
	return this->connectToFunctor<Matrix<Real>>(ptr);
	}
	throw;
	}

	template <typename output, typename T>
	std::shared_ptr<Field> connectToFunctor(T * ptr) {
	return std::make_shared<FieldCompute<T, output>>(*ptr, std::move(func));
	}

	template <typename output, typename SubFieldCompute, typename return_type1,
	typename return_type2>
	std::shared_ptr<Field>
	connectToFunctor(FieldCompute<FieldCompute<SubFieldCompute, return_type1>,
	return_type2> * /ptr/) {
	throw; // return new FieldCompute<T,output>(*ptr,func);
	return nullptr;
	}

	template <typename output, typename SubFieldCompute, typename return_type1,
	typename return_type2, typename return_type3,
	typename return_type4>
	std::shared_ptr<Field> connectToFunctor(
	FieldCompute<FieldCompute<FieldCompute<FieldCompute<SubFieldCompute,
	return_type1>,
	return_type2>,
	return_type3>,
	return_type4> * /ptr/) {
	throw; // return new FieldCompute<T,output>(*ptr,func);
	return nullptr;
	}

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	public:
	std::unique_ptr<ComputeFunctorInterface> func;
	};

	/* ------------------------------------------------------------------------ */
	/// for connection to a FieldCompute
	template <typename SubFieldCompute, typename return_type,
	typename support_type_>
	inline std::shared_ptr<Field>
	FieldCompute<SubFieldCompute, return_type, support_type_>::connect(
	FieldComputeProxy & proxy) {
	return proxy.connectToField(this);
	}

	template <typename SubFieldCompute, typename return_type>
	inline std::shared_ptr<Field>
	FieldCompute<SubFieldCompute, return_type, Element>::connect(
	FieldComputeProxy & proxy) {
	return proxy.connectToField(this);
	}

	/* ------------------------------------------------------------------------ */
	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_COMPUTE_HH_ */
	diff --git a/src/io/dumper/dumper_element_iterator.hh b/src/io/dumper/dumper_element_iterator.hh
	index f2df0326f..6760f3bf9 100644
	--- a/src/io/dumper/dumper_element_iterator.hh
	+++ b/src/io/dumper/dumper_element_iterator.hh
	@@ -1,180 +1,197 @@
	/**
	* @file dumper_element_iterator.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Iterators for elemental fields
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_ELEMENT_ITERATOR_HH_
	#define AKANTU_DUMPER_ELEMENT_ITERATOR_HH_
	/* -------------------------------------------------------------------------- */
	#include "element.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <class types, template <class> class final_iterator>
	+ class element_iterator {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ using it_type = typename types::it_type;
	+ using field_type = typename types::field_type;
	+ using array_type = typename types::array_type;
	+ using array_iterator = typename types::array_iterator;
	+ using iterator = final_iterator<types>;
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ element_iterator(const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it,
	+ const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost)
	+ : field(field), tit(t_it), tit_end(t_it_end), array_it(array_it),
	+ array_it_end(array_it_end), ghost_type(ghost_type) {}
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ public:
	+ bool operator!=(const iterator & it) const {
	+ return (ghost_type != it.ghost_type) \|\|
	+ (tit != it.tit \|\| (array_it != it.array_it));
	+ }
	+
	+ iterator & operator++() {
	+ ++array_it;
	+ while (array_it == array_it_end && tit != tit_end) {
	+ ++tit;
	+ if (tit != tit_end) {

	-template <class types, template <class> class final_iterator>
	-class element_iterator {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- using it_type = typename types::it_type;
	- using field_type = typename types::field_type;
	- using array_type = typename types::array_type;
	- using array_iterator = typename types::array_iterator;
	- using iterator = final_iterator<types>;
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- element_iterator(const field_type & field,
	- const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it,
	- const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost)
	- : field(field), tit(t_it), tit_end(t_it_end), array_it(array_it),
	- array_it_end(array_it_end), ghost_type(ghost_type) {}
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	-public:
	- bool operator!=(const iterator & it) const {
	- return (ghost_type != it.ghost_type) \|\|
	- (tit != it.tit \|\| (array_it != it.array_it));
	- }
	-
	- iterator & operator++() {
	- ++array_it;
	- while (array_it == array_it_end && tit != tit_end) {
	- ++tit;
	- if (tit != tit_end) {
	-
	- const array_type & vect = field(*tit, ghost_type);
	- UInt _nb_data_per_elem = getNbDataPerElem(*tit);
	- UInt nb_component = vect.getNbComponent();
	- UInt size = (vect.size() * nb_component) / _nb_data_per_elem;
	-
	- array_it = vect.begin_reinterpret(_nb_data_per_elem, size);
	- array_it_end = vect.end_reinterpret(_nb_data_per_elem, size);
	+ const array_type & vect = field(*tit, ghost_type);
	+ UInt _nb_data_per_elem = getNbDataPerElem(*tit);
	+ UInt nb_component = vect.getNbComponent();
	+ UInt size = (vect.size() * nb_component) / _nb_data_per_elem;
	+
	+ array_it = vect.begin_reinterpret(_nb_data_per_elem, size);
	+ array_it_end = vect.end_reinterpret(_nb_data_per_elem, size);
	+ }
	}
	- }
	- return (static_cast<iterator >(this));
	- };
	+ return (static_cast<iterator >(this));
	+ };

	- ElementType getType() { return *tit; }
	+ ElementType getType() { return *tit; }

	- UInt element_type() { return getIOHelperType(*tit); }
	+ UInt element_type() { return getIOHelperType(*tit); }

	- Element getCurrentElement() {
	- return Element{*tit, array_it.getCurrentIndex(), _not_ghost};
	- }
	+ Element getCurrentElement() {
	+ return Element{*tit, array_it.getCurrentIndex(), _not_ghost};
	+ }

	- UInt getNbDataPerElem(ElementType type) const {
	- if (!nb_data_per_elem.exists(type, ghost_type)) {
	- return field(type, ghost_type).getNbComponent();
	+ UInt getNbDataPerElem(ElementType type) const {
	+ if (!nb_data_per_elem.exists(type, ghost_type)) {
	+ return field(type, ghost_type).getNbComponent();
	+ }
	+
	+ return nb_data_per_elem(type, ghost_type);
	}

	- return nb_data_per_elem(type, ghost_type);
	- }
	-
	- void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) {
	- this->nb_data_per_elem = nb_data;
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-
	-protected:
	- /// the field to iterate on
	- const field_type & field;
	- /// field iterator
	- typename field_type::type_iterator tit;
	- /// field iterator end
	- typename field_type::type_iterator tit_end;
	- /// array iterator
	- array_iterator array_it;
	- /// internal iterator end
	- array_iterator array_it_end;
	- /// ghost type identification
	- const GhostType ghost_type;
	- /// number of data per element
	- ElementTypeMap<UInt> nb_data_per_elem;
	-};
	+ void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) {
	+ this->nb_data_per_elem = nb_data;
	+ }

	-/* -------------------------------------------------------------------------- */
	-template <typename types>
	-class elemental_field_iterator
	- : public element_iterator<types, elemental_field_iterator> {
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-
	- using parent =
	- element_iterator<types, ::akantu::dumpers::elemental_field_iterator>;
	- using it_type = typename types::it_type;
	- using return_type = typename types::return_type;
	- using field_type = typename types::field_type;
	- using array_iterator = typename types::array_iterator;
	-
	-public:
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-
	- elemental_field_iterator(const field_type & field,
	- const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it,
	- const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {}
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-
	- return_type operator() { return this->array_it; }
	-
	-private:
	-};
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ protected:
	+ /// the field to iterate on
	+ const field_type & field;
	+ /// field iterator
	+ typename field_type::type_iterator tit;
	+ /// field iterator end
	+ typename field_type::type_iterator tit_end;
	+ /// array iterator
	+ array_iterator array_it;
	+ /// internal iterator end
	+ array_iterator array_it_end;
	+ /// ghost type identification
	+ const GhostType ghost_type;
	+ /// number of data per element
	+ ElementTypeMap<UInt> nb_data_per_elem;
	+ };

	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <typename types>
	+ class elemental_field_iterator
	+ : public element_iterator<types, elemental_field_iterator> {
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ using parent =
	+ element_iterator<types, ::akantu::dumpers::elemental_field_iterator>;
	+ using it_type = typename types::it_type;
	+ using return_type = typename types::return_type;
	+ using field_type = typename types::field_type;
	+ using array_iterator = typename types::array_iterator;
	+
	+ public:
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ elemental_field_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {}
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+
	+ return_type operator() { return this->array_it; }
	+
	+ private:
	+ };
	+
	+ /* --------------------------------------------------------------------------
	+ */
	} // namespace dumpers
	} // namespace akantu
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_DUMPER_ELEMENT_ITERATOR_HH_ */
	diff --git a/src/io/dumper/dumper_element_partition.hh b/src/io/dumper/dumper_element_partition.hh
	index 1b3bf50b4..38889f2cf 100644
	--- a/src/io/dumper/dumper_element_partition.hh
	+++ b/src/io/dumper/dumper_element_partition.hh
	@@ -1,138 +1,138 @@
	/**
	* @file dumper_element_partition.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief ElementPartition field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	#ifdef AKANTU_IGFEM
	#include "dumper_igfem_element_partition.hh"
	#endif
	/* --------------------------------------------------------------------------
	*/
	template <class types>
	class element_partition_field_iterator
	: public element_iterator<types, element_partition_field_iterator> {

	/* ------------------------------------------------------------------------
	*/
	/* Typedefs */
	/* ------------------------------------------------------------------------
	*/
	public:
	using parent =
	element_iterator<types, dumpers::element_partition_field_iterator>;
	using return_type =
	typename SingleType<unsigned int, Vector, true>::return_type;
	using array_iterator = typename types::array_iterator;
	using field_type = typename types::field_type;

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/
	public:
	element_partition_field_iterator(
	const field_type & field,
	const typename field_type::type_iterator & t_it,
	const typename field_type::type_iterator & t_it_end,
	const array_iterator & array_it, const array_iterator & array_it_end,
	const GhostType ghost_type = _not_ghost)
	: parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {
	prank = Communicator::getStaticCommunicator().whoAmI();
	}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/
	public:
	return_type operator*() { return return_type(1, prank); }

	/* ------------------------------------------------------------------------
	*/
	/* Class Members */
	/* ------------------------------------------------------------------------
	*/
	protected:
	UInt prank;
	};

	/* --------------------------------------------------------------------------
	*/
	template <bool filtered = false>
	class ElementPartitionField
	: public GenericElementalField<SingleType<UInt, Vector, filtered>,
	element_partition_field_iterator> {
	public:
	/* ------------------------------------------------------------------------
	*/
	/* Typedefs */
	/* ------------------------------------------------------------------------
	*/

	using types = SingleType<UInt, Vector, filtered>;
	using iterator = element_partition_field_iterator<types>;
	using parent =
	GenericElementalField<types, element_partition_field_iterator>;
	using field_type = typename types::field_type;

	public:
	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/

	ElementPartitionField(const field_type & field,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined)
	: parent(field, spatial_dimension, ghost_type, element_kind) {
	this->homogeneous = true;
	}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/

	UInt getDim() override { return 1; }
	};

	/* --------------------------------------------------------------------------
	*/

	-} // namespace dumper
	+} // namespace dumpers
	} // namespace akantu
	diff --git a/src/io/dumper/dumper_elemental_field.hh b/src/io/dumper/dumper_elemental_field.hh
	index 29c201308..ad740e67c 100644
	--- a/src/io/dumper/dumper_elemental_field.hh
	+++ b/src/io/dumper/dumper_elemental_field.hh
	@@ -1,77 +1,83 @@
	/**
	* @file dumper_elemental_field.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief description of elemental fields
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_ELEMENTAL_FIELD_HH_
	#define AKANTU_DUMPER_ELEMENTAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "dumper_field.hh"
	#include "dumper_generic_elemental_field.hh"
	#ifdef AKANTU_IGFEM
	#include "dumper_igfem_elemental_field.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	-template <typename T, template <class> class ret = Vector,
	- bool filtered = false>
	-class ElementalField
	- : public GenericElementalField<SingleType<T, ret, filtered>,
	- elemental_field_iterator> {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- using types = SingleType<T, ret, filtered>;
	- using field_type = typename types::field_type;
	- using iterator = elemental_field_iterator<types>;
	- using support_type = Element;
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- ElementalField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined)
	- : GenericElementalField<types, elemental_field_iterator>(
	- field, spatial_dimension, ghost_type, element_kind) {}
	-};
	+ template <typename T, template <class> class ret = Vector,
	+ bool filtered = false>
	+ class ElementalField
	+ : public GenericElementalField<SingleType<T, ret, filtered>,
	+ elemental_field_iterator> {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ using types = SingleType<T, ret, filtered>;
	+ using field_type = typename types::field_type;
	+ using iterator = elemental_field_iterator<types>;
	+ using support_type = Element;
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ ElementalField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined)
	+ : GenericElementalField<types, elemental_field_iterator>(
	+ field, spatial_dimension, ghost_type, element_kind) {}
	+ };

	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_ELEMENTAL_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_field.hh b/src/io/dumper/dumper_field.hh
	index 8d935070d..ad0cadabf 100644
	--- a/src/io/dumper/dumper_field.hh
	+++ b/src/io/dumper/dumper_field.hh
	@@ -1,138 +1,149 @@
	/**
	* @file dumper_field.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Common interface for fields
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_FIELD_HH_
	#define AKANTU_DUMPER_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-class FieldComputeProxy;
	-class FieldComputeBaseInterface;
	-class ComputeFunctorInterface;
	-class HomogenizerProxy;
	-/* -------------------------------------------------------------------------- */
	-
	-/// Field interface
	-class Field : public std::enable_shared_from_this<Field> {
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- Field() = default;
	- virtual ~Field() = default;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-public:
	+ /* --------------------------------------------------------------------------
	+ */
	+ class FieldComputeProxy;
	+ class FieldComputeBaseInterface;
	+ class ComputeFunctorInterface;
	+ class HomogenizerProxy;
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ /// Field interface
	+ class Field : public std::enable_shared_from_this<Field> {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ Field() = default;
	+ virtual ~Field() = default;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	#ifdef AKANTU_USE_IOHELPER
	- /// register this to the provided dumper
	- virtual void registerToDumper(const std::string & id,
	- iohelper::Dumper & dumper) = 0;
	+ /// register this to the provided dumper
	+ virtual void registerToDumper(const std::string & id,
	+ iohelper::Dumper & dumper) = 0;
	#endif

	- /// set the number of data per item (used for elements fields at the moment)
	- virtual void setNbData([[gnu::unused]] UInt nb_data) {
	- AKANTU_TO_IMPLEMENT();
	- };
	-
	- /// set the number of data per elem (used for elements fields at the moment)
	- virtual void setNbDataPerElem([
	- [gnu::unused]] const ElementTypeMap<UInt> & nb_data) {
	- AKANTU_TO_IMPLEMENT();
	- };
	-
	- /// set the number of data per elem (used for elements fields at the moment)
	- virtual void setNbDataPerElem([[gnu::unused]] UInt nb_data) {
	- AKANTU_TO_IMPLEMENT();
	+ /// set the number of data per item (used for elements fields at the moment)
	+ virtual void setNbData([[gnu::unused]] UInt nb_data) {
	+ AKANTU_TO_IMPLEMENT();
	+ };
	+
	+ /// set the number of data per elem (used for elements fields at the moment)
	+ virtual void
	+ setNbDataPerElem([[gnu::unused]] const ElementTypeMap<UInt> & nb_data) {
	+ AKANTU_TO_IMPLEMENT();
	+ };
	+
	+ /// set the number of data per elem (used for elements fields at the moment)
	+ virtual void setNbDataPerElem([[gnu::unused]] UInt nb_data) {
	+ AKANTU_TO_IMPLEMENT();
	+ };
	+
	+ /// get the number of components of the hosted field
	+ virtual ElementTypeMap<UInt>
	+ getNbComponents([[gnu::unused]] UInt dim = _all_dimensions,
	+ [[gnu::unused]] GhostType ghost_type = _not_ghost,
	+ [[gnu::unused]] ElementKind kind = _ek_not_defined) {
	+ throw;
	+ };
	+
	+ /// for connection to a FieldCompute
	+ inline virtual std::shared_ptr<Field>
	+ connect([[gnu::unused]] FieldComputeProxy & proxy) {
	+ throw;
	+ };
	+
	+ /// for connection to a FieldCompute
	+ inline virtual std::unique_ptr<ComputeFunctorInterface>
	+ connect(HomogenizerProxy & /proxy/) {
	+ throw;
	+ };
	+
	+ /// check if the same quantity of data for all element types
	+ virtual void checkHomogeneity() = 0;
	+
	+ /// return the dumper name
	+ std::string getGroupName() { return group_name; };
	+
	+ /// return the id of the field
	+ std::string getID() { return field_id; };
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Accessors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ /// return the flag to know if the field is homogeneous/contiguous
	+ virtual bool isHomogeneous() { return homogeneous; }
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+ protected:
	+ /// the flag to know if it is homogeneous
	+ bool homogeneous{false};
	+
	+ /// the name of the group it was associated to
	+ std::string group_name;
	+
	+ /// the name of the dumper it was associated to
	+ std::string field_id;
	};

	- /// get the number of components of the hosted field
	- virtual ElementTypeMap<UInt>
	- getNbComponents([[gnu::unused]] UInt dim = _all_dimensions,
	- [[gnu::unused]] GhostType ghost_type = _not_ghost,
	- [[gnu::unused]] ElementKind kind = _ek_not_defined) {
	- throw;
	- };
	-
	- /// for connection to a FieldCompute
	- inline virtual std::shared_ptr<Field> connect([
	- [gnu::unused]] FieldComputeProxy & proxy) {
	- throw;
	- };
	-
	- /// for connection to a FieldCompute
	- inline virtual std::unique_ptr<ComputeFunctorInterface>
	- connect(HomogenizerProxy & /proxy/) {
	- throw;
	- };
	-
	- /// check if the same quantity of data for all element types
	- virtual void checkHomogeneity() = 0;
	-
	- /// return the dumper name
	- std::string getGroupName() { return group_name; };
	-
	- /// return the id of the field
	- std::string getID() { return field_id; };
	-
	- /* ------------------------------------------------------------------------ */
	- /* Accessors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- /// return the flag to know if the field is homogeneous/contiguous
	- virtual bool isHomogeneous() { return homogeneous; }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-protected:
	- /// the flag to know if it is homogeneous
	- bool homogeneous{false};
	-
	- /// the name of the group it was associated to
	- std::string group_name;
	-
	- /// the name of the dumper it was associated to
	- std::string field_id;
	-};
	-
	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_filtered_connectivity.hh b/src/io/dumper/dumper_filtered_connectivity.hh
	index 3517122b6..1b0546521 100644
	--- a/src/io/dumper/dumper_filtered_connectivity.hh
	+++ b/src/io/dumper/dumper_filtered_connectivity.hh
	@@ -1,174 +1,174 @@
	/**
	* @file dumper_filtered_connectivity.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief FilteredConnectivities field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "dumper_generic_elemental_field.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	/* --------------------------------------------------------------------------
	*/

	template <class types>
	class filtered_connectivity_field_iterator
	: public element_iterator<types, filtered_connectivity_field_iterator> {
	/* ------------------------------------------------------------------------
	*/
	/* Typedefs */
	/* ------------------------------------------------------------------------
	*/
	public:
	using parent =
	element_iterator<types, dumpers::filtered_connectivity_field_iterator>;
	using return_type = typename types::return_type;
	using field_type = typename types::field_type;
	using array_iterator = typename types::array_iterator;

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/
	public:
	filtered_connectivity_field_iterator(
	const field_type & field,
	const typename field_type::type_iterator & t_it,
	const typename field_type::type_iterator & t_it_end,
	const array_iterator & array_it, const array_iterator & array_it_end,
	const GhostType ghost_type = _not_ghost)
	: parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/
	public:
	return_type operator*() {
	const Vector<UInt> & old_connect = *this->array_it;
	Vector<UInt> new_connect(old_connect.size());
	Array<UInt>::const_iterator<UInt> nodes_begin = nodal_filter->begin();
	Array<UInt>::const_iterator<UInt> nodes_end = nodal_filter->end();
	for (UInt i(0); i < old_connect.size(); ++i) {
	Array<UInt>::const_iterator<UInt> new_id =
	std::find(nodes_begin, nodes_end, old_connect(i));
	if (new_id == nodes_end) {
	AKANTU_EXCEPTION("Node not found in the filter!");
	}
	new_connect(i) = new_id - nodes_begin;
	}
	return new_connect;
	}

	void setNodalFilter(const Array<UInt> & new_nodal_filter) {
	nodal_filter = &new_nodal_filter;
	}

	/* ------------------------------------------------------------------------
	*/
	/* Class Members */
	/* ------------------------------------------------------------------------
	*/
	private:
	const Array<UInt> * nodal_filter;
	};

	/* --------------------------------------------------------------------------
	*/

	class FilteredConnectivityField
	: public GenericElementalField<SingleType<UInt, Vector, true>,
	filtered_connectivity_field_iterator> {
	/* ------------------------------------------------------------------------
	*/
	/* Typedefs */
	/* ------------------------------------------------------------------------
	*/
	public:
	using types = SingleType<UInt, Vector, true>;
	using iterator = filtered_connectivity_field_iterator<types>;
	using field_type = types::field_type;
	using parent =
	GenericElementalField<types, filtered_connectivity_field_iterator>;

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/
	public:
	FilteredConnectivityField(const field_type & field,
	const Array<UInt> & nodal_filter,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined)
	: parent(field, spatial_dimension, ghost_type, element_kind),
	nodal_filter(nodal_filter) {}

	~FilteredConnectivityField() override {
	// since the field is created in registerFilteredMesh it is destroyed here
	delete const_cast<field_type *>(&this->field);
	}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/
	public:
	iterator begin() override {
	iterator it = parent::begin();
	it.setNodalFilter(nodal_filter);
	return it;
	}

	iterator end() override {
	iterator it = parent::end();
	it.setNodalFilter(nodal_filter);
	return it;
	}

	/* ------------------------------------------------------------------------
	*/
	/* Class Members */
	/* ------------------------------------------------------------------------
	*/
	private:
	const Array<UInt> & nodal_filter;
	};

	/* --------------------------------------------------------------------------
	*/

	} // namespace dumpers
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	diff --git a/src/io/dumper/dumper_generic_elemental_field.hh b/src/io/dumper/dumper_generic_elemental_field.hh
	index 0b9c0dd89..9613b942b 100644
	--- a/src/io/dumper/dumper_generic_elemental_field.hh
	+++ b/src/io/dumper/dumper_generic_elemental_field.hh
	@@ -1,231 +1,241 @@
	/**
	* @file dumper_generic_elemental_field.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Generic interface for elemental fields
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_GENERIC_ELEMENTAL_FIELD_HH_
	#define AKANTU_DUMPER_GENERIC_ELEMENTAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_element_iterator.hh"
	#include "dumper_field.hh"
	#include "dumper_homogenizing_field.hh"
	#include "element_type_map_filter.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	-
	-template <class _types, template <class> class iterator_type>
	-class GenericElementalField : public Field {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- // check dumper_type_traits.hh for additional information over these types
	- using types = _types;
	- using data_type = typename types::data_type;
	- using it_type = typename types::it_type;
	- using field_type = typename types::field_type;
	- using array_type = typename types::array_type;
	- using array_iterator = typename types::array_iterator;
	- using field_type_iterator = typename field_type::type_iterator;
	- using iterator = iterator_type<types>;
	- using support_type = Element;
	-
	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- GenericElementalField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined)
	- : field(field), spatial_dimension(spatial_dimension),
	- ghost_type(ghost_type), element_kind(element_kind) {
	- this->checkHomogeneity();
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Methods */
	- /* ------------------------------------------------------------------------ */
	-public:
	- /// get the number of components of the hosted field
	- ElementTypeMap<UInt>
	- getNbComponents(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	- ElementKind kind = _ek_not_defined) override {
	- return this->field.getNbComponents(dim, ghost_type, kind);
	- };
	+ /* --------------------------------------------------------------------------
	+ */
	+
	+ template <class _types, template <class> class iterator_type>
	+ class GenericElementalField : public Field {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ // check dumper_type_traits.hh for additional information over these types
	+ using types = _types;
	+ using data_type = typename types::data_type;
	+ using it_type = typename types::it_type;
	+ using field_type = typename types::field_type;
	+ using array_type = typename types::array_type;
	+ using array_iterator = typename types::array_iterator;
	+ using field_type_iterator = typename field_type::type_iterator;
	+ using iterator = iterator_type<types>;
	+ using support_type = Element;
	+
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ GenericElementalField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined)
	+ : field(field), spatial_dimension(spatial_dimension),
	+ ghost_type(ghost_type), element_kind(element_kind) {
	+ this->checkHomogeneity();
	+ }

	- /// return the size of the contained data: i.e. the number of elements ?
	- virtual UInt size() {
	- checkHomogeneity();
	- return this->nb_total_element;
	- }
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Methods */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ /// get the number of components of the hosted field
	+ ElementTypeMap<UInt>
	+ getNbComponents(UInt dim = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind kind = _ek_not_defined) override {
	+ return this->field.getNbComponents(dim, ghost_type, kind);
	+ };
	+
	+ /// return the size of the contained data: i.e. the number of elements ?
	+ virtual UInt size() {
	+ checkHomogeneity();
	+ return this->nb_total_element;
	+ }

	- /// return the iohelper datatype to be dumped
	+ /// return the iohelper datatype to be dumped
	template <class T1 = data_type,
	std::enable_if_t<std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<UInt>();
	}

	template <class T1 = data_type,
	std::enable_if_t<not std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<data_type>();
	}

	-protected:
	- /// return the number of entries per element
	- UInt getNbDataPerElem(ElementType type,
	- GhostType ghost_type = _not_ghost) const {
	- if (!nb_data_per_elem.exists(type, ghost_type)) {
	- return field(type, ghost_type).getNbComponent();
	+ protected:
	+ /// return the number of entries per element
	+ UInt getNbDataPerElem(ElementType type,
	+ GhostType ghost_type = _not_ghost) const {
	+ if (!nb_data_per_elem.exists(type, ghost_type)) {
	+ return field(type, ghost_type).getNbComponent();
	+ }
	+
	+ return nb_data_per_elem(type, this->ghost_type);
	+ }
	+
	+ /// check if the same quantity of data for all element types
	+ void checkHomogeneity() override;
	+
	+ public:
	+ void registerToDumper(const std::string & id,
	+ iohelper::Dumper & dumper) override {
	+ dumper.addElemDataField(id, *this);
	}

	- return nb_data_per_elem(type, this->ghost_type);
	- }
	-
	- /// check if the same quantity of data for all element types
	- void checkHomogeneity() override;
	-
	-public:
	- void registerToDumper(const std::string & id,
	- iohelper::Dumper & dumper) override {
	- dumper.addElemDataField(id, *this);
	- }
	-
	- /// for connection to a FieldCompute
	- inline std::shared_ptr<Field> connect(FieldComputeProxy & proxy) override {
	- return proxy.connectToField(this);
	- }
	-
	- /// for connection to a Homogenizer
	- inline std::unique_ptr<ComputeFunctorInterface>
	- connect(HomogenizerProxy & proxy) override {
	- return proxy.connectToField(this);
	- }
	-
	- virtual iterator begin() {
	- /// type iterators on the elemental field
	- auto types = this->field.elementTypes(this->spatial_dimension,
	- this->ghost_type, this->element_kind);
	- auto tit = types.begin();
	- auto end = types.end();
	-
	- /// skip all types without data
	- for (; tit != end and this->field(*tit, this->ghost_type).empty();
	- ++tit) {
	+ /// for connection to a FieldCompute
	+ inline std::shared_ptr<Field> connect(FieldComputeProxy & proxy) override {
	+ return proxy.connectToField(this);
	}

	- auto type = *tit;
	+ /// for connection to a Homogenizer
	+ inline std::unique_ptr<ComputeFunctorInterface>
	+ connect(HomogenizerProxy & proxy) override {
	+ return proxy.connectToField(this);
	+ }

	- if (tit == end) {
	- return this->end();
	+ virtual iterator begin() {
	+ /// type iterators on the elemental field
	+ auto types = this->field.elementTypes(
	+ this->spatial_dimension, this->ghost_type, this->element_kind);
	+ auto tit = types.begin();
	+ auto end = types.end();
	+
	+ /// skip all types without data
	+ for (; tit != end and this->field(*tit, this->ghost_type).empty();
	+ ++tit) {
	+ }
	+
	+ auto type = *tit;
	+
	+ if (tit == end) {
	+ return this->end();
	+ }
	+
	+ /// getting information for the field of the given type
	+ const auto & vect = this->field(type, this->ghost_type);
	+ UInt nb_data_per_elem = this->getNbDataPerElem(type);
	+
	+ /// define element-wise iterator
	+ auto view = make_view(vect, nb_data_per_elem);
	+ auto it = view.begin();
	+ auto it_end = view.end();
	+ /// define data iterator
	+ iterator rit =
	+ iterator(this->field, tit, end, it, it_end, this->ghost_type);
	+ rit.setNbDataPerElem(this->nb_data_per_elem);
	+ return rit;
	}

	- /// getting information for the field of the given type
	- const auto & vect = this->field(type, this->ghost_type);
	- UInt nb_data_per_elem = this->getNbDataPerElem(type);
	-
	- /// define element-wise iterator
	- auto view = make_view(vect, nb_data_per_elem);
	- auto it = view.begin();
	- auto it_end = view.end();
	- /// define data iterator
	- iterator rit =
	- iterator(this->field, tit, end, it, it_end, this->ghost_type);
	- rit.setNbDataPerElem(this->nb_data_per_elem);
	- return rit;
	- }
	-
	- virtual iterator end() {
	- auto types = this->field.elementTypes(this->spatial_dimension,
	- this->ghost_type, this->element_kind);
	- auto tit = types.begin();
	- auto end = types.end();
	-
	- auto type = *tit;
	- for (; tit != end; ++tit) {
	- type = *tit;
	+ virtual iterator end() {
	+ auto types = this->field.elementTypes(
	+ this->spatial_dimension, this->ghost_type, this->element_kind);
	+ auto tit = types.begin();
	+ auto end = types.end();
	+
	+ auto type = *tit;
	+ for (; tit != end; ++tit) {
	+ type = *tit;
	+ }
	+
	+ const array_type & vect = this->field(type, this->ghost_type);
	+ UInt nb_data = this->getNbDataPerElem(type);
	+ auto it = make_view(vect, nb_data).end();
	+ auto rit = iterator(this->field, end, end, it, it, this->ghost_type);
	+ rit.setNbDataPerElem(this->nb_data_per_elem);
	+
	+ return rit;
	+ }
	+
	+ virtual UInt getDim() {
	+ if (this->homogeneous) {
	+ auto tit = this->field
	+ .elementTypes(this->spatial_dimension, this->ghost_type,
	+ this->element_kind)
	+ .begin();
	+ return this->getNbDataPerElem(*tit);
	+ }
	+
	+ throw;
	+ return 0;
	}

	- const array_type & vect = this->field(type, this->ghost_type);
	- UInt nb_data = this->getNbDataPerElem(type);
	- auto it = make_view(vect, nb_data).end();
	- auto rit = iterator(this->field, end, end, it, it, this->ghost_type);
	- rit.setNbDataPerElem(this->nb_data_per_elem);
	-
	- return rit;
	- }
	-
	- virtual UInt getDim() {
	- if (this->homogeneous) {
	- auto tit = this->field
	- .elementTypes(this->spatial_dimension, this->ghost_type,
	- this->element_kind)
	- .begin();
	- return this->getNbDataPerElem(*tit);
	+ void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) override {
	+ nb_data_per_elem = nb_data;
	}

	- throw;
	- return 0;
	- }
	-
	- void setNbDataPerElem(const ElementTypeMap<UInt> & nb_data) override {
	- nb_data_per_elem = nb_data;
	- }
	-
	- /* ------------------------------------------------------------------------ */
	- /* Class Members */
	- /* ------------------------------------------------------------------------ */
	-protected:
	- /// the ElementTypeMapArray embedded in the field
	- const field_type & field;
	- /// total number of elements
	- UInt nb_total_element;
	- /// the spatial dimension of the problem
	- UInt spatial_dimension;
	- /// whether this is a ghost field or not (for type selection)
	- GhostType ghost_type;
	- /// The element kind to operate on
	- ElementKind element_kind;
	- /// The number of data per element type
	- ElementTypeMap<UInt> nb_data_per_elem;
	-};
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Class Members */
	+ /* ------------------------------------------------------------------------
	+ */
	+ protected:
	+ /// the ElementTypeMapArray embedded in the field
	+ const field_type & field;
	+ /// total number of elements
	+ UInt nb_total_element;
	+ /// the spatial dimension of the problem
	+ UInt spatial_dimension;
	+ /// whether this is a ghost field or not (for type selection)
	+ GhostType ghost_type;
	+ /// The element kind to operate on
	+ ElementKind element_kind;
	+ /// The number of data per element type
	+ ElementTypeMap<UInt> nb_data_per_elem;
	+ };

	} // namespace dumpers
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "dumper_generic_elemental_field_tmpl.hh"
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_DUMPER_GENERIC_ELEMENTAL_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_generic_elemental_field_tmpl.hh b/src/io/dumper/dumper_generic_elemental_field_tmpl.hh
	index 777f6e387..9d988650d 100644
	--- a/src/io/dumper/dumper_generic_elemental_field_tmpl.hh
	+++ b/src/io/dumper/dumper_generic_elemental_field_tmpl.hh
	@@ -1,76 +1,76 @@
	/**
	* @file dumper_generic_elemental_field_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of the template functions of the ElementalField
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_generic_elemental_field.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {
	/* ------------------------------------------------------------------------ */
	template <class types, template <class> class iterator>
	void GenericElementalField<types, iterator>::checkHomogeneity() {
	auto types =
	field.elementTypes(spatial_dimension, ghost_type, element_kind);
	auto tit = types.begin();
	auto end = types.end();

	this->nb_total_element = 0;
	UInt nb_comp = 0;

	bool homogen = true;
	if (tit != end) {
	nb_comp = this->field(*tit, ghost_type).getNbComponent();
	for (; tit != end; ++tit) {
	const auto & vect = this->field(*tit, ghost_type);
	auto nb_element = vect.size();
	auto nb_comp_cur = vect.getNbComponent();
	if (homogen && nb_comp != nb_comp_cur) {
	homogen = false;
	}
	this->nb_total_element += nb_element;

	// this->nb_data_per_elem(*tit,this->ghost_type) = nb_comp_cur;
	}

	if (!homogen) {
	nb_comp = 0;
	}
	}

	this->homogeneous = homogen;
	}

	/* --------------------------------------------------------------------------
	*/
	} // namespace dumpers
	} // namespace akantu
	diff --git a/src/io/dumper/dumper_homogenizing_field.hh b/src/io/dumper/dumper_homogenizing_field.hh
	index 478f8ff70..6c0f428d4 100644
	--- a/src/io/dumper/dumper_homogenizing_field.hh
	+++ b/src/io/dumper/dumper_homogenizing_field.hh
	@@ -1,201 +1,201 @@
	/**
	* @file dumper_homogenizing_field.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief description of field homogenizing field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_HOMOGENIZING_FIELD_HH_
	#define AKANTU_DUMPER_HOMOGENIZING_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_compute.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {

	/* ------------------------------------------------------------------------ */
	template <typename type>
	inline type
	typeConverter(const type & input,
	[[gnu::unused]] Vector<typename type::value_type> & res,
	[[gnu::unused]] UInt nb_data) {
	throw;
	return input;
	}

	/* ------------------------------------------------------------------------ */
	template <typename type>
	inline Matrix<type> typeConverter(const Matrix<type> & input,
	Vector<type> & res, UInt nb_data) {

	Matrix<type> tmp(res.storage(), input.rows(), nb_data / input.rows());
	Matrix<type> tmp2(tmp, true);
	return tmp2;
	}

	/* ------------------------------------------------------------------------ */
	template <typename type>
	inline Vector<type> typeConverter(const Vector<type> & /unused/,
	Vector<type> & res, UInt /unused/) {
	return res;
	}

	/* ------------------------------------------------------------------------ */
	template <typename type>
	class AvgHomogenizingFunctor : public ComputeFunctor<type, type> {
	/* ---------------------------------------------------------------------- */
	/* Typedefs */
	/* ---------------------------------------------------------------------- */
	private:
	using value_type = typename type::value_type;

	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	AvgHomogenizingFunctor(ElementTypeMap<UInt> & nb_datas) {

	auto types = nb_datas.elementTypes();
	auto tit = types.begin();
	auto end = types.end();

	nb_data = nb_datas(*tit);

	for (; tit != end; ++tit) {
	if (nb_data != nb_datas(*tit)) {
	throw;
	}
	}
	}

	/* ---------------------------------------------------------------------- */
	/* Methods */
	/* ---------------------------------------------------------------------- */
	public:
	type func(const type & d, Element /global_index/) override {
	Vector<value_type> res(this->nb_data);

	if (d.size() % this->nb_data) {
	throw;
	}
	UInt nb_to_average = d.size() / this->nb_data;

	value_type * ptr = d.storage();
	for (UInt i = 0; i < nb_to_average; ++i) {
	Vector<value_type> tmp(ptr, this->nb_data);
	res += tmp;
	ptr += this->nb_data;
	}
	res /= nb_to_average;
	return typeConverter(d, res, this->nb_data);
	};

	UInt getDim() override { return nb_data; };
	UInt getNbComponent(UInt /old_nb_comp/) override { throw; };

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */

	/// The size of data: i.e. the size of the vector to be returned
	UInt nb_data;
	};
	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	class HomogenizerProxy {
	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	HomogenizerProxy() = default;

	public:
	inline static std::unique_ptr<ComputeFunctorInterface>
	createHomogenizer(Field & field);

	template <typename T>
	inline std::unique_ptr<ComputeFunctorInterface> connectToField(T * field) {
	ElementTypeMap<UInt> nb_components = field->getNbComponents();

	using ret_type = typename T::types::return_type;
	return this->instantiateHomogenizer<ret_type>(nb_components);
	}

	template <typename ret_type>
	inline std::unique_ptr<ComputeFunctorInterface>
	instantiateHomogenizer(ElementTypeMap<UInt> & nb_components);
	};

	/* ------------------------------------------------------------------------ */

	template <typename ret_type>
	inline std::unique_ptr<ComputeFunctorInterface>
	HomogenizerProxy::instantiateHomogenizer(
	ElementTypeMap<UInt> & nb_components) {
	using Homogenizer = dumpers::AvgHomogenizingFunctor<ret_type>;
	return std::make_unique<Homogenizer>(nb_components);
	}

	template <>
	inline std::unique_ptr<ComputeFunctorInterface>
	HomogenizerProxy::instantiateHomogenizer<Vector<iohelper::ElemType>>(
	[[gnu::unused]] ElementTypeMap<UInt> & nb_components) {
	throw;
	return nullptr;
	}

	/* ------------------------------------------------------------------------ */
	/// for connection to a FieldCompute
	template <typename SubFieldCompute, typename return_type,
	typename support_type_>
	inline std::unique_ptr<ComputeFunctorInterface>
	FieldCompute<SubFieldCompute, return_type, support_type_>::connect(
	HomogenizerProxy & proxy) {
	return proxy.connectToField(this);
	}

	template <typename SubFieldCompute, typename return_type>
	inline std::unique_ptr<ComputeFunctorInterface>
	FieldCompute<SubFieldCompute, return_type, Element>::connect(
	HomogenizerProxy & proxy) {
	return proxy.connectToField(this);
	}

	/* ------------------------------------------------------------------------ */
	inline std::unique_ptr<ComputeFunctorInterface>
	HomogenizerProxy::createHomogenizer(Field & field) {
	HomogenizerProxy homogenizer_proxy;
	return field.connect(homogenizer_proxy);
	}

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_HOMOGENIZING_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_internal_material_field.hh b/src/io/dumper/dumper_internal_material_field.hh
	index c94d68d78..759751ca8 100644
	--- a/src/io/dumper/dumper_internal_material_field.hh
	+++ b/src/io/dumper/dumper_internal_material_field.hh
	@@ -1,74 +1,79 @@
	/**
	* @file dumper_internal_material_field.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 04 2020
	*
	* @brief description of material internal field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_INTERNAL_MATERIAL_FIELD_HH_
	#define AKANTU_DUMPER_INTERNAL_MATERIAL_FIELD_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_quadrature_point_iterator.hh"
	#ifdef AKANTU_IGFEM
	#include "dumper_igfem_material_internal_field.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	-template <typename T, bool filtered = false>
	-class InternalMaterialField
	- : public GenericElementalField<SingleType<T, Vector, filtered>,
	- quadrature_point_iterator> {
	+ template <typename T, bool filtered = false>
	+ class InternalMaterialField
	+ : public GenericElementalField<SingleType<T, Vector, filtered>,
	+ quadrature_point_iterator> {

	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */

	-public:
	- using types = SingleType<T, Vector, filtered>;
	- using parent = GenericElementalField<types, quadrature_point_iterator>;
	- using field_type = typename types::field_type;
	- using support_type = Element;
	+ public:
	+ using types = SingleType<T, Vector, filtered>;
	+ using parent = GenericElementalField<types, quadrature_point_iterator>;
	+ using field_type = typename types::field_type;
	+ using support_type = Element;

	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */

	- InternalMaterialField(const field_type & field,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined)
	- : parent(field, spatial_dimension, ghost_type, element_kind) {}
	-};
	+ InternalMaterialField(const field_type & field,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined)
	+ : parent(field, spatial_dimension, ghost_type, element_kind) {}
	+ };

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_INTERNAL_MATERIAL_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_iohelper.cc b/src/io/dumper/dumper_iohelper.cc
	index 3f6b33f52..ba750bf45 100644
	--- a/src/io/dumper/dumper_iohelper.cc
	+++ b/src/io/dumper/dumper_iohelper.cc
	@@ -1,322 +1,322 @@
	/**
	* @file dumper_iohelper.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 26 2012
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of DumperIOHelper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <io_helper.hh>

	#include "dumper_elemental_field.hh"
	#include "dumper_filtered_connectivity.hh"
	#include "dumper_iohelper.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_variable.hh"
	#include "mesh.hh"
	#if defined(AKANTU_IGFEM)
	#include "dumper_igfem_connectivity.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	DumperIOHelper::DumperIOHelper() = default;

	/* -------------------------------------------------------------------------- */
	DumperIOHelper::~DumperIOHelper() = default;

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::setParallelContext(bool is_parallel) {
	UInt whoami = Communicator::getStaticCommunicator().whoAmI();
	UInt nb_proc = Communicator::getStaticCommunicator().getNbProc();

	if (is_parallel) {
	dumper->setParallelContext(whoami, nb_proc);
	} else {
	dumper->setParallelContext(0, 1);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::setDirectory(const std::string & directory) {
	this->directory = directory;
	dumper->setPrefix(directory);
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::setBaseName(const std::string & basename) {
	filename = basename;
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::setTimeStep(Real time_step) {
	if (!time_activated) {
	this->dumper->activateTimeDescFiles(time_step);
	} else {
	this->dumper->setTimeStep(time_step);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::dump() {
	try {
	dumper->dump(filename, count);
	} catch (iohelper::IOHelperException & e) {
	AKANTU_ERROR(
	"I was not able to dump your data with a Dumper: " << e.what());
	}

	++count;
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::dump(UInt step) {
	this->count = step;
	this->dump();
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::dump(Real current_time, UInt step) {
	this->dumper->setCurrentTime(current_time);
	this->dump(step);
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::registerMesh(const Mesh & mesh, UInt spatial_dimension,
	GhostType ghost_type,
	ElementKind element_kind) {

	#if defined(AKANTU_IGFEM)
	if (element_kind == _ek_igfem) {
	registerField("connectivities",
	new dumpers::IGFEMConnectivityField(
	mesh.getConnectivities(), spatial_dimension, ghost_type));
	} else
	#endif

	registerField("connectivities",
	std::make_shared<dumpers::ElementalField<UInt>>(
	mesh.getConnectivities(), spatial_dimension, ghost_type,
	element_kind));

	registerField("positions",
	std::make_shared<dumpers::NodalField<Real>>(mesh.getNodes()));
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::registerFilteredMesh(
	const Mesh & mesh, const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind) {
	auto * f_connectivities = new ElementTypeMapArrayFilter<UInt>(
	mesh.getConnectivities(), elements_filter);

	this->registerField("connectivities",
	std::make_shared<dumpers::FilteredConnectivityField>(
	*f_connectivities, nodes_filter, spatial_dimension,
	ghost_type, element_kind));

	this->registerField("positions",
	std::make_shared<dumpers::NodalField<Real, true>>(
	mesh.getNodes(), 0, 0, &nodes_filter));
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::registerField(
	const std::string & field_id,
	std::shared_ptr<dumpers::Field>
	field) // NOLINT(performance-unnecessary-value-param)
	{
	auto it = fields.find(field_id);
	if (it != fields.end()) {
	AKANTU_DEBUG_WARNING(
	"The field "
	<< field_id << " is already registered in this Dumper. Field ignored.");
	return;
	}

	fields[field_id] = field;
	field->registerToDumper(field_id, *dumper);
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::unRegisterField(const std::string & field_id) {
	auto it = fields.find(field_id);
	if (it == fields.end()) {
	AKANTU_DEBUG_WARNING(
	"The field " << field_id
	<< " is not registered in this Dumper. Nothing to do.");
	return;
	}

	fields.erase(it);
	}

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::registerVariable(
	const std::string & variable_id,
	std::shared_ptr<dumpers::VariableBase>
	variable) // NOLINT(performance-unnecessary-value-param)
	{
	auto it = variables.find(variable_id);

	if (it != variables.end()) {
	AKANTU_DEBUG_WARNING(
	"The Variable "
	<< variable_id
	<< " is already registered in this Dumper. Variable ignored.");
	return;
	}

	variables[variable_id] = variable;
	variable->registerToDumper(variable_id, *dumper);
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	void DumperIOHelper::unRegisterVariable(const std::string & variable_id) {
	auto it = variables.find(variable_id);

	if (it == variables.end()) {
	AKANTU_DEBUG_WARNING(
	"The variable " << variable_id
	<< " is not registered in this Dumper. Nothing to do.");
	return;
	}

	variables.erase(it);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type> iohelper::ElemType getIOHelperType() {
	AKANTU_TO_IMPLEMENT();
	return iohelper::MAX_ELEM_TYPE;
	}

	template <> iohelper::ElemType getIOHelperType<_point_1>() {
	return iohelper::POINT_SET;
	}
	template <> iohelper::ElemType getIOHelperType<_segment_2>() {
	return iohelper::LINE1;
	}
	template <> iohelper::ElemType getIOHelperType<_segment_3>() {
	return iohelper::LINE2;
	}

	template <> iohelper::ElemType getIOHelperType<_triangle_3>() {
	return iohelper::TRIANGLE1;
	}
	template <> iohelper::ElemType getIOHelperType<_triangle_6>() {
	return iohelper::TRIANGLE2;
	}

	template <> iohelper::ElemType getIOHelperType<_quadrangle_4>() {
	return iohelper::QUAD1;
	}
	template <> iohelper::ElemType getIOHelperType<_quadrangle_8>() {
	return iohelper::QUAD2;
	}

	template <> iohelper::ElemType getIOHelperType<_tetrahedron_4>() {
	return iohelper::TETRA1;
	}
	template <> iohelper::ElemType getIOHelperType<_tetrahedron_10>() {
	return iohelper::TETRA2;
	}

	template <> iohelper::ElemType getIOHelperType<_hexahedron_8>() {
	return iohelper::HEX1;
	}
	template <> iohelper::ElemType getIOHelperType<_hexahedron_20>() {
	return iohelper::HEX2;
	}

	template <> iohelper::ElemType getIOHelperType<_pentahedron_6>() {
	return iohelper::PRISM1;
	}
	template <> iohelper::ElemType getIOHelperType<_pentahedron_15>() {
	return iohelper::PRISM2;
	}

	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <> iohelper::ElemType getIOHelperType<_cohesive_1d_2>() {
	return iohelper::COH1D2;
	}

	template <> iohelper::ElemType getIOHelperType<_cohesive_2d_4>() {
	return iohelper::COH2D4;
	}
	template <> iohelper::ElemType getIOHelperType<_cohesive_2d_6>() {
	return iohelper::COH2D6;
	}

	template <> iohelper::ElemType getIOHelperType<_cohesive_3d_6>() {
	return iohelper::COH3D6;
	}
	template <> iohelper::ElemType getIOHelperType<_cohesive_3d_12>() {
	return iohelper::COH3D12;
	}

	template <> iohelper::ElemType getIOHelperType<_cohesive_3d_8>() {
	return iohelper::COH3D8;
	}
	// template <>
	// iohelper::ElemType getIOHelperType<_cohesive_3d_16>() { return
	// iohelper::COH3D16; }
	#endif

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	template <> iohelper::ElemType getIOHelperType<_bernoulli_beam_2>() {
	return iohelper::BEAM2;
	}
	template <> iohelper::ElemType getIOHelperType<_bernoulli_beam_3>() {
	return iohelper::BEAM3;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	UInt getIOHelperType(ElementType type) {
	UInt ioh_type = iohelper::MAX_ELEM_TYPE;
	#define GET_IOHELPER_TYPE(type) ioh_type = getIOHelperType<type>();

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_IOHELPER_TYPE);
	#undef GET_IOHELPER_TYPE
	return ioh_type;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	namespace iohelper {
	template <> DataType getDataType<akantu::NodeFlag>() {
	return getDataType<std::underlying_type_t<akantu::NodeFlag>>();
	}
	} // namespace iohelper
	diff --git a/src/io/dumper/dumper_iohelper.hh b/src/io/dumper/dumper_iohelper.hh
	index 038deacc5..028e5520e 100644
	--- a/src/io/dumper/dumper_iohelper.hh
	+++ b/src/io/dumper/dumper_iohelper.hh
	@@ -1,162 +1,162 @@
	/**
	* @file dumper_iohelper.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 26 2012
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Define the akantu dumper interface for IOhelper dumpers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "aka_types.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DUMPER_IOHELPER_HH_
	#define AKANTU_DUMPER_IOHELPER_HH_
	/* -------------------------------------------------------------------------- */

	namespace iohelper {
	class Dumper;
	}

	namespace akantu {

	UInt getIOHelperType(ElementType type);

	namespace dumpers {
	class Field;
	class VariableBase;
	-} // namespace dumper
	+} // namespace dumpers

	class Mesh;

	class DumperIOHelper : public std::enable_shared_from_this<DumperIOHelper> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperIOHelper();
	virtual ~DumperIOHelper();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register a given Mesh for the current dumper
	virtual void registerMesh(const Mesh & mesh,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	/// register a filtered Mesh (provided filter lists) for the current dumper
	virtual void
	registerFilteredMesh(const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements_filter,
	const Array<UInt> & nodes_filter,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	/// register a Field object identified by name and provided by pointer
	void registerField(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field);
	/// remove the Field identified by name from managed fields
	void unRegisterField(const std::string & field_id);
	/// register a VariableBase object identified by name and provided by pointer
	void registerVariable(const std::string & variable_id,
	std::shared_ptr<dumpers::VariableBase> variable);
	/// remove a VariableBase identified by name from managed fields
	void unRegisterVariable(const std::string & variable_id);

	/// request dump: this calls IOHelper dump routine
	virtual void dump();
	/// request dump: this first set the current step and then calls IOHelper dump
	/// routine
	virtual void dump(UInt step);
	/// request dump: this first set the current step and current time and then
	/// calls IOHelper dump routine
	virtual void dump(Real current_time, UInt step);
	/// set the parallel context for IOHeper
	virtual void setParallelContext(bool is_parallel);
	/// set the directory where to generate the dumped files
	virtual void setDirectory(const std::string & directory);
	/// set the base name (needed by most IOHelper dumpers)
	virtual void setBaseName(const std::string & basename);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// direct access to the iohelper::Dumper object
	AKANTU_GET_MACRO(Dumper, *dumper, iohelper::Dumper &)

	/// set the timestep of the iohelper::Dumper
	void setTimeStep(Real time_step);

	public:
	/* ------------------------------------------------------------------------ */
	/* Variable wrapper */
	template <typename T, bool is_scal = std::is_arithmetic<T>::value>
	class Variable;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// internal iohelper::Dumper
	std::unique_ptr<iohelper::Dumper> dumper;

	using Fields = std::map<std::string, std::shared_ptr<dumpers::Field>>;
	using Variables =
	std::map<std::string, std::shared_ptr<dumpers::VariableBase>>;

	/// list of registered fields to dump
	Fields fields;
	Variables variables;

	/// dump counter
	UInt count{0};

	/// directory name
	std::string directory;

	/// filename prefix
	std::string filename;

	/// is time tracking activated in the dumper
	bool time_activated{false};
	};

	} // namespace akantu

	#endif /* AKANTU_DUMPER_IOHELPER_HH_ */
	diff --git a/src/io/dumper/dumper_iohelper_paraview.cc b/src/io/dumper/dumper_iohelper_paraview.cc
	index c1ab9c0f3..9500e44d4 100644
	--- a/src/io/dumper/dumper_iohelper_paraview.cc
	+++ b/src/io/dumper/dumper_iohelper_paraview.cc
	@@ -1,67 +1,66 @@
	/**
	* @file dumper_iohelper_paraview.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Sep 26 2010
	* @date last modification: Mon Jan 22 2018
	*
	* @brief implementations of DumperParaview
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper_paraview.hh"
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <io_helper.hh>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	DumperParaview::DumperParaview(const std::string & filename,
	- const std::string & directory, bool parallel)
	- {
	+ const std::string & directory, bool parallel) {
	dumper = std::make_unique<iohelper::DumperParaview>();
	setBaseName(filename);

	this->setParallelContext(parallel);

	dumper->setMode(iohelper::BASE64);
	dumper->setPrefix(directory);
	dumper->init();
	}

	/* -------------------------------------------------------------------------- */
	DumperParaview::~DumperParaview() = default;

	/* -------------------------------------------------------------------------- */
	void DumperParaview::setBaseName(const std::string & basename) {
	DumperIOHelper::setBaseName(basename);
	static_cast<iohelper::DumperParaview *>(dumper.get())
	->setVTUSubDirectory(filename + "-VTU");
	}

	} // namespace akantu
	diff --git a/src/io/dumper/dumper_iohelper_paraview.hh b/src/io/dumper/dumper_iohelper_paraview.hh
	index c9a96412d..432df90bd 100644
	--- a/src/io/dumper/dumper_iohelper_paraview.hh
	+++ b/src/io/dumper/dumper_iohelper_paraview.hh
	@@ -1,72 +1,72 @@
	/**
	* @file dumper_iohelper_paraview.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Mon Jan 22 2018
	*
	* @brief Dumper Paraview using IOHelper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DUMPER_PARAVIEW_HH_
	#define AKANTU_DUMPER_PARAVIEW_HH_

	#include "dumper_iohelper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class DumperParaview : public DumperIOHelper {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperParaview(const std::string & filename,
	const std::string & directory = "./paraview",
	bool parallel = true);
	~DumperParaview() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	// void dump();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	void setBaseName(const std::string & basename) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	#endif /* AKANTU_DUMPER_PARAVIEW_HH_ */
	diff --git a/src/io/dumper/dumper_material_padders.hh b/src/io/dumper/dumper_material_padders.hh
	index 20c1022d2..3f7e5f7b6 100644
	--- a/src/io/dumper/dumper_material_padders.hh
	+++ b/src/io/dumper/dumper_material_padders.hh
	@@ -1,307 +1,307 @@
	/**
	* @file dumper_material_padders.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Material padders for plane stress/ plane strain
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_MATERIAL_PADDERS_HH_
	#define AKANTU_DUMPER_MATERIAL_PADDERS_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_padding_helper.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	/* ------------------------------------------------------------------------ */
	class MaterialFunctor {
	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	MaterialFunctor(const SolidMechanicsModel & model)
	: model(model), material_index(model.getMaterialByElement()),
	nb_data_per_element("nb_data_per_element", model.getID()),
	spatial_dimension(model.getSpatialDimension()) {}

	/* ---------------------------------------------------------------------- */
	/* Methods */
	/* ---------------------------------------------------------------------- */
	/// return the material from the global element index
	const Material & getMaterialFromGlobalIndex(Element global_index) {
	UInt index = global_index.element;
	UInt material_id = material_index(global_index.type)(index);
	const Material & material = model.getMaterial(material_id);
	return material;
	}

	/// return the type of the element from global index
	ElementType
	getElementTypeFromGlobalIndex( // NOLINT(readability-convert-member-functions-to-static)
	Element global_index) {
	return global_index.type;
	}

	protected:
	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */

	/// all material padders probably need access to solid mechanics model
	const SolidMechanicsModel & model;

	/// they also need an access to the map from global ids to material id and
	/// local ids
	const ElementTypeMapArray<UInt> & material_index;

	/// the number of data per element
	const ElementTypeMapArray<UInt> nb_data_per_element;

	UInt spatial_dimension;
	};

	/* ------------------------------------------------------------------------ */
	template <class T, class R>
	class MaterialPadder : public MaterialFunctor,
	public PadderGeneric<Vector<T>, R> {
	public:
	MaterialPadder(const SolidMechanicsModel & model)
	: MaterialFunctor(model) {}
	};

	/* ------------------------------------------------------------------------ */

	template <UInt spatial_dimension>
	class StressPadder : public MaterialPadder<Real, Matrix<Real>> {

	public:
	StressPadder(const SolidMechanicsModel & model)
	: MaterialPadder<Real, Matrix<Real>>(model) {
	this->setPadding(3, 3);
	}

	inline Matrix<Real> func(const Vector<Real> & in,
	Element global_element_id) override {
	UInt nrows = spatial_dimension;
	UInt ncols = in.size() / nrows;
	UInt nb_data = in.size() / (nrows * nrows);

	Matrix<Real> stress = this->pad(in, nrows, ncols, nb_data);
	const Material & material =
	this->getMaterialFromGlobalIndex(global_element_id);
	bool plane_strain = true;
	if (spatial_dimension == 2) {
	plane_strain = !((bool)material.getParam("Plane_Stress"));
	}

	if (plane_strain) {
	Real nu = material.getParam("nu");
	for (UInt d = 0; d < nb_data; ++d) {
	stress(2, 2 + 3 * d) =
	nu * (stress(0, 0 + 3 * d) + stress(1, 1 + 3 * d));
	}
	}
	return stress;
	}

	UInt getDim() override { return 9; };

	UInt getNbComponent(UInt /old_nb_comp/) override {
	return this->getDim();
	};
	};

	/* ------------------------------------------------------------------------ */
	template <UInt spatial_dimension>
	class StrainPadder : public MaterialFunctor,
	public PadderGeneric<Matrix<Real>, Matrix<Real>> {
	public:
	StrainPadder(const SolidMechanicsModel & model) : MaterialFunctor(model) {
	this->setPadding(3, 3);
	}

	inline Matrix<Real> func(const Matrix<Real> & in,
	Element global_element_id) override {
	UInt nrows = spatial_dimension;
	UInt nb_data = in.size() / (nrows * nrows);

	Matrix<Real> strain = this->pad(in, nb_data);
	const Material & material =
	this->getMaterialFromGlobalIndex(global_element_id);
	bool plane_stress = material.getParam("Plane_Stress");

	if (plane_stress) {
	Real nu = material.getParam("nu");
	for (UInt d = 0; d < nb_data; ++d) {
	strain(2, 2 + 3 * d) =
	nu / (nu - 1) * (strain(0, 0 + 3 * d) + strain(1, 1 + 3 * d));
	}
	}

	return strain;
	}

	UInt getDim() override { return 9; };

	UInt getNbComponent(UInt /old_nb_comp/) override {
	return this->getDim();
	};
	};

	/* ------------------------------------------------------------------------ */
	template <bool green_strain>
	class ComputeStrain : public MaterialFunctor,
	public ComputeFunctor<Vector<Real>, Matrix<Real>> {
	public:
	ComputeStrain(const SolidMechanicsModel & model) : MaterialFunctor(model) {}

	inline Matrix<Real> func(const Vector<Real> & in,
	Element /global_element_id/) override {
	UInt nrows = spatial_dimension;
	UInt ncols = in.size() / nrows;
	UInt nb_data = in.size() / (nrows * nrows);

	Matrix<Real> ret_all_strain(nrows, ncols);
	Tensor3<Real> all_grad_u(in.storage(), nrows, nrows, nb_data);
	Tensor3<Real> all_strain(ret_all_strain.storage(), nrows, nrows, nb_data);

	for (UInt d = 0; d < nb_data; ++d) {
	Matrix<Real> grad_u = all_grad_u(d);
	Matrix<Real> strain = all_strain(d);

	if (spatial_dimension == 2) {
	if (green_strain) {
	Material::gradUToE<2>(grad_u, strain);
	} else {
	Material::gradUToEpsilon<2>(grad_u, strain);
	}
	} else if (spatial_dimension == 3) {
	if (green_strain) {
	Material::gradUToE<3>(grad_u, strain);
	} else {
	Material::gradUToEpsilon<3>(grad_u, strain);
	}
	}
	}

	return ret_all_strain;
	}

	UInt getDim() override { return spatial_dimension * spatial_dimension; };

	UInt getNbComponent(UInt /old_nb_comp/) override {
	return this->getDim();
	};
	};

	/* ------------------------------------------------------------------------ */
	template <bool green_strain>
	class ComputePrincipalStrain
	: public MaterialFunctor,
	public ComputeFunctor<Vector<Real>, Matrix<Real>> {
	public:
	ComputePrincipalStrain(const SolidMechanicsModel & model)
	: MaterialFunctor(model) {}

	inline Matrix<Real> func(const Vector<Real> & in,
	Element /global_element_id/) override {
	UInt nrows = spatial_dimension;
	UInt nb_data = in.size() / (nrows * nrows);

	Matrix<Real> ret_all_strain(nrows, nb_data);
	Tensor3<Real> all_grad_u(in.storage(), nrows, nrows, nb_data);
	Matrix<Real> strain(nrows, nrows);

	for (UInt d = 0; d < nb_data; ++d) {
	Matrix<Real> grad_u = all_grad_u(d);

	if (spatial_dimension == 2) {
	if (green_strain) {
	Material::gradUToE<2>(grad_u, strain);
	} else {
	Material::gradUToEpsilon<2>(grad_u, strain);
	}
	} else if (spatial_dimension == 3) {
	if (green_strain) {
	Material::gradUToE<3>(grad_u, strain);
	} else {
	Material::gradUToEpsilon<3>(grad_u, strain);
	}
	}

	Vector<Real> principal_strain(ret_all_strain(d));
	strain.eig(principal_strain);
	}

	return ret_all_strain;
	}

	UInt getDim() override { return spatial_dimension; };

	UInt getNbComponent(UInt /old_nb_comp/) override {
	return this->getDim();
	};
	};

	/* ------------------------------------------------------------------------ */
	class ComputeVonMisesStress
	: public MaterialFunctor,
	public ComputeFunctor<Vector<Real>, Vector<Real>> {
	public:
	ComputeVonMisesStress(const SolidMechanicsModel & model)
	: MaterialFunctor(model) {}

	inline Vector<Real> func(const Vector<Real> & in,
	Element /global_element_id/) override {
	UInt nrows = spatial_dimension;
	UInt nb_data = in.size() / (nrows * nrows);

	Vector<Real> von_mises_stress(nb_data);
	Matrix<Real> deviatoric_stress(3, 3);

	for (UInt d = 0; d < nb_data; ++d) {
	Matrix<Real> cauchy_stress(in.storage() + d * nrows * nrows, nrows,
	nrows);
	von_mises_stress(d) = Material::stressToVonMises(cauchy_stress);
	}

	return von_mises_stress;
	}

	UInt getDim() override { return 1; };

	UInt getNbComponent(UInt /old_nb_comp/) override {
	return this->getDim();
	};
	};

	/* ------------------------------------------------------------------------ */

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_MATERIAL_PADDERS_HH_ */
	diff --git a/src/io/dumper/dumper_nodal_field.hh b/src/io/dumper/dumper_nodal_field.hh
	index 7b87c585c..fc701b5fa 100644
	--- a/src/io/dumper/dumper_nodal_field.hh
	+++ b/src/io/dumper/dumper_nodal_field.hh
	@@ -1,189 +1,190 @@
	/**
	* @file dumper_nodal_field.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 26 2012
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Description of nodal fields
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DUMPER_NODAL_FIELD_HH_
	#define AKANTU_DUMPER_NODAL_FIELD_HH_

	/* -------------------------------------------------------------------------- */
	#include "dumper_compute.hh"
	#include "dumper_field.hh"
	#include <io_helper.hh>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {

	/* ------------------------------------------------------------------------ */
	// This represents a iohelper compatible field
	template <typename T, bool filtered = false, class Container = Array<T>,
	class Filter = Array<UInt>>
	class NodalField : public dumpers::Field {
	/* ---------------------------------------------------------------------- */
	/* Typedefs */
	/* ---------------------------------------------------------------------- */
	public:
	using support_type = UInt;
	using types = TypeTraits<T, Vector<T>, Container>;

	class iterator : public iohelper::iterator<T, iterator, Vector<T>> {
	public:
	iterator(T * vect, UInt _offset, UInt _n, UInt _stride,
	const UInt * filter)
	: internal_it(vect), offset(_offset), n(_n), stride(_stride),
	filter(filter) {}

	bool operator!=(const iterator & it) const override {
	if (filter != nullptr) {
	return filter != it.filter;
	}
	return internal_it != it.internal_it;
	}

	iterator & operator++() override {
	if (filter != nullptr) {
	++filter;
	} else {
	internal_it += offset;
	}
	return *this;
	}

	Vector<T> operator*() override {
	if (filter != nullptr) {
	return Vector<T>(internal_it + (filter)offset + stride, n);
	}
	return Vector<T>(internal_it + stride, n);
	}

	private:
	T * internal_it;
	UInt offset, n, stride;
	const UInt * filter{nullptr};
	};

	/* ---------------------------------------------------------------------- */
	/* Constructors/Destructors */
	/* ---------------------------------------------------------------------- */
	public:
	NodalField(const Container & _field, UInt _n = 0, UInt _stride = 0,
	const Filter * filter = nullptr)
	: field(_field), n(_n), stride(_stride), filter(filter), padding(0) {
	AKANTU_DEBUG_ASSERT(((not filtered) and filter == nullptr) or filtered,
	"Filter passed to unfiltered NodalField!");
	AKANTU_DEBUG_ASSERT((filtered and this->filter != nullptr) or
	(not filtered),
	"No filter passed to filtered NodalField!");
	AKANTU_DEBUG_ASSERT(
	(filter != nullptr and this->filter->getNbComponent() == 1) or
	(filter == nullptr),
	"Multi-component filter given to NodalField ("
	<< this->filter->getNbComponent()
	<< " components detected, sould be 1");
	if (n == 0) {
	this->n = field.getNbComponent() - stride;
	}
	}

	/* ---------------------------------------------------------------------- */
	/* Methods */
	/* ---------------------------------------------------------------------- */
	public:
	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addNodeDataField(id, *this);
	}

	inline iterator begin() {
	return iterator(field.storage(), field.getNbComponent(), n, stride,
	filter == nullptr ? nullptr : filter->storage());
	}

	inline iterator end() {
	- return iterator(field.storage(), field.getNbComponent(), n, stride,
	+ return iterator(field.storage() + field.getNbComponent() * field.size(),
	+ field.getNbComponent(), n, stride,
	filter == nullptr ? nullptr
	: filter->storage() + filter->size());
	}

	bool isHomogeneous() override { return true; }
	void checkHomogeneity() override { this->homogeneous = true; }

	virtual UInt getDim() {
	if (this->padding) {
	return this->padding;
	}
	return n;
	}

	void setPadding(UInt padding) { this->padding = padding; }

	UInt size() {
	if (filter != nullptr) {
	return filter->size();
	}
	return field.size();
	}

	inline std::shared_ptr<Field> connect(FieldComputeProxy & proxy) override {
	return proxy.connectToField(this);
	}

	/// for connection to a Homogenizer
	inline std::unique_ptr<ComputeFunctorInterface>
	connect(HomogenizerProxy & /proxy/) override {
	throw;
	}

	template <class T1 = T,
	std::enable_if_t<std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<UInt>();
	}

	template <class T1 = T,
	std::enable_if_t<not std::is_enum<T1>::value> * = nullptr>
	iohelper::DataType getDataType() {
	return iohelper::getDataType<T>();
	}

	/* ---------------------------------------------------------------------- */
	/* Class Members */
	/* ---------------------------------------------------------------------- */
	private:
	const Container & field;
	UInt n, stride;
	const Filter * filter{nullptr};
	UInt padding;
	};

	} // namespace dumpers
	} // namespace akantu
	/* -------------------------------------------------------------------------- */
	#endif /* AKANTU_DUMPER_NODAL_FIELD_HH_ */
	diff --git a/src/io/dumper/dumper_padding_helper.hh b/src/io/dumper/dumper_padding_helper.hh
	index cc621d931..920c40742 100644
	--- a/src/io/dumper/dumper_padding_helper.hh
	+++ b/src/io/dumper/dumper_padding_helper.hh
	@@ -1,152 +1,152 @@
	/**
	* @file dumper_padding_helper.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Padding helper for field iterators
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_PADDING_HELPER_HH_
	#define AKANTU_DUMPER_PADDING_HELPER_HH_
	/* -------------------------------------------------------------------------- */
	#include "dumper_compute.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	namespace dumpers {
	/* --------------------------------------------------------------------------
	*/

	class PadderInterface {

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/

	public:
	PadderInterface() {
	padding_m = 0;
	padding_n = 0;
	}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/

	public:
	void setPadding(UInt m, UInt n = 0) {
	padding_m = m;
	padding_n = n;
	}

	virtual UInt getPaddedDim(UInt nb_data) { return nb_data; }

	/* ------------------------------------------------------------------------
	*/
	/* Class Members */
	/* ------------------------------------------------------------------------
	*/

	public:
	/// padding informations
	UInt padding_n, padding_m;
	};

	/* --------------------------------------------------------------------------
	*/

	template <class input_type, class output_type>
	class PadderGeneric : public ComputeFunctor<input_type, output_type>,
	public PadderInterface {

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/

	public:
	PadderGeneric() : PadderInterface() {}

	/* ------------------------------------------------------------------------
	*/
	/* Methods */
	/* ------------------------------------------------------------------------
	*/

	public:
	inline output_type pad(const input_type & in,
	__attribute__((unused)) UInt nb_data) {
	return in; // trick due to the fact that IOHelper padds the vectors (avoid
	// a copy of data)
	}
	};
	/* --------------------------------------------------------------------------
	*/

	template <class T>
	class PadderGeneric<Vector<T>, Matrix<T>>
	: public ComputeFunctor<Vector<T>, Matrix<T>>, public PadderInterface {

	/* ------------------------------------------------------------------------
	*/
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------
	*/

	public:
	inline Matrix<T> pad(const Vector<T> & _in, UInt nrows, UInt ncols,
	UInt nb_data) {
	Matrix<T> in(_in.storage(), nrows, ncols);

	if (padding_m <= nrows && padding_n * nb_data <= ncols) {
	return in;
	}

	Matrix<T> ret(padding_m, padding_n * nb_data);
	UInt nb_cols_per_data = in.cols() / nb_data;
	for (UInt d = 0; d < nb_data; ++d) {
	for (UInt i = 0; i < in.rows(); ++i) {
	for (UInt j = 0; j < nb_cols_per_data; ++j) {
	ret(i, j + d * padding_n) = in(i, j + d * nb_cols_per_data);
	}
	}
	}
	return ret;
	}
	};

	/* --------------------------------------------------------------------------
	*/

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_PADDING_HELPER_HH_ */
	diff --git a/src/io/dumper/dumper_quadrature_point_iterator.hh b/src/io/dumper/dumper_quadrature_point_iterator.hh
	index a81fd81f7..235aa0bec 100644
	--- a/src/io/dumper/dumper_quadrature_point_iterator.hh
	+++ b/src/io/dumper/dumper_quadrature_point_iterator.hh
	@@ -1,75 +1,81 @@
	/**
	* @file dumper_quadrature_point_iterator.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Description of quadrature point iterator
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_QUADRATURE_POINT_ITERATOR_HH_
	#define AKANTU_DUMPER_QUADRATURE_POINT_ITERATOR_HH_

	/* -------------------------------------------------------------------------- */
	#include "dumper_elemental_field.hh"

	namespace akantu {
	namespace dumpers {

	-/* -------------------------------------------------------------------------- */
	-template <typename types>
	-class quadrature_point_iterator
	- : public element_iterator<types, quadrature_point_iterator> {
	- /* ------------------------------------------------------------------------ */
	- /* Typedefs */
	- /* ------------------------------------------------------------------------ */
	-public:
	- using parent = element_iterator<types, dumpers::quadrature_point_iterator>;
	- using data_type = typename types::data_type;
	- using return_type = typename types::return_type;
	- using field_type = typename types::field_type;
	- using array_iterator = typename types::array_iterator;
	+ /* --------------------------------------------------------------------------
	+ */
	+ template <typename types>
	+ class quadrature_point_iterator
	+ : public element_iterator<types, quadrature_point_iterator> {
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Typedefs */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ using parent = element_iterator<types, dumpers::quadrature_point_iterator>;
	+ using data_type = typename types::data_type;
	+ using return_type = typename types::return_type;
	+ using field_type = typename types::field_type;
	+ using array_iterator = typename types::array_iterator;

	- /* ------------------------------------------------------------------------ */
	- /* Constructors/Destructors */
	- /* ------------------------------------------------------------------------ */
	-public:
	- quadrature_point_iterator(const field_type & field,
	- const typename field_type::type_iterator & t_it,
	- const typename field_type::type_iterator & t_it_end,
	- const array_iterator & array_it,
	- const array_iterator & array_it_end,
	- const GhostType ghost_type = _not_ghost)
	- : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {}
	+ /* ------------------------------------------------------------------------
	+ */
	+ /* Constructors/Destructors */
	+ /* ------------------------------------------------------------------------
	+ */
	+ public:
	+ quadrature_point_iterator(
	+ const field_type & field,
	+ const typename field_type::type_iterator & t_it,
	+ const typename field_type::type_iterator & t_it_end,
	+ const array_iterator & array_it, const array_iterator & array_it_end,
	+ const GhostType ghost_type = _not_ghost)
	+ : parent(field, t_it, t_it_end, array_it, array_it_end, ghost_type) {}

	- return_type operator() { return this->array_it; }
	-};
	+ return_type operator() { return this->array_it; }
	+ };

	-/* -------------------------------------------------------------------------- */
	+ /* --------------------------------------------------------------------------
	+ */

	} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_QUADRATURE_POINT_ITERATOR_HH_ */
	diff --git a/src/io/dumper/dumper_text.cc b/src/io/dumper/dumper_text.cc
	index 83579d7be..9de0872fc 100644
	--- a/src/io/dumper/dumper_text.cc
	+++ b/src/io/dumper/dumper_text.cc
	@@ -1,105 +1,105 @@
	/**
	* @file dumper_text.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of text dumper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_text.hh"
	#include "communicator.hh"
	#include "dumper_compute.hh"
	#include "dumper_homogenizing_field.hh"
	#include "dumper_nodal_field.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <io_helper.hh>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	DumperText::DumperText(const std::string & basename,
	iohelper::TextDumpMode mode, bool parallel) {
	this->dumper = std::make_unique<iohelper::DumperText>(mode);
	this->setBaseName(basename);

	this->setParallelContext(parallel);
	}

	/* -------------------------------------------------------------------------- */
	void DumperText::registerMesh(const Mesh & mesh, UInt /spatial_dimension/,
	GhostType /ghost_type/,
	ElementKind /element_kind/) {
	registerField("position",
	std::make_shared<dumpers::NodalField<Real>>(mesh.getNodes()));
	// in parallel we need node type
	UInt nb_proc = mesh.getCommunicator().getNbProc();
	if (nb_proc > 1) {
	auto func = std::make_unique<dumpers::ComputeUIntFromEnum<ContactState>>();
	std::shared_ptr<dumpers::Field> field =
	std::make_shared<dumpers::NodalField<NodeFlag>>(mesh.getNodesFlags());
	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, std::move(func));
	registerField("nodes_type", field);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DumperText::registerFilteredMesh(
	const Mesh & mesh, const ElementTypeMapArray<UInt> & /elements_filter/,
	const Array<UInt> & nodes_filter, UInt /spatial_dimension/,
	GhostType /ghost_type/, ElementKind /element_kind/) {
	registerField("position", std::make_shared<dumpers::NodalField<Real, true>>(
	mesh.getNodes(), 0, 0, &nodes_filter));

	// in parallel we need node type
	UInt nb_proc = mesh.getCommunicator().getNbProc();
	if (nb_proc > 1) {
	auto func = std::make_unique<dumpers::ComputeUIntFromEnum<ContactState>>();
	std::shared_ptr<dumpers::Field> field =
	std::make_shared<dumpers::NodalField<NodeFlag, true>>(
	mesh.getNodesFlags(), 0, 0, &nodes_filter);
	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, std::move(func));
	registerField("nodes_type", field);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DumperText::setBaseName(const std::string & basename) {
	DumperIOHelper::setBaseName(basename);
	static_cast<iohelper::DumperText *>(this->dumper.get())
	->setDataSubDirectory(this->filename + "-DataFiles");
	}

	/* -------------------------------------------------------------------------- */
	void DumperText::setPrecision(UInt prec) {
	static_cast<iohelper::DumperText *>(this->dumper.get())->setPrecision(prec);
	}

	} // namespace akantu
	diff --git a/src/io/dumper/dumper_text.hh b/src/io/dumper/dumper_text.hh
	index 671ea2113..357010b68 100644
	--- a/src/io/dumper/dumper_text.hh
	+++ b/src/io/dumper/dumper_text.hh
	@@ -1,85 +1,85 @@
	/**
	* @file dumper_text.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief to dump into a text file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper.hh"
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DUMPER_TEXT_HH_
	#define AKANTU_DUMPER_TEXT_HH_
	/* -------------------------------------------------------------------------- */
	#include <io_helper.hh>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class DumperText : public DumperIOHelper {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperText(const std::string & basename = "dumper_text",
	iohelper::TextDumpMode mode = iohelper::_tdm_space,
	bool parallel = true);
	~DumperText() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	- void
	- registerMesh(const Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) override;
	+ void registerMesh(const Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined) override;

	- void registerFilteredMesh(
	- const Mesh & mesh, const ElementTypeMapArray<UInt> & elements_filter,
	- const Array<UInt> & nodes_filter,
	- UInt spatial_dimension = _all_dimensions,
	- GhostType ghost_type = _not_ghost,
	- ElementKind element_kind = _ek_not_defined) override;
	+ void
	+ registerFilteredMesh(const Mesh & mesh,
	+ const ElementTypeMapArray<UInt> & elements_filter,
	+ const Array<UInt> & nodes_filter,
	+ UInt spatial_dimension = _all_dimensions,
	+ GhostType ghost_type = _not_ghost,
	+ ElementKind element_kind = _ek_not_defined) override;

	void setBaseName(const std::string & basename) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	void setPrecision(UInt prec);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	#endif /* AKANTU_DUMPER_TEXT_HH_ */
	diff --git a/src/io/dumper/dumper_type_traits.hh b/src/io/dumper/dumper_type_traits.hh
	index dace0430a..6373419f9 100644
	--- a/src/io/dumper/dumper_type_traits.hh
	+++ b/src/io/dumper/dumper_type_traits.hh
	@@ -1,90 +1,90 @@
	/**
	* @file dumper_type_traits.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Type traits for field properties
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_DUMPER_TYPE_TRAITS_HH_
	#define AKANTU_DUMPER_TYPE_TRAITS_HH_
	/* -------------------------------------------------------------------------- */
	#include "element_type_map.hh"
	#include "element_type_map_filter.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {
	/* ------------------------------------------------------------------------ */
	template <class data, class ret, class field> struct TypeTraits {
	//! the stored data (real, int, uint, ...)
	using data_type = data;
	//! the type returned by the operator *
	using return_type = ret;
	//! the field type (ElementTypeMap or ElementTypeMapFilter)
	using field_type = field;
	//! the type over which we iterate
	using it_type = typename field_type::value_type;
	//! the type of array (Array<T> or ArrayFilter<T>)
	using array_type = typename field_type::array_type;
	//! the iterator over the array
	using array_iterator = typename array_type::const_vector_iterator;
	};

	/* ------------------------------------------------------------------------ */

	// specialization for the case in which input and output types are the same
	template <class T, template <class> class ret, bool filtered>
	struct SingleType : public TypeTraits<T, ret<T>, ElementTypeMapArray<T>> {};

	/* ------------------------------------------------------------------------ */

	// same as before but for filtered data
	template <class T, template <class> class ret>
	struct SingleType<T, ret, true>
	: public TypeTraits<T, ret<T>, ElementTypeMapArrayFilter<T>> {};
	/* ------------------------------------------------------------------------ */

	// specialization for the case in which input and output types are different
	template <class it_type, class data_type, template <class> class ret,
	bool filtered>
	struct DualType : public TypeTraits<data_type, ret<data_type>,
	ElementTypeMapArray<it_type>> {};

	/* ------------------------------------------------------------------------ */

	// same as before but for filtered data
	template <class it_type, class data_type, template <class> class ret>
	struct DualType<it_type, data_type, ret, true>
	: public TypeTraits<data_type, ret<data_type>,
	ElementTypeMapArrayFilter<it_type>> {};
	/* ------------------------------------------------------------------------ */
	} // namespace dumpers
	} // namespace akantu

	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_DUMPER_TYPE_TRAITS_HH_ */
	diff --git a/src/io/dumper/dumper_variable.hh b/src/io/dumper/dumper_variable.hh
	index d72be196c..42c362c51 100644
	--- a/src/io/dumper/dumper_variable.hh
	+++ b/src/io/dumper/dumper_variable.hh
	@@ -1,121 +1,121 @@
	/**
	* @file dumper_variable.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Tue Jun 04 2013
	* @date last modification: Wed Nov 08 2017
	*
	* @brief template of variable
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include <type_traits>

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DUMPER_IOHELPER_TMPL_VARIABLE_HH_
	#define AKANTU_DUMPER_IOHELPER_TMPL_VARIABLE_HH_
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace dumpers {
	/* --------------------------------------------------------------------------
	*/

	/// Variable interface
	class VariableBase {
	public:
	VariableBase() = default;
	virtual ~VariableBase() = default;
	virtual void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) = 0;
	};

	/* --------------------------------------------------------------------------
	*/

	template <typename T, bool is_scal = std::is_arithmetic<T>::value>
	class Variable : public VariableBase {
	public:
	Variable(const T & t) : vari(t) {}

	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addVariable(id, *this);
	}

	const T & operator[](UInt i) const { return vari[i]; }

	UInt getDim() { return vari.size(); }
	iohelper::DataType getDataType() { return iohelper::getDataType<T>(); }

	protected:
	const T & vari;
	};

	/* --------------------------------------------------------------------------
	*/
	template <typename T> class Variable<Vector<T>, false> : public VariableBase {
	public:
	Variable(const Vector<T> & t) : vari(t) {}

	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addVariable(id, *this);
	}

	const T & operator[](UInt i) const { return vari[i]; }

	UInt getDim() { return vari.size(); }
	iohelper::DataType getDataType() { return iohelper::getDataType<T>(); }

	protected:
	const Vector<T> & vari;
	};

	/* --------------------------------------------------------------------------
	*/

	template <typename T> class Variable<T, true> : public VariableBase {
	public:
	Variable(const T & t) : vari(t) {}

	void registerToDumper(const std::string & id,
	iohelper::Dumper & dumper) override {
	dumper.addVariable(id, *this);
	}

	const T & operator[](__attribute__((unused)) UInt i) const { return vari; }

	UInt getDim() { return 1; }
	iohelper::DataType getDataType() { return iohelper::getDataType<T>(); }

	protected:
	const T & vari;
	};

	-} // namespace dumper
	+} // namespace dumpers
	} // namespace akantu

	#endif /* AKANTU_DUMPER_IOHELPER_TMPL_VARIABLE_HH_ */
	diff --git a/src/io/mesh_io.cc b/src/io/mesh_io.cc
	index f7dbd4bc3..2b2679ff4 100644
	--- a/src/io/mesh_io.cc
	+++ b/src/io/mesh_io.cc
	@@ -1,141 +1,141 @@
	/**
	* @file mesh_io.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jun 07 2019
	*
	* @brief common part for all mesh io classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_io.hh"
	#include "aka_common.hh"
	#include "aka_iterators.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MeshIO::MeshIO() {
	canReadSurface = false;
	canReadExtendedData = false;
	}

	/* -------------------------------------------------------------------------- */
	MeshIO::~MeshIO() = default;

	/* -------------------------------------------------------------------------- */
	std::unique_ptr<MeshIO> MeshIO::getMeshIO(const std::string & filename,
	const MeshIOType & type) {
	MeshIOType t = type;
	if (type == _miot_auto) {
	std::string::size_type idx = filename.rfind('.');
	std::string ext;
	if (idx != std::string::npos) {
	ext = filename.substr(idx + 1);
	}

	if (ext == "msh") {
	t = _miot_gmsh;
	} else if (ext == "diana") {
	t = _miot_diana;
	} else {
	AKANTU_EXCEPTION("Cannot guess the type of file of "
	<< filename << " (ext " << ext << "). "
	<< "Please provide the MeshIOType to the read function");
	}
	}

	switch (t) {
	case _miot_gmsh:
	return std::make_unique<MeshIOMSH>();
	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	case _miot_gmsh_struct:
	return std::make_unique<MeshIOMSHStruct>();
	#endif
	case _miot_diana:
	return std::make_unique<MeshIODiana>();
	default:
	return nullptr;
	}
	}

	/* -------------------------------------------------------------------------- */
	void MeshIO::read(const std::string & filename, Mesh & mesh,
	const MeshIOType & type) {
	std::unique_ptr<MeshIO> mesh_io = getMeshIO(filename, type);
	mesh_io->read(filename, mesh);
	}

	/* -------------------------------------------------------------------------- */
	void MeshIO::write(const std::string & filename, Mesh & mesh,
	const MeshIOType & type) {
	std::unique_ptr<MeshIO> mesh_io = getMeshIO(filename, type);
	mesh_io->write(filename, mesh);
	}

	/* -------------------------------------------------------------------------- */
	void MeshIO::constructPhysicalNames(const std::string & tag_name, Mesh & mesh) {
	if (not physical_names.empty()) {
	for (auto type : mesh.elementTypes()) {
	auto & name_vec =
	mesh.getDataPointer<std::string>("physical_names", type);

	const auto & tags_vec = mesh.getData<UInt>(tag_name, type);

	for (auto && pair : zip(tags_vec, name_vec)) {
	auto tag = std::get<0>(pair);
	auto & name = std::get<1>(pair);
	auto map_it = physical_names.find(tag);

	if (map_it == physical_names.end()) {
	std::stringstream sstm;
	sstm << tag;

	name = sstm.str();
	} else {
	name = map_it->second;
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void MeshIO::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	if (not physical_names.empty()) {
	stream << space << "Physical map:" << std::endl;
	for (const auto & pair : physical_names) {
	stream << space << pair.first << ": " << pair.second << std::endl;
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/io/mesh_io.hh b/src/io/mesh_io.hh
	index 12aa47618..27dc19513 100644
	--- a/src/io/mesh_io.hh
	+++ b/src/io/mesh_io.hh
	@@ -1,115 +1,115 @@
	/**
	* @file mesh_io.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jun 07 2019
	*
	* @brief interface of a mesh io class, reader and writer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_IO_HH_
	#define AKANTU_MESH_IO_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshIO {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshIO();

	virtual ~MeshIO();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	static void read(const std::string & filename, Mesh & mesh,
	const MeshIOType & type);
	static void write(const std::string & filename, Mesh & mesh,
	const MeshIOType & type);

	/// read a mesh from the file
	virtual void read(const std::string & /filename/, Mesh & /mesh/) {}

	/// write a mesh to a file
	virtual void write(const std::string & /filename/, const Mesh & /mesh/) {}

	/// function to request the manual construction of the physical names maps
	virtual void constructPhysicalNames(const std::string & tag_name,
	Mesh & mesh);

	/// method to permit to be printed to a generic stream
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/// static contruction of a meshio object
	static std::unique_ptr<MeshIO> getMeshIO(const std::string & filename,
	const MeshIOType & type);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	auto & getPhysicalNames() { return this->physical_names; }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	bool canReadSurface{false};
	bool canReadExtendedData{false};

	/// correspondance between a tag and physical names (if applicable)
	std::map<int, std::string> physical_names;
	};

	/* -------------------------------------------------------------------------- */

	inline std::ostream & operator<<(std::ostream & stream, const MeshIO & _this) {
	_this.printself(stream);
	return stream;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "mesh_io_diana.hh"
	#include "mesh_io_msh.hh"

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	#include "mesh_io_msh_struct.hh"
	#endif

	#endif /* AKANTU_MESH_IO_HH_ */
	diff --git a/src/io/mesh_io/mesh_io_diana.cc b/src/io/mesh_io/mesh_io_diana.cc
	index 7573a9c67..adea68462 100644
	--- a/src/io/mesh_io/mesh_io_diana.cc
	+++ b/src/io/mesh_io/mesh_io_diana.cc
	@@ -1,612 +1,612 @@
	/**
	* @file mesh_io_diana.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Alodie Schneuwly <alodie.schneuwly@epfl.ch>
	*
	* @date creation: Sat Mar 26 2011
	* @date last modification: Fri Feb 28 2020
	*
	* @brief handles diana meshes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "mesh_io_diana.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <string.h>
	/* -------------------------------------------------------------------------- */
	#include <stdio.h>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Methods Implentations */
	/* -------------------------------------------------------------------------- */

	MeshIODiana::MeshIODiana() {
	canReadSurface = true;
	canReadExtendedData = true;
	_diana_to_akantu_element_types["T9TM"] = _triangle_3;
	_diana_to_akantu_element_types["CT6CM"] = _triangle_6;
	_diana_to_akantu_element_types["Q12TM"] = _quadrangle_4;
	_diana_to_akantu_element_types["CQ8CM"] = _quadrangle_8;
	_diana_to_akantu_element_types["TP18L"] = _pentahedron_6;
	_diana_to_akantu_element_types["CTP45"] = _pentahedron_15;
	_diana_to_akantu_element_types["TE12L"] = _tetrahedron_4;
	_diana_to_akantu_element_types["HX24L"] = _hexahedron_8;
	_diana_to_akantu_element_types["CHX60"] = _hexahedron_20;
	_diana_to_akantu_mat_prop["YOUNG"] = "E";
	_diana_to_akantu_mat_prop["DENSIT"] = "rho";
	_diana_to_akantu_mat_prop["POISON"] = "nu";

	std::map<std::string, ElementType>::iterator it;
	for (it = _diana_to_akantu_element_types.begin();
	it != _diana_to_akantu_element_types.end(); ++it) {
	UInt nb_nodes = Mesh::getNbNodesPerElement(it->second);

	auto * tmp = new UInt[nb_nodes];
	for (UInt i = 0; i < nb_nodes; ++i) {
	tmp[i] = i;
	}

	switch (it->second) {
	case _tetrahedron_10:
	tmp[8] = 9;
	tmp[9] = 8;
	break;
	case _pentahedron_15:
	tmp[0] = 2;
	tmp[1] = 8;
	tmp[2] = 0;
	tmp[3] = 6;
	tmp[4] = 1;
	tmp[5] = 7;
	tmp[6] = 11;
	tmp[7] = 9;
	tmp[8] = 10;
	tmp[9] = 5;
	tmp[10] = 14;
	tmp[11] = 3;
	tmp[12] = 12;
	tmp[13] = 4;
	tmp[14] = 13;
	break;
	case _hexahedron_20:
	tmp[0] = 5;
	tmp[1] = 16;
	tmp[2] = 4;
	tmp[3] = 19;
	tmp[4] = 7;
	tmp[5] = 18;
	tmp[6] = 6;
	tmp[7] = 17;
	tmp[8] = 13;
	tmp[9] = 12;
	tmp[10] = 15;
	tmp[11] = 14;
	tmp[12] = 1;
	tmp[13] = 8;
	tmp[14] = 0;
	tmp[15] = 11;
	tmp[16] = 3;
	tmp[17] = 10;
	tmp[18] = 2;
	tmp[19] = 9;
	break;
	default:
	// nothing to change
	break;
	}
	_read_order[it->second] = tmp;
	}
	}

	/* -------------------------------------------------------------------------- */
	MeshIODiana::~MeshIODiana() = default;

	/* -------------------------------------------------------------------------- */
	inline void my_getline(std::ifstream & infile, std::string & line) {
	std::getline(infile, line); // read the line
	size_t pos = line.find('\r'); /// remove the extra \\r if needed
	line = line.substr(0, pos);
	}

	/* -------------------------------------------------------------------------- */
	void MeshIODiana::read(const std::string & filename, Mesh & mesh) {
	AKANTU_DEBUG_IN();

	MeshAccessor mesh_accessor(mesh);

	std::ifstream infile;
	infile.open(filename.c_str());

	std::string line;
	UInt first_node_number = std::numeric_limits<UInt>::max();
	diana_element_number_to_elements.clear();

	if (!infile.good()) {
	AKANTU_ERROR("Cannot open file " << filename);
	}

	while (infile.good()) {
	my_getline(infile, line);

	/// read all nodes
	if (line == "'COORDINATES'") {
	line = readCoordinates(infile, mesh, first_node_number);
	}

	/// read all elements
	if (line == "'ELEMENTS'") {
	line = readElements(infile, mesh, first_node_number);
	}

	/// read the material properties and write a .dat file
	if (line == "'MATERIALS'") {
	line = readMaterial(infile, filename);
	}

	/// read the material properties and write a .dat file
	if (line == "'GROUPS'") {
	line = readGroups(infile, mesh, first_node_number);
	}
	}
	infile.close();

	mesh_accessor.setNbGlobalNodes(mesh.getNbNodes());

	MeshUtils::fillElementToSubElementsData(mesh);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshIODiana::write(__attribute__((unused)) const std::string & filename,
	__attribute__((unused)) const Mesh & mesh) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::
	readCoordinates( // NOLINT(readability-convert-member-functions-to-static)
	std::ifstream & infile, Mesh & mesh, UInt & first_node_number) {
	AKANTU_DEBUG_IN();

	MeshAccessor mesh_accessor(mesh);

	Array<Real> & nodes = mesh_accessor.getNodes();

	std::string line;

	UInt index;
	Vector<Real> coord(3);

	do {
	my_getline(infile, line);
	if ("'ELEMENTS'" == line) {
	break;
	}

	std::stringstream sstr_node(line);
	sstr_node >> index >> coord(0) >> coord(1) >> coord(2);

	first_node_number = first_node_number < index ? first_node_number : index;

	nodes.push_back(coord);
	} while (true);

	AKANTU_DEBUG_OUT();
	return line;
	}

	/* -------------------------------------------------------------------------- */
	UInt MeshIODiana::
	readInterval( // NOLINT(readability-convert-member-functions-to-static)
	std::stringstream & line, std::set<UInt> & interval) {
	UInt first;
	line >> first;
	if (line.fail()) {
	return 0;
	}
	interval.insert(first);

	UInt second;
	int dash;
	dash = line.get();
	if (dash == '-') {
	line >> second;
	interval.insert(second);
	return 2;
	}

	if (line.fail()) {
	line.clear(std::ios::eofbit); // in case of get at end of the line
	} else {
	line.unget();
	}
	return 1;
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::readGroups(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number) {
	AKANTU_DEBUG_IN();

	std::string line;
	my_getline(infile, line);

	bool reading_nodes_group = false;

	while (line != "'SUPPORTS'") {
	if (line == "NODES") {
	reading_nodes_group = true;
	my_getline(infile, line);
	}

	if (line == "ELEMEN") {
	reading_nodes_group = false;
	my_getline(infile, line);
	}

	auto * str = new std::stringstream(line);

	UInt id;
	std::string name;
	char c;
	*str >> id >> name >> c;

	auto * list_ids = new Array<UInt>(0, 1, name);

	UInt s = 1;
	bool end = false;
	while (!end) {
	while (!str->eof() && s != 0) {
	std::set<UInt> interval;
	s = readInterval(*str, interval);
	auto it = interval.begin();
	if (s == 1) {
	list_ids->push_back(*it);
	}
	if (s == 2) {
	UInt first = *it;
	++it;
	UInt second = *it;
	for (UInt i = first; i <= second; ++i) {
	list_ids->push_back(i);
	}
	}
	}
	if (str->fail()) {
	end = true;
	} else {
	my_getline(infile, line);
	delete str;
	str = new std::stringstream(line);
	}
	}

	delete str;

	if (reading_nodes_group) {
	NodeGroup & ng = mesh.createNodeGroup(name);
	for (UInt i = 0; i < list_ids->size(); ++i) {
	UInt node = (*list_ids)(i)-first_node_number;
	ng.add(node, false);
	}
	delete list_ids;

	} else {
	ElementGroup & eg = mesh.createElementGroup(name);
	for (UInt i = 0; i < list_ids->size(); ++i) {
	Element & elem = diana_element_number_to_elements[(*list_ids)(i)];
	if (elem.type != _not_defined) {
	eg.add(elem, false, false);
	}
	}

	eg.optimize();
	delete list_ids;
	}

	my_getline(infile, line);
	}

	AKANTU_DEBUG_OUT();
	return line;
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::readElements(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number) {
	AKANTU_DEBUG_IN();

	std::string line;
	my_getline(infile, line);

	if ("CONNECTIVITY" == line) {
	line = readConnectivity(infile, mesh, first_node_number);
	}

	/// read the line corresponding to the materials
	if ("MATERIALS" == line) {
	line = readMaterialElement(infile, mesh);
	}

	AKANTU_DEBUG_OUT();
	return line;
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::readConnectivity(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number) {
	AKANTU_DEBUG_IN();

	MeshAccessor mesh_accessor(mesh);
	Int index;
	std::string lline;

	std::string diana_type;
	ElementType akantu_type;
	ElementType akantu_type_old = _not_defined;
	Array<UInt> * connectivity = nullptr;
	UInt node_per_element = 0;
	Element elem;
	UInt * read_order = nullptr;

	while (true) {
	my_getline(infile, lline);
	// std::cerr << lline << std::endl;
	std::stringstream sstr_elem(lline);
	if (lline == "MATERIALS") {
	break;
	}

	/// traiter les coordonnees
	sstr_elem >> index;
	sstr_elem >> diana_type;

	akantu_type = _diana_to_akantu_element_types[diana_type];

	if (akantu_type == _not_defined) {
	continue;
	}

	if (akantu_type != akantu_type_old) {
	connectivity = &(mesh_accessor.getConnectivity(akantu_type));

	node_per_element = connectivity->getNbComponent();
	akantu_type_old = akantu_type;
	read_order = _read_order[akantu_type];
	}

	Vector<UInt> local_connect(node_per_element);

	// used if element is written on two lines
	UInt j_last = 0;

	for (UInt j = 0; j < node_per_element; ++j) {
	UInt node_index;
	sstr_elem >> node_index;

	// check s'il y a pas plus rien après un certain point

	if (sstr_elem.fail()) {
	sstr_elem.clear();
	sstr_elem.ignore();
	break;
	}

	node_index -= first_node_number;
	local_connect(read_order[j]) = node_index;
	j_last = j;
	}

	// check if element is written in two lines
	if (j_last != (node_per_element - 1)) {

	// if this is the case, read on more line
	my_getline(infile, lline);
	std::stringstream sstr_elem(lline);

	for (UInt j = (j_last + 1); j < node_per_element; ++j) {

	UInt node_index;
	sstr_elem >> node_index;

	node_index -= first_node_number;
	local_connect(read_order[j]) = node_index;
	}
	}

	connectivity->push_back(local_connect);

	elem.type = akantu_type;
	elem.element = connectivity->size() - 1;

	diana_element_number_to_elements[index] = elem;
	akantu_number_to_diana_number[elem] = index;
	}

	AKANTU_DEBUG_OUT();
	return lline;
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::readMaterialElement(std::ifstream & infile,
	Mesh & mesh) {
	AKANTU_DEBUG_IN();

	std::string line;

	for (auto type : mesh.elementTypes()) {
	UInt nb_element = mesh.getNbElement(type);
	mesh.getDataPointer<UInt>("material", type, _not_ghost, 1)
	.resize(nb_element);
	}

	my_getline(infile, line);
	while (line != "'MATERIALS'") {
	line =
	line.substr(line.find('/') + 1,
	std::string::npos); // erase the first slash / of the line
	char tutu[250] = {'\0'};
	strncpy(tutu, line.c_str(), 249);

	AKANTU_DEBUG_WARNING("reading line " << line);
	Array<UInt> temp_id(0, 2);
	UInt mat;
	while (true) {
	std::stringstream sstr_intervals_elements(line);
	Vector<UInt> id(2);
	char temp;
	while (sstr_intervals_elements.good()) {
	sstr_intervals_elements >> id(0) >> temp >> id(1); // >> "/" >> mat;
	if (!sstr_intervals_elements.fail()) {
	temp_id.push_back(id);
	}
	}
	if (sstr_intervals_elements.fail()) {
	sstr_intervals_elements.clear();
	sstr_intervals_elements.ignore();
	sstr_intervals_elements >> mat;
	break;
	}
	my_getline(infile, line);
	}

	// loop over elements
	// UInt * temp_id_val = temp_id.storage();
	for (UInt i = 0; i < temp_id.size(); ++i) {
	for (UInt j = temp_id(i, 0); j <= temp_id(i, 1); ++j) {
	Element & element = diana_element_number_to_elements[j];
	if (element.type == _not_defined) {
	continue;
	}
	UInt elem = element.element;
	ElementType type = element.type;
	Array<UInt> & data =
	mesh.getDataPointer<UInt>("material", type, _not_ghost);
	data(elem) = mat;
	}
	}

	my_getline(infile, line);
	}

	AKANTU_DEBUG_OUT();
	return line;
	}

	/* -------------------------------------------------------------------------- */
	std::string MeshIODiana::readMaterial(std::ifstream & infile,
	const std::string & filename) {
	AKANTU_DEBUG_IN();

	std::stringstream mat_file_name;

	mat_file_name << "material_" << filename;

	std::ofstream material_file;
	material_file.open(mat_file_name.str().c_str()); // mat_file_name.str());

	UInt mat_index;
	std::string line;

	bool first_mat = true;
	bool end = false;

	UInt mat_id = 0;

	using MatProp = std::map<std::string, Real>;
	MatProp mat_prop;
	do {
	my_getline(infile, line);
	std::stringstream sstr_material(line);
	if (("'GROUPS'" == line) \|\| ("'END'" == line)) {
	if (!mat_prop.empty()) {
	material_file << "material elastic [" << std::endl;
	material_file << "\tname = material" << ++mat_id << std::endl;
	for (auto it = mat_prop.begin(); it != mat_prop.end(); ++it) {
	material_file << "\t" << it->first << " = " << it->second
	<< std::endl;
	}
	material_file << "]" << std::endl;
	mat_prop.clear();
	}
	end = true;
	} else {
	/// traiter les caractéristiques des matériaux
	sstr_material >> mat_index;

	if (!sstr_material.fail()) {
	if (!first_mat) {
	if (!mat_prop.empty()) {
	material_file << "material elastic [" << std::endl;
	material_file << "\tname = material" << ++mat_id << std::endl;
	for (auto it = mat_prop.begin(); it != mat_prop.end(); ++it) {
	material_file << "\t" << it->first << " = " << it->second
	<< std::endl;
	}
	material_file << "]" << std::endl;
	mat_prop.clear();
	}
	}
	first_mat = false;
	} else {
	sstr_material.clear();
	}

	std::string prop_name;
	sstr_material >> prop_name;

	std::map<std::string, std::string>::iterator it;
	it = _diana_to_akantu_mat_prop.find(prop_name);

	if (it != _diana_to_akantu_mat_prop.end()) {
	Real value;
	sstr_material >> value;
	mat_prop[it->second] = value;
	} else {
	AKANTU_DEBUG_INFO("In material reader, property " << prop_name
	<< "not recognized");
	}
	}
	} while (!end);

	AKANTU_DEBUG_OUT();
	return line;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/io/mesh_io/mesh_io_diana.hh b/src/io/mesh_io/mesh_io_diana.hh
	index 8051e5104..0d4d06442 100644
	--- a/src/io/mesh_io/mesh_io_diana.hh
	+++ b/src/io/mesh_io/mesh_io_diana.hh
	@@ -1,109 +1,109 @@
	/**
	* @file mesh_io_diana.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Alodie Schneuwly <alodie.schneuwly@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 08 2017
	*
	* @brief diana mesh reader description
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_IO_DIANA_HH_
	#define AKANTU_MESH_IO_DIANA_HH_

	/* -------------------------------------------------------------------------- */
	#include "mesh_io.hh"

	/* -------------------------------------------------------------------------- */
	#include <vector>

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshIODiana : public MeshIO {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshIODiana();
	~MeshIODiana() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// read a mesh from the file
	void read(const std::string & filename, Mesh & mesh) override;

	/// write a mesh to a file
	void write(const std::string & filename, const Mesh & mesh) override;

	private:
	std::string readCoordinates(std::ifstream & infile, Mesh & mesh,
	UInt & first_node_number);

	std::string readElements(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number);

	std::string readGroups(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number);

	std::string readConnectivity(std::ifstream & infile, Mesh & mesh,
	UInt first_node_number);

	std::string readMaterialElement(std::ifstream & infile, Mesh & mesh);

	std::string readMaterial(std::ifstream & infile,
	const std::string & filename);

	UInt readInterval(std::stringstream & line, std::set<UInt> & interval);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	std::map<std::string, ElementType> _diana_to_akantu_element_types;
	std::map<std::string, std::string> _diana_to_akantu_mat_prop;

	/// order in witch element as to be read, akantu_node_order =
	/// _read_order[diana_node_order]
	std::map<ElementType, UInt *> _read_order;

	std::map<UInt, Element> diana_element_number_to_elements;
	std::map<Element, UInt> akantu_number_to_diana_number;
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_IO_DIANA_HH_ */
	diff --git a/src/io/mesh_io/mesh_io_msh.cc b/src/io/mesh_io/mesh_io_msh.cc
	index d6a160a8e..7832bb016 100644
	--- a/src/io/mesh_io/mesh_io_msh.cc
	+++ b/src/io/mesh_io/mesh_io_msh.cc
	@@ -1,1125 +1,1125 @@
	/**
	* @file mesh_io_msh.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Oct 29 2020
	*
	* @brief Read/Write for MSH files generated by gmsh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -----------------------------------------------------------------------------
	Version (Legacy) 1.0

	$NOD
	number-of-nodes
	node-number x-coord y-coord z-coord
	...
	$ENDNOD
	$ELM
	number-of-elements
	elm-number elm-type reg-phys reg-elem number-of-nodes node-number-list
	...
	$ENDELM
	-----------------------------------------------------------------------------
	Version 2.1

	$MeshFormat
	version-number file-type data-size
	$EndMeshFormat
	$Nodes
	number-of-nodes
	node-number x-coord y-coord z-coord
	...
	$EndNodes
	$Elements
	number-of-elements
	elm-number elm-type number-of-tags < tag > ... node-number-list
	...
	$EndElements
	$PhysicalNames
	number-of-names
	physical-dimension physical-number "physical-name"
	...
	$EndPhysicalNames
	$NodeData
	number-of-string-tags
	< "string-tag" >
	...
	number-of-real-tags
	< real-tag >
	...
	number-of-integer-tags
	< integer-tag >
	...
	node-number value ...
	...
	$EndNodeData
	$ElementData
	number-of-string-tags
	< "string-tag" >
	...
	number-of-real-tags
	< real-tag >
	...
	number-of-integer-tags
	< integer-tag >
	...
	elm-number value ...
	...
	$EndElementData
	$ElementNodeData
	number-of-string-tags
	< "string-tag" >
	...
	number-of-real-tags
	< real-tag >
	...
	number-of-integer-tags
	< integer-tag >
	...
	elm-number number-of-nodes-per-element value ...
	...
	$ElementEndNodeData

	-----------------------------------------------------------------------------
	elem-type

	1: 2-node line.
	2: 3-node triangle.
	3: 4-node quadrangle.
	4: 4-node tetrahedron.
	5: 8-node hexahedron.
	6: 6-node prism.
	7: 5-node pyramid.
	8: 3-node second order line
	9: 6-node second order triangle
	10: 9-node second order quadrangle
	11: 10-node second order tetrahedron
	12: 27-node second order hexahedron
	13: 18-node second order prism
	14: 14-node second order pyramid
	15: 1-node point.
	16: 8-node second order quadrangle
	17: 20-node second order hexahedron
	18: 15-node second order prism
	19: 13-node second order pyramid
	20: 9-node third order incomplete triangle
	21: 10-node third order triangle
	22: 12-node fourth order incomplete triangle
	23: 15-node fourth order triangle
	24: 15-node fifth order incomplete triangle
	25: 21-node fifth order complete triangle
	26: 4-node third order edge
	27: 5-node fourth order edge
	28: 6-node fifth order edge
	29: 20-node third order tetrahedron
	30: 35-node fourth order tetrahedron
	31: 56-node fifth order tetrahedron
	-------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"
	#include "node_group.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Methods Implentations */
	/* -------------------------------------------------------------------------- */
	MeshIOMSH::MeshIOMSH() {
	canReadSurface = true;
	canReadExtendedData = true;

	_msh_nodes_per_elem[_msh_not_defined] = 0;
	_msh_nodes_per_elem[_msh_segment_2] = 2;
	_msh_nodes_per_elem[_msh_triangle_3] = 3;
	_msh_nodes_per_elem[_msh_quadrangle_4] = 4;
	_msh_nodes_per_elem[_msh_tetrahedron_4] = 4;
	_msh_nodes_per_elem[_msh_hexahedron_8] = 8;
	_msh_nodes_per_elem[_msh_prism_1] = 6;
	_msh_nodes_per_elem[_msh_pyramid_1] = 1;
	_msh_nodes_per_elem[_msh_segment_3] = 3;
	_msh_nodes_per_elem[_msh_triangle_6] = 6;
	_msh_nodes_per_elem[_msh_quadrangle_9] = 9;
	_msh_nodes_per_elem[_msh_tetrahedron_10] = 10;
	_msh_nodes_per_elem[_msh_hexahedron_27] = 27;
	_msh_nodes_per_elem[_msh_hexahedron_20] = 20;
	_msh_nodes_per_elem[_msh_prism_18] = 18;
	_msh_nodes_per_elem[_msh_prism_15] = 15;
	_msh_nodes_per_elem[_msh_pyramid_14] = 14;
	_msh_nodes_per_elem[_msh_point] = 1;
	_msh_nodes_per_elem[_msh_quadrangle_8] = 8;

	_msh_to_akantu_element_types[_msh_not_defined] = _not_defined;
	_msh_to_akantu_element_types[_msh_segment_2] = _segment_2;
	_msh_to_akantu_element_types[_msh_triangle_3] = _triangle_3;
	_msh_to_akantu_element_types[_msh_quadrangle_4] = _quadrangle_4;
	_msh_to_akantu_element_types[_msh_tetrahedron_4] = _tetrahedron_4;
	_msh_to_akantu_element_types[_msh_hexahedron_8] = _hexahedron_8;
	_msh_to_akantu_element_types[_msh_prism_1] = _pentahedron_6;
	_msh_to_akantu_element_types[_msh_pyramid_1] = _not_defined;
	_msh_to_akantu_element_types[_msh_segment_3] = _segment_3;
	_msh_to_akantu_element_types[_msh_triangle_6] = _triangle_6;
	_msh_to_akantu_element_types[_msh_quadrangle_9] = _not_defined;
	_msh_to_akantu_element_types[_msh_tetrahedron_10] = _tetrahedron_10;
	_msh_to_akantu_element_types[_msh_hexahedron_27] = _not_defined;
	_msh_to_akantu_element_types[_msh_hexahedron_20] = _hexahedron_20;
	_msh_to_akantu_element_types[_msh_prism_18] = _not_defined;
	_msh_to_akantu_element_types[_msh_prism_15] = _pentahedron_15;
	_msh_to_akantu_element_types[_msh_pyramid_14] = _not_defined;
	_msh_to_akantu_element_types[_msh_point] = _point_1;
	_msh_to_akantu_element_types[_msh_quadrangle_8] = _quadrangle_8;

	_akantu_to_msh_element_types[_not_defined] = _msh_not_defined;
	_akantu_to_msh_element_types[_segment_2] = _msh_segment_2;
	_akantu_to_msh_element_types[_segment_3] = _msh_segment_3;
	_akantu_to_msh_element_types[_triangle_3] = _msh_triangle_3;
	_akantu_to_msh_element_types[_triangle_6] = _msh_triangle_6;
	_akantu_to_msh_element_types[_tetrahedron_4] = _msh_tetrahedron_4;
	_akantu_to_msh_element_types[_tetrahedron_10] = _msh_tetrahedron_10;
	_akantu_to_msh_element_types[_quadrangle_4] = _msh_quadrangle_4;
	_akantu_to_msh_element_types[_quadrangle_8] = _msh_quadrangle_8;
	_akantu_to_msh_element_types[_hexahedron_8] = _msh_hexahedron_8;
	_akantu_to_msh_element_types[_hexahedron_20] = _msh_hexahedron_20;
	_akantu_to_msh_element_types[_pentahedron_6] = _msh_prism_1;
	_akantu_to_msh_element_types[_pentahedron_15] = _msh_prism_15;
	_akantu_to_msh_element_types[_point_1] = _msh_point;

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	_akantu_to_msh_element_types[_bernoulli_beam_2] = _msh_segment_2;
	_akantu_to_msh_element_types[_bernoulli_beam_3] = _msh_segment_2;
	_akantu_to_msh_element_types[_discrete_kirchhoff_triangle_18] =
	_msh_triangle_3;
	#endif

	std::map<ElementType, MSHElementType>::iterator it;
	for (it = _akantu_to_msh_element_types.begin();
	it != _akantu_to_msh_element_types.end(); ++it) {
	UInt nb_nodes = _msh_nodes_per_elem[it->second];

	std::vector<UInt> tmp(nb_nodes);
	for (UInt i = 0; i < nb_nodes; ++i) {
	tmp[i] = i;
	}

	switch (it->first) {
	case _tetrahedron_10:
	tmp[8] = 9;
	tmp[9] = 8;
	break;
	case _pentahedron_6:
	tmp[0] = 2;
	tmp[1] = 0;
	tmp[2] = 1;
	tmp[3] = 5;
	tmp[4] = 3;
	tmp[5] = 4;
	break;
	case _pentahedron_15:
	tmp[0] = 2;
	tmp[1] = 0;
	tmp[2] = 1;
	tmp[3] = 5;
	tmp[4] = 3;
	tmp[5] = 4;
	tmp[6] = 8;
	tmp[8] = 11;
	tmp[9] = 6;
	tmp[10] = 9;
	tmp[11] = 10;
	tmp[12] = 14;
	tmp[14] = 12;
	break;
	case _hexahedron_20:
	tmp[9] = 11;
	tmp[10] = 12;
	tmp[11] = 9;
	tmp[12] = 13;
	tmp[13] = 10;
	tmp[17] = 19;
	tmp[18] = 17;
	tmp[19] = 18;
	break;
	default:
	// nothing to change
	break;
	}
	_read_order[it->first] = tmp;
	}
	}

	/* -------------------------------------------------------------------------- */
	MeshIOMSH::~MeshIOMSH() = default;

	/* -------------------------------------------------------------------------- */
	namespace {
	struct File {
	std::string filename;
	std::ifstream infile;
	std::string line;
	size_t current_line{0};

	size_t first_node_number{std::numeric_limits<UInt>::max()},
	last_node_number{0};
	bool has_physical_names{false};

	std::unordered_map<size_t, size_t> node_tags;
	std::unordered_map<size_t, Element> element_tags;
	double version{0};
	int size_of_size_t{0};
	Mesh & mesh;
	MeshAccessor mesh_accessor;

	std::multimap<std::pair<int, int>, int> entity_tag_to_physical_tags;

	File(const std::string & filename, Mesh & mesh)
	: filename(filename), mesh(mesh), mesh_accessor(mesh) {
	infile.open(filename.c_str());
	if (not infile.good()) {
	AKANTU_EXCEPTION("Cannot open file " << filename);
	}
	}

	~File() { infile.close(); }

	auto good() { return infile.good(); }

	std::stringstream get_line() {
	std::string tmp_str;
	if (infile.eof()) {
	AKANTU_EXCEPTION("Reached the end of the file " << filename);
	}
	std::getline(infile, tmp_str);
	line = trim(tmp_str);
	++current_line;

	return std::stringstream(line);
	}

	template <typename... Ts> void read_line(Ts &&... ts) {
	auto && sstr = get_line();
	(void)std::initializer_list<int>{
	(sstr >> std::forward<decltype(ts)>(ts), 0)...};
	}
	};
	} // namespace

	/* -------------------------------------------------------------------------- */
	template <typename File, typename Readers>
	void MeshIOMSH::populateReaders2(File & file, Readers & readers) {
	readers["$NOD"] = readers["$Nodes"] = [&](const std::string & /unused/) {
	UInt nb_nodes;
	file.read_line(nb_nodes);

	Array<Real> & nodes = file.mesh_accessor.getNodes();
	nodes.resize(nb_nodes);
	file.mesh_accessor.setNbGlobalNodes(nb_nodes);

	size_t index;
	Vector<double> coord(3);

	/// for each node, read the coordinates
	for (auto && data : enumerate(make_view(nodes, nodes.getNbComponent()))) {
	file.read_line(index, coord(0), coord(1), coord(2));

	if (index > std::numeric_limits<UInt>::max()) {
	AKANTU_EXCEPTION(
	"There are more nodes in this files than the index type of akantu "
	"can handle, consider recompiling with a bigger index type");
	}

	file.first_node_number = std::min(file.first_node_number, index);
	file.last_node_number = std::max(file.last_node_number, index);

	for (auto && coord_data : zip(std::get<1>(data), coord)) {
	std::get<0>(coord_data) = std::get<1>(coord_data);
	}
	file.node_tags[index] = std::get<0>(data);
	}
	};

	readers["$ELM"] = readers["$Elements"] = [&](const std::string & /unused/) {
	UInt nb_elements;
	file.read_line(nb_elements);

	Int index;
	UInt msh_type;
	ElementType akantu_type;

	for (UInt i = 0; i < nb_elements; ++i) {
	auto && sstr_elem = file.get_line();

	sstr_elem >> index;
	sstr_elem >> msh_type;

	/// get the connectivity vector depending on the element type
	akantu_type =
	this->_msh_to_akantu_element_types[MSHElementType(msh_type)];

	if (akantu_type == _not_defined) {
	AKANTU_DEBUG_WARNING("Unsuported element kind "
	<< msh_type << " at line " << file.current_line);
	continue;
	}

	Element elem{akantu_type, 0, _not_ghost};

	auto & connectivity = file.mesh_accessor.getConnectivity(akantu_type);
	auto node_per_element = connectivity.getNbComponent();
	auto & read_order = this->_read_order[akantu_type];

	/// read tags informations
	if (file.version < 2) {
	Int tag0;
	Int tag1;
	Int nb_nodes; // reg-phys, reg-elem, number-of-nodes
	sstr_elem >> tag0 >> tag1 >> nb_nodes;

	auto & data0 =
	file.mesh_accessor.template getData<UInt>("tag_0", akantu_type);
	data0.push_back(tag0);

	auto & data1 =
	file.mesh_accessor.template getData<UInt>("tag_1", akantu_type);
	data1.push_back(tag1);
	} else if (file.version < 4) {
	UInt nb_tags;
	sstr_elem >> nb_tags;
	for (UInt j = 0; j < nb_tags; ++j) {
	Int tag;
	sstr_elem >> tag;

	auto & data = file.mesh_accessor.template getData<UInt>(
	"tag_" + std::to_string(j), akantu_type);
	data.push_back(tag);
	}
	}

	Vector<UInt> local_connect(node_per_element);
	for (UInt j = 0; j < node_per_element; ++j) {
	UInt node_index;
	sstr_elem >> node_index;

	AKANTU_DEBUG_ASSERT(node_index <= file.last_node_number,
	"Node number not in range : line "
	<< file.current_line);

	local_connect(read_order[j]) = file.node_tags[node_index];
	}

	connectivity.push_back(local_connect);
	elem.element = connectivity.size() - 1;
	file.element_tags[index] = elem;
	}
	};

	readers["$Periodic"] = [&](const std::string & /unused/) {
	UInt nb_periodic_entities;
	file.read_line(nb_periodic_entities);

	file.mesh_accessor.getNodesFlags().resize(file.mesh.getNbNodes(),
	NodeFlag::_normal);

	for (UInt p = 0; p < nb_periodic_entities; ++p) {
	// dimension slave-tag master-tag
	UInt dimension;
	file.read_line(dimension);

	// transformation
	file.get_line();

	// nb nodes
	UInt nb_nodes;
	file.read_line(nb_nodes);

	for (UInt n = 0; n < nb_nodes; ++n) {
	// slave master
	auto && sstr = file.get_line();

	// The info in the mesh seem inconsistent so they are ignored for now.
	continue;

	if (dimension == file.mesh.getSpatialDimension() - 1) {
	UInt slave;
	UInt master;

	sstr >> slave;
	sstr >> master;
	file.mesh_accessor.addPeriodicSlave(file.node_tags[slave],
	file.node_tags[master]);
	}
	}
	}

	// mesh_accessor.markMeshPeriodic();
	};
	}

	/* -------------------------------------------------------------------------- */
	template <typename File, typename Readers>
	void MeshIOMSH::populateReaders4(File & file, Readers & readers) {
	static std::map<int, std::string> entity_type{
	{0, "points"},
	{1, "curve"},
	{2, "surface"},
	{3, "volume"},
	};

	readers["$Entities"] = [&](const std::string & /unused/) {
	size_t num_entity[4];
	file.read_line(num_entity[0], num_entity[1], num_entity[2], num_entity[3]);

	for (auto entity_dim : arange(4)) {
	for (auto _ [[gnu::unused]] : arange(num_entity[entity_dim])) {
	auto && sstr = file.get_line();

	int tag;
	double min_x;
	double min_y;
	double min_z;
	double max_x;
	double max_y;
	double max_z;
	size_t num_physical_tags;
	sstr >> tag >> min_x >> min_y >> min_z;

	if (entity_dim > 0 or file.version < 4.1) {
	sstr >> max_x >> max_y >> max_z;
	}

	sstr >> num_physical_tags;

	for (auto _ [[gnu::unused]] : arange(num_physical_tags)) {
	int phys_tag;
	sstr >> phys_tag;

	std::string physical_name;
	if (this->physical_names.find(phys_tag) ==
	this->physical_names.end()) {
	physical_name = "msh_block_" + std::to_string(phys_tag);
	} else {
	physical_name = this->physical_names[phys_tag];
	}

	if (not file.mesh.elementGroupExists(physical_name)) {
	file.mesh.createElementGroup(physical_name, entity_dim);
	} else {
	file.mesh.getElementGroup(physical_name).addDimension(entity_dim);
	}
	file.entity_tag_to_physical_tags.insert(
	std::make_pair(std::make_pair(tag, entity_dim), phys_tag));
	}
	}
	}
	};

	readers["$Nodes"] = [&](const std::string & /unused/) {
	size_t num_blocks;
	size_t num_nodes;
	if (file.version >= 4.1) {
	file.read_line(num_blocks, num_nodes, file.first_node_number,
	file.last_node_number);
	} else {
	file.read_line(num_blocks, num_nodes);
	}
	auto & nodes = file.mesh_accessor.getNodes();
	nodes.reserve(num_nodes);
	file.mesh_accessor.setNbGlobalNodes(num_nodes);

	if (num_nodes > std::numeric_limits<UInt>::max()) {
	AKANTU_EXCEPTION(
	"There are more nodes in this files than the index type of akantu "
	"can handle, consider recompiling with a bigger index type");
	}

	size_t node_id{0};

	for (auto block [[gnu::unused]] : arange(num_blocks)) {
	int entity_dim;
	int entity_tag;
	int parametric;
	size_t num_nodes_in_block;
	Vector<double> pos(3);
	Vector<double> real_pos(nodes.getNbComponent());

	if (file.version >= 4.1) {
	file.read_line(entity_dim, entity_tag, parametric, num_nodes_in_block);
	if (parametric) {
	AKANTU_EXCEPTION(
	"Akantu does not support parametric nodes in msh files");
	}
	for (auto _ [[gnu::unused]] : arange(num_nodes_in_block)) {
	size_t tag;
	file.read_line(tag);
	file.node_tags[tag] = node_id;
	++node_id;
	}

	for (auto _ [[gnu::unused]] : arange(num_nodes_in_block)) {
	file.read_line(pos(_x), pos(_y), pos(_z));
	for (auto && data : zip(real_pos, pos)) {
	std::get<0>(data) = std::get<1>(data);
	}

	nodes.push_back(real_pos);
	}
	} else {
	file.read_line(entity_tag, entity_dim, parametric, num_nodes_in_block);

	for (auto _ [[gnu::unused]] : arange(num_nodes_in_block)) {
	size_t tag;
	file.read_line(tag, pos(_x), pos(_y), pos(_z));

	if (file.version < 4.1) {
	file.first_node_number = std::min(file.first_node_number, tag);
	file.last_node_number = std::max(file.last_node_number, tag);
	}

	for (auto && data : zip(real_pos, pos)) {
	std::get<0>(data) = std::get<1>(data);
	}

	nodes.push_back(real_pos);
	file.node_tags[tag] = node_id;
	++node_id;
	}
	}
	}
	};

	readers["$Elements"] = [&](const std::string & /unused/) {
	size_t num_blocks;
	size_t num_elements;
	file.read_line(num_blocks, num_elements);

	for (auto block [[gnu::unused]] : arange(num_blocks)) {
	int entity_dim;
	int entity_tag;
	int element_type;
	size_t num_elements_in_block;

	if (file.version >= 4.1) {
	file.read_line(entity_dim, entity_tag, element_type,
	num_elements_in_block);
	} else {
	file.read_line(entity_tag, entity_dim, element_type,
	num_elements_in_block);
	}

	/// get the connectivity vector depending on the element type
	auto && akantu_type =
	this->_msh_to_akantu_element_types[(MSHElementType)element_type];

	if (akantu_type == _not_defined) {
	AKANTU_DEBUG_WARNING("Unsuported element kind " << element_type
	<< " at line "
	<< file.current_line);
	continue;
	}

	Element elem{akantu_type, 0, _not_ghost};

	auto & connectivity = file.mesh_accessor.getConnectivity(akantu_type);
	Vector<UInt> local_connect(connectivity.getNbComponent());
	auto && read_order = this->_read_order[akantu_type];

	auto & data0 =
	file.mesh_accessor.template getData<UInt>("tag_0", akantu_type);
	data0.resize(data0.size() + num_elements_in_block, 0);

	auto & physical_data = file.mesh_accessor.template getData<std::string>(
	"physical_names", akantu_type);
	physical_data.resize(physical_data.size() + num_elements_in_block, "");

	for (auto _ [[gnu::unused]] : arange(num_elements_in_block)) {
	auto && sstr_elem = file.get_line();
	size_t elem_tag;
	sstr_elem >> elem_tag;
	for (auto && c : arange(connectivity.getNbComponent())) {
	size_t node_tag;
	sstr_elem >> node_tag;

	AKANTU_DEBUG_ASSERT(node_tag <= file.last_node_number,
	"Node number not in range : line "
	<< file.current_line);

	node_tag = file.node_tags[node_tag];
	local_connect(read_order[c]) = node_tag;
	}
	connectivity.push_back(local_connect);
	elem.element = connectivity.size() - 1;
	file.element_tags[elem_tag] = elem;

	auto range = file.entity_tag_to_physical_tags.equal_range(
	std::make_pair(entity_tag, entity_dim));
	bool first = true;
	for (auto it = range.first; it != range.second; ++it) {
	auto phys_it = this->physical_names.find(it->second);
	if (first) {
	data0(elem.element) =
	it->second; // for compatibility with version 2
	if (phys_it != this->physical_names.end()) {
	physical_data(elem.element) = phys_it->second;
	}
	first = false;
	}
	if (phys_it != this->physical_names.end()) {
	file.mesh.getElementGroup(phys_it->second).add(elem, true, false);
	}
	}
	}
	}

	for (auto && element_group : file.mesh.iterateElementGroups()) {
	element_group.getNodeGroup().optimize();
	}
	};
	}

	/* -------------------------------------------------------------------------- */
	void MeshIOMSH::read(const std::string & filename, Mesh & mesh) {

	File file(filename, mesh);

	std::map<std::string, std::function<void(const std::string &)>> readers;

	readers["$MeshFormat"] = [&](const std::string & /unused/) {
	auto && sstr = file.get_line();

	int format;
	sstr >> file.version >> format;

	if (format != 0) {
	AKANTU_ERROR("This reader can only read ASCII files.");
	}

	if (file.version > 2) {
	sstr >> file.size_of_size_t;
	if (file.size_of_size_t > int(sizeof(UInt))) {
	AKANTU_DEBUG_INFO("The size of the indexes in akantu might be to small "
	"to read this file (akantu "
	<< sizeof(UInt) << " vs. msh file "
	<< file.size_of_size_t << ")");
	}
	}

	if (file.version < 4) {
	this->populateReaders2(file, readers);
	} else {
	this->populateReaders4(file, readers);
	}
	};

	auto && read_data = [&](auto && entity_tags, auto && get_data,
	auto && read_data) {
	auto read_data_tags = [&](auto x) {
	UInt number_of_tags{0};
	file.read_line(number_of_tags);
	std::vector<decltype(x)> tags(number_of_tags);

	for (auto && tag : tags) {
	file.read_line(tag);
	}
	return tags;
	};

	auto && string_tags = read_data_tags(std::string{});
	auto && real_tags [[gnu::unused]] = read_data_tags(double{});
	auto && int_tags = read_data_tags(int{});

	for (auto & s : string_tags) {
	s = trim(s, '"');
	}

	auto id = string_tags[0];
	auto size = int_tags[2];
	auto nb_component = int_tags[1];
	auto & data = get_data(id, size, nb_component);

	for (auto n [[gnu::unused]] : arange(size)) {
	auto && sstr = file.get_line();

	size_t tag;
	sstr >> tag;
	const auto & entity = entity_tags[tag];
	read_data(entity, sstr, data, nb_component);
	}
	};

	readers["$NodeData"] = [&](const std::string & /unused/) {
	/* $NodeData
	numStringTags(ASCII int)
	stringTag(string) ...
	numRealTags(ASCII int)
	realTag(ASCII double) ...
	numIntegerTags(ASCII int)
	integerTag(ASCII int) ...
	nodeTag(size_t) value(double) ...
	...
	$EndNodeData */
	read_data(
	file.node_tags,
	[&](auto && id, auto && size [[gnu::unused]],
	auto && nb_component [[gnu::unused]]) -> Array<double> & {
	auto & data =
	file.mesh.template getNodalData<double>(id, nb_component);
	data.resize(size);
	return data;
	},
	[&](auto && node, auto && sstr, auto && data,
	auto && nb_component [[gnu::unused]]) {
	for (auto c : arange(nb_component)) {
	sstr >> data(node, c);
	}
	});
	};

	readers["$ElementData"] = [&](const std::string & /unused/) {
	/* $ElementData
	numStringTags(ASCII int)
	stringTag(string) ...
	numRealTags(ASCII int)
	realTag(ASCII double) ...
	numIntegerTags(ASCII int)
	integerTag(ASCII int) ...
	elementTag(size_t) value(double) ...
	...
	$EndElementData
	*/
	read_data(
	file.element_tags,
	[&](auto && id, auto && size [[gnu::unused]],
	auto && nb_component
	[[gnu::unused]]) -> ElementTypeMapArray<double> & {
	file.mesh.template getElementalData<double>(id);
	return file.mesh.template getElementalData<double>(id);
	},
	[&](auto && element, auto && sstr, auto && data, auto && nb_component) {
	if (not data.exists(element.type)) {
	data.alloc(mesh.getNbElement(element.type), nb_component,
	element.type, element.ghost_type);
	}
	auto & data_array = data(element.type);
	for (auto c : arange(nb_component)) {
	sstr >> data_array(element.element, c);
	}
	});
	};

	readers["$ElementNodeData"] = [&](const std::string & /unused/) {
	/* $ElementNodeData
	numStringTags(ASCII int)
	stringTag(string) ...
	numRealTags(ASCII int)
	realTag(ASCII double) ...
	numIntegerTags(ASCII int)
	integerTag(ASCII int) ...
	elementTag(size_t) value(double) ...
	...
	$EndElementNodeData
	*/
	read_data(
	file.element_tags,
	[&](auto && id, auto && size [[gnu::unused]],
	auto && nb_component
	[[gnu::unused]]) -> ElementTypeMapArray<double> & {
	file.mesh.template getElementalData<double>(id);
	auto & data = file.mesh.template getElementalData<double>(id);
	data.isNodal(true);
	return data;
	},
	[&](auto && element, auto && sstr, auto && data, auto && nb_component) {
	int nb_nodes_per_element;
	sstr >> nb_nodes_per_element;
	if (not data.exists(element.type)) {
	data.alloc(mesh.getNbElement(element.type),
	nb_component * nb_nodes_per_element, element.type,
	element.ghost_type);
	}
	auto & data_array = data(element.type);
	for (auto c : arange(nb_component)) {
	sstr >> data_array(element.element, c);
	}
	});
	};

	readers["$PhysicalNames"] = [&](const std::string & /unused/) {
	file.has_physical_names = true;
	int num_of_phys_names;
	file.read_line(num_of_phys_names); /// the format line

	for (auto k [[gnu::unused]] : arange(num_of_phys_names)) {
	int phys_name_id;
	int phys_dim;
	std::string phys_name;
	file.read_line(phys_dim, phys_name_id, std::quoted(phys_name));

	this->physical_names[phys_name_id] = phys_name;
	}
	};

	readers["Unsupported"] = [&](const std::string & _block) {
	std::string block = _block.substr(1);
	AKANTU_DEBUG_WARNING("Unsupported block_kind " << block << " at line "
	<< file.current_line);
	auto && end_block = "$End" + block;
	while (file.line != end_block) {
	file.get_line();
	}
	};

	while (file.good()) {
	std::string block;
	file.read_line(block);

	auto && it = readers.find(block);

	if (it != readers.end()) {
	it->second(block);

	std::string end_block;
	file.read_line(end_block);
	block = block.substr(1);

	if (end_block != "$End" + block) {
	AKANTU_EXCEPTION("The reader failed to properly read the block "
	<< block << ". Expected a $End" << block << " at line "
	<< file.current_line);
	}
	} else if (not block.empty()) {
	readers["Unsupported"](block);
	}
	}

	// mesh.updateTypesOffsets(_not_ghost);
	if (file.version < 4) {
	this->constructPhysicalNames("tag_0", mesh);
	if (file.has_physical_names) {
	mesh.createGroupsFromMeshData<std::string>("physical_names");
	}
	}

	MeshUtils::fillElementToSubElementsData(mesh);
	}

	/* -------------------------------------------------------------------------- */
	void MeshIOMSH::write(const std::string & filename, const Mesh & mesh) {
	std::ofstream outfile;
	const Array<Real> & nodes = mesh.getNodes();

	outfile.open(filename.c_str());

	outfile << "$MeshFormat"
	<< "\n";
	outfile << "2.2 0 8"
	<< "\n";
	outfile << "$EndMeshFormat"
	<< "\n";

	outfile << std::setprecision(std::numeric_limits<Real>::digits10);
	outfile << "$Nodes"
	<< "\n";

	outfile << nodes.size() << "\n";

	outfile << std::uppercase;
	for (UInt i = 0; i < nodes.size(); ++i) {
	Int offset = i * nodes.getNbComponent();
	outfile << i + 1;
	for (UInt j = 0; j < nodes.getNbComponent(); ++j) {
	outfile << " " << nodes.storage()[offset + j];
	}

	for (UInt p = nodes.getNbComponent(); p < 3; ++p) {
	outfile << " " << 0.;
	}
	outfile << "\n";
	;
	}
	outfile << std::nouppercase;
	outfile << "$EndNodes"
	<< "\n";

	outfile << "$Elements"
	<< "\n";
	Int nb_elements = 0;
	for (auto && type :
	mesh.elementTypes(_all_dimensions, _not_ghost, _ek_not_defined)) {
	const Array<UInt> & connectivity = mesh.getConnectivity(type, _not_ghost);
	nb_elements += connectivity.size();
	}
	outfile << nb_elements << "\n";

	std::map<Element, size_t> element_to_msh_element;

	UInt element_idx = 1;
	auto element = ElementNull;
	for (auto && type :
	mesh.elementTypes(_all_dimensions, _not_ghost, _ek_not_defined)) {
	const auto & connectivity = mesh.getConnectivity(type, _not_ghost);
	element.type = type;

	UInt * tag[2] = {nullptr, nullptr};
	if (mesh.hasData<UInt>("tag_0", type, _not_ghost)) {
	const auto & data_tag_0 = mesh.getData<UInt>("tag_0", type, _not_ghost);
	tag[0] = data_tag_0.storage();
	}

	if (mesh.hasData<UInt>("tag_1", type, _not_ghost)) {
	const auto & data_tag_1 = mesh.getData<UInt>("tag_1", type, _not_ghost);
	tag[1] = data_tag_1.storage();
	}

	for (auto && data :
	enumerate(make_view(connectivity, connectivity.getNbComponent()))) {
	element.element = std::get<0>(data);
	const auto & conn = std::get<1>(data);
	element_to_msh_element.insert(std::make_pair(element, element_idx));

	outfile << element_idx << " " << _akantu_to_msh_element_types[type]
	<< " 2";

	/// \todo write the real data in the file
	for (UInt t = 0; t < 2; ++t) {
	if (tag[t] != nullptr) {
	outfile << " " << tag[t][element.element];
	} else {
	outfile << " 0";
	}
	}

	for (auto && c : conn) {
	outfile << " " << c + 1;
	}
	outfile << "\n";
	element_idx++;
	}
	}
	outfile << "$EndElements"
	<< "\n";

	if (mesh.hasData(MeshDataType::_nodal)) {
	auto && tags = mesh.getTagNames();
	for (auto && tag : tags) {
	auto type = mesh.getTypeCode(tag, MeshDataType::_nodal);
	if (type != MeshDataTypeCode::_real) {
	AKANTU_DEBUG_WARNING(
	"The field "
	<< tag << " is ignored by the MSH writer, msh files do not support "
	<< type << " data");
	continue;
	}
	auto && data = mesh.getNodalData<double>(tag);
	outfile << "$NodeData"
	<< "\n";
	outfile << "1"
	<< "\n";
	outfile << "\"" << tag << "\"\n";
	outfile << "1\n0.0"
	<< "\n";
	outfile << "3\n0"
	<< "\n";
	outfile << data.getNbComponent() << "\n";
	outfile << data.size() << "\n";
	for (auto && d : enumerate(make_view(data, data.getNbComponent()))) {
	outfile << std::get<0>(d) + 1;
	for (auto && v : std::get<1>(d)) {
	outfile << " " << v;
	}
	outfile << "\n";
	}
	outfile << "$EndNodeData"
	<< "\n";
	}
	}

	if (mesh.hasData(MeshDataType::_elemental)) {
	auto && tags = mesh.getTagNames();
	for (auto && tag : tags) {
	auto && data = mesh.getElementalData<double>(tag);
	auto type = mesh.getTypeCode(tag, MeshDataType::_elemental);
	if (type != MeshDataTypeCode::_real) {
	AKANTU_DEBUG_WARNING(
	"The field "
	<< tag << " is ignored by the MSH writer, msh files do not support "
	<< type << " data");
	continue;
	}
	if (data.isNodal()) {
	continue;
	}

	auto size = data.size();
	if (size == 0) {
	continue;
	}
	auto && nb_components = data.getNbComponents();
	auto nb_component = nb_components(*(data.elementTypes().begin()));

	outfile << "$ElementData"
	<< "\n";
	outfile << "1"
	<< "\n";
	outfile << "\"" << tag << "\"\n";
	outfile << "1\n0.0"
	<< "\n";
	outfile << "3\n0"
	<< "\n";
	outfile << nb_component << "\n";
	outfile << size << "\n";

	Element element;
	for (auto type : data.elementTypes()) {
	element.type = type;
	for (auto && _ :
	enumerate(make_view(data(type), nb_components(type)))) {
	element.element = std::get<0>(_);
	outfile << element_to_msh_element[element];
	for (auto && v : std::get<1>(_)) {
	outfile << " " << v;
	}
	outfile << "\n";
	}
	}
	outfile << "$EndElementData"
	<< "\n";
	}
	}

	outfile.close();
	}

	/* --------------------------------------------------------------------------
	*/

	} // namespace akantu
	diff --git a/src/io/mesh_io/mesh_io_msh.hh b/src/io/mesh_io/mesh_io_msh.hh
	index e8a0fe0ca..acfae74fc 100644
	--- a/src/io/mesh_io/mesh_io_msh.hh
	+++ b/src/io/mesh_io/mesh_io_msh.hh
	@@ -1,117 +1,117 @@
	/**
	* @file mesh_io_msh.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue May 21 2019
	*
	* @brief Read/Write for MSH files
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_IO_MSH_HH_
	#define AKANTU_MESH_IO_MSH_HH_

	/* -------------------------------------------------------------------------- */
	#include "mesh_io.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshIOMSH : public MeshIO {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshIOMSH();

	~MeshIOMSH() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// read a mesh from the file
	void read(const std::string & filename, Mesh & mesh) override;

	/// write a mesh to a file
	void write(const std::string & filename, const Mesh & mesh) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// MSH element types
	enum MSHElementType {
	_msh_not_defined = 0,
	_msh_segment_2 = 1, // 2-node line.
	_msh_triangle_3 = 2, // 3-node triangle.
	_msh_quadrangle_4 = 3, // 4-node quadrangle.
	_msh_tetrahedron_4 = 4, // 4-node tetrahedron.
	_msh_hexahedron_8 = 5, // 8-node hexahedron.
	_msh_prism_1 = 6, // 6-node prism.
	_msh_pyramid_1 = 7, // 5-node pyramid.
	_msh_segment_3 = 8, // 3-node second order line
	_msh_triangle_6 = 9, // 6-node second order triangle
	_msh_quadrangle_9 = 10, // 9-node second order quadrangle
	_msh_tetrahedron_10 = 11, // 10-node second order tetrahedron
	_msh_hexahedron_27 = 12, // 27-node second order hexahedron
	_msh_prism_18 = 13, // 18-node second order prism
	_msh_pyramid_14 = 14, // 14-node second order pyramid
	_msh_point = 15, // 1-node point.
	_msh_quadrangle_8 = 16, // 8-node second order quadrangle
	_msh_hexahedron_20 = 17, // 20-node second order hexahedron
	_msh_prism_15 = 18 // 15-node second order prism
	};

	#define MAX_NUMBER_OF_NODE_PER_ELEMENT 10 // tetrahedron of second order

	/// order in witch element as to be read
	std::map<ElementType, std::vector<UInt>> _read_order;

	/// number of nodes per msh element
	std::map<MSHElementType, UInt> _msh_nodes_per_elem;

	/// correspondence between msh element types and akantu element types
	std::map<MSHElementType, ElementType> _msh_to_akantu_element_types;

	/// correspondence between akantu element types and msh element types
	std::map<ElementType, MSHElementType> _akantu_to_msh_element_types;

	protected:
	template <typename File, typename Readers>
	void populateReaders2(File & file, Readers & readers);

	template <typename File, typename Readers>
	void populateReaders4(File & file, Readers & readers);
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_IO_MSH_HH_ */
	diff --git a/src/io/mesh_io/mesh_io_msh_struct.cc b/src/io/mesh_io/mesh_io_msh_struct.cc
	index b966639b5..6c3bdd3fd 100644
	--- a/src/io/mesh_io/mesh_io_msh_struct.cc
	+++ b/src/io/mesh_io/mesh_io_msh_struct.cc
	@@ -1,81 +1,81 @@
	/**
	* @file mesh_io_msh_struct.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jan 26 2018
	*
	* @brief Read/Write for MSH files generated by gmsh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_io_msh_struct.hh"
	/* -------------------------------------------------------------------------- */
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MeshIOMSHStruct::MeshIOMSHStruct() {
	canReadSurface = true;
	canReadExtendedData = true;

	_msh_to_akantu_element_types.clear();
	_msh_to_akantu_element_types[_msh_not_defined] = _not_defined;
	_msh_to_akantu_element_types[_msh_segment_2] = _bernoulli_beam_2;
	_msh_to_akantu_element_types[_msh_triangle_3] =
	_discrete_kirchhoff_triangle_18;

	_akantu_to_msh_element_types.clear();
	_akantu_to_msh_element_types[_not_defined] = _msh_not_defined;
	_akantu_to_msh_element_types[_bernoulli_beam_2] = _msh_segment_2;
	_akantu_to_msh_element_types[_bernoulli_beam_3] = _msh_segment_2;
	_akantu_to_msh_element_types[_discrete_kirchhoff_triangle_18] =
	_msh_triangle_3;

	for (auto & kv_pair : _akantu_to_msh_element_types) {
	UInt nb_nodes = _msh_nodes_per_elem[kv_pair.second];
	std::vector<UInt> tmp(nb_nodes);
	std::iota(tmp.begin(), tmp.end(), 0);
	_read_order[kv_pair.first] = tmp;
	}
	}

	/* -------------------------------------------------------------------------- */
	void MeshIOMSHStruct::read(const std::string & filename, Mesh & mesh) {
	if (mesh.getSpatialDimension() == 2) {
	_msh_to_akantu_element_types[_msh_segment_2] = _bernoulli_beam_2;
	} else if (mesh.getSpatialDimension() == 3) {
	_msh_to_akantu_element_types[_msh_segment_2] = _bernoulli_beam_3;
	AKANTU_DEBUG_WARNING("The MeshIOMSHStruct is reading bernoulli beam 3D be "
	"sure to provide the missing normals with the element "
	"data \"extra_normal\"");
	}

	MeshIOMSH::read(filename, mesh);
	}

	} // namespace akantu
	diff --git a/src/io/mesh_io/mesh_io_msh_struct.hh b/src/io/mesh_io/mesh_io_msh_struct.hh
	index e528f7978..769812dcb 100644
	--- a/src/io/mesh_io/mesh_io_msh_struct.hh
	+++ b/src/io/mesh_io/mesh_io_msh_struct.hh
	@@ -1,55 +1,55 @@
	/**
	* @file mesh_io_msh_struct.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jan 26 2018
	*
	* @brief Read/Write for MSH files
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_IO_MSH_STRUCT_HH_
	#define AKANTU_MESH_IO_MSH_STRUCT_HH_
	/* -------------------------------------------------------------------------- */
	#include "mesh_io.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshIOMSHStruct : public MeshIOMSH {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshIOMSHStruct();

	/// read a mesh from the file
	void read(const std::string & filename, Mesh & mesh) override;
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_IO_MSH_STRUCT_HH_ */
	diff --git a/src/io/parser/algebraic_parser.hh b/src/io/parser/algebraic_parser.hh
	index 0ef86d064..7197ca16d 100644
	--- a/src/io/parser/algebraic_parser.hh
	+++ b/src/io/parser/algebraic_parser.hh
	@@ -1,517 +1,518 @@
	/**
	* @file algebraic_parser.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Tue Mar 03 2020
	*
	* @brief algebraic_parser definition of the grammar
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	// Boost
	#include <boost/config/warning_disable.hpp>
	#include <boost/spirit/include/phoenix.hpp>
	#include <boost/spirit/include/qi.hpp>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ALGEBRAIC_PARSER_HH_
	#define AKANTU_ALGEBRAIC_PARSER_HH_

	namespace spirit = boost::spirit;
	namespace qi = boost::spirit::qi;
	namespace lbs = boost::spirit::qi::labels;
	namespace ascii = boost::spirit::ascii;
	namespace phx = boost::phoenix;

	namespace akantu {
	namespace parser {
	struct algebraic_error_handler_ {
	template <typename, typename, typename> struct result {
	using type = void;
	};

	template <typename Iterator>
	void operator()(qi::info const & what, Iterator err_pos,
	Iterator last) const {
	AKANTU_EXCEPTION(
	"Error! Expecting "
	<< what // what failed?
	<< " here: \""
	<< std::string(err_pos, last) // iterators to error-pos, end
	<< "\"");
	}
	};

	static Real my_min(Real a, Real b) { return std::min(a, b); }
	static Real my_max(Real a, Real b) { return std::max(a, b); }
	static Real my_pow(Real a, Real b) { return std::pow(a, b); }

	static Real eval_param(const ID & a, const ParserSection & section) {
	return section.getParameter(a, _ppsc_current_and_parent_scope);
	}

	static Real unary_func(Real (*func)(Real), Real a) { return func(a); }

	static Real binary_func(Real (*func)(Real, Real), Real a, Real b) {
	return func(a, b);
	}

	template <class Iterator, typename Skipper = spirit::unused_type>
	struct AlgebraicGrammar : qi::grammar<Iterator, Real(), Skipper> {
	AlgebraicGrammar(const ParserSection & section)
	: AlgebraicGrammar::base_type(start, "algebraic_grammar"),
	section(section) {
	// phx::function<lazy_pow_> lazy_pow;
	// phx::function<lazy_unary_func_> lazy_unary_func;
	// phx::function<lazy_binary_func_> lazy_binary_func;
	// phx::function<lazy_eval_param_> lazy_eval_param;
	/* clang-format off */
	start
	= expr.alias()
	;

	expr
	= term [ lbs::_val = lbs::_1 ]
	>> *( ('+' > term [ lbs::_val += lbs::_1 ])
	\| ('-' > term [ lbs::_val -= lbs::_1 ])
	)
	;

	term
	= factor [ lbs::_val = lbs::_1 ]
	>> ( ('' > factor [ lbs::_val *= lbs::_1 ])
	\| ('/' > factor [ lbs::_val /= lbs::_1 ])
	)
	;

	factor
	= number [ lbs::_val = lbs::_1 ]
	>> ("*" > number [ lbs::_val = phx::bind(&my_pow, lbs::_val, lbs::_1) ])
	;

	number
	= real [ lbs::_val = lbs::_1 ]
	\| ('-' > number [ lbs::_val = -lbs::_1 ])
	\| ('+' > number [ lbs::_val = lbs::_1 ])
	\| constant [ lbs::_val = lbs::_1 ]
	\| function [ lbs::_val = lbs::_1 ]
	\| ('(' > expr > ')') [ lbs::_val = lbs::_1 ]
	\| variable [ lbs::_val = lbs::_1 ]
	;

	function
	= (qi::no_case[unary_function]
	> '('
	> expr
	> ')') [ lbs::_val = phx::bind(&unary_func, lbs::_1, lbs::_2) ]
	\| (qi::no_case[binary_function]
	> '(' >> expr
	> ',' >> expr
	> ')') [ lbs::_val = phx::bind(&binary_func ,lbs::_1, lbs::_2, lbs::_3) ]
	;

	variable
	= key [ lbs::_val = phx::bind(&eval_param, lbs::_1, section) ]
	;

	key
	= qi::no_skip[qi::char_("a-zA-Z_") >> *qi::char_("a-zA-Z_0-9")] // coming from the InputFileGrammar
	;

	#ifndef M_PI
	# define M_PI 3.14159265358979323846
	#endif
	#ifndef M_E
	# define M_E 2.7182818284590452354
	#endif
	constant.add
	("pi", M_PI)
	("e", M_E);

	unary_function.add
	("abs" , &std::abs )
	("acos" , &std::acos )
	("asin" , &std::asin )
	("atan" , &std::atan )
	("ceil" , &std::ceil )
	("cos" , &std::cos )
	("cosh" , &std::cosh )
	("exp" , &std::exp )
	("floor" , &std::floor )
	("log10" , &std::log10 )
	("log" , &std::log )
	("sin" , &std::sin )
	("sinh" , &std::sinh )
	("sqrt" , &std::sqrt )
	("tan" , &std::tan )
	("tanh" , &std::tanh )
	("acosh" , &std::acosh )
	("asinh" , &std::asinh )
	("atanh" , &std::atanh )
	("exp2" , &std::exp2 )
	("expm1" , &std::expm1 )
	("log1p" , &std::log1p )
	("log2" , &std::log2 )
	("erf" , &std::erf )
	("erfc" , &std::erfc )
	("lgamma", &std::lgamma)
	("tgamma", &std::tgamma)
	("trunc" , &std::trunc )
	("round" , &std::round )
	// ("crbt" , &std::crbt )
	;

	binary_function.add
	("pow" , &std::pow )
	("min" , &parser::my_min)
	("max" , &parser::my_max)
	("atan2", &std::atan2 )
	("fmod" , &std::fmod )
	("hypot", &std::hypot )
	;

	#if !defined(AKANTU_NDEBUG)
	phx::function<algebraic_error_handler_> const error_handler = algebraic_error_handler_();
	qi::on_error<qi::fail>(start, error_handler(lbs::_4, lbs::_3, lbs::_2));
	#endif

	expr .name("expression");
	term .name("term");
	factor .name("factor");
	number .name("numerical-value");
	variable.name("variable");
	function.name("function");

	constant.name("constants-list");
	unary_function.name("unary-functions-list");
	binary_function.name("binary-functions-list");

	#if !defined AKANTU_NDEBUG
	if(AKANTU_DEBUG_TEST(dblDebug)) {
	qi::debug(expr);
	qi::debug(term);
	qi::debug(factor);
	qi::debug(number);
	qi::debug(variable);
	qi::debug(function);
	}
	#endif
	}
	/* clang-format on */
	private:
	qi::rule<Iterator, Real(), Skipper> start;
	qi::rule<Iterator, Real(), Skipper> expr;
	qi::rule<Iterator, Real(), Skipper> term;
	qi::rule<Iterator, Real(), Skipper> factor;
	qi::rule<Iterator, Real(), Skipper> number;
	qi::rule<Iterator, Real(), Skipper> variable;
	qi::rule<Iterator, Real(), Skipper> function;

	qi::rule<Iterator, std::string(), Skipper> key;

	qi::real_parser<Real, qi::real_policies<Real>> real;

	qi::symbols<char, Real> constant;
	qi::symbols<char, Real (*)(Real)> unary_function;
	qi::symbols<char, Real (*)(Real, Real)> binary_function;

	const ParserSection & section;
	};

	/* ---------------------------------------------------------------------- */
	/* Vector Parser */
	/* ---------------------------------------------------------------------- */
	struct parsable_vector {
	operator Vector<Real>() {
	Vector<Real> tmp(_cells.size());
	auto it = _cells.begin();
	for (UInt i = 0; it != _cells.end(); ++it, ++i) {
	tmp(i) = *it;
	}
	return tmp;
	}

	std::vector<Real> _cells;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const parsable_vector & pv) {
	stream << "pv[";
	auto it = pv._cells.begin();
	if (it != pv._cells.end()) {
	stream << *it;
	for (++it; it != pv._cells.end(); ++it) {
	stream << ", " << *it;
	}
	}
	stream << "]";
	return stream;
	}

	struct parsable_matrix {
	operator Matrix<Real>() {
	size_t cols = 0;
	auto it_rows = _cells.begin();
	for (; it_rows != _cells.end(); ++it_rows) {
	cols = std::max(cols, it_rows->_cells.size());
	}

	Matrix<Real> tmp(_cells.size(), _cells[0]._cells.size(), 0.);

	it_rows = _cells.begin();
	for (UInt i = 0; it_rows != _cells.end(); ++it_rows, ++i) {
	auto it_cols = it_rows->_cells.begin();
	for (UInt j = 0; it_cols != it_rows->_cells.end(); ++it_cols, ++j) {
	tmp(i, j) = *it_cols;
	}
	}
	return tmp;
	}

	std::vector<parsable_vector> _cells;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const parsable_matrix & pm) {
	stream << "pm[";
	auto it = pm._cells.begin();
	if (it != pm._cells.end()) {
	stream << *it;
	for (++it; it != pm._cells.end(); ++it) {
	stream << ", " << *it;
	}
	}
	stream << "]";
	return stream;
	}

	/* ---------------------------------------------------------------------- */
	template <typename T1, typename T2>
	static void cont_add(T1 & cont, T2 & value) {
	cont._cells.push_back(value);
	}

	/* ---------------------------------------------------------------------- */
	template <class Iterator, typename Skipper = spirit::unused_type>
	struct VectorGrammar : qi::grammar<Iterator, parsable_vector(), Skipper> {
	VectorGrammar(const ParserSection & section)
	: VectorGrammar::base_type(start, "vector_algebraic_grammar"),
	number(section) {

	start = '[' > vector > ']';

	vector =
	(number[phx::bind(&cont_add<parsable_vector, Real>, lbs::_a,
	lbs::_1)] >>
	*(',' >> number[phx::bind(&cont_add<parsable_vector, Real>, lbs::_a,
	lbs::_1)]))[lbs::_val = lbs::_a];

	#if !defined(AKANTU_NDEBUG)
	phx::function<algebraic_error_handler_> const error_handler =
	algebraic_error_handler_();
	qi::on_error<qi::fail>(start, error_handler(lbs::_4, lbs::_3, lbs::_2));
	#endif

	start.name("start");
	vector.name("vector");
	number.name("value");

	#if !defined AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDebug)) {
	qi::debug(start);
	qi::debug(vector);
	}
	#endif
	}

	private:
	qi::rule<Iterator, parsable_vector(), Skipper> start;
	qi::rule<Iterator, parsable_vector(), qi::locals<parsable_vector>, Skipper>
	vector;
	qi::rule<Iterator, Real(), Skipper> value;
	AlgebraicGrammar<Iterator, Skipper> number;
	};

	/* ---------------------------------------------------------------------- */
	static inline bool vector_eval(const ID & a, const ParserSection & section,
	parsable_vector & result) {
	std::string value = section.getParameter(a, _ppsc_current_and_parent_scope);
	std::string::const_iterator b = value.begin();
	std::string::const_iterator e = value.end();
	parser::VectorGrammar<std::string::const_iterator, qi::space_type> grammar(
	section);
	return qi::phrase_parse(b, e, grammar, qi::space, result);
	}

	/* ---------------------------------------------------------------------- */
	template <class Iterator, typename Skipper = spirit::unused_type>
	struct MatrixGrammar : qi::grammar<Iterator, parsable_matrix(), Skipper> {
	MatrixGrammar(const ParserSection & section)
	: MatrixGrammar::base_type(start, "matrix_algebraic_grammar"),
	vector(section) {

	start = '[' >> matrix >> ']';

	matrix =
	(rows[phx::bind(&cont_add<parsable_matrix, parsable_vector>, lbs::_a,
	lbs::_1)] >>
	*(',' >> rows[phx::bind(&cont_add<parsable_matrix, parsable_vector>,
	lbs::_a, lbs::_1)]))[lbs::_val = lbs::_a];

	rows = eval_vector \| vector;

	eval_vector = (key[lbs::_pass = phx::bind(&vector_eval, lbs::_1, section,
	lbs::_a)])[lbs::_val = lbs::_a];

	key = qi::char_("a-zA-Z_") >>
	*qi::char_("a-zA-Z_0-9") // coming from the InputFileGrammar
	;

	#if !defined(AKANTU_NDEBUG)
	phx::function<algebraic_error_handler_> const error_handler =
	algebraic_error_handler_();
	qi::on_error<qi::fail>(start, error_handler(lbs::_4, lbs::_3, lbs::_2));
	#endif

	start.name("matrix");
	matrix.name("all_rows");
	rows.name("rows");
	vector.name("vector");
	eval_vector.name("eval_vector");

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDebug)) {
	qi::debug(start);
	qi::debug(matrix);
	qi::debug(rows);
	qi::debug(eval_vector);
	qi::debug(key);
	}
	#endif
	}

	private:
	qi::rule<Iterator, parsable_matrix(), Skipper> start;
	qi::rule<Iterator, parsable_matrix(), qi::locals<parsable_matrix>, Skipper>
	matrix;
	qi::rule<Iterator, parsable_vector(), Skipper> rows;
	qi::rule<Iterator, parsable_vector(), qi::locals<parsable_vector>, Skipper>
	eval_vector;
	qi::rule<Iterator, std::string(), Skipper> key;
	VectorGrammar<Iterator, Skipper> vector;
	};

	/* ---------------------------------------------------------------------- */
	/* Randon Generator */
	/* ---------------------------------------------------------------------- */
	struct ParsableRandomGenerator {
	ParsableRandomGenerator(
	Real base = Real(),
	const RandomDistributionType & type = _rdt_not_defined,
	const parsable_vector & parameters = parsable_vector())
	: base(base), type(type), parameters(parameters) {}

	Real base;
	RandomDistributionType type;
	parsable_vector parameters;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const ParsableRandomGenerator & prg) {
	stream << "prg[" << prg.base << " " << UInt(prg.type) << " "
	<< prg.parameters << "]";
	return stream;
	}

	/* ---------------------------------------------------------------------- */
	template <class Iterator, typename Skipper = spirit::unused_type>
	struct RandomGeneratorGrammar
	: qi::grammar<Iterator, ParsableRandomGenerator(), Skipper> {
	RandomGeneratorGrammar(const ParserSection & section)
	: RandomGeneratorGrammar::base_type(start, "random_generator_grammar"),
	number(section) {

	start = generator.alias();

	generator =
	qi::hold[distribution[lbs::_val = lbs::_1]] \|
	number[lbs::_val = phx::construct<ParsableRandomGenerator>(lbs::_1)];

	distribution = (number >> generator_type >> '[' >> generator_params >>
	']')[lbs::_val = phx::construct<ParsableRandomGenerator>(
	lbs::_1, lbs::_2, lbs::_3)];

	generator_params =
	(number[phx::bind(&cont_add<parsable_vector, Real>, lbs::_a,
	lbs::_1)] >>
	*(',' > number[phx::bind(&cont_add<parsable_vector, Real>, lbs::_a,
	lbs::_1)]))[lbs::_val = lbs::_a];

	#define AKANTU_RANDOM_DISTRIBUTION_TYPE_ADD(r, data, elem) \
	(BOOST_PP_STRINGIZE(BOOST_PP_TUPLE_ELEM(2, 0, elem)), \
	- AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX(BOOST_PP_TUPLE_ELEM(2, 0, elem)))
	+ AKANTU_RANDOM_DISTRIBUTION_TYPES_PREFIX( \
	+ BOOST_PP_TUPLE_ELEM(2, 0, elem)))

	generator_type.add BOOST_PP_SEQ_FOR_EACH(
	AKANTU_RANDOM_DISTRIBUTION_TYPE_ADD, _,
	AKANTU_RANDOM_DISTRIBUTION_TYPES);
	#undef AKANTU_RANDOM_DISTRIBUTION_TYPE_ADD

	#if !defined(AKANTU_NDEBUG)
	phx::function<algebraic_error_handler_> const error_handler =
	algebraic_error_handler_();
	qi::on_error<qi::fail>(start, error_handler(lbs::_4, lbs::_3, lbs::_2));
	#endif

	start.name("random-generator");
	generator.name("random-generator");
	distribution.name("random-distribution");
	generator_type.name("generator-type");
	generator_params.name("generator-parameters");
	number.name("number");

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDebug)) {
	qi::debug(generator);
	qi::debug(distribution);
	qi::debug(generator_params);
	}
	#endif
	}

	private:
	qi::rule<Iterator, ParsableRandomGenerator(), Skipper> start;
	qi::rule<Iterator, ParsableRandomGenerator(), Skipper> generator;
	qi::rule<Iterator, ParsableRandomGenerator(), Skipper> distribution;
	qi::rule<Iterator, parsable_vector(), qi::locals<parsable_vector>, Skipper>
	generator_params;
	AlgebraicGrammar<Iterator, Skipper> number;
	qi::symbols<char, RandomDistributionType> generator_type;
	};
	} // namespace parser
	} // namespace akantu

	#endif /* AKANTU_ALGEBRAIC_PARSER_HH_ */
	diff --git a/src/io/parser/cppargparse/cppargparse.cc b/src/io/parser/cppargparse/cppargparse.cc
	index b85927c1b..084bec23d 100644
	--- a/src/io/parser/cppargparse/cppargparse.cc
	+++ b/src/io/parser/cppargparse/cppargparse.cc
	@@ -1,538 +1,538 @@
	/**
	* @file cppargparse.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Apr 03 2014
	* @date last modification: Wed Jun 12 2019
	*
	* @brief implementation of the ArgumentParser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cppargparse.hh"

	#include <cstdlib>
	#include <cstring>
	#include <libgen.h>

	#include <algorithm>
	#include <iomanip>
	#include <iostream>
	#include <queue>
	#include <sstream>
	#include <string>

	#include <exception>
	#include <stdexcept>
	#include <string.h>

	namespace cppargparse {

	/* -------------------------------------------------------------------------- */
	static inline std::string to_upper(const std::string & str) {
	std::string lstr = str;
	std::transform(lstr.begin(), lstr.end(), lstr.begin(),
	(int (*)(int))std::toupper);
	return lstr;
	}

	/* -------------------------------------------------------------------------- */
	/* ArgumentParser */
	/* -------------------------------------------------------------------------- */
	ArgumentParser::ArgumentParser() {
	this->addArgument("-h;--help", "show this help message and exit", 0, _boolean,
	false, true);
	}

	/* -------------------------------------------------------------------------- */
	ArgumentParser::~ArgumentParser() {
	for (auto it = arguments.begin(); it != arguments.end(); ++it) {
	delete it->second;
	}
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::setParallelContext(int prank, int psize) {
	this->prank = prank;
	this->psize = psize;
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::_exit(const std::string & msg, int status) {
	if (prank == 0) {
	if (not msg.empty()) {
	std::cerr << msg << std::endl;
	std::cerr << std::endl;
	}

	this->print_help(std::cerr);
	}

	if (external_exit != nullptr) {
	(*external_exit)(status);
	} else {
	exit(status);
	}
	}

	/* -------------------------------------------------------------------------- */
	const ArgumentParser::Argument &
	ArgumentParser::operator[](const std::string & name) const {
	auto it = success_parsed.find(name);

	if (it != success_parsed.end()) {
	return *(it->second);
	}
	throw std::range_error("No argument named \'" + name +
	"\' was found in the parsed argument," +
	" make sur to specify it \'required\'" +
	" or to give it a default value");
	}

	/* -------------------------------------------------------------------------- */
	bool ArgumentParser::has(const std::string & name) const {
	return (success_parsed.find(name) != success_parsed.end());
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::addArgument(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type) {
	_addArgument(name_or_flag, help, nargs, type);
	}

	/* -------------------------------------------------------------------------- */
	ArgumentParser::Argument_ &
	ArgumentParser::_addArgument(const std::string & name, const std::string & help,
	int nargs, ArgumentType type) {
	Argument_ * arg = nullptr;

	switch (type) {
	case _string: {
	arg = new ArgumentStorage<std::string>();
	break;
	}
	case _float: {
	arg = new ArgumentStorage<double>();
	break;
	}
	case _integer: {
	arg = new ArgumentStorage<long int>();
	break;
	}
	case _boolean: {
	arg = new ArgumentStorage<bool>();
	break;
	}
	}

	arg->help = help;
	arg->nargs = nargs;
	arg->type = type;

	std::stringstream sstr(name);
	std::string item;
	std::vector<std::string> tmp_keys;
	while (std::getline(sstr, item, ';')) {
	tmp_keys.push_back(item);
	}

	int long_key = -1;
	int short_key = -1;
	bool problem = (tmp_keys.size() > 2) \|\| name.empty();
	for (auto it = tmp_keys.begin(); it != tmp_keys.end(); ++it) {
	if (it->find("--") == 0) {
	problem \|= (long_key != -1);
	long_key = it - tmp_keys.begin();
	} else if (it->find("-") == 0) {
	problem \|= (long_key != -1);
	short_key = it - tmp_keys.begin();
	}
	}

	problem \|= ((tmp_keys.size() == 2) && (long_key == -1 \|\| short_key == -1));

	if (problem) {
	delete arg;
	throw std::invalid_argument("Synthax of name or flags is not correct. "
	"Possible synthax are \'-f\', \'-f;--foo\', "
	"\'--foo\', \'bar\'");
	}

	if (long_key != -1) {
	arg->name = tmp_keys[long_key];
	arg->name.erase(0, 2);
	} else if (short_key != -1) {
	arg->name = tmp_keys[short_key];
	arg->name.erase(0, 1);
	} else {
	arg->name = tmp_keys[0];
	pos_args.push_back(arg);
	arg->required = (nargs != _one_if_possible);
	arg->is_positional = true;
	}

	arguments[arg->name] = arg;

	if (!arg->is_positional) {
	if (short_key != -1) {
	std::string key = tmp_keys[short_key];
	key_args[key] = arg;
	arg->keys.push_back(key);
	}

	if (long_key != -1) {
	std::string key = tmp_keys[long_key];
	key_args[key] = arg;
	arg->keys.push_back(key);
	}
	}

	return *arg;
	}

	#if not HAVE_STRDUP
	static char * strdup(const char * str) {
	size_t len = strlen(str);
	auto * x = (char )malloc(len + 1); / 1 for the null terminator */
	if (x == nullptr) {
	return nullptr; /* malloc could not allocate memory */
	}

	memcpy(x, str, len + 1); /* copy the string into the new buffer */
	return x;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::parse(int & argc, char **& argv, int flags,
	bool parse_help) {
	bool stop_in_not_parsed = (flags & _stop_on_not_parsed) != 0;
	bool remove_parsed = (flags & _remove_parsed) != 0;

	std::vector<std::string> argvs;

	argvs.reserve(argc);
	for (int i = 0; i < argc; ++i) {
	argvs.emplace_back(argv[i]);
	}

	unsigned int current_position = 0;
	if (this->program_name.empty() and argc > 0) {
	std::string prog = argvs[current_position];
	const char * c_prog = prog.c_str();
	char * c_prog_tmp = strdup(c_prog);
	std::string base_prog(basename(c_prog_tmp));
	this->program_name = base_prog;
	std::free(c_prog_tmp);
	}

	std::queue<Argument_ *> positional_queue;
	for (auto it = pos_args.begin(); it != pos_args.end(); ++it) {
	positional_queue.push(*it);
	}

	std::vector<int> argvs_to_remove;
	++current_position; // consume argv[0]
	while (current_position < argvs.size()) {
	std::string arg = argvs[current_position];
	++current_position;

	auto key_it = key_args.find(arg);

	bool is_positional = false;
	Argument_ * argument_ptr = nullptr;
	if (key_it == key_args.end()) {
	if (positional_queue.empty()) {
	if (stop_in_not_parsed) {
	this->_exit("Argument " + arg + " not recognized", EXIT_FAILURE);
	}
	continue;
	}

	argument_ptr = positional_queue.front();
	is_positional = true;
	--current_position;

	} else {
	argument_ptr = key_it->second;
	}

	if (remove_parsed && !is_positional && argument_ptr->name != "help") {
	argvs_to_remove.push_back(current_position - 1);
	}

	Argument_ & argument = *argument_ptr;

	unsigned int min_nb_val{};
	unsigned int max_nb_val{};

	switch (argument.nargs) {
	case _one_if_possible:
	max_nb_val = 1;
	break; // "?"
	case _at_least_one:
	min_nb_val = 1; // "+"
	/* FALLTHRU */
	/* [[fallthrough]]; un-comment when compiler will get it*/
	case _any:
	max_nb_val = argc - current_position;
	break; // "*"
	default:
	min_nb_val = max_nb_val = argument.nargs; // "N"
	}

	std::vector<std::string> values;
	unsigned int arg_consumed = 0;
	if (max_nb_val <= (argc - current_position)) {
	for (; arg_consumed < max_nb_val; ++arg_consumed) {
	std::string v = argvs[current_position];
	++current_position;
	bool is_key = key_args.find(v) != key_args.end();
	bool is_good_type = checkType(argument.type, v);

	if (!is_key && is_good_type) {
	values.push_back(v);
	if (remove_parsed) {
	argvs_to_remove.push_back(current_position - 1);
	}
	} else {
	// unconsume not parsed argument for optional
	if (!is_positional \|\| is_key) {
	--current_position;
	}
	break;
	}
	}
	}

	if (arg_consumed < min_nb_val) {
	if (!is_positional) {
	this->_exit("Not enought values for the argument " + argument.name +
	" where provided",
	EXIT_FAILURE);
	} else {
	if (stop_in_not_parsed) {
	this->_exit("Argument " + arg + " not recognized", EXIT_FAILURE);
	}
	}
	} else {
	if (is_positional) {
	positional_queue.pop();
	}

	if (!argument.parsed) {
	success_parsed[argument.name] = &argument;
	argument.parsed = true;
	if ((argument.nargs == _one_if_possible \|\| argument.nargs == 0) &&
	arg_consumed == 0) {
	if (argument.has_const) {
	argument.setToConst();
	} else if (argument.has_default) {
	argument.setToDefault();
	}
	} else {
	argument.setValues(values);
	}
	} else {
	this->_exit("Argument " + argument.name +
	" already present in the list of argument",
	EXIT_FAILURE);
	}
	}
	}

	for (auto ait = arguments.begin(); ait != arguments.end(); ++ait) {
	Argument_ & argument = *(ait->second);
	if (!argument.parsed) {
	if (argument.has_default) {
	argument.setToDefault();
	success_parsed[argument.name] = &argument;
	}

	if (argument.required) {
	this->_exit("Argument " + argument.name + " required but not given!",
	EXIT_FAILURE);
	}
	}
	}

	// removing the parsed argument if remove_parsed is true
	if (not argvs_to_remove.empty()) {
	std::vector<int>::const_iterator next_to_remove = argvs_to_remove.begin();
	for (int i = 0, c = 0; i < argc; ++i) {
	if (next_to_remove == argvs_to_remove.end() \|\| i != *next_to_remove) {
	argv[c] = argv[i];
	++c;
	} else {
	if (next_to_remove != argvs_to_remove.end()) {
	++next_to_remove;
	}
	}
	}

	argc -= argvs_to_remove.size();
	}

	this->argc = &argc;
	this->argv = &argv;

	if (this->arguments["help"]->parsed && parse_help) {
	this->_exit();
	}
	}

	/* -------------------------------------------------------------------------- */
	bool ArgumentParser::checkType(ArgumentType type, const std::string & value) {
	std::stringstream sstr(value);
	switch (type) {
	case _string: {
	std::string s;
	sstr >> s;
	break;
	}
	case _float: {
	double d;
	sstr >> d;
	break;
	}
	case _integer: {
	long int i;
	sstr >> i;
	break;
	}
	case _boolean: {
	bool b;
	sstr >> b;
	break;
	}
	}

	return (not sstr.fail());
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::printself(std::ostream & stream) const {
	for (auto it = success_parsed.begin(); it != success_parsed.end(); ++it) {
	const Argument & argument = *(it->second);
	argument.printself(stream);
	stream << std::endl;
	}
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::print_usage(std::ostream & stream) const {
	stream << "Usage: " << this->program_name;

	// print shorten usage
	for (auto it = arguments.begin(); it != arguments.end(); ++it) {
	const Argument_ & argument = *(it->second);
	if (!argument.is_positional) {
	if (!argument.required) {
	stream << " [";
	}
	stream << argument.keys[0];
	ArgumentParser::print_usage_nargs(stream, argument);
	if (!argument.required) {
	stream << "]";
	}
	}
	}

	for (auto it = pos_args.begin(); it != pos_args.end(); ++it) {
	const Argument_ & argument = **it;
	ArgumentParser::print_usage_nargs(stream, argument);
	}

	stream << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void ArgumentParser::print_usage_nargs(std::ostream & stream,
	const Argument_ & argument) {
	std::string u_name = to_upper(argument.name);
	switch (argument.nargs) {
	case _one_if_possible:
	stream << " [" << u_name << "]";
	break;
	case _at_least_one:
	stream << " " << u_name;
	/* FALLTHRU */
	/* [[fallthrough]]; un-comment when compiler will get it */
	case _any:
	stream << " [" << u_name << " ...]";
	break;
	default:
	for (int i = 0; i < argument.nargs; ++i) {
	stream << " " << u_name;
	}
	}
	}

	void ArgumentParser::print_help(std::ostream & stream) const {
	this->print_usage(stream);
	if (!pos_args.empty()) {
	stream << std::endl;
	stream << "positional arguments:" << std::endl;
	for (auto it = pos_args.begin(); it != pos_args.end(); ++it) {
	const Argument_ & argument = **it;
	this->print_help_argument(stream, argument);
	}
	}

	if (!key_args.empty()) {
	stream << std::endl;
	stream << "optional arguments:" << std::endl;
	for (auto it = arguments.begin(); it != arguments.end(); ++it) {
	const Argument_ & argument = *(it->second);
	if (!argument.is_positional) {
	this->print_help_argument(stream, argument);
	}
	}
	}
	}

	void ArgumentParser::print_help_argument(std::ostream & stream,
	const Argument_ & argument) const {
	std::string key;
	if (argument.is_positional) {
	key = argument.name;
	} else {
	std::stringstream sstr;
	for (unsigned int i = 0; i < argument.keys.size(); ++i) {
	if (i != 0) {
	sstr << ", ";
	}
	sstr << argument.keys[i];
	this->print_usage_nargs(sstr, argument);
	}
	key = sstr.str();
	}

	stream << " " << std::left << std::setw(15) << key << " " << argument.help;
	argument.printDefault(stream);

	stream << std::endl;
	}
	} // namespace cppargparse
	diff --git a/src/io/parser/cppargparse/cppargparse.hh b/src/io/parser/cppargparse/cppargparse.hh
	index abfdc09b1..ddaa356ee 100644
	--- a/src/io/parser/cppargparse/cppargparse.hh
	+++ b/src/io/parser/cppargparse/cppargparse.hh
	@@ -1,202 +1,202 @@
	/**
	* @file cppargparse.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Apr 03 2014
	* @date last modification: Wed Jun 12 2019
	*
	* @brief Get the commandline options and store them as short, long and others
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>
	#include <map>
	#include <string>
	#include <vector>

	#ifndef CPPARGPARSE_HH_
	#define CPPARGPARSE_HH_

	/* -------------------------------------------------------------------------- */
	namespace cppargparse {

	/// define the types of the arguments
	enum ArgumentType { _string, _integer, _float, _boolean };

	/// Defines how many arguments to expect
	enum ArgumentNargs { _one_if_possible = -1, _at_least_one = -2, _any = -3 };

	/// Flags for the parse function of ArgumentParser
	enum ParseFlags {
	_no_flags = 0x0, ///< Default behavior
	_stop_on_not_parsed = 0x1, ///< Stop on unknown arguments
	_remove_parsed = 0x2 ///< Remove parsed arguments from argc argv
	};

	/// Helps to combine parse flags
	inline ParseFlags operator\|(const ParseFlags & a, const ParseFlags & b) {
	auto tmp = ParseFlags(int(a) \| int(b));
	return tmp;
	}

	/* -------------------------------------------------------------------------- */

	/**
	* ArgumentParser is a class that mimics the Python argparse module
	*/
	class ArgumentParser {
	public:
	/// public definition of an argument
	class Argument {
	public:
	Argument() : name(std::string()) {}
	virtual ~Argument() = default;
	virtual void printself(std::ostream & stream) const = 0;
	template <class T> operator T() const;
	std::string name;
	};

	/// constructor
	ArgumentParser();

	/// destroy everything
	~ArgumentParser();

	/// add an argument with a description
	void addArgument(const std::string & name_or_flag, const std::string & help,
	int nargs = 1, ArgumentType type = _string);

	/// add an argument with an help and a default value
	template <class T>
	void addArgument(const std::string & name_or_flag, const std::string & help,
	int nargs, ArgumentType type, T def);

	/// add an argument with an help and a default + const value
	template <class T>
	void addArgument(const std::string & name_or_flag, const std::string & help,
	int nargs, ArgumentType type, T def, T cons);

	/// parse argc, argv
	void parse(int & argc, char **& argv, int flags = _stop_on_not_parsed,
	bool parse_help = true);

	/// get the last argc parsed
	int & getArgC() { return *(this->argc); }

	/// get the last argv parsed
	char *& getArgV() { return (this->argv); }

	/// print the content in the stream
	void printself(std::ostream & stream) const;

	/// print the help text
	void print_help(std::ostream & stream = std::cout) const;

	/// print the usage text
	void print_usage(std::ostream & stream = std::cout) const;

	/// set an external function to replace the exit function from the stdlib
	void setExternalExitFunction(void (*external_exit)(int)) {
	this->external_exit = external_exit;
	}

	/// accessor for a registered argument that was parsed, throw an exception if
	/// the argument does not exist or was not set (parsed or default value)
	const Argument & operator[](const std::string & name) const;

	/// is the argument present
	bool has(const std::string & /name/) const;

	/// set the parallel context to avoid multiple help messages in
	/// multiproc/thread cases
	void setParallelContext(int prank, int psize);

	public:
	/// Internal class describing the arguments
	struct Argument_;
	/// Stores that value of an argument
	template <class T> class ArgumentStorage;

	private:
	/// Internal function to be used by the public addArgument
	Argument_ & _addArgument(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type);

	void _exit(const std::string & msg = "", int status = 0);
	static bool checkType(ArgumentType type, const std::string & value);

	/// function to help to print help
	static void print_usage_nargs(std::ostream & stream,
	const Argument_ & argument);
	/// function to help to print help
	void print_help_argument(std::ostream & stream,
	const Argument_ & argument) const;

	private:
	/// public arguments storage
	using Arguments = std::map<std::string, Argument *>;
	/// internal arguments storage
	using Arguments_ = std::map<std::string, Argument_ *>;
	/// association key argument
	using ArgumentKeyMap = std::map<std::string, Argument_ *>;
	/// position arguments
	using PositionalArgument = std::vector<Argument_ *>;

	/// internal storage of arguments declared by the user
	Arguments_ arguments;
	/// list of arguments successfully parsed
	Arguments success_parsed;
	/// keys associated to arguments
	ArgumentKeyMap key_args;
	/// positional arguments
	PositionalArgument pos_args;

	/// program name
	std::string program_name;

	/// exit function to use
	void (*external_exit)(int){nullptr};

	/// Parallel context, rank and size of communicator
	int prank{0}, psize{1};

	/// The last argc parsed (those are the modified version after parse)
	int * argc;

	/// The last argv parsed (those are the modified version after parse)
	char *** argv;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const ArgumentParser & argparse) {
	argparse.printself(stream);
	return stream;
	}

	} // namespace cppargparse

	#endif /* CPPARGPARSE_HH_ */

	#include "cppargparse_tmpl.hh"
	diff --git a/src/io/parser/cppargparse/cppargparse_tmpl.hh b/src/io/parser/cppargparse/cppargparse_tmpl.hh
	index 64edce693..49e566256 100644
	--- a/src/io/parser/cppargparse/cppargparse_tmpl.hh
	+++ b/src/io/parser/cppargparse/cppargparse_tmpl.hh
	@@ -1,243 +1,242 @@
	/**
	* @file cppargparse_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Apr 03 2014
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Implementation of the templated part of the commandline argument
	* parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <sstream>
	#include <stdexcept>

	#ifndef CPPARGPARSE_TMPL_HH_
	#define CPPARGPARSE_TMPL_HH_

	namespace cppargparse {
	/* -------------------------------------------------------------------------- */
	/* Argument */
	/* -------------------------------------------------------------------------- */

	/// internal description of arguments
	struct ArgumentParser::Argument_ : public Argument {
	Argument_() = default;
	~Argument_() override = default;

	void setValues(std::vector<std::string> & values) {
	for (auto it = values.begin(); it != values.end(); ++it) {
	this->addValue(*it);
	}
	}

	virtual void addValue(std::string & value) = 0;
	virtual void setToDefault() = 0;
	virtual void setToConst() = 0;

	std::ostream & printDefault(std::ostream & stream) const {
	stream << std::boolalpha;
	if (has_default) {
	stream << " (default: ";
	this->_printDefault(stream);
	stream << ")";
	}
	if (has_const) {
	stream << " (const: ";
	this->_printConst(stream);
	stream << ")";
	}
	return stream;
	}

	virtual std::ostream & _printDefault(std::ostream & stream) const = 0;
	virtual std::ostream & _printConst(std::ostream & stream) const = 0;

	std::string help;
	int nargs{1};
	ArgumentType type{_string};
	bool required{false};
	bool parsed{false};
	bool has_default{false};
	bool has_const{false};
	std::vector<std::string> keys;
	bool is_positional{false};
	};

	/* -------------------------------------------------------------------------- */
	/// typed storage of the arguments
	template <class T>
	class ArgumentParser::ArgumentStorage : public ArgumentParser::Argument_ {
	public:
	ArgumentStorage() : _default(T()), _const(T()), values(std::vector<T>()) {}

	void addValue(std::string & value) override {
	std::stringstream sstr(value);
	T t;
	sstr >> t;
	values.push_back(t);
	}

	void setToDefault() override {
	values.clear();
	values.push_back(_default);
	}

	void setToConst() override {
	values.clear();
	values.push_back(_const);
	}

	void printself(std::ostream & stream) const override {
	stream << this->name << " =";
	stream << std::boolalpha; // for boolean
	for (auto vit = this->values.begin(); vit != this->values.end(); ++vit) {
	stream << " " << *vit;
	}
	}

	std::ostream & _printDefault(std::ostream & stream) const override {
	stream << _default;
	return stream;
	}

	std::ostream & _printConst(std::ostream & stream) const override {
	stream << _const;
	return stream;
	}

	T _default;
	T _const;
	std::vector<T> values;
	};

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ArgumentParser::ArgumentStorage<std::string>::addValue(std::string & value) {
	values.push_back(value);
	}

	template <class T> struct is_vector {
	enum { value = false };
	};

	template <class T> struct is_vector<std::vector<T>> {
	enum { value = true };
	};

	/* -------------------------------------------------------------------------- */
	template <class T, bool is_vector = cppargparse::is_vector<T>::value>
	struct cast_helper {
	static T cast(const ArgumentParser::Argument & arg) {
	const auto & _arg =
	dynamic_cast<const ArgumentParser::ArgumentStorage<T> &>(arg);
	if (_arg.values.size() == 1) {
	return _arg.values[0];
	}
	throw std::length_error("Not enougth or too many argument where passed "
	"for the command line argument: " +
	arg.name);
	}
	};

	template <class T> struct cast_helper<T, true> {
	static T cast(const ArgumentParser::Argument & arg) {
	const auto & _arg =
	dynamic_cast<const ArgumentParser::ArgumentStorage<T> &>(arg);
	return _arg.values;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <class T> ArgumentParser::Argument::operator T() const {
	return cast_helper<T>::cast(*this);
	}

	#if !defined(DOXYGEN)
	-template <>
	-inline ArgumentParser::Argument::operator std::string() const {
	+template <> inline ArgumentParser::Argument::operator std::string() const {
	return cast_helper<std::string>::cast(*this);
	}

	template <> inline ArgumentParser::Argument::operator unsigned int() const {
	return cast_helper<int>::cast(*this);
	}
	#endif

	template <class T>
	void ArgumentParser::addArgument(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type, T def) {
	Argument_ & arg = _addArgument(name_or_flag, help, nargs, type);
	dynamic_cast<ArgumentStorage<T> &>(arg)._default = def;
	arg.has_default = true;
	}

	template <class T>
	void ArgumentParser::addArgument(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type, T def, T cons) {
	Argument_ & arg = _addArgument(name_or_flag, help, nargs, type);
	dynamic_cast<ArgumentStorage<T> &>(arg)._default = def;
	arg.has_default = true;
	dynamic_cast<ArgumentStorage<T> &>(arg)._const = cons;
	arg.has_const = true;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ArgumentParser::addArgument<const char *>(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type, const char * def) {
	this->addArgument<std::string>(name_or_flag, help, nargs, type, def);
	}

	template <>
	inline void
	ArgumentParser::addArgument<unsigned int>(const std::string & name_or_flag,
	const std::string & help, int nargs,
	ArgumentType type, unsigned int def) {
	this->addArgument<int>(name_or_flag, help, nargs, type, def);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ArgumentParser::addArgument<const char *>(
	const std::string & name_or_flag, const std::string & help, int nargs,
	ArgumentType type, const char * def, const char * cons) {
	this->addArgument<std::string>(name_or_flag, help, nargs, type, def, cons);
	}

	template <>
	inline void ArgumentParser::addArgument<unsigned int>(
	const std::string & name_or_flag, const std::string & help, int nargs,
	ArgumentType type, unsigned int def, unsigned int cons) {
	this->addArgument<int>(name_or_flag, help, nargs, type, def, cons);
	}
	} // namespace cppargparse

	#endif /* AKANTU_CPPARGPARSE_TMPL_HH_ */
	diff --git a/src/io/parser/input_file_parser.hh b/src/io/parser/input_file_parser.hh
	index b610ca943..74c83541b 100644
	--- a/src/io/parser/input_file_parser.hh
	+++ b/src/io/parser/input_file_parser.hh
	@@ -1,271 +1,271 @@
	/**
	* @file input_file_parser.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Wed Sep 04 2019
	*
	* @brief Grammar definition for the input files
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// Boost
	/* -------------------------------------------------------------------------- */

	#include <boost/config/warning_disable.hpp>
	#include <boost/spirit/include/phoenix_bind.hpp>
	#include <boost/spirit/include/phoenix_core.hpp>
	#include <boost/spirit/include/phoenix_fusion.hpp>
	#include <boost/spirit/include/phoenix_operator.hpp>
	#include <boost/spirit/include/qi.hpp>
	#include <boost/variant/recursive_variant.hpp>

	#ifndef AKANTU_INPUT_FILE_PARSER_HH_
	#define AKANTU_INPUT_FILE_PARSER_HH_

	namespace spirit = boost::spirit;
	namespace qi = boost::spirit::qi;
	namespace lbs = boost::spirit::qi::labels;
	namespace ascii = boost::spirit::ascii;
	namespace phx = boost::phoenix;

	namespace akantu {

	namespace parser {
	struct error_handler_ {
	template <typename, typename, typename, typename> struct result {
	using type = void;
	};

	template <typename Iterator>
	void operator()(qi::info const & what, Iterator err_pos, Iterator /first/,
	Iterator /last/) const {
	spirit::classic::file_position pos = err_pos.get_position();

	AKANTU_EXCEPTION("Parse error [ "
	<< "Expecting " << what << " instead of \"" << *err_pos
	<< "\" ]"
	<< " in file " << pos.file << " line " << pos.line
	<< " column " << pos.column << std::endl
	<< "'" << err_pos.get_currentline() << "'" << std::endl
	<< std::setw(pos.column) << " "
	<< "^- here");
	}

	private:
	};

	static ParserSection & create_subsection(
	const ParserType & type, const boost::optional<std::string> & opt_name,
	const boost::optional<std::string> & opt_option, ParserSection & sect) {
	std::string option;
	if (opt_option) {
	option = *opt_option;
	}

	static size_t id = 12;
	std::string name = "anonymous_" + std::to_string(id++);
	if (opt_name) {
	name = *opt_name;
	}

	ParserSection sect_tmp(name, type, option, sect);
	return sect.addSubSection(sect_tmp);
	}

	template <typename Iter>
	static bool create_parameter(boost::iterator_range<Iter> & rng,
	std::string & value, ParserSection & sect) {
	try {
	std::string name(rng.begin(), rng.end());
	name = trim(name);
	spirit::classic::file_position pos = rng.begin().get_position();

	ParserParameter param_tmp(name, value, sect);
	param_tmp.setDebugInfo(pos.file, pos.line, pos.column);
	sect.addParameter(param_tmp);
	} catch (debug::Exception & e) {
	return false;
	}
	return true;
	}

	static std::string concatenate(const std::string & t1,
	const std::string & t2) {
	return (t1 + t2);
	}

	/* ---------------------------------------------------------------------- */
	/* Grammars definitions */
	/* ---------------------------------------------------------------------- */
	template <class Iterator>
	struct InputFileGrammar
	: qi::grammar<Iterator, void(), typename Skipper<Iterator>::type> {
	InputFileGrammar(ParserSection * sect)
	: InputFileGrammar::base_type(start, "input_file_grammar"),
	parent_section(sect) {

	/* clang-format off */
	start
	= mini_section(parent_section)
	;

	mini_section
	= *(
	entry (lbs::_r1)
	\| section(lbs::_r1)
	)
	;

	entry
	= (
	qi::raw[key]
	>> '='
	> value
	) [ lbs::_pass = phx::bind(&create_parameter<Iterator>,
	lbs::_1,
	lbs::_2,
	*lbs::_r1) ]
	;

	section
	= (
	qi::no_case[section_type]
	> qi::lexeme
	[
	-section_name
	> -section_option
	]
	) [ lbs::_a = &phx::bind(&create_subsection,
	lbs::_1,
	phx::at_c<0>(lbs::_2),
	phx::at_c<1>(lbs::_2),
	*lbs::_r1) ]
	> '['
	> mini_section(lbs::_a)
	> ']'
	;

	section_name
	= qi::char_("a-zA-Z_") >> *qi::char_("a-zA-Z_0-9")
	;

	section_option
	= (+ascii::space >> section_name) [ lbs::_val = lbs::_2 ]
	;

	key
	= qi::char_("a-zA-Z_") >> *qi::char_("a-zA-Z_0-9")
	;

	value
	= (
	mono_line_value [ lbs::_a = phx::bind(&concatenate, lbs::_a, lbs::_1) ]
	> *(
	'\\' > mono_line_value [ lbs::_a = phx::bind(&concatenate, lbs::_a, lbs::_1) ]
	)
	) [ lbs::_val = lbs::_a ]
	;

	mono_line_value
	= qi::lexeme
	[
	+(qi::char_ - (qi::char_('=') \| spirit::eol \| '#' \| ';' \| '\\'))
	]
	;

	skipper
	= ascii::space
	\| "#" >> *(qi::char_ - spirit::eol)
	;

	/* clang-format on */

	#define AKANTU_SECTION_TYPE_ADD(r, data, elem) \
	(BOOST_PP_STRINGIZE(elem), BOOST_PP_CAT(ParserType::_, elem))

	section_type.add BOOST_PP_SEQ_FOR_EACH(AKANTU_SECTION_TYPE_ADD, _,
	AKANTU_SECTION_TYPES);
	#undef AKANTU_SECTION_TYPE_ADD

	#if !defined(AKANTU_NDEBUG)
	phx::function<error_handler_> const error_handler = error_handler_();
	qi::on_error<qi::fail>(start,
	error_handler(lbs::_4, lbs::_3, lbs::_1, lbs::_2));
	#endif

	section.name("section");
	section_name.name("section-name");
	section_option.name("section-option");
	mini_section.name("section-content");
	entry.name("parameter");
	key.name("parameter-name");
	value.name("parameter-value");
	section_type.name("section-types-list");
	mono_line_value.name("mono-line-value");

	#if !defined AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDebug)) {
	// qi::debug(section);
	qi::debug(section_name);
	qi::debug(section_option);
	// qi::debug(mini_section);
	// qi::debug(entry);
	qi::debug(key);
	qi::debug(value);
	qi::debug(mono_line_value);
	}
	#endif
	}

	const std::string & getErrorMessage() const { return error_message; };

	using skipper_type = typename Skipper<Iterator>::type;
	skipper_type skipper;

	private:
	std::string error_message;

	qi::rule<Iterator, void(ParserSection *), skipper_type> mini_section;
	qi::rule<Iterator, void(ParserSection ), qi::locals<ParserSection >,
	skipper_type>
	section;
	qi::rule<Iterator, void(), skipper_type> start;
	qi::rule<Iterator, std::string()> section_name;
	qi::rule<Iterator, std::string()> section_option;
	qi::rule<Iterator, void(ParserSection *), skipper_type> entry;
	qi::rule<Iterator, std::string(), skipper_type> key;
	qi::rule<Iterator, std::string(), qi::locals<std::string>, skipper_type>
	value;
	qi::rule<Iterator, std::string(), skipper_type> mono_line_value;

	qi::symbols<char, ParserType> section_type;

	ParserSection * parent_section;
	};
	} // namespace parser

	} // namespace akantu

	#endif /* AKANTU_INPUT_FILE_PARSER_HH_ */
	diff --git a/src/io/parser/parameter_registry.cc b/src/io/parser/parameter_registry.cc
	index 39b695a58..ef6c7aefb 100644
	--- a/src/io/parser/parameter_registry.cc
	+++ b/src/io/parser/parameter_registry.cc
	@@ -1,156 +1,156 @@
	/**
	* @file parameter_registry.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 04 2016
	* @date last modification: Thu Feb 01 2018
	*
	* @brief Parameter Registry and derived classes implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <utility>

	#include "parameter_registry.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	Parameter::Parameter() = default;

	/* -------------------------------------------------------------------------- */
	Parameter::Parameter(std::string name, std::string description,
	ParameterAccessType param_type)
	: name(std::move(name)), description(std::move(description)),
	param_type(param_type) {}

	/* -------------------------------------------------------------------------- */
	bool Parameter::isWritable() const { return (param_type & _pat_writable) != 0; }

	/* -------------------------------------------------------------------------- */
	bool Parameter::isReadable() const { return (param_type & _pat_readable) != 0; }

	/* -------------------------------------------------------------------------- */
	bool Parameter::isInternal() const { return (param_type & _pat_internal) != 0; }

	/* -------------------------------------------------------------------------- */
	bool Parameter::isParsable() const { return (param_type & _pat_parsable) != 0; }

	/* -------------------------------------------------------------------------- */
	void Parameter::setAccessType(ParameterAccessType ptype) {
	this->param_type = ptype;
	}

	/* -------------------------------------------------------------------------- */
	void Parameter::printself(std::ostream & stream) const {
	stream << " ";
	if (isInternal()) {
	stream << "iii";
	} else {
	if (isReadable()) {
	stream << "r";
	} else {
	stream << "-";
	}

	if (isWritable()) {
	stream << "w";
	} else {
	stream << "-";
	}

	if (isParsable()) {
	stream << "p";
	} else {
	stream << "-";
	}
	}
	stream << " ";

	std::stringstream sstr;
	sstr << name;
	UInt width = std::max(int(10 - sstr.str().length()), 0);
	sstr.width(width);

	if (not description.empty()) {
	sstr << " [" << description << "]";
	}

	stream << sstr.str();
	width = std::max(int(50 - sstr.str().length()), 0);
	stream.width(width);

	stream << " : ";
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	ParameterRegistry::ParameterRegistry() = default;

	/* -------------------------------------------------------------------------- */
	ParameterRegistry::~ParameterRegistry() {
	for (auto && data : params) {
	delete data.second;
	data.second = NULL;
	}
	this->params.clear();
	}

	/* -------------------------------------------------------------------------- */
	void ParameterRegistry::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	Parameters::const_iterator it;
	for (it = params.begin(); it != params.end(); ++it) {
	stream << space;
	it->second->printself(stream);
	}

	SubRegisteries::const_iterator sub_it;
	for (sub_it = sub_registries.begin(); sub_it != sub_registries.end();
	++sub_it) {
	stream << space << "Registry [" << std::endl;
	sub_it->second->printself(stream, indent + 1);
	stream << space << "]";
	}
	}

	/* -------------------------------------------------------------------------- */
	void ParameterRegistry::registerSubRegistry(const ID & id,
	ParameterRegistry & registry) {
	sub_registries[id] = &registry;
	}

	/* -------------------------------------------------------------------------- */
	void ParameterRegistry::setParameterAccessType(const std::string & name,
	ParameterAccessType ptype) {
	auto it = params.find(name);
	if (it == params.end()) {
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterUnexistingException(name, *this));
	}
	Parameter & param = *(it->second);
	param.setAccessType(ptype);
	}

	} // namespace akantu
	diff --git a/src/io/parser/parameter_registry.hh b/src/io/parser/parameter_registry.hh
	index 29e582909..5395c8729 100644
	--- a/src/io/parser/parameter_registry.hh
	+++ b/src/io/parser/parameter_registry.hh
	@@ -1,227 +1,228 @@
	/**
	* @file parameter_registry.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Aug 09 2012
	* @date last modification: Wed Oct 17 2018
	*
	* @brief Interface of the parameter registry
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PARAMETER_REGISTRY_HH_
	#define AKANTU_PARAMETER_REGISTRY_HH_

	namespace akantu {
	class ParserParameter;
	}

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/// Defines the access modes of parsable parameters
	enum ParameterAccessType {
	_pat_internal = 0x0001,
	_pat_writable = 0x0010,
	_pat_readable = 0x0100,
	_pat_modifiable = 0x0110, //<_pat_readable \| _pat_writable,
	_pat_parsable = 0x1000,
	_pat_parsmod = 0x1110 //< _pat_parsable \| _pat_modifiable
	};

	/// Bit-wise operator between access modes
	inline ParameterAccessType operator\|(const ParameterAccessType & a,
	const ParameterAccessType & b) {
	auto tmp = ParameterAccessType(UInt(a) \| UInt(b));
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> class ParameterTyped;

	/**
	* Interface for the Parameter
	*/
	class Parameter {
	public:
	Parameter();
	Parameter(std::string name, std::string description,
	ParameterAccessType param_type);

	virtual ~Parameter() = default;
	/* ------------------------------------------------------------------------ */
	bool isInternal() const;
	bool isWritable() const;
	bool isReadable() const;
	bool isParsable() const;

	void setAccessType(ParameterAccessType ptype);

	/* ------------------------------------------------------------------------ */
	template <typename T, typename V> void set(const V & value);
	virtual void setAuto(const ParserParameter & param);
	template <typename T> T & get();
	template <typename T> const T & get() const;

	virtual inline operator Real() const { throw std::bad_cast(); };
	template <typename T> inline operator T() const;
	/* ------------------------------------------------------------------------ */
	virtual void printself(std::ostream & stream) const;

	virtual const std::type_info & type() const = 0;

	protected:
	/// Returns const instance of templated sub-class ParameterTyped
	template <typename T> const ParameterTyped<T> & getParameterTyped() const;

	/// Returns instance of templated sub-class ParameterTyped
	template <typename T> ParameterTyped<T> & getParameterTyped();

	protected:
	/// Name of parameter
	std::string name;

	private:
	/// Description of parameter
	std::string description;
	/// Type of access
	ParameterAccessType param_type{_pat_internal};
	};

	/* -------------------------------------------------------------------------- */
	/* Typed Parameter */
	/* -------------------------------------------------------------------------- */
	/**
	* Type parameter transfering a ParserParameter (string: string) to a typed
	* parameter in the memory of the p
	*/
	template <typename T> class ParameterTyped : public Parameter {
	public:
	ParameterTyped(const std::string & name, const std::string & description,
	ParameterAccessType param_type, T & param);

	/* ------------------------------------------------------------------------ */
	template <typename V> void setTyped(const V & value);
	void setAuto(const ParserParameter & value) override;
	T & getTyped();
	const T & getTyped() const;

	void printself(std::ostream & stream) const override;

	inline operator Real() const override;

	inline const std::type_info & type() const override { return typeid(T); }

	private:
	/// Value of parameter
	T & param;
	};

	/* -------------------------------------------------------------------------- */
	/* Parsable Interface */
	/* -------------------------------------------------------------------------- */
	/// Defines interface for classes to manipulate parsable parameters
	class ParameterRegistry {
	public:
	ParameterRegistry();
	virtual ~ParameterRegistry();

	/* ------------------------------------------------------------------------ */
	/// Add parameter to the params map
	template <typename T>
	- void registerParam(const std::string & name, T & variable, ParameterAccessType type,
	+ void registerParam(const std::string & name, T & variable,
	+ ParameterAccessType type,
	const std::string & description = "");

	/// Add parameter to the params map (with default value)
	template <typename T>
	- void registerParam(const std::string &name, T & variable, const T & default_value,
	- ParameterAccessType type,
	+ void registerParam(const std::string & name, T & variable,
	+ const T & default_value, ParameterAccessType type,
	const std::string & description = "");

	/------------------------------------------------------------------------- /
	protected:
	void registerSubRegistry(const ID & id, ParameterRegistry & registry);

	/* ------------------------------------------------------------------------ */
	public:
	/// Set value to a parameter (with possible different type)
	template <typename T, typename V>
	void setMixed(const std::string & name, const V & value);

	/// Set value to a parameter
	template <typename T> void set(const std::string & name, const T & value);

	/// Get value of a parameter
	inline const Parameter & get(const std::string & name) const;

	/// Get value of a parameter
	inline Parameter & get(const std::string & name);

	std::vector<ID> listParameters() const {
	std::vector<ID> params;
	for (const auto & pair : this->params) {
	params.push_back(pair.first);
	}
	return params;
	}

	std::vector<ID> listSubRegisteries() const {
	std::vector<ID> subs;
	for (const auto & pair : this->sub_registries) {
	subs.push_back(pair.first);
	}
	return subs;
	}

	protected:
	template <typename T> T & get_(const std::string & name);

	protected:
	void setParameterAccessType(const std::string & name,
	ParameterAccessType ptype);
	/* ------------------------------------------------------------------------ */
	virtual void printself(std::ostream & stream, int indent) const;

	protected:
	/// Parameters map
	using Parameters = std::map<std::string, Parameter *>;
	Parameters params;

	/// list of sub-registries
	using SubRegisteries = std::map<std::string, ParameterRegistry *>;
	SubRegisteries sub_registries;

	/// should accessor check in sub registries
	bool consisder_sub{true};
	};

	} // namespace akantu

	#include "parameter_registry_tmpl.hh"

	#endif /* AKANTU_PARAMETER_REGISTRY_HH_ */
	diff --git a/src/io/parser/parameter_registry_tmpl.hh b/src/io/parser/parameter_registry_tmpl.hh
	index ee0815b64..47c742c7c 100644
	--- a/src/io/parser/parameter_registry_tmpl.hh
	+++ b/src/io/parser/parameter_registry_tmpl.hh
	@@ -1,459 +1,459 @@
	/**
	* @file parameter_registry_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 04 2016
	* @date last modification: Thu Mar 19 2020
	*
	* @brief implementation of the templated part of ParameterRegistry class and
	* the derivated ones
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_error.hh"
	#include "aka_iterators.hh"
	//#include "parameter_registry.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <set>
	#include <string>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PARAMETER_REGISTRY_TMPL_HH_
	#define AKANTU_PARAMETER_REGISTRY_TMPL_HH_

	namespace akantu {

	namespace debug {
	class ParameterException : public Exception {
	public:
	ParameterException(const std::string & name, const std::string & message)
	: Exception(message), name(name) {}
	const std::string & name;
	};

	class ParameterUnexistingException : public ParameterException {
	public:
	ParameterUnexistingException(const std::string & name,
	const ParameterRegistry & registery)
	: ParameterException(name, "Parameter " + name +
	" does not exists in this scope") {
	auto && params = registery.listParameters();
	this->_info =
	std::accumulate(params.begin(), params.end(),
	this->_info + "\n Possible parameters are: ",
	[](auto && str, auto && param) {
	static auto first = true;
	auto ret = str + (first ? " " : ", ") + param;
	first = false;
	return ret;
	});
	}
	};

	class ParameterAccessRightException : public ParameterException {
	public:
	ParameterAccessRightException(const std::string & name,
	const std::string & perm)
	: ParameterException(name, "Parameter " + name + " is not " + perm) {}
	};

	class ParameterWrongTypeException : public ParameterException {
	public:
	ParameterWrongTypeException(const std::string & name,
	const std::type_info & wrong_type,
	const std::type_info & type)
	: ParameterException(name, "Parameter " + name +
	" type error, cannot convert " +
	debug::demangle(type.name()) + " to " +
	debug::demangle(wrong_type.name())) {}
	};
	} // namespace debug
	/* -------------------------------------------------------------------------- */
	template <typename T>
	const ParameterTyped<T> & Parameter::getParameterTyped() const {
	try {
	const auto & tmp = aka::as_type<ParameterTyped<T>>(*this);
	return tmp;
	} catch (std::bad_cast &) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterWrongTypeException(name, typeid(T), this->type()));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> ParameterTyped<T> & Parameter::getParameterTyped() {
	try {
	auto & tmp = aka::as_type<ParameterTyped<T>>(*this);
	return tmp;
	} catch (std::bad_cast &) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterWrongTypeException(name, typeid(T), this->type()));
	}
	}

	/* ------------------------------------------------------------------------ */
	template <typename T, typename V> void Parameter::set(const V & value) {
	if (not isWritable()) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterAccessRightException(name, "writable"));
	}
	ParameterTyped<T> & typed_param = getParameterTyped<T>();
	typed_param.setTyped(value);
	}

	/* ------------------------------------------------------------------------ */
	inline void Parameter::setAuto(const ParserParameter & /value/) {
	if (not isParsable()) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterAccessRightException(name, "parsable"));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> const T & Parameter::get() const {
	if (not isReadable()) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterAccessRightException(name, "readable"));
	}
	const ParameterTyped<T> & typed_param = getParameterTyped<T>();
	return typed_param.getTyped();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> T & Parameter::get() {
	ParameterTyped<T> & typed_param = getParameterTyped<T>();
	if (not isReadable() or not this->isWritable()) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterAccessRightException(name, "accessible"));
	}
	return typed_param.getTyped();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> inline Parameter::operator T() const {
	return this->get<T>();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	ParameterTyped<T>::ParameterTyped(const std::string & name,
	const std::string & description,
	ParameterAccessType param_type, T & param)
	: Parameter(name, description, param_type), param(param) {}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	template <typename V>
	void ParameterTyped<T>::setTyped(const V & value) {
	param = value;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void ParameterTyped<T>::setAuto(const ParserParameter & value) {
	Parameter::setAuto(value);
	param = static_cast<T>(value);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<std::string>::setAuto(const ParserParameter & value) {
	Parameter::setAuto(value);
	param = value.getValue();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<Vector<Real>>::setAuto(const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	Vector<Real> tmp = in_param;
	if (param.size() == 0) {
	param = tmp;
	} else {
	for (UInt i = 0; i < param.size(); ++i) {
	param(i) = tmp(i);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<Matrix<Real>>::setAuto(const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	Matrix<Real> tmp = in_param;
	if (param.size() == 0) {
	param = tmp;
	} else {
	for (UInt i = 0; i < param.rows(); ++i) {
	for (UInt j = 0; j < param.cols(); ++j) {
	param(i, j) = tmp(i, j);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> const T & ParameterTyped<T>::getTyped() const {
	return param;
	}
	/* -------------------------------------------------------------------------- */
	template <typename T> T & ParameterTyped<T>::getTyped() { return param; }

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void ParameterTyped<T>::printself(std::ostream & stream) const {
	Parameter::printself(stream);
	stream << param << "\n";
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> class ParameterTyped<std::vector<T>> : public Parameter {
	public:
	ParameterTyped(const std::string & name, const std::string & description,
	ParameterAccessType param_type, std::vector<T> & param)
	: Parameter(name, description, param_type), param(param) {}

	/* ------------------------------------------------------------------------
	*/
	template <typename V> void setTyped(const V & value) { param = value; }
	void setAuto(const ParserParameter & value) override {
	Parameter::setAuto(value);
	param.zero();
	const std::vector<T> & tmp = value;
	for (auto && z : tmp) {
	param.emplace_back(z);
	}
	}

	std::vector<T> & getTyped() { return param; }
	const std::vector<T> & getTyped() const { return param; }

	void printself(std::ostream & stream) const override {
	Parameter::printself(stream);
	stream << "[ ";
	for (auto && v : param) {
	stream << v << " ";
	}
	stream << "]\n";
	}

	inline const std::type_info & type() const override {
	return typeid(std::vector<T>);
	}

	private:
	/// Value of parameter
	std::vector<T> & param;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T> class ParameterTyped<std::set<T>> : public Parameter {
	public:
	ParameterTyped(const std::string & name, const std::string & description,
	ParameterAccessType param_type, std::set<T> & param)
	: Parameter(name, description, param_type), param(param) {}

	/* ------------------------------------------------------------------------
	*/
	template <typename V> void setTyped(const V & value) { param = value; }
	void setAuto(const ParserParameter & value) override {
	Parameter::setAuto(value);
	param.clear();
	const std::set<T> & tmp = value;
	for (auto && z : tmp) {
	param.emplace(z);
	}
	}

	std::set<T> & getTyped() { return param; }
	const std::set<T> & getTyped() const { return param; }

	void printself(std::ostream & stream) const override {
	Parameter::printself(stream);
	stream << "[ ";
	for (auto && v : param) {
	stream << v << " ";
	}
	stream << "]\n";
	}

	inline const std::type_info & type() const override {
	return typeid(std::set<T>);
	}

	private:
	/// Value of parameter
	std::set<T> & param;
	};

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ParameterTyped<bool>::printself(std::ostream & stream) const {
	Parameter::printself(stream);
	stream << std::boolalpha << param << "\n";
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void ParameterRegistry::registerParam(const std::string & name, T & variable,
	ParameterAccessType type,
	const std::string & description) {
	auto it = params.find(name);
	if (it != params.end()) {
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterException(
	name, "Parameter named " + name + " already registered."));
	}
	auto * param = new ParameterTyped<T>(name, description, type, variable);
	params[name] = param;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void ParameterRegistry::registerParam(const std::string & name, T & variable,
	const T & default_value,
	ParameterAccessType type,
	const std::string & description) {
	variable = default_value;
	registerParam(name, variable, type, description);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename V>
	void ParameterRegistry::setMixed(const std::string & name, const V & value) {
	auto it = params.find(name);
	if (it == params.end()) {
	if (consisder_sub) {
	for (auto it = sub_registries.begin(); it != sub_registries.end(); ++it) {
	it->second->setMixed<T>(name, value);
	}
	} else {
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterUnexistingException(name, *this));
	}
	} else {
	Parameter & param = *(it->second);
	param.set<T>(value);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void ParameterRegistry::set(const std::string & name, const T & value) {
	this->template setMixed<T>(name, value);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> T & ParameterRegistry::get_(const std::string & name) {
	auto it = params.find(name);
	if (it == params.end()) {
	if (consisder_sub) {
	for (auto it = sub_registries.begin(); it != sub_registries.end(); ++it) {
	try {
	return it->second->get_<T>(name);
	} catch (...) {
	}
	}
	}

	// nothing was found not even in sub registries
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterUnexistingException(name, *this));
	}

	Parameter & param = *(it->second);
	return param.get<T>();
	}

	/* -------------------------------------------------------------------------- */
	const Parameter & ParameterRegistry::get(const std::string & name) const {
	auto it = params.find(name);
	if (it == params.end()) {
	if (consisder_sub) {
	for (auto it = sub_registries.begin(); it != sub_registries.end(); ++it) {
	try {
	return it->second->get(name);
	} catch (...) {
	}
	}
	}

	// nothing was found not even in sub registries
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterUnexistingException(name, *this));
	}

	Parameter & param = *(it->second);
	return param;
	}

	/* -------------------------------------------------------------------------- */
	Parameter & ParameterRegistry::get(const std::string & name) {
	auto it = params.find(name);
	if (it == params.end()) {
	if (consisder_sub) {
	for (auto it = sub_registries.begin(); it != sub_registries.end(); ++it) {
	try {
	return it->second->get(name);
	} catch (...) {
	}
	}
	}

	// nothing was found not even in sub registries
	AKANTU_CUSTOM_EXCEPTION(debug::ParameterUnexistingException(name, *this));
	}

	Parameter & param = *(it->second);
	return param;
	}

	/* -------------------------------------------------------------------------- */
	namespace {
	namespace details {
	template <class T, class R, class Enable = void> struct CastHelper {
	static R convert(const T & /unused/) { throw std::bad_cast(); }
	};

	template <class T, class R>
	struct CastHelper<T, R,
	std::enable_if_t<std::is_convertible<T, R>::value>> {
	static R convert(const T & val) { return val; }
	};
	} // namespace details
	} // namespace

	template <typename T> inline ParameterTyped<T>::operator Real() const {
	if (not isReadable()) {
	AKANTU_CUSTOM_EXCEPTION(
	debug::ParameterAccessRightException(name, "accessible"));
	}
	return details::CastHelper<T, Real>::convert(param);
	}

	} // namespace akantu

	#endif /* AKANTU_PARAMETER_REGISTRY_TMPL_HH_ */
	diff --git a/src/io/parser/parsable.cc b/src/io/parser/parsable.cc
	index 99d9d43a1..140e26e65 100644
	--- a/src/io/parser/parsable.cc
	+++ b/src/io/parser/parsable.cc
	@@ -1,112 +1,112 @@
	/**
	* @file parsable.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Thu Feb 08 2018
	*
	* @brief Parsable implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "parsable.hh"
	#include "aka_random_generator.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Parsable::Parsable(const ParserType & section_type, const ID & id)
	: section_type(section_type), pid(id) {
	this->consisder_sub = false;
	}

	/* -------------------------------------------------------------------------- */
	Parsable::~Parsable() = default;

	/* -------------------------------------------------------------------------- */
	void Parsable::registerSubSection(const ParserType & type,
	const std::string & name,
	Parsable & sub_section) {
	SubSectionKey key(type, name);
	sub_sections[key] = &sub_section;

	this->registerSubRegistry(name, sub_section);
	}

	/* -------------------------------------------------------------------------- */
	void Parsable::parseParam(const ParserParameter & in_param) {
	auto it = params.find(in_param.getName());
	if (it == params.end()) {
	if (Parser::isPermissive()) {
	AKANTU_DEBUG_WARNING("No parameter named " << in_param.getName()
	<< " registered in " << pid
	<< ".");
	return;
	}

	AKANTU_EXCEPTION("No parameter named " << in_param.getName()
	<< " registered in " << pid << ".");
	}
	Parameter & param = *(it->second);
	param.setAuto(in_param);
	}

	/* -------------------------------------------------------------------------- */
	void Parsable::parseSection(const ParserSection & section) {
	if (section_type != section.getType()) {
	AKANTU_EXCEPTION("The object "
	<< pid << " is meant to parse section of type "
	<< section_type << ", so it cannot parse section of type "
	<< section.getType());
	}

	auto params = section.getParameters();
	auto it = params.first;
	for (; it != params.second; ++it) {
	parseParam(*it);
	}

	auto sit = section.getSubSections().first;
	for (; sit != section.getSubSections().second; ++sit) {
	parseSubSection(*sit);
	}
	}

	/* -------------------------------------------------------------------------- */
	void Parsable::parseSubSection(const ParserSection & section) {
	SubSectionKey key(section.getType(), section.getName());
	auto it = sub_sections.find(key);
	if (it != sub_sections.end()) {
	it->second->parseSection(section);
	} else if (!Parser::isPermissive()) {
	AKANTU_EXCEPTION("No parsable defined for sub sections of type <"
	<< key.first << "," << key.second << "> in " << pid);
	} else {
	AKANTU_DEBUG_WARNING("No parsable defined for sub sections of type <"
	<< key.first << "," << key.second << "> in " << pid);
	}
	}

	} // namespace akantu
	diff --git a/src/io/parser/parsable.hh b/src/io/parser/parsable.hh
	index 5aa957288..e64e85bdd 100644
	--- a/src/io/parser/parsable.hh
	+++ b/src/io/parser/parsable.hh
	@@ -1,74 +1,74 @@
	/**
	* @file parsable.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Aug 09 2012
	* @date last modification: Fri Dec 08 2017
	*
	* @brief Interface of the parameter registry
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "parameter_registry.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PARSABLE_HH_
	#define AKANTU_PARSABLE_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Parsable Interface */
	/* -------------------------------------------------------------------------- */
	/// Defines interface for classes to manipulate parsable parameters
	class Parsable : public ParameterRegistry {
	public:
	Parsable(const ParserType & section_type, const ID & id = std::string());
	~Parsable() override;

	/// Add subsection to the sub_sections map
	void registerSubSection(const ParserType & type, const std::string & name,
	Parsable & sub_section);

	/* ------------------------------------------------------------------------ */
	public:
	virtual void parseSection(const ParserSection & section);
	virtual void parseSubSection(const ParserSection & section);
	virtual void parseParam(const ParserParameter & in_param);

	private:
	ParserType section_type;
	/// ID of parsable object
	ID pid;
	using SubSectionKey = std::pair<ParserType, std::string>;
	using SubSections = std::map<SubSectionKey, Parsable *>;
	/// Subsections map
	SubSections sub_sections;
	};

	} // namespace akantu

	#endif /* AKANTU_PARSABLE_HH_ */
	diff --git a/src/io/parser/parser.cc b/src/io/parser/parser.cc
	index 968b2ae9c..8fd0e8811 100644
	--- a/src/io/parser/parser.cc
	+++ b/src/io/parser/parser.cc
	@@ -1,100 +1,100 @@
	/**
	* @file parser.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Thu Feb 01 2018
	*
	* @brief implementation of the parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// STL
	#include <fstream>
	#include <iomanip>
	#include <map>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ParserSection::~ParserSection() { this->clean(); }

	/* -------------------------------------------------------------------------- */
	ParserParameter & ParserSection::addParameter(const ParserParameter & param) {
	if (parameters.find(param.getName()) != parameters.end()) {
	AKANTU_EXCEPTION("The parameter \"" + param.getName() +
	"\" is already defined in this section");
	}

	return (parameters
	.insert(std::pair<std::string, ParserParameter>(param.getName(),
	param))
	.first->second);
	}

	/* -------------------------------------------------------------------------- */
	ParserSection & ParserSection::addSubSection(const ParserSection & section) {
	return ((sub_sections_by_type.insert(std::pair<ParserType, ParserSection>(
	section.getType(), section)))
	->second);
	}

	/* -------------------------------------------------------------------------- */
	std::string Parser::getLastParsedFile() const { return last_parsed_file; }

	/* -------------------------------------------------------------------------- */
	void ParserSection::printself(std::ostream & stream,
	unsigned int indent) const {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "Section(" << this->type << ") " << this->name
	<< ((not option.empty()) ? (" " + option) : "") << " [" << std::endl;
	if (!this->parameters.empty()) {
	stream << space << " Parameters [" << std::endl;
	auto pit = this->parameters.begin();
	for (; pit != this->parameters.end(); ++pit) {
	stream << space << " + ";
	pit->second.printself(stream, indent);
	stream << "\n";
	}
	stream << space << " ]" << std::endl;
	}

	if (!this->sub_sections_by_type.empty()) {
	stream << space << " Subsections [" << std::endl;
	auto sit = this->sub_sections_by_type.begin();
	for (; sit != this->sub_sections_by_type.end(); ++sit) {
	sit->second.printself(stream, indent + 2);
	}
	stream << std::endl;
	stream << space << " ]" << std::endl;
	}
	stream << space << "]" << std::endl;
	}

	} // namespace akantu
	diff --git a/src/io/parser/parser.hh b/src/io/parser/parser.hh
	index 1666886b6..fa1966f8f 100644
	--- a/src/io/parser/parser.hh
	+++ b/src/io/parser/parser.hh
	@@ -1,543 +1,543 @@
	/**
	* @file parser.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Apr 02 2021
	*
	* @brief File parser interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_random_generator.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PARSER_HH_
	#define AKANTU_PARSER_HH_

	namespace akantu {

	#if !defined(DOXYGEN)
	// clang-format off
	#define AKANTU_SECTION_TYPES \
	(cohesive_inserter) \
	(contact) \
	(embedded_interface) \
	(friction) \
	(global) \
	(heat) \
	(integration_scheme) \
	(material) \
	(phasefield) \
	(mesh) \
	(model) \
	(model_solver) \
	(neighborhood) \
	(neighborhoods) \
	(non_linear_solver) \
	(non_local) \
	(rules) \
	(solver) \
	(time_step_solver) \
	(user) \
	(weight_function) \
	(contact_detector) \
	(contact_resolution) \
	(not_defined)
	// clang-format on

	/// Defines the possible section types
	AKANTU_CLASS_ENUM_DECLARE(ParserType, AKANTU_SECTION_TYPES)
	AKANTU_CLASS_ENUM_OUTPUT_STREAM(ParserType, AKANTU_SECTION_TYPES)
	AKANTU_CLASS_ENUM_INPUT_STREAM(ParserType, AKANTU_SECTION_TYPES)
	#else
	enum class ParserType {
	cohesive_inserter,
	contact,
	embedded_interface,
	friction,
	global,
	heat,
	integration_scheme,
	material,
	phasefield,
	mesh,
	model,
	model_solver,
	neighborhood,
	neighborhoods,
	non_linear_solver,
	non_local,
	rules,
	solver,
	time_step_solver,
	user,
	weight_function,
	not_defined
	};
	#endif

	/// Defines the possible search contexts/scopes (for parameter search)
	enum ParserParameterSearchCxt {
	_ppsc_current_scope = 0x1,
	_ppsc_parent_scope = 0x2,
	_ppsc_current_and_parent_scope = 0x3
	};
	/* ------------------------------------------------------------------------ */
	/* Parameters Class */
	/* ------------------------------------------------------------------------ */
	class ParserSection;

	/// @brief The ParserParameter objects represent the end of tree branches as
	/// they
	/// are the different informations contained in the input file.
	class ParserParameter {
	public:
	ParserParameter()
	: name(std::string()), value(std::string()), dbg_filename(std::string()) {
	}

	ParserParameter(const std::string & name, const std::string & value,
	const ParserSection & parent_section)
	: parent_section(&parent_section), name(name), value(value),
	dbg_filename(std::string()) {}

	ParserParameter(const ParserParameter & param) = default;

	virtual ~ParserParameter() = default;

	/// Get parameter name
	const std::string & getName() const { return name; }
	/// Get parameter value
	const std::string & getValue() const { return value; }

	/// Set info for debug output
	void setDebugInfo(const std::string & filename, UInt line, UInt column) {
	dbg_filename = filename;
	dbg_line = line;
	dbg_column = column;
	}

	template <typename T> inline operator T() const;

	// template <typename T> inline operator Vector<T>() const;
	// template <typename T> inline operator Matrix<T>() const;

	/// Print parameter info in stream
	void printself(std::ostream & stream,
	__attribute__((unused)) unsigned int indent = 0) const {
	stream << name << ": " << value << " (" << dbg_filename << ":" << dbg_line
	<< ":" << dbg_column << ")";
	}

	private:
	void setParent(const ParserSection & sect) { parent_section = § }

	friend class ParserSection;

	private:
	/// Pointer to the parent section
	const ParserSection * parent_section{nullptr};
	/// Name of the parameter
	std::string name;
	/// Value of the parameter
	std::string value;
	/// File for debug output
	std::string dbg_filename;
	/// Position of parameter in parsed file
	UInt dbg_line, dbg_column;
	};

	/* ------------------------------------------------------------------------ */
	/* Sections Class */
	/* ------------------------------------------------------------------------ */
	/// ParserSection represents a branch of the parsing tree.
	class ParserSection {
	public:
	using SubSections = std::multimap<ParserType, ParserSection>;
	using Parameters = std::map<std::string, ParserParameter>;

	private:
	using const_section_iterator_ = SubSections::const_iterator;

	public:
	/* ------------------------------------------------------------------------ */
	/* SubSection iterator */
	/* ------------------------------------------------------------------------ */
	/// Iterator on sections
	class const_section_iterator {
	public:
	using iterator_category = std::forward_iterator_tag;
	using value_type = ParserSection;
	using pointer = ParserSection *;
	using reference = ParserSection &;

	const_section_iterator() = default;
	const_section_iterator(const const_section_iterator_ & it) : it(it) {}
	const_section_iterator(const const_section_iterator & other) = default;
	const_section_iterator &
	operator=(const const_section_iterator & other) = default;

	const ParserSection & operator*() const { return it->second; }
	const ParserSection * operator->() const { return &(it->second); }

	bool operator==(const const_section_iterator & other) const {
	return it == other.it;
	}

	bool operator!=(const const_section_iterator & other) const {
	return it != other.it;
	}

	const_section_iterator & operator++() {
	++it;
	return *this;
	}

	const_section_iterator operator++(int) {
	const_section_iterator tmp = *this;
	operator++();
	return tmp;
	}

	private:
	const_section_iterator_ it;
	};

	/* ------------------------------------------------------------------------ */
	/* Parameters iterator */
	/* ------------------------------------------------------------------------ */
	/// Iterator on parameters
	class const_parameter_iterator {
	public:
	const_parameter_iterator(const const_parameter_iterator & other) = default;
	const_parameter_iterator(const Parameters::const_iterator & it) : it(it) {}

	const_parameter_iterator &
	operator=(const const_parameter_iterator & other) {
	if (this != &other) {
	it = other.it;
	}
	return *this;
	}

	const ParserParameter & operator*() const { return it->second; }
	const ParserParameter * operator->() { return &(it->second); };

	bool operator==(const const_parameter_iterator & other) const {
	return it == other.it;
	}

	bool operator!=(const const_parameter_iterator & other) const {
	return it != other.it;
	}

	const_parameter_iterator & operator++() {
	++it;
	return *this;
	}

	const_parameter_iterator operator++(int) {
	const_parameter_iterator tmp = *this;
	operator++();
	return tmp;
	}

	private:
	Parameters::const_iterator it;
	};

	/* ---------------------------------------------------------------------- */
	ParserSection() : name(std::string()) {}

	ParserSection(const std::string & name, ParserType type)
	: name(name), type(type) {}

	ParserSection(const std::string & name, ParserType type,
	const std::string & option,
	const ParserSection & parent_section)
	: parent_section(&parent_section), name(name), type(type),
	option(option) {}

	ParserSection(const ParserSection & section)
	: parent_section(section.parent_section), name(section.name),
	type(section.type), option(section.option),
	parameters(section.parameters),
	sub_sections_by_type(section.sub_sections_by_type) {
	setChldrenPointers();
	}

	ParserSection & operator=(const ParserSection & other) {
	if (&other != this) {
	parent_section = other.parent_section;
	name = other.name;
	type = other.type;
	option = other.option;
	parameters = other.parameters;
	sub_sections_by_type = other.sub_sections_by_type;
	setChldrenPointers();
	}
	return *this;
	}

	virtual ~ParserSection();

	virtual void printself(std::ostream & stream, unsigned int indent = 0) const;

	/* ---------------------------------------------------------------------- */
	/* Creation functions */
	/* ---------------------------------------------------------------------- */
	public:
	ParserParameter & addParameter(const ParserParameter & param);
	ParserSection & addSubSection(const ParserSection & section);

	protected:
	/// Clean ParserSection content
	void clean() {
	parameters.clear();
	sub_sections_by_type.clear();
	}

	private:
	void setChldrenPointers() {
	for (auto && param_pair : this->parameters) {
	param_pair.second.setParent(*this);
	}

	for (auto && sub_sect_pair : this->sub_sections_by_type) {
	sub_sect_pair.second.setParent(*this);
	}
	}

	/* ---------------------------------------------------------------------- */
	/* Accessors */
	/* ---------------------------------------------------------------------- */
	public:
	class SubSectionsRange
	: public std::pair<const_section_iterator, const_section_iterator> {
	public:
	SubSectionsRange(const const_section_iterator & first,
	const const_section_iterator & second)
	: std::pair<const_section_iterator, const_section_iterator>(first,
	second) {}
	auto begin() { return this->first; }
	auto end() { return this->second; }
	};

	/// Get begin and end iterators on subsections of certain type
	auto getSubSections(ParserType type = ParserType::_not_defined) const {
	if (type != ParserType::_not_defined) {
	auto range = sub_sections_by_type.equal_range(type);
	return SubSectionsRange(range.first, range.second);
	}
	return SubSectionsRange(sub_sections_by_type.begin(),
	sub_sections_by_type.end());
	}

	/// Get number of subsections of certain type
	UInt getNbSubSections(ParserType type = ParserType::_not_defined) const {
	if (type != ParserType::_not_defined) {
	return this->sub_sections_by_type.count(type);
	}
	return this->sub_sections_by_type.size();
	}

	/// Get begin and end iterators on parameters
	auto getParameters() const {
	return std::pair<const_parameter_iterator, const_parameter_iterator>(
	parameters.begin(), parameters.end());
	}
	/* ---------------------------------------------------------------------- */
	/// Get parameter within specified context
	const ParserParameter & getParameter(
	const std::string & name,
	ParserParameterSearchCxt search_ctx = _ppsc_current_scope) const {
	Parameters::const_iterator it;
	if ((search_ctx & _ppsc_current_scope) != 0) {
	it = parameters.find(name);
	}

	if (it == parameters.end()) {
	if ((search_ctx & _ppsc_parent_scope) != 0 and
	parent_section != nullptr) {
	return parent_section->getParameter(name, search_ctx);
	}

	AKANTU_SILENT_EXCEPTION(
	"The parameter " << name
	<< " has not been found in the specified context");
	}
	return it->second;
	}

	/* ------------------------------------------------------------------------ */
	/// Get parameter within specified context, with a default value in case the
	/// parameter does not exists
	template <class T>
	T getParameter(
	const std::string & name, const T & default_value,
	ParserParameterSearchCxt search_ctx = _ppsc_current_scope) const {
	try {
	T tmp = this->getParameter(name, search_ctx);
	return tmp;
	} catch (debug::Exception &) {
	return default_value;
	}
	}

	/* ------------------------------------------------------------------------ */
	/// Check if parameter exists within specified context
	bool hasParameter(
	const std::string & name,
	ParserParameterSearchCxt search_ctx = _ppsc_current_scope) const {

	Parameters::const_iterator it;
	if ((search_ctx & _ppsc_current_scope) != 0) {
	it = parameters.find(name);
	}

	if (it == parameters.end()) {
	if ((search_ctx & _ppsc_parent_scope) != 0 and
	parent_section != nullptr) {
	return parent_section->hasParameter(name, search_ctx);
	}
	return false;
	}
	return true;
	}

	/* --------------------------------------------------------------------------
	*/
	/// Get value of given parameter in context
	template <class T>
	T getParameterValue(
	const std::string & name,
	ParserParameterSearchCxt search_ctx = _ppsc_current_scope) const {
	const ParserParameter & tmp_param = getParameter(name, search_ctx);
	T t = tmp_param;
	return t;
	}

	/* --------------------------------------------------------------------------
	*/
	/// Get section name
	std::string getName() const { return name; }
	/// Get section type
	ParserType getType() const { return type; }
	/// Get section option
	std::string getOption(const std::string & def = "") const {
	return (not option.empty()) ? option : def;
	}

	protected:
	void setParent(const ParserSection & sect) { parent_section = § }

	/* ---------------------------------------------------------------------- */
	/* Members */
	/* ---------------------------------------------------------------------- */
	private:
	/// Pointer to the parent section
	const ParserSection * parent_section{nullptr};
	/// Name of section
	std::string name;
	/// Type of section, see AKANTU_SECTION_TYPES
	ParserType type{ParserType::_not_defined};
	/// Section option
	std::string option;
	/// Map of parameters in section
	Parameters parameters;
	/// Multi-map of subsections
	SubSections sub_sections_by_type;
	};

	/* ------------------------------------------------------------------------ */
	/* Parser Class */
	/* ------------------------------------------------------------------------ */
	/// Root of parsing tree, represents the global ParserSection
	class Parser : public ParserSection {
	public:
	Parser() : ParserSection("global", ParserType::_global) {}

	void parse(const std::string & filename);

	std::string getLastParsedFile() const;

	static bool isPermissive() { return permissive_parser; }

	public:
	/// Parse real scalar
	static Real parseReal(const std::string & value,
	const ParserSection & section);
	/// Parse real vector
	static Vector<Real> parseVector(const std::string & value,
	const ParserSection & section);
	/// Parse real matrix
	static Matrix<Real> parseMatrix(const std::string & value,
	const ParserSection & section);
	/// Parse real random parameter
	static RandomParameter<Real>
	parseRandomParameter(const std::string & value,
	const ParserSection & section);

	protected:
	/// General parse function
	template <class T, class Grammar>
	static T parseType(const std::string & value, Grammar & grammar);

	protected:
	// friend class Parsable;
	static bool permissive_parser;
	std::string last_parsed_file;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const ParserParameter & _this) {
	_this.printself(stream);
	return stream;
	}

	inline std::ostream & operator<<(std::ostream & stream,
	const ParserSection & section) {
	section.printself(stream);
	return stream;
	}

	} // namespace akantu

	namespace std {
	template <> struct iterator_traits<::akantu::Parser::const_section_iterator> {
	using iterator_category = input_iterator_tag;
	using value_type = ::akantu::ParserParameter;
	using difference_type = ptrdiff_t;
	using pointer = const ::akantu::ParserParameter *;
	using reference = const ::akantu::ParserParameter &;
	};
	} // namespace std

	#include "parser_tmpl.hh"

	#endif /* AKANTU_PARSER_HH_ */
	diff --git a/src/io/parser/parser_grammar_tmpl.hh b/src/io/parser/parser_grammar_tmpl.hh
	index 32649ed05..ddff996d8 100644
	--- a/src/io/parser/parser_grammar_tmpl.hh
	+++ b/src/io/parser/parser_grammar_tmpl.hh
	@@ -1,83 +1,83 @@
	/**
	* @file parser_grammar_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 11 2015
	* @date last modification: Sun Dec 03 2017
	*
	* @brief implementation of the templated part of ParsableParam Parsable and
	* ParsableParamTyped
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	//#include <boost/config/warning_disable.hpp>
	#include <boost/spirit/include/classic_position_iterator.hpp>
	#include <boost/spirit/include/qi.hpp>
	#include <boost/spirit/include/support_multi_pass.hpp>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PARSER_GRAMMAR_TMPL_HH
	#define AKANTU_PARSER_GRAMMAR_TMPL_HH

	namespace akantu {

	namespace qi = boost::spirit::qi;

	/* -------------------------------------------------------------------------- */
	template <class T, class Grammar>
	T Parser::parseType(const std::string & value, Grammar & grammar) {
	using boost::spirit::ascii::space;

	std::string::const_iterator b = value.begin();
	std::string::const_iterator e = value.end();

	T resultat = T();
	bool res = false;
	try {
	res = qi::phrase_parse(b, e, grammar, space, resultat);
	} catch (debug::Exception & ex) {
	AKANTU_EXCEPTION("Could not parse '"
	<< value << "' as a " << debug::demangle(typeid(T).name())
	<< ", an unknown error append '" << ex.what());
	}

	if (!res \|\| (b != e)) {
	AKANTU_EXCEPTION("Could not parse '"
	<< value << "' as a " << debug::demangle(typeid(T).name())
	<< ", an unknown error append '"
	<< std::string(value.begin(), b) << "<HERE>"
	<< std::string(b, e) << "'");
	}
	return resultat;
	}

	namespace parser {
	template <class Iterator> struct Skipper {
	using type = qi::rule<Iterator, void()>;
	};
	} // namespace parser

	} // namespace akantu

	#endif // AKANTU_PARSER_GRAMMAR_TMPL_HH
	diff --git a/src/io/parser/parser_input_files.cc b/src/io/parser/parser_input_files.cc
	index adbf8d16a..6a77ed7a1 100644
	--- a/src/io/parser/parser_input_files.cc
	+++ b/src/io/parser/parser_input_files.cc
	@@ -1,120 +1,120 @@
	/**
	* @file parser_input_files.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 11 2015
	* @date last modification: Wed Nov 08 2017
	*
	* @brief implementation of the parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#define GCC_VERSION \
	(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	#if GCC_VERSION > 40600
	#pragma GCC diagnostic push
	#endif
	#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
	#endif

	/* -------------------------------------------------------------------------- */
	#include "parser.hh"
	#include "parser_grammar_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "input_file_parser.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void Parser::parse(const std::string & filename) {
	this->clean();
	std::ifstream input(filename.c_str());

	if (!input.good()) {
	AKANTU_EXCEPTION("Could not open file " << filename << "!");
	}

	input.unsetf(std::ios::skipws);

	// wrap istream into iterator
	spirit::istream_iterator fwd_begin(input);
	spirit::istream_iterator fwd_end;

	// wrap forward iterator with position iterator, to record the position
	using pos_iterator_type =
	spirit::classic::position_iterator2<spirit::istream_iterator>;
	pos_iterator_type position_begin(fwd_begin, fwd_end, filename);
	pos_iterator_type position_end;

	// parse
	parser::InputFileGrammar<pos_iterator_type> ag(this);

	bool result = qi::phrase_parse(position_begin, position_end, ag, ag.skipper);

	if (!result \|\| position_begin != position_end) {
	spirit::classic::file_position pos = position_begin.get_position();

	AKANTU_EXCEPTION("Parse error [ "
	<< ag.getErrorMessage() << " ]"
	<< " in file " << filename << " line " << pos.line
	<< " column " << pos.column << std::endl
	<< "'" << position_begin.get_currentline() << "'"
	<< std::endl
	<< std::setw(pos.column) << " "
	<< "^- here");
	}

	try {
	bool permissive = getParameter("permissive_parser", _ppsc_current_scope);

	permissive_parser = permissive;
	AKANTU_DEBUG_INFO("Parser switched permissive mode to "
	<< std::boolalpha << permissive_parser);
	} catch (debug::Exception & e) {
	}

	last_parsed_file = filename;
	input.close();
	}

	} // namespace akantu

	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif defined(__GNUG__)
	#if GCC_VERSION > 40600
	#pragma GCC diagnostic pop
	#else
	#pragma GCC diagnostic warning "-Wunused-local-typedefs"
	#endif
	#endif
	diff --git a/src/io/parser/parser_random.cc b/src/io/parser/parser_random.cc
	index 33f651d5e..c64045fce 100644
	--- a/src/io/parser/parser_random.cc
	+++ b/src/io/parser/parser_random.cc
	@@ -1,116 +1,116 @@
	/**
	* @file parser_random.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Sun Jul 09 2017
	*
	* @brief implementation of the parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#define GCC_VERSION \
	(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	#if GCC_VERSION > 40600
	#pragma GCC diagnostic push
	#endif
	#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
	#endif

	/* -------------------------------------------------------------------------- */
	#include "parser.hh"
	#if !defined(DOXYGEN)
	#include "parser_grammar_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "algebraic_parser.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	RandomParameter<Real>
	Parser::parseRandomParameter(const std::string & value,
	const ParserSection & section) {
	#if !defined(DOXYGEN)
	using boost::spirit::ascii::space_type;
	parser::RandomGeneratorGrammar<std::string::const_iterator, space_type>
	grammar(section);
	grammar.name("random_grammar");
	parser::ParsableRandomGenerator rg =
	Parser::parseType<parser::ParsableRandomGenerator>(value, grammar);
	Vector<Real> params = rg.parameters;

	switch (rg.type) {
	case _rdt_not_defined:
	return RandomParameter<Real>(rg.base,
	std::uniform_real_distribution<Real>(0, 0));
	case _rdt_uniform:
	return RandomParameter<Real>(
	rg.base, std::uniform_real_distribution<Real>(params(0), params(1)));
	case _rdt_exponential:
	return RandomParameter<Real>(
	rg.base, std::exponential_distribution<Real>(params(0)));
	case _rdt_gamma:
	return RandomParameter<Real>(
	rg.base, std::gamma_distribution<Real>(params(0), params(1)));
	case _rdt_weibull:
	return RandomParameter<Real>(
	rg.base, std::weibull_distribution<Real>(params(1), params(0)));
	case _rdt_extreme_value:
	return RandomParameter<Real>(
	rg.base, std::extreme_value_distribution<Real>(params(0), params(1)));
	case _rdt_normal:
	return RandomParameter<Real>(
	rg.base, std::normal_distribution<Real>(params(0), params(1)));
	case _rdt_lognormal:
	return RandomParameter<Real>(
	rg.base, std::lognormal_distribution<Real>(params(0), params(1)));
	case _rdt_chi_squared:
	return RandomParameter<Real>(
	rg.base, std::chi_squared_distribution<Real>(params(0)));
	case _rdt_cauchy:
	return RandomParameter<Real>(
	rg.base, std::cauchy_distribution<Real>(params(0), params(1)));
	case _rdt_fisher_f:
	return RandomParameter<Real>(
	rg.base, std::fisher_f_distribution<Real>(params(0), params(1)));
	case _rdt_student_t:
	return RandomParameter<Real>(rg.base,
	std::student_t_distribution<Real>(params(0)));
	default:
	AKANTU_EXCEPTION("This is an unknown random distribution in the parser");
	}
	#endif
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/io/parser/parser_real.cc b/src/io/parser/parser_real.cc
	index 19558a8b0..c90b067c5 100644
	--- a/src/io/parser/parser_real.cc
	+++ b/src/io/parser/parser_real.cc
	@@ -1,65 +1,65 @@
	/**
	* @file parser_real.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Wed Apr 20 2016
	*
	* @brief implementation of the parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#define GCC_VERSION \
	(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	#if GCC_VERSION > 40600
	#pragma GCC diagnostic push
	#endif
	#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
	#endif

	/* -------------------------------------------------------------------------- */
	#include "parser.hh"
	#include "parser_grammar_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "algebraic_parser.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Real Parser::parseReal(const std::string & value,
	const ParserSection & section) {
	using boost::spirit::ascii::space_type;
	parser::AlgebraicGrammar<std::string::const_iterator, space_type> grammar(
	section);
	grammar.name("algebraic_grammar");
	return Parser::parseType<Real>(value, grammar);
	}

	} // namespace akantu
	diff --git a/src/io/parser/parser_tmpl.hh b/src/io/parser/parser_tmpl.hh
	index 19bb0c6c5..d8c0ed56d 100644
	--- a/src/io/parser/parser_tmpl.hh
	+++ b/src/io/parser/parser_tmpl.hh
	@@ -1,125 +1,125 @@
	/**
	* @file parser_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Thu Mar 19 2020
	*
	* @brief Implementation of the parser templated methods
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <regex>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T> inline ParserParameter::operator T() const {
	T t;
	std::stringstream sstr(value);
	sstr >> t;
	if (sstr.bad()) {
	AKANTU_EXCEPTION("No known conversion of a ParserParameter \""
	<< name << "\" to the type " << typeid(T).name());
	}
	return t;
	}

	#if !defined(DOXYGEN)
	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator const char *() const {
	return value.c_str();
	}

	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator Real() const {
	return Parser::parseReal(value, *parent_section);
	}

	/* --------------------------------------------------------- -----------------
	*/
	template <> inline ParserParameter::operator bool() const {
	bool b;
	std::stringstream sstr(value);
	sstr >> std::boolalpha >> b;
	if (sstr.fail()) {
	sstr.clear();
	sstr >> std::noboolalpha >> b;
	}
	return b;
	}

	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator std::vector<std::string>() const {
	std::vector<std::string> tmp;
	auto string =
	std::regex_replace(value, std::regex("[[:space:]]\|\\[\|\\]"), "");
	std::smatch sm;
	while (std::regex_search(string, sm, std::regex("[^,]+"))) {
	tmp.push_back(sm.str());
	string = sm.suffix();
	}
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator std::set<std::string>() const {
	std::set<std::string> tmp;
	auto string =
	std::regex_replace(value, std::regex("[[:space:]]\|\\[\|\\]"), "");
	std::smatch sm;
	while (std::regex_search(string, sm, std::regex("[^,]+"))) {
	tmp.emplace(sm.str());
	string = sm.suffix();
	}
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator Vector<Real>() const {
	return Parser::parseVector(value, *parent_section);
	}

	/* --------------------------------------------------------- ---------------- */
	template <> inline ParserParameter::operator Vector<UInt>() const {
	Vector<Real> tmp = Parser::parseVector(value, *parent_section);
	Vector<UInt> tmp_uint(tmp.size());
	for (UInt i = 0; i < tmp.size(); ++i) {
	tmp_uint(i) = UInt(tmp(i));
	}
	return tmp_uint;
	}

	/* --------------------------------------------------------- ---------------- */
	template <> inline ParserParameter::operator Matrix<Real>() const {
	return Parser::parseMatrix(value, *parent_section);
	}

	/* -------------------------------------------------------------------------- */
	template <> inline ParserParameter::operator RandomParameter<Real>() const {
	return Parser::parseRandomParameter(value, *parent_section);
	}
	#endif
	} // namespace akantu
	diff --git a/src/io/parser/parser_types.cc b/src/io/parser/parser_types.cc
	index 4c1c4c0cf..c560c090c 100644
	--- a/src/io/parser/parser_types.cc
	+++ b/src/io/parser/parser_types.cc
	@@ -1,77 +1,77 @@
	/**
	* @file parser_types.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Apr 20 2016
	*
	* @brief implementation of the parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#define GCC_VERSION \
	(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
	#if GCC_VERSION > 40600
	#pragma GCC diagnostic push
	#endif
	#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
	#endif

	/* -------------------------------------------------------------------------- */
	#include "parser.hh"
	#include "parser_grammar_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "algebraic_parser.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Vector<Real> Parser::parseVector(const std::string & value,
	const ParserSection & section) {
	using boost::spirit::ascii::space_type;
	parser::VectorGrammar<std::string::const_iterator, space_type> grammar(
	section);
	grammar.name("vector_grammar");
	return Parser::parseType<parser::parsable_vector>(value, grammar);
	}

	/* -------------------------------------------------------------------------- */
	Matrix<Real> Parser::parseMatrix(const std::string & value,
	const ParserSection & section) {
	using boost::spirit::ascii::space_type;
	parser::MatrixGrammar<std::string::const_iterator, space_type> grammar(
	section);
	grammar.name("matrix_grammar");
	return Parser::parseType<parser::parsable_matrix>(value, grammar);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/mesh/element_group.cc b/src/mesh/element_group.cc
	index 7e6d20a6b..7260343bd 100644
	--- a/src/mesh/element_group.cc
	+++ b/src/mesh/element_group.cc
	@@ -1,215 +1,212 @@
	/**
	* @file element_group.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Stores information relevent to the notion of domain boundary and
	* surfaces.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_csr.hh"
	#include "dumpable.hh"
	#include "dumpable_inline_impl.hh"
	#include "group_manager.hh"
	#include "group_manager_inline_impl.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	#include <algorithm>
	#include <iterator>
	#include <sstream>

	#include "element_group.hh"
	#if defined(AKANTU_USE_IOHELPER)
	#include "dumper_iohelper_paraview.hh"
	#endif

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ElementGroup::ElementGroup(const std::string & group_name, const Mesh & mesh,
	NodeGroup & node_group, UInt dimension,
	const std::string & id)
	- : mesh(mesh), name(group_name),
	- elements("elements", id), node_group(node_group),
	- dimension(dimension) {
	+ : mesh(mesh), name(group_name), elements("elements", id),
	+ node_group(node_group), dimension(dimension) {
	AKANTU_DEBUG_IN();

	#if defined(AKANTU_USE_IOHELPER)
	this->registerDumper<DumperParaview>("paraview_" + group_name, group_name,
	true);
	this->addDumpFilteredMesh(mesh, elements, node_group.getNodes(),
	_all_dimensions);
	#endif

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ElementGroup::ElementGroup(const ElementGroup & /other/) = default;

	/* -------------------------------------------------------------------------- */
	-void ElementGroup::clear() {
	- elements.free();
	-}
	+void ElementGroup::clear() { elements.free(); }

	/* -------------------------------------------------------------------------- */
	void ElementGroup::clear(ElementType type, GhostType ghost_type) {
	if (elements.exists(type, ghost_type)) {
	elements(type, ghost_type).clear();
	}
	}

	/* -------------------------------------------------------------------------- */
	bool ElementGroup::empty() const { return elements.empty(); }

	/* -------------------------------------------------------------------------- */
	void ElementGroup::append(const ElementGroup & other_group) {
	AKANTU_DEBUG_IN();

	node_group.append(other_group.node_group);

	/// loop on all element types in all dimensions
	for (auto ghost_type : ghost_types) {
	for (auto type : other_group.elementTypes(_ghost_type = ghost_type,
	_element_kind = _ek_not_defined)) {
	const Array<UInt> & other_elem_list =
	other_group.elements(type, ghost_type);
	UInt nb_other_elem = other_elem_list.size();

	Array<UInt> * elem_list;
	UInt nb_elem = 0;

	/// create current type if doesn't exists, otherwise get information
	if (elements.exists(type, ghost_type)) {
	elem_list = &elements(type, ghost_type);
	nb_elem = elem_list->size();
	} else {
	elem_list = &(elements.alloc(0, 1, type, ghost_type));
	}

	/// append new elements to current list
	elem_list->resize(nb_elem + nb_other_elem);
	std::copy(other_elem_list.begin(), other_elem_list.end(),
	elem_list->begin() + nb_elem);

	/// remove duplicates
	std::sort(elem_list->begin(), elem_list->end());
	Array<UInt>::iterator<> end =
	std::unique(elem_list->begin(), elem_list->end());
	elem_list->resize(end - elem_list->begin());
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ElementGroup::printself(std::ostream & stream, int indent) const {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}

	stream << space << "ElementGroup [" << std::endl;
	stream << space << " + name: " << name << std::endl;
	stream << space << " + dimension: " << dimension << std::endl;
	elements.printself(stream, indent + 1);
	node_group.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void ElementGroup::optimize() {
	// increasing the locality of data when iterating on the element of a group
	for (auto ghost_type : ghost_types) {
	for (auto type : elements.elementTypes(_ghost_type = ghost_type)) {
	Array<UInt> & els = elements(type, ghost_type);
	std::sort(els.begin(), els.end());

	Array<UInt>::iterator<> end = std::unique(els.begin(), els.end());
	els.resize(end - els.begin());
	}
	}

	node_group.optimize();
	}

	/* -------------------------------------------------------------------------- */
	void ElementGroup::fillFromNodeGroup() {
	CSR<Element> node_to_elem;
	MeshUtils::buildNode2Elements(this->mesh, node_to_elem, this->dimension);

	std::set<Element> seen;

	Array<UInt>::const_iterator<> itn = this->node_group.begin();
	Array<UInt>::const_iterator<> endn = this->node_group.end();
	for (; itn != endn; ++itn) {
	CSR<Element>::iterator ite = node_to_elem.begin(*itn);
	CSR<Element>::iterator ende = node_to_elem.end(*itn);
	for (; ite != ende; ++ite) {
	const Element & elem = *ite;
	if (this->dimension != _all_dimensions &&
	this->dimension != Mesh::getSpatialDimension(elem.type)) {
	continue;
	}
	if (seen.find(elem) != seen.end()) {
	continue;
	}

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(elem.type);
	Array<UInt>::const_iterator<Vector<UInt>> conn_it =
	this->mesh.getConnectivity(elem.type, elem.ghost_type)
	.begin(nb_nodes_per_element);
	const Vector<UInt> & conn = conn_it[elem.element];

	UInt count = 0;
	for (UInt n = 0; n < conn.size(); ++n) {
	count +=
	(this->node_group.getNodes().find(conn(n)) != UInt(-1) ? 1 : 0);
	}

	if (count == nb_nodes_per_element) {
	this->add(elem);
	}

	seen.insert(elem);
	}
	}

	this->optimize();
	}

	/* -------------------------------------------------------------------------- */
	void ElementGroup::addDimension(UInt dimension) {
	this->dimension = std::max(dimension, this->dimension);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/mesh/element_group.hh b/src/mesh/element_group.hh
	index 6bf7c208d..6b5cfd2a7 100644
	--- a/src/mesh/element_group.hh
	+++ b/src/mesh/element_group.hh
	@@ -1,205 +1,205 @@
	/**
	* @file element_group.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Mon Mar 08 2021
	*
	* @brief Stores information relevent to the notion of domain boundary and
	* surfaces.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dumpable.hh"
	#include "element_type_map.hh"
	#include "node_group.hh"
	/* -------------------------------------------------------------------------- */
	#include <set>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_GROUP_HH_
	#define AKANTU_ELEMENT_GROUP_HH_

	namespace akantu {
	class Mesh;
	class Element;
	} // namespace akantu

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class ElementGroup : public Dumpable {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ElementGroup(const std::string & name, const Mesh & mesh,
	NodeGroup & node_group, UInt dimension = _all_dimensions,
	const std::string & id = "element_group");

	ElementGroup(const ElementGroup & /unused/);

	/* ------------------------------------------------------------------------ */
	/* Type definitions */
	/* ------------------------------------------------------------------------ */
	public:
	using ElementList = ElementTypeMapArray<UInt>;
	using NodeList = Array<UInt>;

	/* ------------------------------------------------------------------------ */
	/* Element iterator */
	/* ------------------------------------------------------------------------ */

	using type_iterator = ElementList::type_iterator;
	[[deprecated("Use elementTypes instead")]] inline type_iterator
	firstType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_regular) const;

	[[deprecated("Use elementTypes instead")]] inline type_iterator
	lastType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_regular) const;

	template <typename... pack>
	inline decltype(auto) elementTypes(pack &&... _pack) const {
	return elements.elementTypes(_pack...);
	}

	using const_element_iterator = Array<UInt>::const_iterator<UInt>;

	inline const_element_iterator begin(ElementType type,
	GhostType ghost_type = _not_ghost) const;
	inline const_element_iterator end(ElementType type,
	GhostType ghost_type = _not_ghost) const;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// empty the element group
	void clear();
	void clear(ElementType type, GhostType ghost_type = _not_ghost);

	bool empty() const __attribute__((warn_unused_result));

	/// append another group to this group
	/// BE CAREFUL: it doesn't conserve the element order
	void append(const ElementGroup & other_group);

	/// add an element to the group. By default the it does not add the nodes to
	/// the group
	inline void add(const Element & el, bool add_nodes = false,
	bool check_for_duplicate = true);

	/// \todo fix the default for add_nodes : make it coherent with the other
	/// method
	inline void add(ElementType type, UInt element,
	GhostType ghost_type = _not_ghost, bool add_nodes = true,
	bool check_for_duplicate = true);

	inline void addNode(UInt node_id, bool check_for_duplicate = true);

	inline void removeNode(UInt node_id);

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/// fill the elements based on the underlying node group.
	virtual void fillFromNodeGroup();

	// sort and remove duplicated values
	void optimize();

	/// change the dimension if needed
	void addDimension(UInt dimension);

	private:
	inline void addElement(ElementType elem_type, UInt elem_id,
	GhostType ghost_type);

	friend class GroupManager;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	const Array<UInt> & getElements(ElementType type,
	GhostType ghost_type = _not_ghost) const;
	AKANTU_GET_MACRO(Elements, elements, const ElementTypeMapArray<UInt> &);
	AKANTU_GET_MACRO_NOT_CONST(Elements, elements, ElementTypeMapArray<UInt> &);

	template <class... Args> auto size(Args &&... pack) const {
	return elements.size(std::forward<Args>(pack)...);
	}

	decltype(auto) getElementsIterable(ElementType type,
	GhostType ghost_type = _not_ghost) const;

	// AKANTU_GET_MACRO(Nodes, node_group.getNodes(), const Array<UInt> &);

	AKANTU_GET_MACRO(NodeGroup, node_group, const NodeGroup &);
	AKANTU_GET_MACRO_NOT_CONST(NodeGroup, node_group, NodeGroup &);

	AKANTU_GET_MACRO(Dimension, dimension, UInt);
	AKANTU_GET_MACRO(Name, name, std::string);
	inline UInt getNbNodes() const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// Mesh to which this group belongs
	const Mesh & mesh;

	/// name of the group
	std::string name;

	/// list of elements composing the group
	ElementList elements;

	/// sub list of nodes which are composing the elements
	NodeGroup & node_group;

	/// group dimension
	UInt dimension{_all_dimensions};

	/// empty arry for the iterator to work when an element type not present
	Array<UInt> empty_elements;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const ElementGroup & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "element.hh"
	#include "element_group_inline_impl.hh"

	#endif /* AKANTU_ELEMENT_GROUP_HH_ */
	diff --git a/src/mesh/element_group_inline_impl.hh b/src/mesh/element_group_inline_impl.hh
	index d2e447805..80e3fb84d 100644
	--- a/src/mesh/element_group_inline_impl.hh
	+++ b/src/mesh/element_group_inline_impl.hh
	@@ -1,148 +1,148 @@
	/**
	* @file element_group_inline_impl.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Tue Mar 09 2021
	*
	* @brief Stores information relevent to the notion of domain boundary and
	* surfaces.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	+#include "aka_iterators.hh"
	#include "element_group.hh"
	#include "mesh.hh"
	-#include "aka_iterators.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_GROUP_INLINE_IMPL_HH_
	#define AKANTU_ELEMENT_GROUP_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline void ElementGroup::add(const Element & el, bool add_nodes,
	bool check_for_duplicate) {
	this->add(el.type, el.element, el.ghost_type, add_nodes, check_for_duplicate);
	}

	/* -------------------------------------------------------------------------- */

	inline void ElementGroup::add(ElementType type, UInt element,
	GhostType ghost_type, bool add_nodes,
	bool check_for_duplicate) {

	addElement(type, element, ghost_type);

	if (add_nodes) {
	Array<UInt>::const_vector_iterator it =
	mesh.getConnectivity(type, ghost_type)
	.begin(mesh.getNbNodesPerElement(type)) +
	element;
	const Vector<UInt> & conn = *it;
	for (UInt i = 0; i < conn.size(); ++i) {
	addNode(conn[i], check_for_duplicate);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void ElementGroup::addNode(UInt node_id, bool check_for_duplicate) {
	node_group.add(node_id, check_for_duplicate);
	}

	/* -------------------------------------------------------------------------- */
	inline void ElementGroup::removeNode(UInt node_id) {
	node_group.remove(node_id);
	}

	/* -------------------------------------------------------------------------- */
	inline void ElementGroup::addElement(ElementType elem_type, UInt elem_id,
	GhostType ghost_type) {
	if (!(elements.exists(elem_type, ghost_type))) {
	elements.alloc(0, 1, elem_type, ghost_type);
	}

	elements(elem_type, ghost_type).push_back(elem_id);
	this->dimension = UInt(
	std::max(Int(this->dimension), Int(mesh.getSpatialDimension(elem_type))));
	}

	/* -------------------------------------------------------------------------- */
	inline UInt ElementGroup::getNbNodes() const { return node_group.size(); }

	/* -------------------------------------------------------------------------- */
	inline ElementGroup::type_iterator
	ElementGroup::firstType(UInt dim, GhostType ghost_type,
	ElementKind kind) const {
	return elements.elementTypes(dim, ghost_type, kind).begin();
	}

	/* -------------------------------------------------------------------------- */
	inline ElementGroup::type_iterator
	ElementGroup::lastType(UInt dim, GhostType ghost_type, ElementKind kind) const {
	return elements.elementTypes(dim, ghost_type, kind).end();
	}

	/* -------------------------------------------------------------------------- */
	inline ElementGroup::const_element_iterator
	ElementGroup::begin(ElementType type, GhostType ghost_type) const {
	if (elements.exists(type, ghost_type)) {
	return elements(type, ghost_type).begin();
	}
	return empty_elements.begin();
	}

	/* -------------------------------------------------------------------------- */
	inline ElementGroup::const_element_iterator
	ElementGroup::end(ElementType type, GhostType ghost_type) const {
	if (elements.exists(type, ghost_type)) {
	return elements(type, ghost_type).end();
	}
	return empty_elements.end();
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<UInt> &
	ElementGroup::getElements(ElementType type, GhostType ghost_type) const {
	if (elements.exists(type, ghost_type)) {
	return elements(type, ghost_type);
	}
	return empty_elements;
	}

	/* -------------------------------------------------------------------------- */
	inline decltype(auto)
	ElementGroup::getElementsIterable(ElementType type,
	GhostType ghost_type) const {
	return make_transform_adaptor(this->elements(type, ghost_type),
	[type, ghost_type](auto && el) {
	return Element{type, el, ghost_type};
	});
	}

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_GROUP_INLINE_IMPL_HH_ */
	diff --git a/src/mesh/element_type_map.cc b/src/mesh/element_type_map.cc
	index 62ed6ee7e..0a72b2940 100644
	--- a/src/mesh/element_type_map.cc
	+++ b/src/mesh/element_type_map.cc
	@@ -1,75 +1,73 @@
	/**
	* @file element_type_map.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 04 2020
	*
	* @brief storage class by element type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	FEEngineElementTypeMapArrayInitializer::FEEngineElementTypeMapArrayInitializer(
	const FEEngine & fe_engine, UInt nb_component, UInt spatial_dimension,
	GhostType ghost_type, ElementKind element_kind)
	: MeshElementTypeMapArrayInitializer(
	fe_engine.getMesh(), nb_component,
	spatial_dimension == UInt(-2)
	? fe_engine.getMesh().getSpatialDimension()
	: spatial_dimension,
	ghost_type, element_kind, true, false),
	fe_engine(fe_engine) {}

	FEEngineElementTypeMapArrayInitializer::FEEngineElementTypeMapArrayInitializer(
	const FEEngine & fe_engine,
	const ElementTypeMapArrayInitializer::CompFunc & nb_component,
	- UInt spatial_dimension, GhostType ghost_type,
	- ElementKind element_kind)
	+ UInt spatial_dimension, GhostType ghost_type, ElementKind element_kind)
	: MeshElementTypeMapArrayInitializer(
	fe_engine.getMesh(), nb_component,
	spatial_dimension == UInt(-2)
	? fe_engine.getMesh().getSpatialDimension()
	: spatial_dimension,
	ghost_type, element_kind, true, false),
	fe_engine(fe_engine) {}

	-UInt FEEngineElementTypeMapArrayInitializer::size(
	- ElementType type) const {
	+UInt FEEngineElementTypeMapArrayInitializer::size(ElementType type) const {
	return MeshElementTypeMapArrayInitializer::size(type) *
	fe_engine.getNbIntegrationPoints(type, this->ghost_type);
	}

	FEEngineElementTypeMapArrayInitializer::ElementTypesIteratorHelper
	FEEngineElementTypeMapArrayInitializer::elementTypes() const {
	return this->fe_engine.elementTypes(spatial_dimension, ghost_type,
	element_kind);
	}

	} // namespace akantu
	diff --git a/src/mesh/element_type_map.hh b/src/mesh/element_type_map.hh
	index 8df2e43bb..be672563d 100644
	--- a/src/mesh/element_type_map.hh
	+++ b/src/mesh/element_type_map.hh
	@@ -1,492 +1,492 @@
	/**
	* @file element_type_map.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 31 2011
	* @date last modification: Thu Mar 11 2021
	*
	* @brief storage class by element type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_named_argument.hh"
	#include "element.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_TYPE_MAP_HH_
	#define AKANTU_ELEMENT_TYPE_MAP_HH_

	namespace akantu {
	class FEEngine;
	} // namespace akantu

	namespace akantu {

	namespace {
	DECLARE_NAMED_ARGUMENT(all_ghost_types);
	DECLARE_NAMED_ARGUMENT(default_value);
	DECLARE_NAMED_ARGUMENT(element_kind);
	DECLARE_NAMED_ARGUMENT(ghost_type);
	DECLARE_NAMED_ARGUMENT(nb_component);
	DECLARE_NAMED_ARGUMENT(nb_component_functor);
	DECLARE_NAMED_ARGUMENT(with_nb_element);
	DECLARE_NAMED_ARGUMENT(with_nb_nodes_per_element);
	DECLARE_NAMED_ARGUMENT(spatial_dimension);
	DECLARE_NAMED_ARGUMENT(do_not_default);
	DECLARE_NAMED_ARGUMENT(element_filter);
	} // namespace

	template <class Stored, typename SupportType = ElementType>
	class ElementTypeMap;

	/* -------------------------------------------------------------------------- */
	/* ElementTypeMapBase */
	/* -------------------------------------------------------------------------- */
	/// Common non templated base class for the ElementTypeMap class
	class ElementTypeMapBase {
	public:
	virtual ~ElementTypeMapBase() = default;
	};

	/* -------------------------------------------------------------------------- */
	/* ElementTypeMap */
	/* -------------------------------------------------------------------------- */

	template <class Stored, typename SupportType>
	class ElementTypeMap : public ElementTypeMapBase {

	public:
	ElementTypeMap();
	~ElementTypeMap() override;

	inline static std::string printType(const SupportType & type,
	GhostType ghost_type);

	/*! Tests whether a type is present in the object
	* @param type the type to check for
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is searched
	* @return true if the type is present. */
	inline bool exists(const SupportType & type,
	GhostType ghost_type = _not_ghost) const;

	/*! get the stored data corresponding to a type
	* @param type the type to check for
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is searched
	* @return stored data corresponding to type. */
	inline const Stored & operator()(const SupportType & type,
	GhostType ghost_type = _not_ghost) const;

	/*! get the stored data corresponding to a type
	* @param type the type to check for
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is searched
	* @return stored data corresponding to type. */
	inline Stored & operator()(const SupportType & type,
	GhostType ghost_type = _not_ghost);

	/*! insert data of a new type (not yet present) into the map. THIS METHOD IS
	* NOT ARRAY SAFE, when using ElementTypeMapArray, use setArray instead
	* @param data to insert
	* @param type type of data (if this type is already present in the map,
	* an exception is thrown).
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is searched
	* @return stored data corresponding to type. */
	template <typename U>
	inline Stored & operator()(U && insertee, const SupportType & type,
	GhostType ghost_type = _not_ghost);

	public:
	/// print helper
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/* ------------------------------------------------------------------------ */
	/* Element type Iterator */
	/* ------------------------------------------------------------------------ */
	/*! iterator allows to iterate over type-data pairs of the map. The interface
	* expects the SupportType to be ElementType. */
	using DataMap = std::map<SupportType, Stored>;

	/// helper class to use in range for constructions
	class type_iterator
	: private std::iterator<std::forward_iterator_tag, const SupportType> {
	public:
	using value_type = const SupportType;
	using pointer = const SupportType *;
	using reference = const SupportType &;

	protected:
	using DataMapIterator =
	typename ElementTypeMap<Stored>::DataMap::const_iterator;

	public:
	type_iterator(DataMapIterator & list_begin, DataMapIterator & list_end,
	UInt dim, ElementKind ek);

	type_iterator(const type_iterator & it);
	type_iterator() = default;

	inline reference operator*();
	inline reference operator*() const;
	inline type_iterator & operator++();
	type_iterator operator++(int);
	inline bool operator==(const type_iterator & other) const;
	inline bool operator!=(const type_iterator & other) const;
	type_iterator & operator=(const type_iterator & it);

	private:
	DataMapIterator list_begin;
	DataMapIterator list_end;
	UInt dim;
	ElementKind kind;
	};

	/// helper class to use in range for constructions
	class ElementTypesIteratorHelper {
	public:
	using Container = ElementTypeMap<Stored, SupportType>;
	using iterator = typename Container::type_iterator;

	ElementTypesIteratorHelper(const Container & container, UInt dim,
	GhostType ghost_type, ElementKind kind)
	: container(std::cref(container)), dim(dim), ghost_type(ghost_type),
	kind(kind) {}

	template <typename... pack>
	ElementTypesIteratorHelper(const Container & container,
	use_named_args_t /unused/, pack &&... _pack)
	: ElementTypesIteratorHelper(
	container, OPTIONAL_NAMED_ARG(spatial_dimension, _all_dimensions),
	OPTIONAL_NAMED_ARG(ghost_type, _not_ghost),
	OPTIONAL_NAMED_ARG(element_kind, _ek_not_defined)) {}

	ElementTypesIteratorHelper(const ElementTypesIteratorHelper &) = default;
	ElementTypesIteratorHelper &
	operator=(const ElementTypesIteratorHelper &) = default;
	ElementTypesIteratorHelper &
	operator=(ElementTypesIteratorHelper &&) noexcept = default;

	iterator begin();
	iterator end();

	private:
	std::reference_wrapper<const Container> container;
	UInt dim;
	GhostType ghost_type;
	ElementKind kind;
	};

	private:
	ElementTypesIteratorHelper
	elementTypesImpl(UInt dim = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const;

	template <typename... pack>
	ElementTypesIteratorHelper
	elementTypesImpl(const use_named_args_t & /unused/, pack &&... _pack) const;

	public:
	/*!
	* \param _pack
	* \parblock
	* represent optional parameters:
	* \li \c _spatial_dimension filter for elements of given spatial
	* dimension
	* \li \c _ghost_type filter for a certain ghost_type
	* \li \c _element_kind filter for elements of given kind
	* \endparblock
	*/
	template <typename... pack>
	std::enable_if_t<are_named_argument<pack...>::value,
	ElementTypesIteratorHelper>
	elementTypes(pack &&... _pack) const {
	return elementTypesImpl(use_named_args,
	std::forward<decltype(_pack)>(_pack)...);
	}

	template <typename... pack>
	std::enable_if_t<not are_named_argument<pack...>::value,
	ElementTypesIteratorHelper>
	elementTypes(pack &&... _pack) const {
	return elementTypesImpl(std::forward<decltype(_pack)>(_pack)...);
	}

	/*! Get an iterator to the beginning of a subset datamap. This method expects
	* the SupportType to be ElementType.
	* @param dim optional: iterate over data of dimension dim (e.g. when
	* iterating over (surface) facets of a 3D mesh, dim would be 2).
	* by default, all dimensions are considered.
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is iterated over.
	* @param kind optional: the kind of element to search for (see
	* aka_common.hh), by default all kinds are considered
	* @return an iterator to the first stored data matching the filters
	* or an iterator to the end of the map if none match*/
	[[deprecated("Use elementTypes instead")]] inline type_iterator
	firstType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const;
	/*! Get an iterator to the end of a subset datamap. This method expects
	* the SupportType to be ElementType.
	* @param dim optional: iterate over data of dimension dim (e.g. when
	* iterating over (surface) facets of a 3D mesh, dim would be 2).
	* by default, all dimensions are considered.
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is iterated over.
	* @param kind optional: the kind of element to search for (see
	* aka_common.hh), by default all kinds are considered
	* @return an iterator to the last stored data matching the filters
	* or an iterator to the end of the map if none match */
	[[deprecated("Use elementTypes instead")]] inline type_iterator
	lastType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const;

	/*! Direct access to the underlying data map. for internal use by daughter
	* classes only
	* @param ghost_type whether to return the data map or the ghost_data map
	* @return the raw map */
	inline DataMap & getData(GhostType ghost_type);
	/*! Direct access to the underlying data map. for internal use by daughter
	* classes only
	* @param ghost_type whether to return the data map or the ghost_data map
	* @return the raw map */
	inline const DataMap & getData(GhostType ghost_type) const;

	/* ------------------------------------------------------------------------ */
	protected:
	DataMap data;
	DataMap ghost_data;
	};

	/* -------------------------------------------------------------------------- */
	/* Some typedefs */
	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	class ElementTypeMapArray
	: public ElementTypeMap<std::unique_ptr<Array<T>>, SupportType> {
	public:
	using value_type = T;
	using array_type = Array<T>;

	protected:
	using parent = ElementTypeMap<std::unique_ptr<Array<T>>, SupportType>;
	using DataMap = typename parent::DataMap;

	public:
	using type_iterator = typename parent::type_iterator;

	/// standard assigment (copy) operator
	void operator=(const ElementTypeMapArray &) = delete;
	ElementTypeMapArray(const ElementTypeMapArray & /other/);

	/// explicit copy
	void copy(const ElementTypeMapArray & other);

	/*! Constructor
	* @param id optional: identifier (string)
	* @param parent_id optional: parent identifier. for organizational purposes
	* only
	*/
	ElementTypeMapArray(const ID & id = "by_element_type_array",
	const ID & parent_id = "no_parent")
	: parent(), id(parent_id + ":" + id), name(id){};

	/*! allocate memory for a new array
	* @param size number of tuples of the new array
	* @param nb_component tuple size
	* @param type the type under which the array is indexed in the map
	* @param ghost_type whether to add the field to the data map or the
	* ghost_data map
	* @param default_value the default value to use to fill the array
	* @return a reference to the allocated array */
	inline Array<T> & alloc(UInt size, UInt nb_component,
	const SupportType & type, GhostType ghost_type,
	const T & default_value = T());

	/*! allocate memory for a new array in both the data and the ghost_data map
	* @param size number of tuples of the new array
	* @param nb_component tuple size
	* @param type the type under which the array is indexed in the map
	* @param default_value the default value to use to fill the array
	*/
	inline void alloc(UInt size, UInt nb_component, const SupportType & type,
	const T & default_value = T());

	/* get a reference to the array of certain type
	* @param type data filed under type is returned
	* @param ghost_type optional: by default the non-ghost map is searched
	* @return a reference to the array */
	inline const Array<T> & operator()(const SupportType & type,
	GhostType ghost_type = _not_ghost) const;

	/// access the data of an element, this combine the map and array accessor
	inline const T & operator()(const Element & element,
	UInt component = 0) const;

	/// access the data of an element, this combine the map and array accessor
	inline T & operator()(const Element & element, UInt component = 0);

	/// access the data of an element, this combine the map and array accessor
	inline decltype(auto) get(const Element & element);
	inline decltype(auto) get(const Element & element) const;

	/* get a reference to the array of certain type
	* @param type data filed under type is returned
	* @param ghost_type optional: by default the non-ghost map is searched
	* @return a const reference to the array */
	inline Array<T> & operator()(const SupportType & type,
	GhostType ghost_type = _not_ghost);

	/*! insert data of a new type (not yet present) into the map.
	* @param type type of data (if this type is already present in the map,
	* an exception is thrown).
	* @param ghost_type optional: by default, the data map for non-ghost
	* elements is searched
	* @param vect the vector to include into the map
	* @return stored data corresponding to type. */
	inline void setArray(const SupportType & type, GhostType ghost_type,
	const Array<T> & vect);
	/! frees all memory related to the data/
	inline void free();

	inline void clear();

	inline bool empty() const __attribute__((warn_unused_result));

	/! set all values in the ElementTypeMap to zero/
	inline void zero() { this->set(T()); }

	/! set all values in the ElementTypeMap to value /
	template <typename ST> inline void set(const ST & value);

	/*! deletes and reorders entries in the stored arrays
	* @param new_numbering a ElementTypeMapArray of new indices. UInt(-1)
	* indicates
	* deleted entries. */
	inline void
	onElementsRemoved(const ElementTypeMapArray<UInt> & new_numbering);

	/// text output helper
	void printself(std::ostream & stream, int indent = 0) const override;

	/*! set the id
	* @param id the new name
	*/
	inline void setID(const ID & id) { this->id = id; }

	/// return the id
	inline auto getID() const -> ID { return this->id; }

	ElementTypeMap<UInt>
	getNbComponents(UInt dim = _all_dimensions,
	GhostType requested_ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const {
	ElementTypeMap<UInt> nb_components;
	bool all_ghost_types = requested_ghost_type == _casper;
	for (auto ghost_type : ghost_types) {
	if ((not(ghost_type == requested_ghost_type)) and (not all_ghost_types)) {
	continue;
	}

	for (auto & type : this->elementTypes(dim, ghost_type, kind)) {
	UInt nb_comp = (*this)(type, ghost_type).getNbComponent();
	nb_components(type, ghost_type) = nb_comp;
	}
	}
	return nb_components;
	}

	/* ------------------------------------------------------------------------ */
	/* more evolved allocators */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the arrays in accordance to a functor
	template <class Func>
	void initialize(const Func & f, const T & default_value, bool do_not_default);

	/// initialize with sizes and number of components in accordance of a mesh
	/// content
	template <typename... pack>
	void initialize(const Mesh & mesh, pack &&... _pack);

	/// initialize with sizes and number of components in accordance of a fe
	/// engine content (aka integration points)
	template <typename... pack>
	void initialize(const FEEngine & fe_engine, pack &&... _pack);

	/* ------------------------------------------------------------------------ */
	/* Accesssors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the name of the internal field
	AKANTU_GET_MACRO(Name, name, ID);

	/**
	* get the size of the ElementTypeMapArray<T>
	* @param[in] _pack
	* \parblock
	* optional arguments can be any of:
	* \li \c _spatial_dimension the dimension to consider (default:
	* _all_dimensions)
	* \li \c _ghost_type (default: _not_ghost)
	* \li \c _element_kind (default: _ek_not_defined)
	* \li \c _all_ghost_types (default: false)
	* \endparblock
	**/
	template <typename... pack> UInt size(pack &&... _pack) const;

	bool isNodal() const { return is_nodal; }
	void isNodal(bool is_nodal) { this->is_nodal = is_nodal; }

	private:
	UInt sizeImpl(UInt spatial_dimension, GhostType ghost_type,
	ElementKind kind) const;

	private:
	ID id;

	protected:
	/// name of the element type map: e.g. connectivity, grad_u
	ID name;

	/// Is the data stored by node of the element
	bool is_nodal{false};
	};

	/// to store data Array<Real> by element type
	using ElementTypeMapReal = ElementTypeMapArray<Real>;
	/// to store data Array<Int> by element type
	using ElementTypeMapInt = ElementTypeMapArray<Int>;
	/// to store data Array<UInt> by element type
	using ElementTypeMapUInt = ElementTypeMapArray<UInt, ElementType>;

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_TYPE_MAP_HH_ */
	diff --git a/src/mesh/element_type_map_filter.hh b/src/mesh/element_type_map_filter.hh
	index 8713d0300..2ad599dc2 100644
	--- a/src/mesh/element_type_map_filter.hh
	+++ b/src/mesh/element_type_map_filter.hh
	@@ -1,130 +1,130 @@
	/**
	* @file element_type_map_filter.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 02 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Filtered version based on a an akantu::ElementGroup of a
	* akantu::ElementTypeMap
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/
	/* -------------------------------------------------------------------------- */
	#include "aka_array_filter.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BY_ELEMENT_TYPE_FILTER_HH_
	#define AKANTU_BY_ELEMENT_TYPE_FILTER_HH_
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* ElementTypeMapFilter */
	/* -------------------------------------------------------------------------- */

	template <class T, typename SupportType = ElementType>
	class ElementTypeMapArrayFilter {

	/* ------------------------------------------------------------------------ */
	/* Typedefs */
	/* ------------------------------------------------------------------------ */

	public:
	using array_type = ArrayFilter<T>;
	using value_type = typename array_type::value_type;

	using type_iterator =
	typename ElementTypeMapArray<UInt, SupportType>::type_iterator;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ElementTypeMapArrayFilter(
	const ElementTypeMapArray<T, SupportType> & array,
	const ElementTypeMapArray<UInt, SupportType> & filter,
	const ElementTypeMap<UInt, SupportType> & nb_data_per_elem)
	: array(array), filter(filter), nb_data_per_elem(nb_data_per_elem) {}

	ElementTypeMapArrayFilter(
	const ElementTypeMapArray<T, SupportType> & array,
	const ElementTypeMapArray<UInt, SupportType> & filter)
	: array(array), filter(filter) {}

	~ElementTypeMapArrayFilter() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */

	inline ArrayFilter<T> operator()(const SupportType & type,
	GhostType ghost_type = _not_ghost) const {
	if (filter.exists(type, ghost_type)) {
	if (nb_data_per_elem.exists(type, ghost_type)) {
	return ArrayFilter<T>(array(type, ghost_type), filter(type, ghost_type),
	nb_data_per_elem(type, ghost_type) /
	array(type, ghost_type).getNbComponent());
	}
	return ArrayFilter<T>(array(type, ghost_type), filter(type, ghost_type),
	1);
	}
	return ArrayFilter<T>(empty_array, empty_filter, 1);
	};

	template <typename... Args>
	decltype(auto) elementTypes(Args &&... args) const {
	return filter.elementTypes(std::forward<decltype(args)>(args)...);
	}

	decltype(auto) getNbComponents(UInt dim = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const {
	return this->array.getNbComponents(dim, ghost_type, kind);
	};

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	std::string getID() {
	return std::string("filtered:" + this->array().getID());
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */

	protected:
	const ElementTypeMapArray<T, SupportType> & array;
	const ElementTypeMapArray<UInt, SupportType> & filter;
	ElementTypeMap<UInt> nb_data_per_elem;

	/// Empty array to be able to return consistent filtered arrays
	Array<T> empty_array;
	Array<UInt> empty_filter;
	};

	} // namespace akantu

	#endif /* AKANTU_BY_ELEMENT_TYPE_FILTER_HH_ */
	diff --git a/src/mesh/element_type_map_tmpl.hh b/src/mesh/element_type_map_tmpl.hh
	index ca6ee7313..a17a06e1f 100644
	--- a/src/mesh/element_type_map_tmpl.hh
	+++ b/src/mesh/element_type_map_tmpl.hh
	@@ -1,852 +1,852 @@
	/**
	* @file element_type_map_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 31 2011
	* @date last modification: Thu Mar 11 2021
	*
	* @brief implementation of template functions of the ElementTypeMap and
	* ElementTypeMapArray classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_static_if.hh"
	#include "element_type_map.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_type_conversion.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_TYPE_MAP_TMPL_HH_
	#define AKANTU_ELEMENT_TYPE_MAP_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* ElementTypeMap */
	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline std::string
	ElementTypeMap<Stored, SupportType>::printType(const SupportType & type,
	GhostType ghost_type) {
	std::stringstream sstr;
	sstr << "(" << ghost_type << ":" << type << ")";
	return sstr.str();
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline bool
	ElementTypeMap<Stored, SupportType>::exists(const SupportType & type,
	GhostType ghost_type) const {
	return this->getData(ghost_type).find(type) !=
	this->getData(ghost_type).end();
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline const Stored &
	ElementTypeMap<Stored, SupportType>::operator()(const SupportType & type,
	GhostType ghost_type) const {
	auto it = this->getData(ghost_type).find(type);

	if (it == this->getData(ghost_type).end()) {
	AKANTU_SILENT_EXCEPTION("No element of type "
	<< ElementTypeMap::printType(type, ghost_type)
	<< " in this ElementTypeMap<"
	<< debug::demangle(typeid(Stored).name())
	<< "> class");
	}
	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline Stored &
	ElementTypeMap<Stored, SupportType>::operator()(const SupportType & type,
	GhostType ghost_type) {
	return this->getData(ghost_type)[type];
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	template <typename U>
	inline Stored & ElementTypeMap<Stored, SupportType>::operator()(
	U && insertee, const SupportType & type, GhostType ghost_type) {
	auto it = this->getData(ghost_type).find(type);

	if (it != this->getData(ghost_type).end()) {
	AKANTU_SILENT_EXCEPTION("Element of type "
	<< ElementTypeMap::printType(type, ghost_type)
	<< " already in this ElementTypeMap<"
	<< debug::demangle(typeid(Stored).name())
	<< "> class");
	} else {
	auto & data = this->getData(ghost_type);
	const auto & res =
	data.insert(std::make_pair(type, std::forward<U>(insertee)));
	it = res.first;
	}

	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline typename ElementTypeMap<Stored, SupportType>::DataMap &
	ElementTypeMap<Stored, SupportType>::getData(GhostType ghost_type) {
	if (ghost_type == _not_ghost) {
	return data;
	}

	return ghost_data;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline const typename ElementTypeMap<Stored, SupportType>::DataMap &
	ElementTypeMap<Stored, SupportType>::getData(GhostType ghost_type) const {
	if (ghost_type == _not_ghost) {
	return data;
	}

	return ghost_data;
	}

	/* -------------------------------------------------------------------------- */
	/// Works only if stored is a pointer to a class with a printself method
	template <class Stored, typename SupportType>
	void ElementTypeMap<Stored, SupportType>::printself(std::ostream & stream,
	int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "ElementTypeMap<" << debug::demangle(typeid(Stored).name())
	<< "> [" << std::endl;
	for (auto && gt : ghost_types) {
	const DataMap & data = getData(gt);
	for (auto & pair : data) {
	stream << space << space << ElementTypeMap::printType(pair.first, gt)
	<< std::endl;
	}
	}

	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	ElementTypeMap<Stored, SupportType>::ElementTypeMap() = default;

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	ElementTypeMap<Stored, SupportType>::~ElementTypeMap() = default;

	/* -------------------------------------------------------------------------- */
	/* ElementTypeMapArray */
	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	void ElementTypeMapArray<T, SupportType>::copy(
	const ElementTypeMapArray & other) {
	for (auto ghost_type : ghost_types) {
	for (auto type :
	this->elementTypes(_all_dimensions, ghost_type, _ek_not_defined)) {
	const auto & array_to_copy = other(type, ghost_type);
	auto & array =
	this->alloc(0, array_to_copy.getNbComponent(), type, ghost_type);
	array.copy(array_to_copy);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	ElementTypeMapArray<T, SupportType>::ElementTypeMapArray(
	const ElementTypeMapArray & other)
	: parent(), id(other.id + "_copy"), name(other.name + "_copy") {
	this->copy(other);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline Array<T> & ElementTypeMapArray<T, SupportType>::alloc(
	UInt size, UInt nb_component, const SupportType & type,
	GhostType ghost_type, const T & default_value) {
	std::string ghost_id;
	if (ghost_type == _ghost) {
	ghost_id = ":ghost";
	}

	auto it = this->getData(ghost_type).find(type);

	if (it == this->getData(ghost_type).end()) {
	auto id = this->id + ":" + std::to_string(type) + ghost_id;

	this->getData(ghost_type)[type] =
	std::make_unique<Array<T>>(size, nb_component, default_value, id);
	return *(this->getData(ghost_type)[type]);
	}

	AKANTU_DEBUG_INFO("The vector "
	<< this->id << this->printType(type, ghost_type)
	<< " already exists, it is resized instead of allocated.");
	auto && array = *(it->second);
	array.resize(size);
	return array;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline void
	ElementTypeMapArray<T, SupportType>::alloc(UInt size, UInt nb_component,
	const SupportType & type,
	const T & default_value) {
	this->alloc(size, nb_component, type, _not_ghost, default_value);
	this->alloc(size, nb_component, type, _ghost, default_value);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline void ElementTypeMapArray<T, SupportType>::free() {
	AKANTU_DEBUG_IN();

	for (auto gt : ghost_types) {
	auto & data = this->getData(gt);
	data.clear();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline void ElementTypeMapArray<T, SupportType>::clear() {
	for (auto gt : ghost_types) {
	auto & data = this->getData(gt);
	for (auto & vect : data) {
	vect.second->clear();
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline bool ElementTypeMapArray<T, SupportType>::empty() const {
	bool is_empty = true;
	for (auto gt : ghost_types) {
	auto & data = this->getData(gt);
	for (auto & vect : data) {
	is_empty &= vect.second->empty();
	if (not is_empty) {
	return false;
	}
	}
	}
	return is_empty;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	template <typename ST>
	inline void ElementTypeMapArray<T, SupportType>::set(const ST & value) {
	for (auto gt : ghost_types) {
	auto & data = this->getData(gt);
	for (auto & vect : data) {
	vect.second->set(value);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline const Array<T> &
	ElementTypeMapArray<T, SupportType>::operator()(const SupportType & type,
	GhostType ghost_type) const {
	auto it = this->getData(ghost_type).find(type);

	if (it == this->getData(ghost_type).end()) {
	AKANTU_SILENT_EXCEPTION("No element of type "
	<< ElementTypeMapArray::printType(type, ghost_type)
	<< " in this const ElementTypeMapArray<"
	<< debug::demangle(typeid(T).name()) << "> class(\""
	<< this->id << "\")");
	}
	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline Array<T> &
	ElementTypeMapArray<T, SupportType>::operator()(const SupportType & type,
	GhostType ghost_type) {
	auto it = this->getData(ghost_type).find(type);

	if (it == this->getData(ghost_type).end()) {
	AKANTU_SILENT_EXCEPTION("No element of type "
	<< ElementTypeMapArray::printType(type, ghost_type)
	<< " in this ElementTypeMapArray<"
	<< debug::demangle(typeid(T).name())
	<< "> class (\"" << this->id << "\")");
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline void ElementTypeMapArray<T, SupportType>::setArray(
	const SupportType & type, GhostType ghost_type, const Array<T> & vect) {
	auto it = this->getData(ghost_type).find(type);

	if (AKANTU_DEBUG_TEST(dblWarning) && it != this->getData(ghost_type).end() &&
	it->second != &vect) {
	AKANTU_DEBUG_WARNING(
	"The Array "
	<< this->printType(type, ghost_type)
	<< " is already registred, this call can lead to a memory leak.");
	}

	this->getData(ghost_type)[type] = &(const_cast<Array<T> &>(vect));
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	inline void ElementTypeMapArray<T, SupportType>::onElementsRemoved(
	const ElementTypeMapArray<UInt> & new_numbering) {
	for (auto gt : ghost_types) {
	for (auto && type :
	new_numbering.elementTypes(_all_dimensions, gt, _ek_not_defined)) {
	auto support_type = convertType<ElementType, SupportType>(type);
	if (this->exists(support_type, gt)) {
	const auto & renumbering = new_numbering(type, gt);
	if (renumbering.empty()) {
	continue;
	}

	auto & vect = this->operator()(support_type, gt);
	auto nb_component = vect.getNbComponent();
	Array<T> tmp(renumbering.size(), nb_component);
	UInt new_size = 0;

	for (UInt i = 0; i < vect.size(); ++i) {
	UInt new_i = renumbering(i);
	if (new_i != UInt(-1)) {
	std::copy_n(vect.storage() + i * nb_component, nb_component,
	tmp.storage() + new_i * nb_component);
	++new_size;
	}
	}
	tmp.resize(new_size);
	vect.copy(tmp);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	void ElementTypeMapArray<T, SupportType>::printself(std::ostream & stream,
	int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "ElementTypeMapArray<" << debug::demangle(typeid(T).name())
	<< "> [" << std::endl;
	for (UInt g = _not_ghost; g <= _ghost; ++g) {
	auto gt = (GhostType)g;

	const DataMap & data = this->getData(gt);
	typename DataMap::const_iterator it;
	for (it = data.begin(); it != data.end(); ++it) {
	stream << space << space << ElementTypeMapArray::printType(it->first, gt)
	<< " [" << std::endl;
	it->second->printself(stream, indent + 3);
	stream << space << space << " ]" << std::endl;
	}
	}
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	/* SupportType Iterator */
	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	ElementTypeMap<Stored, SupportType>::type_iterator::type_iterator(
	DataMapIterator & list_begin, DataMapIterator & list_end, UInt dim,
	ElementKind ek)
	: list_begin(list_begin), list_end(list_end), dim(dim), kind(ek) {}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	ElementTypeMap<Stored, SupportType>::type_iterator::type_iterator(
	const type_iterator & it)
	: list_begin(it.list_begin), list_end(it.list_end), dim(it.dim),
	kind(it.kind) {}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	typename ElementTypeMap<Stored, SupportType>::type_iterator &
	ElementTypeMap<Stored, SupportType>::type_iterator::operator=(
	const type_iterator & it) {
	if (this != &it) {
	list_begin = it.list_begin;
	list_end = it.list_end;
	dim = it.dim;
	kind = it.kind;
	}
	return *this;
	}
	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline typename ElementTypeMap<Stored, SupportType>::type_iterator::reference
	ElementTypeMap<Stored, SupportType>::type_iterator::operator*() {
	return list_begin->first;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline typename ElementTypeMap<Stored, SupportType>::type_iterator::reference
	ElementTypeMap<Stored, SupportType>::type_iterator::operator*() const {
	return list_begin->first;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline typename ElementTypeMap<Stored, SupportType>::type_iterator &
	ElementTypeMap<Stored, SupportType>::type_iterator::operator++() {
	++list_begin;
	while ((list_begin != list_end) &&
	(((dim != _all_dimensions) &&
	(dim != Mesh::getSpatialDimension(list_begin->first))) \|\|
	((kind != _ek_not_defined) &&
	(kind != Mesh::getKind(list_begin->first))))) {
	++list_begin;
	}
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	typename ElementTypeMap<Stored, SupportType>::type_iterator
	ElementTypeMap<Stored, SupportType>::type_iterator::operator++(int) {
	type_iterator tmp(*this);
	operator++();
	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline bool ElementTypeMap<Stored, SupportType>::type_iterator::operator==(
	const type_iterator & other) const {
	return this->list_begin == other.list_begin;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline bool ElementTypeMap<Stored, SupportType>::type_iterator::operator!=(
	const type_iterator & other) const {
	return this->list_begin != other.list_begin;
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	auto ElementTypeMap<Stored, SupportType>::ElementTypesIteratorHelper::begin()
	-> iterator {
	auto b = container.get().getData(ghost_type).begin();
	auto e = container.get().getData(ghost_type).end();

	// loop until the first valid type
	while ((b != e) &&
	(((dim != _all_dimensions) &&
	(dim != Mesh::getSpatialDimension(b->first))) \|\|
	((kind != _ek_not_defined) && (kind != Mesh::getKind(b->first))))) {
	++b;
	}

	return iterator(b, e, dim, kind);
	}

	template <class Stored, typename SupportType>
	auto ElementTypeMap<Stored, SupportType>::ElementTypesIteratorHelper::end()
	-> iterator {
	auto e = container.get().getData(ghost_type).end();
	return iterator(e, e, dim, kind);
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	auto ElementTypeMap<Stored, SupportType>::elementTypesImpl(
	UInt dim, GhostType ghost_type, ElementKind kind) const
	-> ElementTypesIteratorHelper {
	return ElementTypesIteratorHelper(*this, dim, ghost_type, kind);
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	template <typename... pack>
	auto ElementTypeMap<Stored, SupportType>::elementTypesImpl(
	const use_named_args_t & unused, pack &&... _pack) const
	-> ElementTypesIteratorHelper {
	return ElementTypesIteratorHelper(*this, unused, _pack...);
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline auto ElementTypeMap<Stored, SupportType>::firstType(
	UInt dim, GhostType ghost_type, ElementKind kind) const -> type_iterator {
	return elementTypes(dim, ghost_type, kind).begin();
	}

	/* -------------------------------------------------------------------------- */
	template <class Stored, typename SupportType>
	inline auto ElementTypeMap<Stored, SupportType>::lastType(
	UInt dim, GhostType ghost_type, ElementKind kind) const -> type_iterator {
	typename DataMap::const_iterator e;
	e = getData(ghost_type).end();
	return typename ElementTypeMap<Stored, SupportType>::type_iterator(e, e, dim,
	kind);
	}

	/* -------------------------------------------------------------------------- */

	/// standard output stream operator
	template <class Stored, typename SupportType>
	inline std::ostream &
	operator<<(std::ostream & stream,
	const ElementTypeMap<Stored, SupportType> & _this) {
	_this.printself(stream);
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	class ElementTypeMapArrayInitializer {
	protected:
	using CompFunc = std::function<UInt(ElementType, GhostType)>;

	public:
	ElementTypeMapArrayInitializer(const CompFunc & comp_func,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined)
	: comp_func(comp_func), spatial_dimension(spatial_dimension),
	ghost_type(ghost_type), element_kind(element_kind) {}

	GhostType ghostType() const { return ghost_type; }

	virtual UInt nbComponent(ElementType type) const {
	return comp_func(type, ghostType());
	}

	virtual bool isNodal() const { return false; }

	protected:
	CompFunc comp_func;
	UInt spatial_dimension;
	GhostType ghost_type;
	ElementKind element_kind;
	};

	/* -------------------------------------------------------------------------- */
	class MeshElementTypeMapArrayInitializer
	: public ElementTypeMapArrayInitializer {
	using CompFunc = ElementTypeMapArrayInitializer::CompFunc;

	public:
	MeshElementTypeMapArrayInitializer(
	const Mesh & mesh, UInt nb_component = 1,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined, bool with_nb_element = false,
	bool with_nb_nodes_per_element = false,
	const ElementTypeMapArray<UInt> * filter = nullptr)
	: MeshElementTypeMapArrayInitializer(
	mesh,
	[nb_component](ElementType /unused/, GhostType /unused/)
	-> UInt { return nb_component; },
	spatial_dimension, ghost_type, element_kind, with_nb_element,
	with_nb_nodes_per_element, filter) {}

	MeshElementTypeMapArrayInitializer(
	const Mesh & mesh, const CompFunc & comp_func,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined, bool with_nb_element = false,
	bool with_nb_nodes_per_element = false,
	const ElementTypeMapArray<UInt> * filter = nullptr)
	: ElementTypeMapArrayInitializer(comp_func, spatial_dimension, ghost_type,
	element_kind),
	mesh(mesh), with_nb_element(with_nb_element),
	with_nb_nodes_per_element(with_nb_nodes_per_element), filter(filter) {}

	decltype(auto) elementTypes() const {
	- if (filter) {
	+ if (filter != nullptr) {
	return filter->elementTypes(this->spatial_dimension, this->ghost_type,
	this->element_kind);
	}
	return mesh.elementTypes(this->spatial_dimension, this->ghost_type,
	this->element_kind);
	}

	virtual UInt size(ElementType type) const {
	if (with_nb_element) {
	- if (filter) {
	+ if (filter != nullptr) {
	return (*filter)(type, this->ghost_type).size();
	}
	return mesh.getNbElement(type, this->ghost_type);
	}

	return 0;
	}

	UInt nbComponent(ElementType type) const override {
	UInt res = ElementTypeMapArrayInitializer::nbComponent(type);
	if (with_nb_nodes_per_element) {
	return (res * Mesh::getNbNodesPerElement(type));
	}

	return res;
	}

	bool isNodal() const override { return with_nb_nodes_per_element; }

	protected:
	const Mesh & mesh;
	bool with_nb_element{false};
	bool with_nb_nodes_per_element{false};
	const ElementTypeMapArray<UInt> * filter{nullptr};
	};

	/* -------------------------------------------------------------------------- */
	class FEEngineElementTypeMapArrayInitializer
	: public MeshElementTypeMapArrayInitializer {
	public:
	FEEngineElementTypeMapArrayInitializer(
	const FEEngine & fe_engine, UInt nb_component = 1,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	FEEngineElementTypeMapArrayInitializer(
	const FEEngine & fe_engine,
	const ElementTypeMapArrayInitializer::CompFunc & nb_component,
	UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined);

	UInt size(ElementType type) const override;

	using ElementTypesIteratorHelper =
	ElementTypeMapArray<Real, ElementType>::ElementTypesIteratorHelper;

	ElementTypesIteratorHelper elementTypes() const;

	protected:
	const FEEngine & fe_engine;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T, typename SupportType>
	template <class Func>
	void ElementTypeMapArray<T, SupportType>::initialize(const Func & f,
	const T & default_value,
	bool do_not_default) {
	this->is_nodal = f.isNodal();
	auto ghost_type = f.ghostType();
	for (auto & type : f.elementTypes()) {
	if (not this->exists(type, ghost_type)) {
	if (do_not_default) {
	auto & array = this->alloc(0, f.nbComponent(type), type, ghost_type);
	array.resize(f.size(type));
	} else {
	this->alloc(f.size(type), f.nbComponent(type), type, ghost_type,
	default_value);
	}
	} else {
	auto & array = this->operator()(type, ghost_type);
	if (not do_not_default) {
	array.resize(f.size(type), default_value);
	} else {
	array.resize(f.size(type));
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* All parameters are named optionals
	* \param _nb_component a functor giving the number of components per
	* (ElementType, GhostType) pair or a scalar giving a unique number of
	* components
	* regardless of type
	* \param _spatial_dimension a filter for the elements of a specific dimension
	* \param _element_kind filter with element kind (_ek_regular, _ek_structural,
	* ...)
	* \param _with_nb_element allocate the arrays with the number of elements for
	* each
	* type in the mesh
	* \param _with_nb_nodes_per_element multiply the number of components by the
	* number of nodes per element
	* \param _default_value default inital value
	* \param _do_not_default do not initialize the allocated arrays
	* \param _ghost_type filter a type of ghost
	*/
	template <typename T, typename SupportType>
	template <typename... pack>
	void ElementTypeMapArray<T, SupportType>::initialize(const Mesh & mesh,
	pack &&... _pack) {
	GhostType requested_ghost_type = OPTIONAL_NAMED_ARG(ghost_type, _casper);
	bool all_ghost_types =
	OPTIONAL_NAMED_ARG(all_ghost_types, requested_ghost_type == _casper);

	for (GhostType ghost_type : ghost_types) {
	if ((not(ghost_type == requested_ghost_type)) and (not all_ghost_types)) {
	continue;
	}

	auto functor = MeshElementTypeMapArrayInitializer(
	mesh, OPTIONAL_NAMED_ARG(nb_component, 1),
	OPTIONAL_NAMED_ARG(spatial_dimension, mesh.getSpatialDimension()),
	ghost_type, OPTIONAL_NAMED_ARG(element_kind, _ek_not_defined),
	OPTIONAL_NAMED_ARG(with_nb_element, false),
	OPTIONAL_NAMED_ARG(with_nb_nodes_per_element, false),
	OPTIONAL_NAMED_ARG(element_filter, nullptr));

	this->initialize(functor, OPTIONAL_NAMED_ARG(default_value, T()),
	OPTIONAL_NAMED_ARG(do_not_default, false));
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* All parameters are named optionals
	* \param _nb_component a functor giving the number of components per
	* (ElementType, GhostType) pair or a scalar giving a unique number of
	* components
	* regardless of type
	* \param _spatial_dimension a filter for the elements of a specific dimension
	* \param _element_kind filter with element kind (_ek_regular, _ek_structural,
	* ...)
	* \param _default_value default inital value
	* \param _do_not_default do not initialize the allocated arrays
	* \param _ghost_type filter a specific ghost type
	* \param _all_ghost_types get all ghost types
	*/
	template <typename T, typename SupportType>
	template <typename... pack>
	void ElementTypeMapArray<T, SupportType>::initialize(const FEEngine & fe_engine,
	pack &&... _pack) {
	GhostType requested_ghost_type = OPTIONAL_NAMED_ARG(ghost_type, _casper);
	bool all_ghost_types =
	OPTIONAL_NAMED_ARG(all_ghost_types, requested_ghost_type == _casper);

	for (auto ghost_type : ghost_types) {
	if ((not(ghost_type == requested_ghost_type)) and (not all_ghost_types)) {
	continue;
	}

	auto functor = FEEngineElementTypeMapArrayInitializer(
	fe_engine, OPTIONAL_NAMED_ARG(nb_component, 1),
	OPTIONAL_NAMED_ARG(spatial_dimension, UInt(-2)), ghost_type,
	OPTIONAL_NAMED_ARG(element_kind, _ek_not_defined));

	this->initialize(functor, OPTIONAL_NAMED_ARG(default_value, T()),
	OPTIONAL_NAMED_ARG(do_not_default, false));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	inline T &
	ElementTypeMapArray<T, SupportType>::operator()(const Element & element,
	UInt component) {
	return this->operator()(element.type, element.ghost_type)(element.element,
	component);
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	inline const T &
	ElementTypeMapArray<T, SupportType>::operator()(const Element & element,
	UInt component) const {
	return this->operator()(element.type, element.ghost_type)(element.element,
	component);
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	inline decltype(auto)
	ElementTypeMapArray<T, SupportType>::get(const Element & element) {
	auto & array = operator()(element.type, element.ghost_type);
	auto it = array.begin(array.getNbComponent());
	return it[element.element];
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	inline decltype(auto)
	ElementTypeMapArray<T, SupportType>::get(const Element & element) const {
	auto & array = operator()(element.type, element.ghost_type);
	auto it = array.begin(array.getNbComponent());
	return it[element.element];
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	UInt ElementTypeMapArray<T, SupportType>::sizeImpl(UInt spatial_dimension,
	GhostType ghost_type,
	ElementKind kind) const {
	UInt size = 0;
	for (auto && type : this->elementTypes(spatial_dimension, ghost_type, kind)) {
	size += this->operator()(type, ghost_type).size();
	}
	return size;
	}

	/* -------------------------------------------------------------------------- */
	template <class T, typename SupportType>
	template <typename... pack>
	UInt ElementTypeMapArray<T, SupportType>::size(pack &&... _pack) const {
	UInt size = 0;
	GhostType requested_ghost_type = OPTIONAL_NAMED_ARG(ghost_type, _casper);
	bool all_ghost_types =
	OPTIONAL_NAMED_ARG(all_ghost_types, requested_ghost_type == _casper);

	for (auto ghost_type : ghost_types) {
	if ((not(ghost_type == requested_ghost_type)) and (not all_ghost_types)) {
	continue;
	}

	size +=
	sizeImpl(OPTIONAL_NAMED_ARG(spatial_dimension, _all_dimensions),
	ghost_type, OPTIONAL_NAMED_ARG(element_kind, _ek_not_defined));
	}
	return size;
	}

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_TYPE_MAP_TMPL_HH_ */
	diff --git a/src/mesh/group_manager.cc b/src/mesh/group_manager.cc
	index d2d9984be..e2a9598df 100644
	--- a/src/mesh/group_manager.cc
	+++ b/src/mesh/group_manager.cc
	@@ -1,1035 +1,1034 @@
	/**
	* @file group_manager.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@gmail.com>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Thu Nov 12 2020
	*
	* @brief Stores information about ElementGroup and NodeGroup
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "group_manager.hh"
	#include "aka_csr.hh"
	#include "data_accessor.hh"
	#include "element_group.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "mesh_utils.hh"
	#include "node_group.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <iterator>
	#include <list>
	#include <numeric>
	#include <queue>
	#include <sstream>
	#include <utility>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-GroupManager::GroupManager(Mesh & mesh, const ID & id)
	- : id(id), mesh(mesh) {
	+GroupManager::GroupManager(Mesh & mesh, const ID & id) : id(id), mesh(mesh) {

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	GroupManager::~GroupManager() = default;

	/* -------------------------------------------------------------------------- */
	NodeGroup & GroupManager::createNodeGroup(const std::string & group_name,
	bool replace_group) {
	AKANTU_DEBUG_IN();

	auto it = node_groups.find(group_name);

	if (it != node_groups.end()) {
	if (replace_group) {
	it->second.reset();
	} else {
	AKANTU_EXCEPTION(
	"Trying to create a node group that already exists:" << group_name);
	}
	}

	std::stringstream sstr;
	sstr << this->id << ":" << group_name << "_node_group";

	- auto && ptr =
	- std::make_unique<NodeGroup>(group_name, mesh, sstr.str());
	+ auto && ptr = std::make_unique<NodeGroup>(group_name, mesh, sstr.str());

	auto & node_group = *ptr;

	// \todo insert_or_assign in c++17
	if (it != node_groups.end()) {
	it->second = std::move(ptr);
	} else {
	node_groups[group_name] = std::move(ptr);
	}

	AKANTU_DEBUG_OUT();

	return node_group;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	NodeGroup &
	GroupManager::createFilteredNodeGroup(const std::string & group_name,
	const NodeGroup & source_node_group,
	T & filter) {
	AKANTU_DEBUG_IN();

	NodeGroup & node_group = this->createNodeGroup(group_name);
	node_group.append(source_node_group);
	if (T::type == FilterFunctor::_node_filter_functor) {
	node_group.applyNodeFilter(filter);
	} else {
	AKANTU_ERROR("ElementFilter cannot be applied to NodeGroup yet."
	<< " Needs to be implemented.");
	}

	AKANTU_DEBUG_OUT();
	return node_group;
	}

	/* -------------------------------------------------------------------------- */
	ElementGroup & GroupManager::createElementGroup(const std::string & group_name,
	UInt dimension,
	bool replace_group) {
	AKANTU_DEBUG_IN();

	auto it = element_groups.find(group_name);
	if (it != element_groups.end()) {
	if (replace_group) {
	it->second.reset();
	} else {
	AKANTU_EXCEPTION("Trying to create a element group that already exists:"
	<< group_name);
	}
	}

	NodeGroup & new_node_group =
	createNodeGroup(group_name + "_nodes", replace_group);

	auto && ptr = std::make_unique<ElementGroup>(
	group_name, mesh, new_node_group, dimension,
	this->id + ":" + group_name + "_element_group");

	auto & element_group = *ptr;

	if (it != element_groups.end()) {
	it->second = std::move(ptr);
	} else {
	element_groups[group_name] = std::move(ptr);
	}

	AKANTU_DEBUG_OUT();

	return element_group;
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::destroyElementGroup(const std::string & group_name,
	bool destroy_node_group) {
	AKANTU_DEBUG_IN();

	auto eit = element_groups.find(group_name);
	if (eit != element_groups.end()) {
	if (destroy_node_group) {
	destroyNodeGroup(eit->second->getNodeGroup().getName());
	}
	element_groups.erase(eit);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::destroyNodeGroup(const std::string & group_name) {
	AKANTU_DEBUG_IN();

	auto nit = node_groups.find(group_name);
	if (nit != node_groups.end()) {
	node_groups.erase(nit);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ElementGroup & GroupManager::createElementGroup(const std::string & group_name,
	UInt dimension,
	NodeGroup & node_group) {
	AKANTU_DEBUG_IN();

	if (element_groups.find(group_name) != element_groups.end()) {
	AKANTU_EXCEPTION(
	"Trying to create a element group that already exists:" << group_name);
	}

	- auto && ptr = std::make_unique<ElementGroup>(
	- group_name, mesh, node_group, dimension,
	- id + ":" + group_name + "_element_group");
	+ auto && ptr =
	+ std::make_unique<ElementGroup>(group_name, mesh, node_group, dimension,
	+ id + ":" + group_name + "_element_group");

	auto & element_group = *ptr;
	element_groups[group_name] = std::move(ptr);

	AKANTU_DEBUG_OUT();

	return element_group;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	ElementGroup & GroupManager::createFilteredElementGroup(
	const std::string & group_name, UInt dimension,
	const NodeGroup & node_group, T & filter) {
	AKANTU_DEBUG_IN();

	if (T::type == FilterFunctor::_node_filter_functor) {
	auto & filtered_node_group = this->createFilteredNodeGroup(
	group_name + "_nodes", node_group, filter);

	AKANTU_DEBUG_OUT();
	return this->createElementGroup(group_name, dimension, filtered_node_group);
	}
	if (T::type == FilterFunctor::_element_filter_functor) {
	AKANTU_ERROR(
	"Cannot handle an ElementFilter yet. Needs to be implemented.");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	class ClusterSynchronizer : public DataAccessor<Element> {
	using DistantIDs = std::set<std::pair<UInt, UInt>>;

	public:
	ClusterSynchronizer(GroupManager & group_manager, UInt element_dimension,
	std::string cluster_name_prefix,
	ElementTypeMapArray<UInt> & element_to_fragment,
	const ElementSynchronizer & element_synchronizer,
	UInt nb_cluster)
	: group_manager(group_manager), element_dimension(element_dimension),
	cluster_name_prefix(std::move(cluster_name_prefix)),
	element_to_fragment(element_to_fragment),
	element_synchronizer(element_synchronizer), nb_cluster(nb_cluster) {}

	UInt synchronize() {
	Communicator & comm = Communicator::getStaticCommunicator();
	UInt rank = comm.whoAmI();
	UInt nb_proc = comm.getNbProc();

	/// find starting index to renumber local clusters
	Array<UInt> nb_cluster_per_proc(nb_proc);
	nb_cluster_per_proc(rank) = nb_cluster;
	comm.allGather(nb_cluster_per_proc);

	starting_index = std::accumulate(nb_cluster_per_proc.begin(),
	nb_cluster_per_proc.begin() + rank, 0U);

	UInt global_nb_fragment =
	std::accumulate(nb_cluster_per_proc.begin() + rank,
	nb_cluster_per_proc.end(), starting_index);

	/// create the local to distant cluster pairs with neighbors
	element_synchronizer.synchronizeOnce(*this,
	SynchronizationTag::_gm_clusters);

	/// count total number of pairs
	Array<int> nb_pairs(nb_proc); // This is potentially a bug for more than
	// 2**31 pairs, but due to a all gatherv after
	// it must be int to match MPI interfaces
	nb_pairs(rank) = distant_ids.size();
	comm.allGather(nb_pairs);

	UInt total_nb_pairs = std::accumulate(nb_pairs.begin(), nb_pairs.end(), 0);

	/// generate pairs global array
	UInt local_pair_index =
	std::accumulate(nb_pairs.storage(), nb_pairs.storage() + rank, 0);

	Array<UInt> total_pairs(total_nb_pairs, 2);

	for (const auto & ids : distant_ids) {
	total_pairs(local_pair_index, 0) = ids.first;
	total_pairs(local_pair_index, 1) = ids.second;
	++local_pair_index;
	}

	/// communicate pairs to all processors
	nb_pairs *= 2;
	comm.allGatherV(total_pairs, nb_pairs);

	/// renumber clusters

	/// generate fragment list
	std::vector<std::set<UInt>> global_clusters;
	UInt total_nb_cluster = 0;

	Array<bool> is_fragment_in_cluster(global_nb_fragment, 1, false);
	std::queue<UInt> fragment_check_list;

	while (not total_pairs.empty()) {
	/// create a new cluster
	++total_nb_cluster;
	global_clusters.resize(total_nb_cluster);
	std::set<UInt> & current_cluster = global_clusters[total_nb_cluster - 1];

	UInt first_fragment = total_pairs(0, 0);
	UInt second_fragment = total_pairs(0, 1);
	total_pairs.erase(0);

	fragment_check_list.push(first_fragment);
	fragment_check_list.push(second_fragment);

	while (!fragment_check_list.empty()) {
	UInt current_fragment = fragment_check_list.front();

	UInt * total_pairs_end = total_pairs.storage() + total_pairs.size() * 2;

	UInt * fragment_found =
	std::find(total_pairs.storage(), total_pairs_end, current_fragment);

	if (fragment_found != total_pairs_end) {
	UInt position = fragment_found - total_pairs.storage();
	UInt pair = position / 2;
	UInt other_index = (position + 1) % 2;
	fragment_check_list.push(total_pairs(pair, other_index));
	total_pairs.erase(pair);
	} else {
	fragment_check_list.pop();
	current_cluster.insert(current_fragment);
	is_fragment_in_cluster(current_fragment) = true;
	}
	}
	}

	/// add to FragmentToCluster all local fragments
	for (UInt c = 0; c < global_nb_fragment; ++c) {
	if (!is_fragment_in_cluster(c)) {
	++total_nb_cluster;
	global_clusters.resize(total_nb_cluster);
	std::set<UInt> & current_cluster =
	global_clusters[total_nb_cluster - 1];

	current_cluster.insert(c);
	}
	}

	/// reorganize element groups to match global clusters
	for (UInt c = 0; c < global_clusters.size(); ++c) {

	/// create new element group corresponding to current cluster
	std::stringstream sstr;
	sstr << cluster_name_prefix << "_" << c;
	ElementGroup & cluster =
	group_manager.createElementGroup(sstr.str(), element_dimension, true);

	auto it = global_clusters[c].begin();
	auto end = global_clusters[c].end();

	/// append to current element group all fragments that belong to
	/// the same cluster if they exist
	for (; it != end; ++it) {
	Int local_index = *it - starting_index;

	if (local_index < 0 \|\| local_index >= Int(nb_cluster)) {
	continue;
	}

	std::stringstream tmp_sstr;
	tmp_sstr << "tmp_" << cluster_name_prefix << "_" << local_index;

	AKANTU_DEBUG_ASSERT(group_manager.elementGroupExists(tmp_sstr.str()),
	"Temporary fragment \"" << tmp_sstr.str()
	<< "\" not found");

	cluster.append(group_manager.getElementGroup(tmp_sstr.str()));
	group_manager.destroyElementGroup(tmp_sstr.str(), true);
	}
	}

	return total_nb_cluster;
	}

	private:
	/// functions for parallel communications
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	if (tag == SynchronizationTag::_gm_clusters) {
	return elements.size() * sizeof(UInt);
	}

	return 0;
	}

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	if (tag != SynchronizationTag::_gm_clusters) {
	return;
	}

	Array<Element>::const_iterator<> el_it = elements.begin();
	Array<Element>::const_iterator<> el_end = elements.end();

	for (; el_it != el_end; ++el_it) {

	const Element & el = *el_it;

	/// for each element pack its global cluster index
	buffer << element_to_fragment(el.type, el.ghost_type)(el.element) +
	starting_index;
	}
	}

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override {
	if (tag != SynchronizationTag::_gm_clusters) {
	return;
	}

	Array<Element>::const_iterator<> el_it = elements.begin();
	Array<Element>::const_iterator<> el_end = elements.end();

	for (; el_it != el_end; ++el_it) {
	UInt distant_cluster;

	buffer >> distant_cluster;

	const Element & el = *el_it;
	UInt local_cluster =
	element_to_fragment(el.type, el.ghost_type)(el.element) +
	starting_index;

	distant_ids.insert(std::make_pair(local_cluster, distant_cluster));
	}
	}

	private:
	GroupManager & group_manager;
	UInt element_dimension;
	std::string cluster_name_prefix;
	ElementTypeMapArray<UInt> & element_to_fragment;
	const ElementSynchronizer & element_synchronizer;

	UInt nb_cluster;
	DistantIDs distant_ids;

	UInt starting_index;
	};

	/* -------------------------------------------------------------------------- */
	/// \todo this function doesn't work in 1D
	UInt GroupManager::createBoundaryGroupFromGeometry() {
	UInt spatial_dimension = mesh.getSpatialDimension();

	return createClusters(spatial_dimension - 1, "boundary");
	}

	/* -------------------------------------------------------------------------- */
	UInt GroupManager::createClusters(
	UInt element_dimension, Mesh & mesh_facets,
	const std::string & cluster_name_prefix,
	const GroupManager::ClusteringFilter & filter) {
	return createClusters(element_dimension, cluster_name_prefix, filter,
	mesh_facets);
	}

	/* -------------------------------------------------------------------------- */
	UInt GroupManager::createClusters(
	UInt element_dimension, const std::string & cluster_name_prefix,
	const GroupManager::ClusteringFilter & filter) {

	MeshAccessor mesh_accessor(mesh);
	auto mesh_facets = std::make_unique<Mesh>(mesh.getSpatialDimension(),
	mesh_accessor.getNodesSharedPtr(),
	"mesh_facets_for_clusters");

	mesh_facets->defineMeshParent(mesh);
	MeshUtils::buildAllFacets(mesh, *mesh_facets, element_dimension,
	element_dimension - 1);

	return createClusters(element_dimension, cluster_name_prefix, filter,
	*mesh_facets);
	}

	/* -------------------------------------------------------------------------- */
	//// \todo if needed element list construction can be optimized by
	//// templating the filter class
	UInt GroupManager::createClusters(UInt element_dimension,
	const std::string & cluster_name_prefix,
	const GroupManager::ClusteringFilter & filter,
	Mesh & mesh_facets) {
	AKANTU_DEBUG_IN();

	UInt nb_proc = mesh.getCommunicator().getNbProc();
	std::string tmp_cluster_name_prefix = cluster_name_prefix;

	ElementTypeMapArray<UInt> * element_to_fragment = nullptr;

	if (nb_proc > 1 && mesh.isDistributed()) {
	element_to_fragment =
	new ElementTypeMapArray<UInt>("element_to_fragment", id);

	element_to_fragment->initialize(
	mesh, _nb_component = 1, _spatial_dimension = element_dimension,
	_element_kind = _ek_not_defined, _with_nb_element = true);
	// mesh.initElementTypeMapArray(*element_to_fragment, 1, element_dimension,
	// false, _ek_not_defined, true);
	tmp_cluster_name_prefix = "tmp_" + tmp_cluster_name_prefix;
	}

	ElementTypeMapArray<bool> seen_elements("seen_elements", id);
	seen_elements.initialize(mesh, _spatial_dimension = element_dimension,
	_element_kind = _ek_not_defined,
	_with_nb_element = true);
	// mesh.initElementTypeMapArray(seen_elements, 1, element_dimension, false,
	// _ek_not_defined, true);

	for (auto ghost_type : ghost_types) {
	Element el;
	el.ghost_type = ghost_type;
	for (auto type :
	mesh.elementTypes(_spatial_dimension = element_dimension,
	_ghost_type = ghost_type, _element_kind = _ek_not_defined)) {
	el.type = type;
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	Array<bool> & seen_elements_array = seen_elements(type, ghost_type);

	for (UInt e = 0; e < nb_element; ++e) {
	el.element = e;
	if (!filter(el)) {
	seen_elements_array(e) = true;
	}
	}
	}
	}

	Array<bool> checked_node(mesh.getNbNodes(), 1, false);

	UInt nb_cluster = 0;

	for (auto ghost_type : ghost_types) {
	Element uns_el;
	uns_el.ghost_type = ghost_type;
	for (auto type :
	mesh.elementTypes(_spatial_dimension = element_dimension,
	_ghost_type = ghost_type, _element_kind = _ek_not_defined)) {
	uns_el.type = type;
	Array<bool> & seen_elements_vec =
	seen_elements(uns_el.type, uns_el.ghost_type);

	for (UInt e = 0; e < seen_elements_vec.size(); ++e) {
	// skip elements that have been already seen
	if (seen_elements_vec(e)) {
	continue;
	}

	// set current element
	uns_el.element = e;
	seen_elements_vec(e) = true;

	/// create a new cluster
	std::stringstream sstr;
	sstr << tmp_cluster_name_prefix << "_" << nb_cluster;
	ElementGroup & cluster =
	createElementGroup(sstr.str(), element_dimension, true);
	++nb_cluster;

	// point element are cluster by themself
	if (element_dimension == 0) {
	cluster.add(uns_el);

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(uns_el.type);
	Vector<UInt> connect =
	mesh.getConnectivity(uns_el.type, uns_el.ghost_type)
	.begin(nb_nodes_per_element)[uns_el.element];
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	/// add element's nodes to the cluster
	UInt node = connect[n];
	if (!checked_node(node)) {
	cluster.addNode(node);
	checked_node(node) = true;
	}
	}

	continue;
	}

	std::queue<Element> element_to_add;
	element_to_add.push(uns_el);

	/// keep looping until current cluster is complete (no more
	/// connected elements)
	while (!element_to_add.empty()) {

	/// take first element and erase it in the queue
	Element el = element_to_add.front();
	element_to_add.pop();

	/// if parallel, store cluster index per element
	if (nb_proc > 1 && mesh.isDistributed()) {
	(*element_to_fragment)(el.type, el.ghost_type)(el.element) =
	nb_cluster - 1;
	}

	/// add current element to the cluster
	cluster.add(el);

	const Array<Element> & element_to_facet =
	mesh_facets.getSubelementToElement(el.type, el.ghost_type);

	UInt nb_facet_per_element = element_to_facet.getNbComponent();

	for (UInt f = 0; f < nb_facet_per_element; ++f) {
	const Element & facet = element_to_facet(el.element, f);

	if (facet == ElementNull) {
	continue;
	}

	const std::vector<Element> & connected_elements =
	mesh_facets.getElementToSubelement(
	facet.type, facet.ghost_type)(facet.element);

	for (UInt elem = 0; elem < connected_elements.size(); ++elem) {
	const Element & check_el = connected_elements[elem];

	// check if this element has to be skipped
	if (check_el == ElementNull \|\| check_el == el) {
	continue;
	}

	Array<bool> & seen_elements_vec_current =
	seen_elements(check_el.type, check_el.ghost_type);

	if (not seen_elements_vec_current(check_el.element)) {
	seen_elements_vec_current(check_el.element) = true;
	element_to_add.push(check_el);
	}
	}
	}

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(el.type);
	Vector<UInt> connect = mesh.getConnectivity(el.type, el.ghost_type)
	.begin(nb_nodes_per_element)[el.element];
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	/// add element's nodes to the cluster
	UInt node = connect[n];
	if (!checked_node(node)) {
	cluster.addNode(node, false);
	checked_node(node) = true;
	}
	}
	}
	}
	}
	}

	if (nb_proc > 1 && mesh.isDistributed()) {
	ClusterSynchronizer cluster_synchronizer(
	this, element_dimension, cluster_name_prefix, element_to_fragment,
	this->mesh.getElementSynchronizer(), nb_cluster);
	nb_cluster = cluster_synchronizer.synchronize();
	delete element_to_fragment;
	}

	if (mesh.isDistributed()) {
	this->synchronizeGroupNames();
	}

	AKANTU_DEBUG_OUT();
	return nb_cluster;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void GroupManager::createGroupsFromMeshData(const std::string & dataset_name) {
	std::set<std::string> group_names;
	const auto & datas = mesh.getData<T>(dataset_name);

	std::map<std::string, UInt> group_dim;

	for (auto ghost_type : ghost_types) {
	for (auto type : datas.elementTypes(_ghost_type = ghost_type)) {
	const Array<T> & dataset = datas(type, ghost_type);
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	AKANTU_DEBUG_ASSERT(dataset.size() == nb_element,
	"Not the same number of elements ("
	<< type << ":" << ghost_type
	<< ") in the map from MeshData ("
	<< dataset.size() << ") " << dataset_name
	<< " and in the mesh (" << nb_element << ")!");
	for (UInt e(0); e < nb_element; ++e) {
	std::stringstream sstr;
	sstr << dataset(e);
	std::string gname = sstr.str();
	group_names.insert(gname);

	auto it = group_dim.find(gname);
	if (it == group_dim.end()) {
	group_dim[gname] = mesh.getSpatialDimension(type);
	} else {
	it->second = std::max(it->second, mesh.getSpatialDimension(type));
	}
	}
	}
	}

	for (auto && name : group_names) {
	createElementGroup(name, group_dim[name]);
	}

	if (mesh.isDistributed()) {
	this->synchronizeGroupNames();
	}

	Element el;
	for (auto ghost_type : ghost_types) {
	el.ghost_type = ghost_type;
	for (auto type : datas.elementTypes(_ghost_type = ghost_type)) {
	el.type = type;
	const Array<T> & dataset = datas(type, ghost_type);
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	AKANTU_DEBUG_ASSERT(dataset.size() == nb_element,
	"Not the same number of elements in the map from "
	"MeshData and in the mesh!");

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(el.type);

	Array<UInt>::const_iterator<Vector<UInt>> cit =
	mesh.getConnectivity(type, ghost_type).begin(nb_nodes_per_element);

	for (UInt e(0); e < nb_element; ++e, ++cit) {
	el.element = e;
	std::stringstream sstr;
	sstr << dataset(e);
	ElementGroup & group = getElementGroup(sstr.str());
	group.add(el, false, false);

	const Vector<UInt> & connect = *cit;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connect[n];
	group.addNode(node, false);
	}
	}
	}
	}

	for (auto && name : group_names) {
	getElementGroup(name).optimize();
	}
	}

	template void GroupManager::createGroupsFromMeshData<std::string>(
	const std::string & dataset_name);
	template void
	GroupManager::createGroupsFromMeshData<UInt>(const std::string & dataset_name);

	/* -------------------------------------------------------------------------- */
	void GroupManager::createElementGroupFromNodeGroup(
	const std::string & name, const std::string & node_group_name,
	UInt dimension) {
	NodeGroup & node_group = getNodeGroup(node_group_name);
	ElementGroup & group = createElementGroup(name, dimension, node_group);

	group.fillFromNodeGroup();
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "GroupManager [" << std::endl;

	std::set<std::string> node_group_seen;
	for (auto & group : iterateElementGroups()) {
	group.printself(stream, indent + 1);
	node_group_seen.insert(group.getNodeGroup().getName());
	}

	for (auto & group : iterateNodeGroups()) {
	if (node_group_seen.find(group.getName()) == node_group_seen.end()) {
	group.printself(stream, indent + 1);
	}
	}

	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	UInt GroupManager::getNbElementGroups(UInt dimension) const {
	if (dimension == _all_dimensions) {
	return element_groups.size();
	}

	- return std::count_if(
	- element_groups.begin(), element_groups.end(),
	- [dimension](auto && eg) { return eg.second->getDimension() == dimension; });
	+ return std::count_if(element_groups.begin(), element_groups.end(),
	+ [dimension](auto && eg) {
	+ return eg.second->getDimension() == dimension;
	+ });
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::checkAndAddGroups(DynamicCommunicationBuffer & buffer) {
	AKANTU_DEBUG_IN();

	UInt nb_node_group;
	buffer >> nb_node_group;
	AKANTU_DEBUG_INFO("Received " << nb_node_group << " node group names");

	for (UInt ng = 0; ng < nb_node_group; ++ng) {
	std::string node_group_name;
	buffer >> node_group_name;

	if (node_groups.find(node_group_name) == node_groups.end()) {
	this->createNodeGroup(node_group_name);
	}

	AKANTU_DEBUG_INFO("Received node goup name: " << node_group_name);
	}

	UInt nb_element_group;
	buffer >> nb_element_group;
	AKANTU_DEBUG_INFO("Received " << nb_element_group << " element group names");
	for (UInt eg = 0; eg < nb_element_group; ++eg) {
	std::string element_group_name;
	buffer >> element_group_name;
	std::string node_group_name;
	buffer >> node_group_name;
	UInt dim;
	buffer >> dim;

	AKANTU_DEBUG_INFO("Received element group name: "
	<< element_group_name << " corresponding to a "
	<< Int(dim) << "D group with node group "
	<< node_group_name);

	NodeGroup & node_group = *node_groups[node_group_name];

	if (element_groups.find(element_group_name) == element_groups.end()) {
	this->createElementGroup(element_group_name, dim, node_group);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::fillBufferWithGroupNames(
	DynamicCommunicationBuffer & comm_buffer) const {
	AKANTU_DEBUG_IN();

	// packing node group names;
	UInt nb_groups = this->node_groups.size();
	comm_buffer << nb_groups;
	AKANTU_DEBUG_INFO("Sending " << nb_groups << " node group names");

	auto nnames_it = node_groups.begin();
	auto nnames_end = node_groups.end();
	for (; nnames_it != nnames_end; ++nnames_it) {
	std::string node_group_name = nnames_it->first;
	comm_buffer << node_group_name;
	AKANTU_DEBUG_INFO("Sending node goupe name: " << node_group_name);
	}

	// packing element group names with there associated node group name
	nb_groups = this->element_groups.size();
	comm_buffer << nb_groups;
	AKANTU_DEBUG_INFO("Sending " << nb_groups << " element group names");
	auto gnames_it = this->element_groups.begin();
	auto gnames_end = this->element_groups.end();
	for (; gnames_it != gnames_end; ++gnames_it) {
	ElementGroup & element_group = *(gnames_it->second);
	std::string element_group_name = gnames_it->first;
	std::string node_group_name = element_group.getNodeGroup().getName();
	UInt dim = element_group.getDimension();

	comm_buffer << element_group_name;
	comm_buffer << node_group_name;
	comm_buffer << dim;

	AKANTU_DEBUG_INFO("Sending element group name: "
	<< element_group_name << " corresponding to a "
	<< Int(dim) << "D group with the node group "
	<< node_group_name);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::synchronizeGroupNames() {
	AKANTU_DEBUG_IN();

	const Communicator & comm = mesh.getCommunicator();
	Int nb_proc = comm.getNbProc();
	Int my_rank = comm.whoAmI();

	if (nb_proc == 1) {
	return;
	}

	if (my_rank == 0) {
	for (Int p = 1; p < nb_proc; ++p) {
	DynamicCommunicationBuffer recv_buffer;
	auto tag = Tag::genTag(p, 0, Tag::_element_group);
	comm.receive(recv_buffer, p, tag);
	AKANTU_DEBUG_INFO("Got " << printMemorySize<char>(recv_buffer.size())
	<< " from proc " << p << " " << tag);
	this->checkAndAddGroups(recv_buffer);
	}

	DynamicCommunicationBuffer comm_buffer;
	this->fillBufferWithGroupNames(comm_buffer);

	AKANTU_DEBUG_INFO("Initiating broadcast with "
	<< printMemorySize<char>(comm_buffer.size()));
	comm.broadcast(comm_buffer);

	} else {
	DynamicCommunicationBuffer comm_buffer;
	this->fillBufferWithGroupNames(comm_buffer);

	auto tag = Tag::genTag(my_rank, 0, Tag::_element_group);
	AKANTU_DEBUG_INFO("Sending " << printMemorySize<char>(comm_buffer.size())
	<< " to proc " << 0 << " " << tag);
	comm.send(comm_buffer, 0, tag);

	DynamicCommunicationBuffer recv_buffer;
	comm.broadcast(recv_buffer);
	AKANTU_DEBUG_INFO("Receiving broadcast with "
	<< printMemorySize<char>(recv_buffer.size()));

	this->checkAndAddGroups(recv_buffer);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	const ElementGroup &
	GroupManager::getElementGroup(const std::string & name) const {
	auto it = element_groups.find(name);
	if (it == element_groups.end()) {
	AKANTU_EXCEPTION("There are no element groups named "
	<< name << " associated to the group manager: " << id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	ElementGroup & GroupManager::getElementGroup(const std::string & name) {
	auto it = element_groups.find(name);
	if (it == element_groups.end()) {
	AKANTU_EXCEPTION("There are no element groups named "
	<< name << " associated to the group manager: " << id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	const NodeGroup & GroupManager::getNodeGroup(const std::string & name) const {
	auto it = node_groups.find(name);
	if (it == node_groups.end()) {
	AKANTU_EXCEPTION("There are no node groups named "
	<< name << " associated to the group manager: " << id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	NodeGroup & GroupManager::getNodeGroup(const std::string & name) {
	auto it = node_groups.find(name);
	if (it == node_groups.end()) {
	AKANTU_EXCEPTION("There are no node groups named "
	<< name << " associated to the group manager: " << id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	template <typename GroupsType>
	void GroupManager::renameGroup(GroupsType & groups, const std::string & name,
	const std::string & new_name) {
	auto it = groups.find(name);
	if (it == groups.end()) {
	AKANTU_EXCEPTION("There are no group named "
	<< name << " associated to the group manager: " << id);
	}

	auto && group_ptr = std::move(it->second);

	group_ptr->name = new_name;

	groups.erase(it);
	groups[new_name] = std::move(group_ptr);
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::renameElementGroup(const std::string & name,
	const std::string & new_name) {
	renameGroup(element_groups, name, new_name);
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::renameNodeGroup(const std::string & name,
	const std::string & new_name) {
	renameGroup(node_groups, name, new_name);
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::copyElementGroup(const std::string & name,
	const std::string & new_name) {
	const auto & grp = getElementGroup(name);
	auto & new_grp = createElementGroup(new_name, grp.getDimension());

	new_grp.getElements().copy(grp.getElements());
	}

	/* -------------------------------------------------------------------------- */
	void GroupManager::copyNodeGroup(const std::string & name,
	const std::string & new_name) {
	const auto & grp = getNodeGroup(name);
	auto & new_grp = createNodeGroup(new_name);

	new_grp.getNodes().copy(grp.getNodes());
	}

	} // namespace akantu
	diff --git a/src/mesh/group_manager.hh b/src/mesh/group_manager.hh
	index 4cd70f563..40c30bde6 100644
	--- a/src/mesh/group_manager.hh
	+++ b/src/mesh/group_manager.hh
	@@ -1,350 +1,349 @@
	/**
	* @file group_manager.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@gmail.com>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Stores information relevent to the notion of element and nodes
	* groups.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_GROUP_MANAGER_HH_
	#define AKANTU_GROUP_MANAGER_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_iterators.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */
	#include <set>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class ElementGroup;
	class NodeGroup;
	class Mesh;
	class Element;
	class ElementSynchronizer;
	template <bool> class CommunicationBufferTemplated;
	namespace dumpers {
	class Field;
	}
	} // namespace akantu

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class GroupManager {
	/* ------------------------------------------------------------------------ */
	/* Typedefs */
	/* ------------------------------------------------------------------------ */
	private:
	using ElementGroups = std::map<std::string, std::unique_ptr<ElementGroup>>;
	using NodeGroups = std::map<std::string, std::unique_ptr<NodeGroup>>;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	GroupManager(Mesh & mesh, const ID & id = "group_manager");
	virtual ~GroupManager();

	/* ------------------------------------------------------------------------ */
	/* Groups iterators */
	/* ------------------------------------------------------------------------ */
	public:
	using node_group_iterator = NodeGroups::iterator;
	using element_group_iterator = ElementGroups::iterator;

	using const_node_group_iterator = NodeGroups::const_iterator;
	using const_element_group_iterator = ElementGroups::const_iterator;

	#define AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION(group_type, function, \
	param_in, param_out) \
	[[deprecated( \
	"use iterate(Element\|Node)Groups or " \
	"(element\|node)GroupExists")]] inline BOOST_PP_CAT(BOOST_PP_CAT(const_, \
	group_type), \
	_iterator) \
	BOOST_PP_CAT(BOOST_PP_CAT(group_type, _), function)(param_in) const { \
	return BOOST_PP_CAT(group_type, s).function(param_out); \
	}; \
	\
	[[deprecated("use iterate(Element\|Node)Groups or " \
	"(element\|node)GroupExists")]] inline BOOST_PP_CAT(group_type, \
	_iterator) \
	BOOST_PP_CAT(BOOST_PP_CAT(group_type, _), function)(param_in) { \
	return BOOST_PP_CAT(group_type, s).function(param_out); \
	}

	#define AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION_NP(group_type, function) \
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION( \
	group_type, function, BOOST_PP_EMPTY(), BOOST_PP_EMPTY())

	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION_NP(node_group, begin);
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION_NP(node_group, end);
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION_NP(element_group, begin);
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION_NP(element_group, end);
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION(element_group, find,
	const std::string & name, name);
	AKANTU_GROUP_MANAGER_DEFINE_ITERATOR_FUNCTION(node_group, find,
	const std::string & name, name);

	public:
	decltype(auto) iterateNodeGroups() {
	return make_dereference_adaptor(make_values_adaptor(node_groups));
	}
	decltype(auto) iterateNodeGroups() const {
	return make_dereference_adaptor(make_values_adaptor(node_groups));
	}

	decltype(auto) iterateElementGroups() {
	return make_dereference_adaptor(make_values_adaptor(element_groups));
	}
	decltype(auto) iterateElementGroups() const {
	return make_dereference_adaptor(make_values_adaptor(element_groups));
	}

	/* ------------------------------------------------------------------------ */
	/* Clustering filter */
	/* ------------------------------------------------------------------------ */
	public:
	class ClusteringFilter {
	public:
	virtual bool operator()(const Element & /unused/) const { return true; }
	};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// create an empty node group
	NodeGroup & createNodeGroup(const std::string & group_name,
	bool replace_group = false);

	/// create an element group and the associated node group
	ElementGroup & createElementGroup(const std::string & group_name,
	UInt dimension = _all_dimensions,
	bool replace_group = false);

	/* ------------------------------------------------------------------------ */
	/// renames an element group
	void renameElementGroup(const std::string & name,
	const std::string & new_name);

	/// renames a node group
	void renameNodeGroup(const std::string & name, const std::string & new_name);

	/// copy an existing element group
	void copyElementGroup(const std::string & name, const std::string & new_name);

	/// copy an existing node group
	void copyNodeGroup(const std::string & name, const std::string & new_name);

	/* ------------------------------------------------------------------------ */

	/// create a node group from another node group but filtered
	template <typename T>
	NodeGroup & createFilteredNodeGroup(const std::string & group_name,
	const NodeGroup & node_group, T & filter);

	/// create an element group from another element group but filtered
	template <typename T>
	ElementGroup &
	createFilteredElementGroup(const std::string & group_name, UInt dimension,
	const NodeGroup & node_group, T & filter);

	/// destroy a node group
	void destroyNodeGroup(const std::string & group_name);

	/// destroy an element group and the associated node group
	void destroyElementGroup(const std::string & group_name,
	bool destroy_node_group = false);

	// /// destroy all element groups and the associated node groups
	// void destroyAllElementGroups(bool destroy_node_groups = false);

	/// create a element group using an existing node group
	ElementGroup & createElementGroup(const std::string & group_name,
	UInt dimension, NodeGroup & node_group);

	/// create groups based on values stored in a given mesh data
	template <typename T>
	void createGroupsFromMeshData(const std::string & dataset_name);

	/// create boundaries group by a clustering algorithm \todo extend to parallel
	UInt createBoundaryGroupFromGeometry();

	/// create element clusters for a given dimension
	UInt createClusters(UInt element_dimension, Mesh & mesh_facets,
	const std::string & cluster_name_prefix = "cluster",
	const ClusteringFilter & filter = ClusteringFilter());

	/// create element clusters for a given dimension
	UInt createClusters(UInt element_dimension,
	const std::string & cluster_name_prefix = "cluster",
	const ClusteringFilter & filter = ClusteringFilter());

	private:
	/// create element clusters for a given dimension
	UInt createClusters(UInt element_dimension,
	const std::string & cluster_name_prefix,
	const ClusteringFilter & filter, Mesh & mesh_facets);

	public:
	/// Create an ElementGroup based on a NodeGroup
	void createElementGroupFromNodeGroup(const std::string & name,
	const std::string & node_group,
	UInt dimension = _all_dimensions);

	virtual void printself(std::ostream & stream, int indent = 0) const;

	/// this function insure that the group names are present on all processors
	/// /!\ it is a SMP call
	void synchronizeGroupNames();

	/// register an elemental field to the given group name (overloading for
	/// ElementalPartionField)
	template <typename T, template <bool> class dump_type>
	std::shared_ptr<dumpers::Field> createElementalField(
	const ElementTypeMapArray<T> & field, const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem = ElementTypeMap<UInt>());

	/// register an elemental field to the given group name (overloading for
	/// ElementalField)
	template <typename T, template <class> class ret_type,
	template <class, template <class> class, bool> class dump_type>
	std::shared_ptr<dumpers::Field> createElementalField(
	const ElementTypeMapArray<T> & field, const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem = ElementTypeMap<UInt>());

	/// register an elemental field to the given group name (overloading for
	/// MaterialInternalField)
	template <typename T,
	/// type of InternalMaterialField
	template <typename, bool filtered> class dump_type>
	std::shared_ptr<dumpers::Field>
	createElementalField(const ElementTypeMapArray<T> & field,
	const std::string & group_name, UInt spatial_dimension,
	- ElementKind kind,
	- ElementTypeMap<UInt> nb_data_per_elem);
	+ ElementKind kind, ElementTypeMap<UInt> nb_data_per_elem);

	template <typename type, bool flag, template <class, bool> class ftype>
	std::shared_ptr<dumpers::Field>
	createNodalField(const ftype<type, flag> * field,
	const std::string & group_name, UInt padding_size = 0);

	template <typename type, bool flag, template <class, bool> class ftype>
	std::shared_ptr<dumpers::Field>
	createStridedNodalField(const ftype<type, flag> * field,
	const std::string & group_name, UInt size,
	UInt stride, UInt padding_size);

	protected:
	/// fill a buffer with all the group names
	void fillBufferWithGroupNames(
	CommunicationBufferTemplated<false> & comm_buffer) const;

	/// take a buffer and create the missing groups localy
	void checkAndAddGroups(CommunicationBufferTemplated<false> & buffer);

	/// register an elemental field to the given group name
	template <class dump_type, typename field_type>
	inline std::shared_ptr<dumpers::Field>
	createElementalField(const field_type & field, const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	const ElementTypeMap<UInt> & nb_data_per_elem);

	/// register an elemental field to the given group name
	template <class dump_type, typename field_type>
	inline std::shared_ptr<dumpers::Field>
	createElementalFilteredField(const field_type & field,
	const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem);

	/* ------------------------------------------------------------------------ */
	/* Accessor */
	/* ------------------------------------------------------------------------ */
	public:
	// AKANTU_GET_MACRO(ElementGroups, element_groups, const ElementGroups &);

	const ElementGroup & getElementGroup(const std::string & name) const;
	const NodeGroup & getNodeGroup(const std::string & name) const;

	ElementGroup & getElementGroup(const std::string & name);
	NodeGroup & getNodeGroup(const std::string & name);

	UInt getNbElementGroups(UInt dimension = _all_dimensions) const;
	UInt getNbNodeGroups() { return node_groups.size(); };

	bool elementGroupExists(const std::string & name) {
	return element_groups.find(name) != element_groups.end();
	}

	bool nodeGroupExists(const std::string & name) {
	return node_groups.find(name) != node_groups.end();
	}

	private:
	template <typename GroupsType>
	void renameGroup(GroupsType & groups, const std::string & name,
	const std::string & new_name);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// id to create element and node groups
	ID id;

	/// list of the node groups managed
	NodeGroups node_groups;

	/// list of the element groups managed
	ElementGroups element_groups;

	/// Mesh to which the element belongs
	Mesh & mesh;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const GroupManager & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_GROUP_MANAGER_HH_ */
	diff --git a/src/mesh/group_manager_inline_impl.hh b/src/mesh/group_manager_inline_impl.hh
	index 32942bc13..f6cc96643 100644
	--- a/src/mesh/group_manager_inline_impl.hh
	+++ b/src/mesh/group_manager_inline_impl.hh
	@@ -1,198 +1,198 @@
	/**
	* @file group_manager_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Tue Mar 03 2020
	*
	* @brief Stores information relevent to the notion of domain boundary and
	* surfaces.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_field.hh"
	#include "element_group.hh"
	#include "element_type_map_filter.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_nodal_field.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T, template <bool> class dump_type>
	std::shared_ptr<dumpers::Field>
	GroupManager::createElementalField(const ElementTypeMapArray<T> & field,
	const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem) {

	const ElementTypeMapArray<T> * field_ptr = &field;
	if (field_ptr == nullptr) {
	return nullptr;
	}
	if (group_name == "all") {
	return this->createElementalField<dump_type<false>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}
	return this->createElementalFilteredField<dump_type<true>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, template <class> class T2,
	template <class, template <class> class, bool> class dump_type>
	std::shared_ptr<dumpers::Field>
	GroupManager::createElementalField(const ElementTypeMapArray<T> & field,
	const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem) {

	const ElementTypeMapArray<T> * field_ptr = &field;
	if (field_ptr == nullptr) {
	return nullptr;
	}
	if (group_name == "all") {
	return this->createElementalField<dump_type<T, T2, false>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}
	return this->createElementalFilteredField<dump_type<T, T2, true>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename T2, bool filtered>
	- class dump_type> ///< type of InternalMaterialField
	+ class dump_type> ///< type of InternalMaterialField
	std::shared_ptr<dumpers::Field>
	GroupManager::createElementalField(const ElementTypeMapArray<T> & field,
	const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem) {
	const ElementTypeMapArray<T> * field_ptr = &field;

	if (field_ptr == nullptr) {
	return nullptr;
	}
	if (group_name == "all") {
	return this->createElementalField<dump_type<T, false>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}
	return this->createElementalFilteredField<dump_type<T, true>>(
	field, group_name, spatial_dimension, kind, nb_data_per_elem);
	}

	/* -------------------------------------------------------------------------- */
	template <typename dump_type, typename field_type>
	std::shared_ptr<dumpers::Field> GroupManager::createElementalField(
	const field_type & field, const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	const ElementTypeMap<UInt> & nb_data_per_elem) {
	const field_type * field_ptr = &field;
	if (field_ptr == nullptr) {
	return nullptr;
	}

	if (group_name != "all") {
	throw;
	}

	auto dumper =
	std::make_shared<dump_type>(field, spatial_dimension, _not_ghost, kind);
	dumper->setNbDataPerElem(nb_data_per_elem);
	return dumper;
	}

	/* -------------------------------------------------------------------------- */
	template <typename dump_type, typename field_type>
	std::shared_ptr<dumpers::Field> GroupManager::createElementalFilteredField(
	const field_type & field, const std::string & group_name,
	UInt spatial_dimension, ElementKind kind,
	ElementTypeMap<UInt> nb_data_per_elem) {

	const field_type * field_ptr = &field;
	if (field_ptr == nullptr) {
	return nullptr;
	}
	if (group_name == "all") {
	throw;
	}

	using T = typename field_type::value_type;
	ElementGroup & group = this->getElementGroup(group_name);
	UInt dim = group.getDimension();
	if (dim != spatial_dimension) {
	throw;
	}
	const ElementTypeMapArray<UInt> & elemental_filter = group.getElements();

	auto * filtered = new ElementTypeMapArrayFilter<T>(field, elemental_filter,
	nb_data_per_elem);

	auto dumper = std::make_shared<dump_type>(*filtered, dim, _not_ghost, kind);
	dumper->setNbDataPerElem(nb_data_per_elem);

	return dumper;
	}

	/* -------------------------------------------------------------------------- */
	template <typename type, bool flag, template <class, bool> class ftype>
	std::shared_ptr<dumpers::Field>
	GroupManager::createNodalField(const ftype<type, flag> * field,
	const std::string & group_name,
	UInt padding_size) {
	return createStridedNodalField(field, group_name, 0, 0, padding_size);
	}

	/* -------------------------------------------------------------------------- */
	template <typename type, bool flag, template <class, bool> class ftype>
	std::shared_ptr<dumpers::Field>
	GroupManager::createStridedNodalField(const ftype<type, flag> * field,
	const std::string & group_name, UInt size,
	UInt stride, UInt padding_size) {
	if (not field) {
	return nullptr;
	}

	if (group_name == "all") {
	using DumpType = typename dumpers::NodalField<type, false>;
	auto dumper = std::make_shared<DumpType>(*field, size, stride);
	dumper->setPadding(padding_size);
	return dumper;
	}

	ElementGroup & group = this->getElementGroup(group_name);
	const Array<UInt> * nodal_filter = &(group.getNodeGroup().getNodes());
	using DumpType = typename dumpers::NodalField<type, true>;
	auto dumper = std::make_shared<DumpType>(*field, size, stride, nodal_filter);
	dumper->setPadding(padding_size);
	return dumper;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif
	diff --git a/src/mesh/mesh.cc b/src/mesh/mesh.cc
	index c450603d1..16f852a5a 100644
	--- a/src/mesh/mesh.cc
	+++ b/src/mesh/mesh.cc
	@@ -1,661 +1,661 @@
	/**
	* @file mesh.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Feb 09 2021
	*
	* @brief class handling meshes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_config.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_class.hh"
	#include "group_manager_inline_impl.hh"
	#include "mesh.hh"
	#include "mesh_global_data_updater.hh"
	#include "mesh_io.hh"
	#include "mesh_iterators.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "element_synchronizer.hh"
	#include "facet_synchronizer.hh"
	#include "mesh_utils_distribution.hh"
	#include "node_synchronizer.hh"
	#include "periodic_node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_field.hh"
	#include "dumper_internal_material_field.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	#include <limits>
	#include <sstream>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Mesh::Mesh(UInt spatial_dimension, const ID & id, Communicator & communicator)
	: GroupManager(*this, id + ":group_manager"), MeshData("mesh_data", id),
	id(id), connectivities("connectivities", id),
	ghosts_counters("ghosts_counters", id), normals("normals", id),
	spatial_dimension(spatial_dimension), size(spatial_dimension, 0.),
	bbox(spatial_dimension), bbox_local(spatial_dimension),
	communicator(&communicator) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Mesh::Mesh(UInt spatial_dimension, Communicator & communicator, const ID & id)
	: Mesh(spatial_dimension, id, communicator) {
	AKANTU_DEBUG_IN();

	this->nodes =
	std::make_shared<Array<Real>>(0, spatial_dimension, id + ":coordinates");
	this->nodes_flags = std::make_shared<Array<NodeFlag>>(0, 1, NodeFlag::_normal,
	id + ":nodes_flags");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Mesh::Mesh(UInt spatial_dimension, const ID & id)
	: Mesh(spatial_dimension, Communicator::getStaticCommunicator(), id) {}

	/* -------------------------------------------------------------------------- */
	Mesh::Mesh(UInt spatial_dimension, const std::shared_ptr<Array<Real>> & nodes,
	const ID & id)
	: Mesh(spatial_dimension, id, Communicator::getStaticCommunicator()) {
	this->nodes = nodes;

	this->nb_global_nodes = this->nodes->size();

	this->nodes_to_elements.resize(nodes->size());
	for (auto & node_set : nodes_to_elements) {
	node_set = std::make_unique<std::set<Element>>();
	}

	this->computeBoundingBox();
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::getBarycenters(Array<Real> & barycenter, ElementType type,
	GhostType ghost_type) const {
	barycenter.resize(getNbElement(type, ghost_type));
	for (auto && data : enumerate(make_view(barycenter, spatial_dimension))) {
	getBarycenter(Element{type, UInt(std::get<0>(data)), ghost_type},
	std::get<1>(data));
	}
	}

	class FacetGlobalConnectivityAccessor : public DataAccessor<Element> {
	public:
	FacetGlobalConnectivityAccessor(Mesh & mesh)
	: global_connectivity("global_connectivity",
	"facet_connectivity_synchronizer") {
	global_connectivity.initialize(
	mesh, _spatial_dimension = _all_dimensions, _with_nb_element = true,
	_with_nb_nodes_per_element = true, _element_kind = _ek_regular);
	mesh.getGlobalConnectivity(global_connectivity);
	}

	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	UInt size = 0;
	if (tag == SynchronizationTag::_smmc_facets_conn) {
	UInt nb_nodes = Mesh::getNbNodesPerElementList(elements);
	size += nb_nodes * sizeof(UInt);
	}
	return size;
	}

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	if (tag == SynchronizationTag::_smmc_facets_conn) {
	for (const auto & element : elements) {
	const auto & conns =
	global_connectivity(element.type, element.ghost_type);
	for (auto n : arange(conns.getNbComponent())) {
	buffer << conns(element.element, n);
	}
	}
	}
	}

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override {
	if (tag == SynchronizationTag::_smmc_facets_conn) {
	for (const auto & element : elements) {
	auto & conns = global_connectivity(element.type, element.ghost_type);
	for (auto n : arange(conns.getNbComponent())) {
	buffer >> conns(element.element, n);
	}
	}
	}
	}

	AKANTU_GET_MACRO(GlobalConnectivity, (global_connectivity), decltype(auto));

	protected:
	ElementTypeMapArray<UInt> global_connectivity;
	};

	/* -------------------------------------------------------------------------- */
	Mesh & Mesh::initMeshFacets(const ID & id) {
	AKANTU_DEBUG_IN();

	if (mesh_facets) {
	AKANTU_DEBUG_OUT();
	return *mesh_facets;
	}

	mesh_facets = std::make_unique<Mesh>(spatial_dimension, this->nodes,
	getID() + ":" + id);

	mesh_facets->mesh_parent = this;
	mesh_facets->is_mesh_facets = true;
	mesh_facets->nodes_flags = this->nodes_flags;
	mesh_facets->nodes_global_ids = this->nodes_global_ids;

	MeshUtils::buildAllFacets(this, mesh_facets, 0);

	if (mesh.isDistributed()) {
	mesh_facets->is_distributed = true;
	mesh_facets->element_synchronizer = std::make_unique<FacetSynchronizer>(
	*mesh_facets, mesh.getElementSynchronizer());

	FacetGlobalConnectivityAccessor data_accessor(*mesh_facets);
	/// communicate
	mesh_facets->element_synchronizer->synchronizeOnce(
	data_accessor, SynchronizationTag::_smmc_facets_conn);

	/// flip facets
	MeshUtils::flipFacets(*mesh_facets, data_accessor.getGlobalConnectivity(),
	_ghost);
	}

	/// transfers the the mesh physical names to the mesh facets
	if (not this->hasData("physical_names")) {
	AKANTU_DEBUG_OUT();
	return *mesh_facets;
	}

	auto & mesh_phys_data = this->getData<std::string>("physical_names");
	auto & phys_data = mesh_facets->getData<std::string>("physical_names");
	phys_data.initialize(*mesh_facets, _spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true);

	ElementTypeMapArray<Real> barycenters(getID(), "temporary_barycenters");
	barycenters.initialize(*mesh_facets, _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true);

	for (auto && ghost_type : ghost_types) {
	for (auto && type :
	barycenters.elementTypes(spatial_dimension - 1, ghost_type)) {
	mesh_facets->getBarycenters(barycenters(type, ghost_type), type,
	ghost_type);
	}
	}

	for_each_element(
	mesh,
	[&](auto && element) {
	Vector<Real> barycenter(spatial_dimension);
	mesh.getBarycenter(element, barycenter);
	auto norm_barycenter = barycenter.norm();
	auto tolerance = Math::getTolerance();
	if (norm_barycenter > tolerance) {
	tolerance *= norm_barycenter;
	}

	Vector<Real> barycenter_facet(spatial_dimension);

	auto range = enumerate(make_view(
	barycenters(element.type, element.ghost_type), spatial_dimension));
	#ifndef AKANTU_NDEBUG
	auto min_dist = std::numeric_limits<Real>::max();
	#endif
	// this is a spacial search coded the most inefficient way.
	auto facet =
	std::find_if(range.begin(), range.end(), [&](auto && data) {
	auto norm_distance = barycenter.distance(std::get<1>(data));
	#ifndef AKANTU_NDEBUG
	min_dist = std::min(min_dist, norm_distance);
	#endif
	return (norm_distance < tolerance);
	});

	if (facet == range.end()) {
	AKANTU_DEBUG_INFO("The element "
	<< element
	<< " did not find its associated facet in the "
	"mesh_facets! Try to decrease math tolerance. "
	"The closest element was at a distance of "
	<< min_dist);
	return;
	}

	// set physical name
	auto && facet_element = Element{element.type, UInt(std::get<0>(*facet)),
	element.ghost_type};
	phys_data(facet_element) = mesh_phys_data(element);
	},
	_spatial_dimension = spatial_dimension - 1);

	mesh_facets->createGroupsFromMeshData<std::string>("physical_names");

	AKANTU_DEBUG_OUT();
	return *mesh_facets;
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::defineMeshParent(const Mesh & mesh) {
	AKANTU_DEBUG_IN();

	this->mesh_parent = &mesh;
	this->is_mesh_facets = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Mesh::~Mesh() = default;

	/* -------------------------------------------------------------------------- */
	void Mesh::read(const std::string & filename, const MeshIOType & mesh_io_type) {

	AKANTU_DEBUG_ASSERT(not is_distributed,
	"You cannot read a mesh that is already distributed");

	MeshIO::read(filename, *this, mesh_io_type);

	auto types =
	this->elementTypes(spatial_dimension, _not_ghost, _ek_not_defined);
	auto it = types.begin();
	auto last = types.end();
	if (it == last) {
	AKANTU_DEBUG_WARNING(
	"The mesh contained in the file "
	<< filename << " does not seem to be of the good dimension."
	<< " No element of dimension " << spatial_dimension << " were read.");
	}

	this->makeReady();
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::write(const std::string & filename,
	const MeshIOType & mesh_io_type) {
	MeshIO::write(filename, *this, mesh_io_type);
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::makeReady() {
	this->nb_global_nodes = this->nodes->size();
	this->computeBoundingBox();
	this->nodes_flags->resize(nodes->size(), NodeFlag::_normal);
	this->nodes_to_elements.resize(nodes->size());
	for (auto & node_set : nodes_to_elements) {
	node_set = std::make_unique<std::set<Element>>();
	}
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "Mesh [" << std::endl;
	stream << space << " + id : " << getID() << std::endl;
	stream << space << " + spatial dimension : " << this->spatial_dimension
	<< std::endl;
	stream << space << " + nodes [" << std::endl;
	nodes->printself(stream, indent + 2);
	stream << space << " + connectivities [" << std::endl;
	connectivities.printself(stream, indent + 2);
	stream << space << " ]" << std::endl;

	GroupManager::printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::computeBoundingBox() {
	AKANTU_DEBUG_IN();

	bbox_local.reset();

	for (auto & pos : make_view(*nodes, spatial_dimension)) {
	// if(!isPureGhostNode(i))
	bbox_local += pos;
	}

	if (this->is_distributed) {
	bbox = bbox_local.allSum(*communicator);
	} else {
	bbox = bbox_local;
	}

	size = bbox.size();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::initNormals() {
	normals.initialize(*this, _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_element_kind = _ek_not_defined);
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::getGlobalConnectivity(
	ElementTypeMapArray<UInt> & global_connectivity) {
	AKANTU_DEBUG_IN();

	for (auto && ghost_type : ghost_types) {
	for (auto type :
	global_connectivity.elementTypes(_spatial_dimension = _all_dimensions,
	_element_kind = _ek_not_defined, _ghost_type = ghost_type)) {
	if (not connectivities.exists(type, ghost_type)) {
	continue;
	}

	auto & local_conn = connectivities(type, ghost_type);
	auto & g_connectivity = global_connectivity(type, ghost_type);

	UInt nb_nodes = local_conn.size() * local_conn.getNbComponent();

	std::transform(local_conn.begin_reinterpret(nb_nodes),
	local_conn.end_reinterpret(nb_nodes),
	g_connectivity.begin_reinterpret(nb_nodes),
	[&](UInt l) -> UInt { return this->getNodeGlobalId(l); });
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	DumperIOHelper & Mesh::getGroupDumper(const std::string & dumper_name,
	const std::string & group_name) {
	if (group_name == "all") {
	return this->getDumper(dumper_name);
	}
	return element_groups[group_name]->getDumper(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	ElementTypeMap<UInt> Mesh::getNbDataPerElem(ElementTypeMapArray<T> & arrays) {
	ElementTypeMap<UInt> nb_data_per_elem;

	for (auto type : arrays.elementTypes(_element_kind = _ek_not_defined)) {
	UInt nb_elements = this->getNbElement(type);
	auto & array = arrays(type);

	nb_data_per_elem(type) = array.getNbComponent() * array.size();
	nb_data_per_elem(type) /= nb_elements;
	}

	return nb_data_per_elem;
	}

	/* -------------------------------------------------------------------------- */
	template ElementTypeMap<UInt>
	Mesh::getNbDataPerElem(ElementTypeMapArray<Real> & array);

	template ElementTypeMap<UInt>
	Mesh::getNbDataPerElem(ElementTypeMapArray<UInt> & array);

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	template <typename T>
	std::shared_ptr<dumpers::Field>
	Mesh::createFieldFromAttachedData(const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind) {

	std::shared_ptr<dumpers::Field> field;
	ElementTypeMapArray<T> * internal = nullptr;
	try {
	internal = &(this->getData<T>(field_id));
	} catch (...) {
	return nullptr;
	}

	ElementTypeMap<UInt> nb_data_per_elem = this->getNbDataPerElem(*internal);

	field = this->createElementalField<T, dumpers::InternalMaterialField>(
	*internal, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);

	return field;
	}

	template std::shared_ptr<dumpers::Field>
	Mesh::createFieldFromAttachedData<Real>(const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind);

	template std::shared_ptr<dumpers::Field>
	Mesh::createFieldFromAttachedData<UInt>(const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind);
	#endif

	/* -------------------------------------------------------------------------- */
	void Mesh::distributeImpl(
	Communicator & communicator,
	const std::function<Int(const Element &, const Element &)> &
	edge_weight_function [[gnu::unused]],
	const std::function<Int(const Element &)> & vertex_weight_function
	[[gnu::unused]]) {
	AKANTU_DEBUG_ASSERT(is_distributed == false,
	"This mesh is already distribute");
	this->communicator = &communicator;

	this->element_synchronizer = std::make_unique<ElementSynchronizer>(
	*this, this->getID() + ":element_synchronizer", true);

	this->node_synchronizer = std::make_unique<NodeSynchronizer>(
	*this, this->getID() + ":node_synchronizer", true);

	Int psize = this->communicator->getNbProc();

	if (psize > 1) {
	#ifdef AKANTU_USE_SCOTCH
	Int prank = this->communicator->whoAmI();
	if (prank == 0) {
	MeshPartitionScotch partition(*this, spatial_dimension);
	partition.partitionate(psize, edge_weight_function,
	vertex_weight_function);

	MeshUtilsDistribution::distributeMeshCentralized(*this, 0, partition);
	} else {
	MeshUtilsDistribution::distributeMeshCentralized(*this, 0);
	}
	#else
	if (psize > 1) {
	AKANTU_ERROR("Cannot distribute a mesh without a partitioning tool");
	}
	#endif
	}

	// if (psize > 1)
	this->is_distributed = true;

	this->computeBoundingBox();
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::getAssociatedElements(const Array<UInt> & node_list,
	Array<Element> & elements) const {
	for (const auto & node : node_list) {
	for (const auto & element : *nodes_to_elements[node]) {
	elements.push_back(element);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::getAssociatedElements(const UInt & node,
	Array<Element> & elements) const {
	for (const auto & element : *nodes_to_elements[node]) {
	elements.push_back(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::fillNodesToElements(UInt dimension) {
	Element e;

	UInt nb_nodes = nodes->size();
	this->nodes_to_elements.resize(nb_nodes);

	for (UInt n = 0; n < nb_nodes; ++n) {
	if (this->nodes_to_elements[n]) {
	this->nodes_to_elements[n]->clear();
	} else {
	this->nodes_to_elements[n] = std::make_unique<std::set<Element>>();
	}
	}

	for (auto ghost_type : ghost_types) {
	e.ghost_type = ghost_type;
	for (const auto & type :
	elementTypes(dimension, ghost_type, _ek_not_defined)) {
	e.type = type;

	UInt nb_element = this->getNbElement(type, ghost_type);
	auto connectivity = connectivities(type, ghost_type);
	auto conn_it = connectivity.begin(connectivity.getNbComponent());

	for (UInt el = 0; el < nb_element; ++el, ++conn_it) {
	e.element = el;
	const Vector<UInt> & conn = *conn_it;
	for (auto node : conn) {
	nodes_to_elements[node]->insert(e);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<UInt, UInt>
	Mesh::updateGlobalData(NewNodesEvent & nodes_event,
	NewElementsEvent & elements_event) {
	if (global_data_updater) {
	return this->global_data_updater->updateData(nodes_event, elements_event);
	}
	return std::make_tuple(nodes_event.getList().size(),
	elements_event.getList().size());
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::registerGlobalDataUpdater(
	std::unique_ptr<MeshGlobalDataUpdater> && global_data_updater) {
	this->global_data_updater = std::move(global_data_updater);
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::eraseElements(const Array<Element> & elements) {
	ElementTypeMap<UInt> last_element;

	RemovedElementsEvent event(*this, "new_numbering", AKANTU_CURRENT_FUNCTION);
	auto & remove_list = event.getList();
	auto & new_numbering = event.getNewNumbering();

	for (auto && el : elements) {
	if (el.ghost_type != _not_ghost) {
	auto & count = ghosts_counters(el);
	--count;
	if (count > 0) {
	continue;
	}
	}

	remove_list.push_back(el);
	if (not new_numbering.exists(el.type, el.ghost_type)) {
	auto nb_element = mesh.getNbElement(el.type, el.ghost_type);
	auto & numbering =
	new_numbering.alloc(nb_element, 1, el.type, el.ghost_type);
	for (auto && pair : enumerate(numbering)) {
	std::get<1>(pair) = std::get<0>(pair);
	}
	}

	new_numbering(el) = UInt(-1);
	}

	auto find_last_not_deleted = [](auto && array, Int start) -> Int {
	do {
	--start;
	} while (start >= 0 and array[start] == UInt(-1));

	return start;
	};

	auto find_first_deleted = [](auto && array, Int start) -> Int {
	auto begin = array.begin();
	auto it = std::find_if(begin + start, array.end(),
	[](auto & el) { return el == UInt(-1); });
	return Int(it - begin);
	};

	for (auto ghost_type : ghost_types) {
	for (auto type : new_numbering.elementTypes(_ghost_type = ghost_type)) {
	auto & numbering = new_numbering(type, ghost_type);
	auto last_not_delete = find_last_not_deleted(numbering, numbering.size());

	if (last_not_delete < 0) {
	continue;
	}

	auto pos = find_first_deleted(numbering, 0);

	while (pos < last_not_delete) {
	std::swap(numbering[pos], numbering[last_not_delete]);
	last_not_delete = find_last_not_deleted(numbering, last_not_delete);
	pos = find_first_deleted(numbering, pos + 1);
	}
	}
	}
	this->sendEvent(event);
	}

	} // namespace akantu
	diff --git a/src/mesh/mesh.hh b/src/mesh/mesh.hh
	index e2a5827de..19f23d05e 100644
	--- a/src/mesh/mesh.hh
	+++ b/src/mesh/mesh.hh
	@@ -1,701 +1,699 @@
	/**
	* @file mesh.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Nov 12 2020
	*
	* @brief the class representing the meshes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_HH_
	#define AKANTU_MESH_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_bbox.hh"
	#include "aka_event_handler_manager.hh"
	#include "communicator.hh"
	#include "dumpable.hh"
	#include "element.hh"
	#include "element_class.hh"
	#include "element_type_map.hh"
	#include "group_manager.hh"
	#include "mesh_data.hh"
	#include "mesh_events.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	#include <set>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class ElementSynchronizer;
	class NodeSynchronizer;
	class PeriodicNodeSynchronizer;
	class MeshGlobalDataUpdater;
	} // namespace akantu

	namespace akantu {

	namespace {
	DECLARE_NAMED_ARGUMENT(communicator);
	DECLARE_NAMED_ARGUMENT(edge_weight_function);
	DECLARE_NAMED_ARGUMENT(vertex_weight_function);
	} // namespace

	/* -------------------------------------------------------------------------- */
	/* Mesh */
	/* -------------------------------------------------------------------------- */

	/**
	* @class Mesh mesh.hh
	*
	* This class contaisn the coordinates of the nodes in the Mesh.nodes
	* akant::Array, and the connectivity. The connectivity are stored in by element
	* types.
	*
	* In order to loop on all element you have to loop on all types like this :
	* @code{.cpp}
	for(auto & type : mesh.elementTypes()) {
	UInt nb_element = mesh.getNbElement(type);
	const Array<UInt> & conn = mesh.getConnectivity(type);
	for(UInt e = 0; e < nb_element; ++e) {
	...
	}
	}

	or

	for_each_element(mesh, [](Element & element) {
	std::cout << element << std::endl
	});
	@endcode
	*/
	class Mesh : public EventHandlerManager<MeshEventHandler>,
	public GroupManager,
	public MeshData,
	public Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	private:
	/// default constructor used for chaining, the last parameter is just to
	/// differentiate constructors
	- Mesh(UInt spatial_dimension, const ID & id,
	- Communicator & communicator);
	+ Mesh(UInt spatial_dimension, const ID & id, Communicator & communicator);

	public:
	/// constructor that create nodes coordinates array
	Mesh(UInt spatial_dimension, const ID & id = "mesh");

	/// mesh not distributed and not using the default communicator
	Mesh(UInt spatial_dimension, Communicator & communicator,
	const ID & id = "mesh");

	/**
	* constructor that use an existing nodes coordinates
	* array, by getting the vector of coordinates
	*/
	Mesh(UInt spatial_dimension, const std::shared_ptr<Array<Real>> & nodes,
	const ID & id = "mesh");

	~Mesh() override;

	/// read the mesh from a file
	void read(const std::string & filename,
	const MeshIOType & mesh_io_type = _miot_auto);
	/// write the mesh to a file
	void write(const std::string & filename,
	const MeshIOType & mesh_io_type = _miot_auto);

	protected:
	void makeReady();

	private:
	/// initialize the connectivity to NULL and other stuff
	void init();

	/// function that computes the bounding box (fills xmin, xmax)
	void computeBoundingBox();

	/* ------------------------------------------------------------------------ */
	/* Distributed memory methods and accessors */
	/* ------------------------------------------------------------------------ */
	public:
	protected:
	/// patitionate the mesh among the processors involved in their computation
	virtual void distributeImpl(
	Communicator & communicator,
	const std::function<Int(const Element &, const Element &)> &
	edge_weight_function,
	const std::function<Int(const Element &)> & vertex_weight_function);

	public:
	/// with the arguments to pass to the partitionner
	template <typename... pack>
	std::enable_if_t<are_named_argument<pack...>::value>
	distribute(pack &&... _pack) {
	distributeImpl(
	OPTIONAL_NAMED_ARG(communicator, Communicator::getStaticCommunicator()),
	OPTIONAL_NAMED_ARG(edge_weight_function,
	[](auto &&, auto &&) { return 1; }),
	OPTIONAL_NAMED_ARG(vertex_weight_function, [](auto &&) { return 1; }));
	}

	/// defines is the mesh is distributed or not
	inline bool isDistributed() const { return this->is_distributed; }

	/* ------------------------------------------------------------------------ */
	/* Periodicity methods and accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// set the periodicity in a given direction
	void makePeriodic(const SpatialDirection & direction);
	void makePeriodic(const SpatialDirection & direction, const ID & list_1,
	const ID & list_2);

	protected:
	void makePeriodic(const SpatialDirection & direction,
	const Array<UInt> & list_left,
	const Array<UInt> & list_right);

	/// Removes the face that the mesh is periodic
	void wipePeriodicInfo();

	inline void addPeriodicSlave(UInt slave, UInt master);

	template <typename T>
	void synchronizePeriodicSlaveDataWithMaster(Array<T> & data);

	// update the periodic synchronizer (creates it if it does not exists)
	void updatePeriodicSynchronizer();

	public:
	/// defines if the mesh is periodic or not
	inline bool isPeriodic() const { return this->is_periodic; }

	inline bool isPeriodic(const SpatialDirection & /direction/) const {
	return this->is_periodic;
	}

	class PeriodicSlaves;

	/// get the master node for a given slave nodes, except if node not a slave
	inline UInt getPeriodicMaster(UInt slave) const;

	/// get an iterable list of slaves for a given master node
	inline decltype(auto) getPeriodicSlaves(UInt master) const;

	/* ------------------------------------------------------------------------ */
	/* General Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/// extract coordinates of nodes from an element
	template <typename T>
	inline void
	extractNodalValuesFromElement(const Array<T> & nodal_values, T * local_coord,
	const UInt * connectivity, UInt n_nodes,
	UInt nb_degree_of_freedom) const;

	// /// extract coordinates of nodes from a reversed element
	// inline void extractNodalCoordinatesFromPBCElement(Real * local_coords,
	// UInt * connectivity,
	// UInt n_nodes);

	/// add a Array of connectivity for the given ElementType and GhostType .
	inline void addConnectivityType(ElementType type,
	GhostType ghost_type = _not_ghost);

	/* ------------------------------------------------------------------------ */
	template <class Event> inline void sendEvent(Event & event) {
	// if(event.getList().size() != 0)
	EventHandlerManager<MeshEventHandler>::sendEvent<Event>(event);
	}

	/// prepare the event to remove the elements listed
	void eraseElements(const Array<Element> & elements);

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void removeNodesFromArray(Array<T> & vect,
	const Array<UInt> & new_numbering);

	/// initialize normals
	void initNormals();

	/// init facets' mesh
	Mesh & initMeshFacets(const ID & id = "mesh_facets");

	/// define parent mesh
	void defineMeshParent(const Mesh & mesh);

	/// get global connectivity array
	void getGlobalConnectivity(ElementTypeMapArray<UInt> & global_connectivity);

	public:
	void getAssociatedElements(const Array<UInt> & node_list,
	Array<Element> & elements) const;

	void getAssociatedElements(const UInt & node,
	Array<Element> & elements) const;

	public:
	/// fills the nodes_to_elements for given dimension elements
	void fillNodesToElements(UInt dimension = _all_dimensions);
	-
	+
	private:
	/// update the global ids, nodes type, ...
	std::tuple<UInt, UInt> updateGlobalData(NewNodesEvent & nodes_event,
	NewElementsEvent & elements_event);

	void registerGlobalDataUpdater(
	std::unique_ptr<MeshGlobalDataUpdater> && global_data_updater);
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the id of the mesh
	AKANTU_GET_MACRO(ID, id, const ID &);

	/// get the spatial dimension of the mesh = number of component of the
	/// coordinates
	AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);

	/// get the nodes Array aka coordinates
	AKANTU_GET_MACRO(Nodes, *nodes, const Array<Real> &);
	AKANTU_GET_MACRO_NOT_CONST(Nodes, *nodes, Array<Real> &);

	/// get the normals for the elements
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(Normals, normals, Real);

	/// get the number of nodes
	AKANTU_GET_MACRO(NbNodes, nodes->size(), UInt);

	/// get the Array of global ids of the nodes (only used in parallel)
	AKANTU_GET_MACRO(GlobalNodesIds, *nodes_global_ids, const Array<UInt> &);
	// AKANTU_GET_MACRO_NOT_CONST(GlobalNodesIds, *nodes_global_ids, Array<UInt>
	// &);

	/// get the global id of a node
	inline UInt getNodeGlobalId(UInt local_id) const;

	/// get the global id of a node
	inline UInt getNodeLocalId(UInt global_id) const;

	/// get the global number of nodes
	inline UInt getNbGlobalNodes() const;

	/// get the nodes type Array
	AKANTU_GET_MACRO(NodesFlags, *nodes_flags, const Array<NodeFlag> &);

	protected:
	AKANTU_GET_MACRO_NOT_CONST(NodesFlags, *nodes_flags, Array<NodeFlag> &);

	public:
	inline NodeFlag getNodeFlag(UInt local_id) const;
	inline Int getNodePrank(UInt local_id) const;

	/// say if a node is a pure ghost node
	inline bool isPureGhostNode(UInt n) const;

	/// say if a node is pur local or master node
	inline bool isLocalOrMasterNode(UInt n) const;

	inline bool isLocalNode(UInt n) const;
	inline bool isMasterNode(UInt n) const;
	inline bool isSlaveNode(UInt n) const;

	inline bool isPeriodicSlave(UInt n) const;
	inline bool isPeriodicMaster(UInt n) const;

	const Vector<Real> & getLowerBounds() const { return bbox.getLowerBounds(); }
	const Vector<Real> & getUpperBounds() const { return bbox.getUpperBounds(); }
	AKANTU_GET_MACRO(BBox, bbox, const BBox &);

	const Vector<Real> & getLocalLowerBounds() const {
	return bbox_local.getLowerBounds();
	}
	const Vector<Real> & getLocalUpperBounds() const {
	return bbox_local.getUpperBounds();
	}
	AKANTU_GET_MACRO(LocalBBox, bbox_local, const BBox &);

	/// get the connectivity Array for a given type
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Connectivity, connectivities, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(Connectivity, connectivities, UInt);
	AKANTU_GET_MACRO(Connectivities, connectivities,
	const ElementTypeMapArray<UInt> &);

	/// get the number of element of a type in the mesh
	inline UInt getNbElement(ElementType type,
	GhostType ghost_type = _not_ghost) const;

	/// get the number of element for a given ghost_type and a given dimension
	inline UInt getNbElement(UInt spatial_dimension = _all_dimensions,
	GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_not_defined) const;

	/// compute the barycenter of a given element
	inline void getBarycenter(const Element & element,
	Vector<Real> & barycenter) const;

	void getBarycenters(Array<Real> & barycenter, ElementType type,
	GhostType ghost_type) const;

	/// get the element connected to a subelement (element of lower dimension)
	const auto & getElementToSubelement() const;

	/// get the element connected to a subelement
	const auto & getElementToSubelement(ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	/// get the elements connected to a subelement
	const auto & getElementToSubelement(const Element & element) const;

	/// get the subelement (element of lower dimension) connected to a element
	const auto & getSubelementToElement() const;

	/// get the subelement connected to an element
	- const auto &
	- getSubelementToElement(ElementType el_type,
	- GhostType ghost_type = _not_ghost) const;
	+ const auto & getSubelementToElement(ElementType el_type,
	+ GhostType ghost_type = _not_ghost) const;

	/// get the subelement (element of lower dimension) connected to a element
	VectorProxy<Element> getSubelementToElement(const Element & element) const;

	/// get connectivity of a given element
	inline VectorProxy<UInt> getConnectivity(const Element & element) const;
	inline Vector<UInt>
	getConnectivityWithPeriodicity(const Element & element) const;

	protected:
	/// get the element connected to a subelement (element of lower dimension)
	auto & getElementToSubelementNC();
	auto & getSubelementToElementNC();
	inline auto & getElementToSubelementNC(const Element & element);
	- inline VectorProxy<Element> getSubelementToElementNC(const Element & element);
	+ inline VectorProxy<Element>
	+ getSubelementToElementNC(const Element & element) const;
	/// get the element connected to a subelement
	auto & getElementToSubelementNC(ElementType el_type,
	GhostType ghost_type = _not_ghost);
	/// get the subelement connected to an element
	auto & getSubelementToElementNC(ElementType el_type,
	GhostType ghost_type = _not_ghost);

	inline VectorProxy<UInt> getConnectivityNC(const Element & element);

	public:
	/// get a name field associated to the mesh
	template <typename T>
	inline const Array<T> & getData(const ID & data_name, ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	/// get a name field associated to the mesh
	template <typename T>
	inline Array<T> & getData(const ID & data_name, ElementType el_type,
	GhostType ghost_type = _not_ghost);

	/// get a name field associated to the mesh
	template <typename T>
	inline const ElementTypeMapArray<T> & getData(const ID & data_name) const;

	/// get a name field associated to the mesh
	template <typename T>
	inline ElementTypeMapArray<T> & getData(const ID & data_name);

	template <typename T>
	ElementTypeMap<UInt> getNbDataPerElem(ElementTypeMapArray<T> & array);

	template <typename T>
	std::shared_ptr<dumpers::Field>
	createFieldFromAttachedData(const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind);

	/// templated getter returning the pointer to data in MeshData (modifiable)
	template <typename T>
	inline Array<T> &
	getDataPointer(const std::string & data_name, ElementType el_type,
	GhostType ghost_type = _not_ghost, UInt nb_component = 1,
	bool size_to_nb_element = true,
	bool resize_with_parent = false);

	template <typename T>
	inline Array<T> & getDataPointer(const ID & data_name, ElementType el_type,
	GhostType ghost_type, UInt nb_component,
	bool size_to_nb_element,
	bool resize_with_parent, const T & defaul_);

	/// Facets mesh accessor
	inline const Mesh & getMeshFacets() const;
	inline Mesh & getMeshFacets();

	inline auto hasMeshFacets() const { return mesh_facets != nullptr; }

	/// Parent mesh accessor
	inline const Mesh & getMeshParent() const;

	inline bool isMeshFacets() const { return this->is_mesh_facets; }

	/// return the dumper from a group and and a dumper name
	DumperIOHelper & getGroupDumper(const std::string & dumper_name,
	const std::string & group_name);

	/* ------------------------------------------------------------------------ */
	/* Wrappers on ElementClass functions */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the number of nodes per element for a given element type
	static inline UInt getNbNodesPerElement(ElementType type);

	/// get the number of nodes per element for a given element type considered as
	/// a first order element
	static inline ElementType getP1ElementType(ElementType type);

	/// get the kind of the element type
	static inline ElementKind getKind(ElementType type);

	/// get spatial dimension of a type of element
	static inline UInt getSpatialDimension(ElementType type);

	/// get the natural space dimension of a type of element
	static inline UInt getNaturalSpaceDimension(const ElementType & type);
	-
	+
	/// get number of facets of a given element type
	static inline UInt getNbFacetsPerElement(ElementType type);

	/// get number of facets of a given element type
	static inline UInt getNbFacetsPerElement(ElementType type, UInt t);

	/// get local connectivity of a facet for a given facet type
	static inline auto getFacetLocalConnectivity(ElementType type, UInt t = 0);

	/// get connectivity of facets for a given element
	inline auto getFacetConnectivity(const Element & element, UInt t = 0) const;

	/// get the number of type of the surface element associated to a given
	/// element type
	static inline UInt getNbFacetTypes(ElementType type, UInt t = 0);

	/// get the type of the surface element associated to a given element
	static inline constexpr auto getFacetType(ElementType type, UInt t = 0);

	/// get all the type of the surface element associated to a given element
	static inline constexpr auto getAllFacetTypes(ElementType type);

	/// get the number of nodes in the given element list
	static inline UInt getNbNodesPerElementList(const Array<Element> & elements);

	/* ------------------------------------------------------------------------ */
	/* Element type Iterator */
	/* ------------------------------------------------------------------------ */

	- using type_iterator =
	- ElementTypeMapArray<UInt, ElementType>::type_iterator;
	+ using type_iterator = ElementTypeMapArray<UInt, ElementType>::type_iterator;
	using ElementTypesIteratorHelper =
	ElementTypeMapArray<UInt, ElementType>::ElementTypesIteratorHelper;

	template <typename... pack>
	ElementTypesIteratorHelper elementTypes(pack &&... _pack) const;

	[[deprecated("Use elementTypes instead")]] inline decltype(auto)
	firstType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_regular) const {
	return connectivities.elementTypes(dim, ghost_type, kind).begin();
	}

	[[deprecated("Use elementTypes instead")]] inline decltype(auto)
	lastType(UInt dim = _all_dimensions, GhostType ghost_type = _not_ghost,
	ElementKind kind = _ek_regular) const {
	return connectivities.elementTypes(dim, ghost_type, kind).end();
	}

	AKANTU_GET_MACRO(ElementSynchronizer, *element_synchronizer,
	const ElementSynchronizer &);
	AKANTU_GET_MACRO_NOT_CONST(ElementSynchronizer, *element_synchronizer,
	ElementSynchronizer &);
	AKANTU_GET_MACRO(NodeSynchronizer, *node_synchronizer,
	const NodeSynchronizer &);
	AKANTU_GET_MACRO_NOT_CONST(NodeSynchronizer, *node_synchronizer,
	NodeSynchronizer &);
	AKANTU_GET_MACRO(PeriodicNodeSynchronizer, *periodic_node_synchronizer,
	const PeriodicNodeSynchronizer &);
	AKANTU_GET_MACRO_NOT_CONST(PeriodicNodeSynchronizer,
	*periodic_node_synchronizer,
	PeriodicNodeSynchronizer &);

	// AKANTU_GET_MACRO_NOT_CONST(Communicator, *communicator, StaticCommunicator
	// &);
	AKANTU_GET_MACRO(Communicator, *communicator, const auto &);
	AKANTU_GET_MACRO_NOT_CONST(Communicator, *communicator, auto &);
	AKANTU_GET_MACRO(PeriodicMasterSlaves, periodic_master_slave, const auto &);

	/* ------------------------------------------------------------------------ */
	/* Private methods for friends */
	/* ------------------------------------------------------------------------ */
	private:
	friend class MeshAccessor;
	friend class MeshUtils;

	AKANTU_GET_MACRO(NodesPointer, *nodes, Array<Real> &);

	/// get a pointer to the nodes_global_ids Array<UInt> and create it if
	/// necessary
	inline Array<UInt> & getNodesGlobalIdsPointer();

	/// get a pointer to the nodes_type Array<Int> and create it if necessary
	inline Array<NodeFlag> & getNodesFlagsPointer();

	/// get a pointer to the connectivity Array for the given type and create it
	/// if necessary
	inline Array<UInt> &
	getConnectivityPointer(ElementType type, GhostType ghost_type = _not_ghost);

	/// get the ghost element counter
	inline Array<UInt> & getGhostsCounters(ElementType type,
	GhostType ghost_type = _ghost) {
	AKANTU_DEBUG_ASSERT(ghost_type != _not_ghost,
	"No ghost counter for _not_ghost elements");
	return ghosts_counters(type, ghost_type);
	}

	/// get a pointer to the element_to_subelement Array for the given type and
	/// create it if necessary
	inline Array<std::vector<Element>> &
	getElementToSubelementPointer(ElementType type,
	GhostType ghost_type = _not_ghost);

	/// get a pointer to the subelement_to_element Array for the given type and
	/// create it if necessary
	inline Array<Element> &
	getSubelementToElementPointer(ElementType type,
	GhostType ghost_type = _not_ghost);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	ID id;

	/// array of the nodes coordinates
	std::shared_ptr<Array<Real>> nodes;

	/// global node ids
	std::shared_ptr<Array<UInt>> nodes_global_ids;

	/// node flags (shared/periodic/...)
	std::shared_ptr<Array<NodeFlag>> nodes_flags;

	/// processor handling the node when not local or master
	std::unordered_map<UInt, Int> nodes_prank;

	/// global number of nodes;
	UInt nb_global_nodes{0};

	/// all class of elements present in this mesh (for heterogenous meshes)
	ElementTypeMapArray<UInt> connectivities;

	/// count the references on ghost elements
	ElementTypeMapArray<UInt> ghosts_counters;

	/// map to normals for all class of elements present in this mesh
	ElementTypeMapArray<Real> normals;

	/// the spatial dimension of this mesh
	UInt spatial_dimension{0};

	/// size covered by the mesh on each direction
	Vector<Real> size;
	/// global bounding box
	BBox bbox;

	/// local bounding box
	BBox bbox_local;

	/// Extra data loaded from the mesh file
	// MeshData mesh_data;

	/// facets' mesh
	std::unique_ptr<Mesh> mesh_facets;

	/// parent mesh (this is set for mesh_facets meshes)
	const Mesh * mesh_parent{nullptr};

	/// defines if current mesh is mesh_facets or not
	bool is_mesh_facets{false};

	/// defines if the mesh is centralized or distributed
	bool is_distributed{false};

	/// defines if the mesh is periodic
	bool is_periodic{false};

	/// Communicator on which mesh is distributed
	Communicator * communicator;

	/// Element synchronizer
	std::unique_ptr<ElementSynchronizer> element_synchronizer;

	/// Node synchronizer
	std::unique_ptr<NodeSynchronizer> node_synchronizer;

	/// Node synchronizer for periodic nodes
	std::unique_ptr<PeriodicNodeSynchronizer> periodic_node_synchronizer;

	using NodesToElements = std::vector<std::unique_ptr<std::set<Element>>>;

	/// class to update global data using external knowledge
	std::unique_ptr<MeshGlobalDataUpdater> global_data_updater;

	/// This info is stored to simplify the dynamic changes
	NodesToElements nodes_to_elements;

	/// periodicity local info
	std::unordered_map<UInt, UInt> periodic_slave_master;
	std::unordered_multimap<UInt, UInt> periodic_master_slave;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream, const Mesh & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* Inline functions */
	/* -------------------------------------------------------------------------- */
	#include "element_type_map_tmpl.hh"
	#include "mesh_inline_impl.hh"

	#endif /* AKANTU_MESH_HH_ */
	diff --git a/src/mesh/mesh_accessor.hh b/src/mesh/mesh_accessor.hh
	index 0eff39457..6388c6ed2 100644
	--- a/src/mesh/mesh_accessor.hh
	+++ b/src/mesh/mesh_accessor.hh
	@@ -1,221 +1,221 @@
	/**
	* @file mesh_accessor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jun 30 2015
	* @date last modification: Tue Feb 09 2021
	*
	* @brief this class allow to access some private member of mesh it is used for
	* IO for examples
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_ACCESSOR_HH_
	#define AKANTU_MESH_ACCESSOR_HH_

	namespace akantu {
	class NodeSynchronizer;
	class ElementSynchronizer;
	class MeshGlobalDataUpdater;
	} // namespace akantu

	namespace akantu {

	class MeshAccessor {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	explicit MeshAccessor(Mesh & mesh) : _mesh(mesh) {}
	virtual ~MeshAccessor() = default;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the global number of nodes
	inline UInt getNbGlobalNodes() const { return this->_mesh.nb_global_nodes; }

	/// set the global number of nodes
	inline void setNbGlobalNodes(UInt nb_global_nodes) {
	this->_mesh.nb_global_nodes = nb_global_nodes;
	}

	/// set the mesh as being distributed
	inline void setDistributed() { this->_mesh.is_distributed = true; }

	/// get a pointer to the nodes_global_ids Array<UInt> and create it if
	/// necessary
	inline auto & getNodesGlobalIds() {
	return this->_mesh.getNodesGlobalIdsPointer();
	}

	/// get a pointer to the nodes_type Array<Int> and create it if necessary
	inline auto & getNodesFlags() { return this->_mesh.getNodesFlags(); }

	/// get a pointer to the nodes_type Array<Int> and create it if necessary
	inline void setNodePrank(UInt node, Int prank) {
	this->_mesh.nodes_prank[node] = prank;
	}

	/// get a pointer to the coordinates Array
	inline auto & getNodes() { return this->_mesh.getNodesPointer(); }

	/// get a pointer to the coordinates Array
	inline auto getNodesSharedPtr() { return this->_mesh.nodes; }

	/// get the connectivities
	inline auto & getConnectivities() { return this->_mesh.connectivities; }

	/// get the connectivity Array for the given type and create it
	/// if necessary
	inline auto & getConnectivity(ElementType type,
	GhostType ghost_type = _not_ghost) {
	return this->_mesh.getConnectivityPointer(type, ghost_type);
	}

	/// resize the connectivity (use carefully)
	inline void resizeConnectivity(UInt new_size, ElementType type,
	GhostType ghost_type = _not_ghost) {
	this->getConnectivity(type, ghost_type).resize(new_size, UInt(-1));
	}

	/// resize the nodes (use carefully)
	inline void resizeNodes(UInt new_size) {
	this->getNodes().resize(new_size, UInt(-1));
	}

	/// get the connectivity for the given element
	inline decltype(auto) getConnectivity(const Element & element) {
	return this->_mesh.getConnectivityNC(element);
	}

	/// get the ghost element counter
	inline auto & getGhostsCounters(ElementType type,
	GhostType ghost_type = _ghost) {
	return this->_mesh.getGhostsCounters(type, ghost_type);
	}

	/// get the element_to_subelement Array for the given type and
	/// create it if necessary
	inline auto & getElementToSubelement(ElementType type,
	GhostType ghost_type = _not_ghost) {
	return this->_mesh.getElementToSubelementPointer(type, ghost_type);
	}

	inline decltype(auto)
	getElementToSubelementNC(const ElementType & type,
	const GhostType & ghost_type = _not_ghost) {
	return this->_mesh.getElementToSubelementNC(type, ghost_type);
	}

	/// get the subelement_to_element Array for the given type and
	/// create it if necessary
	inline auto & getSubelementToElement(ElementType type,
	GhostType ghost_type = _not_ghost) {
	return this->_mesh.getSubelementToElementPointer(type, ghost_type);
	}

	inline decltype(auto)
	getSubelementToElementNC(const ElementType & type,
	const GhostType & ghost_type = _not_ghost) {
	return this->_mesh.getSubelementToElementNC(type, ghost_type);
	}

	/// get the element_to_subelement, creates it if necessary
	inline decltype(auto) getElementToSubelement() {
	return this->_mesh.getElementToSubelementNC();
	}

	/// get subelement_to_element, creates it if necessary
	inline decltype(auto) getSubelementToElement() {
	return this->_mesh.getSubelementToElementNC();
	}

	/// get a pointer to the element_to_subelement Array for element and
	/// create it if necessary
	inline decltype(auto) getElementToSubelement(const Element & element) {
	return this->_mesh.getElementToSubelementNC(element);
	}

	/// get a pointer to the subelement_to_element Array for the given element and
	/// create it if necessary
	inline decltype(auto) getSubelementToElement(const Element & element) {
	return this->_mesh.getSubelementToElementNC(element);
	}

	template <typename T>
	inline auto & getData(const std::string & data_name, ElementType el_type,
	GhostType ghost_type = _not_ghost,
	UInt nb_component = 1, bool size_to_nb_element = true,
	bool resize_with_parent = false) {
	return this->_mesh.getDataPointer<T>(data_name, el_type, ghost_type,
	nb_component, size_to_nb_element,
	resize_with_parent);
	}

	/// get the node synchonizer
	auto & getNodeSynchronizer() { return *this->_mesh.node_synchronizer; }

	/// get the element synchonizer
	auto & getElementSynchronizer() { return *this->_mesh.element_synchronizer; }

	decltype(auto) updateGlobalData(NewNodesEvent & nodes_event,
	NewElementsEvent & elements_event) {
	return this->_mesh.updateGlobalData(nodes_event, elements_event);
	}

	void registerGlobalDataUpdater(
	std::unique_ptr<MeshGlobalDataUpdater> && global_data_updater) {
	this->_mesh.registerGlobalDataUpdater(
	std::forward<std::unique_ptr<MeshGlobalDataUpdater>>(
	global_data_updater));
	}

	/* ------------------------------------------------------------------------ */
	void makeReady() { this->_mesh.makeReady(); }

	/* ------------------------------------------------------------------------ */
	void addPeriodicSlave(UInt slave, UInt master) {
	this->_mesh.addPeriodicSlave(slave, master);
	}

	void markMeshPeriodic() {
	for (UInt s : arange(this->_mesh.spatial_dimension)) {
	this->_mesh.is_periodic \|= 1 << s;
	}
	}

	void wipePeriodicInfo() { this->_mesh.wipePeriodicInfo(); }

	private:
	Mesh & _mesh;
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_ACCESSOR_HH_ */
	diff --git a/src/mesh/mesh_data.cc b/src/mesh/mesh_data.cc
	index 1d4c1f322..1a6b86d5b 100644
	--- a/src/mesh/mesh_data.cc
	+++ b/src/mesh/mesh_data.cc
	@@ -1,41 +1,41 @@
	/**
	* @file mesh_data.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Wed Sep 12 2018
	*
	* @brief Stores generic data loaded from the mesh file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "mesh_data.hh"
	#include "mesh.hh"

	namespace akantu {

	MeshData::MeshData(const ID & _id, const ID & parent_id)
	: _id(parent_id + ":" + _id) {}

	} // namespace akantu
	diff --git a/src/mesh/mesh_data.hh b/src/mesh/mesh_data.hh
	index e9c85f2e1..b478bb69f 100644
	--- a/src/mesh/mesh_data.hh
	+++ b/src/mesh/mesh_data.hh
	@@ -1,190 +1,189 @@
	/**
	* @file mesh_data.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Fri Dec 28 2018
	*
	* @brief Stores generic data loaded from the mesh file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_DATA_HH_
	#define AKANTU_MESH_DATA_HH_

	/* -------------------------------------------------------------------------- */
	#include "element_type_map.hh"
	#include <map>
	#include <string>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	#define AKANTU_MESH_DATA_TYPES \
	((_int, Int))((_uint, UInt))((_real, Real))((_bool, bool))( \
	(_element, Element))((_std_string, std::string))( \
	(_std_vector_element, std::vector<Element>))

	#define AKANTU_MESH_DATA_TUPLE_FIRST_ELEM(s, data, elem) \
	BOOST_PP_TUPLE_ELEM(2, 0, elem)
	enum class MeshDataTypeCode : int {
	BOOST_PP_SEQ_ENUM(BOOST_PP_SEQ_TRANSFORM(AKANTU_MESH_DATA_TUPLE_FIRST_ELEM, ,
	AKANTU_MESH_DATA_TYPES)),
	_unknown
	};

	enum class MeshDataType {
	_nodal,
	_elemental,
	};

	class MeshData {
	/* ------------------------------------------------------------------------ */
	/* Typedefs */
	/* ------------------------------------------------------------------------ */
	private:
	using TypeCode = MeshDataTypeCode;
	using ElementalDataMap =
	std::map<std::string, std::unique_ptr<ElementTypeMapBase>>;
	using NodalDataMap = std::map<std::string, std::unique_ptr<ArrayBase>>;
	using TypeCodeMap = std::map<std::string, TypeCode>;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshData(const ID & id = "mesh_data", const ID & parent_id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods and accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// tells if the given array exists
	template <typename T>
	bool hasData(const ID & data_name, ElementType elem_type,
	GhostType ghost_type = _not_ghost) const;

	/// tells if the given data exists
	bool hasData(const ID & data_name,
	MeshDataType type = MeshDataType::_elemental) const;

	bool hasData(MeshDataType type = MeshDataType::_elemental) const;

	/// get the names of the data stored in elemental_data
	inline auto getTagNames(ElementType type,
	GhostType ghost_type = _not_ghost) const;

	/// get the names of the data stored in elemental_data
	inline auto getTagNames() const;

	/// get the type of the data stored in elemental_data
	template <typename T> TypeCode getTypeCode() const;
	inline TypeCode
	getTypeCode(const ID & name,
	MeshDataType type = MeshDataType::_elemental) const;

	/// Get an existing elemental data array
	template <typename T>
	const Array<T> &
	getElementalDataArray(const ID & data_name, ElementType elem_type,
	GhostType ghost_type = _not_ghost) const;
	template <typename T>
	- Array<T> & getElementalDataArray(const ID & data_name,
	- ElementType elem_type,
	+ Array<T> & getElementalDataArray(const ID & data_name, ElementType elem_type,
	GhostType ghost_type = _not_ghost);

	/// Get an elemental data array, if it does not exist: allocate it
	template <typename T>
	- Array<T> & getElementalDataArrayAlloc(
	- const ID & data_name, ElementType elem_type,
	- GhostType ghost_type = _not_ghost, UInt nb_component = 1);
	+ Array<T> & getElementalDataArrayAlloc(const ID & data_name,
	+ ElementType elem_type,
	+ GhostType ghost_type = _not_ghost,
	+ UInt nb_component = 1);

	template <typename T>
	- inline UInt getNbComponentTemplated(const ID & name,
	- ElementType el_type,
	+ inline UInt getNbComponentTemplated(const ID & name, ElementType el_type,
	GhostType ghost_type) const;
	inline UInt getNbComponent(const ID & name, ElementType el_type,
	GhostType ghost_type = _not_ghost) const;

	inline UInt getNbComponent(const ID & name) const;

	/// Get an existing elemental data
	template <typename T>
	const ElementTypeMapArray<T> & getElementalData(const ID & name) const;
	template <typename T>
	ElementTypeMapArray<T> & getElementalData(const ID & name);

	template <typename T>
	Array<T> & getNodalData(const ID & name, UInt nb_components = 1);
	template <typename T> const Array<T> & getNodalData(const ID & name) const;

	private:
	/// Register new elemental data (and alloc data) with check if the name is
	/// new
	template <typename T>
	ElementTypeMapArray<T> & registerElementalData(const ID & name);
	inline void registerElementalData(const ID & name, TypeCode type);

	/// Register new nodal data (and alloc data) with check if the name is
	/// new
	template <typename T>
	Array<T> & registerNodalData(const ID & name, UInt nb_components = 1);
	inline void registerNodalData(const ID & name, UInt nb_components,
	TypeCode type);

	/// Register new elemental data (add alloc data)
	template <typename T>
	ElementTypeMapArray<T> & allocElementalData(const ID & name);

	/// Register new nodal data (add alloc data)
	template <typename T>
	Array<T> & allocNodalData(const ID & name, UInt nb_components);

	friend class SlaveNodeInfoPerProc;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	ID _id;

	/// Map when elemental data is stored as ElementTypeMap
	ElementalDataMap elemental_data;

	/// Map when elemental data is stored as ElementTypeMap
	NodalDataMap nodal_data;

	/// Map when elementalType of the data stored in elemental_data
	std::map<MeshDataType, TypeCodeMap> typecode_map{
	{MeshDataType::_elemental, {}}, {MeshDataType::_nodal, {}}};
	};

	} // namespace akantu

	#include "mesh_data_tmpl.hh"
	#undef AKANTU_MESH_DATA_TUPLE_FIRST_ELEM

	#endif /* AKANTU_MESH_DATA_HH_ */
	diff --git a/src/mesh/mesh_data_tmpl.hh b/src/mesh/mesh_data_tmpl.hh
	index bdfccfb0e..a8ea53f4d 100644
	--- a/src/mesh/mesh_data_tmpl.hh
	+++ b/src/mesh/mesh_data_tmpl.hh
	@@ -1,414 +1,411 @@
	/**
	* @file mesh_data_tmpl.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Fri Dec 28 2018
	*
	* @brief Stores generic data loaded from the mesh file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_data.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_DATA_TMPL_HH_
	#define AKANTU_MESH_DATA_TMPL_HH_

	namespace akantu {

	#define AKANTU_MESH_DATA_OSTREAM(r, name, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	stream << BOOST_PP_STRINGIZE(BOOST_PP_TUPLE_ELEM(2, 1, elem)); \
	break; \
	}

	inline std::ostream & operator<<(std::ostream & stream,
	const MeshDataTypeCode & type_code) {
	switch (type_code) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_MESH_DATA_OSTREAM, name,
	AKANTU_MESH_DATA_TYPES)
	default:
	stream << "(unknown type)";
	}
	return stream;
	}
	#undef AKANTU_MESH_DATA_OSTREAM

	#define MESH_DATA_GET_TYPE(r, data, type) \
	template <> \
	inline MeshDataTypeCode \
	MeshData::getTypeCode<BOOST_PP_TUPLE_ELEM(2, 1, type)>() const { \
	return MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, type); \
	}

	/* -------------------------------------------------------------------------- */
	// get the type of the data stored in elemental_data
	template <typename T> inline MeshDataTypeCode MeshData::getTypeCode() const {
	AKANTU_ERROR("Type " << debug::demangle(typeid(T).name())
	<< " not implemented by MeshData.");
	}

	/* -------------------------------------------------------------------------- */
	BOOST_PP_SEQ_FOR_EACH(MESH_DATA_GET_TYPE, void, AKANTU_MESH_DATA_TYPES)
	#undef MESH_DATA_GET_TYPE

	inline MeshDataTypeCode MeshData::getTypeCode(const ID & name,
	MeshDataType type) const {
	auto it = typecode_map.at(type).find(name);
	if (it == typecode_map.at(type).end()) {
	AKANTU_EXCEPTION("No dataset named " << name << " found.");
	}
	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	// Register new elemental data templated (and alloc data) with check if the
	// name is new
	template <typename T>
	ElementTypeMapArray<T> & MeshData::registerElementalData(const ID & name) {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	return allocElementalData<T>(name);
	}
	AKANTU_DEBUG_INFO("Data named " << name << " already registered.");
	return getElementalData<T>(name);
	}

	/* -------------------------------------------------------------------------- */
	// Register new elemental data of a given MeshDataTypeCode with check if the
	// name is new
	#define AKANTU_MESH_DATA_CASE_MACRO(r, name, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	registerElementalData<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(name); \
	break; \
	}

	inline void MeshData::registerElementalData(const ID & name,
	MeshDataTypeCode type) {
	switch (type) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_MESH_DATA_CASE_MACRO, name,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Type " << type << "not implemented by MeshData.");
	}
	}
	#undef AKANTU_MESH_DATA_CASE_MACRO

	/* -------------------------------------------------------------------------- */
	/// Register new elemental data (and alloc data)
	template <typename T>
	ElementTypeMapArray<T> & MeshData::allocElementalData(const ID & name) {
	- auto dataset =
	- std::make_unique<ElementTypeMapArray<T>>(name, _id);
	+ auto dataset = std::make_unique<ElementTypeMapArray<T>>(name, _id);
	auto * dataset_typed = dataset.get();
	elemental_data[name] = std::move(dataset);
	typecode_map[MeshDataType::_elemental][name] = getTypeCode<T>();
	return *dataset_typed;
	}

	/* -------------------------------------------------------------------------- */
	// Register new nodal data templated (and alloc data) with check if the
	// name is new
	template <typename T>
	Array<T> & MeshData::registerNodalData(const ID & name, UInt nb_components) {
	auto it = nodal_data.find(name);
	if (it == nodal_data.end()) {
	return allocNodalData<T>(name, nb_components);
	}
	AKANTU_DEBUG_INFO("Data named " << name << " already registered.");
	return getNodalData<T>(name);
	}

	/* -------------------------------------------------------------------------- */
	// Register new elemental data of a given MeshDataTypeCode with check if the
	// name is new
	#define AKANTU_MESH_NODAL_DATA_CASE_MACRO(r, name, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	registerNodalData<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(name, nb_components); \
	break; \
	}

	inline void MeshData::registerNodalData(const ID & name, UInt nb_components,
	MeshDataTypeCode type) {
	switch (type) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_MESH_NODAL_DATA_CASE_MACRO, name,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Type " << type << "not implemented by MeshData.");
	}
	}
	#undef AKANTU_MESH_NODAL_DATA_CASE_MACRO

	/* -------------------------------------------------------------------------- */
	/// Register new elemental data (and alloc data)
	template <typename T>
	Array<T> & MeshData::allocNodalData(const ID & name, UInt nb_components) {
	auto dataset =
	std::make_unique<Array<T>>(0, nb_components, T(), _id + ":" + name);
	auto * dataset_typed = dataset.get();
	nodal_data[name] = std::move(dataset);
	typecode_map[MeshDataType::_nodal][name] = getTypeCode<T>();
	return *dataset_typed;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	const Array<T> & MeshData::getNodalData(const ID & name) const {
	auto it = nodal_data.find(name);
	if (it == nodal_data.end()) {
	AKANTU_EXCEPTION("No nodal dataset named " << name << " found.");
	}
	return aka::as_type<Array<T>>(*(it->second.get()));
	}

	/* -------------------------------------------------------------------------- */
	// Get an existing elemental data
	template <typename T>
	Array<T> & MeshData::getNodalData(const ID & name, UInt nb_components) {
	auto it = nodal_data.find(name);
	if (it == nodal_data.end()) {
	return allocNodalData<T>(name, nb_components);
	}

	return aka::as_type<Array<T>>(*(it->second.get()));
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	const ElementTypeMapArray<T> &
	MeshData::getElementalData(const ID & name) const {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	AKANTU_EXCEPTION("No dataset named " << name << " found.");
	}
	return aka::as_type<ElementTypeMapArray<T>>(*(it->second.get()));
	}

	/* -------------------------------------------------------------------------- */
	// Get an existing elemental data
	template <typename T>
	ElementTypeMapArray<T> & MeshData::getElementalData(const ID & name) {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	return allocElementalData<T>(name);
	}

	return aka::as_type<ElementTypeMapArray<T>>(*(it->second.get()));
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	bool MeshData::hasData(const ID & name, ElementType elem_type,
	GhostType ghost_type) const {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	return false;
	}

	auto & elem_map = aka::as_type<ElementTypeMapArray<T>>(*(it->second));
	return elem_map.exists(elem_type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline bool MeshData::hasData(const ID & name, MeshDataType type) const {
	if (type == MeshDataType::_elemental) {
	auto it = elemental_data.find(name);
	return (it != elemental_data.end());
	}

	if (type == MeshDataType::_nodal) {
	auto it = nodal_data.find(name);
	return (it != nodal_data.end());
	}

	return false;
	}

	/* -------------------------------------------------------------------------- */
	inline bool MeshData::hasData(MeshDataType type) const {
	switch (type) {
	case MeshDataType::_elemental:
	return (not elemental_data.empty());
	case MeshDataType::_nodal:
	return (not nodal_data.empty());
	}

	return false;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	-const Array<T> &
	-MeshData::getElementalDataArray(const ID & name, ElementType elem_type,
	- GhostType ghost_type) const {
	+const Array<T> & MeshData::getElementalDataArray(const ID & name,
	+ ElementType elem_type,
	+ GhostType ghost_type) const {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	AKANTU_EXCEPTION("Data named " << name
	<< " not registered for type: " << elem_type
	<< " - ghost_type:" << ghost_type << "!");
	}
	return aka::as_type<ElementTypeMapArray<T>>(*(it->second))(elem_type,
	ghost_type);
	}

	template <typename T>
	Array<T> & MeshData::getElementalDataArray(const ID & name,
	ElementType elem_type,
	GhostType ghost_type) {
	auto it = elemental_data.find(name);
	if (it == elemental_data.end()) {
	AKANTU_EXCEPTION("Data named " << name
	<< " not registered for type: " << elem_type
	<< " - ghost_type:" << ghost_type << "!");
	}
	return aka::as_type<ElementTypeMapArray<T>>(*(it->second.get()))(elem_type,
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	// Get an elemental data array, if it does not exist: allocate it
	template <typename T>
	-Array<T> & MeshData::getElementalDataArrayAlloc(const ID & name,
	- ElementType elem_type,
	- GhostType ghost_type,
	- UInt nb_component) {
	+Array<T> &
	+MeshData::getElementalDataArrayAlloc(const ID & name, ElementType elem_type,
	+ GhostType ghost_type, UInt nb_component) {
	auto it = elemental_data.find(name);
	ElementTypeMapArray<T> * dataset;
	if (it == elemental_data.end()) {
	dataset = &allocElementalData<T>(name);
	} else {
	dataset = dynamic_cast<ElementTypeMapArray<T> *>(it->second.get());
	}
	AKANTU_DEBUG_ASSERT(
	getTypeCode<T>() ==
	typecode_map.at(MeshDataType::_elemental).find(name)->second,
	"Function getElementalDataArrayAlloc called with the wrong type!");
	if (!(dataset->exists(elem_type, ghost_type))) {
	dataset->alloc(0, nb_component, elem_type, ghost_type);
	}
	return (*dataset)(elem_type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	#define AKANTU_MESH_DATA_CASE_MACRO(r, name, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	nb_comp = getNbComponentTemplated<BOOST_PP_TUPLE_ELEM(2, 1, elem)>( \
	name, el_type, ghost_type); \
	break; \
	}

	-inline UInt MeshData::getNbComponent(const ID & name,
	- ElementType el_type,
	+inline UInt MeshData::getNbComponent(const ID & name, ElementType el_type,
	GhostType ghost_type) const {
	auto it = typecode_map.at(MeshDataType::_elemental).find(name);
	UInt nb_comp(0);
	if (it == typecode_map.at(MeshDataType::_elemental).end()) {
	AKANTU_EXCEPTION("Could not determine the type held in dataset "
	<< name << " for type: " << el_type
	<< " - ghost_type:" << ghost_type << ".");
	}
	MeshDataTypeCode type = it->second;
	switch (type) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_MESH_DATA_CASE_MACRO, name,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR(
	"Could not call the correct instance of getNbComponentTemplated.");
	break;
	}
	return nb_comp;
	}
	#undef AKANTU_MESH_DATA_CASE_MACRO

	/* -------------------------------------------------------------------------- */
	template <typename T>
	-inline UInt
	-MeshData::getNbComponentTemplated(const ID & name, ElementType el_type,
	- GhostType ghost_type) const {
	+inline UInt MeshData::getNbComponentTemplated(const ID & name,
	+ ElementType el_type,
	+ GhostType ghost_type) const {
	return getElementalDataArray<T>(name, el_type, ghost_type).getNbComponent();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt MeshData::getNbComponent(const ID & name) const {
	auto it = nodal_data.find(name);
	if (it == nodal_data.end()) {
	AKANTU_EXCEPTION("No nodal dataset registered with the name" << name
	<< ".");
	}

	return it->second->getNbComponent();
	}

	/* -------------------------------------------------------------------------- */
	// get the names of the data stored in elemental_data
	#define AKANTU_MESH_DATA_CASE_MACRO(r, name, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	ElementTypeMapArray<BOOST_PP_TUPLE_ELEM(2, 1, elem)> * dataset; \
	dataset = \
	dynamic_cast<ElementTypeMapArray<BOOST_PP_TUPLE_ELEM(2, 1, elem)> *>( \
	it->second.get()); \
	exists = dataset->exists(el_type, ghost_type); \
	break; \
	}

	inline auto MeshData::getTagNames(ElementType el_type,
	GhostType ghost_type) const {
	std::vector<std::string> tags;
	bool exists(false);

	auto it = elemental_data.begin();
	auto it_end = elemental_data.end();
	for (; it != it_end; ++it) {
	MeshDataTypeCode type = getTypeCode(it->first);
	switch (type) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_MESH_DATA_CASE_MACRO, ,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Could not determine the proper type to (dynamic-)cast.");
	break;
	}
	if (exists) {
	tags.push_back(it->first);
	}
	}

	return tags;
	}
	#undef AKANTU_MESH_DATA_CASE_MACRO

	/* -------------------------------------------------------------------------- */
	inline auto MeshData::getTagNames() const {
	std::vector<std::string> tags;
	for (auto && data : nodal_data) {
	tags.push_back(std::get<0>(data));
	}
	return tags;
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* AKANTU_MESH_DATA_TMPL_HH_ */
	diff --git a/src/mesh/mesh_events.hh b/src/mesh/mesh_events.hh
	index eced63fb7..bceb620f7 100644
	--- a/src/mesh/mesh_events.hh
	+++ b/src/mesh/mesh_events.hh
	@@ -1,204 +1,206 @@
	/**
	* @file mesh_events.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Feb 20 2015
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Classes corresponding to mesh events type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <utility>

	#include "aka_array.hh"
	#include "element.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_EVENTS_HH_
	#define AKANTU_MESH_EVENTS_HH_

	namespace akantu {

	/// akantu::MeshEvent is the base event for meshes
	template <class Entity> class MeshEvent {
	public:
	MeshEvent(const std::string & origin = "") : origin_(origin) {}

	virtual ~MeshEvent() = default;
	/// Get the list of entity modified by the event nodes or elements
	const Array<Entity> & getList() const { return list; }
	/// Get the list of entity modified by the event nodes or elements
	Array<Entity> & getList() { return list; }

	std::string origin() const { return origin_; }
	-
	+
	protected:
	Array<Entity> list;

	private:
	std::string origin_;
	};

	class Mesh;

	/// akantu::MeshEvent related to new nodes in the mesh
	class NewNodesEvent : public MeshEvent<UInt> {
	public:
	NewNodesEvent(const std::string & origin = "") : MeshEvent(origin) {}
	~NewNodesEvent() override = default;
	};

	/// akantu::MeshEvent related to nodes removed from the mesh
	class RemovedNodesEvent : public MeshEvent<UInt> {
	public:
	inline RemovedNodesEvent(const Mesh & mesh, const std::string & origin = "");

	~RemovedNodesEvent() override = default;
	/// Get the new numbering following suppression of nodes from nodes arrays
	AKANTU_GET_MACRO_NOT_CONST(NewNumbering, new_numbering, Array<UInt> &);
	/// Get the new numbering following suppression of nodes from nodes arrays
	AKANTU_GET_MACRO(NewNumbering, new_numbering, const Array<UInt> &);

	private:
	Array<UInt> new_numbering;
	};

	/// akantu::MeshEvent related to new elements in the mesh
	class NewElementsEvent : public MeshEvent<Element> {
	public:
	- NewElementsEvent(const std::string & origin = "") : MeshEvent<Element>(origin) {}
	+ NewElementsEvent(const std::string & origin = "")
	+ : MeshEvent<Element>(origin) {}
	~NewElementsEvent() override = default;
	};

	/// akantu::MeshEvent related to elements removed from the mesh
	class RemovedElementsEvent : public MeshEvent<Element> {
	public:
	inline RemovedElementsEvent(const Mesh & mesh,
	const ID & new_numbering_id = "new_numbering",
	const std::string & origin = "");

	~RemovedElementsEvent() override = default;

	/// Get the new numbering following suppression of elements from elements
	/// arrays
	AKANTU_GET_MACRO(NewNumbering, new_numbering,
	const ElementTypeMapArray<UInt> &);
	/// Get the new numbering following suppression of elements from elements
	/// arrays
	AKANTU_GET_MACRO_NOT_CONST(NewNumbering, new_numbering,
	ElementTypeMapArray<UInt> &);
	/// Get the new numbering following suppression of elements from elements
	/// arrays
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(NewNumbering, new_numbering, UInt);
	/// Get the new numbering following suppression of elements from elements
	/// arrays
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(NewNumbering, new_numbering, UInt);

	protected:
	ElementTypeMapArray<UInt> new_numbering;
	};

	/// akantu::MeshEvent for element that changed in some sort, can be seen as a
	/// combination of removed and added elements
	class ChangedElementsEvent : public RemovedElementsEvent {
	public:
	inline ChangedElementsEvent(
	- const Mesh & mesh, const ID & new_numbering_id = "changed_event:new_numbering",
	+ const Mesh & mesh,
	+ const ID & new_numbering_id = "changed_event:new_numbering",
	const std::string & origin = "")
	: RemovedElementsEvent(mesh, new_numbering_id, origin) {}

	~ChangedElementsEvent() override = default;
	AKANTU_GET_MACRO(ListOld, list, const Array<Element> &);
	AKANTU_GET_MACRO_NOT_CONST(ListOld, list, Array<Element> &);
	AKANTU_GET_MACRO(ListNew, new_list, const Array<Element> &);
	AKANTU_GET_MACRO_NOT_CONST(ListNew, new_list, Array<Element> &);

	protected:
	Array<Element> new_list;
	};

	/* -------------------------------------------------------------------------- */

	class MeshEventHandler {
	public:
	virtual ~MeshEventHandler() = default;
	/* ------------------------------------------------------------------------ */
	/* Internal code */
	/* ------------------------------------------------------------------------ */
	private:
	/// send a akantu::NewNodesEvent
	inline void sendEvent(const NewNodesEvent & event) {
	onNodesAdded(event.getList(), event);
	}
	/// send a akantu::RemovedNodesEvent
	inline void sendEvent(const RemovedNodesEvent & event) {
	onNodesRemoved(event.getList(), event.getNewNumbering(), event);
	}
	/// send a akantu::NewElementsEvent
	inline void sendEvent(const NewElementsEvent & event) {
	onElementsAdded(event.getList(), event);
	}
	/// send a akantu::RemovedElementsEvent
	inline void sendEvent(const RemovedElementsEvent & event) {
	onElementsRemoved(event.getList(), event.getNewNumbering(), event);
	}
	/// send a akantu::ChangedElementsEvent
	inline void sendEvent(const ChangedElementsEvent & event) {
	onElementsChanged(event.getListOld(), event.getListNew(),
	event.getNewNumbering(), event);
	}
	template <class EventHandler> friend class EventHandlerManager;

	/* ------------------------------------------------------------------------ */
	/* Interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to implement to react on akantu::NewNodesEvent
	virtual void onNodesAdded(const Array<UInt> & /nodes_list/,
	const NewNodesEvent & /event/) {}
	/// function to implement to react on akantu::RemovedNodesEvent
	virtual void onNodesRemoved(const Array<UInt> & /nodes_list/,
	const Array<UInt> & /new_numbering/,
	const RemovedNodesEvent & /event/) {}
	/// function to implement to react on akantu::NewElementsEvent
	virtual void onElementsAdded(const Array<Element> & /elements_list/,
	const NewElementsEvent & /event/) {}
	/// function to implement to react on akantu::RemovedElementsEvent
	virtual void
	onElementsRemoved(const Array<Element> & /elements_list/,
	const ElementTypeMapArray<UInt> & /new_numbering/,
	const RemovedElementsEvent & /event/) {}
	/// function to implement to react on akantu::ChangedElementsEvent
	virtual void
	onElementsChanged(const Array<Element> & /old_elements_list/,
	const Array<Element> & /new_elements_list/,
	const ElementTypeMapArray<UInt> & /new_numbering/,
	const ChangedElementsEvent & /event/) {}
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_EVENTS_HH_ */
	diff --git a/src/mesh/mesh_filter.hh b/src/mesh/mesh_filter.hh
	index 4e227ec39..99785064a 100644
	--- a/src/mesh/mesh_filter.hh
	+++ b/src/mesh/mesh_filter.hh
	@@ -1,73 +1,73 @@
	/**
	* @file mesh_filter.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Feb 20 2018
	*
	* @brief the class representing the meshes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_FILTER_HH_
	#define AKANTU_MESH_FILTER_HH_

	/* -------------------------------------------------------------------------- */
	#include "element.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Filter Functors */
	/* -------------------------------------------------------------------------- */

	/// struct for the possible filter functors
	struct FilterFunctor {
	enum Type { _node_filter_functor, _element_filter_functor };
	};

	/// class (functor) for the node filter
	class NodeFilterFunctor : public FilterFunctor {
	public:
	bool operator()(__attribute__((unused)) UInt node) { AKANTU_TO_IMPLEMENT(); }

	public:
	static const Type type = _node_filter_functor;
	};

	/// class (functor) for the element filter
	class ElementFilterFunctor : public FilterFunctor {
	public:
	bool operator()(__attribute__((unused)) const Element & element) {
	AKANTU_TO_IMPLEMENT();
	}

	public:
	static const Type type = _element_filter_functor;
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_FILTER_HH_ */
	diff --git a/src/mesh/mesh_global_data_updater.hh b/src/mesh/mesh_global_data_updater.hh
	index b1bc7b5e9..f9972607e 100644
	--- a/src/mesh/mesh_global_data_updater.hh
	+++ b/src/mesh/mesh_global_data_updater.hh
	@@ -1,54 +1,54 @@
	/**
	* @file mesh_global_data_updater.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Oct 11 2017
	*
	* @brief interface for the global data updater
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MESH_GLOBAL_DATA_UPDATER_HH_
	#define AKANTU_MESH_GLOBAL_DATA_UPDATER_HH_

	namespace akantu {

	class NewNodesEvent;
	class NewElementsEvent;

	class MeshGlobalDataUpdater {
	public:
	virtual ~MeshGlobalDataUpdater() = default;

	virtual std::tuple<UInt, UInt>
	updateData(NewNodesEvent & /nodes_event/,
	NewElementsEvent & /elements_event/) {
	return std::make_tuple(0, 0);
	}
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_GLOBAL_DATA_UPDATER_HH_ */
	diff --git a/src/mesh/mesh_inline_impl.hh b/src/mesh/mesh_inline_impl.hh
	index e222a051e..7b5e3aff2 100644
	--- a/src/mesh/mesh_inline_impl.hh
	+++ b/src/mesh/mesh_inline_impl.hh
	@@ -1,764 +1,764 @@
	/**
	* @file mesh_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Thu Jul 15 2010
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Implementation of the inline functions of the mesh class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "element_class.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_INLINE_IMPL_HH_
	#define AKANTU_MESH_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	inline ElementKind Element::kind() const { return Mesh::getKind(type); }

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <typename... pack>
	Mesh::ElementTypesIteratorHelper Mesh::elementTypes(pack &&... _pack) const {
	return connectivities.elementTypes(_pack...);
	}

	/* -------------------------------------------------------------------------- */
	inline RemovedNodesEvent::RemovedNodesEvent(const Mesh & mesh,
	const std::string & origin)
	: MeshEvent<UInt>(origin),
	new_numbering(mesh.getNbNodes(), 1, "new_numbering") {}

	/* -------------------------------------------------------------------------- */
	inline RemovedElementsEvent::RemovedElementsEvent(const Mesh & mesh,
	const ID & new_numbering_id,
	const std::string & origin)
	: MeshEvent<Element>(origin),
	new_numbering(new_numbering_id, mesh.getID()) {}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void Mesh::sendEvent<NewElementsEvent>(NewElementsEvent & event) {
	this->fillNodesToElements();
	EventHandlerManager<MeshEventHandler>::sendEvent(event);
	}

	/* -------------------------------------------------------------------------- */
	template <> inline void Mesh::sendEvent<NewNodesEvent>(NewNodesEvent & event) {
	this->computeBoundingBox();
	this->nodes_flags->resize(this->nodes->size(), NodeFlag::_normal);
	EventHandlerManager<MeshEventHandler>::sendEvent(event);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	Mesh::sendEvent<RemovedElementsEvent>(RemovedElementsEvent & event) {
	this->connectivities.onElementsRemoved(event.getNewNumbering());
	this->fillNodesToElements();
	this->computeBoundingBox();

	EventHandlerManager<MeshEventHandler>::sendEvent(event);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void Mesh::sendEvent<RemovedNodesEvent>(RemovedNodesEvent & event) {
	const auto & new_numbering = event.getNewNumbering();
	this->removeNodesFromArray(*nodes, new_numbering);
	if (nodes_global_ids and not is_mesh_facets) {
	this->removeNodesFromArray(*nodes_global_ids, new_numbering);
	}
	if (not is_mesh_facets) {
	this->removeNodesFromArray(*nodes_flags, new_numbering);
	}

	if (not nodes_to_elements.empty()) {
	std::vector<std::unique_ptr<std::set<Element>>> tmp(
	nodes_to_elements.size());
	auto it = nodes_to_elements.begin();

	UInt new_nb_nodes = 0;
	for (auto new_i : new_numbering) {
	if (new_i != UInt(-1)) {
	tmp[new_i] = std::move(*it);
	++new_nb_nodes;
	}
	++it;
	}

	tmp.resize(new_nb_nodes);
	std::move(tmp.begin(), tmp.end(), nodes_to_elements.begin());
	}

	computeBoundingBox();

	EventHandlerManager<MeshEventHandler>::sendEvent(event);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Mesh::removeNodesFromArray(Array<T> & vect,
	const Array<UInt> & new_numbering) {
	Array<T> tmp(vect.size(), vect.getNbComponent());
	UInt nb_component = vect.getNbComponent();
	UInt new_nb_nodes = 0;
	for (UInt i = 0; i < new_numbering.size(); ++i) {
	UInt new_i = new_numbering(i);
	if (new_i != UInt(-1)) {
	T * to_copy = vect.storage() + i * nb_component;
	std::uninitialized_copy(to_copy, to_copy + nb_component,
	tmp.storage() + new_i * nb_component);
	++new_nb_nodes;
	}
	}

	tmp.resize(new_nb_nodes);
	vect.copy(tmp);
	}

	/* -------------------------------------------------------------------------- */
	inline Array<UInt> & Mesh::getNodesGlobalIdsPointer() {
	AKANTU_DEBUG_IN();
	if (not nodes_global_ids) {
	nodes_global_ids = std::make_shared<Array<UInt>>(
	nodes->size(), 1, getID() + ":nodes_global_ids");

	for (auto && global_ids : enumerate(*nodes_global_ids)) {
	std::get<1>(global_ids) = std::get<0>(global_ids);
	}
	}

	AKANTU_DEBUG_OUT();
	return *nodes_global_ids;
	}

	/* -------------------------------------------------------------------------- */
	inline Array<UInt> & Mesh::getConnectivityPointer(ElementType type,
	GhostType ghost_type) {
	if (connectivities.exists(type, ghost_type)) {
	return connectivities(type, ghost_type);
	}

	if (ghost_type != _not_ghost) {
	ghosts_counters.alloc(0, 1, type, ghost_type, 1);
	}

	AKANTU_DEBUG_INFO("The connectivity vector for the type " << type
	<< " created");

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	return connectivities.alloc(0, nb_nodes_per_element, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline Array<std::vector<Element>> &
	Mesh::getElementToSubelementPointer(ElementType type, GhostType ghost_type) {
	return getDataPointer<std::vector<Element>>("element_to_subelement", type,
	ghost_type, 1, true);
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Element> &
	Mesh::getSubelementToElementPointer(ElementType type, GhostType ghost_type) {
	auto & array = getDataPointer<Element>(
	"subelement_to_element", type, ghost_type, getNbFacetsPerElement(type),
	false, is_mesh_facets, ElementNull);
	return array;
	}

	/* -------------------------------------------------------------------------- */
	inline const auto & Mesh::getElementToSubelement() const {
	return getData<std::vector<Element>>("element_to_subelement");
	}

	/* -------------------------------------------------------------------------- */
	inline auto & Mesh::getElementToSubelementNC() {
	return getData<std::vector<Element>>("element_to_subelement");
	}

	/* -------------------------------------------------------------------------- */
	inline const auto & Mesh::getElementToSubelement(ElementType type,
	GhostType ghost_type) const {
	return getData<std::vector<Element>>("element_to_subelement", type,
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline auto & Mesh::getElementToSubelementNC(ElementType type,
	GhostType ghost_type) {
	return getData<std::vector<Element>>("element_to_subelement", type,
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline const auto &
	Mesh::getElementToSubelement(const Element & element) const {
	return getData<std::vector<Element>>("element_to_subelement")(element, 0);
	}

	/* -------------------------------------------------------------------------- */
	inline auto & Mesh::getElementToSubelementNC(const Element & element) {
	return getData<std::vector<Element>>("element_to_subelement")(element, 0);
	}

	/* -------------------------------------------------------------------------- */
	inline const auto & Mesh::getSubelementToElement() const {
	return getData<Element>("subelement_to_element");
	}

	/* -------------------------------------------------------------------------- */
	inline auto & Mesh::getSubelementToElementNC() {
	return getData<Element>("subelement_to_element");
	}

	/* -------------------------------------------------------------------------- */
	inline const auto & Mesh::getSubelementToElement(ElementType type,
	GhostType ghost_type) const {
	return getData<Element>("subelement_to_element", type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline auto & Mesh::getSubelementToElementNC(ElementType type,
	GhostType ghost_type) {
	return getData<Element>("subelement_to_element", type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline VectorProxy<Element>
	Mesh::getSubelementToElement(const Element & element) const {
	return this->getSubelementToElement().get(element);
	}

	/* -------------------------------------------------------------------------- */
	inline VectorProxy<Element>
	-Mesh::getSubelementToElementNC(const Element & element) {
	+Mesh::getSubelementToElementNC(const Element & element) const {
	return this->getSubelementToElement().get(element);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline Array<T> &
	Mesh::getDataPointer(const ID & data_name, ElementType el_type,
	GhostType ghost_type, UInt nb_component,
	bool size_to_nb_element, bool resize_with_parent) {
	Array<T> & tmp = this->getElementalDataArrayAlloc<T>(
	data_name, el_type, ghost_type, nb_component);

	if (size_to_nb_element) {
	if (resize_with_parent) {
	tmp.resize(mesh_parent->getNbElement(el_type, ghost_type));
	} else {
	tmp.resize(this->getNbElement(el_type, ghost_type));
	}
	}

	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline Array<T> &
	Mesh::getDataPointer(const ID & data_name, ElementType el_type,
	GhostType ghost_type, UInt nb_component,
	bool size_to_nb_element, bool resize_with_parent,
	const T & defaul_) {
	Array<T> & tmp = this->getElementalDataArrayAlloc<T>(
	data_name, el_type, ghost_type, nb_component);

	if (size_to_nb_element) {
	if (resize_with_parent) {
	tmp.resize(mesh_parent->getNbElement(el_type, ghost_type), defaul_);
	} else {
	tmp.resize(this->getNbElement(el_type, ghost_type), defaul_);
	}
	}

	return tmp;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline const Array<T> & Mesh::getData(const ID & data_name, ElementType el_type,
	GhostType ghost_type) const {
	return this->getElementalDataArray<T>(data_name, el_type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline Array<T> & Mesh::getData(const ID & data_name, ElementType el_type,
	GhostType ghost_type) {
	return this->getElementalDataArray<T>(data_name, el_type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline const ElementTypeMapArray<T> &
	Mesh::getData(const ID & data_name) const {
	return this->getElementalData<T>(data_name);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline ElementTypeMapArray<T> & Mesh::getData(const ID & data_name) {
	return this->getElementalData<T>(data_name);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbElement(ElementType type, GhostType ghost_type) const {
	try {

	const Array<UInt> & conn = connectivities(type, ghost_type);
	return conn.size();
	} catch (...) {
	return 0;
	}
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbElement(const UInt spatial_dimension,
	GhostType ghost_type, ElementKind kind) const {
	AKANTU_DEBUG_ASSERT(spatial_dimension <= 3 \|\| spatial_dimension == UInt(-1),
	"spatial_dimension is " << spatial_dimension
	<< " and is greater than 3 !");
	UInt nb_element = 0;

	for (auto type : elementTypes(spatial_dimension, ghost_type, kind)) {
	nb_element += getNbElement(type, ghost_type);
	}

	return nb_element;
	}

	/* -------------------------------------------------------------------------- */
	inline void Mesh::getBarycenter(const Element & element,
	Vector<Real> & barycenter) const {
	Vector<UInt> conn = getConnectivity(element);
	Matrix<Real> local_coord(spatial_dimension, conn.size());
	auto node_begin = make_view(*nodes, spatial_dimension).begin();

	for (auto && node : enumerate(conn)) {
	local_coord(std::get<0>(node)) =
	Vector<Real>(node_begin[std::get<1>(node)]);
	}

	Math::barycenter(local_coord.storage(), conn.size(), spatial_dimension,
	barycenter.storage());
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbNodesPerElement(ElementType type) {
	UInt nb_nodes_per_element = 0;
	#define GET_NB_NODES_PER_ELEMENT(type) \
	nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement()
	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NB_NODES_PER_ELEMENT);
	#undef GET_NB_NODES_PER_ELEMENT
	return nb_nodes_per_element;
	}

	/* -------------------------------------------------------------------------- */
	inline ElementType Mesh::getP1ElementType(ElementType type) {
	ElementType p1_type = _not_defined;
	#define GET_P1_TYPE(type) p1_type = ElementClass<type>::getP1ElementType()

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_P1_TYPE);
	#undef GET_P1_TYPE
	return p1_type;
	}

	/* -------------------------------------------------------------------------- */
	inline ElementKind Mesh::getKind(ElementType type) {
	ElementKind kind = _ek_not_defined;
	#define GET_KIND(type) kind = ElementClass<type>::getKind()
	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_KIND);
	#undef GET_KIND
	return kind;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getSpatialDimension(ElementType type) {
	UInt spatial_dimension = 0;
	#define GET_SPATIAL_DIMENSION(type) \
	spatial_dimension = ElementClass<type>::getSpatialDimension()
	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SPATIAL_DIMENSION);
	#undef GET_SPATIAL_DIMENSION

	return spatial_dimension;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNaturalSpaceDimension(const ElementType & type) {
	UInt natural_dimension = 0;
	#define GET_NATURAL_DIMENSION(type) \
	natural_dimension = ElementClass<type>::getNaturalSpaceDimension()
	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NATURAL_DIMENSION);
	#undef GET_NATURAL_DIMENSION

	return natural_dimension;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbFacetTypes(ElementType type, UInt /t/) {
	UInt nb = 0;
	#define GET_NB_FACET_TYPE(type) nb = ElementClass<type>::getNbFacetTypes()

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NB_FACET_TYPE);
	#undef GET_NB_FACET_TYPE
	return nb;
	}

	/* -------------------------------------------------------------------------- */
	inline constexpr auto Mesh::getFacetType(ElementType type, UInt t) {
	#define GET_FACET_TYPE(type) return ElementClass<type>::getFacetType(t);

	AKANTU_BOOST_ALL_ELEMENT_SWITCH_NO_DEFAULT(GET_FACET_TYPE);

	#undef GET_FACET_TYPE

	return _not_defined;
	}

	/* -------------------------------------------------------------------------- */
	inline constexpr auto Mesh::getAllFacetTypes(ElementType type) {
	#define GET_FACET_TYPE(type) return ElementClass<type>::getFacetTypes();

	AKANTU_BOOST_ALL_ELEMENT_SWITCH_NO_DEFAULT(GET_FACET_TYPE);
	#undef GET_FACET_TYPE

	return ElementClass<_not_defined>::getFacetTypes();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbFacetsPerElement(ElementType type) {
	AKANTU_DEBUG_IN();

	UInt n_facet = 0;
	#define GET_NB_FACET(type) n_facet = ElementClass<type>::getNbFacetsPerElement()

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NB_FACET);
	#undef GET_NB_FACET

	AKANTU_DEBUG_OUT();
	return n_facet;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbFacetsPerElement(ElementType type, UInt t) {
	AKANTU_DEBUG_IN();

	UInt n_facet = 0;
	#define GET_NB_FACET(type) \
	n_facet = ElementClass<type>::getNbFacetsPerElement(t)

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NB_FACET);
	#undef GET_NB_FACET

	AKANTU_DEBUG_OUT();
	return n_facet;
	}

	/* -------------------------------------------------------------------------- */
	inline auto Mesh::getFacetLocalConnectivity(ElementType type, UInt t) {
	AKANTU_DEBUG_IN();

	#define GET_FACET_CON(type) \
	AKANTU_DEBUG_OUT(); \
	return ElementClass<type>::getFacetLocalConnectivityPerElement(t)

	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_FACET_CON);
	#undef GET_FACET_CON

	AKANTU_DEBUG_OUT();
	return ElementClass<_not_defined>::getFacetLocalConnectivityPerElement(0);
	// This avoid a compilation warning but will certainly
	// also cause a segfault if reached
	}

	/* -------------------------------------------------------------------------- */
	inline auto Mesh::getFacetConnectivity(const Element & element, UInt t) const {
	AKANTU_DEBUG_IN();

	Matrix<const UInt> local_facets(getFacetLocalConnectivity(element.type, t));
	Matrix<UInt> facets(local_facets.rows(), local_facets.cols());

	const Array<UInt> & conn = connectivities(element.type, element.ghost_type);

	for (UInt f = 0; f < facets.rows(); ++f) {
	for (UInt n = 0; n < facets.cols(); ++n) {
	facets(f, n) = conn(element.element, local_facets(f, n));
	}
	}

	AKANTU_DEBUG_OUT();
	return facets;
	}

	/* -------------------------------------------------------------------------- */
	inline VectorProxy<UInt> Mesh::getConnectivity(const Element & element) const {
	return connectivities.get(element);
	}

	/* -------------------------------------------------------------------------- */
	inline VectorProxy<UInt> Mesh::getConnectivityNC(const Element & element) {
	return connectivities.get(element);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Mesh::extractNodalValuesFromElement(
	const Array<T> & nodal_values, T * local_coord, const UInt * connectivity,
	UInt n_nodes, UInt nb_degree_of_freedom) const {
	for (UInt n = 0; n < n_nodes; ++n) {
	memcpy(local_coord + n * nb_degree_of_freedom,
	nodal_values.storage() + connectivity[n] * nb_degree_of_freedom,
	nb_degree_of_freedom * sizeof(T));
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void Mesh::addConnectivityType(ElementType type, GhostType ghost_type) {
	getConnectivityPointer(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isPureGhostNode(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_pure_ghost;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isLocalOrMasterNode(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_local_master_mask) == NodeFlag::_normal;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isLocalNode(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_normal;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isMasterNode(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_master;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isSlaveNode(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_slave;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isPeriodicSlave(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_periodic_mask) ==
	NodeFlag::_periodic_slave;
	}

	/* -------------------------------------------------------------------------- */
	inline bool Mesh::isPeriodicMaster(UInt n) const {
	return ((*nodes_flags)(n)&NodeFlag::_periodic_mask) ==
	NodeFlag::_periodic_master;
	}

	/* -------------------------------------------------------------------------- */
	inline NodeFlag Mesh::getNodeFlag(UInt local_id) const {
	return (*nodes_flags)(local_id);
	}

	/* -------------------------------------------------------------------------- */
	inline Int Mesh::getNodePrank(UInt local_id) const {
	auto it = nodes_prank.find(local_id);
	return it == nodes_prank.end() ? -1 : it->second;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNodeGlobalId(UInt local_id) const {
	return nodes_global_ids ? (*nodes_global_ids)(local_id) : local_id;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNodeLocalId(UInt global_id) const {
	if (nodes_global_ids == nullptr) {
	return global_id;
	}
	return nodes_global_ids->find(global_id);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbGlobalNodes() const {
	return nodes_global_ids ? nb_global_nodes : nodes->size();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Mesh::getNbNodesPerElementList(const Array<Element> & elements) {
	UInt nb_nodes_per_element = 0;
	UInt nb_nodes = 0;
	ElementType current_element_type = _not_defined;

	for (const auto & el : elements) {
	if (el.type != current_element_type) {
	current_element_type = el.type;
	nb_nodes_per_element = Mesh::getNbNodesPerElement(current_element_type);
	}

	nb_nodes += nb_nodes_per_element;
	}

	return nb_nodes;
	}

	/* -------------------------------------------------------------------------- */
	inline Mesh & Mesh::getMeshFacets() {
	if (this->mesh_facets == nullptr) {
	AKANTU_SILENT_EXCEPTION(
	"No facet mesh is defined yet! check the buildFacets functions");
	}

	return *this->mesh_facets;
	}

	/* -------------------------------------------------------------------------- */
	inline const Mesh & Mesh::getMeshFacets() const {
	if (this->mesh_facets == nullptr) {
	AKANTU_SILENT_EXCEPTION(
	"No facet mesh is defined yet! check the buildFacets functions");
	}

	return *this->mesh_facets;
	}
	/* -------------------------------------------------------------------------- */
	inline const Mesh & Mesh::getMeshParent() const {
	if (this->mesh_parent == nullptr) {
	AKANTU_SILENT_EXCEPTION(
	"No parent mesh is defined! This is only valid in a mesh_facets");
	}

	return *this->mesh_parent;
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::addPeriodicSlave(UInt slave, UInt master) {
	if (master == slave) {
	return;
	}

	// if pair already registered
	auto master_slaves = periodic_master_slave.equal_range(master);
	auto slave_it =
	std::find_if(master_slaves.first, master_slaves.second,
	[&](auto & pair) { return pair.second == slave; });
	if (slave_it == master_slaves.second) {
	// no duplicates
	periodic_master_slave.insert(std::make_pair(master, slave));
	AKANTU_DEBUG_INFO("adding periodic slave, slave gid:"
	<< getNodeGlobalId(slave) << " [lid: " << slave << "]"
	<< ", master gid:" << getNodeGlobalId(master)
	<< " [lid: " << master << "]");
	// std::cout << "adding periodic slave, slave gid:" <<
	// getNodeGlobalId(slave)
	// << " [lid: " << slave << "]"
	// << ", master gid:" << getNodeGlobalId(master)
	// << " [lid: " << master << "]" << std::endl;
	}

	periodic_slave_master[slave] = master;

	auto set_flag = [&](auto node, auto flag) {
	(*nodes_flags)[node] &= ~NodeFlag::_periodic_mask; // clean periodic flags
	(*nodes_flags)[node] \|= flag;
	};

	set_flag(slave, NodeFlag::_periodic_slave);
	set_flag(master, NodeFlag::_periodic_master);
	}

	/* -------------------------------------------------------------------------- */
	UInt Mesh::getPeriodicMaster(UInt slave) const {
	return periodic_slave_master.at(slave);
	}

	/* -------------------------------------------------------------------------- */
	class Mesh::PeriodicSlaves {
	using internal_iterator = std::unordered_multimap<UInt, UInt>::const_iterator;
	std::pair<internal_iterator, internal_iterator> pair;

	public:
	PeriodicSlaves(const Mesh & mesh, UInt master)
	: pair(mesh.getPeriodicMasterSlaves().equal_range(master)) {}

	PeriodicSlaves(const PeriodicSlaves & other) = default;
	PeriodicSlaves(PeriodicSlaves && other) = default;
	PeriodicSlaves & operator=(const PeriodicSlaves & other) = default;

	class const_iterator {
	internal_iterator it;

	public:
	const_iterator(internal_iterator it) : it(it) {}

	const_iterator operator++() {
	++it;
	return *this;
	}
	bool operator!=(const const_iterator & other) { return other.it != it; }
	auto operator*() { return it->second; }
	};

	auto begin() const { return const_iterator(pair.first); }
	auto end() const { return const_iterator(pair.second); }
	};

	/* -------------------------------------------------------------------------- */
	inline decltype(auto) Mesh::getPeriodicSlaves(UInt master) const {
	return PeriodicSlaves(*this, master);
	}

	/* -------------------------------------------------------------------------- */
	inline Vector<UInt>
	Mesh::getConnectivityWithPeriodicity(const Element & element) const {
	Vector<UInt> conn = getConnectivity(element);
	if (not isPeriodic()) {
	return conn;
	}

	for (auto && node : conn) {
	if (isPeriodicSlave(node)) {
	node = getPeriodicMaster(node);
	}
	}

	return conn;
	}

	} // namespace akantu

	#endif /* AKANTU_MESH_INLINE_IMPL_HH_ */
	diff --git a/src/mesh/mesh_iterators.hh b/src/mesh/mesh_iterators.hh
	index cf3ff81ae..f6652d182 100644
	--- a/src/mesh/mesh_iterators.hh
	+++ b/src/mesh/mesh_iterators.hh
	@@ -1,226 +1,226 @@
	/**
	* @file mesh_iterators.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jul 16 2015
	* @date last modification: Thu Mar 11 2021
	*
	* @brief Set of helper classes to have fun with range based for
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_named_argument.hh"
	#include "aka_static_if.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_ITERATORS_HH_
	#define AKANTU_MESH_ITERATORS_HH_

	namespace akantu {

	class MeshElementsByTypes {
	using elements_iterator = Array<Element>::scalar_iterator;

	public:
	explicit MeshElementsByTypes(const Array<Element> & elements) {
	this->elements.copy(elements);
	std::sort(this->elements.begin(), this->elements.end());
	}

	/* ------------------------------------------------------------------------ */
	class MeshElementsRange {
	public:
	MeshElementsRange() = default;

	MeshElementsRange(const elements_iterator & begin,
	const elements_iterator & end)
	: type((begin).type), ghost_type((begin).ghost_type), begin(begin),
	end(end) {}

	AKANTU_GET_MACRO(Type, type, ElementType);
	AKANTU_GET_MACRO(GhostType, ghost_type, GhostType);

	const Array<UInt> & getElements() {
	elements.resize(end - begin);
	auto el_it = elements.begin();
	for (auto it = begin; it != end; ++it, ++el_it) {
	*el_it = it->element;
	}

	return elements;
	}

	private:
	ElementType type{_not_defined};
	GhostType ghost_type{_casper};
	elements_iterator begin;
	elements_iterator end;
	Array<UInt> elements;
	};

	/* ------------------------------------------------------------------------ */
	class iterator {
	struct element_comparator {
	bool operator()(const Element & lhs, const Element & rhs) const {
	return ((rhs == ElementNull) \|\| std::tie(lhs.ghost_type, lhs.type) <
	std::tie(rhs.ghost_type, rhs.type));
	}
	};

	public:
	iterator(const iterator &) = default;
	iterator(const elements_iterator & first, const elements_iterator & last)
	: range(std::equal_range(first, last, *first, element_comparator())),
	first(first), last(last) {}

	decltype(auto) operator*() const {
	return MeshElementsRange(range.first, range.second);
	}

	iterator operator++() {
	first = range.second;
	range = std::equal_range(first, last, *first, element_comparator());
	return *this;
	}

	bool operator==(const iterator & other) const {
	return (first == other.first and last == other.last);
	}

	bool operator!=(const iterator & other) const {
	return (not operator==(other));
	}

	private:
	std::pair<elements_iterator, elements_iterator> range;
	elements_iterator first;
	elements_iterator last;
	};

	iterator begin() { return iterator(elements.begin(), elements.end()); }
	iterator end() { return iterator(elements.end(), elements.end()); }

	private:
	Array<Element> elements;
	};

	/* -------------------------------------------------------------------------- */
	namespace mesh_iterators {
	namespace details {
	template <class internal_iterator> class delegated_iterator {
	public:
	using value_type = std::remove_pointer_t<
	typename internal_iterator::value_type::second_type>;
	using difference_type = std::ptrdiff_t;
	using pointer = value_type *;
	using reference = value_type &;
	using iterator_category = std::input_iterator_tag;

	explicit delegated_iterator(internal_iterator it) : it(std::move(it)) {}

	decltype(auto) operator*() {
	return std::forward<decltype((it->second))>((it->second));
	}

	delegated_iterator operator++() {
	++it;
	return *this;
	}

	bool operator==(const delegated_iterator & other) const {
	return other.it == it;
	}

	bool operator!=(const delegated_iterator & other) const {
	return other.it != it;
	}

	private:
	internal_iterator it;
	};
	} // namespace details
	} // namespace mesh_iterators

	/* -------------------------------------------------------------------------- */
	template <class Func>
	void for_each_element(UInt nb_elements, const Array<UInt> & filter_elements,
	Func && function) {
	if (filter_elements != empty_filter) {
	std::for_each(filter_elements.begin(), filter_elements.end(),
	std::forward<Func>(function));
	} else {
	auto && range = arange(nb_elements);
	std::for_each(range.begin(), range.end(), std::forward<Func>(function));
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Func, typename... pack>
	void for_each_element(const Mesh & mesh, Func && function, pack &&... _pack) {
	auto requested_ghost_type = OPTIONAL_NAMED_ARG(ghost_type, _casper);
	const ElementTypeMapArray<UInt> * filter =
	OPTIONAL_NAMED_ARG(element_filter, nullptr);

	bool all_ghost_types = requested_ghost_type == _casper;

	auto spatial_dimension =
	OPTIONAL_NAMED_ARG(spatial_dimension, mesh.getSpatialDimension());
	auto element_kind = OPTIONAL_NAMED_ARG(element_kind, _ek_not_defined);

	for (auto ghost_type : ghost_types) {
	if ((not(ghost_type == requested_ghost_type)) and (not all_ghost_types)) {
	continue;
	}

	auto element_types =
	mesh.elementTypes(spatial_dimension, ghost_type, element_kind);

	if (filter) {
	element_types =
	filter->elementTypes(spatial_dimension, ghost_type, element_kind);
	}

	for (auto type : element_types) {
	const Array<UInt> * filter_array;

	if (filter) {
	filter_array = &((*filter)(type, ghost_type));
	} else {
	filter_array = &empty_filter;
	}

	auto nb_elements = mesh.getNbElement(type, ghost_type);

	for_each_element(nb_elements, *filter_array, [&](auto && el) {
	auto element = Element{type, el, ghost_type};
	std::forward<Func>(function)(element);
	});
	}
	}
	}

	} // namespace akantu

	#endif /* AKANTU_MESH_ITERATORS_HH_ */
	diff --git a/src/mesh/mesh_periodic.cc b/src/mesh/mesh_periodic.cc
	index 55c2e67d5..c585c548f 100644
	--- a/src/mesh/mesh_periodic.cc
	+++ b/src/mesh/mesh_periodic.cc
	@@ -1,466 +1,466 @@
	/**
	* @file mesh_periodic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Feb 12 2018
	* @date last modification: Sun Mar 15 2020
	*
	* @brief Implementation of the perdiodicity capabilities in the mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_tag.hh"
	#include "communicator.hh"
	#include "element_group.hh"
	#include "mesh.hh"
	#include "periodic_node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void Mesh::makePeriodic(const SpatialDirection & direction) {
	Array<UInt> list_1;
	Array<UInt> list_2;
	Real tolerance = 1e-10;

	auto lower_bound = this->getLowerBounds();
	auto upper_bound = this->getUpperBounds();
	auto length = upper_bound(direction) - lower_bound(direction);

	const auto & positions = *nodes;

	for (auto && data : enumerate(make_view(positions, spatial_dimension))) {
	UInt node = std::get<0>(data);
	const auto & pos = std::get<1>(data);

	if (std::abs((pos(direction) - lower_bound(direction)) / length) <
	tolerance) {
	list_1.push_back(node);
	}

	if (std::abs((pos(direction) - upper_bound(direction)) / length) <
	tolerance) {
	list_2.push_back(node);
	}
	}

	this->makePeriodic(direction, list_1, list_2);
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::makePeriodic(const SpatialDirection & direction, const ID & list_1,
	const ID & list_2) {
	const auto & list_nodes_1 =
	mesh.getElementGroup(list_1).getNodeGroup().getNodes();
	const auto & list_nodes_2 =
	mesh.getElementGroup(list_2).getNodeGroup().getNodes();

	this->makePeriodic(direction, list_nodes_1, list_nodes_2);
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	namespace {
	struct NodeInfo {
	NodeInfo() = default;
	NodeInfo(UInt spatial_dimension) : position(spatial_dimension) {}
	NodeInfo(UInt node, const Vector<Real> & position,
	const SpatialDirection & direction)
	: node(node), position(position) {
	this->direction_position = position(direction);
	this->position(direction) = 0.;
	}

	NodeInfo(const NodeInfo & other) = default;
	NodeInfo(NodeInfo && other) noexcept = default;
	NodeInfo & operator=(const NodeInfo & other) = default;
	- NodeInfo & operator=(NodeInfo && other) = default;
	+ NodeInfo & operator=(NodeInfo && other) = default;

	UInt node{0};
	Vector<Real> position;
	Real direction_position{0.};
	};
	} // namespace

	/* -------------------------------------------------------------------------- */
	// left is for lower values on direction and right for highest values
	void Mesh::makePeriodic(const SpatialDirection & direction,
	const Array<UInt> & list_left,
	const Array<UInt> & list_right) {
	Real tolerance = 1e-10;

	const auto & positions = *nodes;
	auto lower_bound = this->getLowerBounds();
	auto upper_bound = this->getUpperBounds();
	auto length = upper_bound(direction) - lower_bound(direction);

	lower_bound(direction) = 0;
	upper_bound(direction) = 0;

	auto prank = communicator->whoAmI();

	std::vector<NodeInfo> nodes_left(list_left.size());
	std::vector<NodeInfo> nodes_right(list_right.size());

	BBox bbox(spatial_dimension);
	auto to_position = [&](UInt node) {
	Vector<Real> pos(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	pos(s) = positions(node, s);
	}
	auto && info = NodeInfo(node, pos, direction);
	bbox += info.position;
	return std::move(info);
	};

	std::transform(list_left.begin(), list_left.end(), nodes_left.begin(),
	to_position);
	BBox bbox_left = bbox;

	bbox.reset();
	std::transform(list_right.begin(), list_right.end(), nodes_right.begin(),
	to_position);
	BBox bbox_right = bbox;

	std::vector<UInt> new_nodes;
	if (is_distributed) {
	NewNodesEvent event(AKANTU_CURRENT_FUNCTION);

	/* ---------------------------------------------------------------------- */
	// function to send nodes in bboxes intersections
	auto extract_and_send_nodes = [&](const auto & bbox, const auto & node_list,
	auto & buffers, auto proc, auto cnt) {
	// buffers.resize(buffers.size() + 1);
	buffers.push_back(std::make_unique<DynamicCommunicationBuffer>());
	auto & buffer = *buffers.back();

	// std::cout << "Sending to " << proc << std::endl;
	for (auto & info : node_list) {
	if (bbox.contains(info.position) and isLocalOrMasterNode(info.node)) {
	Vector<Real> pos = info.position;
	pos(direction) = info.direction_position;

	NodeFlag flag = (*nodes_flags)(info.node) & NodeFlag::_periodic_mask;
	UInt gnode = getNodeGlobalId(info.node);
	buffer << gnode;
	buffer << pos;
	buffer << flag;

	// std::cout << " - node " << getNodeGlobalId(info.node);

	// if is slave sends master info
	if (flag == NodeFlag::_periodic_slave) {
	UInt master = getNodeGlobalId(periodic_slave_master[info.node]);
	// std::cout << " slave of " << master << std::endl;
	buffer << master;
	}

	// if is master sends list of slaves
	if (flag == NodeFlag::_periodic_master) {
	UInt nb_slaves = periodic_master_slave.count(info.node);
	buffer << nb_slaves;

	// std::cout << " master of " << nb_slaves << " nodes : [";
	auto slaves = periodic_master_slave.equal_range(info.node);
	for (auto it = slaves.first; it != slaves.second; ++it) {
	UInt gslave = getNodeGlobalId(it->second);
	// std::cout << (it == slaves.first ? "" : ", ") << gslave;
	buffer << gslave;
	}
	// std::cout << "]";
	}
	// std::cout << std::endl;
	}
	}

	auto tag = Tag::genTag(prank, 10 * direction + cnt, Tag::_periodic_nodes);
	// std::cout << "SBuffer size " << buffer.size() << " " << tag <<
	// std::endl;
	return communicator->asyncSend(buffer, proc, tag);
	};

	/* ---------------------------------------------------------------------- */
	// function to receive nodes in bboxes intersections
	auto recv_and_extract_nodes = [&](auto & node_list, const auto proc,
	auto cnt) {
	DynamicCommunicationBuffer buffer;
	auto tag = Tag::genTag(proc, 10 * direction + cnt, Tag::_periodic_nodes);
	communicator->receive(buffer, proc, tag);
	// std::cout << "RBuffer size " << buffer.size() << " " << tag <<
	// std::endl; std::cout << "Receiving from " << proc << std::endl;

	while (not buffer.empty()) {
	Vector<Real> pos(spatial_dimension);
	UInt global_node;
	NodeFlag flag;
	buffer >> global_node;
	buffer >> pos;
	buffer >> flag;

	// std::cout << " - node " << global_node;
	auto local_node = getNodeLocalId(global_node);

	// get the master info of is slave
	if (flag == NodeFlag::_periodic_slave) {
	UInt master_node;
	buffer >> master_node;
	// std::cout << " slave of " << master_node << std::endl;
	// auto local_master_node = getNodeLocalId(master_node);
	// AKANTU_DEBUG_ASSERT(local_master_node != UInt(-1),
	//"Should I know the master node " << master_node);
	}

	// get the list of slaves if is master
	if ((flag & NodeFlag::_periodic_mask) == NodeFlag::_periodic_master) {
	UInt nb_slaves;
	buffer >> nb_slaves;
	// std::cout << " master of " << nb_slaves << " nodes : [";
	for (auto ns [[gnu::unused]] : arange(nb_slaves)) {
	UInt gslave_node;
	buffer >> gslave_node;
	// std::cout << (ns == 0 ? "" : ", ") << gslave_node;
	// auto lslave_node = getNodeLocalId(gslave_node);
	// AKANTU_DEBUG_ASSERT(lslave_node != UInt(-1),
	// "Should I know the slave node " <<
	// gslave_node);
	}
	// std::cout << "]";
	}
	// std::cout << std::endl;
	if (local_node != UInt(-1)) {
	continue;
	}

	local_node = nodes->size();

	NodeInfo info(local_node, pos, direction);
	nodes->push_back(pos);
	nodes_global_ids->push_back(global_node);
	nodes_flags->push_back(flag \| NodeFlag::_pure_ghost);
	new_nodes.push_back(info.node);
	node_list.push_back(info);

	nodes_prank[info.node] = proc;
	event.getList().push_back(local_node);
	}
	};

	/* ---------------------------------------------------------------------- */
	auto && intersections_with_right =
	bbox_left.intersection(bbox_right, *communicator);
	auto && intersections_with_left =
	bbox_right.intersection(bbox_left, *communicator);

	std::vector<CommunicationRequest> send_requests;
	std::vector<std::unique_ptr<DynamicCommunicationBuffer>> send_buffers;

	// sending nodes in the common zones
	auto send_intersections = [&](auto & intersections, auto send_count) {
	for (auto && data : intersections) {
	auto proc = std::get<0>(data);

	// Send local nodes if intersects with remote
	const auto & intersection_with_proc = std::get<1>(data);
	if (intersection_with_proc) {
	send_requests.push_back(
	extract_and_send_nodes(intersection_with_proc, nodes_right,
	send_buffers, proc, send_count));
	}

	send_count += 2;
	}
	};

	auto recv_intersections = [&](auto & intersections, auto recv_count) {
	for (auto && data : intersections) {
	auto proc = std::get<0>(data);

	// receive remote nodes if intersects with local
	const auto & intersection_with_proc = std::get<1>(data);
	if (intersection_with_proc) {
	recv_and_extract_nodes(nodes_right, proc, recv_count);
	}

	recv_count += 2;
	}
	};

	send_intersections(intersections_with_left, 0);
	send_intersections(intersections_with_right, 1);

	recv_intersections(intersections_with_right, 0);
	recv_intersections(intersections_with_right, 1);

	Communicator::waitAll(send_requests);
	Communicator::freeCommunicationRequest(send_requests);

	this->sendEvent(event);
	} // end distributed work

	auto to_sort = [&](auto && info1, auto && info2) -> bool {
	return info1.position < info2.position;
	};

	// sort nodes based on their distance to lower corner
	std::sort(nodes_left.begin(), nodes_left.end(), to_sort);
	std::sort(nodes_right.begin(), nodes_right.end(), to_sort);

	// function to change the master of nodes
	auto updating_master = [&](auto & old_master, auto & new_master) {
	if (old_master == new_master) {
	return;
	}

	auto slaves = periodic_master_slave.equal_range(old_master);
	AKANTU_DEBUG_ASSERT(
	isPeriodicMaster(
	old_master), // slaves.first != periodic_master_slave.end(),
	"Cannot update master " << old_master << ", its not a master node!");
	decltype(periodic_master_slave) tmp_master_slave;
	for (auto it = slaves.first; it != slaves.second; ++it) {
	auto slave = it->second;
	tmp_master_slave.insert(std::make_pair(new_master, slave));
	periodic_slave_master[slave] = new_master;
	}

	periodic_master_slave.erase(old_master);
	(*nodes_flags)[old_master] &= ~NodeFlag::_periodic_master;
	addPeriodicSlave(old_master, new_master);

	for (auto && data : tmp_master_slave) {
	addPeriodicSlave(data.second, data.first);
	}
	};

	// handling 2 nodes that are periodic
	auto match_found = [&](auto & info1, auto & info2) {
	const auto & node1 = info1.node;
	const auto & node2 = info2.node;

	auto master = node1;
	bool node1_side_master = false;
	if (isPeriodicMaster(node1)) {
	node1_side_master = true;
	} else if (isPeriodicSlave(node1)) {
	node1_side_master = true;
	master = periodic_slave_master[node1];
	}

	auto node2_master = node2;
	if (isPeriodicSlave(node2)) {
	node2_master = periodic_slave_master[node2];
	}

	if (node1_side_master) {
	if (isPeriodicSlave(node2)) {
	updating_master(node2_master, master);
	return;
	}

	if (isPeriodicMaster(node2)) {
	updating_master(node2, master);
	return;
	}

	addPeriodicSlave(node2, master);
	} else {
	if (isPeriodicSlave(node2)) {
	addPeriodicSlave(node1, node2_master);
	return;
	}

	if (isPeriodicMaster(node2)) {
	addPeriodicSlave(node1, node2);
	return;
	}

	addPeriodicSlave(node2, node1);
	}
	};

	// matching the nodes from 2 lists
	auto match_pairs = [&](auto & nodes_1, auto & nodes_2) {
	// Guillaume to Nico: It seems that the list of nodes is not sorted
	// as it was: therefore the loop cannot be truncated anymore.
	// Otherwise many pairs are missing.
	// I replaced (temporarily?) for the N^2 loop so as not to miss
	// any pbc pair.
	//

	// auto it = nodes_2.begin();
	// for every nodes in 1st list
	for (auto && info1 : nodes_1) {
	auto & pos1 = info1.position;
	// auto it_cur = it;

	// try to find a match in 2nd list
	for (auto && info2 : nodes_2) {
	// auto & info2 = *it_cur;
	auto & pos2 = info2.position;

	auto dist = pos1.distance(pos2) / length;
	if (dist < tolerance) {
	// handles the found matches
	match_found(info1, info2);
	// it = it_cur;
	break;
	}
	}
	}
	};

	match_pairs(nodes_left, nodes_right);
	// match_pairs(nodes_right, nodes_left);

	this->updatePeriodicSynchronizer();

	this->is_periodic = true;
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::wipePeriodicInfo() {
	this->is_periodic = false;

	this->periodic_slave_master.clear();
	this->periodic_master_slave.clear();

	for (auto && flags : *nodes_flags) {
	flags &= ~NodeFlag::_periodic_mask;
	}
	}

	/* -------------------------------------------------------------------------- */
	void Mesh::updatePeriodicSynchronizer() {
	if (not this->periodic_node_synchronizer) {
	this->periodic_node_synchronizer =
	std::make_unique<PeriodicNodeSynchronizer>(
	*this, this->getID() + ":periodic_synchronizer", false);
	}

	this->periodic_node_synchronizer->update();
	}

	} // namespace akantu
	diff --git a/src/mesh/node_group.cc b/src/mesh/node_group.cc
	index e4983d36b..8528232fa 100644
	--- a/src/mesh/node_group.cc
	+++ b/src/mesh/node_group.cc
	@@ -1,99 +1,98 @@
	/**
	* @file node_group.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Implementation of the node group
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "node_group.hh"
	#include "dumpable.hh"
	#include "dumpable_inline_impl.hh"
	#include "mesh.hh"
	#if defined(AKANTU_USE_IOHELPER)
	#include "dumper_iohelper_paraview.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NodeGroup::NodeGroup(const std::string & name, const Mesh & mesh,
	const std::string & id)
	- : name(name),
	- node_group(0, 1, std::string(id + ":nodes")) {
	+ : name(name), node_group(0, 1, std::string(id + ":nodes")) {
	#if defined(AKANTU_USE_IOHELPER)
	this->registerDumper<DumperParaview>("paraview_" + name, name, true);
	auto field = std::make_shared<dumpers::NodalField<Real, true>>(
	mesh.getNodes(), 0, 0, &this->getNodes());
	this->getDumper().registerField("positions", field);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	NodeGroup::~NodeGroup() = default;

	/* -------------------------------------------------------------------------- */
	void NodeGroup::clear() { node_group.resize(0); }
	/* -------------------------------------------------------------------------- */
	// bool NodeGroup::empty() { return node_group.empty(); }
	/* -------------------------------------------------------------------------- */
	void NodeGroup::optimize() {
	std::sort(node_group.begin(), node_group.end());
	Array<UInt>::iterator<> end =
	std::unique(node_group.begin(), node_group.end());
	node_group.resize(end - node_group.begin());
	}

	/* -------------------------------------------------------------------------- */
	void NodeGroup::append(const NodeGroup & other_group) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = node_group.size();

	/// append new nodes to current list
	node_group.resize(nb_nodes + other_group.node_group.size());
	std::copy(other_group.node_group.begin(), other_group.node_group.end(),
	node_group.begin() + nb_nodes);

	optimize();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NodeGroup::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "NodeGroup [" << std::endl;
	stream << space << " + name: " << name << std::endl;
	node_group.printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}

	} // namespace akantu
	diff --git a/src/mesh/node_group.hh b/src/mesh/node_group.hh
	index c1f479d23..98afddd7e 100644
	--- a/src/mesh/node_group.hh
	+++ b/src/mesh/node_group.hh
	@@ -1,134 +1,134 @@
	/**
	* @file node_group.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Node group definition
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "dumpable.hh"
	#include "mesh_filter.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NODE_GROUP_HH_
	#define AKANTU_NODE_GROUP_HH_

	namespace akantu {

	class NodeGroup : public Dumpable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NodeGroup(const std::string & name, const Mesh & mesh,
	const std::string & id = "node_group");
	~NodeGroup() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	using const_node_iterator = Array<UInt>::const_iterator<UInt>;

	/// empty the node group
	void clear();

	/// returns treu if the group is empty \warning this changed beahavior if you
	/// want to empty the group use clear
	bool empty() const __attribute__((warn_unused_result));

	/// iterator to the beginning of the node group
	inline const_node_iterator begin() const;
	/// iterator to the end of the node group
	inline const_node_iterator end() const;

	/// add a node and give the local position through an iterator
	inline const_node_iterator add(UInt node, bool check_for_duplicate = true);

	/// remove a node
	inline void remove(UInt node);

	inline decltype(auto) find(UInt node) const { return node_group.find(node); }

	/// remove duplicated nodes
	void optimize();

	/// append a group to current one
	void append(const NodeGroup & other_group);

	/// apply a filter on current node group
	template <typename T> void applyNodeFilter(T & filter);

	/// function to print the contain of the class
	virtual void printself(std::ostream & stream, int indent = 0) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO_NOT_CONST(Nodes, node_group, Array<UInt> &);
	AKANTU_GET_MACRO(Nodes, node_group, const Array<UInt> &);
	AKANTU_GET_MACRO(Name, name, const std::string &);

	/// give the number of nodes in the current group
	inline UInt size() const;

	// UInt * storage() { return node_group.storage(); };

	friend class GroupManager;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// name of the group
	std::string name;

	/// list of nodes in the group
	Array<UInt> node_group;

	/// reference to the mesh in question
	// const Mesh & mesh;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const NodeGroup & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "node_group_inline_impl.hh"

	#endif /* AKANTU_NODE_GROUP_HH_ */
	diff --git a/src/mesh/node_group_inline_impl.hh b/src/mesh/node_group_inline_impl.hh
	index 1fdac9958..d933608a9 100644
	--- a/src/mesh/node_group_inline_impl.hh
	+++ b/src/mesh/node_group_inline_impl.hh
	@@ -1,102 +1,102 @@
	/**
	* @file node_group_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Node group inline function definitions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline NodeGroup::const_node_iterator NodeGroup::begin() const {
	return node_group.begin();
	}

	/* -------------------------------------------------------------------------- */
	inline NodeGroup::const_node_iterator NodeGroup::end() const {
	return node_group.end();
	}

	/* -------------------------------------------------------------------------- */
	inline NodeGroup::const_node_iterator NodeGroup::add(UInt node,
	bool check_for_duplicate) {
	if (check_for_duplicate) {
	const_node_iterator it = std::find(begin(), end(), node);
	if (it == node_group.end()) {
	node_group.push_back(node);
	return (node_group.end() - 1);
	}
	return it;
	}

	node_group.push_back(node);
	return (node_group.end() - 1);
	}

	/* -------------------------------------------------------------------------- */
	inline void NodeGroup::remove(UInt node) {
	Array<UInt>::iterator<> it = this->node_group.begin();
	Array<UInt>::iterator<> end = this->node_group.end();
	AKANTU_DEBUG_ASSERT(it != end, "The node group is empty!!");
	for (; it != node_group.end(); ++it) {
	if (*it == node) {
	it = node_group.erase(it);
	}
	}
	AKANTU_DEBUG_ASSERT(it != end, "The node was not found!");
	}

	/* -------------------------------------------------------------------------- */
	inline bool NodeGroup::empty() const { return node_group.empty(); }

	/* -------------------------------------------------------------------------- */
	inline UInt NodeGroup::size() const { return node_group.size(); }

	/* -------------------------------------------------------------------------- */
	struct FilterFunctor;

	template <typename T> void NodeGroup::applyNodeFilter(T & filter) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(T::type == FilterFunctor::_node_filter_functor,
	"NodeFilter can only apply node filter functor");

	Array<UInt>::iterator<> it = this->node_group.begin();

	for (; it != node_group.end(); ++it) {
	/// filter == true -> keep node
	if (!filter(*it)) {
	it = node_group.erase(it);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/cohesive_element_inserter.cc b/src/mesh_utils/cohesive_element_inserter.cc
	index 3e3f87751..a0e122d75 100644
	--- a/src/mesh_utils/cohesive_element_inserter.cc
	+++ b/src/mesh_utils/cohesive_element_inserter.cc
	@@ -1,328 +1,328 @@
	/**
	* @file cohesive_element_inserter.cc
	*
	* @author Mathias Lebihain <mathias.lebihain@enpc.fr>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Dec 04 2013
	* @date last modification: Wed Nov 11 2020
	*
	* @brief Cohesive element inserter functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_element_inserter.hh"
	#include "cohesive_element_inserter_helper.hh"
	#include "communicator.hh"
	#include "element_group.hh"
	#include "element_synchronizer.hh"
	#include "global_ids_updater.hh"
	#include "mesh_accessor.hh"
	#include "mesh_iterators.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	CohesiveElementInserter::CohesiveElementInserter(Mesh & mesh, const ID & id)
	: Parsable(ParserType::_cohesive_inserter), id(id), mesh(mesh),
	mesh_facets(mesh.initMeshFacets()),
	insertion_facets("insertion_facets", id),
	insertion_limits(mesh.getSpatialDimension(), 2),
	check_facets("check_facets", id) {

	this->registerParam("cohesive_surfaces", physical_surfaces, _pat_parsable,
	"List of groups to consider for insertion");
	this->registerParam("cohesive_zones", physical_zones, _pat_parsable,
	"List of groups to consider for insertion");
	this->registerParam("bounding_box", insertion_limits, _pat_parsable,
	"Global limit for insertion");

	UInt spatial_dimension = mesh.getSpatialDimension();

	/// init insertion limits
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	insertion_limits(dim, 0) = std::numeric_limits<Real>::max() * Real(-1.);
	insertion_limits(dim, 1) = std::numeric_limits<Real>::max();
	}

	insertion_facets.initialize(mesh_facets,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true, _default_value = false);
	}

	/* -------------------------------------------------------------------------- */
	CohesiveElementInserter::~CohesiveElementInserter() = default;

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserter::parseSection(const ParserSection & section) {
	Parsable::parseSection(section);

	if (is_extrinsic) {
	limitCheckFacets(this->check_facets);
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserter::limitCheckFacets() {
	limitCheckFacets(this->check_facets);
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserter::setLimit(SpatialDirection axis, Real first_limit,
	Real second_limit) {
	AKANTU_DEBUG_ASSERT(
	axis < mesh.getSpatialDimension(),
	"You are trying to limit insertion in a direction that doesn't exist");

	insertion_limits(axis, 0) = std::min(first_limit, second_limit);
	insertion_limits(axis, 1) = std::max(first_limit, second_limit);
	}

	/* -------------------------------------------------------------------------- */
	UInt CohesiveElementInserter::insertIntrinsicElements() {
	limitCheckFacets(insertion_facets);
	return insertElements();
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserter::limitCheckFacets(
	ElementTypeMapArray<bool> & check_facets) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	check_facets.initialize(mesh_facets,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true, _default_value = true);
	check_facets.set(true);

	// remove the pure ghost elements
	for_each_element(
	mesh_facets,
	[&](auto && facet) {
	const auto & element_to_facet = mesh_facets.getElementToSubelement(
	facet.type, facet.ghost_type)(facet.element);
	auto & left = element_to_facet[0];
	auto & right = element_to_facet[1];
	if (right == ElementNull \|\|
	(left.ghost_type == _ghost && right.ghost_type == _ghost)) {
	check_facets(facet) = false;
	return;
	}
	#ifndef AKANTU_NDEBUG
	if (left == ElementNull) {
	AKANTU_DEBUG_WARNING("By convention element should not have "
	"ElementNull on there first side: "
	<< facet);
	}
	#endif

	if (left.kind() == _ek_cohesive or right.kind() == _ek_cohesive) {
	check_facets(facet) = false;
	}
	},
	_spatial_dimension = spatial_dimension - 1);

	auto tolerance = Math::getTolerance();
	Vector<Real> bary_facet(spatial_dimension);
	// set the limits to the bounding box
	for_each_element(
	mesh_facets,
	[&](auto && facet) {
	auto & need_check = check_facets(facet);
	if (not need_check) {
	return;
	}

	mesh_facets.getBarycenter(facet, bary_facet);
	UInt coord_in_limit = 0;

	while (coord_in_limit < spatial_dimension and
	bary_facet(coord_in_limit) >
	(insertion_limits(coord_in_limit, 0) - tolerance) and
	bary_facet(coord_in_limit) <
	(insertion_limits(coord_in_limit, 1) + tolerance)) {
	++coord_in_limit;
	}

	if (coord_in_limit != spatial_dimension) {
	need_check = false;
	}
	},
	_spatial_dimension = spatial_dimension - 1);

	// remove the physical zones
	if (mesh.hasData("physical_names") and not physical_zones.empty()) {
	auto && physical_names = mesh.getData<std::string>("physical_names");
	for_each_element(
	mesh_facets,
	[&](auto && facet) {
	const auto & element_to_facet = mesh_facets.getElementToSubelement(
	facet.type, facet.ghost_type)(facet.element);
	auto count = 0;
	for (auto i : arange(2)) {
	const auto & element = element_to_facet[i];
	if (element == ElementNull) {
	continue;
	}
	const auto & name = physical_names(element);
	count += find(physical_zones.begin(), physical_zones.end(), name) !=
	physical_zones.end();
	}

	if (count != 2) {
	check_facets(facet) = false;
	}
	},
	_spatial_dimension = spatial_dimension - 1);
	}

	if (physical_surfaces.empty()) {
	AKANTU_DEBUG_OUT();
	return;
	}

	if (not mesh_facets.hasData("physical_names")) {
	AKANTU_DEBUG_ASSERT(
	physical_surfaces.empty(),
	"No physical names in the mesh but insertion limited to a group");
	AKANTU_DEBUG_OUT();
	return;
	}

	const auto & physical_ids =
	mesh_facets.getData<std::string>("physical_names");

	// set the limits to the physical surfaces
	for_each_element(
	mesh_facets,
	[&](auto && facet) {
	auto & need_check = check_facets(facet, 0);
	if (not need_check) {
	return;
	}

	const auto & physical_id = physical_ids(facet);
	auto it = find(physical_surfaces.begin(), physical_surfaces.end(),
	physical_id);

	need_check = (it != physical_surfaces.end());
	},
	_spatial_dimension = spatial_dimension - 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt CohesiveElementInserter::insertElements(bool only_double_facets) {
	CohesiveNewNodesEvent node_event(AKANTU_CURRENT_FUNCTION);
	NewElementsEvent element_event(AKANTU_CURRENT_FUNCTION);

	if (mesh_facets.isDistributed()) {
	mesh_facets.getElementSynchronizer().synchronizeOnce(
	*this, SynchronizationTag::_ce_groups);
	}

	CohesiveElementInserterHelper cohesive_element_inserter_helper(
	mesh, insertion_facets);

	UInt nb_new_elements{0};
	if (only_double_facets) {
	nb_new_elements = cohesive_element_inserter_helper.insertFacetsOnly();
	} else {
	nb_new_elements = cohesive_element_inserter_helper.insertCohesiveElement();
	element_event.getList().copy(
	cohesive_element_inserter_helper.getNewElements());
	}

	auto && doubled_nodes = cohesive_element_inserter_helper.getDoubledNodes();
	auto nb_new_nodes = doubled_nodes.size();

	node_event.getList().reserve(nb_new_nodes);
	node_event.getOldNodesList().reserve(nb_new_nodes);

	for (auto && doubled_node : make_view(doubled_nodes, 2)) {
	node_event.getList().push_back(doubled_node(1));
	node_event.getOldNodesList().push_back(doubled_node(0));
	}

	if (nb_new_elements > 0) {
	updateInsertionFacets();
	}

	MeshAccessor mesh_accessor(mesh);
	std::tie(nb_new_nodes, nb_new_elements) =
	mesh_accessor.updateGlobalData(node_event, element_event);

	return nb_new_elements;
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserter::updateInsertionFacets() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	for (auto && facet_gt : ghost_types) {
	for (auto && facet_type :
	mesh_facets.elementTypes(spatial_dimension - 1, facet_gt)) {
	auto & ins_facets = insertion_facets(facet_type, facet_gt);

	// this is the intrinsic case
	if (not is_extrinsic) {
	continue;
	}

	auto & f_check = check_facets(facet_type, facet_gt);
	for (auto && pair : zip(ins_facets, f_check)) {
	bool & ins = std::get<0>(pair);
	bool & check = std::get<1>(pair);
	if (ins) {
	ins = check = false;
	}
	}
	}
	}

	// resize for the newly added facets
	insertion_facets.initialize(mesh_facets,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true, _default_value = false);

	// resize for the newly added facets
	if (is_extrinsic) {
	check_facets.initialize(mesh_facets,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true, _default_value = false);
	} else {
	insertion_facets.set(false);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/cohesive_element_inserter.hh b/src/mesh_utils/cohesive_element_inserter.hh
	index 0ec5aa80f..43bbb6624 100644
	--- a/src/mesh_utils/cohesive_element_inserter.hh
	+++ b/src/mesh_utils/cohesive_element_inserter.hh
	@@ -1,175 +1,175 @@
	/**
	* @file cohesive_element_inserter.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Dec 04 2013
	* @date last modification: Tue Jul 21 2020
	*
	* @brief Cohesive element inserter
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "mesh_utils.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COHESIVE_ELEMENT_INSERTER_HH_
	#define AKANTU_COHESIVE_ELEMENT_INSERTER_HH_

	namespace akantu {
	class GlobalIdsUpdater;
	class FacetSynchronizer;
	class SolidMechanicsModeslCohesivel;
	} // namespace akantu

	namespace akantu {

	class CohesiveElementInserter : public DataAccessor<Element>, public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	CohesiveElementInserter(Mesh & mesh,
	const ID & id = "cohesive_element_inserter");

	~CohesiveElementInserter() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// set range limitation for intrinsic cohesive element insertion
	void setLimit(SpatialDirection axis, Real first_limit, Real second_limit);

	/// insert intrinsic cohesive elements in a predefined range
	auto insertIntrinsicElements() -> UInt;

	/// insert extrinsic cohesive elements (returns the number of new
	/// cohesive elements)
	UInt insertElements(bool only_double_facets = false);

	/// limit check facets to match given insertion limits
	void limitCheckFacets();

	protected:
	void parseSection(const ParserSection & section) override;

	protected:
	/// internal version of limitCheckFacets
	void limitCheckFacets(ElementTypeMapArray<bool> & check_facets);

	/// update facet insertion arrays after facets doubling
	void updateInsertionFacets();

	/// functions for parallel communications
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO_NOT_CONST(InsertionFacetsByElement, insertion_facets,
	ElementTypeMapArray<bool> &);
	AKANTU_GET_MACRO(InsertionFacetsByElement, insertion_facets,
	const ElementTypeMapArray<bool> &);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(InsertionFacets, insertion_facets, bool);

	AKANTU_GET_MACRO(CheckFacets, check_facets,
	const ElementTypeMapArray<bool> &);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(CheckFacets, check_facets, bool);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(CheckFacets, check_facets, bool);

	AKANTU_GET_MACRO(MeshFacets, mesh_facets, const Mesh &);
	AKANTU_GET_MACRO_NOT_CONST(MeshFacets, mesh_facets, Mesh &);

	AKANTU_SET_MACRO(IsExtrinsic, is_extrinsic, bool);

	public:
	friend class SolidMechanicsModelCohesive;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// object id
	ID id;

	/// main mesh where to insert cohesive elements
	Mesh & mesh;

	/// mesh containing facets
	Mesh & mesh_facets;

	/// list of facets where to insert elements
	ElementTypeMapArray<bool> insertion_facets;

	/// limits for element insertion
	Matrix<Real> insertion_limits;

	/// list of groups to consider for insertion, ignored if empty
	std::set<ID> physical_surfaces;

	/// list of groups in between which an inside which element are insterted
	std::set<ID> physical_zones;

	/// vector containing facets in which extrinsic cohesive elements can be
	/// inserted
	ElementTypeMapArray<bool> check_facets;

	/// global connectivity ids updater
	std::unique_ptr<GlobalIdsUpdater> global_ids_updater;

	/// is this inserter used in extrinsic
	bool is_extrinsic{false};
	};

	class CohesiveNewNodesEvent : public NewNodesEvent {
	public:
	CohesiveNewNodesEvent(const std::string & origin) : NewNodesEvent(origin) {}
	~CohesiveNewNodesEvent() override = default;

	AKANTU_GET_MACRO_NOT_CONST(OldNodesList, old_nodes, Array<UInt> &);
	AKANTU_GET_MACRO(OldNodesList, old_nodes, const Array<UInt> &);

	private:
	Array<UInt> old_nodes;
	};

	} // namespace akantu

	#include "cohesive_element_inserter_inline_impl.hh"

	#endif /* AKANTU_COHESIVE_ELEMENT_INSERTER_HH_ */
	diff --git a/src/mesh_utils/cohesive_element_inserter_helper.cc b/src/mesh_utils/cohesive_element_inserter_helper.cc
	index 8c5ed9d99..0ebd97ef5 100644
	--- a/src/mesh_utils/cohesive_element_inserter_helper.cc
	+++ b/src/mesh_utils/cohesive_element_inserter_helper.cc
	@@ -1,953 +1,952 @@
	/**
	* @file cohesive_element_inserter_helper.cc
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 08 2020
	* @date last modification: Wed Dec 23 2020
	*
	* @brief An helper class to handle cohesive element insertion
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_element_inserter_helper.hh"
	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh_accessor.hh"
	/* -------------------------------------------------------------------------- */
	#include <queue>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	CohesiveElementInserterHelper::CohesiveElementInserterHelper(
	Mesh & mesh, const ElementTypeMapArray<bool> & facet_insertion)
	: doubled_nodes(0, 2, "doubled_nodes"), mesh(mesh),
	mesh_facets(mesh.getMeshFacets()) {

	auto spatial_dimension = mesh_facets.getSpatialDimension();

	for (auto gt : ghost_types) {
	for (auto type : mesh_facets.elementTypes(_ghost_type = gt)) {
	nb_new_facets(type, gt) = mesh_facets.getNbElement(type, gt);
	}
	}

	std::array<Int, 2> nb_facet_to_insert{0, 0};
	// creates a vector of the facets to insert
	std::vector<Element> potential_facets_to_double;
	for (auto gt_facet : ghost_types) {
	for (auto type_facet :
	mesh_facets.elementTypes(spatial_dimension - 1, gt_facet)) {
	const auto & f_insertion = facet_insertion(type_facet, gt_facet);
	auto & counter = nb_facet_to_insert[gt_facet == _not_ghost ? 0 : 1];

	for (auto && data : enumerate(f_insertion)) {
	if (std::get<1>(data)) {
	UInt el = std::get<0>(data);
	potential_facets_to_double.push_back({type_facet, el, gt_facet});
	++counter;
	}
	}
	}
	}

	// Defines a global order of insertion oof cohesive element to ensure node
	// doubling appens in the smae order, this is necessary for the global node
	// numbering
	if (mesh_facets.isDistributed()) {
	const auto & comm = mesh_facets.getCommunicator();

	ElementTypeMapArray<Int> global_orderings;

	global_orderings.initialize(mesh_facets,
	_spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true, _default_value = -1);

	auto starting_index = nb_facet_to_insert[0];
	comm.exclusiveScan(starting_index);

	// define the local numbers for facet to insert
	for (auto gt_facet : ghost_types) {
	for (auto type_facet :
	mesh_facets.elementTypes(spatial_dimension - 1, gt_facet)) {
	for (auto data : zip(facet_insertion(type_facet, gt_facet),
	global_orderings(type_facet, gt_facet))) {
	if (std::get<0>(data)) {
	std::get<1>(data) = starting_index;
	++starting_index;
	}
	}
	}
	}

	// retreives the oorder number from neighoring processors
	auto && synchronizer = mesh_facets.getElementSynchronizer();
	SimpleElementDataAccessor<Int> data_accessor(
	global_orderings, SynchronizationTag::_ce_insertion_order);
	synchronizer.synchronizeOnce(data_accessor,
	SynchronizationTag::_ce_insertion_order);

	// sort the facets to double based on this global ordering
	std::sort(potential_facets_to_double.begin(),
	potential_facets_to_double.end(),
	[&global_orderings](auto && el1, auto && el2) {
	return global_orderings(el1) < global_orderings(el2);
	});
	}

	for (auto d : arange(spatial_dimension)) {
	facets_to_double_by_dim[d] = std::make_unique<Array<Element>>(
	0, 2, "facets_to_double_" + std::to_string(d));
	}

	auto & facets_to_double = *facets_to_double_by_dim[spatial_dimension - 1];

	MeshAccessor mesh_accessor(mesh_facets);
	auto & elements_to_subelements = mesh_accessor.getElementToSubelement();

	for (auto && facet_to_double : potential_facets_to_double) {
	auto gt_facet = facet_to_double.ghost_type;
	auto type_facet = facet_to_double.type;
	auto & elements_to_facets = elements_to_subelements(type_facet, gt_facet);

	auto & elements_to_facet = elements_to_facets(facet_to_double.element);
	if (elements_to_facet[1].type == _not_defined
	#if defined(AKANTU_COHESIVE_ELEMENT)
	\|\| elements_to_facet[1].kind() == _ek_cohesive
	#endif
	) {
	AKANTU_DEBUG_WARNING("attempt to double a facet on the boundary");
	continue;
	}

	auto new_facet = nb_new_facets(type_facet, gt_facet)++;

	facets_to_double.push_back(Vector<Element>{
	facet_to_double, Element{type_facet, new_facet, gt_facet}});

	/// update facet_to_element vector
	auto & element_to_update = elements_to_facet[1];
	auto el = element_to_update.element;

	const auto & facets_to_elements = mesh_facets.getSubelementToElement(
	element_to_update.type, element_to_update.ghost_type);
	auto facets_to_element = Vector<Element>(
	make_view(facets_to_elements, facets_to_elements.getNbComponent())
	.begin()[el]);
	auto facet_to_update = std::find(facets_to_element.begin(),
	facets_to_element.end(), facet_to_double);

	AKANTU_DEBUG_ASSERT(facet_to_update != facets_to_element.end(),
	"Facet not found");

	facet_to_update->element = new_facet;

	/// update elements connected to facet
	const auto & first_facet_list = elements_to_facet;
	elements_to_facets.push_back(first_facet_list);

	/// set new and original facets as boundary facets
	elements_to_facets(new_facet)[0] = elements_to_facets(new_facet)[1];
	elements_to_facets(new_facet)[1] = ElementNull;

	elements_to_facets(facet_to_double.element)[1] = ElementNull;
	}
	}

	/* -------------------------------------------------------------------------- */
	inline auto
	CohesiveElementInserterHelper::hasElement(const Vector<UInt> & nodes_element,
	const Vector<UInt> & nodes) -> bool {
	// if one of the nodes of "nodes" is not in "nodes_element" it stops
	auto it = std::mismatch(nodes.begin(), nodes.end(), nodes_element.begin(),
	[&](auto && node, auto && /node2/) -> bool {
	auto it = std::find(nodes_element.begin(),
	nodes_element.end(), node);
	return (it != nodes_element.end());
	});

	// true if all "nodes" where found in "nodes_element"
	return (it.first == nodes.end());
	}

	/* -------------------------------------------------------------------------- */
	inline auto CohesiveElementInserterHelper::removeElementsInVector(
	const std::vector<Element> & elem_to_remove,
	std::vector<Element> & elem_list) -> bool {
	if (elem_list.size() <= elem_to_remove.size()) {
	return true;
	}

	auto el_it = elem_to_remove.begin();
	auto el_last = elem_to_remove.end();
	std::vector<Element>::iterator el_del;

	UInt deletions = 0;

	for (; el_it != el_last; ++el_it) {
	el_del = std::find(elem_list.begin(), elem_list.end(), *el_it);

	if (el_del != elem_list.end()) {
	elem_list.erase(el_del);
	++deletions;
	}
	}

	AKANTU_DEBUG_ASSERT(deletions == 0 \|\| deletions == elem_to_remove.size(),
	"Not all elements have been erased");

	return deletions == 0;
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::updateElementalConnectivity(
	Mesh & mesh, UInt old_node, UInt new_node,
	const std::vector<Element> & element_list,
	const std::vector<Element> * facet_list) {
	AKANTU_DEBUG_IN();

	for (const auto & element : element_list) {
	if (element.type == _not_defined) {
	continue;
	}

	Vector<UInt> connectivity = mesh.getConnectivity(element);

	if (element.kind() == _ek_cohesive) {
	AKANTU_DEBUG_ASSERT(
	facet_list != nullptr,
	"Provide a facet list in order to update cohesive elements");

	const Vector<Element> facets =
	mesh_facets.getSubelementToElement(element);

	auto facet_nb_nodes = connectivity.size() / 2;

	/// loop over cohesive element's facets
	for (const auto & facet : enumerate(facets)) {
	/// skip facets if not present in the list
	if (std::find(facet_list->begin(), facet_list->end(),
	std::get<1>(facet)) == facet_list->end()) {
	continue;
	}

	auto n = std::get<0>(facet);

	auto begin =
	connectivity.begin() + static_cast<UInt>(n * facet_nb_nodes);
	auto end = begin + facet_nb_nodes;

	auto it = std::find(begin, end, old_node);
	AKANTU_DEBUG_ASSERT(it != end, "Node not found in current element");

	*it = new_node;
	}
	} else {
	auto it = std::find(connectivity.begin(), connectivity.end(), old_node);
	AKANTU_DEBUG_ASSERT(it != connectivity.end(),
	"Node not found in current element");

	/// update connectivity
	*it = new_node;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::updateSubelementToElement(UInt dim,
	bool facet_mode) {
	auto & facets_to_double = *facets_to_double_by_dim[dim];
	auto & facets_to_subfacets = elementsOfDimToElementsOfDim(
	dim + static_cast<decltype(dim)>(facet_mode), dim);

	for (auto && data :
	zip(make_view(facets_to_double, 2), facets_to_subfacets)) {
	const auto & old_subfacet = std::get<0>(data)[0];
	const auto & new_subfacet = std::get<0>(data)[1];
	auto & facet_to_subfacets = std::get<1>(data);

	MeshAccessor mesh_accessor(mesh_facets);
	for (auto & facet : facet_to_subfacets) {
	Vector<Element> subfacets = mesh_accessor.getSubelementToElement(facet);

	auto && subfacet_to_update_it =
	std::find(subfacets.begin(), subfacets.end(), old_subfacet);

	AKANTU_DEBUG_ASSERT(subfacet_to_update_it != subfacets.end(),
	"Subfacet not found");

	*subfacet_to_update_it = new_subfacet;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::updateElementToSubelement(UInt dim,
	bool facet_mode) {
	auto & facets_to_double = *facets_to_double_by_dim[dim];
	auto & facets_to_subfacets = elementsOfDimToElementsOfDim(
	dim + static_cast<decltype(dim)>(facet_mode), dim);

	MeshAccessor mesh_accessor(mesh_facets);
	// resize the arrays
	mesh_accessor.getElementToSubelement().initialize(
	mesh_facets, _spatial_dimension = dim, _with_nb_element = true);

	for (auto && data :
	zip(make_view(facets_to_double, 2), facets_to_subfacets)) {
	const auto & new_facet = std::get<0>(data)[1];
	mesh_accessor.getElementToSubelement(new_facet) = std::get<1>(data);
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::updateQuadraticSegments(UInt dim) {
	AKANTU_DEBUG_IN();
	auto spatial_dimension = mesh.getSpatialDimension();
	auto & facets_to_double = *facets_to_double_by_dim[dim];

	MeshAccessor mesh_accessor(mesh_facets);
	auto & connectivities = mesh_accessor.getConnectivities();

	/// this ones matter only for segments in 3D
	Array<std::vector<Element>> * element_to_subfacet_double = nullptr;
	Array<std::vector<Element>> * facet_to_subfacet_double = nullptr;

	if (dim == spatial_dimension - 2) {
	element_to_subfacet_double = &elementsOfDimToElementsOfDim(dim + 2, dim);
	facet_to_subfacet_double = &elementsOfDimToElementsOfDim(dim + 1, dim);
	}

	const auto & element_to_subelement = mesh_facets.getElementToSubelement();
	std::vector<UInt> middle_nodes;

	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto & old_facet = facet_to_double[0];
	if (old_facet.type != _segment_3) {
	continue;
	}

	auto node = connectivities(old_facet, 2);
	if (not mesh.isPureGhostNode(node)) {
	middle_nodes.push_back(node);
	}
	}

	auto n = doubled_nodes.size();
	doubleNodes(middle_nodes);

	for (auto && data : enumerate(make_view(facets_to_double, 2))) {
	auto facet = std::get<0>(data);
	auto & old_facet = std::get<1>(data)[0];
	if (old_facet.type != _segment_3) {
	continue;
	}

	auto old_node = connectivities(old_facet, 2);

	if (mesh.isPureGhostNode(old_node)) {
	continue;
	}

	auto new_node = doubled_nodes(n, 1);

	auto & new_facet = std::get<1>(data)[1];
	connectivities(new_facet, 2) = new_node;

	if (dim == spatial_dimension - 2) {
	updateElementalConnectivity(mesh_facets, old_node, new_node,
	element_to_subelement(new_facet, 0));

	updateElementalConnectivity(mesh, old_node, new_node,
	(*element_to_subfacet_double)(facet),
	&(*facet_to_subfacet_double)(facet));
	} else {
	updateElementalConnectivity(mesh, old_node, new_node,
	element_to_subelement(new_facet, 0));
	}

	++n;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt CohesiveElementInserterHelper::insertCohesiveElement() {
	auto nb_new_facets = insertFacetsOnly();
	if (nb_new_facets == 0) {
	return 0;
	}

	updateCohesiveData();
	return nb_new_facets;
	}

	/* -------------------------------------------------------------------------- */
	UInt CohesiveElementInserterHelper::insertFacetsOnly() {
	UInt spatial_dimension = mesh.getSpatialDimension();

	if (facets_to_double_by_dim[spatial_dimension - 1]->empty()) {
	return 0;
	}

	if (spatial_dimension == 1) {
	doublePointFacet();
	} else if (spatial_dimension == 2) {
	doubleFacets<1>();
	findSubfacetToDouble<1>();

	doubleSubfacet<2>();

	} else if (spatial_dimension == 3) {
	doubleFacets<2>();
	findSubfacetToDouble<2>();

	doubleFacets<1>();
	findSubfacetToDouble<1>();

	doubleSubfacet<3>();
	}

	return facets_to_double_by_dim[spatial_dimension - 1]->size();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void CohesiveElementInserterHelper::doubleFacets() {
	AKANTU_DEBUG_IN();
	NewElementsEvent new_facets;
	auto spatial_dimension = mesh_facets.getSpatialDimension();

	auto & facets_to_double = *facets_to_double_by_dim[dim];
	MeshAccessor mesh_accessor(mesh_facets);
	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto && old_facet = facet_to_double[0];
	auto && new_facet = facet_to_double[1];

	auto & facets_connectivities =
	mesh_accessor.getConnectivity(old_facet.type, old_facet.ghost_type);
	facets_connectivities.resize(
	nb_new_facets(old_facet.type, old_facet.ghost_type));

	auto facets_connectivities_begin =
	make_view(facets_connectivities, facets_connectivities.getNbComponent())
	.begin();

	// copy the connectivities
	Vector<UInt> new_conn(facets_connectivities_begin[new_facet.element]);
	Vector<UInt> old_conn(facets_connectivities_begin[old_facet.element]);
	new_conn = old_conn;

	// this will fail if multiple facet types exists for a given element type
	// \TODO handle multiple sub-facet types
	auto nb_subfacet_per_facet = Mesh::getNbFacetsPerElement(old_facet.type);

	auto & subfacets_to_facets = mesh_accessor.getSubelementToElementNC(
	old_facet.type, old_facet.ghost_type);

	subfacets_to_facets.resize(
	nb_new_facets(old_facet.type, old_facet.ghost_type), ElementNull);

	auto subfacets_to_facets_begin =
	make_view(subfacets_to_facets, nb_subfacet_per_facet).begin();

	// copy the subfacet to facets information
	Vector<Element> old_subfacets_to_facet(
	subfacets_to_facets_begin[old_facet.element]);
	Vector<Element> new_subfacet_to_facet(
	subfacets_to_facets_begin[new_facet.element]);
	new_subfacet_to_facet = old_subfacets_to_facet;

	for (auto & subfacet : old_subfacets_to_facet) {
	if (subfacet == ElementNull) {
	continue;
	}

	/// update facet_to_subfacet array
	mesh_accessor.getElementToSubelement(subfacet).push_back(new_facet);
	}

	new_facets.getList().push_back(new_facet);
	}

	/// update facet_to_subfacet and _segment_3 facets if any
	if (dim != spatial_dimension - 1) {
	updateSubelementToElement(dim, true);
	updateElementToSubelement(dim, true);
	updateQuadraticSegments(dim);
	} else {
	updateQuadraticSegments(dim);
	}

	mesh_facets.sendEvent(new_facets);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void CohesiveElementInserterHelper::findSubfacetToDouble() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh_facets.getSpatialDimension();

	MeshAccessor mesh_accessor(mesh_facets);

	auto & facets_to_double = *facets_to_double_by_dim[spatial_dimension - 1];
	- auto & subfacets_to_facets = mesh_facets.getSubelementToElement();
	+ const auto & subfacets_to_facets = mesh_facets.getSubelementToElement();
	auto & elements_to_facets = mesh_accessor.getElementToSubelement();

	/// loop on every facet
	for (auto f : arange(2)) {
	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto old_facet = facet_to_double[f];
	auto new_facet = facet_to_double[1 - f];

	const auto & starting_element = elements_to_facets(new_facet, 0)[0];
	auto current_facet = old_facet;

	Vector<Element> subfacets_to_facet = subfacets_to_facets.get(old_facet);
	/// loop on every subfacet
	for (auto & subfacet : subfacets_to_facet) {
	if (subfacet == ElementNull) {
	continue;
	}

	if (dim == spatial_dimension - 2) {
	Vector<Element> subsubfacets_to_subfacet =
	subfacets_to_facets.get(subfacet);
	/// loop on every subsubfacet
	for (auto & subsubfacet : subsubfacets_to_subfacet) {
	if (subsubfacet == ElementNull) {
	continue;
	}

	Vector<UInt> subsubfacet_connectivity =
	mesh_facets.getConnectivity(subsubfacet);

	std::vector<Element> element_list;
	std::vector<Element> facet_list;
	std::vector<Element> subfacet_list;

	/// check if subsubfacet is to be doubled
	- if (findElementsAroundSubfacet(
	+ if (!findElementsAroundSubfacet(
	starting_element, current_facet, subsubfacet_connectivity,
	- element_list, facet_list, &subfacet_list) == false and
	- removeElementsInVector(
	- subfacet_list, elements_to_facets(subsubfacet)) == false) {
	+ element_list, facet_list, &subfacet_list) and
	+ !removeElementsInVector(subfacet_list,
	+ elements_to_facets(subsubfacet))) {
	Element new_subsubfacet{
	subsubfacet.type,
	nb_new_facets(subsubfacet.type, subsubfacet.ghost_type)++,
	subsubfacet.ghost_type};
	facets_to_double_by_dim[dim - 1]->push_back(
	Vector<Element>{subsubfacet, new_subsubfacet});
	elementsOfDimToElementsOfDim(dim - 1, dim - 1)
	.push_back(subfacet_list);
	- elementsOfDimToElementsOfDim(dim, dim - 1)
	- .push_back(facet_list);
	+ elementsOfDimToElementsOfDim(dim, dim - 1).push_back(facet_list);
	elementsOfDimToElementsOfDim(dim + 1, dim - 1)
	.push_back(element_list);
	}
	}
	} else {
	std::vector<Element> element_list;
	std::vector<Element> facet_list;

	Vector<UInt> subfacet_connectivity =
	mesh_facets.getConnectivity(subfacet);

	/// check if subfacet is to be doubled
	- if (findElementsAroundSubfacet(starting_element, current_facet,
	- subfacet_connectivity, element_list,
	- facet_list) == false and
	- removeElementsInVector(facet_list,
	- elements_to_facets(subfacet)) == false) {
	+ if (!findElementsAroundSubfacet(starting_element, current_facet,
	+ subfacet_connectivity, element_list,
	+ facet_list) and
	+ !removeElementsInVector(facet_list,
	+ elements_to_facets(subfacet))) {
	Element new_subfacet{
	subfacet.type,
	nb_new_facets(subfacet.type, subfacet.ghost_type)++,
	subfacet.ghost_type};
	facets_to_double_by_dim[dim - 1]->push_back(
	Vector<Element>{subfacet, new_subfacet});

	elementsOfDimToElementsOfDim(dim, dim - 1).push_back(facet_list);
	elementsOfDimToElementsOfDim(dim + 1, dim - 1)
	.push_back(element_list);
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::doubleNodes(
	const std::vector<UInt> & old_nodes) {
	auto & position = mesh.getNodes();
	auto spatial_dimension = mesh.getSpatialDimension();

	auto old_nb_nodes = position.size();
	position.reserve(old_nb_nodes + old_nodes.size());
	doubled_nodes.reserve(doubled_nodes.size() + old_nodes.size());

	auto position_begin = position.begin(spatial_dimension);
	for (auto && data : enumerate(old_nodes)) {
	auto n = std::get<0>(data);
	auto old_node = std::get<1>(data);
	decltype(old_node) new_node = old_nb_nodes + n;

	/// store doubled nodes
	doubled_nodes.push_back(Vector<UInt>{old_node, new_node});

	/// update position
	Vector<Real> coords = Vector<Real>(position_begin[old_node]);
	position.push_back(coords);
	}
	}

	/* -------------------------------------------------------------------------- */
	bool CohesiveElementInserterHelper::findElementsAroundSubfacet(
	const Element & starting_element, const Element & end_facet,
	const Vector<UInt> & subfacet_connectivity,
	std::vector<Element> & element_list, std::vector<Element> & facet_list,
	std::vector<Element> * subfacet_list) {
	bool facet_matched = false;

	element_list.push_back(starting_element);

	std::queue<Element> elements_to_check;
	elements_to_check.push(starting_element);

	/// keep going as long as there are elements to check
	while (not elements_to_check.empty()) {
	/// check current element
	Element & current_element = elements_to_check.front();

	const Vector<Element> facets_to_element =
	mesh_facets.getSubelementToElement(current_element);

	// for every facet of the element
	- for (auto & current_facet : facets_to_element) {
	+ for (const auto & current_facet : facets_to_element) {
	if (current_facet == ElementNull) {
	continue;
	}

	if (current_facet == end_facet) {
	facet_matched = true;
	}

	auto find_facet =
	std::find(facet_list.begin(), facet_list.end(), current_facet);

	// facet already listed or subfacet_connectivity is not in the
	// connectivity of current_facet;
	if ((find_facet != facet_list.end()) or
	not hasElement(mesh_facets.getConnectivity(current_facet),
	subfacet_connectivity)) {
	continue;
	}

	facet_list.push_back(current_facet);

	if (subfacet_list != nullptr) {
	const Vector<Element> subfacets_of_facet =
	mesh_facets.getSubelementToElement(current_facet);

	/// check subfacets
	for (const auto & current_subfacet : subfacets_of_facet) {
	if (current_subfacet == ElementNull) {
	continue;
	}

	auto find_subfacet = std::find(
	subfacet_list->begin(), subfacet_list->end(), current_subfacet);
	if ((find_subfacet != subfacet_list->end()) or
	not hasElement(mesh_facets.getConnectivity(current_subfacet),
	subfacet_connectivity)) {
	continue;
	}

	subfacet_list->push_back(current_subfacet);
	}
	}

	/// consider opposing element
	const auto & elements_to_facet =
	mesh_facets.getElementToSubelement(current_facet);
	UInt opposing = 0;
	if (elements_to_facet[0] == current_element) {
	opposing = 1;
	}

	- auto & opposing_element = elements_to_facet[opposing];
	+ const auto & opposing_element = elements_to_facet[opposing];

	/// skip null elements since they are on a boundary
	if (opposing_element == ElementNull) {
	continue;
	}

	/// skip this element if already added
	if (std::find(element_list.begin(), element_list.end(),
	opposing_element) != element_list.end()) {
	continue;
	}

	/// only regular elements have to be checked
	if (opposing_element.kind() == _ek_regular) {
	elements_to_check.push(opposing_element);
	}

	element_list.push_back(opposing_element);

	AKANTU_DEBUG_ASSERT(hasElement(mesh.getConnectivity(opposing_element),
	subfacet_connectivity),
	"Subfacet doesn't belong to this element");
	}

	/// erased checked element from the list
	elements_to_check.pop();
	}

	return facet_matched;
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::updateCohesiveData() {

	UInt spatial_dimension = mesh.getSpatialDimension();
	bool third_dimension = spatial_dimension == 3;

	MeshAccessor mesh_accessor(mesh);
	MeshAccessor mesh_facets_accessor(mesh_facets);

	for (auto ghost_type : ghost_types) {
	for (auto cohesive_type : mesh.elementTypes(_element_kind = _ek_cohesive)) {
	auto nb_cohesive_elements = mesh.getNbElement(cohesive_type, ghost_type);
	nb_new_facets(cohesive_type, ghost_type) = nb_cohesive_elements;

	mesh_facets_accessor.getSubelementToElement(cohesive_type, ghost_type);
	}
	}

	auto & facets_to_double = *facets_to_double_by_dim[spatial_dimension - 1];

	new_elements.reserve(new_elements.size() + facets_to_double.size());

	std::array<Element, 2> facets;

	auto & element_to_facet = mesh_facets_accessor.getElementToSubelement();
	auto & facets_to_cohesive_elements =
	mesh_facets_accessor.getSubelementToElement();

	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto & old_facet = facet_to_double[0];

	/// (in 3D cohesive elements connectivity is inverted)
	facets[third_dimension ? 1 : 0] = old_facet;
	facets[third_dimension ? 0 : 1] = facet_to_double[1];

	auto type_cohesive = FEEngine::getCohesiveElementType(old_facet.type);

	auto & facet_connectivities =
	mesh_facets.getConnectivity(old_facet.type, old_facet.ghost_type);
	auto facet_connectivity_it =
	facet_connectivities.begin(facet_connectivities.getNbComponent());

	auto cohesive_element = Element{
	type_cohesive, nb_new_facets(type_cohesive, old_facet.ghost_type)++,
	old_facet.ghost_type};

	auto & cohesives_connectivities =
	mesh_accessor.getConnectivity(type_cohesive, old_facet.ghost_type);
	Matrix<UInt> connectivity(facet_connectivities.getNbComponent(), 2);
	Vector<Element> facets_to_cohesive_element(2);

	for (auto s : arange(2)) {
	/// store doubled facets
	facets_to_cohesive_element[s] = facets[s];

	// update connectivities
	connectivity(s) = Vector<UInt>(facet_connectivity_it[facets[s].element]);

	/// update element_to_facet vectors
	element_to_facet(facets[s], 0)[1] = cohesive_element;
	}

	cohesives_connectivities.push_back(connectivity);

	facets_to_cohesive_elements(type_cohesive, old_facet.ghost_type)
	.push_back(facets_to_cohesive_element);

	/// add cohesive element to the element event list
	new_elements.push_back(cohesive_element);
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveElementInserterHelper::doublePointFacet() {
	UInt spatial_dimension = mesh.getSpatialDimension();
	if (spatial_dimension != 1) {
	return;
	}

	NewElementsEvent new_facets_event;

	auto & facets_to_double = *facets_to_double_by_dim[spatial_dimension - 1];
	const auto & element_to_facet = mesh_facets.getElementToSubelement();
	auto & position = mesh.getNodes();
	MeshAccessor mesh_accessor(mesh_facets);

	for (auto ghost_type : ghost_types) {
	for (auto facet_type : nb_new_facets.elementTypes(
	spatial_dimension - 1, ghost_type, _ek_regular)) {
	auto nb_new_element = nb_new_facets(facet_type, ghost_type);
	auto & connectivities =
	mesh_accessor.getConnectivity(facet_type, ghost_type);
	connectivities.resize(nb_new_element);
	}
	}

	position.reserve(position.size() + facets_to_double.size());
	for (auto facet_to_double : make_view(facets_to_double, 2)) {
	auto & old_facet = facet_to_double[0];
	auto & new_facet = facet_to_double[1];

	auto element = element_to_facet(new_facet)[0];
	auto & facet_connectivities =
	mesh_accessor.getConnectivity(old_facet.type, old_facet.ghost_type);
	auto old_node = facet_connectivities(old_facet.element);
	auto new_node = position.size();

	/// update position
	position.push_back(position(old_node));
	facet_connectivities(new_facet.element) = new_node;

	Vector<UInt> segment_conectivity = mesh.getConnectivity(element);

	/// update facet connectivity
	auto it = std::find(segment_conectivity.begin(), segment_conectivity.end(),
	old_node);
	*it = new_node;

	doubled_nodes.push_back(Vector<UInt>{old_node, new_node});
	new_facets_event.getList().push_back(new_facet);
	}

	mesh_facets.sendEvent(new_facets_event);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void CohesiveElementInserterHelper::doubleSubfacet() {
	if (spatial_dimension == 1) {
	return;
	}

	NewElementsEvent new_facets_event;

	std::vector<UInt> nodes_to_double;
	MeshAccessor mesh_accessor(mesh_facets);
	auto & connectivities = mesh_accessor.getConnectivities();

	auto & facets_to_double = *facets_to_double_by_dim[0];
	ElementTypeMap<Int> nb_new_elements;
	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto && old_element = facet_to_double[0];
	nb_new_elements(old_element.type, old_element.ghost_type) = 0;
	}

	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto && old_element = facet_to_double[0];
	++nb_new_elements(old_element.type, old_element.ghost_type);
	}

	for (auto ghost_type : ghost_types) {
	for (auto facet_type :
	nb_new_elements.elementTypes(0, ghost_type, _ek_regular)) {
	auto & connectivities =
	mesh_accessor.getConnectivity(facet_type, ghost_type);
	connectivities.resize(connectivities.size() +
	nb_new_elements(facet_type, ghost_type));
	}
	}

	for (auto && facet_to_double : make_view(facets_to_double, 2)) {
	auto & old_facet = facet_to_double(0);
	// auto & new_facet = facet_to_double(1);

	AKANTU_DEBUG_ASSERT(
	old_facet.type == _point_1,
	"Only _point_1 subfacet doubling is supported at the moment");

	/// list nodes double
	nodes_to_double.push_back(connectivities(old_facet));
	}

	auto old_nb_doubled_nodes = doubled_nodes.size();
	doubleNodes(nodes_to_double);

	auto double_nodes_view = make_view(doubled_nodes, 2);

	for (auto && data :
	zip(make_view(facets_to_double, 2),
	range(double_nodes_view.begin() + old_nb_doubled_nodes,
	double_nodes_view.end()),
	arange(facets_to_double.size()))) {
	// auto & old_facet = std::get<0>(data)[0];
	auto & new_facet = std::get<0>(data)[1];

	new_facets_event.getList().push_back(new_facet);

	auto & nodes = std::get<1>(data);
	auto old_node = nodes(0);
	auto new_node = nodes(1);

	auto f = std::get<2>(data);

	/// add new nodes in connectivity
	connectivities(new_facet) = new_node;

	updateElementalConnectivity(mesh, old_node, new_node,
	elementsOfDimToElementsOfDim(2, 0)(f),
	&elementsOfDimToElementsOfDim(1, 0)(f));

	updateElementalConnectivity(mesh_facets, old_node, new_node,
	elementsOfDimToElementsOfDim(1, 0)(f));

	if (spatial_dimension == 3) {
	updateElementalConnectivity(mesh_facets, old_node, new_node,
	elementsOfDimToElementsOfDim(0, 0)(f));
	}
	}

	updateSubelementToElement(0, spatial_dimension == 2);
	updateElementToSubelement(0, spatial_dimension == 2);

	mesh_facets.sendEvent(new_facets_event);
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/cohesive_element_inserter_helper.hh b/src/mesh_utils/cohesive_element_inserter_helper.hh
	index 3bdac0a3a..b330a8d86 100644
	--- a/src/mesh_utils/cohesive_element_inserter_helper.hh
	+++ b/src/mesh_utils/cohesive_element_inserter_helper.hh
	@@ -1,118 +1,118 @@
	/**
	* @file cohesive_element_inserter_helper.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 08 2020
	* @date last modification: Wed Nov 11 2020
	*
	* @brief An helper class to handle cohesive element insertion
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_COHESIVE_ELEMENT_INSERTER_HELPER_HH__
	#define __AKANTU_COHESIVE_ELEMENT_INSERTER_HELPER_HH__

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class CohesiveElementInserterHelper {
	public:
	CohesiveElementInserterHelper(
	Mesh & mesh, const ElementTypeMapArray<bool> & facet_insertion);

	UInt insertCohesiveElement();
	UInt insertFacetsOnly();

	private:
	template <UInt dim> UInt insertFacetsOnlyImpl();
	template <UInt dim> void doubleFacets();
	template <UInt dim> void findSubfacetToDouble();

	void doubleNodes(const std::vector<UInt> & old_nodes);

	bool findElementsAroundSubfacet(
	const Element & starting_element, const Element & end_facet,
	const Vector<UInt> & subfacet_connectivity,
	std::vector<Element> & element_list, std::vector<Element> & facet_list,
	std::vector<Element> * subfacet_list = nullptr);

	static inline bool hasElement(const Vector<UInt> & nodes_element,
	const Vector<UInt> & nodes);
	static inline bool
	removeElementsInVector(const std::vector<Element> & elem_to_remove,
	std::vector<Element> & elem_list);

	void updateElementalConnectivity(
	Mesh & mesh, UInt old_node, UInt new_node,
	const std::vector<Element> & element_list,
	const std::vector<Element> * facet_list = nullptr);

	// update functions
	void updateElementToSubelement(UInt dim, bool facet_mode);
	void updateSubelementToElement(UInt dim, bool facet_mode);
	void updateQuadraticSegments(UInt dim);

	void updateCohesiveData();
	void doublePointFacet();
	template <UInt spatial_dimension> void doubleSubfacet();

	decltype(auto) elementsOfDimToElementsOfDim(Int dim1, Int dim2) {
	AKANTU_DEBUG_ASSERT(dim1 >= 0 and dim1 <= 3,
	"dimension of target element out of range");
	AKANTU_DEBUG_ASSERT(dim2 >= 0 and dim2 <= 3,
	"dimension of source element out of range");

	auto & array = dimelements_to_dimelements[dim1][dim2];
	if (not array) {
	array = std::make_unique<Array<std::vector<Element>>>();
	}

	return (*array);
	}

	public:
	decltype(auto) getNewElements() const { return (new_elements); }
	decltype(auto) getDoubledNodes() const { return (doubled_nodes); }

	private:
	std::array<std::unique_ptr<Array<Element>>, 3> facets_to_double_by_dim;
	std::array<std::array<std::unique_ptr<Array<std::vector<Element>>>, 2>, 4>
	dimelements_to_dimelements;

	Array<UInt> doubled_nodes;
	Array<Element> new_elements;

	Mesh & mesh;
	Mesh & mesh_facets;

	ElementTypeMap<UInt> nb_new_facets;
	};

	} // namespace akantu

	#endif /* __AKANTU_COHESIVE_ELEMENT_INSERTER_HELPER_HH__ */
	diff --git a/src/mesh_utils/cohesive_element_inserter_inline_impl.hh b/src/mesh_utils/cohesive_element_inserter_inline_impl.hh
	index 7a41290be..a3afb8ae5 100644
	--- a/src/mesh_utils/cohesive_element_inserter_inline_impl.hh
	+++ b/src/mesh_utils/cohesive_element_inserter_inline_impl.hh
	@@ -1,91 +1,91 @@
	/**
	* @file cohesive_element_inserter_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 11 2020
	*
	* @brief Cohesive element inserter inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_element_inserter.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COHESIVE_ELEMENT_INSERTER_INLINE_IMPL_HH_
	#define AKANTU_COHESIVE_ELEMENT_INSERTER_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt
	CohesiveElementInserter::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;

	if (tag == SynchronizationTag::_ce_groups) {
	size = elements.size() * sizeof(bool);
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	CohesiveElementInserter::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();
	if (tag == SynchronizationTag::_ce_groups) {
	for (const auto & el : elements) {
	const bool & data = insertion_facets(el);
	buffer << data;
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline void
	CohesiveElementInserter::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	if (tag == SynchronizationTag::_ce_groups) {
	for (const auto & el : elements) {
	bool & data = insertion_facets(el);
	buffer >> data;
	}
	}
	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_COHESIVE_ELEMENT_INSERTER_INLINE_IMPL_HH_ */
	diff --git a/src/mesh_utils/cohesive_element_inserter_parallel.cc b/src/mesh_utils/cohesive_element_inserter_parallel.cc
	index 9c72e265c..acc1f51bc 100644
	--- a/src/mesh_utils/cohesive_element_inserter_parallel.cc
	+++ b/src/mesh_utils/cohesive_element_inserter_parallel.cc
	@@ -1,38 +1,37 @@
	/**
	* @file cohesive_element_inserter_parallel.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Oct 11 2017
	*
	* @brief Parallel functions for the cohesive element inserter
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_element_inserter.hh"
	#include "global_ids_updater.hh"
	#include "mesh_accessor.hh"
	/* -------------------------------------------------------------------------- */
	-
	diff --git a/src/mesh_utils/global_ids_updater.cc b/src/mesh_utils/global_ids_updater.cc
	index f4bef39f6..70db9fd16 100644
	--- a/src/mesh_utils/global_ids_updater.cc
	+++ b/src/mesh_utils/global_ids_updater.cc
	@@ -1,143 +1,143 @@
	/**
	* @file global_ids_updater.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Functions of the GlobalIdsUpdater
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "global_ids_updater.hh"
	#include "element_synchronizer.hh"
	#include "mesh_accessor.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	UInt GlobalIdsUpdater::updateGlobalIDs(UInt local_nb_new_nodes) {
	if (mesh.getCommunicator().getNbProc() == 1) {
	return local_nb_new_nodes;
	}

	UInt total_nb_new_nodes = this->updateGlobalIDsLocally(local_nb_new_nodes);

	if (mesh.isDistributed()) {
	this->synchronizeGlobalIDs();
	}
	return total_nb_new_nodes;
	}

	UInt GlobalIdsUpdater::updateGlobalIDsLocally(UInt local_nb_new_nodes) {
	const auto & comm = mesh.getCommunicator();
	Int nb_proc = comm.getNbProc();
	if (nb_proc == 1) {
	return local_nb_new_nodes;
	}

	/// resize global ids array
	MeshAccessor mesh_accessor(mesh);
	auto && nodes_global_ids = mesh_accessor.getNodesGlobalIds();
	UInt old_nb_nodes = mesh.getNbNodes() - local_nb_new_nodes;

	nodes_global_ids.resize(mesh.getNbNodes(), -1);

	auto && local_or_master_pred = [this](auto && n) {
	return this->mesh.isLocalOrMasterNode(n);
	};

	Vector<UInt> local_master_nodes(2, 0);
	/// compute the number of global nodes based on the number of old nodes
	auto range_old = arange(old_nb_nodes);
	local_master_nodes(0) =
	std::count_if(range_old.begin(), range_old.end(), local_or_master_pred);

	/// compute amount of local or master doubled nodes
	auto range_new = arange(old_nb_nodes, mesh.getNbNodes());
	local_master_nodes(1) =
	std::count_if(range_new.begin(), range_new.end(), local_or_master_pred);

	auto starting_index = local_master_nodes(1);

	comm.allReduce(local_master_nodes);

	UInt old_global_nodes = local_master_nodes(0);
	UInt total_nb_new_nodes = local_master_nodes(1);

	if (total_nb_new_nodes == 0) {
	return 0;
	}

	/// set global ids of local and master nodes
	comm.exclusiveScan(starting_index);
	starting_index += old_global_nodes;

	for (auto n : range_new) {
	if (mesh.isLocalOrMasterNode(n)) {
	nodes_global_ids(n) = starting_index;
	++starting_index;
	}
	}

	mesh_accessor.setNbGlobalNodes(old_global_nodes + total_nb_new_nodes);
	return total_nb_new_nodes;
	}

	void GlobalIdsUpdater::synchronizeGlobalIDs() {
	this->reduce = true;
	this->synchronizer.slaveReductionOnce(*this,
	SynchronizationTag::_giu_global_conn);

	#ifndef AKANTU_NDEBUG
	for (auto node : nodes_flags) {
	auto node_flag = mesh.getNodeFlag(node.first);
	if (node_flag != NodeFlag::_pure_ghost) {
	continue;
	}
	auto n = 0U;

	for (auto & pair : node.second) {
	if (std::get<1>(pair) == NodeFlag::_pure_ghost) {
	++n;
	}
	}

	if (n == node.second.size()) {
	AKANTU_DEBUG_WARNING(
	"The node " << n << "is ghost on all the neighboring processors");
	}
	}
	#endif

	this->reduce = false;
	this->synchronizer.synchronizeOnce(*this,
	SynchronizationTag::_giu_global_conn);
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/global_ids_updater.hh b/src/mesh_utils/global_ids_updater.hh
	index 8d7f3b2ac..764d3630f 100644
	--- a/src/mesh_utils/global_ids_updater.hh
	+++ b/src/mesh_utils/global_ids_updater.hh
	@@ -1,108 +1,108 @@
	/**
	* @file global_ids_updater.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 02 2015
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Class that updates the global ids of new nodes that are
	* inserted in the mesh. The functions in this class must be called
	* after updating the node types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_GLOBAL_IDS_UPDATER_HH_
	#define AKANTU_GLOBAL_IDS_UPDATER_HH_

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class ElementSynchronizer;
	} // namespace akantu

	namespace akantu {

	class GlobalIdsUpdater : public DataAccessor<Element> {
	public:
	GlobalIdsUpdater(Mesh & mesh, ElementSynchronizer & synchronizer)
	: mesh(mesh), synchronizer(synchronizer) {}

	/// function to update and synchronize the global connectivity of
	/// new inserted nodes. It must be called after updating the node
	/// types. (It calls in sequence the functions
	/// updateGlobalIDsLocally and synchronizeGlobalIDs)
	UInt updateGlobalIDs(UInt local_nb_new_nodes);

	/// function to update the global connectivity (only locally) of new
	/// inserted nodes. It must be called after updating the node types.
	UInt updateGlobalIDsLocally(UInt local_nb_new_nodes);

	/// function to synchronize the global connectivity of new inserted
	/// nodes among the processors. It must be called after updating the
	/// node types.
	void synchronizeGlobalIDs();

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;
	/* ------------------------------------------------------------------------ */
	template <bool pack_mode>
	inline void
	packUnpackGlobalConnectivity(CommunicationBuffer & buffer,
	const Array<Element> & elements) const;

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// Reference to the mesh to update
	Mesh & mesh;

	/// distributed synchronizer to communicate the connectivity
	ElementSynchronizer & synchronizer;

	/// Tells if a reduction is taking place or not
	bool reduce{false};

	std::unordered_map<UInt, std::vector<std::pair<UInt, NodeFlag>>> nodes_flags;
	};

	} // namespace akantu

	#include "global_ids_updater_inline_impl.hh"

	#endif /* AKANTU_GLOBAL_IDS_UPDATER_HH_ */
	diff --git a/src/mesh_utils/mesh_partition.cc b/src/mesh_utils/mesh_partition.cc
	index 64f8d599b..03d68bb22 100644
	--- a/src/mesh_utils/mesh_partition.cc
	+++ b/src/mesh_utils/mesh_partition.cc
	@@ -1,406 +1,406 @@
	/**
	* @file mesh_partition.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 17 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of common part of all partitioner
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_partition.hh"
	#include "aka_iterators.hh"
	#include "aka_types.hh"
	#include "mesh_accessor.hh"
	#include "mesh_iterators.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <numeric>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MeshPartition::MeshPartition(Mesh & mesh, UInt spatial_dimension, const ID & id)
	: mesh(mesh), spatial_dimension(spatial_dimension),
	partitions("partition", id), ghost_partitions("ghost_partition", id),
	ghost_partitions_offset("ghost_partition_offset", id),
	saved_connectivity("saved_connectivity", id) {
	AKANTU_DEBUG_IN();

	UInt nb_total_element = 0;
	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	linearized_offsets.emplace_back(type, nb_total_element);
	nb_total_element += mesh.getConnectivity(type).size();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MeshPartition::~MeshPartition() = default;

	/* -------------------------------------------------------------------------- */
	UInt MeshPartition::linearized(const Element & element) {
	auto it =
	std::find_if(linearized_offsets.begin(), linearized_offsets.end(),
	[&element](auto & a) { return a.first == element.type; });
	AKANTU_DEBUG_ASSERT(it != linearized_offsets.end(),
	"A bug might be crawling around this corner...");
	return (it->second + element.element);
	}

	/* -------------------------------------------------------------------------- */
	Element MeshPartition::unlinearized(UInt lin_element) {
	ElementType type{_not_defined};
	UInt offset{0};
	for (auto & pair : linearized_offsets) {
	if (lin_element < pair.second) {
	continue;
	}
	std::tie(type, offset) = pair;
	}

	return Element{type, lin_element - offset, _not_ghost};
	}

	/* -------------------------------------------------------------------------- */
	/**
	* conversion in c++ of the METIS_MeshToDual (mesh.c) function wrote by George
	* in Metis (University of Minnesota)
	*/
	void MeshPartition::buildDualGraph(
	Array<Int> & dxadj, Array<Int> & dadjncy, Array<Int> & edge_loads,
	const std::function<Int(const Element &, const Element &)> & edge_load_func,
	Array<Int> & vertex_loads,
	const std::function<Int(const Element &)> & vertex_load_func) {

	CSR<Element> nodes_to_elements;
	MeshUtils::buildNode2Elements(mesh, nodes_to_elements);

	std::unordered_map<UInt, std::vector<UInt>> adjacent_elements;

	// for each elements look for its connected elements
	for_each_element(
	mesh,
	[&](auto && element) {
	const auto & conn =
	const_cast<const Mesh &>(mesh).getConnectivity(element);
	std::map<Element, UInt> hits;

	// count the number of nodes shared with a given element
	for (auto && node : conn) {
	for (auto && connected_element : nodes_to_elements.getRow(node)) {
	++hits[connected_element];
	}
	}

	// define a minumum number of nodes to share to be considered as a
	// ajacent element
	UInt magic_number{conn.size()};
	for (auto n : arange(mesh.getNbFacetTypes(element.type))) {
	magic_number = std::min(
	mesh.getNbNodesPerElement(mesh.getFacetType(element.type, n)),
	magic_number);
	}

	// check all neighbors to see which ones are "adjacent"
	for (auto && data : hits) {
	const auto & adjacent_element = data.first;
	// not adjacent to miself
	if (adjacent_element == element) {
	continue;
	}

	// not enough shared nodes
	if (data.second < magic_number) {
	continue;
	}

	/// Patch in order to prevent neighboring cohesive elements
	/// from detecting each other
	#if defined(AKANTU_COHESIVE_ELEMENT)
	auto element_kind = element.kind();
	auto adjacent_element_kind = adjacent_element.kind();

	if (element_kind == adjacent_element_kind &&
	element_kind == _ek_cohesive) {
	continue;
	}
	#endif

	adjacent_elements[this->linearized(element)].push_back(
	this->linearized(adjacent_element));
	}
	},
	_spatial_dimension = mesh.getSpatialDimension(),
	_element_kind = _ek_not_defined);

	// prepare the arrays
	auto nb_elements{adjacent_elements.size()};
	dxadj.resize(nb_elements + 1);
	vertex_loads.resize(nb_elements);

	for (auto && data : adjacent_elements) {
	const auto & element{data.first};
	const auto & neighbors{data.second};
	dxadj[element] = neighbors.size();
	}

	/// convert the dxadj array of sizes in a csr one of offsets
	for (UInt i = 1; i < nb_elements; ++i) {
	dxadj(i) += dxadj(i - 1);
	}
	for (UInt i = nb_elements; i > 0; --i) {
	dxadj(i) = dxadj(i - 1);
	}
	dxadj(0) = 0;

	dadjncy.resize(dxadj(nb_elements));
	edge_loads.resize(dadjncy.size());

	// fill the different arrays
	for (auto && data : adjacent_elements) {
	const auto & element{data.first};
	const auto & neighbors{data.second};

	auto unlinearized_element = unlinearized(element);
	vertex_loads(element) = vertex_load_func(unlinearized_element);

	auto pos = dxadj(element);

	for (auto && neighbor : neighbors) {
	dadjncy(pos) = neighbor;
	edge_loads(pos) =
	edge_load_func(unlinearized_element, unlinearized(neighbor));
	++pos;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::fillPartitionInformation(
	const Mesh & mesh, const Int * linearized_partitions) {
	AKANTU_DEBUG_IN();

	CSR<Element> node_to_elem;

	MeshUtils::buildNode2Elements(mesh, node_to_elem);

	UInt linearized_el = 0;
	for (const auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto & partition = partitions.alloc(nb_element, 1, type, _not_ghost);
	auto & ghost_part_csr = ghost_partitions_csr(type, _not_ghost);
	ghost_part_csr.resizeRows(nb_element);

	auto & ghost_partition_offset =
	ghost_partitions_offset.alloc(nb_element + 1, 1, type, _ghost);
	auto & ghost_partition = ghost_partitions.alloc(0, 1, type, _ghost);

	const auto & connectivity = mesh.getConnectivity(type, _not_ghost);
	auto conn_it = connectivity.begin(connectivity.getNbComponent());

	for (UInt el = 0; el < nb_element; ++el, ++linearized_el) {
	UInt part = linearized_partitions[linearized_el];

	partition(el) = part;
	std::list<UInt> list_adj_part;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	auto conn = Vector<UInt>(*(conn_it + el));
	UInt node = conn(n);
	for (const auto & adj_element : node_to_elem.getRow(node)) {
	UInt adj_el = linearized(adj_element);
	UInt adj_part = linearized_partitions[adj_el];
	if (part != adj_part) {
	list_adj_part.push_back(adj_part);
	}
	}
	}

	list_adj_part.sort();
	list_adj_part.unique();

	for (auto & adj_part : list_adj_part) {
	ghost_part_csr.getRows().push_back(adj_part);
	ghost_part_csr.rowOffset(el)++;

	ghost_partition.push_back(adj_part);
	ghost_partition_offset(el)++;
	}
	}

	ghost_part_csr.countToCSR();

	/// convert the ghost_partitions_offset array in an offset array
	auto & ghost_partitions_offset_ptr = ghost_partitions_offset(type, _ghost);
	for (UInt i = 1; i < nb_element; ++i) {
	ghost_partitions_offset_ptr(i) += ghost_partitions_offset_ptr(i - 1);
	}
	for (UInt i = nb_element; i > 0; --i) {
	ghost_partitions_offset_ptr(i) = ghost_partitions_offset_ptr(i - 1);
	}
	ghost_partitions_offset_ptr(0) = 0;
	}

	// All Facets
	for (Int sp = spatial_dimension - 1; sp >= 0; --sp) {
	for (const auto & type :
	mesh.elementTypes(sp, _not_ghost, _ek_not_defined)) {
	UInt nb_element = mesh.getNbElement(type);

	auto & partition = partitions.alloc(nb_element, 1, type, _not_ghost);
	AKANTU_DEBUG_INFO("Allocating partitions for " << type);
	auto & ghost_part_csr = ghost_partitions_csr(type, _not_ghost);
	ghost_part_csr.resizeRows(nb_element);

	auto & ghost_partition_offset =
	ghost_partitions_offset.alloc(nb_element + 1, 1, type, _ghost);
	auto & ghost_partition = ghost_partitions.alloc(0, 1, type, _ghost);
	AKANTU_DEBUG_INFO("Allocating ghost_partitions for " << type);
	const Array<std::vector<Element>> & elem_to_subelem =
	mesh.getElementToSubelement(type, _not_ghost);

	// Facet loop
	for (UInt i(0); i < mesh.getNbElement(type, _not_ghost); ++i) {
	const auto & adjacent_elems = elem_to_subelem(i);
	if (adjacent_elems.empty()) {
	partition(i) = 0;
	continue;
	}
	Element min_elem{_max_element_type, std::numeric_limits<UInt>::max(),
	*(ghost_type_t{}.end())};
	UInt min_part(std::numeric_limits<UInt>::max());
	std::set<UInt> adjacent_parts;

	for (auto adj_elem : adjacent_elems) {
	if (adj_elem == ElementNull) { // case of boundary elements
	continue;
	}

	auto adjacent_elem_part = partitions(adj_elem);
	if (adjacent_elem_part < min_part) {
	min_part = adjacent_elem_part;
	min_elem = adj_elem;
	}
	adjacent_parts.insert(adjacent_elem_part);
	}
	partition(i) = min_part;

	auto git = ghost_partitions_csr(min_elem.type, _not_ghost)
	.begin(min_elem.element);
	auto gend = ghost_partitions_csr(min_elem.type, _not_ghost)
	.end(min_elem.element);
	for (; git != gend; ++git) {
	adjacent_parts.insert(*git);
	}

	adjacent_parts.erase(min_part);
	for (const auto & part : adjacent_parts) {
	ghost_part_csr.getRows().push_back(part);
	ghost_part_csr.rowOffset(i)++;
	ghost_partition.push_back(part);
	}

	ghost_partition_offset(i + 1) =
	ghost_partition_offset(i + 1) + adjacent_elems.size();
	}
	ghost_part_csr.countToCSR();
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::tweakConnectivity() {
	AKANTU_DEBUG_IN();

	MeshAccessor mesh_accessor(const_cast<Mesh &>(mesh));

	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	auto & connectivity = mesh_accessor.getConnectivity(type, _not_ghost);

	auto & saved_conn = saved_connectivity.alloc(
	connectivity.size(), connectivity.getNbComponent(), type, _not_ghost);
	saved_conn.copy(connectivity);

	for (auto && conn :
	make_view(connectivity, connectivity.getNbComponent())) {
	for (auto && node : conn) {
	if (mesh.isPeriodicSlave(node)) {
	node = mesh.getPeriodicMaster(node);
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::restoreConnectivity() {
	AKANTU_DEBUG_IN();
	MeshAccessor mesh_accessor(const_cast<Mesh &>(mesh));
	for (auto && type : saved_connectivity.elementTypes(
	spatial_dimension, _not_ghost, _ek_not_defined)) {
	auto & conn = mesh_accessor.getConnectivity(type, _not_ghost);
	auto & saved_conn = saved_connectivity(type, _not_ghost);
	conn.copy(saved_conn);
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	bool MeshPartition::hasPartitions(ElementType type, GhostType ghost_type) {
	return partitions.exists(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "MeshPartition ["
	<< "\n";
	stream << space << " + id : " << id << "\n";
	stream << space << " + nb partitions: " << nb_partitions << "\n";
	stream << space << " + partitions [ "
	<< "\n";
	partitions.printself(stream, indent + 2);
	stream << space << " ]"
	<< "\n";
	stream << space << "]"
	<< "\n";
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/mesh_utils/mesh_partition.hh b/src/mesh_utils/mesh_partition.hh
	index d3d99167d..de2c9df1f 100644
	--- a/src/mesh_utils/mesh_partition.hh
	+++ b/src/mesh_utils/mesh_partition.hh
	@@ -1,153 +1,152 @@
	/**
	* @file mesh_partition.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief tools to partitionate a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_csr.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_PARTITION_HH_
	#define AKANTU_MESH_PARTITION_HH_

	-
	namespace akantu {

	class MeshPartition {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshPartition(Mesh & mesh, UInt spatial_dimension,
	const ID & id = "MeshPartitioner");

	virtual ~MeshPartition();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// define a partition of the mesh
	virtual void partitionate(
	UInt nb_part,
	const std::function<Int(const Element &, const Element &)> &
	edge_load_func =
	[](auto && /unused/, auto && /unused/) { return 1; },
	const std::function<Int(const Element &)> & vertex_load_func =
	[](auto && /unused/) { return 1; }) = 0;

	/// reorder the nodes to reduce the filling during the factorization of a
	/// matrix that has a profil based on the connectivity of the mesh
	virtual void reorder() = 0;

	/// fill the partitions array with a given linearized partition information
	void fillPartitionInformation(const Mesh & mesh,
	const Int * linearized_partitions);

	virtual void printself(std::ostream & stream, int indent = 0) const;

	protected:
	/// build the dual graph of the mesh, for all element of spatial_dimension
	void
	buildDualGraph(Array<Int> & dxadj, Array<Int> & dadjncy,
	Array<Int> & edge_loads,
	const std::function<Int(const Element &, const Element &)> &
	edge_load_func,
	Array<Int> & vertex_loads,
	const std::function<Int(const Element &)> & vertex_load_func);

	/// tweak the mesh to handle the PBC pairs
	void tweakConnectivity();
	/// restore the mesh that has been tweaked
	void restoreConnectivity();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	bool hasPartitions(ElementType type, GhostType ghost_type);
	AKANTU_GET_MACRO(Partitions, partitions, const ElementTypeMapArray<UInt> &);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Partition, partitions, UInt);

	AKANTU_GET_MACRO(GhostPartitionCSR, ghost_partitions_csr,
	const ElementTypeMap<CSR<UInt>> &);

	AKANTU_GET_MACRO(NbPartition, nb_partitions, UInt);
	AKANTU_SET_MACRO(NbPartition, nb_partitions, UInt);

	protected:
	UInt linearized(const Element & element);
	Element unlinearized(UInt lin_element);
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// id
	ID id;

	/// the mesh to partition
	Mesh & mesh;

	/// dimension of the elements to consider in the mesh
	UInt spatial_dimension;

	/// number of partitions
	UInt nb_partitions;

	/// partition numbers
	ElementTypeMapArray<UInt> partitions;

	ElementTypeMap<CSR<UInt>> ghost_partitions_csr;
	ElementTypeMapArray<UInt> ghost_partitions;
	ElementTypeMapArray<UInt> ghost_partitions_offset;

	Array<UInt> * permutation;

	ElementTypeMapArray<UInt> saved_connectivity;

	// vector of pair to ensure the iteration order
	std::vector<std::pair<ElementType, UInt>> linearized_offsets;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const MeshPartition & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#ifdef AKANTU_USE_SCOTCH
	#include "mesh_partition_scotch.hh"
	#endif

	#endif /* AKANTU_MESH_PARTITION_HH_ */
	diff --git a/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.cc b/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.cc
	index 8aa2b514c..4c78a0c9c 100644
	--- a/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.cc
	+++ b/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.cc
	@@ -1,141 +1,141 @@
	/**
	* @file mesh_partition_mesh_data.cc
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of the MeshPartitionMeshData class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "mesh_partition_mesh_data.hh"
	#if !defined(AKANTU_NDEBUG)
	#include <set>
	#endif

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MeshPartitionMeshData::MeshPartitionMeshData(Mesh & mesh,
	UInt spatial_dimension,
	const ID & id)
	: MeshPartition(mesh, spatial_dimension, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MeshPartitionMeshData::MeshPartitionMeshData(
	Mesh & mesh, const ElementTypeMapArray<UInt> & mapping,
	UInt spatial_dimension, const ID & id)
	- : MeshPartition(mesh, spatial_dimension, id),
	- partition_mapping(&mapping) {
	+ : MeshPartition(mesh, spatial_dimension, id), partition_mapping(&mapping) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartitionMeshData::partitionate(
	UInt nb_part,
	- const std::function<Int(const Element &, const Element &)> &/edge_load_func/,
	- const std::function<Int(const Element &)> &/vertex_load_func/) {
	+ const std::function<Int(const Element &,
	+ const Element &)> & /edge_load_func/,
	+ const std::function<Int(const Element &)> & /vertex_load_func/) {
	AKANTU_DEBUG_IN();

	if (mesh.isPeriodic()) {
	tweakConnectivity();
	}

	nb_partitions = nb_part;

	auto ghost_type = _not_ghost;
	auto spatial_dimension = mesh.getSpatialDimension();

	UInt linearized_el = 0;
	auto nb_elements = mesh.getNbElement(mesh.getSpatialDimension(), ghost_type);
	- auto *partition_list = new Int[nb_elements];
	+ auto * partition_list = new Int[nb_elements];

	#if !defined(AKANTU_NDEBUG)
	std::set<UInt> partitions;
	#endif
	for (auto type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_not_defined)) {
	const auto & partition_array = (*partition_mapping)(type, ghost_type);
	AKANTU_DEBUG_ASSERT(partition_array.size() ==
	mesh.getNbElement(type, ghost_type),
	"The partition mapping does not have the right number "
	<< "of entries for type " << type
	<< " and ghost type " << ghost_type << "."
	<< " Tags=" << partition_array.size()
	<< " Mesh=" << mesh.getNbElement(type, ghost_type));

	for (auto && part : partition_array) {
	partition_list[linearized_el] = part;
	#if !defined(AKANTU_NDEBUG)
	partitions.insert(part);
	#endif
	++linearized_el;
	}
	}

	#if !defined(AKANTU_NDEBUG)
	AKANTU_DEBUG_ASSERT(partitions.size() == nb_part,
	"The number of real partitions does not match with the "
	"number of asked partitions");
	#endif

	fillPartitionInformation(mesh, partition_list);

	delete[] partition_list;

	if (mesh.isPeriodic()) {
	restoreConnectivity();
	}

	AKANTU_DEBUG_OUT();
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	void MeshPartitionMeshData::reorder() { AKANTU_TO_IMPLEMENT(); }

	/* -------------------------------------------------------------------------- */
	void MeshPartitionMeshData::setPartitionMapping(
	const ElementTypeMapArray<UInt> & mapping) {
	partition_mapping = &mapping;
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartitionMeshData::setPartitionMappingFromMeshData(
	const std::string & data_name) {
	partition_mapping = &(mesh.getData<UInt>(data_name));
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.hh b/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.hh
	index 10e73281d..241d8abd0 100644
	--- a/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.hh
	+++ b/src/mesh_utils/mesh_partition/mesh_partition_mesh_data.hh
	@@ -1,95 +1,94 @@
	/**
	* @file mesh_partition_mesh_data.hh
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief mesh partitioning based on data provided in the mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_PARTITION_MESH_DATA_HH_
	#define AKANTU_MESH_PARTITION_MESH_DATA_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh_partition.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshPartitionMeshData : public MeshPartition {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshPartitionMeshData(Mesh & mesh, UInt spatial_dimension,
	- const ID & id = "MeshPartitionerMeshData"
	- );
	+ const ID & id = "MeshPartitionerMeshData");

	- MeshPartitionMeshData(Mesh & mesh,
	- const ElementTypeMapArray<UInt> & mapping,
	+ MeshPartitionMeshData(Mesh & mesh, const ElementTypeMapArray<UInt> & mapping,
	UInt spatial_dimension,
	const ID & id = "MeshPartitionerMeshData");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void partitionate(
	UInt nb_part,
	- const std::function<Int(const Element &, const Element &)> &edge_load_func =
	- [](auto && /unused/, auto && /unused/) { return 1; },
	- const std::function<Int(const Element &)> &vertex_load_func =
	+ const std::function<Int(const Element &, const Element &)> &
	+ edge_load_func =
	+ [](auto && /unused/, auto && /unused/) { return 1; },
	+ const std::function<Int(const Element &)> & vertex_load_func =
	[](auto && /unused/) { return 1; }) override;

	void reorder() override;

	void setPartitionMapping(const ElementTypeMapArray<UInt> & mapping);

	void setPartitionMappingFromMeshData(const std::string & data_name);

	private:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	const ElementTypeMapArray<UInt> * partition_mapping;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_MESH_PARTITION_MESH_DATA_HH_ */
	diff --git a/src/mesh_utils/mesh_partition/mesh_partition_scotch.cc b/src/mesh_utils/mesh_partition/mesh_partition_scotch.cc
	index 638375a22..be839b1fd 100644
	--- a/src/mesh_utils/mesh_partition/mesh_partition_scotch.cc
	+++ b/src/mesh_utils/mesh_partition/mesh_partition_scotch.cc
	@@ -1,473 +1,473 @@
	/**
	* @file mesh_partition_scotch.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of the MeshPartitionScotch class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_partition_scotch.hh"
	#include "aka_common.hh"
	#include "aka_random_generator.hh"
	#include "aka_static_if.hh"
	#include "mesh_accessor.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstdio>
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	#if !defined(AKANTU_USE_PTSCOTCH)
	#ifndef AKANTU_SCOTCH_NO_EXTERN
	extern "C" {
	#endif // AKANTU_SCOTCH_NO_EXTERN
	#include <scotch.h>
	#ifndef AKANTU_SCOTCH_NO_EXTERN
	}
	#endif // AKANTU_SCOTCH_NO_EXTERN
	#else // AKANTU_USE_PTSCOTCH
	#include <ptscotch.h>
	#endif // AKANTU_USE_PTSCOTCH

	namespace akantu {

	namespace {
	constexpr int scotch_version = int(SCOTCH_VERSION);
	}

	/* -------------------------------------------------------------------------- */
	MeshPartitionScotch::MeshPartitionScotch(Mesh & mesh, UInt spatial_dimension,
	const ID & id)
	: MeshPartition(mesh, spatial_dimension, id) {
	AKANTU_DEBUG_IN();

	// check if the akantu types and Scotch one are consistent
	static_assert(
	sizeof(Int) == sizeof(SCOTCH_Num),
	"The integer type of Akantu does not match the one from Scotch");

	static_if(aka::bool_constant<scotch_version >= 6>{})
	.then([](auto && y) { SCOTCH_randomSeed(y); })
	.else_([](auto && y) { srandom(y); })(
	std::forward<UInt>(RandomGenerator<UInt>::seed()));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	static SCOTCH_Mesh * createMesh(const Mesh & mesh) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes = mesh.getNbNodes();

	UInt total_nb_element = 0;
	UInt nb_edge = 0;

	for (const auto & type : mesh.elementTypes(spatial_dimension)) {
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	total_nb_element += nb_element;
	nb_edge += nb_element * nb_nodes_per_element;
	}

	SCOTCH_Num vnodbas = 0;
	SCOTCH_Num vnodnbr = nb_nodes;

	SCOTCH_Num velmbas = vnodnbr;
	SCOTCH_Num velmnbr = total_nb_element;

	auto * verttab = new SCOTCH_Num[vnodnbr + velmnbr + 1];
	SCOTCH_Num * vendtab = verttab + 1;

	SCOTCH_Num * velotab = nullptr;
	SCOTCH_Num * vnlotab = nullptr;
	SCOTCH_Num * vlbltab = nullptr;

	memset(verttab, 0, (vnodnbr + velmnbr + 1) * sizeof(SCOTCH_Num));

	for (const auto & type : mesh.elementTypes(spatial_dimension)) {
	if (Mesh::getSpatialDimension(type) != spatial_dimension) {
	continue;
	}

	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type, _not_ghost);

	/// count number of occurrence of each node
	for (UInt el = 0; el < nb_element; ++el) {
	UInt * conn_val = connectivity.storage() + el * nb_nodes_per_element;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	verttab[*(conn_val++)]++;
	}
	}
	}

	/// convert the occurrence array in a csr one
	for (UInt i = 1; i < nb_nodes; ++i) {
	verttab[i] += verttab[i - 1];
	}
	for (UInt i = nb_nodes; i > 0; --i) {
	verttab[i] = verttab[i - 1];
	}
	verttab[0] = 0;

	/// rearrange element to get the node-element list
	SCOTCH_Num edgenbr = verttab[vnodnbr] + nb_edge;
	auto * edgetab = new SCOTCH_Num[edgenbr];

	UInt linearized_el = 0;

	for (const auto & type : mesh.elementTypes(spatial_dimension)) {
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const auto & connectivity = mesh.getConnectivity(type, _not_ghost);

	for (auto && conn : make_view(connectivity, nb_nodes_per_element)) {
	for (auto c : conn) {
	edgetab[verttab[c]++] = linearized_el + velmbas;
	}
	++linearized_el;
	}
	}

	for (UInt i = nb_nodes; i > 0; --i) {
	verttab[i] = verttab[i - 1];
	}
	verttab[0] = 0;

	SCOTCH_Num * verttab_tmp = verttab + vnodnbr + 1;
	SCOTCH_Num * edgetab_tmp = edgetab + verttab[vnodnbr];

	for (const auto & type : mesh.elementTypes(spatial_dimension)) {
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const auto & connectivity = mesh.getConnectivity(type, _not_ghost);

	for (auto && conn : make_view(connectivity, nb_nodes_per_element)) {
	verttab_tmp = (verttab_tmp - 1) + nb_nodes_per_element;
	verttab_tmp++;

	for (auto c : conn) {
	*(edgetab_tmp++) = c + vnodbas;
	}
	}
	}

	auto * meshptr = new SCOTCH_Mesh;

	SCOTCH_meshInit(meshptr);

	SCOTCH_meshBuild(meshptr, velmbas, vnodbas, velmnbr, vnodnbr, verttab,
	vendtab, velotab, vnlotab, vlbltab, edgenbr, edgetab);

	/// Check the mesh
	AKANTU_DEBUG_ASSERT(SCOTCH_meshCheck(meshptr) == 0,
	"Scotch mesh is not consistent");

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDump)) {
	/// save initial graph
	FILE * fmesh = fopen("ScotchMesh.msh", "w");
	SCOTCH_meshSave(meshptr, fmesh);
	fclose(fmesh);

	/// write geometry file
	std::ofstream fgeominit;
	fgeominit.open("ScotchMesh.xyz");
	fgeominit << spatial_dimension << std::endl << nb_nodes << std::endl;

	const Array<Real> & nodes = mesh.getNodes();
	Real * nodes_val = nodes.storage();
	for (UInt i = 0; i < nb_nodes; ++i) {
	fgeominit << i << " ";
	for (UInt s = 0; s < spatial_dimension; ++s) {
	fgeominit << *(nodes_val++) << " ";
	}
	fgeominit << std::endl;
	;
	}
	fgeominit.close();
	}
	#endif

	AKANTU_DEBUG_OUT();
	return meshptr;
	}

	/* -------------------------------------------------------------------------- */
	static void destroyMesh(SCOTCH_Mesh * meshptr) {
	AKANTU_DEBUG_IN();

	SCOTCH_Num velmbas;
	SCOTCH_Num vnodbas;
	SCOTCH_Num vnodnbr;
	SCOTCH_Num velmnbr;
	SCOTCH_Num * verttab;
	SCOTCH_Num * vendtab;
	SCOTCH_Num * velotab;
	SCOTCH_Num * vnlotab;
	SCOTCH_Num * vlbltab;
	SCOTCH_Num edgenbr;
	SCOTCH_Num * edgetab;
	SCOTCH_Num degrptr;

	SCOTCH_meshData(meshptr, &velmbas, &vnodbas, &velmnbr, &vnodnbr, &verttab,
	&vendtab, &velotab, &vnlotab, &vlbltab, &edgenbr, &edgetab,
	&degrptr);

	delete[] verttab;
	delete[] edgetab;

	SCOTCH_meshExit(meshptr);

	delete meshptr;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartitionScotch::partitionate(
	UInt nb_part,
	const std::function<Int(const Element &, const Element &)> & edge_load_func,
	const std::function<Int(const Element &)> & vertex_load_func) {
	AKANTU_DEBUG_IN();

	nb_partitions = nb_part;

	if (mesh.isPeriodic()) {
	tweakConnectivity();
	}

	AKANTU_DEBUG_INFO("Partitioning the mesh " << mesh.getID() << " in "
	<< nb_part << " parts.");

	Array<Int> dxadj;
	Array<Int> dadjncy;
	Array<Int> edge_loads;
	Array<Int> vertex_loads;
	buildDualGraph(dxadj, dadjncy, edge_loads, edge_load_func, vertex_loads,
	vertex_load_func);

	/// variables that will hold our structures in scotch format
	SCOTCH_Graph scotch_graph;
	SCOTCH_Strat scotch_strat;

	/// description number and arrays for struct mesh for scotch
	SCOTCH_Num baseval = 0; // base numbering for element and
	// nodes (0 -> C , 1 -> fortran)
	SCOTCH_Num vertnbr = dxadj.size() - 1; // number of vertexes
	SCOTCH_Num * parttab; // array of partitions
	SCOTCH_Num edgenbr = dxadj(vertnbr); // twice the number of "edges"
	//(an "edge" bounds two nodes)
	SCOTCH_Num * verttab = dxadj.storage(); // array of start indices in edgetab
	SCOTCH_Num * vendtab = nullptr; // array of after-last indices in edgetab
	SCOTCH_Num * velotab =
	vertex_loads.storage(); // integer load associated with
	// every vertex ( optional )
	SCOTCH_Num * edlotab = edge_loads.storage(); // integer load associated with
	// every edge ( optional )
	SCOTCH_Num * edgetab = dadjncy.storage(); // adjacency array of every vertex
	SCOTCH_Num * vlbltab = nullptr; // vertex label array (optional)

	/// Allocate space for Scotch arrays
	parttab = new SCOTCH_Num[vertnbr];

	/// Initialize the strategy structure
	SCOTCH_stratInit(&scotch_strat);

	/// Initialize the graph structure
	SCOTCH_graphInit(&scotch_graph);

	/// Build the graph from the adjacency arrays
	SCOTCH_graphBuild(&scotch_graph, baseval, vertnbr, verttab, vendtab, velotab,
	vlbltab, edgenbr, edgetab, edlotab);

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDump)) {
	/// save initial graph
	FILE * fgraphinit = fopen("GraphIniFile.grf", "w");
	SCOTCH_graphSave(&scotch_graph, fgraphinit);
	fclose(fgraphinit);

	/// write geometry file
	std::ofstream fgeominit;
	fgeominit.open("GeomIniFile.xyz");
	fgeominit << spatial_dimension << std::endl << vertnbr << std::endl;

	const Array<Real> & nodes = mesh.getNodes();

	auto nodes_it = nodes.begin(spatial_dimension);

	UInt out_linerized_el = 0;
	for (const auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type);

	Vector<Real> mid(spatial_dimension);
	for (auto && conn : make_view(connectivity, nb_nodes_per_element)) {
	mid.set(0.);
	for (auto node : conn) {
	mid += Vector<Real>(nodes_it[node]);
	}
	mid /= nb_nodes_per_element;

	fgeominit << out_linerized_el++ << " ";
	for (UInt s = 0; s < spatial_dimension; ++s) {
	fgeominit << mid[s] << " ";
	}

	fgeominit << std::endl;
	;
	}
	}
	fgeominit.close();
	}
	#endif

	/// Check the graph
	AKANTU_DEBUG_ASSERT(SCOTCH_graphCheck(&scotch_graph) == 0,
	"Graph to partition is not consistent");

	/// Partition the mesh
	SCOTCH_graphPart(&scotch_graph, nb_part, &scotch_strat, parttab);

	/// Check the graph
	AKANTU_DEBUG_ASSERT(SCOTCH_graphCheck(&scotch_graph) == 0,
	"Partitioned graph is not consistent");

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDump)) {
	/// save the partitioned graph
	FILE * fgraph = fopen("GraphFile.grf", "w");
	SCOTCH_graphSave(&scotch_graph, fgraph);
	fclose(fgraph);

	/// save the partition map
	std::ofstream fmap;
	fmap.open("MapFile.map");
	fmap << vertnbr << std::endl;
	for (Int i = 0; i < vertnbr; i++) {
	fmap << i << " " << parttab[i] << std::endl;
	}
	fmap.close();
	}
	#endif

	/// free the scotch data structures
	SCOTCH_stratExit(&scotch_strat);
	SCOTCH_graphFree(&scotch_graph);
	SCOTCH_graphExit(&scotch_graph);

	fillPartitionInformation(mesh, parttab);

	delete[] parttab;

	if (mesh.isPeriodic()) {
	restoreConnectivity();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartitionScotch::reorder() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Reordering the mesh " << mesh.getID());
	SCOTCH_Mesh * scotch_mesh = createMesh(mesh);

	UInt nb_nodes = mesh.getNbNodes();

	SCOTCH_Strat scotch_strat;
	// SCOTCH_Ordering scotch_order;

	auto * permtab = new SCOTCH_Num[nb_nodes];
	SCOTCH_Num * peritab = nullptr;
	SCOTCH_Num cblknbr = 0;
	SCOTCH_Num * rangtab = nullptr;
	SCOTCH_Num * treetab = nullptr;

	/// Initialize the strategy structure
	SCOTCH_stratInit(&scotch_strat);

	SCOTCH_Graph scotch_graph;

	SCOTCH_graphInit(&scotch_graph);
	SCOTCH_meshGraph(scotch_mesh, &scotch_graph);

	#ifndef AKANTU_NDEBUG
	if (AKANTU_DEBUG_TEST(dblDump)) {
	FILE * fgraphinit = fopen("ScotchMesh.grf", "w");
	SCOTCH_graphSave(&scotch_graph, fgraphinit);
	fclose(fgraphinit);
	}
	#endif

	/// Check the graph
	// AKANTU_DEBUG_ASSERT(SCOTCH_graphCheck(&scotch_graph) == 0,
	// "Mesh to Graph is not consistent");

	SCOTCH_graphOrder(&scotch_graph, &scotch_strat, permtab, peritab, &cblknbr,
	rangtab, treetab);

	SCOTCH_graphExit(&scotch_graph);
	SCOTCH_stratExit(&scotch_strat);
	destroyMesh(scotch_mesh);

	/// Renumbering
	UInt spatial_dimension = mesh.getSpatialDimension();
	MeshAccessor mesh_accessor(mesh);
	for (auto gt : ghost_types) {
	for (const auto & type : mesh.elementTypes(_ghost_type = gt)) {
	auto & connectivity = mesh_accessor.getConnectivity(type, gt);
	for (auto && c : make_view(connectivity)) {
	c = permtab[c];
	}
	}
	}

	/// \todo think of a in-place way to do it
	auto * new_coordinates = new Real[spatial_dimension * nb_nodes];
	Real * old_coordinates = mesh.getNodes().storage();
	for (UInt i = 0; i < nb_nodes; ++i) {
	memcpy(new_coordinates + permtab[i] * spatial_dimension,
	old_coordinates + i * spatial_dimension,
	spatial_dimension * sizeof(Real));
	}
	memcpy(old_coordinates, new_coordinates,
	nb_nodes * spatial_dimension * sizeof(Real));
	delete[] new_coordinates;

	delete[] permtab;

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/mesh_partition/mesh_partition_scotch.hh b/src/mesh_utils/mesh_partition/mesh_partition_scotch.hh
	index f7e3e2e4e..382b1de69 100644
	--- a/src/mesh_utils/mesh_partition/mesh_partition_scotch.hh
	+++ b/src/mesh_utils/mesh_partition/mesh_partition_scotch.hh
	@@ -1,78 +1,78 @@
	/**
	* @file mesh_partition_scotch.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief mesh partitioning based on libScotch
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_partition.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_PARTITION_SCOTCH_HH_
	#define AKANTU_MESH_PARTITION_SCOTCH_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class MeshPartitionScotch : public MeshPartition {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MeshPartitionScotch(Mesh & mesh, UInt spatial_dimension,
	const ID & id = "mesh_partition_scotch");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void partitionate(
	UInt nb_part,
	const std::function<Int(const Element &, const Element &)> &
	edge_load_func =
	[](auto && /unused/, auto && /unused/) { return 1; },
	const std::function<Int(const Element &)> & vertex_load_func =
	[](auto && /unused/) { return 1; }) override;

	void reorder() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	#endif /* AKANTU_MESH_PARTITION_SCOTCH_HH_ */
	diff --git a/src/mesh_utils/mesh_utils.cc b/src/mesh_utils/mesh_utils.cc
	index f2683399c..032193b3b 100644
	--- a/src/mesh_utils/mesh_utils.cc
	+++ b/src/mesh_utils/mesh_utils.cc
	@@ -1,812 +1,812 @@
	/**
	* @file mesh_utils.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Aug 20 2010
	* @date last modification: Thu Jan 14 2021
	*
	* @brief All mesh utils necessary for various tasks
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	+#include "mesh_utils.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh_accessor.hh"
	#include "mesh_iterators.hh"
	-#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <limits>
	#include <numeric>
	#include <queue>
	#include <set>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildNode2Elements(const Mesh & mesh,
	CSR<Element> & node_to_elem,
	UInt spatial_dimension) {
	AKANTU_DEBUG_IN();
	if (spatial_dimension == _all_dimensions) {
	spatial_dimension = mesh.getSpatialDimension();
	}

	/// count number of occurrence of each node
	UInt nb_nodes = mesh.getNbNodes();

	/// array for the node-element list
	node_to_elem.resizeRows(nb_nodes);
	node_to_elem.clearRows();

	for_each_element(
	mesh,
	[&](auto && element) {
	Vector<UInt> conn = mesh.getConnectivity(element);
	for (auto && node : conn) {
	++node_to_elem.rowOffset(node);
	}
	},
	_spatial_dimension = spatial_dimension, _element_kind = _ek_not_defined);

	node_to_elem.countToCSR();
	node_to_elem.resizeCols();

	/// rearrange element to get the node-element list
	// Element e;
	node_to_elem.beginInsertions();

	for_each_element(
	mesh,
	[&](auto && element) {
	Vector<UInt> conn = mesh.getConnectivity(element);
	for (auto && node : conn) {
	node_to_elem.insertInRow(node, element);
	}
	},
	_spatial_dimension = spatial_dimension, _element_kind = _ek_not_defined);

	node_to_elem.endInsertions();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildNode2ElementsElementTypeMap(const Mesh & mesh,
	CSR<UInt> & node_to_elem,
	ElementType type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_elements = mesh.getConnectivity(type, ghost_type).size();

	UInt * conn_val = mesh.getConnectivity(type, ghost_type).storage();

	/// array for the node-element list
	node_to_elem.resizeRows(nb_nodes);
	node_to_elem.clearRows();

	/// count number of occurrence of each node
	for (UInt el = 0; el < nb_elements; ++el) {
	UInt el_offset = el * nb_nodes_per_element;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	++node_to_elem.rowOffset(conn_val[el_offset + n]);
	}
	}

	/// convert the occurrence array in a csr one
	node_to_elem.countToCSR();

	node_to_elem.resizeCols();
	node_to_elem.beginInsertions();

	/// save the element index in the node-element list
	for (UInt el = 0; el < nb_elements; ++el) {
	UInt el_offset = el * nb_nodes_per_element;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	node_to_elem.insertInRow(conn_val[el_offset + n], el);
	}
	}

	node_to_elem.endInsertions();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildFacets(Mesh & mesh) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	for (auto ghost_type : ghost_types) {
	for (const auto & type :
	mesh.elementTypes(spatial_dimension - 1, ghost_type)) {
	mesh.getConnectivity(type, ghost_type).resize(0);
	// \todo inform the mesh event handler
	}
	}

	buildFacetsDimension(mesh, mesh, true, spatial_dimension);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildAllFacets(const Mesh & mesh, Mesh & mesh_facets,
	UInt to_dimension) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	buildAllFacets(mesh, mesh_facets, spatial_dimension, to_dimension);

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildAllFacets(const Mesh & mesh, Mesh & mesh_facets,
	UInt from_dimension, UInt to_dimension) {
	AKANTU_DEBUG_IN();

	to_dimension = std::max(to_dimension, UInt(0));

	AKANTU_DEBUG_ASSERT(
	mesh_facets.isMeshFacets(),
	"The mesh_facets should be initialized with initMeshFacets");

	/// generate facets
	buildFacetsDimension(mesh, mesh_facets, false, from_dimension);

	/// sort facets and generate sub-facets
	for (UInt i = from_dimension - 1; i > to_dimension; --i) {
	buildFacetsDimension(mesh_facets, mesh_facets, false, i);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::buildFacetsDimension(const Mesh & mesh, Mesh & mesh_facets,
	bool boundary_only, UInt dimension) {
	AKANTU_DEBUG_IN();

	// save the current parent of mesh_facets and set it temporarly to mesh since
	// mesh is the one containing the elements for which mesh_facets has the
	// sub-elements
	// example: if the function is called with mesh = mesh_facets
	const Mesh * mesh_facets_parent = nullptr;
	try {
	mesh_facets_parent = &mesh_facets.getMeshParent();
	} catch (...) {
	}

	mesh_facets.defineMeshParent(mesh);
	MeshAccessor mesh_accessor(mesh_facets);

	UInt spatial_dimension = mesh.getSpatialDimension();

	const Array<Real> & mesh_facets_nodes = mesh_facets.getNodes();
	const auto mesh_facets_nodes_it = mesh_facets_nodes.begin(spatial_dimension);

	CSR<Element> node_to_elem;
	buildNode2Elements(mesh, node_to_elem, dimension);

	Array<UInt> counter;
	std::vector<Element> connected_elements;

	NewElementsEvent event(AKANTU_CURRENT_FUNCTION);

	// init the SubelementToElement data to improve performance
	for (auto && ghost_type : ghost_types) {
	for (auto && type : mesh.elementTypes(dimension, ghost_type)) {
	auto & subelement_to_element =
	mesh_accessor.getSubelementToElement(type, ghost_type);
	subelement_to_element.resize(mesh.getNbElement(type, ghost_type),
	ElementNull);

	auto facet_types = mesh.getAllFacetTypes(type);

	for (auto && ft : arange(facet_types.size())) {
	auto facet_type = facet_types(ft);
	mesh_accessor.getElementToSubelement(facet_type, ghost_type);
	mesh_accessor.getConnectivity(facet_type, ghost_type);
	}
	}
	}

	const ElementSynchronizer * synchronizer = nullptr;
	if (mesh.isDistributed()) {
	synchronizer = &(mesh.getElementSynchronizer());
	}

	Element current_element;
	for (auto && ghost_type : ghost_types) {
	GhostType facet_ghost_type = ghost_type;
	current_element.ghost_type = ghost_type;

	for (auto && type : mesh.elementTypes(dimension, ghost_type)) {
	auto facet_types = mesh.getAllFacetTypes(type);
	current_element.type = type;

	for (auto && ft : arange(facet_types.size())) {
	auto facet_type = facet_types(ft);
	auto nb_element = mesh.getNbElement(type, ghost_type);

	auto && element_to_subelement =
	&mesh_accessor.getElementToSubelementNC(facet_type, ghost_type);
	auto && connectivity_facets =
	&mesh_accessor.getConnectivity(facet_type, ghost_type);

	auto nb_nodes_per_facet = connectivity_facets->getNbComponent();
	// Vector<UInt> facet(nb_nodes_per_facet);

	for (UInt el = 0; el < nb_element; ++el) {
	current_element.element = el;

	auto && facets =
	mesh.getFacetConnectivity(current_element, ft).transpose();

	for (auto facet : facets) {
	// facet = facets(f);

	UInt first_node_nb_elements = node_to_elem.getNbCols(facet(0));
	counter.resize(first_node_nb_elements);
	counter.zero();

	// loop over the other nodes to search intersecting elements,
	// which are the elements that share another node with the
	// starting element after first_node
	for (auto && data : enumerate(node_to_elem.getRow(facet(0)))) {
	auto && local_el = std::get<0>(data);
	auto && first_node = std::get<1>(data);
	for (auto n : arange(1, nb_nodes_per_facet)) {
	auto && node_elements = node_to_elem.getRow(facet(n));
	counter(local_el) += std::count(
	node_elements.begin(), node_elements.end(), first_node);
	}
	}

	// counting the number of elements connected to the facets and
	// taking the minimum element number, because the facet should
	// be inserted just once
	UInt nb_element_connected_to_facet = 0;
	Element minimum_el = ElementNull;
	connected_elements.clear();
	for (auto && data : enumerate(node_to_elem.getRow(facet(0)))) {

	if (not(counter(std::get<0>(data)) == nb_nodes_per_facet - 1)) {
	continue;
	}

	auto && real_el = std::get<1>(data);

	++nb_element_connected_to_facet;
	minimum_el = std::min(minimum_el, real_el);
	connected_elements.push_back(real_el);
	}

	if (minimum_el != current_element) {
	continue;
	}

	bool full_ghost_facet = false;

	UInt n = 0;
	while (n < nb_nodes_per_facet and mesh.isPureGhostNode(facet(n))) {
	++n;
	}
	if (n == nb_nodes_per_facet) {
	full_ghost_facet = true;
	}

	if (full_ghost_facet) {
	continue;
	}

	if (boundary_only and nb_element_connected_to_facet != 1) {
	continue;
	}

	std::vector<Element> elements;

	// build elements_on_facets: linearized_el must come first
	// in order to store the facet in the correct direction
	// and avoid to invert the sign in the normal computation
	elements.reserve(elements.size() + connected_elements.size());
	for (auto && connected_element : connected_elements) {
	elements.push_back(connected_element);
	}

	if (nb_element_connected_to_facet == 1) { /// boundary facet
	elements.push_back(ElementNull);
	} else if (nb_element_connected_to_facet == 2) { /// internal facet
	/// check if facet is in between ghost and normal
	/// elements: if it's the case, the facet is either
	/// ghost or not ghost. The criterion to decide this
	/// is arbitrary. It was chosen to check the processor
	/// id (prank) of the two neighboring elements. If
	/// prank of the ghost element is lower than prank of
	/// the normal one, the facet is not ghost, otherwise
	/// it's ghost
	GhostType gt[2] = {_not_ghost, _not_ghost};

	for (UInt el = 0; el < connected_elements.size(); ++el) {
	gt[el] = connected_elements[el].ghost_type;
	}

	if ((gt[0] == _not_ghost) xor (gt[1] == _not_ghost)) {
	UInt prank[2];
	for (UInt el = 0; el < 2; ++el) {
	prank[el] = synchronizer->getRank(connected_elements[el]);
	}

	// ugly trick from Marco detected :P
	bool ghost_one = (gt[0] != _ghost);
	if (prank[ghost_one] > prank[!ghost_one]) {
	facet_ghost_type = _not_ghost;
	} else {
	facet_ghost_type = _ghost;
	}

	connectivity_facets = &mesh_accessor.getConnectivity(
	facet_type, facet_ghost_type);
	element_to_subelement = &mesh_accessor.getElementToSubelementNC(
	facet_type, facet_ghost_type);
	}
	}

	element_to_subelement->push_back(elements);
	connectivity_facets->push_back(facet);

	/// current facet index
	UInt current_facet = connectivity_facets->size() - 1;
	Element facet_element{facet_type, current_facet, facet_ghost_type};
	event.getList().push_back(facet_element);
	/// loop on every element connected to current facet and
	/// insert current facet in the first free spot of the
	/// subelement_to_element vector
	for (auto & loc_el : elements) {
	if (loc_el == ElementNull) {
	continue;
	}

	auto && subelements =
	mesh_accessor.getSubelementToElement(loc_el);

	for (auto & el : subelements) {
	if (el != ElementNull) {
	continue;
	}

	el = facet_element;
	break;
	}
	}

	/// reset connectivity in case a facet was found in
	/// between ghost and normal elements
	if (facet_ghost_type != ghost_type) {
	facet_ghost_type = ghost_type;
	connectivity_facets =
	&mesh_accessor.getConnectivity(facet_type, facet_ghost_type);
	element_to_subelement = &mesh_accessor.getElementToSubelement(
	facet_type, facet_ghost_type);
	}
	}
	}
	}
	}
	}

	mesh_facets.sendEvent(event);

	// restore the parent of mesh_facet
	if (mesh_facets_parent != nullptr) {
	mesh_facets.defineMeshParent(*mesh_facets_parent);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::renumberMeshNodes(Mesh & mesh,
	Array<UInt> & local_connectivities,
	UInt nb_local_element, UInt nb_ghost_element,
	ElementType type,
	Array<UInt> & old_nodes_numbers) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	std::map<UInt, UInt> renumbering_map;
	for (UInt i = 0; i < old_nodes_numbers.size(); ++i) {
	renumbering_map[old_nodes_numbers(i)] = i;
	}

	/// renumber the nodes
	renumberNodesInConnectivity(local_connectivities,
	(nb_local_element + nb_ghost_element) *
	nb_nodes_per_element,
	renumbering_map);

	old_nodes_numbers.resize(renumbering_map.size());
	for (auto & renumber_pair : renumbering_map) {
	old_nodes_numbers(renumber_pair.second) = renumber_pair.first;
	}
	renumbering_map.clear();

	MeshAccessor mesh_accessor(mesh);

	/// copy the renumbered connectivity to the right place
	auto & local_conn = mesh_accessor.getConnectivity(type);
	local_conn.resize(nb_local_element);

	if (nb_local_element > 0) {
	memcpy(local_conn.storage(), local_connectivities.storage(),
	nb_local_element * nb_nodes_per_element * sizeof(UInt));
	}

	auto & ghost_conn = mesh_accessor.getConnectivity(type, _ghost);
	ghost_conn.resize(nb_ghost_element);

	if (nb_ghost_element > 0) {
	std::memcpy(ghost_conn.storage(),
	local_connectivities.storage() +
	nb_local_element * nb_nodes_per_element,
	nb_ghost_element * nb_nodes_per_element * sizeof(UInt));
	}

	auto & ghost_counter = mesh_accessor.getGhostsCounters(type, _ghost);
	ghost_counter.resize(nb_ghost_element, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::renumberNodesInConnectivity(
	Array<UInt> & list_nodes, UInt nb_nodes,
	std::map<UInt, UInt> & renumbering_map) {
	AKANTU_DEBUG_IN();

	UInt * connectivity = list_nodes.storage();
	UInt new_node_num = renumbering_map.size();
	for (UInt n = 0; n < nb_nodes; ++n, ++connectivity) {
	UInt & node = *connectivity;
	auto it = renumbering_map.find(node);
	if (it == renumbering_map.end()) {
	UInt old_node = node;
	renumbering_map[old_node] = new_node_num;
	node = new_node_num;
	++new_node_num;
	} else {
	node = it->second;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::purifyMesh(Mesh & mesh) {
	AKANTU_DEBUG_IN();

	std::map<UInt, UInt> renumbering_map;

	RemovedNodesEvent remove_nodes(mesh, AKANTU_CURRENT_FUNCTION);
	Array<UInt> & nodes_removed = remove_nodes.getList();

	for (auto ghost_type : ghost_types) {
	for (auto type :
	mesh.elementTypes(_all_dimensions, ghost_type, _ek_not_defined)) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);
	UInt nb_element(connectivity.size());

	renumberNodesInConnectivity(
	connectivity, nb_element * nb_nodes_per_element, renumbering_map);
	}
	}

	Array<UInt> & new_numbering = remove_nodes.getNewNumbering();
	std::fill(new_numbering.begin(), new_numbering.end(), UInt(-1));

	for (auto && pair : renumbering_map) {
	new_numbering(std::get<0>(pair)) = std::get<1>(pair);
	}

	for (UInt i = 0; i < new_numbering.size(); ++i) {
	if (new_numbering(i) == UInt(-1)) {
	nodes_removed.push_back(i);
	}
	}

	mesh.sendEvent(remove_nodes);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::flipFacets(
	Mesh & mesh_facets,
	const ElementTypeMapArray<UInt> & remote_global_connectivities,
	GhostType gt_facet) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh_facets.getSpatialDimension();

	/// get global connectivity for local mesh
	ElementTypeMapArray<UInt> local_global_connectivities(
	"local_global_connectivity", mesh_facets.getID());

	local_global_connectivities.initialize(
	mesh_facets, _spatial_dimension = spatial_dimension - 1,
	_ghost_type = gt_facet, _with_nb_nodes_per_element = true,
	_with_nb_element = true);

	mesh_facets.getGlobalConnectivity(local_global_connectivities);
	MeshAccessor mesh_accessor(mesh_facets);

	/// loop on every facet
	for (auto type_facet :
	mesh_facets.elementTypes(spatial_dimension - 1, gt_facet)) {

	auto & connectivity = mesh_accessor.getConnectivity(type_facet, gt_facet);
	auto & local_global_connectivity =
	local_global_connectivities(type_facet, gt_facet);
	const auto & remote_global_connectivity =
	remote_global_connectivities(type_facet, gt_facet);

	auto & element_per_facet =
	mesh_accessor.getElementToSubelementNC(type_facet, gt_facet);
	auto & subfacet_to_facet =
	mesh_accessor.getSubelementToElementNC(type_facet, gt_facet);

	auto nb_nodes_per_facet = connectivity.getNbComponent();
	auto nb_nodes_per_P1_facet =
	Mesh::getNbNodesPerElement(Mesh::getP1ElementType(type_facet));

	for (auto && data :
	zip(make_view(connectivity, nb_nodes_per_facet),
	make_view(local_global_connectivity, nb_nodes_per_facet),
	make_view(remote_global_connectivity, nb_nodes_per_facet),
	make_view(subfacet_to_facet, subfacet_to_facet.getNbComponent()),
	make_view(element_per_facet))) {

	auto & conn = std::get<0>(data);
	auto & local_gconn = std::get<1>(data);
	const auto & remote_gconn = std::get<2>(data);

	/// skip facet if connectivities are the same
	if (local_gconn == remote_gconn) {
	continue;
	}

	/// re-arrange connectivity
	auto conn_tmp = conn;
	auto begin = local_gconn.begin();
	auto end = local_gconn.end();

	AKANTU_DEBUG_ASSERT(std::is_permutation(begin, end, remote_gconn.begin()),
	"This facets are not just permutation of each other, "
	<< local_gconn << " and " << remote_gconn);

	for (auto && data : enumerate(remote_gconn)) {
	auto it = std::find(begin, end, std::get<1>(data));
	AKANTU_DEBUG_ASSERT(it != end, "Node not found");
	UInt new_position = it - begin;
	conn(new_position) = conn_tmp(std::get<0>(data));
	;
	}
	// std::transform(remote_gconn.begin(), remote_gconn.end(), conn.begin(),
	// [&](auto && gnode) {
	// auto it = std::find(begin, end, gnode);
	// AKANTU_DEBUG_ASSERT(it != end, "Node not found");
	// return conn_tmp(it - begin);
	// });

	/// if 3D, check if facets are just rotated
	if (spatial_dimension == 3) {
	auto begin = remote_gconn.begin();
	/// find first node
	auto it = std::find(begin, remote_gconn.end(), local_gconn(0));

	UInt n;
	UInt start = it - begin;
	/// count how many nodes in the received connectivity follow
	/// the same order of those in the local connectivity
	for (n = 1; n < nb_nodes_per_P1_facet &&
	local_gconn(n) ==
	remote_gconn((start + n) % nb_nodes_per_P1_facet);
	++n) {
	;
	}

	/// skip the facet inversion if facet is just rotated
	if (n == nb_nodes_per_P1_facet) {
	continue;
	}
	}

	/// update data to invert facet
	auto & element_per_facet = std::get<4>(data);
	if (element_per_facet[1] !=
	ElementNull) { // by convention the first facet
	// cannot be a ElementNull
	std::swap(element_per_facet[0], element_per_facet[1]);
	}

	auto & subfacets_of_facet = std::get<3>(data);
	std::swap(subfacets_of_facet(0), subfacets_of_facet(1));
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::fillElementToSubElementsData(Mesh & mesh) {
	AKANTU_DEBUG_IN();

	if (mesh.getNbElement(mesh.getSpatialDimension() - 1) == 0) {
	AKANTU_DEBUG_INFO("There are not facets, add them in the mesh file or call "
	"the buildFacet method.");
	return;
	}

	UInt spatial_dimension = mesh.getSpatialDimension();
	ElementTypeMapArray<Real> barycenters("barycenter_tmp", mesh.getID());
	barycenters.initialize(mesh, _nb_component = spatial_dimension,
	_spatial_dimension = _all_dimensions);

	Element element;
	for (auto ghost_type : ghost_types) {
	element.ghost_type = ghost_type;
	for (const auto & type : mesh.elementTypes(_all_dimensions, ghost_type)) {
	element.type = type;

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	Array<Real> & barycenters_arr = barycenters(type, ghost_type);
	barycenters_arr.resize(nb_element);
	auto bary = barycenters_arr.begin(spatial_dimension);
	auto bary_end = barycenters_arr.end(spatial_dimension);

	for (UInt el = 0; bary != bary_end; ++bary, ++el) {
	element.element = el;
	mesh.getBarycenter(element, *bary);
	}
	}
	}

	MeshAccessor mesh_accessor(mesh);
	for (Int sp(spatial_dimension); sp >= 1; --sp) {
	if (mesh.getNbElement(sp) == 0) {
	continue;
	}

	for (auto ghost_type : ghost_types) {
	- for (auto & type : mesh.elementTypes(sp, ghost_type)) {
	+ for (const auto & type : mesh.elementTypes(sp, ghost_type)) {
	auto & subelement_to_element =
	mesh_accessor.getSubelementToElement(type, ghost_type);
	subelement_to_element.resize(mesh.getNbElement(type, ghost_type));
	subelement_to_element.set(ElementNull);
	}

	- for (auto & type : mesh.elementTypes(sp - 1, ghost_type)) {
	+ for (const auto & type : mesh.elementTypes(sp - 1, ghost_type)) {
	auto & element_to_subelement =
	mesh_accessor.getElementToSubelement(type, ghost_type);
	element_to_subelement.resize(mesh.getNbElement(type, ghost_type));
	element_to_subelement.clear();
	}
	}

	CSR<Element> nodes_to_elements;
	buildNode2Elements(mesh, nodes_to_elements, sp);

	Element facet_element;

	for (auto ghost_type : ghost_types) {
	facet_element.ghost_type = ghost_type;
	for (const auto & type : mesh.elementTypes(sp - 1, ghost_type)) {
	facet_element.type = type;

	auto & element_to_subelement =
	mesh_accessor.getElementToSubelement(type, ghost_type);

	const auto & connectivity = mesh.getConnectivity(type, ghost_type);
	- //element_to_subelement.resize(connectivity.size());
	+ // element_to_subelement.resize(connectivity.size());

	for (auto && data : enumerate(
	make_view(connectivity, mesh.getNbNodesPerElement(type)))) {
	const auto & facet = std::get<1>(data);
	facet_element.element = std::get<0>(data);

	std::map<Element, UInt> element_seen_counter;
	auto nb_nodes_per_facet =
	mesh.getNbNodesPerElement(Mesh::getP1ElementType(type));

	// count the number of node in common between the facet and the
	// other element connected to the nodes of the facet
	for (auto node : arange(nb_nodes_per_facet)) {
	for (auto & elem : nodes_to_elements.getRow(facet(node))) {
	auto cit = element_seen_counter.find(elem);
	if (cit != element_seen_counter.end()) {
	cit->second++;
	} else {
	element_seen_counter[elem] = 1;
	}
	}
	}

	// check which are the connected elements
	std::vector<Element> connected_elements;
	for (auto && cit : element_seen_counter) {
	if (cit.second == nb_nodes_per_facet) {
	connected_elements.push_back(cit.first);
	}
	}

	// add the connected elements as sub-elements
	for (auto & connected_element : connected_elements) {
	element_to_subelement(facet_element.element)
	.push_back(connected_element);
	}

	// add the element as sub-element to the connected elements
	for (auto & connected_element : connected_elements) {
	Vector<Element> subelements_to_element =
	mesh.getSubelementToElement(connected_element);

	// find the position where to insert the element
	auto it = std::find(subelements_to_element.begin(),
	subelements_to_element.end(), ElementNull);

	AKANTU_DEBUG_ASSERT(
	it != subelements_to_element.end(),
	"The element "
	<< connected_element << " seems to have too many facets!! ("
	<< (it - subelements_to_element.begin()) << " < "
	<< mesh.getNbFacetsPerElement(connected_element.type)
	<< ")");

	*it = facet_element;
	}
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/mesh_utils/mesh_utils.hh b/src/mesh_utils/mesh_utils.hh
	index cbcb22468..a2013784b 100644
	--- a/src/mesh_utils/mesh_utils.hh
	+++ b/src/mesh_utils/mesh_utils.hh
	@@ -1,140 +1,139 @@
	/**
	* @file mesh_utils.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Jan 14 2021
	*
	* @brief All mesh utils necessary for various tasks
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_UTILS_HH_
	#define AKANTU_MESH_UTILS_HH_

	namespace akantu {

	class MeshUtils {
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// build a CSR<Element> that contains for each node the list of connected
	/// elements of a given spatial dimension
	static void buildNode2Elements(const Mesh & mesh, CSR<Element> & node_to_elem,
	UInt spatial_dimension = _all_dimensions);

	/// build a CSR<UInt> that contains for each node the number of
	/// the connected elements of a given ElementType
	static void
	buildNode2ElementsElementTypeMap(const Mesh & mesh, CSR<UInt> & node_to_elem,
	ElementType type,
	GhostType ghost_type = _not_ghost);

	/// build the facets elements on the boundaries of a mesh
	static void buildFacets(Mesh & mesh);

	/// build all the facets elements: boundary and internals and store them in
	/// the mesh_facets for element of dimension from_dimension to to_dimension
	static void buildAllFacets(const Mesh & mesh, Mesh & mesh_facets,
	UInt from_dimension, UInt to_dimension);

	/// build all the facets elements: boundary and internals and store them in
	/// the mesh_facets
	static void buildAllFacets(const Mesh & mesh, Mesh & mesh_facets,
	UInt to_dimension = 0);

	/// build facets for a given spatial dimension
	static void buildFacetsDimension(const Mesh & mesh, Mesh & mesh_facets,
	bool boundary_only, UInt dimension);

	/// take the local_connectivity array as the array of local and ghost
	/// connectivity, renumber the nodes and set the connectivity of the mesh
	static void renumberMeshNodes(Mesh & mesh, Array<UInt> & local_connectivities,
	UInt nb_local_element, UInt nb_ghost_element,
	ElementType type, Array<UInt> & old_nodes);

	/// compute pbc pair for a given direction
	static void computePBCMap(const Mesh & mymesh, UInt dir,
	std::map<UInt, UInt> & pbc_pair);
	/// compute pbc pair for a surface pair
	static void computePBCMap(const Mesh & mymesh,
	const std::pair<ID, ID> & surface_pair,
	std::map<UInt, UInt> & pbc_pair);

	/// remove not connected nodes /!\ this functions renumbers the nodes.
	static void purifyMesh(Mesh & mesh);

	-
	/// fill the subelement to element and the elements to subelements data
	static void fillElementToSubElementsData(Mesh & mesh);

	/// flip facets based on global connectivity
	static void
	flipFacets(Mesh & mesh_facets,
	const ElementTypeMapArray<UInt> & remote_global_connectivities,
	GhostType gt_facet);

	private:
	/// match pairs that are on the associated pbc's
	static void matchPBCPairs(const Mesh & mymesh, UInt dir,
	Array<UInt> & selected_left,
	Array<UInt> & selected_right,
	std::map<UInt, UInt> & pbc_pair);

	/// function used by all the renumbering functions
	static void
	renumberNodesInConnectivity(Array<UInt> & list_nodes, UInt nb_nodes,
	std::map<UInt, UInt> & renumbering_map);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "mesh_utils_inline_impl.hh"

	#endif /* AKANTU_MESH_UTILS_HH_ */
	diff --git a/src/mesh_utils/mesh_utils_distribution.cc b/src/mesh_utils/mesh_utils_distribution.cc
	index 81d184f48..3d80c271c 100644
	--- a/src/mesh_utils/mesh_utils_distribution.cc
	+++ b/src/mesh_utils/mesh_utils_distribution.cc
	@@ -1,164 +1,164 @@
	/**
	* @file mesh_utils_distribution.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Implementation of the methods of mesh utils distribute
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_utils_distribution.hh"
	#include "element_info_per_processor.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "mesh_partition.hh"
	#include "mesh_utils.hh"
	#include "node_info_per_processor.hh"
	#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace MeshUtilsDistribution {
	/* ------------------------------------------------------------------------ */
	void distributeMeshCentralized(Mesh & mesh, UInt /unused/,
	const MeshPartition & partition) {
	MeshAccessor mesh_accessor(mesh);
	ElementSynchronizer & element_synchronizer =
	mesh_accessor.getElementSynchronizer();
	NodeSynchronizer & node_synchronizer = mesh_accessor.getNodeSynchronizer();

	const Communicator & comm = element_synchronizer.getCommunicator();

	UInt nb_proc = comm.getNbProc();
	UInt my_rank = comm.whoAmI();

	mesh_accessor.setNbGlobalNodes(mesh.getNbNodes());
	auto & gids = mesh_accessor.getNodesGlobalIds();

	if (nb_proc == 1) {
	return;
	}

	gids.resize(0);

	mesh.synchronizeGroupNames();

	AKANTU_DEBUG_ASSERT(
	partition.getNbPartition() == nb_proc,
	"The number of partition does not match the number of processors: "
	<< partition.getNbPartition() << " != " << nb_proc);

	/**
	* connectivity and communications scheme construction
	*/
	UInt count = 0;
	/* --- MAIN LOOP ON TYPES --- */
	for (auto && type :
	mesh.elementTypes(_all_dimensions, _not_ghost, _ek_not_defined)) {
	/// \todo change this ugly way to avoid a problem if an element
	/// type is present in the mesh but not in the partitions
	try {
	partition.getPartition(type, _not_ghost);
	} catch (...) {
	continue;
	}

	MasterElementInfoPerProc proc_infos(element_synchronizer, count, my_rank,
	type, partition);
	proc_infos.synchronize();
	++count;
	}

	{ /// Ending the synchronization of elements by sending a stop message
	MasterElementInfoPerProc proc_infos(element_synchronizer, count, my_rank,
	_not_defined, partition);
	proc_infos.synchronize();
	++count;
	}

	/**
	* Nodes synchronization
	*/
	MasterNodeInfoPerProc node_proc_infos(node_synchronizer, count, my_rank);
	node_proc_infos.synchronize();

	MeshUtils::fillElementToSubElementsData(mesh);

	mesh_accessor.setDistributed();

	AKANTU_DEBUG_OUT();
	}

	/* ------------------------------------------------------------------------ */
	void distributeMeshCentralized(Mesh & mesh, UInt root) {
	MeshAccessor mesh_accessor(mesh);
	ElementSynchronizer & element_synchronizer =
	mesh_accessor.getElementSynchronizer();
	NodeSynchronizer & node_synchronizer = mesh_accessor.getNodeSynchronizer();

	const Communicator & comm = element_synchronizer.getCommunicator();

	UInt nb_proc = comm.getNbProc();

	mesh_accessor.getNodesGlobalIds().resize(0);

	if (nb_proc == 1) {
	return;
	}

	mesh.synchronizeGroupNames();

	/**
	* connectivity and communications scheme construction on distant
	* processors
	*/
	UInt count = 0;
	bool need_synchronize = true;
	do {
	/* --------<<<<-SIZE--------------------------------------------------- */
	SlaveElementInfoPerProc proc_infos(element_synchronizer, count, root);
	need_synchronize = proc_infos.synchronize();

	++count;
	} while (need_synchronize);

	/**
	* Nodes synchronization
	*/

	SlaveNodeInfoPerProc node_proc_infos(node_synchronizer, count, root);
	node_proc_infos.synchronize();

	MeshUtils::fillElementToSubElementsData(mesh);

	mesh_accessor.setDistributed();
	}

	} // namespace MeshUtilsDistribution

	} // namespace akantu
	diff --git a/src/mesh_utils/mesh_utils_distribution.hh b/src/mesh_utils/mesh_utils_distribution.hh
	index e9adb97b9..8ca21a95f 100644
	--- a/src/mesh_utils/mesh_utils_distribution.hh
	+++ b/src/mesh_utils/mesh_utils_distribution.hh
	@@ -1,56 +1,56 @@
	/**
	* @file mesh_utils_distribution.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Sat Apr 01 2017
	*
	* @brief Mesh utils to distribute a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_UTILS_DISTRIBUTION_HH_
	#define AKANTU_MESH_UTILS_DISTRIBUTION_HH_

	namespace akantu {
	class Mesh;
	class MeshPartition;
	} // namespace akantu

	namespace akantu {
	namespace MeshUtilsDistribution {
	/// Master call to distribute a mesh in a centralized manner (the UInt is just
	/// to avoid some shitty access from the slave...)
	void distributeMeshCentralized(Mesh & mesh, UInt /unused/,
	const MeshPartition & partition);
	/// Slave call to distribute a mesh in a centralized manner
	void distributeMeshCentralized(Mesh & mesh, UInt root);
	} // namespace MeshUtilsDistribution

	} // namespace akantu

	#endif /* AKANTU_MESH_UTILS_DISTRIBUTION_HH_ */
	diff --git a/src/mesh_utils/mesh_utils_inline_impl.hh b/src/mesh_utils/mesh_utils_inline_impl.hh
	index 19663c824..01252790b 100644
	--- a/src/mesh_utils/mesh_utils_inline_impl.hh
	+++ b/src/mesh_utils/mesh_utils_inline_impl.hh
	@@ -1,45 +1,42 @@
	/**
	* @file mesh_utils_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Aug 20 2010
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Mesh utils inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MESH_UTILS_INLINE_IMPL_HH_
	#define AKANTU_MESH_UTILS_INLINE_IMPL_HH_

	-namespace akantu {
	-
	-
	-} // namespace akantu
	+namespace akantu {} // namespace akantu

	#endif /* AKANTU_MESH_UTILS_INLINE_IMPL_HH_ */
	diff --git a/src/mesh_utils/mesh_utils_pbc.cc b/src/mesh_utils/mesh_utils_pbc.cc
	index 8a44625af..33465e238 100644
	--- a/src/mesh_utils/mesh_utils_pbc.cc
	+++ b/src/mesh_utils/mesh_utils_pbc.cc
	@@ -1,311 +1,311 @@
	/**
	* @file mesh_utils_pbc.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Wed Feb 09 2011
	* @date last modification: Wed Mar 04 2020
	*
	* @brief periodic boundary condition connectivity tweak
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "mesh_accessor.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/// class that sorts a set of nodes of same coordinates in 'dir' direction
	class CoordinatesComparison {
	public:
	CoordinatesComparison(const UInt dimension, const UInt dir_1,
	const UInt dir_2, Real normalization, Real tolerance,
	const Array<Real> & coords)
	: dim(dimension), dir_1(dir_1), dir_2(dir_2),
	normalization(normalization), tolerance(tolerance),
	coords_it(coords.begin(dim)) {}
	// answers the question whether n2 is larger or equal to n1
	bool operator()(const UInt n1, const UInt n2) {
	Vector<Real> coords_n1 = coords_it[n1];
	Vector<Real> coords_n2 = coords_it[n2];
	return this->operator()(coords_n1, coords_n2);
	}

	bool operator()(const Vector<Real> & coords_n1,
	const Vector<Real> & coords_n2) const {
	Real diff = coords_n1(dir_1) - coords_n2(dir_1);
	;
	if (dim == 2 \|\| std::abs(diff) / normalization > tolerance) {
	return (diff <= 0.);
	}
	if (dim > 2) {
	diff = coords_n1(dir_2) - coords_n2(dir_2);
	return (diff <= 0);
	}
	return true;
	}

	private:
	UInt dim;
	UInt dir_1;
	UInt dir_2;
	Real normalization;
	Real tolerance;
	const Array<Real>::const_vector_iterator coords_it;
	};

	/* -------------------------------------------------------------------------- */
	void MeshUtils::computePBCMap(const Mesh & mesh, const UInt dir,
	std::map<UInt, UInt> & pbc_pair) {
	Array<UInt> selected_left;
	Array<UInt> selected_right;

	const UInt dim = mesh.getSpatialDimension();
	auto it = mesh.getNodes().begin(dim);
	auto end = mesh.getNodes().end(dim);

	if (dim <= dir) {
	return;
	}

	const Vector<Real> & lower_bounds = mesh.getLowerBounds();
	const Vector<Real> & upper_bounds = mesh.getUpperBounds();

	AKANTU_DEBUG_INFO("min " << lower_bounds(dir));
	AKANTU_DEBUG_INFO("max " << upper_bounds(dir));

	for (UInt node = 0; it != end; ++it, ++node) {
	const Vector<Real> & coords = *it;
	AKANTU_DEBUG_TRACE("treating " << coords(dir));
	if (Math::are_float_equal(coords(dir), lower_bounds(dir))) {
	AKANTU_DEBUG_TRACE("pushing node " << node << " on the left side");
	selected_left.push_back(node);
	} else if (Math::are_float_equal(coords(dir), upper_bounds(dir))) {
	selected_right.push_back(node);
	AKANTU_DEBUG_TRACE("pushing node " << node << " on the right side");
	}
	}

	AKANTU_DEBUG_INFO("found "
	<< selected_left.size() << " and " << selected_right.size()
	<< " nodes at each boundary for direction " << dir);

	// match pairs
	MeshUtils::matchPBCPairs(mesh, dir, selected_left, selected_right, pbc_pair);
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::computePBCMap(const Mesh & mesh,
	const std::pair<ID, ID> & surface_pair,
	std::map<UInt, UInt> & pbc_pair) {

	Array<UInt> selected_first;
	Array<UInt> selected_second;

	// find nodes on surfaces
	const ElementGroup & first_surf = mesh.getElementGroup(surface_pair.first);
	const ElementGroup & second_surf = mesh.getElementGroup(surface_pair.second);

	// if this surface pair is not on this proc
	if (first_surf.getNbNodes() == 0 \|\| second_surf.getNbNodes() == 0) {
	AKANTU_DEBUG_WARNING("computePBCMap has at least one surface without any "
	"nodes. I will ignore it.");
	return;
	}

	// copy nodes from element group
	selected_first.copy(first_surf.getNodeGroup().getNodes());
	selected_second.copy(second_surf.getNodeGroup().getNodes());

	// coordinates
	const Array<Real> & coords = mesh.getNodes();
	const UInt dim = mesh.getSpatialDimension();

	// variables to find min and max of surfaces
	Real first_max[3];
	Real first_min[3];
	Real second_max[3];
	Real second_min[3];
	for (UInt i = 0; i < dim; ++i) {
	first_min[i] = std::numeric_limits<Real>::max();
	second_min[i] = std::numeric_limits<Real>::max();
	first_max[i] = -std::numeric_limits<Real>::max();
	second_max[i] = -std::numeric_limits<Real>::max();
	}

	// find min and max of surface nodes
	for (auto it = selected_first.begin(); it != selected_first.end(); ++it) {
	for (UInt i = 0; i < dim; ++i) {
	if (first_min[i] > coords(*it, i)) {
	first_min[i] = coords(*it, i);
	}
	if (first_max[i] < coords(*it, i)) {
	first_max[i] = coords(*it, i);
	}
	}
	}
	for (auto it = selected_second.begin(); it != selected_second.end(); ++it) {
	for (UInt i = 0; i < dim; ++i) {
	if (second_min[i] > coords(*it, i)) {
	second_min[i] = coords(*it, i);
	}
	if (second_max[i] < coords(*it, i)) {
	second_max[i] = coords(*it, i);
	}
	}
	}

	// find direction of pbc
	Int first_dir = -1;
	#ifndef AKANTU_NDEBUG
	Int second_dir = -2;
	#endif
	for (UInt i = 0; i < dim; ++i) {
	if (Math::are_float_equal(first_min[i], first_max[i])) {
	first_dir = i;
	}
	#ifndef AKANTU_NDEBUG
	if (Math::are_float_equal(second_min[i], second_max[i])) {
	second_dir = i;
	}
	#endif
	}

	AKANTU_DEBUG_ASSERT(first_dir == second_dir,
	"Surface pair has not same direction. Surface "
	<< surface_pair.first << " dir=" << first_dir
	<< " ; Surface " << surface_pair.second
	<< " dir=" << second_dir);
	UInt dir = first_dir;

	// match pairs
	if (first_min[dir] < second_min[dir]) {
	MeshUtils::matchPBCPairs(mesh, dir, selected_first, selected_second,
	pbc_pair);
	} else {
	MeshUtils::matchPBCPairs(mesh, dir, selected_second, selected_first,
	pbc_pair);
	}
	}

	/* -------------------------------------------------------------------------- */
	void MeshUtils::matchPBCPairs(const Mesh & mesh, const UInt dir,
	Array<UInt> & selected_left,
	Array<UInt> & selected_right,
	std::map<UInt, UInt> & pbc_pair) {

	// tolerance is that large because most meshers generate points coordinates
	// with single precision only (it is the case of GMSH for instance)
	Real tolerance = 1e-7;
	const UInt dim = mesh.getSpatialDimension();
	Real normalization = mesh.getUpperBounds()(dir) - mesh.getLowerBounds()(dir);

	AKANTU_DEBUG_ASSERT(std::abs(normalization) > Math::getTolerance(),
	"In matchPBCPairs: The normalization is zero. "
	<< "Did you compute the bounding box of the mesh?");

	auto odir_1 = UInt(-1);
	auto odir_2 = UInt(-1);

	if (dim == 3) {
	if (dir == _x) {
	odir_1 = _y;
	odir_2 = _z;
	} else if (dir == _y) {
	odir_1 = _x;
	odir_2 = _z;
	} else if (dir == _z) {
	odir_1 = _x;
	odir_2 = _y;
	}
	} else if (dim == 2) {
	if (dir == _x) {
	odir_1 = _y;
	} else if (dir == _y) {
	odir_1 = _x;
	}
	}

	CoordinatesComparison compare_nodes(dim, odir_1, odir_2, normalization,
	tolerance, mesh.getNodes());

	std::sort(selected_left.begin(), selected_left.end(), compare_nodes);
	std::sort(selected_right.begin(), selected_right.end(), compare_nodes);

	auto it_left = selected_left.begin();
	auto end_left = selected_left.end();

	auto it_right = selected_right.begin();
	auto end_right = selected_right.end();

	auto nit = mesh.getNodes().begin(dim);

	while ((it_left != end_left) && (it_right != end_right)) {
	UInt i1 = *it_left;
	UInt i2 = *it_right;

	Vector<Real> coords1 = nit[i1];
	Vector<Real> coords2 = nit[i2];

	AKANTU_DEBUG_TRACE("do I pair? " << i1 << "(" << coords1 << ") with" << i2
	<< "(" << coords2 << ") in direction "
	<< dir);

	Real dx = 0.0;
	Real dy = 0.0;
	if (dim >= 2) {
	dx = coords1(odir_1) - coords2(odir_1);
	}
	if (dim == 3) {
	dy = coords1(odir_2) - coords2(odir_2);
	}

	if (std::abs(dx * dx + dy * dy) / normalization < tolerance) {
	// then i match these pairs
	if (pbc_pair.count(i2) != 0U) {
	i2 = pbc_pair[i2];
	}
	pbc_pair[i1] = i2;

	AKANTU_DEBUG_TRACE("pairing " << i1 << "(" << coords1 << ") with" << i2
	<< "(" << coords2 << ") in direction "
	<< dir);
	++it_left;
	++it_right;
	} else if (compare_nodes(coords1, coords2)) {
	++it_left;
	} else {
	++it_right;
	}
	}
	AKANTU_DEBUG_INFO("found " << pbc_pair.size() << " pairs for direction "
	<< dir);
	}

	} // namespace akantu
	diff --git a/src/model/common/boundary_condition/boundary_condition.hh b/src/model/common/boundary_condition/boundary_condition.hh
	index 4a08f2267..30c4147c2 100644
	--- a/src/model/common/boundary_condition/boundary_condition.hh
	+++ b/src/model/common/boundary_condition/boundary_condition.hh
	@@ -1,101 +1,100 @@
	/**
	* @file boundary_condition.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief XXX
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BOUNDARY_CONDITION_HH_
	#define AKANTU_BOUNDARY_CONDITION_HH_

	#include "aka_common.hh"
	#include "boundary_condition_functor.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <class ModelType> class BoundaryCondition {

	/* ------------------------------------------------------------------------ */
	/* Typedefs */
	/* ------------------------------------------------------------------------ */
	private:
	/* ------------------------------------------------------------------------ */
	/* Constructors / Destructors / Initializers */
	/* ------------------------------------------------------------------------ */
	public:
	BoundaryCondition() : model(nullptr) {}
	/// Initialize the boundary conditions
	void initBC(ModelType & model, Array<Real> & primal, Array<Real> & dual);
	void initBC(ModelType & model, Array<Real> & primal,
	Array<Real> & primal_increment, Array<Real> & dual);
	/* ------------------------------------------------------------------------ */
	/* Methods and accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Apply the boundary conditions
	- template <typename FunctorType>
	- inline void applyBC(const FunctorType & func);
	+ template <typename FunctorType> inline void applyBC(const FunctorType & func);

	template <class FunctorType>
	inline void applyBC(const FunctorType & func, const std::string & group_name);

	template <class FunctorType>
	inline void applyBC(const FunctorType & func,
	const ElementGroup & element_group);

	AKANTU_GET_MACRO_NOT_CONST(Model, *model, ModelType &);
	AKANTU_GET_MACRO_NOT_CONST(Primal, *primal, Array<Real> &);
	AKANTU_GET_MACRO_NOT_CONST(Dual, *dual, Array<Real> &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */

	public:
	template <class FunctorType, BC::Functor::Type type = FunctorType::type>
	struct TemplateFunctionWrapper;

	private:
	ModelType * model;
	Array<Real> * primal{nullptr};
	Array<Real> * dual{nullptr};
	Array<Real> * primal_increment{nullptr};
	};

	} // namespace akantu

	#include "boundary_condition_tmpl.hh"

	#endif /* AKANTU_BOUNDARY_CONDITION_HH_ */
	diff --git a/src/model/common/boundary_condition/boundary_condition_functor.hh b/src/model/common/boundary_condition/boundary_condition_functor.hh
	index 19138acbe..1faab2239 100644
	--- a/src/model/common/boundary_condition/boundary_condition_functor.hh
	+++ b/src/model/common/boundary_condition/boundary_condition_functor.hh
	@@ -1,215 +1,215 @@
	/**
	* @file boundary_condition_functor.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Definitions of the functors to apply boundary conditions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "fe_engine.hh"
	#include "integration_point.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BOUNDARY_CONDITION_FUNCTOR_HH_
	#define AKANTU_BOUNDARY_CONDITION_FUNCTOR_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	namespace BC {
	using Axis = ::akantu::SpatialDirection;

	/* ---------------------------------------------------------------------- */
	struct Functor {
	enum Type { _dirichlet, _neumann };
	virtual ~Functor() = default;
	};

	/* ---------------------------------------------------------------------- */
	namespace Dirichlet {

	class DirichletFunctor : public Functor {
	public:
	DirichletFunctor() = default;
	explicit DirichletFunctor(Axis ax) : axis(ax) {}

	virtual void operator()(__attribute__((unused)) UInt node,
	__attribute__((unused)) Vector<bool> & flags,
	__attribute__((unused)) Vector<Real> & primal,
	__attribute__((unused))
	const Vector<Real> & coord) const {
	AKANTU_TO_IMPLEMENT();
	}

	public:
	static const Type type = _dirichlet;

	protected:
	Axis axis{_x};
	};

	/* ---------------------------------------------------------------------- */
	class FlagOnly : public DirichletFunctor {
	public:
	explicit FlagOnly(Axis ax = _x) : DirichletFunctor(ax) {}

	public:
	inline void operator()(UInt node, Vector<bool> & flags,
	Vector<Real> & primal,
	const Vector<Real> & coord) const override;
	};

	/* ---------------------------------------------------------------------- */
	// class FreeBoundary : public DirichletFunctor {
	// public:
	// explicit FreeBoundary(Axis ax = _x) : DirichletFunctor(ax) {}

	// public:
	// inline void operator()(UInt node, Vector<bool> & flags,
	// Vector<Real> & primal,
	// const Vector<Real> & coord) const;
	// };

	/* ---------------------------------------------------------------------- */
	class FixedValue : public DirichletFunctor {
	public:
	FixedValue(Real val, Axis ax = _x) : DirichletFunctor(ax), value(val) {}

	public:
	inline void operator()(UInt node, Vector<bool> & flags,
	Vector<Real> & primal,
	const Vector<Real> & coord) const override;

	protected:
	Real value;
	};

	/* ---------------------------------------------------------------------- */
	class IncrementValue : public DirichletFunctor {
	public:
	IncrementValue(Real val, Axis ax = _x)
	: DirichletFunctor(ax), value(val) {}

	public:
	inline void operator()(UInt node, Vector<bool> & flags,
	Vector<Real> & primal,
	const Vector<Real> & coord) const override;

	inline void setIncrement(Real val) { this->value = val; }

	protected:
	Real value;
	};

	/* ---------------------------------------------------------------------- */
	class Increment : public DirichletFunctor {
	public:
	explicit Increment(const Vector<Real> & val)
	: DirichletFunctor(_x), value(val) {}

	public:
	inline void operator()(UInt node, Vector<bool> & flags,
	Vector<Real> & primal,
	const Vector<Real> & coord) const override;

	inline void setIncrement(const Vector<Real> & val) { this->value = val; }

	protected:
	Vector<Real> value;
	};
	} // namespace Dirichlet

	/* ------------------------------------------------------------------------ */
	/* Neumann */
	/* ------------------------------------------------------------------------ */
	namespace Neumann {

	class NeumannFunctor : public Functor {

	protected:
	NeumannFunctor() = default;

	public:
	virtual void operator()(const IntegrationPoint & quad_point,
	Vector<Real> & dual, const Vector<Real> & coord,
	const Vector<Real> & normals) const = 0;

	~NeumannFunctor() override = default;

	public:
	static const Type type = _neumann;
	};

	/* ---------------------------------------------------------------------- */
	class FromHigherDim : public NeumannFunctor {
	public:
	explicit FromHigherDim(const Matrix<Real> & mat) : bc_data(mat) {}
	~FromHigherDim() override = default;

	public:
	inline void operator()(const IntegrationPoint & quad_point,
	Vector<Real> & dual, const Vector<Real> & coord,
	const Vector<Real> & normals) const override;

	protected:
	Matrix<Real> bc_data;
	};

	/* ---------------------------------------------------------------------- */
	class FromSameDim : public NeumannFunctor {
	public:
	explicit FromSameDim(const Vector<Real> & vec) : bc_data(vec) {}
	~FromSameDim() override = default;

	public:
	inline void operator()(const IntegrationPoint & quad_point,
	Vector<Real> & dual, const Vector<Real> & coord,
	const Vector<Real> & normals) const override;

	protected:
	Vector<Real> bc_data;
	};

	/* ---------------------------------------------------------------------- */
	class FreeBoundary : public NeumannFunctor {
	public:
	inline void operator()(const IntegrationPoint & quad_point,
	Vector<Real> & dual, const Vector<Real> & coord,
	const Vector<Real> & normals) const override;
	};
	} // namespace Neumann
	} // namespace BC
	} // namespace akantu

	#include "boundary_condition_functor_inline_impl.hh"

	#endif /* AKANTU_BOUNDARY_CONDITION_FUNCTOR_HH_ */
	diff --git a/src/model/common/boundary_condition/boundary_condition_functor_inline_impl.hh b/src/model/common/boundary_condition/boundary_condition_functor_inline_impl.hh
	index d19c4aa3a..cddbd6e63 100644
	--- a/src/model/common/boundary_condition/boundary_condition_functor_inline_impl.hh
	+++ b/src/model/common/boundary_condition/boundary_condition_functor_inline_impl.hh
	@@ -1,148 +1,148 @@
	/**
	* @file boundary_condition_functor_inline_impl.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Sat Dec 22 2018
	*
	* @brief implementation of the BC::Functors
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition_functor.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BOUNDARY_CONDITION_FUNCTOR_INLINE_IMPL_HH_
	#define AKANTU_BOUNDARY_CONDITION_FUNCTOR_INLINE_IMPL_HH_

	/* -------------------------------------------------------------------------- */
	#define DIRICHLET_SANITY_CHECK \
	- AKANTU_DEBUG_ASSERT( \
	- primal.size() <= flags.size(), \
	- "The primal vector and flags vectors given" \
	+ AKANTU_DEBUG_ASSERT( \
	+ primal.size() <= flags.size(), \
	+ "The primal vector and flags vectors given" \
	<< " to the boundary condition functor have different sizes!");

	#define NEUMANN_SANITY_CHECK \
	AKANTU_DEBUG_ASSERT( \
	coord.size() <= normals.size(), \
	"The coordinates and normals vectors given to the" \
	- << " boundary condition functor have different sizes!"); \
	-
	+ << " boundary condition functor have different sizes!");
	+
	namespace akantu {
	namespace BC {
	/* ---------------------------------------------------------------------- */
	namespace Dirichlet {
	- inline void FlagOnly::
	- operator()(__attribute__((unused)) UInt node, Vector<bool> & flags,
	- __attribute__((unused)) Vector<Real> & primal,
	- __attribute__((unused)) const Vector<Real> & coord) const {
	+ inline void FlagOnly::operator()(__attribute__((unused)) UInt node,
	+ Vector<bool> & flags,
	+ __attribute__((unused))
	+ Vector<Real> & primal,
	+ __attribute__((unused))
	+ const Vector<Real> & coord) const {

	DIRICHLET_SANITY_CHECK;

	flags(this->axis) = true;
	}

	/* ---------------------------------------------------------------------- */
	// inline void FreeBoundary::
	// operator()(__attribute__((unused)) UInt node, Vector<bool> & flags,
	// __attribute__((unused)) Vector<Real> & primal,
	// __attribute__((unused)) const Vector<Real> & coord) const {

	// DIRICHLET_SANITY_CHECK;

	// flags(this->axis) = false;
	// }

	/* ---------------------------------------------------------------------- */
	inline void FixedValue::operator()(__attribute__((unused)) UInt node,
	Vector<bool> & flags,
	Vector<Real> & primal,
	__attribute__((unused))
	const Vector<Real> & coord) const {
	DIRICHLET_SANITY_CHECK;
	flags(this->axis) = true;
	primal(this->axis) = value;
	}

	/* ---------------------------------------------------------------------- */
	inline void IncrementValue::operator()(__attribute__((unused)) UInt node,
	Vector<bool> & flags,
	Vector<Real> & primal,
	__attribute__((unused))
	const Vector<Real> & coord) const {
	DIRICHLET_SANITY_CHECK;
	flags(this->axis) = true;
	primal(this->axis) += value;
	}

	/* ---------------------------------------------------------------------- */
	inline void Increment::operator()(__attribute__((unused)) UInt node,
	Vector<bool> & flags,
	Vector<Real> & primal,
	__attribute__((unused))
	const Vector<Real> & coord) const {
	DIRICHLET_SANITY_CHECK;
	flags.set(true);
	primal += value;
	}
	} // namespace Dirichlet
	/* ------------------------------------------------------------------------ */
	/* Neumann */
	/* ------------------------------------------------------------------------ */

	namespace Neumann {
	- inline void FreeBoundary::
	- operator()(__attribute__((unused)) const IntegrationPoint & quad_point,
	- Vector<Real> & dual,
	- __attribute__((unused)) const Vector<Real> & coord,
	- __attribute__((unused)) const Vector<Real> & normals) const {
	+ inline void FreeBoundary::operator()(
	+ __attribute__((unused)) const IntegrationPoint & quad_point,
	+ Vector<Real> & dual, __attribute__((unused)) const Vector<Real> & coord,
	+ __attribute__((unused)) const Vector<Real> & normals) const {
	for (UInt i(0); i < dual.size(); ++i) {
	dual(i) = 0.0;
	}
	}

	/* ---------------------------------------------------------------------- */
	inline void FromHigherDim::operator()(__attribute__((unused))
	const IntegrationPoint & quad_point,
	Vector<Real> & dual,
	__attribute__((unused))
	const Vector<Real> & coord,
	const Vector<Real> & normals) const {
	dual.mul<false>(this->bc_data, normals);
	}

	/* ---------------------------------------------------------------------- */
	- inline void FromSameDim::
	- operator()(__attribute__((unused)) const IntegrationPoint & quad_point,
	- Vector<Real> & dual,
	- __attribute__((unused)) const Vector<Real> & coord,
	- __attribute__((unused)) const Vector<Real> & normals) const {
	+ inline void FromSameDim::operator()(
	+ __attribute__((unused)) const IntegrationPoint & quad_point,
	+ Vector<Real> & dual, __attribute__((unused)) const Vector<Real> & coord,
	+ __attribute__((unused)) const Vector<Real> & normals) const {
	dual = this->bc_data;
	}
	} // namespace Neumann
	} // namespace BC
	} // namespace akantu

	#endif /* AKANTU_BOUNDARY_CONDITION_FUNCTOR_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/boundary_condition/boundary_condition_tmpl.hh b/src/model/common/boundary_condition/boundary_condition_tmpl.hh
	index d98a09e01..07ba189f1 100644
	--- a/src/model/common/boundary_condition/boundary_condition_tmpl.hh
	+++ b/src/model/common/boundary_condition/boundary_condition_tmpl.hh
	@@ -1,233 +1,233 @@
	/**
	* @file boundary_condition_tmpl.hh
	*
	* @author Dana Christen <dana.christen@gmail.com>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 03 2013
	* @date last modification: Mon Oct 28 2019
	*
	* @brief implementation of the applyBC
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition.hh"
	#include "element_group.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BOUNDARY_CONDITION_TMPL_HH_
	#define AKANTU_BOUNDARY_CONDITION_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename ModelType>
	void BoundaryCondition<ModelType>::initBC(ModelType & model,
	Array<Real> & primal,
	Array<Real> & dual) {
	this->model = &model;
	this->primal = &primal;
	this->dual = &dual;
	}

	/* -------------------------------------------------------------------------- */
	template <typename ModelType>
	void BoundaryCondition<ModelType>::initBC(ModelType & model,
	Array<Real> & primal,
	Array<Real> & primal_increment,
	Array<Real> & dual) {
	this->initBC(model, primal, dual);
	this->primal_increment = &primal_increment;
	}

	/* -------------------------------------------------------------------------- */
	/* Partial specialization for DIRICHLET functors */
	template <typename ModelType>
	template <typename FunctorType>
	struct BoundaryCondition<ModelType>::TemplateFunctionWrapper<
	FunctorType, BC::Functor::_dirichlet> {
	static inline void applyBC(const FunctorType & func,
	const ElementGroup & group,
	BoundaryCondition<ModelType> & bc_instance) {
	auto & model = bc_instance.getModel();
	auto & primal = bc_instance.getPrimal();

	const auto & coords = model.getMesh().getNodes();
	auto & boundary_flags = model.getBlockedDOFs();
	UInt dim = model.getMesh().getSpatialDimension();

	auto primal_iter = primal.begin(primal.getNbComponent());
	auto coords_iter = coords.begin(dim);
	auto flags_iter = boundary_flags.begin(boundary_flags.getNbComponent());

	for (auto n : group.getNodeGroup()) {
	Vector<bool> flag(flags_iter[n]);
	Vector<Real> primal(primal_iter[n]);
	Vector<Real> coords(coords_iter[n]);
	func(n, flag, primal, coords);
	}
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Partial specialization for NEUMANN functors */
	template <typename ModelType>
	template <typename FunctorType>
	struct BoundaryCondition<ModelType>::TemplateFunctionWrapper<
	FunctorType, BC::Functor::_neumann> {
	static inline void applyBC(const FunctorType & func,
	const ElementGroup & group,
	BoundaryCondition<ModelType> & bc_instance) {
	UInt dim = bc_instance.getModel().getSpatialDimension();
	switch (dim) {
	case 1: {
	AKANTU_TO_IMPLEMENT();
	break;
	}
	case 2:
	case 3: {
	applyBC(func, group, bc_instance, _not_ghost);
	applyBC(func, group, bc_instance, _ghost);
	break;
	}
	}
	}

	static inline void applyBC(const FunctorType & func,
	const ElementGroup & group,
	BoundaryCondition<ModelType> & bc_instance,
	GhostType ghost_type) {
	auto & model = bc_instance.getModel();
	auto & dual = bc_instance.getDual();
	const auto & mesh = model.getMesh();
	const auto & nodes_coords = mesh.getNodes();
	const auto & fem_boundary = model.getFEEngineBoundary();
	-
	+
	UInt dim = model.getSpatialDimension();
	UInt nb_degree_of_freedom = dual.getNbComponent();

	IntegrationPoint quad_point;
	quad_point.ghost_type = ghost_type;

	// Loop over the boundary element types
	for (auto && type : group.elementTypes(dim - 1, ghost_type)) {
	const auto & element_ids = group.getElements(type, ghost_type);

	UInt nb_quad_points =
	fem_boundary.getNbIntegrationPoints(type, ghost_type);
	UInt nb_elements = element_ids.size();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	Array<Real> dual_before_integ(nb_elements * nb_quad_points,
	nb_degree_of_freedom, 0.);
	Array<Real> quad_coords(nb_elements * nb_quad_points, dim);

	const auto & normals_on_quad =
	fem_boundary.getNormalsOnIntegrationPoints(type, ghost_type);

	fem_boundary.interpolateOnIntegrationPoints(
	nodes_coords, quad_coords, dim, type, ghost_type, element_ids);
	auto normals_begin = normals_on_quad.begin(dim);
	decltype(normals_begin) normals_iter;
	auto quad_coords_iter = quad_coords.begin(dim);
	auto dual_iter = dual_before_integ.begin(nb_degree_of_freedom);

	quad_point.type = type;
	for (auto el : element_ids) {
	quad_point.element = el;
	normals_iter = normals_begin + el * nb_quad_points;
	for (auto q : arange(nb_quad_points)) {
	quad_point.num_point = q;
	func(quad_point, dual_iter, quad_coords_iter, *normals_iter);
	++dual_iter;
	++quad_coords_iter;
	++normals_iter;
	}
	}

	Array<Real> dual_by_shapes(nb_elements * nb_quad_points,
	nb_degree_of_freedom * nb_nodes_per_element);

	fem_boundary.computeNtb(dual_before_integ, dual_by_shapes, type,
	ghost_type, element_ids);

	Array<Real> dual_by_shapes_integ(nb_elements, nb_degree_of_freedom *
	nb_nodes_per_element);
	fem_boundary.integrate(dual_by_shapes, dual_by_shapes_integ,
	nb_degree_of_freedom * nb_nodes_per_element, type,
	ghost_type, element_ids);

	// assemble the result into force vector
	model.getDOFManager().assembleElementalArrayLocalArray(
	dual_by_shapes_integ, dual, type, ghost_type, 1., element_ids);
	}
	}
	};

	/* -------------------------------------------------------------------------- */
	template <typename ModelType>
	template <typename FunctorType>
	inline void BoundaryCondition<ModelType>::applyBC(const FunctorType & func) {
	auto bit = model->getMesh().getGroupManager().element_group_begin();
	auto bend = model->getMesh().getGroupManager().element_group_end();
	for (; bit != bend; ++bit) {
	applyBC(func, *bit);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename ModelType>
	template <typename FunctorType>
	inline void
	BoundaryCondition<ModelType>::applyBC(const FunctorType & func,
	const std::string & group_name) {
	try {
	const ElementGroup & element_group =
	model->getMesh().getElementGroup(group_name);
	applyBC(func, element_group);
	} catch (akantu::debug::Exception & e) {
	AKANTU_EXCEPTION("Error applying a boundary condition onto \""
	<< group_name << "\"! [" << e.what() << "]");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename ModelType>
	template <typename FunctorType>
	inline void
	BoundaryCondition<ModelType>::applyBC(const FunctorType & func,
	const ElementGroup & element_group) {
	#if !defined(AKANTU_NDEBUG)
	if (element_group.getDimension() != model->getSpatialDimension() - 1) {
	AKANTU_DEBUG_WARNING("The group "
	<< element_group.getName()
	<< " does not contain only boundaries elements");
	}
	#endif

	TemplateFunctionWrapper<FunctorType>::applyBC(func, element_group, *this);
	}

	#endif /* AKANTU_BOUNDARY_CONDITION_TMPL_HH_ */

	} // namespace akantu
	diff --git a/src/model/common/dof_manager/dof_manager.cc b/src/model/common/dof_manager/dof_manager.cc
	index 5c0918248..137192f11 100644
	--- a/src/model/common/dof_manager/dof_manager.cc
	+++ b/src/model/common/dof_manager/dof_manager.cc
	@@ -1,1017 +1,1017 @@
	/**
	* @file dof_manager.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Sat Mar 06 2021
	*
	* @brief Implementation of the common parts of the DOFManagers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	#include "communicator.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	#include "node_group.hh"
	#include "node_synchronizer.hh"
	#include "non_linear_solver.hh"
	#include "periodic_node_synchronizer.hh"
	#include "time_step_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	DOFManager::DOFManager(const ID & id)
	: id(id), dofs_flag(0, 1, std::string(id + ":dofs_type")),
	global_equation_number(0, 1, "global_equation_number"),
	communicator(Communicator::getStaticCommunicator()) {}

	/* -------------------------------------------------------------------------- */
	DOFManager::DOFManager(Mesh & mesh, const ID & id)
	: id(id), mesh(&mesh), dofs_flag(0, 1, std::string(id + ":dofs_type")),
	global_equation_number(0, 1, "global_equation_number"),
	communicator(mesh.getCommunicator()) {
	this->mesh->registerEventHandler(*this, _ehp_dof_manager);
	}

	/* -------------------------------------------------------------------------- */
	DOFManager::~DOFManager() = default;

	/* -------------------------------------------------------------------------- */
	std::vector<ID> DOFManager::getDOFIDs() const {
	std::vector<ID> keys;
	for (const auto & dof_data : this->dofs) {
	keys.push_back(dof_data.first);
	}

	return keys;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleElementalArrayLocalArray(
	const Array<Real> & elementary_vect, Array<Real> & array_assembeled,
	ElementType type, GhostType ghost_type, Real scale_factor,
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	UInt nb_element;
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_degree_of_freedom =
	elementary_vect.getNbComponent() / nb_nodes_per_element;

	UInt * filter_it = nullptr;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	filter_it = filter_elements.storage();
	} else {
	nb_element = this->mesh->getNbElement(type, ghost_type);
	}

	AKANTU_DEBUG_ASSERT(elementary_vect.size() == nb_element,
	"The vector elementary_vect("
	<< elementary_vect.getID()
	<< ") has not the good size.");

	const Array<UInt> & connectivity =
	this->mesh->getConnectivity(type, ghost_type);

	Array<Real>::const_matrix_iterator elem_it =
	elementary_vect.begin(nb_degree_of_freedom, nb_nodes_per_element);

	for (UInt el = 0; el < nb_element; ++el, ++elem_it) {
	UInt element = el;
	if (filter_it != nullptr) {
	// conn_it = conn_begin + *filter_it;
	element = *filter_it;
	}

	// const Vector<UInt> & conn = *conn_it;
	const Matrix<Real> & elemental_val = *elem_it;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt offset_node = connectivity(element, n) * nb_degree_of_freedom;
	Vector<Real> assemble(array_assembeled.storage() + offset_node,
	nb_degree_of_freedom);
	Vector<Real> elem_val = elemental_val(n);
	assemble.aXplusY(elem_val, scale_factor);
	}

	if (filter_it != nullptr) {
	++filter_it;
	}
	// else
	// ++conn_it;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleElementalArrayToResidual(
	const ID & dof_id, const Array<Real> & elementary_vect, ElementType type,
	GhostType ghost_type, Real scale_factor,
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_degree_of_freedom =
	elementary_vect.getNbComponent() / nb_nodes_per_element;
	Array<Real> array_localy_assembeled(this->mesh->getNbNodes(),
	nb_degree_of_freedom);

	array_localy_assembeled.zero();

	this->assembleElementalArrayLocalArray(
	elementary_vect, array_localy_assembeled, type, ghost_type, scale_factor,
	filter_elements);

	this->assembleToResidual(dof_id, array_localy_assembeled, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleElementalArrayToLumpedMatrix(
	const ID & dof_id, const Array<Real> & elementary_vect,
	const ID & lumped_mtx, ElementType type, GhostType ghost_type,
	Real scale_factor, const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_degree_of_freedom =
	elementary_vect.getNbComponent() / nb_nodes_per_element;
	Array<Real> array_localy_assembeled(this->mesh->getNbNodes(),
	nb_degree_of_freedom);

	array_localy_assembeled.zero();

	this->assembleElementalArrayLocalArray(
	elementary_vect, array_localy_assembeled, type, ghost_type, scale_factor,
	filter_elements);

	this->assembleToLumpedMatrix(dof_id, array_localy_assembeled, lumped_mtx, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleMatMulDOFsToResidual(const ID & A_id,
	Real scale_factor) {
	for (auto & pair : this->dofs) {
	const auto & dof_id = pair.first;
	auto & dof_data = *pair.second;

	this->assembleMatMulVectToResidual(dof_id, A_id, *dof_data.dof,
	scale_factor);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::splitSolutionPerDOFs() {
	for (auto && data : this->dofs) {
	auto & dof_data = *data.second;
	dof_data.solution.resize(dof_data.dof->size() *
	dof_data.dof->getNbComponent());
	this->getSolutionPerDOFs(data.first, dof_data.solution);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::getSolutionPerDOFs(const ID & dof_id,
	Array<Real> & solution_array) {
	AKANTU_DEBUG_IN();
	this->getArrayPerDOFs(dof_id, this->getSolution(), solution_array);
	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void DOFManager::getLumpedMatrixPerDOFs(const ID & dof_id,
	const ID & lumped_mtx,
	Array<Real> & lumped) {
	AKANTU_DEBUG_IN();
	this->getArrayPerDOFs(dof_id, this->getLumpedMatrix(lumped_mtx), lumped);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleToResidual(const ID & dof_id,
	Array<Real> & array_to_assemble,
	Real scale_factor) {
	AKANTU_DEBUG_IN();

	// this->makeConsistentForPeriodicity(dof_id, array_to_assemble);
	this->assembleToGlobalArray(dof_id, array_to_assemble, this->getResidual(),
	scale_factor);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleToLumpedMatrix(const ID & dof_id,
	Array<Real> & array_to_assemble,
	const ID & lumped_mtx,
	Real scale_factor) {
	AKANTU_DEBUG_IN();

	// this->makeConsistentForPeriodicity(dof_id, array_to_assemble);
	auto & lumped = this->getLumpedMatrix(lumped_mtx);
	this->assembleToGlobalArray(dof_id, array_to_assemble, lumped, scale_factor);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	DOFManager::DOFData::DOFData(const ID & dof_id)
	: support_type(_dst_generic), group_support("__mesh__"),
	solution(0, 1, dof_id + ":solution"),
	local_equation_number(0, 1, dof_id + ":local_equation_number"),
	associated_nodes(0, 1, dof_id + "associated_nodes") {}

	/* -------------------------------------------------------------------------- */
	DOFManager::DOFData::~DOFData() = default;

	/* -------------------------------------------------------------------------- */
	template <typename Func>
	auto DOFManager::countDOFsForNodes(const DOFData & dof_data, UInt nb_nodes,
	Func && getNode) {
	auto nb_local_dofs = nb_nodes;
	decltype(nb_local_dofs) nb_pure_local = 0;
	for (auto n : arange(nb_nodes)) {
	UInt node = getNode(n);

	// http://www.open-std.org/jtc1/sc22/open/n2356/conv.html
	// bool are by convention casted to 0 and 1 when promoted to int
	nb_pure_local += this->mesh->isLocalOrMasterNode(node);
	nb_local_dofs -= this->mesh->isPeriodicSlave(node);
	}

	const auto & dofs_array = *dof_data.dof;
	nb_pure_local *= dofs_array.getNbComponent();
	nb_local_dofs *= dofs_array.getNbComponent();
	return std::make_pair(nb_local_dofs, nb_pure_local);
	}

	/* -------------------------------------------------------------------------- */
	auto DOFManager::getNewDOFDataInternal(const ID & dof_id) -> DOFData & {
	auto it = this->dofs.find(dof_id);
	if (it != this->dofs.end()) {
	AKANTU_EXCEPTION("This dof array has already been registered");
	}

	std::unique_ptr<DOFData> dof_data_ptr = this->getNewDOFData(dof_id);
	DOFData & dof_data = *dof_data_ptr;

	this->dofs[dof_id] = std::move(dof_data_ptr);
	return dof_data;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	const DOFSupportType & support_type) {
	auto & dofs_storage = this->getNewDOFDataInternal(dof_id);
	dofs_storage.support_type = support_type;

	this->registerDOFsInternal(dof_id, dofs_array);

	resizeGlobalArrays();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	const ID & support_group) {
	auto & dofs_storage = this->getNewDOFDataInternal(dof_id);
	dofs_storage.support_type = _dst_nodal;
	dofs_storage.group_support = support_group;

	this->registerDOFsInternal(dof_id, dofs_array);

	resizeGlobalArrays();
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<UInt, UInt, UInt>
	DOFManager::registerDOFsInternal(const ID & dof_id, Array<Real> & dofs_array) {
	DOFData & dof_data = this->getDOFData(dof_id);
	dof_data.dof = &dofs_array;

	UInt nb_local_dofs = 0;
	UInt nb_pure_local = 0;

	const auto & support_type = dof_data.support_type;

	switch (support_type) {
	case _dst_nodal: {
	const auto & group = dof_data.group_support;

	std::function<UInt(UInt)> getNode;
	if (group == "__mesh__") {
	AKANTU_DEBUG_ASSERT(
	dofs_array.size() == this->mesh->getNbNodes(),
	"The array of dof is too short to be associated to nodes.");

	std::tie(nb_local_dofs, nb_pure_local) = countDOFsForNodes(
	dof_data, this->mesh->getNbNodes(), [](auto && n) { return n; });
	} else {
	const auto & node_group =
	this->mesh->getElementGroup(group).getNodeGroup().getNodes();

	AKANTU_DEBUG_ASSERT(
	dofs_array.size() == node_group.size(),
	"The array of dof is too shot to be associated to nodes.");

	std::tie(nb_local_dofs, nb_pure_local) =
	countDOFsForNodes(dof_data, node_group.size(),
	[&node_group](auto && n) { return node_group(n); });
	}

	break;
	}
	case _dst_generic: {
	nb_local_dofs = nb_pure_local =
	dofs_array.size() * dofs_array.getNbComponent();
	break;
	}
	default: {
	AKANTU_EXCEPTION("This type of dofs is not handled yet.");
	}
	}

	dof_data.local_nb_dofs = nb_local_dofs;
	dof_data.pure_local_nb_dofs = nb_pure_local;
	dof_data.ghosts_nb_dofs = nb_local_dofs - nb_pure_local;

	this->pure_local_system_size += nb_pure_local;
	this->local_system_size += nb_local_dofs;

	auto nb_total_pure_local = nb_pure_local;
	communicator.allReduce(nb_total_pure_local, SynchronizerOperation::_sum);

	this->system_size += nb_total_pure_local;

	// updating the dofs data after counting is finished
	switch (support_type) {
	case _dst_nodal: {
	const auto & group = dof_data.group_support;
	if (group != "__mesh__") {
	auto & support_nodes =
	this->mesh->getElementGroup(group).getNodeGroup().getNodes();
	this->updateDOFsData(
	dof_data, nb_local_dofs, nb_pure_local, support_nodes.size(),
	[&support_nodes](UInt node) -> UInt { return support_nodes[node]; });
	} else {
	this->updateDOFsData(dof_data, nb_local_dofs, nb_pure_local,
	mesh->getNbNodes(),
	[](UInt node) -> UInt { return node; });
	}
	break;
	}
	case _dst_generic: {
	this->updateDOFsData(dof_data, nb_local_dofs, nb_pure_local);
	break;
	}
	}

	return std::make_tuple(nb_local_dofs, nb_pure_local, nb_total_pure_local);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerDOFsPrevious(const ID & dof_id, Array<Real> & array) {
	DOFData & dof = this->getDOFData(dof_id);

	if (dof.previous != nullptr) {
	AKANTU_EXCEPTION("The previous dofs array for "
	<< dof_id << " has already been registered");
	}

	dof.previous = &array;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerDOFsIncrement(const ID & dof_id, Array<Real> & array) {
	DOFData & dof = this->getDOFData(dof_id);

	if (dof.increment != nullptr) {
	AKANTU_EXCEPTION("The dofs increment array for "
	<< dof_id << " has already been registered");
	}

	dof.increment = &array;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerDOFsDerivative(const ID & dof_id, UInt order,
	Array<Real> & dofs_derivative) {
	DOFData & dof = this->getDOFData(dof_id);
	std::vector<Array<Real> *> & derivatives = dof.dof_derivatives;

	if (derivatives.size() < order) {
	derivatives.resize(order, nullptr);
	} else {
	if (derivatives[order - 1] != nullptr) {
	AKANTU_EXCEPTION("The dof derivatives of order "
	<< order << " already been registered for this dof ("
	<< dof_id << ")");
	}
	}

	derivatives[order - 1] = &dofs_derivative;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::registerBlockedDOFs(const ID & dof_id,
	Array<bool> & blocked_dofs) {
	DOFData & dof = this->getDOFData(dof_id);

	if (dof.blocked_dofs != nullptr) {
	AKANTU_EXCEPTION("The blocked dofs array for "
	<< dof_id << " has already been registered");
	}

	dof.blocked_dofs = &blocked_dofs;
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix &
	DOFManager::registerSparseMatrix(const ID & matrix_id,
	std::unique_ptr<SparseMatrix> & matrix) {
	auto it = this->matrices.find(matrix_id);
	if (it != this->matrices.end()) {
	AKANTU_EXCEPTION("The matrix " << matrix_id << " already exists in "
	<< this->id);
	}

	auto & ret = *matrix;
	this->matrices[matrix_id] = std::move(matrix);
	return ret;
	}

	/* -------------------------------------------------------------------------- */
	/// Get an instance of a new SparseMatrix
	SolverVector &
	DOFManager::registerLumpedMatrix(const ID & matrix_id,
	std::unique_ptr<SolverVector> & matrix) {
	auto it = this->lumped_matrices.find(matrix_id);
	if (it != this->lumped_matrices.end()) {
	AKANTU_EXCEPTION("The lumped matrix " << matrix_id << " already exists in "
	<< this->id);
	}

	auto & ret = *matrix;
	this->lumped_matrices[matrix_id] = std::move(matrix);
	ret.resize();
	return ret;
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver & DOFManager::registerNonLinearSolver(
	const ID & non_linear_solver_id,
	std::unique_ptr<NonLinearSolver> & non_linear_solver) {
	NonLinearSolversMap::const_iterator it =
	this->non_linear_solvers.find(non_linear_solver_id);
	if (it != this->non_linear_solvers.end()) {
	AKANTU_EXCEPTION("The non linear solver " << non_linear_solver_id
	<< " already exists in "
	<< this->id);
	}

	NonLinearSolver & ret = *non_linear_solver;
	this->non_linear_solvers[non_linear_solver_id] = std::move(non_linear_solver);

	return ret;
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & DOFManager::registerTimeStepSolver(
	const ID & time_step_solver_id,
	std::unique_ptr<TimeStepSolver> & time_step_solver) {
	TimeStepSolversMap::const_iterator it =
	this->time_step_solvers.find(time_step_solver_id);
	if (it != this->time_step_solvers.end()) {
	AKANTU_EXCEPTION("The non linear solver " << time_step_solver_id
	<< " already exists in "
	<< this->id);
	}

	TimeStepSolver & ret = *time_step_solver;
	this->time_step_solvers[time_step_solver_id] = std::move(time_step_solver);
	return ret;
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManager::getMatrix(const ID & id) {
	ID matrix_id = this->id + ":mtx:" + id;
	SparseMatricesMap::const_iterator it = this->matrices.find(matrix_id);
	if (it == this->matrices.end()) {
	AKANTU_SILENT_EXCEPTION("The matrix " << matrix_id << " does not exists in "
	<< this->id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	bool DOFManager::hasMatrix(const ID & id) const {
	ID mtx_id = this->id + ":mtx:" + id;
	auto it = this->matrices.find(mtx_id);
	return it != this->matrices.end();
	}

	/* -------------------------------------------------------------------------- */
	SolverVector & DOFManager::getLumpedMatrix(const ID & id) {
	ID matrix_id = this->id + ":lumped_mtx:" + id;
	LumpedMatricesMap::const_iterator it = this->lumped_matrices.find(matrix_id);
	if (it == this->lumped_matrices.end()) {
	AKANTU_SILENT_EXCEPTION("The lumped matrix "
	<< matrix_id << " does not exists in " << this->id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	const SolverVector & DOFManager::getLumpedMatrix(const ID & id) const {
	ID matrix_id = this->id + ":lumped_mtx:" + id;
	auto it = this->lumped_matrices.find(matrix_id);
	if (it == this->lumped_matrices.end()) {
	AKANTU_SILENT_EXCEPTION("The lumped matrix "
	<< matrix_id << " does not exists in " << this->id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	bool DOFManager::hasLumpedMatrix(const ID & id) const {
	ID mtx_id = this->id + ":lumped_mtx:" + id;
	auto it = this->lumped_matrices.find(mtx_id);
	return it != this->lumped_matrices.end();
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver & DOFManager::getNonLinearSolver(const ID & id) {
	ID non_linear_solver_id = this->id + ":nls:" + id;
	NonLinearSolversMap::const_iterator it =
	this->non_linear_solvers.find(non_linear_solver_id);
	if (it == this->non_linear_solvers.end()) {
	AKANTU_EXCEPTION("The non linear solver " << non_linear_solver_id
	<< " does not exists in "
	<< this->id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	bool DOFManager::hasNonLinearSolver(const ID & id) const {
	ID solver_id = this->id + ":nls:" + id;
	auto it = this->non_linear_solvers.find(solver_id);
	return it != this->non_linear_solvers.end();
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & DOFManager::getTimeStepSolver(const ID & id) {
	ID time_step_solver_id = this->id + ":tss:" + id;
	TimeStepSolversMap::const_iterator it =
	this->time_step_solvers.find(time_step_solver_id);
	if (it == this->time_step_solvers.end()) {
	AKANTU_EXCEPTION("The non linear solver " << time_step_solver_id
	<< " does not exists in "
	<< this->id);
	}

	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	bool DOFManager::hasTimeStepSolver(const ID & solver_id) const {
	ID time_step_solver_id = this->id + ":tss:" + solver_id;
	auto it = this->time_step_solvers.find(time_step_solver_id);
	return it != this->time_step_solvers.end();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::savePreviousDOFs(const ID & dofs_id) {
	this->getPreviousDOFs(dofs_id).copy(this->getDOFs(dofs_id));
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::zeroResidual() { this->residual->zero(); }

	/* -------------------------------------------------------------------------- */
	void DOFManager::zeroMatrix(const ID & mtx) { this->getMatrix(mtx).zero(); }

	/* -------------------------------------------------------------------------- */
	void DOFManager::zeroLumpedMatrix(const ID & mtx) {
	this->getLumpedMatrix(mtx).zero();
	}

	/* -------------------------------------------------------------------------- */
	/* Mesh Events */
	/* -------------------------------------------------------------------------- */
	std::pair<UInt, UInt>
	DOFManager::updateNodalDOFs(const ID & dof_id, const Array<UInt> & nodes_list) {
	auto & dof_data = this->getDOFData(dof_id);
	UInt nb_new_local_dofs;
	UInt nb_new_pure_local;

	std::tie(nb_new_local_dofs, nb_new_pure_local) =
	countDOFsForNodes(dof_data, nodes_list.size(),
	[&nodes_list](auto && n) { return nodes_list(n); });

	this->pure_local_system_size += nb_new_pure_local;
	this->local_system_size += nb_new_local_dofs;

	UInt nb_new_global = nb_new_pure_local;
	communicator.allReduce(nb_new_global, SynchronizerOperation::_sum);

	this->system_size += nb_new_global;

	dof_data.solution.resize(local_system_size);

	updateDOFsData(dof_data, nb_new_local_dofs, nb_new_pure_local,
	nodes_list.size(),
	[&nodes_list](UInt pos) -> UInt { return nodes_list[pos]; });

	return std::make_pair(nb_new_local_dofs, nb_new_pure_local);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::resizeGlobalArrays() {
	// resize all relevant arrays
	this->residual->resize();
	this->solution->resize();
	this->data_cache->resize();

	for (auto & lumped_matrix : lumped_matrices) {
	lumped_matrix.second->resize();
	}

	for (auto & matrix : matrices) {
	matrix.second->clearProfile();
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & /unused/) {
	for (auto & pair : this->dofs) {
	const auto & dof_id = pair.first;
	auto & dof_data = this->getDOFData(dof_id);
	if (dof_data.support_type != _dst_nodal) {
	continue;
	}

	const auto & group = dof_data.group_support;

	if (group == "__mesh__") {
	this->updateNodalDOFs(dof_id, nodes_list);
	} else {
	const auto & node_group =
	this->mesh->getElementGroup(group).getNodeGroup();
	Array<UInt> new_nodes_list;
	for (const auto & node : nodes_list) {
	if (node_group.find(node) != UInt(-1)) {
	new_nodes_list.push_back(node);
	}
	}

	this->updateNodalDOFs(dof_id, new_nodes_list);
	}
	}

	this->resizeGlobalArrays();
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	class GlobalDOFInfoDataAccessor : public DataAccessor<UInt> {
	public:
	using size_type =
	typename std::unordered_map<UInt, std::vector<UInt>>::size_type;

	GlobalDOFInfoDataAccessor(DOFManager::DOFData & dof_data,
	DOFManager & dof_manager)
	: dof_data(dof_data), dof_manager(dof_manager) {
	for (auto && pair :
	zip(dof_data.local_equation_number, dof_data.associated_nodes)) {
	UInt node;
	Int dof;
	std::tie(dof, node) = pair;

	dofs_per_node[node].push_back(dof);
	}
	}

	UInt getNbData(const Array<UInt> & nodes,
	const SynchronizationTag & tag) const override {
	if (tag == SynchronizationTag::_ask_nodes or
	tag == SynchronizationTag::_giu_global_conn) {
	return nodes.size() * dof_data.dof->getNbComponent() * sizeof(Int);
	}

	return 0;
	}

	void packData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag & tag) const override {
	if (tag == SynchronizationTag::_ask_nodes or
	tag == SynchronizationTag::_giu_global_conn) {
	for (const auto & node : nodes) {
	const auto & dofs = dofs_per_node.at(node);
	for (const auto & dof : dofs) {
	buffer << dof_manager.global_equation_number(dof);
	}
	}
	}
	}

	void unpackData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag & tag) override {
	if (tag == SynchronizationTag::_ask_nodes or
	tag == SynchronizationTag::_giu_global_conn) {
	for (const auto & node : nodes) {
	const auto & dofs = dofs_per_node[node];
	for (const auto & dof : dofs) {
	Int global_dof;
	buffer >> global_dof;
	AKANTU_DEBUG_ASSERT(
	(dof_manager.global_equation_number(dof) == -1 or
	dof_manager.global_equation_number(dof) == global_dof),
	"This dof already had a global_dof_id which is different from "
	"the received one. "
	<< dof_manager.global_equation_number(dof)
	<< " != " << global_dof);
	dof_manager.global_equation_number(dof) = global_dof;
	dof_manager.global_to_local_mapping[global_dof] = dof;
	}
	}
	}
	}

	protected:
	std::unordered_map<UInt, std::vector<Int>> dofs_per_node;
	DOFManager::DOFData & dof_data;
	DOFManager & dof_manager;
	};

	/* -------------------------------------------------------------------------- */
	auto DOFManager::computeFirstDOFIDs(UInt nb_new_local_dofs,
	UInt nb_new_pure_local) {
	// determine the first local/global dof id to use
	UInt offset = 0;

	this->communicator.exclusiveScan(nb_new_pure_local, offset);

	auto first_global_dof_id = this->first_global_dof_id + offset;
	auto first_local_dof_id = this->local_system_size - nb_new_local_dofs;

	offset = nb_new_pure_local;
	this->communicator.allReduce(offset);
	this->first_global_dof_id += offset;

	return std::make_pair(first_local_dof_id, first_global_dof_id);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
	UInt nb_new_pure_local, UInt nb_node,
	const std::function<UInt(UInt)> & getNode) {
	auto nb_local_dofs_added = nb_node * dof_data.dof->getNbComponent();

	auto first_dof_pos = dof_data.local_equation_number.size();
	dof_data.local_equation_number.reserve(dof_data.local_equation_number.size() +
	nb_local_dofs_added);
	dof_data.associated_nodes.reserve(dof_data.associated_nodes.size() +
	nb_local_dofs_added);

	this->dofs_flag.resize(this->local_system_size, NodeFlag::_normal);
	this->global_equation_number.resize(this->local_system_size, -1);

	std::unordered_map<std::pair<UInt, UInt>, UInt> masters_dofs;

	// update per dof info
	UInt local_eq_num;
	UInt first_global_dof_id;
	std::tie(local_eq_num, first_global_dof_id) =
	computeFirstDOFIDs(nb_new_local_dofs, nb_new_pure_local);
	for (auto d : arange(nb_local_dofs_added)) {
	auto node = getNode(d / dof_data.dof->getNbComponent());
	auto dof_flag = this->mesh->getNodeFlag(node);

	dof_data.associated_nodes.push_back(node);
	auto is_local_dof = this->mesh->isLocalOrMasterNode(node);
	auto is_periodic_slave = this->mesh->isPeriodicSlave(node);
	auto is_periodic_master = this->mesh->isPeriodicMaster(node);

	if (is_periodic_slave) {
	dof_data.local_equation_number.push_back(-1);
	continue;
	}

	// update equation numbers
	this->dofs_flag(local_eq_num) = dof_flag;
	dof_data.local_equation_number.push_back(local_eq_num);

	if (is_local_dof) {
	this->global_equation_number(local_eq_num) = first_global_dof_id;
	this->global_to_local_mapping[first_global_dof_id] = local_eq_num;
	++first_global_dof_id;
	} else {
	this->global_equation_number(local_eq_num) = -1;
	}

	if (is_periodic_master) {
	auto node = getNode(d / dof_data.dof->getNbComponent());
	auto dof = d % dof_data.dof->getNbComponent();
	masters_dofs.insert(
	std::make_pair(std::make_pair(node, dof), local_eq_num));
	}

	++local_eq_num;
	}

	// correct periodic slave equation numbers
	if (this->mesh->isPeriodic()) {
	auto assoc_begin = dof_data.associated_nodes.begin();
	for (auto d : arange(nb_local_dofs_added)) {
	auto node = dof_data.associated_nodes(first_dof_pos + d);
	if (not this->mesh->isPeriodicSlave(node)) {
	continue;
	}

	auto master_node = this->mesh->getPeriodicMaster(node);
	auto dof = d % dof_data.dof->getNbComponent();
	dof_data.local_equation_number(first_dof_pos + d) =
	masters_dofs[std::make_pair(master_node, dof)];
	}
	}

	// synchronize the global numbering for slaves nodes
	if (this->mesh->isDistributed()) {
	GlobalDOFInfoDataAccessor data_accessor(dof_data, *this);

	if (this->mesh->isPeriodic()) {
	mesh->getPeriodicNodeSynchronizer().synchronizeOnce(
	data_accessor, SynchronizationTag::_giu_global_conn);
	}

	auto & node_synchronizer = this->mesh->getNodeSynchronizer();
	node_synchronizer.synchronizeOnce(data_accessor,
	SynchronizationTag::_ask_nodes);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
	UInt nb_new_pure_local) {
	dof_data.local_equation_number.reserve(dof_data.local_equation_number.size() +
	nb_new_local_dofs);

	UInt first_local_dof_id;
	UInt first_global_dof_id;
	std::tie(first_local_dof_id, first_global_dof_id) =
	computeFirstDOFIDs(nb_new_local_dofs, nb_new_pure_local);

	this->dofs_flag.resize(this->local_system_size, NodeFlag::_normal);
	this->global_equation_number.resize(this->local_system_size, -1);

	// update per dof info
	for (auto _ [[gnu::unused]] : arange(nb_new_local_dofs)) {
	// update equation numbers
	this->dofs_flag(first_local_dof_id) = NodeFlag::_normal;

	dof_data.local_equation_number.push_back(first_local_dof_id);

	this->global_equation_number(first_local_dof_id) = first_global_dof_id;
	this->global_to_local_mapping[first_global_dof_id] = first_local_dof_id;

	++first_global_dof_id;
	++first_local_dof_id;
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::onNodesRemoved(const Array<UInt> & /unused/,
	const Array<UInt> & /unused/,
	const RemovedNodesEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	void DOFManager::onElementsAdded(const Array<Element> & /unused/,
	const NewElementsEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	void DOFManager::onElementsRemoved(const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const RemovedElementsEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	void DOFManager::onElementsChanged(const Array<Element> & /unused/,
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) {}

	/* -------------------------------------------------------------------------- */
	void DOFManager::updateGlobalBlockedDofs() {
	this->previous_global_blocked_dofs.copy(this->global_blocked_dofs);
	this->global_blocked_dofs.reserve(this->local_system_size, 0);
	this->previous_global_blocked_dofs_release =
	this->global_blocked_dofs_release;

	for (auto & pair : dofs) {
	if (not this->hasBlockedDOFs(pair.first)) {
	continue;
	}

	DOFData & dof_data = *pair.second;
	for (auto && data : zip(dof_data.getLocalEquationsNumbers(),
	make_view(*dof_data.blocked_dofs))) {
	const auto & dof = std::get<0>(data);
	const auto & is_blocked = std::get<1>(data);
	if (is_blocked) {
	this->global_blocked_dofs.push_back(dof);
	}
	}
	}

	std::sort(this->global_blocked_dofs.begin(), this->global_blocked_dofs.end());
	auto last = std::unique(this->global_blocked_dofs.begin(),
	this->global_blocked_dofs.end());
	this->global_blocked_dofs.resize(last - this->global_blocked_dofs.begin());

	auto are_equal =
	global_blocked_dofs.size() == previous_global_blocked_dofs.size() and
	std::equal(global_blocked_dofs.begin(), global_blocked_dofs.end(),
	previous_global_blocked_dofs.begin());

	if (not are_equal) {
	++this->global_blocked_dofs_release;
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::applyBoundary(const ID & matrix_id) {
	auto & J = this->getMatrix(matrix_id);

	if (this->jacobian_release == J.getRelease()) {
	if (this->hasBlockedDOFsChanged()) {
	J.applyBoundary();
	}

	previous_global_blocked_dofs.copy(global_blocked_dofs);
	} else {
	J.applyBoundary();
	}

	this->jacobian_release = J.getRelease();
	this->previous_global_blocked_dofs_release =
	- this->global_blocked_dofs_release;
	+ this->global_blocked_dofs_release;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleMatMulVectToGlobalArray(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	SolverVector & array,
	Real scale_factor) {
	auto & A = this->getMatrix(A_id);

	data_cache->resize();
	data_cache->zero();
	this->assembleToGlobalArray(dof_id, x, *data_cache, 1.);

	A.matVecMul(*data_cache, array, scale_factor, 1.);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManager::assembleMatMulVectToResidual(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	Real scale_factor) {
	assembleMatMulVectToGlobalArray(dof_id, A_id, x, *residual, scale_factor);
	}

	} // namespace akantu
	diff --git a/src/model/common/dof_manager/dof_manager.hh b/src/model/common/dof_manager/dof_manager.hh
	index 2b3e6362a..adb40379c 100644
	--- a/src/model/common/dof_manager/dof_manager.hh
	+++ b/src/model/common/dof_manager/dof_manager.hh
	@@ -1,723 +1,719 @@
	/**
	* @file dof_manager.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Class handling the different types of dofs
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_factory.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	#include <set>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_MANAGER_HH_
	#define AKANTU_DOF_MANAGER_HH_

	namespace akantu {
	class TermsToAssemble;
	class NonLinearSolver;
	class TimeStepSolver;
	class SparseMatrix;
	class SolverVector;
	class SolverCallback;
	} // namespace akantu

	namespace akantu {

	class DOFManager : protected MeshEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	protected:
	struct DOFData;

	public:
	DOFManager(const ID & id = "dof_manager");
	DOFManager(Mesh & mesh, const ID & id = "dof_manager");
	~DOFManager() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// register an array of degree of freedom
	virtual void registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	const DOFSupportType & support_type);

	/// the dof as an implied type of _dst_nodal and is defined only on a subset
	/// of nodes
	virtual void registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	const ID & support_group);

	/// register an array of previous values of the degree of freedom
	virtual void registerDOFsPrevious(const ID & dof_id,
	Array<Real> & dofs_array);

	/// register an array of increment of degree of freedom
	virtual void registerDOFsIncrement(const ID & dof_id,
	Array<Real> & dofs_array);

	/// register an array of derivatives for a particular dof array
	virtual void registerDOFsDerivative(const ID & dof_id, UInt order,
	Array<Real> & dofs_derivative);

	/// register array representing the blocked degree of freedoms
	virtual void registerBlockedDOFs(const ID & dof_id,
	Array<bool> & blocked_dofs);

	/// Assemble an array to the global residual array
	virtual void assembleToResidual(const ID & dof_id,
	Array<Real> & array_to_assemble,
	Real scale_factor = 1.);

	/// Assemble an array to the global lumped matrix array
	virtual void assembleToLumpedMatrix(const ID & dof_id,
	Array<Real> & array_to_assemble,
	const ID & lumped_mtx,
	Real scale_factor = 1.);

	/**
	* Assemble elementary values to a local array of the size nb_nodes *
	* nb_dof_per_node. The dof number is implicitly considered as
	* conn(el, n) * nb_nodes_per_element + d.
	* With 0 < n < nb_nodes_per_element and 0 < d < nb_dof_per_node
	**/
	virtual void assembleElementalArrayLocalArray(
	const Array<Real> & elementary_vect, Array<Real> & array_assembeled,
	- ElementType type, GhostType ghost_type,
	- Real scale_factor = 1.,
	+ ElementType type, GhostType ghost_type, Real scale_factor = 1.,
	const Array<UInt> & filter_elements = empty_filter);

	/**
	* Assemble elementary values to the global residual array. The dof number is
	* implicitly considered as conn(el, n) * nb_nodes_per_element + d.
	* With 0 < n < nb_nodes_per_element and 0 < d < nb_dof_per_node
	**/
	virtual void assembleElementalArrayToResidual(
	- const ID & dof_id, const Array<Real> & elementary_vect,
	- ElementType type, GhostType ghost_type,
	- Real scale_factor = 1.,
	+ const ID & dof_id, const Array<Real> & elementary_vect, ElementType type,
	+ GhostType ghost_type, Real scale_factor = 1.,
	const Array<UInt> & filter_elements = empty_filter);

	/**
	* Assemble elementary values to a global array corresponding to a lumped
	* matrix
	*/
	virtual void assembleElementalArrayToLumpedMatrix(
	const ID & dof_id, const Array<Real> & elementary_vect,
	- const ID & lumped_mtx, ElementType type,
	- GhostType ghost_type, Real scale_factor = 1.,
	+ const ID & lumped_mtx, ElementType type, GhostType ghost_type,
	+ Real scale_factor = 1.,
	const Array<UInt> & filter_elements = empty_filter);

	/**
	* Assemble elementary values to the global residual array. The dof number is
	* implicitly considered as conn(el, n) * nb_nodes_per_element + d. With 0 <
	* n < nb_nodes_per_element and 0 < d < nb_dof_per_node
	**/
	virtual void assembleElementalMatricesToMatrix(
	const ID & matrix_id, const ID & dof_id,
	const Array<Real> & elementary_mat, ElementType type,
	GhostType ghost_type = _not_ghost,
	const MatrixType & elemental_matrix_type = _symmetric,
	const Array<UInt> & filter_elements = empty_filter) = 0;

	/// multiply a vector by a matrix and assemble the result to the residual
	virtual void assembleMatMulVectToArray(const ID & dof_id, const ID & A_id,
	const Array<Real> & x,
	Array<Real> & array,
	Real scale_factor = 1) = 0;

	/// multiply a vector by a lumped matrix and assemble the result to the
	/// residual
	virtual void assembleLumpedMatMulVectToResidual(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	Real scale_factor = 1) = 0;

	/// assemble coupling terms between to dofs
	virtual void assemblePreassembledMatrix(const ID & dof_id_m,
	const ID & dof_id_n,
	const ID & matrix_id,
	const TermsToAssemble & terms) = 0;

	/// multiply a vector by a matrix and assemble the result to the residual
	virtual void assembleMatMulVectToResidual(const ID & dof_id, const ID & A_id,
	const Array<Real> & x,
	Real scale_factor = 1);

	/// multiply the dofs by a matrix and assemble the result to the residual
	virtual void assembleMatMulDOFsToResidual(const ID & A_id,
	Real scale_factor = 1);

	/// updates the global blocked_dofs array
	virtual void updateGlobalBlockedDofs();

	/// sets the residual to 0
	virtual void zeroResidual();
	/// sets the matrix to 0
	virtual void zeroMatrix(const ID & mtx);
	/// sets the lumped matrix to 0
	virtual void zeroLumpedMatrix(const ID & mtx);

	virtual void applyBoundary(const ID & matrix_id = "J");
	// virtual void applyBoundaryLumped(const ID & matrix_id = "J");

	/// extract a lumped matrix part corresponding to a given dof
	virtual void getLumpedMatrixPerDOFs(const ID & dof_id, const ID & lumped_mtx,
	Array<Real> & lumped);

	/// splits the solution storage from a global view to the per dof storages
	void splitSolutionPerDOFs();

	private:
	/// dispatch the creation of the dof data and register it
	DOFData & getNewDOFDataInternal(const ID & dof_id);

	protected:
	/// common function to help registering dofs the return values are the add new
	/// numbers of local dofs, pure local dofs, and system size
	virtual std::tuple<UInt, UInt, UInt>
	registerDOFsInternal(const ID & dof_id, Array<Real> & dofs_array);

	/// minimum functionality to implement per derived version of the DOFManager
	/// to allow the splitSolutionPerDOFs function to work
	virtual void getSolutionPerDOFs(const ID & dof_id,
	Array<Real> & solution_array);

	/// fill a Vector with the equation numbers corresponding to the given
	/// connectivity
	static inline void extractElementEquationNumber(
	const Array<Int> & equation_numbers, const Vector<UInt> & connectivity,
	UInt nb_degree_of_freedom, Vector<Int> & element_equation_number);

	/// Assemble a array to a global one
	void assembleMatMulVectToGlobalArray(const ID & dof_id, const ID & A_id,
	const Array<Real> & x,
	SolverVector & array,
	Real scale_factor = 1.);

	/// common function that can be called by derived class with proper matrice
	/// types
	template <typename Mat>
	void assemblePreassembledMatrix_(Mat & A, const ID & dof_id_m,
	const ID & dof_id_n,
	const TermsToAssemble & terms);

	template <typename Mat>
	- void assembleElementalMatricesToMatrix_(
	- Mat & A, const ID & dof_id, const Array<Real> & elementary_mat,
	- ElementType type, GhostType ghost_type,
	- const MatrixType & elemental_matrix_type,
	- const Array<UInt> & filter_elements);
	+ void
	+ assembleElementalMatricesToMatrix_(Mat & A, const ID & dof_id,
	+ const Array<Real> & elementary_mat,
	+ ElementType type, GhostType ghost_type,
	+ const MatrixType & elemental_matrix_type,
	+ const Array<UInt> & filter_elements);

	template <typename Vec>
	void assembleMatMulVectToArray_(const ID & dof_id, const ID & A_id,
	const Array<Real> & x, Array<Real> & array,
	Real scale_factor);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Get the location type of a given dof
	inline bool isLocalOrMasterDOF(UInt local_dof_num);

	/// Answer to the question is a dof a slave dof ?
	inline bool isSlaveDOF(UInt local_dof_num);

	/// Answer to the question is a dof a slave dof ?
	inline bool isPureGhostDOF(UInt local_dof_num);

	/// tells if the dof manager knows about a global dof
	bool hasGlobalEquationNumber(Int global) const;

	/// return the local index of the global equation number
	inline Int globalToLocalEquationNumber(Int global) const;

	/// converts local equation numbers to global equation numbers;
	inline Int localToGlobalEquationNumber(Int local) const;

	/// get the array of dof types (use only if you know what you do...)
	inline NodeFlag getDOFFlag(Int local_id) const;

	/// defines if the boundary changed
	- bool hasBlockedDOFsChanged() {
	- return this->global_blocked_dofs_release !=
	- this->previous_global_blocked_dofs_release;
	+ bool hasBlockedDOFsChanged() const {
	+ return this->global_blocked_dofs_release !=
	+ this->previous_global_blocked_dofs_release;
	}

	/// Global number of dofs
	AKANTU_GET_MACRO(SystemSize, this->system_size, UInt);

	/// Local number of dofs
	AKANTU_GET_MACRO(LocalSystemSize, this->local_system_size, UInt);

	/// Pure local number of dofs
	AKANTU_GET_MACRO(PureLocalSystemSize, this->pure_local_system_size, UInt);

	/// Retrieve all the registered DOFs
	std::vector<ID> getDOFIDs() const;

	/* ------------------------------------------------------------------------ */
	/* DOFs and derivatives accessors */
	/* ------------------------------------------------------------------------ */
	/// Get a reference to the registered dof array for a given id
	inline Array<Real> & getDOFs(const ID & dofs_id);

	/// Get the support type of a given dof
	inline DOFSupportType getSupportType(const ID & dofs_id) const;

	/// are the dofs registered
	inline bool hasDOFs(const ID & dof_id) const;

	/// Get a reference to the registered dof derivatives array for a given id
	inline Array<Real> & getDOFsDerivatives(const ID & dofs_id, UInt order);

	/// Does the dof has derivatives
	inline bool hasDOFsDerivatives(const ID & dofs_id, UInt order) const;

	/// Get a reference to the blocked dofs array registered for the given id
	inline const Array<bool> & getBlockedDOFs(const ID & dofs_id) const;

	/// Does the dof has a blocked array
	inline bool hasBlockedDOFs(const ID & dofs_id) const;

	/// Get a reference to the registered dof increment array for a given id
	inline Array<Real> & getDOFsIncrement(const ID & dofs_id);

	/// Does the dof has a increment array
	inline bool hasDOFsIncrement(const ID & dofs_id) const;

	/// Does the dof has a previous array
	inline Array<Real> & getPreviousDOFs(const ID & dofs_id);

	/// Get a reference to the registered dof array for previous step values a
	/// given id
	inline bool hasPreviousDOFs(const ID & dofs_id) const;

	/// saves the values from dofs to previous dofs
	virtual void savePreviousDOFs(const ID & dofs_id);

	/// Get a reference to the solution array registered for the given id
	inline const Array<Real> & getSolution(const ID & dofs_id) const;

	/// Get a reference to the solution array registered for the given id
	inline Array<Real> & getSolution(const ID & dofs_id);

	/// Get the blocked dofs array
	AKANTU_GET_MACRO(GlobalBlockedDOFs, global_blocked_dofs, const Array<Int> &);
	/// Get the blocked dofs array
	AKANTU_GET_MACRO(PreviousGlobalBlockedDOFs, previous_global_blocked_dofs,
	const Array<Int> &);

	/* ------------------------------------------------------------------------ */
	/* Matrices accessors */
	/* ------------------------------------------------------------------------ */
	/// Get an instance of a new SparseMatrix
	virtual SparseMatrix & getNewMatrix(const ID & matrix_id,
	const MatrixType & matrix_type) = 0;

	/// Get an instance of a new SparseMatrix as a copy of the SparseMatrix
	/// matrix_to_copy_id
	virtual SparseMatrix & getNewMatrix(const ID & matrix_id,
	const ID & matrix_to_copy_id) = 0;

	/// Get the equation numbers corresponding to a dof_id. This might be used to
	/// access the matrix.
	inline const Array<Int> & getLocalEquationsNumbers(const ID & dof_id) const;

	protected:
	/// get the array of dof types (use only if you know what you do...)
	inline const Array<UInt> & getDOFsAssociatedNodes(const ID & dof_id) const;

	protected:
	/* ------------------------------------------------------------------------ */
	/// register a matrix
	SparseMatrix & registerSparseMatrix(const ID & matrix_id,
	std::unique_ptr<SparseMatrix> & matrix);

	/// register a lumped matrix (aka a Vector)
	SolverVector & registerLumpedMatrix(const ID & matrix_id,
	std::unique_ptr<SolverVector> & matrix);

	/// register a non linear solver instantiated by a derived class
	NonLinearSolver &
	registerNonLinearSolver(const ID & non_linear_solver_id,
	std::unique_ptr<NonLinearSolver> & non_linear_solver);

	/// register a time step solver instantiated by a derived class
	TimeStepSolver &
	registerTimeStepSolver(const ID & time_step_solver_id,
	std::unique_ptr<TimeStepSolver> & time_step_solver);

	template <class NLSType, class DMType>
	NonLinearSolver & registerNonLinearSolver(DMType & dm, const ID & id,
	const NonLinearSolverType & type) {
	ID non_linear_solver_id = this->id + ":nls:" + id;
	- std::unique_ptr<NonLinearSolver> nls = std::make_unique<NLSType>(
	- dm, type, non_linear_solver_id);
	+ std::unique_ptr<NonLinearSolver> nls =
	+ std::make_unique<NLSType>(dm, type, non_linear_solver_id);
	return this->registerNonLinearSolver(non_linear_solver_id, nls);
	}

	template <class TSSType, class DMType>
	TimeStepSolver & registerTimeStepSolver(DMType & dm, const ID & id,
	const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback) {
	ID time_step_solver_id = this->id + ":tss:" + id;
	- std::unique_ptr<TimeStepSolver> tss =
	- std::make_unique<TSSType>(dm, type, non_linear_solver, solver_callback,
	- time_step_solver_id);
	+ std::unique_ptr<TimeStepSolver> tss = std::make_unique<TSSType>(
	+ dm, type, non_linear_solver, solver_callback, time_step_solver_id);
	return this->registerTimeStepSolver(time_step_solver_id, tss);
	}

	template <class MatType, class DMType>
	SparseMatrix & registerSparseMatrix(DMType & dm, const ID & id,
	const MatrixType & matrix_type) {
	ID matrix_id = this->id + ":mtx:" + id;
	std::unique_ptr<SparseMatrix> sm =
	std::make_unique<MatType>(dm, matrix_type, matrix_id);
	return this->registerSparseMatrix(matrix_id, sm);
	}

	template <class MatType>
	SparseMatrix & registerSparseMatrix(const ID & id,
	const ID & matrix_to_copy_id) {
	ID matrix_id = this->id + ":mtx:" + id;
	auto & sm_to_copy =
	aka::as_type<MatType>(this->getMatrix(matrix_to_copy_id));
	std::unique_ptr<SparseMatrix> sm =
	std::make_unique<MatType>(sm_to_copy, matrix_id);
	return this->registerSparseMatrix(matrix_id, sm);
	}

	template <class MatType, class DMType>
	SolverVector & registerLumpedMatrix(DMType & dm, const ID & id) {
	ID matrix_id = this->id + ":lumped_mtx:" + id;
	std::unique_ptr<SolverVector> sm = std::make_unique<MatType>(dm, matrix_id);
	return this->registerLumpedMatrix(matrix_id, sm);
	}

	protected:
	virtual void makeConsistentForPeriodicity(const ID & dof_id,
	SolverVector & array) = 0;

	virtual void assembleToGlobalArray(const ID & dof_id,
	const Array<Real> & array_to_assemble,
	SolverVector & global_array,
	Real scale_factor) = 0;

	public:
	/// extract degrees of freedom (identified by ID) from a global solver array
	virtual void getArrayPerDOFs(const ID & dof_id, const SolverVector & global,
	Array<Real> & local) = 0;

	/// Get the reference of an existing matrix
	SparseMatrix & getMatrix(const ID & matrix_id);

	/// check if the given matrix exists
	bool hasMatrix(const ID & matrix_id) const;

	/// Get an instance of a new lumped matrix
	virtual SolverVector & getNewLumpedMatrix(const ID & matrix_id) = 0;
	/// Get the lumped version of a given matrix
	const SolverVector & getLumpedMatrix(const ID & matrix_id) const;
	/// Get the lumped version of a given matrix
	SolverVector & getLumpedMatrix(const ID & matrix_id);

	/// check if the given matrix exists
	bool hasLumpedMatrix(const ID & matrix_id) const;

	/* ------------------------------------------------------------------------ */
	/* Non linear system solver */
	/* ------------------------------------------------------------------------ */
	/// Get instance of a non linear solver
	virtual NonLinearSolver & getNewNonLinearSolver(
	const ID & nls_solver_id,
	const NonLinearSolverType & _non_linear_solver_type) = 0;

	/// get instance of a non linear solver
	virtual NonLinearSolver & getNonLinearSolver(const ID & nls_solver_id);

	/// check if the given solver exists
	bool hasNonLinearSolver(const ID & solver_id) const;

	/* ------------------------------------------------------------------------ */
	/* Time-Step Solver */
	/* ------------------------------------------------------------------------ */
	/// Get instance of a time step solver
	virtual TimeStepSolver &
	getNewTimeStepSolver(const ID & time_step_solver_id,
	const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback) = 0;

	/// get instance of a time step solver
	virtual TimeStepSolver & getTimeStepSolver(const ID & time_step_solver_id);

	/// check if the given solver exists
	bool hasTimeStepSolver(const ID & solver_id) const;

	/* ------------------------------------------------------------------------ */
	const Mesh & getMesh() {
	if (mesh != nullptr) {
	return *mesh;
	}
	AKANTU_EXCEPTION("No mesh registered in this dof manager");
	}

	/* ------------------------------------------------------------------------ */
	AKANTU_GET_MACRO(Communicator, communicator, const auto &);
	AKANTU_GET_MACRO_NOT_CONST(Communicator, communicator, auto &);

	/* ------------------------------------------------------------------------ */
	AKANTU_GET_MACRO(Solution, *(solution.get()), const auto &);
	AKANTU_GET_MACRO_NOT_CONST(Solution, *(solution.get()), auto &);

	AKANTU_GET_MACRO(Residual, *(residual.get()), const auto &);
	AKANTU_GET_MACRO_NOT_CONST(Residual, *(residual.get()), auto &);

	/* ------------------------------------------------------------------------ */
	/* MeshEventHandler interface */
	/* ------------------------------------------------------------------------ */
	protected:
	friend class GlobalDOFInfoDataAccessor;
	/// helper function for the DOFManager::onNodesAdded method
	virtual std::pair<UInt, UInt> updateNodalDOFs(const ID & dof_id,
	const Array<UInt> & nodes_list);

	template <typename Func>
	auto countDOFsForNodes(const DOFData & dof_data, UInt nb_nodes,
	Func && getNode);

	void updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
	UInt nb_new_pure_local, UInt nb_nodes,
	const std::function<UInt(UInt)> & getNode);

	void updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
	UInt nb_new_pure_local);

	auto computeFirstDOFIDs(UInt nb_new_local_dofs, UInt nb_new_pure_local);

	/// resize all the global information and takes the needed measure like
	/// cleaning matrices profiles
	virtual void resizeGlobalArrays();

	public:
	/// function to implement to react on akantu::NewNodesEvent
	void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) override;
	/// function to implement to react on akantu::RemovedNodesEvent
	void onNodesRemoved(const Array<UInt> & nodes_list,
	const Array<UInt> & new_numbering,
	const RemovedNodesEvent & event) override;
	/// function to implement to react on akantu::NewElementsEvent
	void onElementsAdded(const Array<Element> & elements_list,
	const NewElementsEvent & event) override;
	/// function to implement to react on akantu::RemovedElementsEvent
	void onElementsRemoved(const Array<Element> & elements_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) override;
	/// function to implement to react on akantu::ChangedElementsEvent
	void onElementsChanged(const Array<Element> & old_elements_list,
	const Array<Element> & new_elements_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const ChangedElementsEvent & event) override;

	protected:
	inline DOFData & getDOFData(const ID & dof_id);
	inline const DOFData & getDOFData(const ID & dof_id) const;
	template <class DOFData_>
	inline DOFData_ & getDOFDataTyped(const ID & dof_id);
	template <class DOFData_>
	inline const DOFData_ & getDOFDataTyped(const ID & dof_id) const;

	virtual std::unique_ptr<DOFData> getNewDOFData(const ID & dof_id) = 0;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// dof representations in the dof manager
	struct DOFData {
	DOFData() = delete;
	explicit DOFData(const ID & dof_id);
	virtual ~DOFData();

	/// DOF support type (nodal, general) this is needed to determine how the
	/// dof are shared among processors
	DOFSupportType support_type;

	ID group_support;

	/// Degree of freedom array
	Array<Real> * dof{nullptr};

	/// Blocked degree of freedoms array
	Array<bool> * blocked_dofs{nullptr};

	/// Degree of freedoms increment
	Array<Real> * increment{nullptr};

	/// Degree of freedoms at previous step
	Array<Real> * previous{nullptr};

	/// Solution associated to the dof
	Array<Real> solution;

	/* ---------------------------------------------------------------------- */
	/* data for dynamic simulations */
	/* ---------------------------------------------------------------------- */
	/// Degree of freedom derivatives arrays
	std::vector<Array<Real> *> dof_derivatives;

	/* ---------------------------------------------------------------------- */
	/// number of dofs to consider locally for this dof id
	UInt local_nb_dofs{0};

	/// Number of purely local dofs
	UInt pure_local_nb_dofs{0};

	/// number of ghost dofs
	UInt ghosts_nb_dofs{0};

	/// local numbering equation numbers
	Array<Int> local_equation_number;

	/// associated node for _dst_nodal dofs only
	Array<UInt> associated_nodes;

	virtual Array<Int> & getLocalEquationsNumbers() {
	return local_equation_number;
	}
	};

	/// type to store dofs information
	using DOFStorage = std::map<ID, std::unique_ptr<DOFData>>;

	/// type to store all the matrices
	using SparseMatricesMap = std::map<ID, std::unique_ptr<SparseMatrix>>;

	/// type to store all the lumped matrices
	using LumpedMatricesMap = std::map<ID, std::unique_ptr<SolverVector>>;

	/// type to store all the non linear solver
	using NonLinearSolversMap = std::map<ID, std::unique_ptr<NonLinearSolver>>;

	/// type to store all the time step solver
	using TimeStepSolversMap = std::map<ID, std::unique_ptr<TimeStepSolver>>;

	ID id;

	/// store a reference to the dof arrays
	DOFStorage dofs;

	/// list of sparse matrices that where created
	SparseMatricesMap matrices;

	/// list of lumped matrices
	LumpedMatricesMap lumped_matrices;

	/// non linear solvers storage
	NonLinearSolversMap non_linear_solvers;

	/// time step solvers storage
	TimeStepSolversMap time_step_solvers;

	/// reference to the underlying mesh
	Mesh * mesh{nullptr};

	/// Total number of degrees of freedom (size with the ghosts)
	UInt local_system_size{0};

	/// Number of purely local dofs (size without the ghosts)
	UInt pure_local_system_size{0};

	/// Total number of degrees of freedom
	UInt system_size{0};

	/// rhs to the system of equation corresponding to the residual linked to the
	/// different dofs
	std::unique_ptr<SolverVector> residual;

	/// solution of the system of equation corresponding to the different dofs
	std::unique_ptr<SolverVector> solution;

	/// a vector that helps internally to perform some tasks
	std::unique_ptr<SolverVector> data_cache;

	/// define the dofs type, local, shared, ghost
	Array<NodeFlag> dofs_flag;

	/// equation number in global numbering
	Array<Int> global_equation_number;

	using equation_numbers_map = std::unordered_map<Int, Int>;

	/// dual information of global_equation_number
	equation_numbers_map global_to_local_mapping;

	/// Communicator used for this manager, should be the same as in the mesh if a
	/// mesh is registered
	Communicator & communicator;

	/// accumulator to know what would be the next global id to use
	UInt first_global_dof_id{0};

	/// Release at last apply boundary on jacobian
	UInt jacobian_release{0};

	/// blocked degree of freedom in the system equation corresponding to the
	/// different dofs
	Array<Int> global_blocked_dofs;

	UInt global_blocked_dofs_release{0};

	/// blocked degree of freedom in the system equation corresponding to the
	/// different dofs
	Array<Int> previous_global_blocked_dofs;

	UInt previous_global_blocked_dofs_release{0};

	private:
	/// This is for unit testing
	friend class DOFManagerTester;
	};

	-using DefaultDOFManagerFactory =
	- Factory<DOFManager, ID, const ID &>;
	-using DOFManagerFactory =
	- Factory<DOFManager, ID, Mesh &, const ID &>;
	+using DefaultDOFManagerFactory = Factory<DOFManager, ID, const ID &>;
	+using DOFManagerFactory = Factory<DOFManager, ID, Mesh &, const ID &>;

	} // namespace akantu

	#include "dof_manager_inline_impl.hh"

	#endif /* AKANTU_DOF_MANAGER_HH_ */
	diff --git a/src/model/common/dof_manager/dof_manager_default.cc b/src/model/common/dof_manager/dof_manager_default.cc
	index feda05c7d..2c7bee9fd 100644
	--- a/src/model/common/dof_manager/dof_manager_default.cc
	+++ b/src/model/common/dof_manager/dof_manager_default.cc
	@@ -1,491 +1,490 @@
	/**
	* @file dof_manager_default.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Tue Mar 30 2021
	*
	* @brief Implementation of the default DOFManager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_default.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_group.hh"
	#include "non_linear_solver_default.hh"
	#include "periodic_node_synchronizer.hh"
	#include "solver_vector_default.hh"
	#include "solver_vector_distributed.hh"
	#include "sparse_matrix_aij.hh"
	#include "time_step_solver_default.hh"

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <memory>
	#include <numeric>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFManagerDefault(const ID & id)
	: DOFManager(id), synchronizer(nullptr) {
	residual = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":residual"));
	solution = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":solution"));
	data_cache = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":data_cache"));
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFManagerDefault(Mesh & mesh, const ID & id)
	: DOFManager(mesh, id), synchronizer(nullptr) {
	if (this->mesh->isDistributed()) {
	this->synchronizer = std::make_unique<DOFSynchronizer>(
	*this, this->id + ":dof_synchronizer");
	residual = std::make_unique<SolverVectorDistributed>(
	*this, std::string(id + ":residual"));
	solution = std::make_unique<SolverVectorDistributed>(
	*this, std::string(id + ":solution"));
	data_cache = std::make_unique<SolverVectorDistributed>(
	*this, std::string(id + ":data_cache"));

	} else {
	residual = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":residual"));
	solution = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":solution"));
	data_cache = std::make_unique<SolverVectorDefault>(
	*this, std::string(id + ":data_cache"));
	}
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::~DOFManagerDefault() = default;

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::makeConsistentForPeriodicity(const ID & dof_id,
	SolverVector & array) {
	auto & dof_data = this->getDOFDataTyped<DOFDataDefault>(dof_id);
	if (dof_data.support_type != _dst_nodal) {
	return;
	}

	if (not mesh->isPeriodic()) {
	return;
	}

	this->mesh->getPeriodicNodeSynchronizer()
	.reduceSynchronizeWithPBCSlaves<AddOperation>(
	aka::as_type<SolverVectorDefault>(array).getVector());
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void DOFManagerDefault::assembleToGlobalArray(
	const ID & dof_id, const Array<T> & array_to_assemble,
	Array<T> & global_array, T scale_factor) {
	AKANTU_DEBUG_IN();

	auto & dof_data = this->getDOFDataTyped<DOFDataDefault>(dof_id);
	AKANTU_DEBUG_ASSERT(dof_data.local_equation_number.size() ==
	array_to_assemble.size() *
	array_to_assemble.getNbComponent(),
	"The array to assemble does not have a correct size."
	<< " (" << array_to_assemble.getID() << ")");

	if (dof_data.support_type == _dst_nodal and mesh->isPeriodic()) {
	for (auto && data :
	zip(dof_data.local_equation_number, dof_data.associated_nodes,
	make_view(array_to_assemble))) {
	auto && equ_num = std::get<0>(data);
	// auto && node = std::get<1>(data);
	auto && arr = std::get<2>(data);

	// Guillaume to Nico:
	// This filter of periodic slave should not be.
	// Indeed you want to get the contribution even
	// from periodic slaves and cumulate to the right
	// equation number.

	global_array(equ_num) += scale_factor * (arr);
	// scale_factor * (arr) * (not this->mesh->isPeriodicSlave(node));
	}
	} else {
	for (auto && data :
	zip(dof_data.local_equation_number, make_view(array_to_assemble))) {
	auto && equ_num = std::get<0>(data);
	auto && arr = std::get<1>(data);
	global_array(equ_num) += scale_factor * (arr);
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleToGlobalArray(
	const ID & dof_id, const Array<Real> & array_to_assemble,
	SolverVector & global_array_v, Real scale_factor) {

	assembleToGlobalArray(
	dof_id, array_to_assemble,
	aka::as_type<SolverVectorDefault>(global_array_v).getVector(),
	scale_factor);
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFDataDefault::DOFDataDefault(const ID & dof_id)
	: DOFData(dof_id) {}

	/* -------------------------------------------------------------------------- */
	auto DOFManagerDefault::getNewDOFData(const ID & dof_id)
	-> std::unique_ptr<DOFData> {
	return std::make_unique<DOFDataDefault>(dof_id);
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<UInt, UInt, UInt>
	DOFManagerDefault::registerDOFsInternal(const ID & dof_id,
	Array<Real> & dofs_array) {
	auto ret = DOFManager::registerDOFsInternal(dof_id, dofs_array);

	// update the synchronizer if needed
	if (this->synchronizer) {
	this->synchronizer->registerDOFs(dof_id);
	}

	return ret;
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerDefault::getNewMatrix(const ID & id,
	const MatrixType & matrix_type) {
	return this->registerSparseMatrix<SparseMatrixAIJ>(*this, id, matrix_type);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerDefault::getNewMatrix(const ID & id,
	const ID & matrix_to_copy_id) {
	return this->registerSparseMatrix<SparseMatrixAIJ>(id, matrix_to_copy_id);
	}

	/* -------------------------------------------------------------------------- */
	SolverVector & DOFManagerDefault::getNewLumpedMatrix(const ID & id) {
	return this->registerLumpedMatrix<SolverVectorDefault>(*this, id);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrixAIJ & DOFManagerDefault::getMatrix(const ID & id) {
	auto & matrix = DOFManager::getMatrix(id);
	return aka::as_type<SparseMatrixAIJ>(matrix);
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver &
	DOFManagerDefault::getNewNonLinearSolver(const ID & id,
	const NonLinearSolverType & type) {
	switch (type) {
	#if defined(AKANTU_USE_MUMPS)
	case NonLinearSolverType::_newton_raphson:
	/* FALLTHRU */
	/* [[fallthrough]]; un-comment when compiler will get it */
	case NonLinearSolverType::_newton_raphson_contact:
	case NonLinearSolverType::_newton_raphson_modified: {
	return this->registerNonLinearSolver<NonLinearSolverNewtonRaphson>(
	*this, id, type);
	}
	case NonLinearSolverType::_linear: {
	return this->registerNonLinearSolver<NonLinearSolverLinear>(*this, id,
	type);
	}
	#endif
	case NonLinearSolverType::_lumped: {
	return this->registerNonLinearSolver<NonLinearSolverLumped>(*this, id,
	type);
	}
	default:
	AKANTU_EXCEPTION("The asked type of non linear solver is not supported by "
	"this dof manager");
	}
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & DOFManagerDefault::getNewTimeStepSolver(
	const ID & id, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver, SolverCallback & solver_callback) {
	return this->registerTimeStepSolver<TimeStepSolverDefault>(
	*this, id, type, non_linear_solver, solver_callback);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void DOFManagerDefault::getArrayPerDOFs(const ID & dof_id,
	const Array<T> & global_array,
	Array<T> & local_array) const {
	AKANTU_DEBUG_IN();

	const Array<Int> & equation_number = this->getLocalEquationsNumbers(dof_id);

	UInt nb_degree_of_freedoms = equation_number.size();
	local_array.resize(nb_degree_of_freedoms / local_array.getNbComponent());

	auto loc_it = local_array.begin_reinterpret(nb_degree_of_freedoms);
	auto equ_it = equation_number.begin();

	for (UInt d = 0; d < nb_degree_of_freedoms; ++d, ++loc_it, ++equ_it) {
	(loc_it) = global_array(equ_it);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::getArrayPerDOFs(const ID & dof_id,
	const SolverVector & global_array,
	Array<Real> & local_array) {
	getArrayPerDOFs(dof_id,
	aka::as_type<SolverVectorDefault>(global_array).getVector(),
	local_array);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleLumpedMatMulVectToResidual(
	const ID & dof_id, const ID & A_id, const Array<Real> & x,
	Real scale_factor) {
	const Array<Real> & A = this->getLumpedMatrix(A_id);
	auto & cache = aka::as_type<SolverVectorArray>(*this->data_cache);

	cache.zero();
	this->assembleToGlobalArray(dof_id, x, cache.getVector(), scale_factor);

	for (auto && data : zip(make_view(A), make_view(cache.getVector()),
	make_view(this->getResidualArray()))) {
	const auto & A = std::get<0>(data);
	const auto & x = std::get<1>(data);
	auto & r = std::get<2>(data);
	r += A * x;
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleElementalMatricesToMatrix(
	const ID & matrix_id, const ID & dof_id, const Array<Real> & elementary_mat,
	ElementType type, GhostType ghost_type,
	const MatrixType & elemental_matrix_type,
	const Array<UInt> & filter_elements) {
	this->addToProfile(matrix_id, dof_id, type, ghost_type);
	auto & A = getMatrix(matrix_id);
	DOFManager::assembleElementalMatricesToMatrix_(
	A, dof_id, elementary_mat, type, ghost_type, elemental_matrix_type,
	filter_elements);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assemblePreassembledMatrix(
	const ID & dof_id_m, const ID & dof_id_n, const ID & matrix_id,
	const TermsToAssemble & terms) {
	auto & A = getMatrix(matrix_id);
	DOFManager::assemblePreassembledMatrix_(A, dof_id_m, dof_id_n, terms);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleMatMulVectToArray(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	Array<Real> & array,
	Real scale_factor) {
	if (mesh->isDistributed()) {
	DOFManager::assembleMatMulVectToArray_<SolverVectorDistributed>(
	dof_id, A_id, x, array, scale_factor);
	} else {
	DOFManager::assembleMatMulVectToArray_<SolverVectorDefault>(
	dof_id, A_id, x, array, scale_factor);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::addToProfile(const ID & matrix_id, const ID & dof_id,
	ElementType type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	const auto & dof_data = this->getDOFData(dof_id);

	if (dof_data.support_type != _dst_nodal) {
	return;
	}

	auto mat_dof = std::make_pair(matrix_id, dof_id);
	auto type_pair = std::make_pair(type, ghost_type);

	auto prof_it = this->matrix_profiled_dofs.find(mat_dof);
	if (prof_it != this->matrix_profiled_dofs.end() &&
	std::find(prof_it->second.begin(), prof_it->second.end(), type_pair) !=
	prof_it->second.end()) {
	return;
	}

	auto nb_degree_of_freedom_per_node = dof_data.dof->getNbComponent();

	const auto & equation_number = this->getLocalEquationsNumbers(dof_id);

	auto & A = this->getMatrix(matrix_id);
	A.resize(system_size);
	auto size = A.size();

	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	const auto & connectivity = this->mesh->getConnectivity(type, ghost_type);
	auto cbegin = connectivity.begin(nb_nodes_per_element);
	auto cit = cbegin;

	auto nb_elements = connectivity.size();
	UInt * ge_it = nullptr;
	if (dof_data.group_support != "__mesh__") {
	const auto & group_elements =
	this->mesh->getElementGroup(dof_data.group_support)
	.getElements(type, ghost_type);
	ge_it = group_elements.storage();
	nb_elements = group_elements.size();
	}

	UInt size_mat = nb_nodes_per_element * nb_degree_of_freedom_per_node;
	Vector<Int> element_eq_nb(size_mat);

	for (UInt e = 0; e < nb_elements; ++e) {
	if (ge_it != nullptr) {
	cit = cbegin + *ge_it;
	}

	this->extractElementEquationNumber(
	equation_number, *cit, nb_degree_of_freedom_per_node, element_eq_nb);
	std::transform(
	element_eq_nb.storage(), element_eq_nb.storage() + element_eq_nb.size(),
	element_eq_nb.storage(),
	[&](auto & local) { return this->localToGlobalEquationNumber(local); });

	if (ge_it != nullptr) {
	++ge_it;
	} else {
	++cit;
	}

	for (UInt i = 0; i < size_mat; ++i) {
	UInt c_irn = element_eq_nb(i);
	if (c_irn < size) {
	for (UInt j = 0; j < size_mat; ++j) {
	UInt c_jcn = element_eq_nb(j);
	if (c_jcn < size) {
	A.add(c_irn, c_jcn);
	}
	}
	}
	}
	}

	this->matrix_profiled_dofs[mat_dof].push_back(type_pair);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Array<Real> & DOFManagerDefault::getSolutionArray() {
	return dynamic_cast<SolverVectorDefault *>(this->solution.get())->getVector();
	}

	/* -------------------------------------------------------------------------- */
	const Array<Real> & DOFManagerDefault::getResidualArray() const {
	return dynamic_cast<SolverVectorDefault *>(this->residual.get())->getVector();
	}

	/* -------------------------------------------------------------------------- */
	Array<Real> & DOFManagerDefault::getResidualArray() {
	return dynamic_cast<SolverVectorDefault *>(this->residual.get())->getVector();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) {
	DOFManager::onNodesAdded(nodes_list, event);

	if (this->synchronizer) {
	this->synchronizer->onNodesAdded(nodes_list);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::resizeGlobalArrays() {
	DOFManager::resizeGlobalArrays();

	this->global_blocked_dofs.resize(this->local_system_size, 1);
	this->previous_global_blocked_dofs.resize(this->local_system_size, 1);

	matrix_profiled_dofs.clear();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::updateGlobalBlockedDofs() {
	DOFManager::updateGlobalBlockedDofs();

	if (this->global_blocked_dofs_release ==
	this->previous_global_blocked_dofs_release) {
	return;
	}

	global_blocked_dofs_uint.resize(local_system_size);
	global_blocked_dofs_uint.set(false);
	for (const auto & dof : global_blocked_dofs) {
	global_blocked_dofs_uint[dof] = true;
	}
	}

	/* -------------------------------------------------------------------------- */
	Array<bool> & DOFManagerDefault::getBlockedDOFs() {
	return global_blocked_dofs_uint;
	}

	/* -------------------------------------------------------------------------- */
	const Array<bool> & DOFManagerDefault::getBlockedDOFs() const {
	return global_blocked_dofs_uint;
	}

	/* -------------------------------------------------------------------------- */
	static bool dof_manager_is_registered [[gnu::unused]] =
	DOFManagerFactory::getInstance().registerAllocator(
	"default",
	[](Mesh & mesh, const ID & id) -> std::unique_ptr<DOFManager> {
	return std::make_unique<DOFManagerDefault>(mesh, id);
	});

	static bool dof_manager_is_registered_mumps [[gnu::unused]] =
	DOFManagerFactory::getInstance().registerAllocator(
	- "mumps",
	- [](Mesh & mesh, const ID & id) -> std::unique_ptr<DOFManager> {
	+ "mumps", [](Mesh & mesh, const ID & id) -> std::unique_ptr<DOFManager> {
	return std::make_unique<DOFManagerDefault>(mesh, id);
	});

	} // namespace akantu
	diff --git a/src/model/common/dof_manager/dof_manager_default.hh b/src/model/common/dof_manager/dof_manager_default.hh
	index f12072ff8..dfd9160d5 100644
	--- a/src/model/common/dof_manager/dof_manager_default.hh
	+++ b/src/model/common/dof_manager/dof_manager_default.hh
	@@ -1,255 +1,255 @@
	/**
	* @file dof_manager_default.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Default implementation of the dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_MANAGER_DEFAULT_HH_
	#define AKANTU_DOF_MANAGER_DEFAULT_HH_

	namespace akantu {
	class SparseMatrixAIJ;
	class NonLinearSolverDefault;
	class TimeStepSolverDefault;
	class DOFSynchronizer;
	} // namespace akantu

	namespace akantu {

	class DOFManagerDefault : public DOFManager {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DOFManagerDefault(const ID & id = "dof_manager_default");
	DOFManagerDefault(Mesh & mesh, const ID & id = "dof_manager_default");
	~DOFManagerDefault() override;

	protected:
	struct DOFDataDefault : public DOFData {
	explicit DOFDataDefault(const ID & dof_id);
	};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	// /// register an array of degree of freedom
	// void registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	// const DOFSupportType & support_type) override;

	// /// the dof as an implied type of _dst_nodal and is defined only on a
	// subset
	// /// of nodes
	// void registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
	// const ID & group_support) override;

	/**
	* Assemble elementary values to the global matrix. The dof number is
	* implicitly considered as conn(el, n) * nb_nodes_per_element + d.
	* With 0 < n < nb_nodes_per_element and 0 < d < nb_dof_per_node
	**/
	void assembleElementalMatricesToMatrix(
	const ID & matrix_id, const ID & dof_id,
	const Array<Real> & elementary_mat, ElementType type,
	GhostType ghost_type, const MatrixType & elemental_matrix_type,
	const Array<UInt> & filter_elements) override;

	void assembleMatMulVectToArray(const ID & dof_id, const ID & A_id,
	const Array<Real> & x, Array<Real> & array,
	Real scale_factor = 1.) override;

	/// multiply a vector by a lumped matrix and assemble the result to the
	/// residual
	void assembleLumpedMatMulVectToResidual(const ID & dof_id, const ID & A_id,
	const Array<Real> & x,
	Real scale_factor = 1) override;

	/// assemble coupling terms between to dofs
	void assemblePreassembledMatrix(const ID & dof_id_m, const ID & dof_id_n,
	const ID & matrix_id,
	const TermsToAssemble & terms) override;

	protected:
	void assembleToGlobalArray(const ID & dof_id,
	const Array<Real> & array_to_assemble,
	SolverVector & global_array,
	Real scale_factor) override;

	template <typename T>
	void assembleToGlobalArray(const ID & dof_id,
	const Array<T> & array_to_assemble,
	Array<T> & global_array, T scale_factor);

	void getArrayPerDOFs(const ID & dof_id, const SolverVector & global,
	Array<Real> & local) override;

	template <typename T>
	void getArrayPerDOFs(const ID & dof_id, const Array<T> & global_array,
	Array<T> & local_array) const;
	void makeConsistentForPeriodicity(const ID & dof_id,
	SolverVector & array) override;

	public:
	/// update the global dofs vector
	void updateGlobalBlockedDofs() override;

	// /// apply boundary conditions to jacobian matrix
	// void applyBoundary(const ID & matrix_id = "J") override;

	private:
	/// Add a symmetric matrices to a symmetric sparse matrix
	void addSymmetricElementalMatrixToSymmetric(
	SparseMatrixAIJ & matrix, const Matrix<Real> & element_mat,
	const Vector<Int> & equation_numbers, UInt max_size);

	/// Add a unsymmetric matrices to a symmetric sparse matrix (i.e. cohesive
	/// elements)
	void addUnsymmetricElementalMatrixToSymmetric(
	SparseMatrixAIJ & matrix, const Matrix<Real> & element_mat,
	const Vector<Int> & equation_numbers, UInt max_size);

	/// Add a matrices to a unsymmetric sparse matrix
	void addElementalMatrixToUnsymmetric(SparseMatrixAIJ & matrix,
	const Matrix<Real> & element_mat,
	const Vector<Int> & equation_numbers,
	UInt max_size);

	- void addToProfile(const ID & matrix_id, const ID & dof_id,
	- ElementType type, GhostType ghost_type);
	+ void addToProfile(const ID & matrix_id, const ID & dof_id, ElementType type,
	+ GhostType ghost_type);

	/* ------------------------------------------------------------------------ */
	/* MeshEventHandler interface */
	/* ------------------------------------------------------------------------ */
	protected:
	std::tuple<UInt, UInt, UInt>
	registerDOFsInternal(const ID & dof_id, Array<Real> & dofs_array) override;

	// std::pair<UInt, UInt>
	// updateNodalDOFs(const ID & dof_id, const Array<UInt> & nodes_list)
	// override;

	void resizeGlobalArrays() override;

	public:
	/// function to implement to react on akantu::NewNodesEvent
	void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Get an instance of a new SparseMatrix
	SparseMatrix & getNewMatrix(const ID & matrix_id,
	const MatrixType & matrix_type) override;

	/// Get an instance of a new SparseMatrix as a copy of the SparseMatrix
	/// matrix_to_copy_id
	SparseMatrix & getNewMatrix(const ID & matrix_id,
	const ID & matrix_to_copy_id) override;

	/// Get the reference of an existing matrix
	SparseMatrixAIJ & getMatrix(const ID & matrix_id);

	/// Get an instance of a new lumped matrix
	SolverVector & getNewLumpedMatrix(const ID & matrix_id) override;

	/* ------------------------------------------------------------------------ */
	/* Non Linear Solver */
	/* ------------------------------------------------------------------------ */
	/// Get instance of a non linear solver
	NonLinearSolver & getNewNonLinearSolver(
	const ID & nls_solver_id,
	const NonLinearSolverType & _non_linear_solver_type) override;

	/* ------------------------------------------------------------------------ */
	/* Time-Step Solver */
	/* ------------------------------------------------------------------------ */
	/// Get instance of a time step solver
	TimeStepSolver &
	getNewTimeStepSolver(const ID & id, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback) override;

	/* ------------------------------------------------------------------------ */
	private:
	/// Get the solution array
	Array<Real> & getSolutionArray();

	/// Get the residual array
	const Array<Real> & getResidualArray() const;

	/// Get the residual array
	Array<Real> & getResidualArray();

	public:
	/// access the internal dof_synchronizer
	AKANTU_GET_MACRO_NOT_CONST(Synchronizer, *synchronizer, DOFSynchronizer &);

	/// access the internal dof_synchronizer
	bool hasSynchronizer() const { return synchronizer != nullptr; }

	Array<bool> & getBlockedDOFs();
	const Array<bool> & getBlockedDOFs() const;

	protected:
	std::unique_ptr<DOFData> getNewDOFData(const ID & dof_id) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	using DOFToMatrixProfile =
	std::map<std::pair<ID, ID>,
	std::vector<std::pair<ElementType, GhostType>>>;

	/// contains the the dofs that where added to the profile of a given matrix.
	DOFToMatrixProfile matrix_profiled_dofs;

	/// synchronizer to maintain coherency in dof fields
	std::unique_ptr<DOFSynchronizer> synchronizer;

	friend class DOFSynchronizer;

	/// Array containing the true or false if the node is in global_blocked_dofs
	Array<bool> global_blocked_dofs_uint;
	};

	} // namespace akantu

	#include "dof_manager_default_inline_impl.hh"

	#endif /* AKANTU_DOF_MANAGER_DEFAULT_HH_ */
	diff --git a/src/model/common/dof_manager/dof_manager_default_inline_impl.hh b/src/model/common/dof_manager/dof_manager_default_inline_impl.hh
	index 862af9ba9..bea008782 100644
	--- a/src/model/common/dof_manager/dof_manager_default_inline_impl.hh
	+++ b/src/model/common/dof_manager/dof_manager_default_inline_impl.hh
	@@ -1,41 +1,41 @@
	/**
	* @file dof_manager_default_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Wed Mar 13 2019
	*
	* @brief Implementation of the DOFManagerDefault inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_default.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_MANAGER_DEFAULT_INLINE_IMPL_HH_
	#define AKANTU_DOF_MANAGER_DEFAULT_INLINE_IMPL_HH_

	namespace akantu {} // namespace akantu

	#endif /* __AKANTU_DOF_MANAGER_DEFAULT_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/dof_manager/dof_manager_inline_impl.hh b/src/model/common/dof_manager/dof_manager_inline_impl.hh
	index 1fc5bb2b5..772c95a82 100644
	--- a/src/model/common/dof_manager/dof_manager_inline_impl.hh
	+++ b/src/model/common/dof_manager/dof_manager_inline_impl.hh
	@@ -1,337 +1,337 @@
	/**
	* @file dof_manager_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Thu Feb 20 2020
	*
	* @brief inline functions of the dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	#include "element_group.hh"
	#include "solver_vector.hh"
	#include "sparse_matrix.hh"
	#include "terms_to_assemble.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_MANAGER_INLINE_IMPL_HH_
	#define AKANTU_DOF_MANAGER_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasDOFs(const ID & dof_id) const {
	auto it = this->dofs.find(dof_id);
	return it != this->dofs.end();
	}

	/* -------------------------------------------------------------------------- */
	inline DOFManager::DOFData & DOFManager::getDOFData(const ID & dof_id) {
	auto it = this->dofs.find(dof_id);
	if (it == this->dofs.end()) {
	AKANTU_EXCEPTION("The dof " << dof_id << " does not exists in "
	<< this->id);
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	const DOFManager::DOFData & DOFManager::getDOFData(const ID & dof_id) const {
	auto it = this->dofs.find(dof_id);
	if (it == this->dofs.end()) {
	AKANTU_EXCEPTION("The dof " << dof_id << " does not exists in "
	<< this->id);
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	inline void DOFManager::extractElementEquationNumber(
	const Array<Int> & equation_numbers, const Vector<UInt> & connectivity,
	UInt nb_degree_of_freedom, Vector<Int> & element_equation_number) {
	for (UInt i = 0, ld = 0; i < connectivity.size(); ++i) {
	UInt n = connectivity(i);
	for (UInt d = 0; d < nb_degree_of_freedom; ++d, ++ld) {
	element_equation_number(ld) =
	equation_numbers(n * nb_degree_of_freedom + d);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class DOFData_>
	inline DOFData_ & DOFManager::getDOFDataTyped(const ID & dof_id) {
	return aka::as_type<DOFData_>(this->getDOFData(dof_id));
	}

	/* -------------------------------------------------------------------------- */
	template <class DOFData_>
	inline const DOFData_ & DOFManager::getDOFDataTyped(const ID & dof_id) const {
	return aka::as_type<DOFData_>(this->getDOFData(dof_id));
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Real> & DOFManager::getDOFs(const ID & dofs_id) {
	return *(this->getDOFData(dofs_id).dof);
	}

	/* -------------------------------------------------------------------------- */
	inline DOFSupportType DOFManager::getSupportType(const ID & dofs_id) const {
	return this->getDOFData(dofs_id).support_type;
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Real> & DOFManager::getPreviousDOFs(const ID & dofs_id) {
	return *(this->getDOFData(dofs_id).previous);
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasPreviousDOFs(const ID & dofs_id) const {
	return (this->getDOFData(dofs_id).previous != nullptr);
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Real> & DOFManager::getDOFsIncrement(const ID & dofs_id) {
	return *(this->getDOFData(dofs_id).increment);
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasDOFsIncrement(const ID & dofs_id) const {
	return (this->getDOFData(dofs_id).increment != nullptr);
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Real> & DOFManager::getDOFsDerivatives(const ID & dofs_id,
	UInt order) {

	if (order == 0) {
	return getDOFs(dofs_id);
	}

	std::vector<Array<Real> *> & derivatives =
	this->getDOFData(dofs_id).dof_derivatives;
	if ((order > derivatives.size()) \|\| (derivatives[order - 1] == nullptr)) {
	AKANTU_EXCEPTION("No derivatives of order " << order << " present in "
	<< this->id << " for dof "
	<< dofs_id);
	}

	return *derivatives[order - 1];
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasDOFsDerivatives(const ID & dofs_id,
	UInt order) const {
	const std::vector<Array<Real> *> & derivatives =
	this->getDOFData(dofs_id).dof_derivatives;
	return ((order < derivatives.size()) && (derivatives[order - 1] != nullptr));
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> & DOFManager::getSolution(const ID & dofs_id) const {
	return this->getDOFData(dofs_id).solution;
	}

	/* -------------------------------------------------------------------------- */
	inline Array<Real> & DOFManager::getSolution(const ID & dofs_id) {
	return this->getDOFData(dofs_id).solution;
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<bool> &
	DOFManager::getBlockedDOFs(const ID & dofs_id) const {
	return *(this->getDOFData(dofs_id).blocked_dofs);
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasBlockedDOFs(const ID & dofs_id) const {
	return (this->getDOFData(dofs_id).blocked_dofs != nullptr);
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::isLocalOrMasterDOF(UInt dof_num) {
	auto dof_flag = this->dofs_flag(dof_num);
	return (dof_flag & NodeFlag::_local_master_mask) == NodeFlag::_normal;
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::isSlaveDOF(UInt dof_num) {
	auto dof_flag = this->dofs_flag(dof_num);
	return (dof_flag & NodeFlag::_shared_mask) == NodeFlag::_slave;
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::isPureGhostDOF(UInt dof_num) {
	auto dof_flag = this->dofs_flag(dof_num);
	return (dof_flag & NodeFlag::_shared_mask) == NodeFlag::_pure_ghost;
	}

	/* -------------------------------------------------------------------------- */
	inline Int DOFManager::localToGlobalEquationNumber(Int local) const {
	return this->global_equation_number(local);
	}

	/* -------------------------------------------------------------------------- */
	inline bool DOFManager::hasGlobalEquationNumber(Int global) const {
	auto it = this->global_to_local_mapping.find(global);
	return (it != this->global_to_local_mapping.end());
	}

	/* -------------------------------------------------------------------------- */
	inline Int DOFManager::globalToLocalEquationNumber(Int global) const {
	auto it = this->global_to_local_mapping.find(global);
	AKANTU_DEBUG_ASSERT(it != this->global_to_local_mapping.end(),
	"This global equation number "
	<< global << " does not exists in " << this->id);

	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	inline NodeFlag DOFManager::getDOFFlag(Int local_id) const {
	return this->dofs_flag(local_id);
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<UInt> &
	DOFManager::getDOFsAssociatedNodes(const ID & dof_id) const {
	const auto & dof_data = this->getDOFData(dof_id);
	return dof_data.associated_nodes;
	}

	/* -------------------------------------------------------------------------- */
	const Array<Int> &
	DOFManager::getLocalEquationsNumbers(const ID & dof_id) const {
	return getDOFData(dof_id).local_equation_number;
	}

	/* -------------------------------------------------------------------------- */
	template <typename Vec>
	void DOFManager::assembleMatMulVectToArray_(const ID & dof_id, const ID & A_id,
	const Array<Real> & x,
	Array<Real> & array,
	Real scale_factor) {
	Vec tmp_array(aka::as_type<Vec>(*data_cache), this->id + ":tmp_array");
	tmp_array.zero();
	assembleMatMulVectToGlobalArray(dof_id, A_id, x, tmp_array, scale_factor);
	getArrayPerDOFs(dof_id, tmp_array, array);
	}

	/* -------------------------------------------------------------------------- */
	template <typename Mat>
	void DOFManager::assembleElementalMatricesToMatrix_(
	Mat & A, const ID & dof_id, const Array<Real> & elementary_mat,
	ElementType type, GhostType ghost_type,
	const MatrixType & elemental_matrix_type,
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_IN();

	auto & dof_data = this->getDOFData(dof_id);

	AKANTU_DEBUG_ASSERT(dof_data.support_type == _dst_nodal,
	"This function applies only on Nodal dofs");

	const auto & equation_number = this->getLocalEquationsNumbers(dof_id);

	UInt nb_element;
	UInt * filter_it = nullptr;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	filter_it = filter_elements.storage();
	} else {
	if (dof_data.group_support != "__mesh__") {
	const auto & group_elements =
	this->mesh->getElementGroup(dof_data.group_support)
	.getElements(type, ghost_type);
	nb_element = group_elements.size();
	filter_it = group_elements.storage();
	} else {
	nb_element = this->mesh->getNbElement(type, ghost_type);
	}
	}

	AKANTU_DEBUG_ASSERT(elementary_mat.size() == nb_element,
	"The vector elementary_mat("
	<< elementary_mat.getID()
	<< ") has not the good size.");

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	UInt nb_degree_of_freedom = dof_data.dof->getNbComponent();

	const Array<UInt> & connectivity =
	this->mesh->getConnectivity(type, ghost_type);
	auto conn_begin = connectivity.begin(nb_nodes_per_element);
	auto conn_it = conn_begin;
	auto size_mat = nb_nodes_per_element * nb_degree_of_freedom;

	Vector<Int> element_eq_nb(nb_degree_of_freedom * nb_nodes_per_element);
	auto el_mat_it = elementary_mat.begin(size_mat, size_mat);

	for (UInt e = 0; e < nb_element; ++e, ++el_mat_it) {
	if (filter_it) {
	conn_it = conn_begin + *filter_it;
	}

	this->extractElementEquationNumber(equation_number, *conn_it,
	nb_degree_of_freedom, element_eq_nb);
	std::transform(element_eq_nb.begin(), element_eq_nb.end(),
	element_eq_nb.begin(), [&](auto && local) {
	return this->localToGlobalEquationNumber(local);
	});

	if (filter_it) {
	++filter_it;
	} else {
	++conn_it;
	}

	A.addValues(element_eq_nb, element_eq_nb, *el_mat_it,
	elemental_matrix_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename Mat>
	void DOFManager::assemblePreassembledMatrix_(Mat & A, const ID & dof_id_m,
	const ID & dof_id_n,
	const TermsToAssemble & terms) {
	const auto & equation_number_m = this->getLocalEquationsNumbers(dof_id_m);
	const auto & equation_number_n = this->getLocalEquationsNumbers(dof_id_n);

	for (const auto & term : terms) {
	auto gi = this->localToGlobalEquationNumber(equation_number_m(term.i()));
	auto gj = this->localToGlobalEquationNumber(equation_number_n(term.j()));
	A.add(gi, gj, term);
	}
	}
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_DOF_MANAGER_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/dof_manager/dof_manager_petsc.cc b/src/model/common/dof_manager/dof_manager_petsc.cc
	index 32a0e5568..4cc729c8d 100644
	--- a/src/model/common/dof_manager/dof_manager_petsc.cc
	+++ b/src/model/common/dof_manager/dof_manager_petsc.cc
	@@ -1,305 +1,301 @@
	/**
	* @file dof_manager_petsc.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 07 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief DOFManaterPETSc is the PETSc implementation of the DOFManager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_petsc.hh"
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "cppargparse.hh"
	#include "non_linear_solver_petsc.hh"
	#include "solver_vector_petsc.hh"
	#include "sparse_matrix_petsc.hh"
	#include "time_step_solver_default.hh"
	#if defined(AKANTU_USE_MPI)
	#include "mpi_communicator_data.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	#include <petscis.h>
	#include <petscsys.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class PETScSingleton {
	private:
	PETScSingleton() {
	PETSc_call(PetscInitialized, &is_initialized);

	if (is_initialized == 0U) {
	cppargparse::ArgumentParser & argparser = getStaticArgumentParser();
	int & argc = argparser.getArgC();
	char **& argv = argparser.getArgV();
	PETSc_call(PetscInitialize, &argc, &argv, nullptr, nullptr);
	PETSc_call(
	PetscPopErrorHandler); // remove the default PETSc signal handler
	PETSc_call(PetscPushErrorHandler, PetscIgnoreErrorHandler, nullptr);
	}
	}

	public:
	PETScSingleton(const PETScSingleton &) = delete;
	PETScSingleton & operator=(const PETScSingleton &) = delete;

	~PETScSingleton() {
	if (is_initialized == 0U) {
	PetscFinalize();
	}
	}

	static PETScSingleton & getInstance() {
	static PETScSingleton instance;
	return instance;
	}

	private:
	PetscBool is_initialized;
	};

	/* -------------------------------------------------------------------------- */
	DOFManagerPETSc::DOFDataPETSc::DOFDataPETSc(const ID & dof_id)
	: DOFData(dof_id) {}

	/* -------------------------------------------------------------------------- */
	-DOFManagerPETSc::DOFManagerPETSc(const ID & id)
	- : DOFManager(id) {
	- init();
	-}
	+DOFManagerPETSc::DOFManagerPETSc(const ID & id) : DOFManager(id) { init(); }

	/* -------------------------------------------------------------------------- */
	DOFManagerPETSc::DOFManagerPETSc(Mesh & mesh, const ID & id)
	: DOFManager(mesh, id) {
	init();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::init() {
	// check if the akantu types and PETSc one are consistant
	static_assert(sizeof(Int) == sizeof(PetscInt),
	"The integer type of Akantu does not match the one from PETSc");
	static_assert(sizeof(Real) == sizeof(PetscReal),
	"The integer type of Akantu does not match the one from PETSc");

	#if defined(AKANTU_USE_MPI)

	const auto & mpi_data =
	aka::as_type<MPICommunicatorData>(communicator.getCommunicatorData());
	MPI_Comm mpi_comm = mpi_data.getMPICommunicator();
	this->mpi_communicator = mpi_comm;
	#else
	this->mpi_communicator = PETSC_COMM_SELF;
	#endif

	PETScSingleton & instance [[gnu::unused]] = PETScSingleton::getInstance();
	}

	/* -------------------------------------------------------------------------- */
	auto DOFManagerPETSc::getNewDOFData(const ID & dof_id)
	-> std::unique_ptr<DOFData> {
	return std::make_unique<DOFDataPETSc>(dof_id);
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<UInt, UInt, UInt>
	DOFManagerPETSc::registerDOFsInternal(const ID & dof_id,
	Array<Real> & dofs_array) {
	dofs_ids.push_back(dof_id);
	auto ret = DOFManager::registerDOFsInternal(dof_id, dofs_array);
	UInt nb_dofs;
	UInt nb_pure_local_dofs;
	std::tie(nb_dofs, nb_pure_local_dofs, std::ignore) = ret;

	auto && vector = std::make_unique<SolverVectorPETSc>(*this, id + ":solution");
	- auto *x = vector->getVec();
	+ auto * x = vector->getVec();
	PETSc_call(VecGetLocalToGlobalMapping, x, &is_ltog_map);

	// redoing the indexes based on the petsc numbering
	for (auto & dof_id : dofs_ids) {
	auto & dof_data = this->getDOFDataTyped<DOFDataPETSc>(dof_id);

	Array<PetscInt> gidx(dof_data.local_equation_number.size());
	for (auto && data : zip(dof_data.local_equation_number, gidx)) {
	std::get<1>(data) = localToGlobalEquationNumber(std::get<0>(data));
	}

	auto & lidx = dof_data.local_equation_number_petsc;
	if (is_ltog_map != nullptr) {
	lidx.resize(gidx.size());

	PetscInt n;
	PETSc_call(ISGlobalToLocalMappingApply, is_ltog_map, IS_GTOLM_MASK,
	gidx.size(), gidx.storage(), &n, lidx.storage());
	}
	}

	residual = std::make_unique<SolverVectorPETSc>(*vector, id + ":residual");
	data_cache = std::make_unique<SolverVectorPETSc>(*vector, id + ":data_cache");
	solution = std::move(vector);

	for (auto & mat : matrices) {
	auto & A = this->getMatrix(mat.first);
	A.resize();
	}

	return ret;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::assembleToGlobalArray(
	const ID & dof_id, const Array<Real> & array_to_assemble,
	SolverVector & global_array, Real scale_factor) {
	const auto & dof_data = getDOFDataTyped<DOFDataPETSc>(dof_id);
	auto & g = aka::as_type<SolverVectorPETSc>(global_array);

	AKANTU_DEBUG_ASSERT(array_to_assemble.size() *
	array_to_assemble.getNbComponent() ==
	dof_data.local_nb_dofs,
	"The array to assemble does not have the proper size");

	g.addValuesLocal(dof_data.local_equation_number_petsc, array_to_assemble,
	scale_factor);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::getArrayPerDOFs(const ID & dof_id,
	const SolverVector & global_array,
	Array<Real> & local) {
	const auto & dof_data = getDOFDataTyped<DOFDataPETSc>(dof_id);
	const auto & petsc_vector = aka::as_type<SolverVectorPETSc>(global_array);

	AKANTU_DEBUG_ASSERT(
	local.size() * local.getNbComponent() == dof_data.local_nb_dofs,
	"The array to get the values does not have the proper size");

	petsc_vector.getValuesLocal(dof_data.local_equation_number_petsc, local);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::assembleElementalMatricesToMatrix(
	const ID & matrix_id, const ID & dof_id, const Array<Real> & elementary_mat,
	ElementType type, GhostType ghost_type,
	const MatrixType & elemental_matrix_type,
	const Array<UInt> & filter_elements) {
	auto & A = getMatrix(matrix_id);
	DOFManager::assembleElementalMatricesToMatrix_(
	A, dof_id, elementary_mat, type, ghost_type, elemental_matrix_type,
	filter_elements);

	A.applyModifications();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::assemblePreassembledMatrix(
	const ID & dof_id_m, const ID & dof_id_n, const ID & matrix_id,
	const TermsToAssemble & terms) {
	auto & A = getMatrix(matrix_id);
	DOFManager::assemblePreassembledMatrix_(A, dof_id_m, dof_id_n, terms);

	A.applyModifications();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::assembleMatMulVectToArray(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	Array<Real> & array,
	Real scale_factor) {
	DOFManager::assembleMatMulVectToArray_<SolverVectorPETSc>(
	dof_id, A_id, x, array, scale_factor);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerPETSc::makeConsistentForPeriodicity(const ID & /dof_id/,
	SolverVector & /array/) {}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver &
	DOFManagerPETSc::getNewNonLinearSolver(const ID & id,
	const NonLinearSolverType & type) {
	return this->registerNonLinearSolver<NonLinearSolverPETSc>(*this, id, type);
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & DOFManagerPETSc::getNewTimeStepSolver(
	const ID & id, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver, SolverCallback & callback) {
	return this->registerTimeStepSolver<TimeStepSolverDefault>(
	*this, id, type, non_linear_solver, callback);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerPETSc::getNewMatrix(const ID & id,
	const MatrixType & matrix_type) {
	return this->registerSparseMatrix<SparseMatrixPETSc>(*this, id, matrix_type);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerPETSc::getNewMatrix(const ID & id,
	const ID & matrix_to_copy_id) {
	return this->registerSparseMatrix<SparseMatrixPETSc>(id, matrix_to_copy_id);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrixPETSc & DOFManagerPETSc::getMatrix(const ID & id) {
	auto & matrix = DOFManager::getMatrix(id);
	return aka::as_type<SparseMatrixPETSc>(matrix);
	}

	/* -------------------------------------------------------------------------- */
	SolverVector & DOFManagerPETSc::getNewLumpedMatrix(const ID & id) {
	return this->registerLumpedMatrix<SolverVectorPETSc>(*this, id);
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc & DOFManagerPETSc::getSolution() {
	return aka::as_type<SolverVectorPETSc>(*this->solution);
	}

	const SolverVectorPETSc & DOFManagerPETSc::getSolution() const {
	return aka::as_type<SolverVectorPETSc>(*this->solution);
	}

	SolverVectorPETSc & DOFManagerPETSc::getResidual() {
	return aka::as_type<SolverVectorPETSc>(*this->residual);
	}

	const SolverVectorPETSc & DOFManagerPETSc::getResidual() const {
	return aka::as_type<SolverVectorPETSc>(*this->residual);
	}

	/* -------------------------------------------------------------------------- */
	static bool dof_manager_is_registered [[gnu::unused]] =
	DOFManagerFactory::getInstance().registerAllocator(
	- "petsc",
	- [](Mesh & mesh, const ID & id) -> std::unique_ptr<DOFManager> {
	+ "petsc", [](Mesh & mesh, const ID & id) -> std::unique_ptr<DOFManager> {
	return std::make_unique<DOFManagerPETSc>(mesh, id);
	});

	} // namespace akantu
	diff --git a/src/model/common/dof_manager/dof_manager_petsc.hh b/src/model/common/dof_manager/dof_manager_petsc.hh
	index eb138f6bc..033cbfb9a 100644
	--- a/src/model/common/dof_manager/dof_manager_petsc.hh
	+++ b/src/model/common/dof_manager/dof_manager_petsc.hh
	@@ -1,219 +1,218 @@
	/**
	* @file dof_manager_petsc.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief PETSc implementation of the dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscis.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_MANAGER_PETSC_HH_
	#define AKANTU_DOF_MANAGER_PETSC_HH_

	#define PETSc_call(func, ...) \
	do { \
	auto ierr = func(__VA_ARGS__); \
	if (PetscUnlikely(ierr != 0)) { \
	const char * desc; \
	PetscErrorMessage(ierr, &desc, nullptr); \
	AKANTU_EXCEPTION("Error in PETSc call to \'" << #func \
	<< "\': " << desc); \
	} \
	} while (false)

	namespace akantu {
	namespace detail {
	template <typename T> void PETScSetName(T t, const ID & id) {
	PETSc_call(PetscObjectSetName, reinterpret_cast<PetscObject>(t),
	id.c_str());
	}
	} // namespace detail
	} // namespace akantu

	namespace akantu {
	class SparseMatrixPETSc;
	class SolverVectorPETSc;
	} // namespace akantu

	namespace akantu {

	class DOFManagerPETSc : public DOFManager {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DOFManagerPETSc(const ID & id = "dof_manager_petsc");
	DOFManagerPETSc(Mesh & mesh, const ID & id = "dof_manager_petsc");

	~DOFManagerPETSc() override = default;

	protected:
	void init();

	struct DOFDataPETSc : public DOFData {
	explicit DOFDataPETSc(const ID & dof_id);

	/// petsc compressed version of local_equation_number
	Array<PetscInt> local_equation_number_petsc;

	Array<Int> & getLocalEquationsNumbers() override {
	return local_equation_number_petsc;
	}
	};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void assembleToLumpedMatrix(const ID & /dof_id/,
	Array<Real> & /array_to_assemble/,
	const ID & /lumped_mtx/,
	Real /scale_factor/ = 1.) override {
	AKANTU_TO_IMPLEMENT();
	}

	void assembleElementalMatricesToMatrix(
	const ID & /matrix_id/, const ID & /dof_id/,
	const Array<Real> & /elementary_mat/, ElementType /type/,
	- GhostType /ghost_type/,
	- const MatrixType & /elemental_matrix_type/,
	+ GhostType /ghost_type/, const MatrixType & /elemental_matrix_type/,
	const Array<UInt> & /filter_elements/) override;

	void assembleMatMulVectToArray(const ID & /dof_id/, const ID & /A_id/,
	const Array<Real> & /x/,
	Array<Real> & /array/,
	Real /scale_factor/ = 1.) override;

	void assembleLumpedMatMulVectToResidual(const ID & /dof_id/,
	const ID & /A_id/,
	const Array<Real> & /x/,
	Real /scale_factor/ = 1) override {
	AKANTU_TO_IMPLEMENT();
	}

	void assemblePreassembledMatrix(const ID & /* dof_id_m*/,
	const ID & /dof_id_n/,
	const ID & /matrix_id/,
	const TermsToAssemble & /terms/) override;

	protected:
	void assembleToGlobalArray(const ID & dof_id,
	const Array<Real> & array_to_assemble,
	SolverVector & global_array,
	Real scale_factor) override;
	void getArrayPerDOFs(const ID & dof_id, const SolverVector & global,
	Array<Real> & local) override;

	void makeConsistentForPeriodicity(const ID & dof_id,
	SolverVector & array) override;

	std::unique_ptr<DOFData> getNewDOFData(const ID & dof_id) override;

	std::tuple<UInt, UInt, UInt>
	registerDOFsInternal(const ID & dof_id, Array<Real> & dofs_array) override;

	void updateDOFsData(DOFDataPETSc & dof_data, UInt nb_new_local_dofs,
	UInt nb_new_pure_local, UInt nb_node,
	const std::function<UInt(UInt)> & getNode);

	protected:
	void getLumpedMatrixPerDOFs(const ID & /dof_id/, const ID & /lumped_mtx/,
	Array<Real> & /lumped/) override {}

	NonLinearSolver & getNewNonLinearSolver(
	const ID & nls_solver_id,
	const NonLinearSolverType & non_linear_solver_type) override;

	TimeStepSolver &
	getNewTimeStepSolver(const ID & id, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Get an instance of a new SparseMatrix
	SparseMatrix & getNewMatrix(const ID & matrix_id,
	const MatrixType & matrix_type) override;

	/// Get an instance of a new SparseMatrix as a copy of the SparseMatrix
	/// matrix_to_copy_id
	SparseMatrix & getNewMatrix(const ID & matrix_id,
	const ID & matrix_to_copy_id) override;

	/// Get the reference of an existing matrix
	SparseMatrixPETSc & getMatrix(const ID & matrix_id);

	/// Get an instance of a new lumped matrix
	SolverVector & getNewLumpedMatrix(const ID & matrix_id) override;

	/// Get the blocked dofs array
	// AKANTU_GET_MACRO(BlockedDOFs, blocked_dofs, const Array<bool> &);
	AKANTU_GET_MACRO(MPIComm, mpi_communicator, MPI_Comm);

	AKANTU_GET_MACRO_NOT_CONST(ISLocalToGlobalMapping, is_ltog_map,
	ISLocalToGlobalMapping &);

	SolverVectorPETSc & getSolution();
	const SolverVectorPETSc & getSolution() const;

	SolverVectorPETSc & getResidual();
	const SolverVectorPETSc & getResidual() const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	using PETScMatrixMap = std::map<ID, SparseMatrixPETSc *>;
	using PETScLumpedMatrixMap = std::map<ID, SolverVectorPETSc *>;

	/// list of matrices registered to the dof manager
	PETScMatrixMap petsc_matrices;

	/// list of lumped matrices registered
	PETScLumpedMatrixMap petsc_lumped_matrices;

	/// PETSc local to global mapping of dofs
	ISLocalToGlobalMapping is_ltog_map{nullptr};

	/// Communicator associated to PETSc
	MPI_Comm mpi_communicator;

	/// list of the dof ids to be able to always iterate in the same order
	std::vector<ID> dofs_ids;
	};

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_DOF_MANAGER_PETSC_HH_ */
	diff --git a/src/model/common/integration_scheme/generalized_trapezoidal.cc b/src/model/common/integration_scheme/generalized_trapezoidal.cc
	index 4ca0d930d..35b9548f1 100644
	--- a/src/model/common/integration_scheme/generalized_trapezoidal.cc
	+++ b/src/model/common/integration_scheme/generalized_trapezoidal.cc
	@@ -1,197 +1,197 @@
	/**
	* @file generalized_trapezoidal.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 23 2015
	* @date last modification: Wed Mar 27 2019
	*
	* @brief implementation of inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "generalized_trapezoidal.hh"
	#include "aka_array.hh"
	#include "dof_manager.hh"
	#include "mesh.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	GeneralizedTrapezoidal::GeneralizedTrapezoidal(DOFManager & dof_manager,
	const ID & dof_id, Real alpha)
	: IntegrationScheme1stOrder(dof_manager, dof_id), alpha(alpha) {

	this->registerParam("alpha", this->alpha, alpha, _pat_parsmod,
	"The alpha parameter");
	}

	/* -------------------------------------------------------------------------- */
	void GeneralizedTrapezoidal::predictor(Real delta_t, Array<Real> & u,
	Array<Real> & u_dot,
	const Array<bool> & blocked_dofs) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = u.size();
	UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;

	Real * u_val = u.storage();
	Real * u_dot_val = u_dot.storage();
	bool * blocked_dofs_val = blocked_dofs.storage();

	for (UInt d = 0; d < nb_degree_of_freedom; d++) {
	if (!(*blocked_dofs_val)) {
	u_val += (1. - alpha) delta_t * *u_dot_val;
	}
	u_val++;
	u_dot_val++;
	blocked_dofs_val++;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void GeneralizedTrapezoidal::corrector(const SolutionType & type, Real delta_t,
	Array<Real> & u, Array<Real> & u_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const {
	AKANTU_DEBUG_IN();

	switch (type) {
	case _temperature:
	this->allCorrector<_temperature>(delta_t, u, u_dot, blocked_dofs, delta);
	break;
	case _temperature_rate:
	this->allCorrector<_temperature_rate>(delta_t, u, u_dot, blocked_dofs,
	delta);
	break;
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	Real GeneralizedTrapezoidal::getTemperatureCoefficient(
	const SolutionType & type, Real delta_t) const {
	switch (type) {
	case _temperature:
	return 1.;
	case _temperature_rate:
	return alpha * delta_t;
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}
	}

	/* -------------------------------------------------------------------------- */
	Real GeneralizedTrapezoidal::getTemperatureRateCoefficient(
	const SolutionType & type, Real delta_t) const {
	switch (type) {
	case _temperature:
	return 1. / (alpha * delta_t);
	case _temperature_rate:
	return 1.;
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <IntegrationScheme::SolutionType type>
	void GeneralizedTrapezoidal::allCorrector(Real delta_t, Array<Real> & u,
	Array<Real> & u_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = u.size();
	UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;

	Real e = getTemperatureCoefficient(type, delta_t);
	Real d = getTemperatureRateCoefficient(type, delta_t);

	Real * u_val = u.storage();
	Real * u_dot_val = u_dot.storage();
	Real * delta_val = delta.storage();
	bool * blocked_dofs_val = blocked_dofs.storage();

	for (UInt dof = 0; dof < nb_degree_of_freedom; dof++) {
	if (!(*blocked_dofs_val)) {
	u_val += e *delta_val;
	u_dot_val += d *delta_val;
	}
	u_val++;
	u_dot_val++;
	delta_val++;
	blocked_dofs_val++;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void GeneralizedTrapezoidal::assembleJacobian(const SolutionType & type,
	Real delta_t) {
	AKANTU_DEBUG_IN();

	SparseMatrix & J = this->dof_manager.getMatrix("J");

	const SparseMatrix & M = this->dof_manager.getMatrix("M");
	const SparseMatrix & K = this->dof_manager.getMatrix("K");

	bool does_j_need_update = false;
	does_j_need_update \|= M.getRelease() != m_release;
	does_j_need_update \|= K.getRelease() != k_release;
	does_j_need_update \|= this->dof_manager.hasBlockedDOFsChanged();

	if (not does_j_need_update) {
	AKANTU_DEBUG_OUT();
	return;
	}

	J.copyProfile(K);
	// J.zero();

	Real c = this->getTemperatureRateCoefficient(type, delta_t);
	Real e = this->getTemperatureCoefficient(type, delta_t);

	J.add(M, e);
	J.add(K, c);

	m_release = M.getRelease();
	k_release = K.getRelease();

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/generalized_trapezoidal.hh b/src/model/common/integration_scheme/generalized_trapezoidal.hh
	index 91c0bb9a8..b1673acfd 100644
	--- a/src/model/common/integration_scheme/generalized_trapezoidal.hh
	+++ b/src/model/common/integration_scheme/generalized_trapezoidal.hh
	@@ -1,163 +1,163 @@
	/**
	* @file generalized_trapezoidal.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jul 04 2011
	* @date last modification: Wed Mar 13 2019
	*
	* @brief Generalized Trapezoidal Method. This implementation is taken from
	* Méthodes numériques en mécanique des solides by Alain Curnier \note{ISBN:
	* 2-88074-247-1}
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_GENERALIZED_TRAPEZOIDAL_HH_
	#define AKANTU_GENERALIZED_TRAPEZOIDAL_HH_

	#include "integration_scheme_1st_order.hh"

	namespace akantu {

	/**
	* The two differentiate equation (thermal and kinematic) are :
	* \f{eqnarray*}{
	* C\dot{u}_{n+1} + Ku_{n+1} = q_{n+1}\\
	* u_{n+1} = u_{n} + (1-\alpha) \Delta t \dot{u}_{n} + \alpha \Delta t
	*\dot{u}_{n+1}
	* \f}
	*
	* To solve it :
	* Predictor :
	* \f{eqnarray*}{
	* u^0_{n+1} &=& u_{n} + (1-\alpha) \Delta t v_{n} \\
	* \dot{u}^0_{n+1} &=& \dot{u}_{n}
	* \f}
	*
	* Solve :
	* \f[ (a C + b K^i_{n+1}) w = q_{n+1} - f^i_{n+1} - C \dot{u}^i_{n+1} \f]
	*
	* Corrector :
	* \f{eqnarray*}{
	* \dot{u}^{i+1}_{n+1} &=& \dot{u}^{i}_{n+1} + a w \\
	* u^{i+1}_{n+1} &=& u^{i}_{n+1} + b w
	* \f}
	*
	* a and b depends on the resolution method : temperature (u) or temperature
	*rate (\f$\dot{u}\f$)
	*
	* For temperature : \f$ w = \delta u, a = 1 / (\alpha \Delta t) , b = 1 \f$ @n
	* For temperature rate : \f$ w = \delta \dot{u}, a = 1, b = \alpha \Delta t \f$
	*/
	class GeneralizedTrapezoidal : public IntegrationScheme1stOrder {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	GeneralizedTrapezoidal(DOFManager & dof_manager, const ID & dof_id,
	Real alpha = 0);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	const Array<bool> & blocked_dofs) const override;

	void corrector(const SolutionType & type, Real delta_t, Array<Real> & u,
	Array<Real> & u_dot, const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const override;

	void assembleJacobian(const SolutionType & type, Real delta_t) override;

	public:
	/// the coeffichent \f$ b \f$ in the description
	Real getTemperatureCoefficient(const SolutionType & type,
	Real delta_t) const override;

	/// the coeffichent \f$ a \f$ in the description
	Real getTemperatureRateCoefficient(const SolutionType & type,
	Real delta_t) const override;

	private:
	template <SolutionType type>
	void allCorrector(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Alpha, alpha, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// the \f$\alpha\f$ parameter
	Real alpha;

	/// last release of K matrix
	UInt k_release;
	};

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	/**
	* Forward Euler (explicit) -> condition on delta_t
	*/
	class ForwardEuler : public GeneralizedTrapezoidal {
	public:
	ForwardEuler(DOFManager & dof_manager, const ID & dof_id)
	: GeneralizedTrapezoidal(dof_manager, dof_id, 0.){};

	std::vector<std::string> getNeededMatrixList() override { return {"M"}; }
	};

	/**
	* Trapezoidal rule (implicit), midpoint rule or Crank-Nicolson
	*/
	class TrapezoidalRule1 : public GeneralizedTrapezoidal {
	public:
	TrapezoidalRule1(DOFManager & dof_manager, const ID & dof_id)
	: GeneralizedTrapezoidal(dof_manager, dof_id, .5){};
	};

	/**
	* Backward Euler (implicit)
	*/
	class BackwardEuler : public GeneralizedTrapezoidal {
	public:
	BackwardEuler(DOFManager & dof_manager, const ID & dof_id)
	: GeneralizedTrapezoidal(dof_manager, dof_id, 1.){};
	};

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_GENERALIZED_TRAPEZOIDAL_HH_ */
	diff --git a/src/model/common/integration_scheme/integration_scheme.cc b/src/model/common/integration_scheme/integration_scheme.cc
	index efe03552f..6d7956131 100644
	--- a/src/model/common/integration_scheme/integration_scheme.cc
	+++ b/src/model/common/integration_scheme/integration_scheme.cc
	@@ -1,94 +1,94 @@
	/**
	* @file integration_scheme.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Common interface to all interface schemes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme.hh"
	#include "dof_manager.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	IntegrationScheme::IntegrationScheme(DOFManager & dof_manager,
	const ID & dof_id, UInt order)
	: Parsable(ParserType::_integration_scheme, dof_id),
	- dof_manager(dof_manager), dof_id(dof_id), order(order), u_store(order + 1) {}
	+ dof_manager(dof_manager), dof_id(dof_id), order(order),
	+ u_store(order + 1) {}

	/* -------------------------------------------------------------------------- */
	/// standard input stream operator for SolutionType
	std::istream & operator>>(std::istream & stream,
	IntegrationScheme::SolutionType & type) {
	std::string str;
	stream >> str;
	if (str == "displacement") {
	type = IntegrationScheme::_displacement;
	} else if (str == "temperature") {
	type = IntegrationScheme::_temperature;
	} else if (str == "velocity") {
	type = IntegrationScheme::_velocity;
	} else if (str == "temperature_rate") {
	type = IntegrationScheme::_temperature_rate;
	} else if (str == "acceleration") {
	type = IntegrationScheme::_acceleration;
	} else if (str == "damage") {
	type = IntegrationScheme::_damage;
	} else {
	stream.setstate(std::ios::failbit);
	}

	return stream;
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme::store() {
	for (auto data : enumerate(u_store)) {
	auto o = std::get<0>(data);
	auto & u_store = std::get<1>(data);
	auto & u_o = dof_manager.getDOFsDerivatives(dof_id, o);
	if (not u_store) {
	u_store = std::make_unique<Array<Real>>(
	u_o, "integration_scheme_store:" + dof_id + ":" + std::to_string(o));
	} else {
	u_store->copy(u_o);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme::restore() {
	for (auto o : arange(order)) {
	auto & u_o = dof_manager.getDOFsDerivatives(dof_id, o);
	u_o.copy(*u_store[o]);
	}
	}

	-
	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/integration_scheme.hh b/src/model/common/integration_scheme/integration_scheme.hh
	index 112f30c07..6c861fc62 100644
	--- a/src/model/common/integration_scheme/integration_scheme.hh
	+++ b/src/model/common/integration_scheme/integration_scheme.hh
	@@ -1,125 +1,125 @@
	/**
	* @file integration_scheme.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief This class is just a base class for the integration schemes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTEGRATION_SCHEME_HH_
	#define AKANTU_INTEGRATION_SCHEME_HH_

	namespace akantu {
	class DOFManager;
	}

	namespace akantu {

	class IntegrationScheme : public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	enum SolutionType {
	_not_defined = -1,
	_displacement = 0,
	_temperature = 0,
	_damage = 0,
	_velocity = 1,
	_temperature_rate = 1,
	_acceleration = 2,
	};

	IntegrationScheme(DOFManager & dof_manager, const ID & dof_id, UInt order);
	~IntegrationScheme() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// generic interface of a predictor
	virtual void predictor(Real delta_t) = 0;

	/// generic interface of a corrector
	virtual void corrector(const SolutionType & type, Real delta_t) = 0;

	/// assemble the jacobian matrix
	virtual void assembleJacobian(const SolutionType & type, Real delta_t) = 0;

	/// assemble the residual
	virtual void assembleResidual(bool is_lumped) = 0;

	/// returns a list of needed matrices
	virtual std::vector<std::string> getNeededMatrixList() = 0;

	/// store dofs info (beginning of steps)
	virtual void store();

	/// restore dofs (solve failed)
	virtual void restore();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// return the order of the integration scheme
	UInt getOrder() const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// The underlying DOFManager
	DOFManager & dof_manager;

	/// The id of the dof treated by this integration scheme.
	ID dof_id;

	/// The order of the integrator
	UInt order;

	/// last release of M matrix
	UInt m_release{UInt(-1)};

	/// stores the values at begining of solve
	std::vector<std::unique_ptr<Array<Real>>> u_store;
	};

	/* -------------------------------------------------------------------------- */
	// std::ostream & operator<<(std::ostream & stream,
	// const IntegrationScheme::SolutionType & type);
	std::istream & operator>>(std::istream & stream,
	IntegrationScheme::SolutionType & type);
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_INTEGRATION_SCHEME_HH_ */
	diff --git a/src/model/common/integration_scheme/integration_scheme_1st_order.cc b/src/model/common/integration_scheme/integration_scheme_1st_order.cc
	index c61b52d40..c98548ac4 100644
	--- a/src/model/common/integration_scheme/integration_scheme_1st_order.cc
	+++ b/src/model/common/integration_scheme/integration_scheme_1st_order.cc
	@@ -1,99 +1,99 @@
	/**
	* @file integration_scheme_1st_order.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Implementation of the common functions for 1st order time
	* integrations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme_1st_order.hh"
	#include "dof_manager.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	std::vector<std::string> IntegrationScheme1stOrder::getNeededMatrixList() {
	return {"K", "M"};
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme1stOrder::predictor(Real delta_t) {
	AKANTU_DEBUG_IN();

	Array<Real> & u = this->dof_manager.getDOFs(this->dof_id);
	Array<Real> & u_dot = this->dof_manager.getDOFsDerivatives(this->dof_id, 1);
	const Array<bool> & blocked_dofs =
	this->dof_manager.getBlockedDOFs(this->dof_id);

	this->predictor(delta_t, u, u_dot, blocked_dofs);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme1stOrder::corrector(const SolutionType & type,
	Real delta_t) {
	AKANTU_DEBUG_IN();

	Array<Real> & u = this->dof_manager.getDOFs(this->dof_id);
	Array<Real> & u_dot = this->dof_manager.getDOFsDerivatives(this->dof_id, 1);

	const Array<Real> & solution = this->dof_manager.getSolution(this->dof_id);
	const Array<bool> & blocked_dofs =
	this->dof_manager.getBlockedDOFs(this->dof_id);

	this->corrector(type, delta_t, u, u_dot, blocked_dofs, solution);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme1stOrder::assembleResidual(bool is_lumped) {
	AKANTU_DEBUG_IN();

	const Array<Real> & first_derivative =
	dof_manager.getDOFsDerivatives(this->dof_id, 1);
	if (not is_lumped) {
	if (this->dof_manager.hasMatrix("M")) {
	this->dof_manager.assembleMatMulVectToResidual(this->dof_id, "M",
	first_derivative, -1);
	}
	} else {
	if (this->dof_manager.hasLumpedMatrix("M")) {
	this->dof_manager.assembleLumpedMatMulVectToResidual(
	this->dof_id, "M", first_derivative, -1);
	}
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/integration_scheme_1st_order.hh b/src/model/common/integration_scheme/integration_scheme_1st_order.hh
	index a60424531..c555f6e30 100644
	--- a/src/model/common/integration_scheme/integration_scheme_1st_order.hh
	+++ b/src/model/common/integration_scheme/integration_scheme_1st_order.hh
	@@ -1,96 +1,96 @@
	/**
	* @file integration_scheme_1st_order.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 27 2019
	*
	* @brief Interface of the time integrator of first order
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "integration_scheme.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTEGRATION_SCHEME_1ST_ORDER_HH_
	#define AKANTU_INTEGRATION_SCHEME_1ST_ORDER_HH_

	namespace akantu {

	class IntegrationScheme1stOrder : public IntegrationScheme {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	IntegrationScheme1stOrder(DOFManager & dof_manager, const ID & dof_id)
	: IntegrationScheme(dof_manager, dof_id, 1){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// get list of needed matrices
	std::vector<std::string> getNeededMatrixList() override;

	/// generic interface of a predictor
	void predictor(Real delta_t) override;
	/// generic interface of a corrector
	void corrector(const SolutionType & type, Real delta_t) override;

	/// assemble the residual
	void assembleResidual(bool is_lumped) override;

	protected:
	/// generic interface of a predictor of 1st order
	virtual void predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	const Array<bool> & boundary) const = 0;

	/// generic interface of a corrector of 1st order
	virtual void corrector(const SolutionType & type, Real delta_t,
	Array<Real> & u, Array<Real> & u_dot,
	const Array<bool> & boundary,
	const Array<Real> & delta) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	protected:
	virtual Real getTemperatureCoefficient(const SolutionType & type,
	Real delta_t) const = 0;
	virtual Real getTemperatureRateCoefficient(const SolutionType & type,
	Real delta_t) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	std::unique_ptr<Real> u_dot_store;
	};

	} // namespace akantu

	#include "generalized_trapezoidal.hh"

	#endif /* AKANTU_INTEGRATION_SCHEME_1ST_ORDER_HH_ */
	diff --git a/src/model/common/integration_scheme/integration_scheme_2nd_order.cc b/src/model/common/integration_scheme/integration_scheme_2nd_order.cc
	index 22049e95f..d8fec6105 100644
	--- a/src/model/common/integration_scheme/integration_scheme_2nd_order.cc
	+++ b/src/model/common/integration_scheme/integration_scheme_2nd_order.cc
	@@ -1,107 +1,107 @@
	/**
	* @file integration_scheme_2nd_order.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 23 2015
	* @date last modification: Fri Apr 05 2019
	*
	* @brief Implementation of the common part of 2nd order integration schemes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme_2nd_order.hh"
	#include "dof_manager.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	std::vector<std::string> IntegrationScheme2ndOrder::getNeededMatrixList() {
	return {"K", "M", "C"};
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme2ndOrder::predictor(Real delta_t) {
	AKANTU_DEBUG_IN();

	Array<Real> & u = this->dof_manager.getDOFs(this->dof_id);
	Array<Real> & u_dot = this->dof_manager.getDOFsDerivatives(this->dof_id, 1);
	Array<Real> & u_dot_dot =
	this->dof_manager.getDOFsDerivatives(this->dof_id, 2);
	const Array<bool> & blocked_dofs =
	this->dof_manager.getBlockedDOFs(this->dof_id);

	this->predictor(delta_t, u, u_dot, u_dot_dot, blocked_dofs);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme2ndOrder::corrector(const SolutionType & type,
	Real delta_t) {
	AKANTU_DEBUG_IN();

	Array<Real> & u = this->dof_manager.getDOFs(this->dof_id);
	Array<Real> & u_dot = this->dof_manager.getDOFsDerivatives(this->dof_id, 1);
	Array<Real> & u_dot_dot =
	this->dof_manager.getDOFsDerivatives(this->dof_id, 2);

	const Array<Real> & solution = this->dof_manager.getSolution(this->dof_id);
	const Array<bool> & blocked_dofs =
	this->dof_manager.getBlockedDOFs(this->dof_id);

	this->corrector(type, delta_t, u, u_dot, u_dot_dot, blocked_dofs, solution);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void IntegrationScheme2ndOrder::assembleResidual(bool is_lumped) {
	AKANTU_DEBUG_IN();

	if (this->dof_manager.hasMatrix("C")) {
	const Array<Real> & first_derivative =
	this->dof_manager.getDOFsDerivatives(this->dof_id, 1);

	this->dof_manager.assembleMatMulVectToResidual(this->dof_id, "C",
	first_derivative, -1);
	}

	const Array<Real> & second_derivative =
	this->dof_manager.getDOFsDerivatives(this->dof_id, 2);

	if (not is_lumped) {
	this->dof_manager.assembleMatMulVectToResidual(this->dof_id, "M",
	second_derivative, -1);
	} else {
	this->dof_manager.assembleLumpedMatMulVectToResidual(this->dof_id, "M",
	second_derivative, -1);
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/integration_scheme_2nd_order.hh b/src/model/common/integration_scheme/integration_scheme_2nd_order.hh
	index a8d62a889..5c7fa644f 100644
	--- a/src/model/common/integration_scheme/integration_scheme_2nd_order.hh
	+++ b/src/model/common/integration_scheme/integration_scheme_2nd_order.hh
	@@ -1,108 +1,108 @@
	/**
	* @file integration_scheme_2nd_order.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Interface of the integrator of second order
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "integration_scheme.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTEGRATION_SCHEME_2ND_ORDER_HH_
	#define AKANTU_INTEGRATION_SCHEME_2ND_ORDER_HH_

	namespace akantu {
	class SparseMatrix;
	}

	namespace akantu {

	class IntegrationScheme2ndOrder : public IntegrationScheme {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	IntegrationScheme2ndOrder(DOFManager & dof_manager, const ID & dof_id)
	: IntegrationScheme(dof_manager, dof_id, 2){};

	~IntegrationScheme2ndOrder() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// get list of needed matrices
	std::vector<std::string> getNeededMatrixList() override;

	/// generic interface of a predictor
	void predictor(Real delta_t) override;

	/// generic interface of a corrector
	void corrector(const SolutionType & type, Real delta_t) override;

	void assembleResidual(bool is_lumped) override;

	protected:
	/// generic interface of a predictor of 2nd order
	virtual void predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs) const = 0;

	/// generic interface of a corrector of 2nd order
	virtual void corrector(const SolutionType & type, Real delta_t,
	Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	protected:
	virtual Real getAccelerationCoefficient(const SolutionType & type,
	Real delta_t) const = 0;

	virtual Real getVelocityCoefficient(const SolutionType & type,
	Real delta_t) const = 0;

	virtual Real getDisplacementCoefficient(const SolutionType & type,
	Real delta_t) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	#include "newmark-beta.hh"

	#endif /* AKANTU_INTEGRATION_SCHEME_2ND_ORDER_HH_ */
	diff --git a/src/model/common/integration_scheme/newmark-beta.cc b/src/model/common/integration_scheme/newmark-beta.cc
	index 8a2f0b91a..ac76951a9 100644
	--- a/src/model/common/integration_scheme/newmark-beta.cc
	+++ b/src/model/common/integration_scheme/newmark-beta.cc
	@@ -1,264 +1,264 @@
	/**
	* @file newmark-beta.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Oct 23 2015
	* @date last modification: Wed Mar 27 2019
	*
	* @brief implementation of the newmark-@f$\beta@f$ integration scheme. This
	* implementation is taken from Méthodes numériques en mécanique des solides by
	* Alain Curnier \note{ISBN: 2-88074-247-1}
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "newmark-beta.hh"
	#include "dof_manager.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NewmarkBeta::NewmarkBeta(DOFManager & dof_manager, const ID & dof_id,
	Real alpha, Real beta)
	: IntegrationScheme2ndOrder(dof_manager, dof_id), beta(beta), alpha(alpha),
	k(0.), h(0.), m_release(0), k_release(0), c_release(0) {

	this->registerParam("alpha", this->alpha, alpha, _pat_parsmod,
	"The alpha parameter");
	this->registerParam("beta", this->beta, beta, _pat_parsmod,
	"The beta parameter");
	}

	/* -------------------------------------------------------------------------- */
	/*
	* @f$ \tilde{u_{n+1}} = u_{n} + \Delta t \dot{u}_n + \frac{\Delta t^2}{2}
	* \ddot{u}_n @f$
	* @f$ \tilde{\dot{u}_{n+1}} = \dot{u}_{n} + \Delta t \ddot{u}_{n} @f$
	* @f$ \tilde{\ddot{u}_{n}} = \ddot{u}_{n} @f$
	*/
	void NewmarkBeta::predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = u.size();
	UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;

	Real * u_val = u.storage();
	Real * u_dot_val = u_dot.storage();
	Real * u_dot_dot_val = u_dot_dot.storage();
	bool * blocked_dofs_val = blocked_dofs.storage();

	for (UInt d = 0; d < nb_degree_of_freedom; d++) {
	if (!(*blocked_dofs_val)) {
	Real dt_a_n = delta_t * *u_dot_dot_val;

	u_val += (1 - k alpha) * delta_t * *u_dot_val +
	(.5 - h * alpha * beta) * delta_t * dt_a_n;
	u_dot_val = (1 - k) u_dot_val + (1 - h beta) * dt_a_n;
	u_dot_dot_val = (1 - h) *u_dot_dot_val;
	}
	u_val++;
	u_dot_val++;
	u_dot_dot_val++;
	blocked_dofs_val++;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NewmarkBeta::corrector(const SolutionType & type, Real delta_t,
	Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const {
	AKANTU_DEBUG_IN();

	switch (type) {
	case _acceleration: {
	this->allCorrector<_acceleration>(delta_t, u, u_dot, u_dot_dot,
	blocked_dofs, delta);
	break;
	}
	case _velocity: {
	this->allCorrector<_velocity>(delta_t, u, u_dot, u_dot_dot, blocked_dofs,
	delta);
	break;
	}
	case _displacement: {
	this->allCorrector<_displacement>(delta_t, u, u_dot, u_dot_dot,
	blocked_dofs, delta);
	break;
	}
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real NewmarkBeta::getAccelerationCoefficient(const SolutionType & type,
	Real delta_t) const {
	switch (type) {
	case _acceleration:
	return 1.;
	case _velocity:
	return 1. / (beta * delta_t);
	case _displacement:
	return 1. / (alpha * beta * delta_t * delta_t);
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}
	}

	/* -------------------------------------------------------------------------- */
	Real NewmarkBeta::getVelocityCoefficient(const SolutionType & type,
	Real delta_t) const {
	switch (type) {
	case _acceleration:
	return beta * delta_t;
	case _velocity:
	return 1.;
	case _displacement:
	return 1. / (alpha * delta_t);
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}
	}

	/* -------------------------------------------------------------------------- */
	Real NewmarkBeta::getDisplacementCoefficient(const SolutionType & type,
	Real delta_t) const {
	switch (type) {
	case _acceleration:
	return alpha * beta * delta_t * delta_t;
	case _velocity:
	return alpha * delta_t;
	case _displacement:
	return 1.;
	default:
	AKANTU_EXCEPTION("The corrector type : "
	<< type
	<< " is not supported by this type of integration scheme");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <IntegrationScheme::SolutionType type>
	void NewmarkBeta::allCorrector(Real delta_t, Array<Real> & u,
	Array<Real> & u_dot, Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = u.size();
	UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;

	Real c = getAccelerationCoefficient(type, delta_t);
	Real d = getVelocityCoefficient(type, delta_t);
	Real e = getDisplacementCoefficient(type, delta_t);

	Real * u_val = u.storage();
	Real * u_dot_val = u_dot.storage();
	Real * u_dot_dot_val = u_dot_dot.storage();
	Real * delta_val = delta.storage();
	bool * blocked_dofs_val = blocked_dofs.storage();

	for (UInt dof = 0; dof < nb_degree_of_freedom; dof++) {
	if (!(*blocked_dofs_val)) {
	u_val += e *delta_val;
	u_dot_val += d *delta_val;
	u_dot_dot_val += c *delta_val;
	}
	u_val++;
	u_dot_val++;
	u_dot_dot_val++;
	delta_val++;
	blocked_dofs_val++;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NewmarkBeta::assembleJacobian(const SolutionType & type, Real delta_t) {
	AKANTU_DEBUG_IN();

	SparseMatrix & J = this->dof_manager.getMatrix("J");

	const SparseMatrix & M = this->dof_manager.getMatrix("M");
	const SparseMatrix & K = this->dof_manager.getMatrix("K");

	bool does_j_need_update = false;
	does_j_need_update \|= M.getRelease() != m_release;
	does_j_need_update \|= K.getRelease() != k_release;
	if (this->dof_manager.hasMatrix("C")) {
	const SparseMatrix & C = this->dof_manager.getMatrix("C");
	does_j_need_update \|= C.getRelease() != c_release;
	}

	does_j_need_update \|= this->dof_manager.hasBlockedDOFsChanged();

	if (!does_j_need_update) {
	AKANTU_DEBUG_OUT();
	return;
	}

	J.copyProfile(K);
	// J.zero();

	Real c = this->getAccelerationCoefficient(type, delta_t);
	Real e = this->getDisplacementCoefficient(type, delta_t);

	if (!(e == 0.)) { // in explicit this coefficient is exactly 0.
	J.add(K, e);
	}

	J.add(M, c);

	m_release = M.getRelease();
	k_release = K.getRelease();

	if (this->dof_manager.hasMatrix("C")) {
	Real d = this->getVelocityCoefficient(type, delta_t);
	const SparseMatrix & C = this->dof_manager.getMatrix("C");
	J.add(C, d);
	c_release = C.getRelease();
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/newmark-beta.hh b/src/model/common/integration_scheme/newmark-beta.hh
	index d7a4ee298..163dcc8e9 100644
	--- a/src/model/common/integration_scheme/newmark-beta.hh
	+++ b/src/model/common/integration_scheme/newmark-beta.hh
	@@ -1,197 +1,197 @@
	/**
	* @file newmark-beta.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Oct 05 2010
	* @date last modification: Sat Sep 12 2020
	*
	* @brief implementation of the newmark-@f$\beta@f$ integration scheme. This
	* implementation is taken from Méthodes numériques en mécanique des solides by
	* Alain Curnier \note{ISBN: 2-88074-247-1}
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme_2nd_order.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NEWMARK_BETA_HH_
	#define AKANTU_NEWMARK_BETA_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* The three differentiate equations (dynamic and cinematic) are :
	* \f{eqnarray*}{
	* M \ddot{u}_{n+1} + C \dot{u}_{n+1} + K u_{n+1} &=& q_{n+1} \\
	* u_{n+1} &=& u_{n} + (1 - \alpha) \Delta t \dot{u}_{n} + \alpha \Delta t
	*\dot{u}_{n+1} + (1/2 - \alpha) \Delta t^2 \ddot{u}_n \\
	* \dot{u}_{n+1} &=& \dot{u}_{n} + (1 - \beta) \Delta t \ddot{u}_{n} + \beta
	*\Delta t \ddot{u}_{n+1}
	* \f}
	*
	* Predictor:
	* \f{eqnarray*}{
	* u^{0}_{n+1} &=& u_{n} + \Delta t \dot{u}_n + \frac{\Delta t^2}{2}
	*\ddot{u}_n \\
	* \dot{u}^{0}_{n+1} &=& \dot{u}_{n} + \Delta t \ddot{u}_{n} \\
	* \ddot{u}^{0}_{n+1} &=& \ddot{u}_{n}
	* \f}
	*
	* Solve :
	* \f[ (c M + d C + e K^i_{n+1}) w = = q_{n+1} - f^i_{n+1} - C \dot{u}^i_{n+1}
	*- M \ddot{u}^i_{n+1} \f]
	*
	* Corrector :
	* \f{eqnarray*}{
	* \ddot{u}^{i+1}_{n+1} &=& \ddot{u}^{i}_{n+1} + c w \\
	* \dot{u}^{i+1}_{n+1} &=& \dot{u}^{i}_{n+1} + d w \\
	* u^{i+1}_{n+1} &=& u^{i}_{n+1} + e w
	* \f}
	*
	* c, d and e are parameters depending on the method used to solve the equations
	*\n
	* For acceleration : \f$ w = \delta \ddot{u}, e = \alpha \beta \Delta t^2, d =
	*\beta \Delta t, c = 1 \f$ \n
	* For velocity : \f$ w = \delta \dot{u}, e = 1/\beta \Delta t, d =
	*1, c = \alpha \Delta t \f$ \n
	* For displacement : \f$ w = \delta u, e = 1, d =
	*1/\alpha \Delta t, c = 1/\alpha \beta \Delta t^2 \f$
	*/

	class NewmarkBeta : public IntegrationScheme2ndOrder {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NewmarkBeta(DOFManager & dof_manager, const ID & dof_id, Real alpha = 0.,
	Real beta = 0.);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs) const override;

	void corrector(const SolutionType & type, Real delta_t, Array<Real> & u,
	Array<Real> & u_dot, Array<Real> & u_dot_dot,
	const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const override;

	void assembleJacobian(const SolutionType & type, Real delta_t) override;

	public:
	Real getAccelerationCoefficient(const SolutionType & type,
	Real delta_t) const override;

	Real getVelocityCoefficient(const SolutionType & type,
	Real delta_t) const override;

	Real getDisplacementCoefficient(const SolutionType & type,
	Real delta_t) const override;

	private:
	template <SolutionType type>
	void allCorrector(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
	Array<Real> & u_dot_dot, const Array<bool> & blocked_dofs,
	const Array<Real> & delta) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Beta, beta, Real);
	AKANTU_GET_MACRO(Alpha, alpha, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// the \f$\beta\f$ parameter
	Real beta;

	/// the \f$\alpha\f$ parameter
	Real alpha;

	Real k;
	Real h;

	/// last release of M matrix
	UInt m_release;

	/// last release of K matrix
	UInt k_release;

	/// last release of C matrix
	UInt c_release;
	};

	/**
	* central difference method (explicit)
	* undamped stability condition :
	* \f$ \Delta t = \alpha \Delta t_{crit} = \frac{2}{\omega_{max}} \leq \min_{e}
	*\frac{l_e}{c_e}\f$
	*
	*/
	class CentralDifference : public NewmarkBeta {
	public:
	CentralDifference(DOFManager & dof_manager, const ID & dof_id)
	- : NewmarkBeta(dof_manager, dof_id, 0., 1./2.){};
	+ : NewmarkBeta(dof_manager, dof_id, 0., 1. / 2.){};

	std::vector<std::string> getNeededMatrixList() override { return {"M", "C"}; }
	};

	//#include "integration_scheme/central_difference.hh"

	/// undamped trapezoidal rule (implicit)
	class TrapezoidalRule2 : public NewmarkBeta {
	public:
	TrapezoidalRule2(DOFManager & dof_manager, const ID & dof_id)
	: NewmarkBeta(dof_manager, dof_id, 1. / 2., 1. / 2.){};
	};

	/// Fox-Goodwin rule (implicit)
	class FoxGoodwin : public NewmarkBeta {
	public:
	FoxGoodwin(DOFManager & dof_manager, const ID & dof_id)
	: NewmarkBeta(dof_manager, dof_id, 1. / 6., 1. / 2.){};
	};

	/// Linear acceleration (implicit)
	class LinearAceleration : public NewmarkBeta {
	public:
	LinearAceleration(DOFManager & dof_manager, const ID & dof_id)
	: NewmarkBeta(dof_manager, dof_id, 1. / 3., 1. / 2.){};
	};

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_NEWMARK_BETA_HH_ */
	diff --git a/src/model/common/integration_scheme/pseudo_time.cc b/src/model/common/integration_scheme/pseudo_time.cc
	index aaeacd5a7..f4d49cbe4 100644
	--- a/src/model/common/integration_scheme/pseudo_time.cc
	+++ b/src/model/common/integration_scheme/pseudo_time.cc
	@@ -1,91 +1,91 @@
	/**
	* @file pseudo_time.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Feb 19 2016
	* @date last modification: Wed Mar 27 2019
	*
	* @brief Implementation of a really simple integration scheme
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "pseudo_time.hh"
	#include "dof_manager.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	PseudoTime::PseudoTime(DOFManager & dof_manager, const ID & dof_id)
	: IntegrationScheme(dof_manager, dof_id, 0), k_release(0) {}

	/* -------------------------------------------------------------------------- */
	std::vector<std::string> PseudoTime::getNeededMatrixList() { return {"K"}; }

	/* -------------------------------------------------------------------------- */
	void PseudoTime::predictor(Real /delta_t/) {}

	/* -------------------------------------------------------------------------- */
	void PseudoTime::corrector(const SolutionType & /type/, Real /delta_t/) {
	auto & us = this->dof_manager.getDOFs(this->dof_id);
	const auto & deltas = this->dof_manager.getSolution(this->dof_id);
	const auto & blocked_dofs = this->dof_manager.getBlockedDOFs(this->dof_id);

	for (auto && tuple : zip(make_view(us), deltas, make_view(blocked_dofs))) {
	auto & u = std::get<0>(tuple);
	const auto & delta = std::get<1>(tuple);
	const auto & bld = std::get<2>(tuple);
	if (not bld) {
	u += delta;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void PseudoTime::assembleJacobian(const SolutionType & /type/,
	Real /delta_t/) {
	SparseMatrix & J = this->dof_manager.getMatrix("J");
	const SparseMatrix & K = this->dof_manager.getMatrix("K");

	bool does_j_need_update = false;
	does_j_need_update \|= K.getRelease() != k_release;
	does_j_need_update \|= this->dof_manager.hasBlockedDOFsChanged();

	if (not does_j_need_update) {
	AKANTU_DEBUG_OUT();
	return;
	}

	J.copyProfile(K);
	// J.zero();
	J.add(K);
	k_release = K.getRelease();
	}

	/* -------------------------------------------------------------------------- */
	void PseudoTime::assembleResidual(bool /is_lumped/) {}
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/integration_scheme/pseudo_time.hh b/src/model/common/integration_scheme/pseudo_time.hh
	index 363b3bdc2..ca7cacf84 100644
	--- a/src/model/common/integration_scheme/pseudo_time.hh
	+++ b/src/model/common/integration_scheme/pseudo_time.hh
	@@ -1,74 +1,74 @@
	/**
	* @file pseudo_time.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Pseudo time integration scheme
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PSEUDO_TIME_HH_
	#define AKANTU_PSEUDO_TIME_HH_

	namespace akantu {

	class PseudoTime : public IntegrationScheme {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	PseudoTime(DOFManager & dof_manager, const ID & dof_id);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// get list of needed matrices
	std::vector<std::string> getNeededMatrixList() override;

	/// generic interface of a predictor
	void predictor(Real delta_t) override;

	/// generic interface of a corrector
	void corrector(const SolutionType & type, Real delta_t) override;

	/// assemble the jacobian matrix
	void assembleJacobian(const SolutionType & type, Real delta_t) override;

	/// assemble the residual
	void assembleResidual(bool is_lumped) override;

	protected:
	/// last release of K matrix
	UInt k_release;
	};

	} // namespace akantu

	#endif /* AKANTU_PSEUDO_TIME_HH_ */
	diff --git a/src/model/common/model_solver.cc b/src/model/common/model_solver.cc
	index d839deade..3c6de5ad3 100644
	--- a/src/model/common/model_solver.cc
	+++ b/src/model/common/model_solver.cc
	@@ -1,406 +1,404 @@
	/**
	* @file model_solver.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Tue Mar 30 2021
	*
	* @brief Implementation of ModelSolver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "model_solver.hh"
	#include "dof_manager.hh"
	#include "dof_manager_default.hh"
	#include "mesh.hh"
	#include "non_linear_solver.hh"
	#include "time_step_solver.hh"

	#if defined(AKANTU_USE_PETSC)
	#include "dof_manager_petsc.hh"
	#endif

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T> static T getOptionToType(const std::string & opt_str) {
	std::stringstream sstr(opt_str);
	T opt;
	sstr >> opt;

	return opt;
	}

	/* -------------------------------------------------------------------------- */
	ModelSolver::ModelSolver(Mesh & mesh, const ModelType & type, const ID & id)
	- : Parsable(ParserType::_model, id), model_type(type),
	- parent_id(id), mesh(mesh) {
	-}
	+ : Parsable(ParserType::_model, id), model_type(type), parent_id(id),
	+ mesh(mesh) {}

	/* -------------------------------------------------------------------------- */
	ModelSolver::ModelSolver(Mesh & mesh, const ModelType & type, const ID & id,
	std::shared_ptr<DOFManager> dof_manager)
	: ModelSolver(mesh, type, id) {
	if (not dof_manager) {
	this->initDOFManager();
	} else {
	this->dof_manager = dof_manager;
	this->setDOFManager(*this->dof_manager);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolver::~ModelSolver() = default;

	/* -------------------------------------------------------------------------- */
	std::tuple<ParserSection, bool> ModelSolver::getParserSection() {
	auto sub_sections = getStaticParser().getSubSections(ParserType::_model);

	auto it = std::find_if(
	sub_sections.begin(), sub_sections.end(), [&](auto && section) {
	auto type = getOptionToType<ModelType>(section.getName());
	// default id should be the model type if not defined
	std::string name = section.getParameter("name", this->parent_id);
	return type == model_type and name == this->parent_id;
	});

	if (it == sub_sections.end()) {
	return std::make_tuple(ParserSection(), true);
	}

	return std::make_tuple(*it, false);
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<DOFManager> ModelSolver::initDOFManager() {
	// default without external solver activated at compilation same as mumps that
	// is the historical solver but with only the lumped solver
	ID solver_type = "default";

	#if defined(AKANTU_USE_MUMPS)
	solver_type = "default";
	#elif defined(AKANTU_USE_PETSC)
	solver_type = "petsc";
	#endif

	ParserSection section;
	bool is_empty;
	std::tie(section, is_empty) = this->getParserSection();

	if (not is_empty) {
	solver_type = section.getOption(solver_type);
	return this->initDOFManager(section, solver_type);
	- } else {
	- return this->initDOFManager(solver_type);
	}
	+ return this->initDOFManager(solver_type);
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<DOFManager>
	ModelSolver::initDOFManager(const ID & solver_type) {
	if (dof_manager) {
	AKANTU_EXCEPTION("The DOF manager for this model is already initialized !");
	}

	try {
	this->dof_manager = DOFManagerFactory::getInstance().allocate(
	solver_type, mesh, this->parent_id + ":dof_manager_" + solver_type);
	} catch (...) {
	AKANTU_EXCEPTION(
	"To use the solver "
	<< solver_type
	<< " you will have to code it. This is an unknown solver type.");
	}

	this->setDOFManager(*this->dof_manager);
	return this->dof_manager;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<DOFManager>
	ModelSolver::initDOFManager(const ParserSection & section,
	const ID & solver_type) {
	this->initDOFManager(solver_type);
	auto sub_sections = section.getSubSections(ParserType::_time_step_solver);

	// parsing the time step solvers
	for (auto && section : sub_sections) {
	ID type = section.getName();
	ID solver_id = section.getParameter("name", type);

	auto tss_type = getOptionToType<TimeStepSolverType>(type);
	auto tss_options = this->getDefaultSolverOptions(tss_type);

	auto sub_solvers_sect =
	section.getSubSections(ParserType::_non_linear_solver);
	auto nb_non_linear_solver_section =
	section.getNbSubSections(ParserType::_non_linear_solver);

	auto nls_type = tss_options.non_linear_solver_type;

	if (nb_non_linear_solver_section == 1) {
	auto && nls_section = *(sub_solvers_sect.first);
	nls_type = getOptionToType<NonLinearSolverType>(nls_section.getName());
	} else if (nb_non_linear_solver_section > 0) {
	AKANTU_EXCEPTION("More than one non linear solver are provided for the "
	"time step solver "
	<< solver_id);
	}

	this->getNewSolver(solver_id, tss_type, nls_type);
	if (nb_non_linear_solver_section == 1) {
	const auto & nls_section = *(sub_solvers_sect.first);
	this->dof_manager->getNonLinearSolver(solver_id).parseSection(
	nls_section);
	}

	auto sub_integrator_sections =
	section.getSubSections(ParserType::_integration_scheme);

	for (auto && is_section : sub_integrator_sections) {
	const auto & dof_type_str = is_section.getName();
	ID dof_id;
	try {
	ID tmp = is_section.getParameter("name");
	dof_id = tmp;
	} catch (...) {
	AKANTU_EXCEPTION("No degree of freedom name specified for the "
	"integration scheme of type "
	<< dof_type_str);
	}

	auto it_type = getOptionToType<IntegrationSchemeType>(dof_type_str);

	IntegrationScheme::SolutionType s_type = is_section.getParameter(
	"solution_type", tss_options.solution_type[dof_id]);
	this->setIntegrationScheme(solver_id, dof_id, it_type, s_type);
	}

	for (auto & is_type : tss_options.integration_scheme_type) {
	if (!this->hasIntegrationScheme(solver_id, is_type.first)) {
	this->setIntegrationScheme(solver_id, is_type.first, is_type.second,
	tss_options.solution_type[is_type.first]);
	}
	}
	}

	if (section.hasParameter("default_solver")) {
	ID default_solver = section.getParameter("default_solver");
	if (this->hasSolver(default_solver)) {
	this->setDefaultSolver(default_solver);
	} else {
	AKANTU_EXCEPTION(
	"The solver \""
	<< default_solver
	<< "\" was not created, it cannot be set as default solver");
	}
	}

	return this->dof_manager;
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & ModelSolver::getSolver(const ID & solver_id) {
	ID tmp_solver_id = solver_id;
	if (tmp_solver_id.empty()) {
	tmp_solver_id = this->default_solver_id;
	}

	TimeStepSolver & tss = this->dof_manager->getTimeStepSolver(tmp_solver_id);
	return tss;
	}

	/* -------------------------------------------------------------------------- */
	const TimeStepSolver & ModelSolver::getSolver(const ID & solver_id) const {
	ID tmp_solver_id = solver_id;
	if (solver_id.empty()) {
	tmp_solver_id = this->default_solver_id;
	}

	const TimeStepSolver & tss =
	this->dof_manager->getTimeStepSolver(tmp_solver_id);
	return tss;
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & ModelSolver::getTimeStepSolver(const ID & solver_id) {
	return this->getSolver(solver_id);
	}

	/* -------------------------------------------------------------------------- */
	const TimeStepSolver &
	ModelSolver::getTimeStepSolver(const ID & solver_id) const {
	return this->getSolver(solver_id);
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver & ModelSolver::getNonLinearSolver(const ID & solver_id) {
	return this->getSolver(solver_id).getNonLinearSolver();
	}
	/* -------------------------------------------------------------------------- */
	const NonLinearSolver &
	ModelSolver::getNonLinearSolver(const ID & solver_id) const {
	return this->getSolver(solver_id).getNonLinearSolver();
	}

	/* -------------------------------------------------------------------------- */
	bool ModelSolver::hasSolver(const ID & solver_id) const {
	ID tmp_solver_id = solver_id;
	if (solver_id.empty()) {
	tmp_solver_id = this->default_solver_id;
	}

	if (not this->dof_manager) {
	AKANTU_EXCEPTION("No DOF manager was initialized");
	}
	return this->dof_manager->hasTimeStepSolver(tmp_solver_id);
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::setDefaultSolver(const ID & solver_id) {
	AKANTU_DEBUG_ASSERT(
	this->hasSolver(solver_id),
	"Cannot set the default solver to a solver that does not exists");
	this->default_solver_id = solver_id;
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::solveStep(SolverCallback & callback, const ID & solver_id) {
	AKANTU_DEBUG_IN();

	TimeStepSolver & tss = this->getSolver(solver_id);
	// make one non linear solve
	tss.solveStep(callback);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::solveStep(const ID & solver_id) {
	solveStep(*this, solver_id);
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::getNewSolver(const ID & solver_id,
	TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type) {
	if (this->default_solver_id.empty()) {
	this->default_solver_id = solver_id;
	}

	if (non_linear_solver_type == NonLinearSolverType::_auto) {
	switch (time_step_solver_type) {
	case TimeStepSolverType::_dynamic:
	case TimeStepSolverType::_static:
	non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	break;
	case TimeStepSolverType::_dynamic_lumped:
	non_linear_solver_type = NonLinearSolverType::_lumped;
	break;
	case TimeStepSolverType::_not_defined:
	AKANTU_EXCEPTION(time_step_solver_type
	<< " is not a valid time step solver type");
	break;
	}
	}

	this->initSolver(time_step_solver_type, non_linear_solver_type);

	NonLinearSolver & nls = this->dof_manager->getNewNonLinearSolver(
	solver_id, non_linear_solver_type);

	this->dof_manager->getNewTimeStepSolver(solver_id, time_step_solver_type, nls,
	*this);
	}

	/* -------------------------------------------------------------------------- */
	Real ModelSolver::getTimeStep(const ID & solver_id) const {
	const TimeStepSolver & tss = this->getSolver(solver_id);

	return tss.getTimeStep();
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::setTimeStep(Real time_step, const ID & solver_id) {
	TimeStepSolver & tss = this->getSolver(solver_id);

	return tss.setTimeStep(time_step);
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::setIntegrationScheme(
	const ID & solver_id, const ID & dof_id,
	const IntegrationSchemeType & integration_scheme_type,
	IntegrationScheme::SolutionType solution_type) {
	TimeStepSolver & tss = this->dof_manager->getTimeStepSolver(solver_id);

	tss.setIntegrationScheme(dof_id, integration_scheme_type, solution_type);
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::setIntegrationScheme(
	const ID & solver_id, const ID & dof_id,
	std::unique_ptr<IntegrationScheme> & integration_scheme,
	IntegrationScheme::SolutionType solution_type) {
	TimeStepSolver & tss = this->dof_manager->getTimeStepSolver(solver_id);

	tss.setIntegrationScheme(dof_id, integration_scheme, solution_type);
	}

	/* -------------------------------------------------------------------------- */
	bool ModelSolver::hasDefaultSolver() const {
	return (not this->default_solver_id.empty());
	}

	/* -------------------------------------------------------------------------- */
	bool ModelSolver::hasIntegrationScheme(const ID & solver_id,
	const ID & dof_id) const {
	TimeStepSolver & tss = this->dof_manager->getTimeStepSolver(solver_id);
	return tss.hasIntegrationScheme(dof_id);
	}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::predictor() {}

	/* -------------------------------------------------------------------------- */
	void ModelSolver::corrector() {}

	/* -------------------------------------------------------------------------- */
	TimeStepSolverType ModelSolver::getDefaultSolverType() const {
	return TimeStepSolverType::_dynamic_lumped;
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions
	ModelSolver::getDefaultSolverOptions(__attribute__((unused))
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;
	options.non_linear_solver_type = NonLinearSolverType::_auto;
	return options;
	}

	} // namespace akantu
	diff --git a/src/model/common/model_solver.hh b/src/model/common/model_solver.hh
	index 71aca285b..3cb511baf 100644
	--- a/src/model/common/model_solver.hh
	+++ b/src/model/common/model_solver.hh
	@@ -1,205 +1,204 @@
	/**
	* @file model_solver.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri May 14 2021
	*
	* @brief Class regrouping the common solve interface to the different models
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "integration_scheme.hh"
	#include "parsable.hh"
	#include "solver_callback.hh"
	#include "synchronizer_registry.hh"
	/* -------------------------------------------------------------------------- */
	#include <set>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MODEL_SOLVER_HH_
	#define AKANTU_MODEL_SOLVER_HH_

	namespace akantu {
	class Mesh;
	class DOFManager;
	class TimeStepSolver;
	class NonLinearSolver;
	struct ModelSolverOptions;
	} // namespace akantu

	namespace akantu {

	class ModelSolver : public Parsable,
	public SolverCallback,
	public SynchronizerRegistry {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ModelSolver(Mesh & mesh, const ModelType & type, const ID & id);
	ModelSolver(Mesh & mesh, const ModelType & type, const ID & id,
	std::shared_ptr<DOFManager> dof_manager);

	~ModelSolver() override;

	/// initialize the dof manager based on solver type passed in the input file
	std::shared_ptr<DOFManager> initDOFManager();
	/// initialize the dof manager based on the used chosen solver type
	std::shared_ptr<DOFManager> initDOFManager(const ID & solver_type);

	protected:
	/// initialize the dof manager based on the used chosen solver type
	std::shared_ptr<DOFManager> initDOFManager(const ParserSection & section,
	const ID & solver_type);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Callback for the model to instantiate the matricees when needed
	virtual void initSolver(TimeStepSolverType /time_step_solver_type/,
	NonLinearSolverType /non_linear_solver_type/) {}

	/// get the section in the input file (if it exsits) corresponding to this
	/// model
	std::tuple<ParserSection, bool> getParserSection();

	-
	/// solve a step using a given pre instantiated time step solver and
	/// non linear solver
	virtual void solveStep(const ID & solver_id = "");

	/// solve a step using a given pre instantiated time step solver and
	/// non linear solver with a user defined callback instead of the
	/// model itself /!\ This can mess up everything
	virtual void solveStep(SolverCallback & callback, const ID & solver_id = "");

	/// Initialize a time solver that can be used afterwards with its id
	void getNewSolver(
	const ID & solver_id, TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type = NonLinearSolverType::_auto);

	/// set an integration scheme for a given dof and a given solver
	void
	setIntegrationScheme(const ID & solver_id, const ID & dof_id,
	const IntegrationSchemeType & integration_scheme_type,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined);

	/// set an externally instantiated integration scheme
	void
	setIntegrationScheme(const ID & solver_id, const ID & dof_id,
	std::unique_ptr<IntegrationScheme> & integration_scheme,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined);

	/* ------------------------------------------------------------------------ */
	/* SolverCallback interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// Predictor interface for the callback
	void predictor() override;

	/// Corrector interface for the callback
	void corrector() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Default time step solver to instantiate for this model
	virtual TimeStepSolverType getDefaultSolverType() const;

	/// Default configurations for a given time step solver
	virtual ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const;

	/// get access to the internal dof manager
	DOFManager & getDOFManager() { return *this->dof_manager; }

	/// get the time step of a given solver
	Real getTimeStep(const ID & solver_id = "") const;
	/// set the time step of a given solver
	virtual void setTimeStep(Real time_step, const ID & solver_id = "");

	/// set the parameter 'param' of the solver 'solver_id'
	// template <typename T>
	// void set(const ID & param, const T & value, const ID & solver_id = "");

	/// get the parameter 'param' of the solver 'solver_id'
	// const Parameter & get(const ID & param, const ID & solver_id = "") const;

	/// answer to the question "does the solver exists ?"
	bool hasSolver(const ID & solver_id) const;

	/// changes the current default solver
	void setDefaultSolver(const ID & solver_id);

	/// is a default solver defined
	bool hasDefaultSolver() const;

	/// is an integration scheme set for a given solver and a given dof
	bool hasIntegrationScheme(const ID & solver_id, const ID & dof_id) const;

	TimeStepSolver & getTimeStepSolver(const ID & solver_id = "");
	NonLinearSolver & getNonLinearSolver(const ID & solver_id = "");

	const TimeStepSolver & getTimeStepSolver(const ID & solver_id = "") const;
	const NonLinearSolver & getNonLinearSolver(const ID & solver_id = "") const;

	private:
	TimeStepSolver & getSolver(const ID & solver_id);
	const TimeStepSolver & getSolver(const ID & solver_id) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ModelType model_type;

	/// Underlying dof_manager (the brain...)
	std::shared_ptr<DOFManager> dof_manager;

	private:
	ID parent_id;

	/// Underlying mesh
	Mesh & mesh;

	/// Default time step solver to use
	ID default_solver_id;
	};

	struct ModelSolverOptions {
	NonLinearSolverType non_linear_solver_type;
	std::map<ID, IntegrationSchemeType> integration_scheme_type;
	std::map<ID, IntegrationScheme::SolutionType> solution_type;
	};

	} // namespace akantu

	#endif /* AKANTU_MODEL_SOLVER_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver.cc b/src/model/common/non_linear_solver/non_linear_solver.cc
	index bf784c111..ca25aebb3 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver.cc
	+++ b/src/model/common/non_linear_solver/non_linear_solver.cc
	@@ -1,80 +1,80 @@
	/**
	* @file non_linear_solver.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 20 2010
	* @date last modification: Tue Jan 01 2019
	*
	* @brief Implementation of the base class NonLinearSolver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "dof_manager.hh"
	#include "solver_callback.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLinearSolver::NonLinearSolver(
	DOFManager & dof_manager,
	const NonLinearSolverType & non_linear_solver_type, const ID & id)
	: Parsable(ParserType::_non_linear_solver, id), id(id),
	_dof_manager(dof_manager),
	non_linear_solver_type(non_linear_solver_type) {

	this->registerParam("type", this->non_linear_solver_type, _pat_parsable,
	"Non linear solver type");
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver::~NonLinearSolver() = default;

	/* -------------------------------------------------------------------------- */
	void NonLinearSolver::checkIfTypeIsSupported() {
	if (this->supported_type.find(this->non_linear_solver_type) ==
	this->supported_type.end() and
	this->non_linear_solver_type != NonLinearSolverType::_auto) {
	AKANTU_EXCEPTION("The resolution method "
	<< this->non_linear_solver_type
	<< " is not implemented in the non linear solver "
	<< this->id << "!");
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLinearSolver::assembleResidual(SolverCallback & solver_callback) {
	if (solver_callback.canSplitResidual() and
	non_linear_solver_type == NonLinearSolverType::_linear) {
	this->_dof_manager.zeroResidual();
	solver_callback.assembleResidual("external");
	this->_dof_manager.assembleMatMulDOFsToResidual("K", -1.);
	solver_callback.assembleResidual("inertial");
	} else {
	solver_callback.assembleResidual();
	}
	}

	} // namespace akantu
	diff --git a/src/model/common/non_linear_solver/non_linear_solver.hh b/src/model/common/non_linear_solver/non_linear_solver.hh
	index 6e0561ba7..bc8127e8f 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver.hh
	@@ -1,115 +1,115 @@
	/**
	* @file non_linear_solver.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 27 2019
	*
	* @brief Non linear solver interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */
	#include <set>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_HH_
	#define AKANTU_NON_LINEAR_SOLVER_HH_

	namespace akantu {
	class DOFManager;
	class SolverCallback;
	} // namespace akantu

	namespace akantu {

	class NonLinearSolver : public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLinearSolver(DOFManager & dof_manager,
	const NonLinearSolverType & non_linear_solver_type,
	const ID & id = "non_linear_solver");
	~NonLinearSolver() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// solve the system described by the jacobian matrix, and rhs contained in
	/// the dof manager
	virtual void solve(SolverCallback & callback) = 0;

	/// intercept the call to set for options
	template <typename T> void set(const ID & param, T && t) {
	if (has_internal_set_param) {
	set_param(param, std::to_string(t));
	} else {
	ParameterRegistry::set(param, t);
	}
	}

	protected:
	void checkIfTypeIsSupported();

	void assembleResidual(SolverCallback & callback);

	/// internal set param for solvers that should intercept the parameters
	virtual void set_param(const ID & /param/, const std::string & /value/) {}
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	DOFManager & _dof_manager;

	/// type of non linear solver
	NonLinearSolverType non_linear_solver_type;

	/// list of supported non linear solver types
	std::set<NonLinearSolverType> supported_type;

	/// specifies if the set param should be redirected
	bool has_internal_set_param{false};
	};

	namespace debug {
	class NLSNotConvergedException : public Exception {
	public:
	NLSNotConvergedException(Real threshold, UInt niter, Real error)
	: Exception("The non linear solver did not converge."),
	threshold(threshold), niter(niter), error(error) {}
	Real threshold;
	UInt niter;
	Real error;
	};
	} // namespace debug

	} // namespace akantu

	#endif /* AKANTU_NON_LINEAR_SOLVER_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_default.hh b/src/model/common/non_linear_solver/non_linear_solver_default.hh
	index 56712fc87..cb90dc137 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_default.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver_default.hh
	@@ -1,46 +1,46 @@
	/**
	* @file non_linear_solver_default.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Dec 18 2019
	*
	* @brief Include for the default non linear solvers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_DEFAULT_HH_
	#define AKANTU_NON_LINEAR_SOLVER_DEFAULT_HH_

	#if defined(AKANTU_USE_MUMPS)
	#include "non_linear_solver_linear.hh"
	#include "non_linear_solver_newton_raphson.hh"
	#endif

	#include "non_linear_solver_lumped.hh"

	#endif /* AKANTU_NON_LINEAR_SOLVER_DEFAULT_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_linear.cc b/src/model/common/non_linear_solver/non_linear_solver_linear.cc
	index 18a920440..f73911c5c 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_linear.cc
	+++ b/src/model/common/non_linear_solver/non_linear_solver_linear.cc
	@@ -1,83 +1,83 @@
	/**
	* @file non_linear_solver_linear.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 20 2010
	* @date last modification: Fri Feb 05 2021
	*
	* @brief Implementation of the default NonLinearSolver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver_linear.hh"
	#include "dof_manager_default.hh"
	#include "solver_callback.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLinearSolverLinear::NonLinearSolverLinear(
	DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type, const ID & id)
	: NonLinearSolver(dof_manager, non_linear_solver_type, id),
	dof_manager(dof_manager),
	solver(dof_manager, "J", id + ":sparse_solver") {

	this->supported_type.insert(NonLinearSolverType::_linear);
	this->checkIfTypeIsSupported();
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolverLinear::~NonLinearSolverLinear() = default;

	/* ------------------------------------------------------------------------ */
	void NonLinearSolverLinear::solve(SolverCallback & solver_callback) {
	solver_callback.beforeSolveStep();
	this->dof_manager.updateGlobalBlockedDofs();

	solver_callback.predictor();

	solver_callback.assembleMatrix("J");

	// Residual computed after J to allow the model to use K to compute the
	// residual
	this->assembleResidual(solver_callback);

	this->solver.solve();

	solver_callback.corrector();

	if (solver_callback.canSplitResidual()) {
	solver_callback.assembleResidual("internal");
	} else {
	this->assembleResidual(solver_callback);
	}

	solver_callback.afterSolveStep(true);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_linear.hh b/src/model/common/non_linear_solver/non_linear_solver_linear.hh
	index 07382f525..811bbd4fd 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_linear.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver_linear.hh
	@@ -1,80 +1,80 @@
	/**
	* @file non_linear_solver_linear.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Default implementation of NonLinearSolver, in case no external
	* library
	* is there to do the job
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "sparse_solver_mumps.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_LINEAR_HH_
	#define AKANTU_NON_LINEAR_SOLVER_LINEAR_HH_

	namespace akantu {
	class DOFManagerDefault;
	}

	namespace akantu {

	class NonLinearSolverLinear : public NonLinearSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLinearSolverLinear(DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type,
	const ID & id = "non_linear_solver_linear");
	~NonLinearSolverLinear() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Function that solve the non linear system described by the dof manager and
	/// the solver callback functions
	void solve(SolverCallback & solver_callback) override;

	AKANTU_GET_MACRO_NOT_CONST(Solver, solver, SparseSolverMumps &);
	AKANTU_GET_MACRO(Solver, solver, const SparseSolverMumps &);
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	DOFManagerDefault & dof_manager;

	/// Sparse solver used for the linear solves
	SparseSolverMumps solver;
	};

	} // namespace akantu

	#endif /* AKANTU_NON_LINEAR_SOLVER_LINEAR_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_lumped.cc b/src/model/common/non_linear_solver/non_linear_solver_lumped.cc
	index 316c884de..d1439e974 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_lumped.cc
	+++ b/src/model/common/non_linear_solver/non_linear_solver_lumped.cc
	@@ -1,103 +1,103 @@
	/**
	* @file non_linear_solver_lumped.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 16 2016
	* @date last modification: Sat May 23 2020
	*
	* @brief Implementation of the default NonLinearSolver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver_lumped.hh"
	#include "communicator.hh"
	#include "dof_manager_default.hh"
	#include "solver_callback.hh"
	#include "solver_vector_default.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLinearSolverLumped::NonLinearSolverLumped(
	DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type, const ID & id)
	: NonLinearSolver(dof_manager, non_linear_solver_type, id),
	dof_manager(dof_manager) {
	this->supported_type.insert(NonLinearSolverType::_lumped);
	this->checkIfTypeIsSupported();

	this->registerParam("b_a2x", this->alpha, 1., _pat_parsmod,
	"Conversion coefficient between x and A^{-1} b");
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolverLumped::~NonLinearSolverLumped() = default;

	/* ------------------------------------------------------------------------ */
	void NonLinearSolverLumped::solve(SolverCallback & solver_callback) {
	solver_callback.beforeSolveStep();
	this->dof_manager.updateGlobalBlockedDofs();
	solver_callback.predictor();

	solver_callback.assembleResidual();

	auto & x = aka::as_type<SolverVectorDefault>(this->dof_manager.getSolution());
	const auto & b = this->dof_manager.getResidual();

	x.resize();

	const auto & blocked_dofs = this->dof_manager.getBlockedDOFs();
	const auto & A = this->dof_manager.getLumpedMatrix("M");

	// alpha is the conversion factor from from force/mass to acceleration needed
	// in model coupled with atomistic \todo find a way to define alpha per dof
	// type
	NonLinearSolverLumped::solveLumped(A, x, b, alpha, blocked_dofs);

	this->dof_manager.splitSolutionPerDOFs();

	solver_callback.corrector();
	solver_callback.afterSolveStep(true);
	}

	/* -------------------------------------------------------------------------- */
	void NonLinearSolverLumped::solveLumped(const Array<Real> & A, Array<Real> & x,
	const Array<Real> & b, Real alpha,
	const Array<bool> & blocked_dofs) {
	for (auto && data :
	zip(make_view(A), make_view(x), make_view(b), make_view(blocked_dofs))) {
	const auto & A = std::get<0>(data);
	auto & x = std::get<1>(data);
	const auto & b = std::get<2>(data);
	const auto & blocked = std::get<3>(data);
	if (not blocked) {
	x = alpha * (b / A);
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_lumped.hh b/src/model/common/non_linear_solver/non_linear_solver_lumped.hh
	index 5d8ca75cc..e71bf3758 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_lumped.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver_lumped.hh
	@@ -1,81 +1,81 @@
	/**
	* @file non_linear_solver_lumped.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 13 2019
	*
	* @brief Default implementation of NonLinearSolver, in case no external
	* library
	* is there to do the job
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_LUMPED_HH_
	#define AKANTU_NON_LINEAR_SOLVER_LUMPED_HH_

	namespace akantu {
	class DOFManagerDefault;
	}

	namespace akantu {

	class NonLinearSolverLumped : public NonLinearSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLinearSolverLumped(DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type,
	const ID & id = "non_linear_solver_lumped");
	~NonLinearSolverLumped() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Function that solve the non linear system described by the dof manager and
	/// the solver callback functions
	void solve(SolverCallback & solver_callback) override;

	static void solveLumped(const Array<Real> & A, Array<Real> & x,
	const Array<Real> & b, Real alpha,
	const Array<bool> & blocked_dofs);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	DOFManagerDefault & dof_manager;

	/// Coefficient to apply between x and A^{-1} b
	Real alpha;
	};

	} // namespace akantu

	#endif /* AKANTU_NON_LINEAR_SOLVER_LUMPED_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.cc b/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.cc
	index 3def8f178..39f94397a 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.cc
	+++ b/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.cc
	@@ -1,211 +1,210 @@
	/**
	* @file non_linear_solver_newton_raphson.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 15 2015
	* @date last modification: Tue Mar 30 2021
	*
	* @brief Implementation of the default NonLinearSolver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver_newton_raphson.hh"
	#include "communicator.hh"
	#include "dof_manager_default.hh"
	#include "solver_callback.hh"
	#include "solver_vector.hh"
	#include "sparse_solver_mumps.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLinearSolverNewtonRaphson::NonLinearSolverNewtonRaphson(
	DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type, const ID & id)
	: NonLinearSolver(dof_manager, non_linear_solver_type, id),
	- dof_manager(dof_manager),
	- solver(std::make_unique<SparseSolverMumps>(
	- dof_manager, "J", id + ":sparse_solver")) {
	+ dof_manager(dof_manager), solver(std::make_unique<SparseSolverMumps>(
	+ dof_manager, "J", id + ":sparse_solver")) {

	this->supported_type.insert(NonLinearSolverType::_newton_raphson_modified);
	this->supported_type.insert(NonLinearSolverType::_newton_raphson_contact);
	this->supported_type.insert(NonLinearSolverType::_newton_raphson);
	this->supported_type.insert(NonLinearSolverType::_linear);

	this->checkIfTypeIsSupported();

	this->registerParam("threshold", convergence_criteria, 1e-10, _pat_parsmod,
	"Threshold to consider results as converged");
	this->registerParam("convergence_type", convergence_criteria_type,
	SolveConvergenceCriteria::_solution, _pat_parsmod,
	"Type of convergence criteria");
	this->registerParam("max_iterations", max_iterations, 10, _pat_parsmod,
	"Max number of iterations");
	this->registerParam("error", error, _pat_readable, "Last reached error");
	this->registerParam("nb_iterations", n_iter, _pat_readable,
	"Last reached number of iterations");
	this->registerParam("converged", converged, _pat_readable,
	"Did last solve converged");
	this->registerParam("force_linear_recompute", force_linear_recompute, true,
	_pat_modifiable,
	"Force reassembly of the jacobian matrix");
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolverNewtonRaphson::~NonLinearSolverNewtonRaphson() = default;

	/* ------------------------------------------------------------------------ */
	void NonLinearSolverNewtonRaphson::solve(SolverCallback & solver_callback) {
	solver_callback.beforeSolveStep();

	this->dof_manager.updateGlobalBlockedDofs();

	solver_callback.predictor();

	if (non_linear_solver_type == NonLinearSolverType::_linear and
	solver_callback.canSplitResidual()) {
	solver_callback.assembleMatrix("K");
	}

	this->assembleResidual(solver_callback);

	if (this->non_linear_solver_type ==
	NonLinearSolverType::_newton_raphson_modified \|\|
	(this->non_linear_solver_type == NonLinearSolverType::_linear &&
	this->force_linear_recompute)) {
	solver_callback.assembleMatrix("J");
	this->force_linear_recompute = false;
	}

	this->n_iter = 0;
	this->converged = false;

	this->convergence_criteria_normalized = this->convergence_criteria;

	if (this->convergence_criteria_type == SolveConvergenceCriteria::_residual) {
	this->converged = this->testConvergence(this->dof_manager.getResidual());

	if (this->converged) {
	return;
	}

	this->convergence_criteria_normalized =
	this->error * this->convergence_criteria;
	}

	do {
	if (this->non_linear_solver_type == NonLinearSolverType::_newton_raphson or
	this->non_linear_solver_type ==
	NonLinearSolverType::_newton_raphson_contact) {
	solver_callback.assembleMatrix("J");
	}

	this->solver->solve();

	solver_callback.corrector();

	// EventManager::sendEvent(NonLinearSolver::AfterSparseSolve(method));

	if (this->convergence_criteria_type ==
	SolveConvergenceCriteria::_residual) {
	this->assembleResidual(solver_callback);
	this->converged = this->testConvergence(this->dof_manager.getResidual());
	} else {
	this->converged = this->testConvergence(this->dof_manager.getSolution());
	}

	if (this->convergence_criteria_type ==
	SolveConvergenceCriteria::_solution and
	not this->converged) {
	this->assembleResidual(solver_callback);
	}

	this->n_iter++;
	AKANTU_DEBUG_INFO(
	"[" << this->convergence_criteria_type << "] Convergence iteration "
	<< std::setw(std::log10(this->max_iterations)) << this->n_iter
	<< ": error " << this->error << (this->converged ? " < " : " > ")
	<< this->convergence_criteria);
	} while (not this->converged and this->n_iter <= this->max_iterations);

	// this makes sure that you have correct strains and stresses after the
	// solveStep function (e.g., for dumping)
	if (this->convergence_criteria_type == SolveConvergenceCriteria::_solution) {
	this->assembleResidual(solver_callback);
	}

	this->converged =
	this->converged and not(this->n_iter > this->max_iterations);

	solver_callback.afterSolveStep(this->converged);

	if (not this->converged) {
	AKANTU_CUSTOM_EXCEPTION(debug::NLSNotConvergedException(
	this->convergence_criteria, this->n_iter, this->error));

	AKANTU_DEBUG_WARNING("[" << this->convergence_criteria_type
	<< "] Convergence not reached after "
	<< std::setw(std::log10(this->max_iterations))
	<< this->n_iter << " iteration"
	<< (this->n_iter == 1 ? "" : "s") << "!");
	}
	}

	/* -------------------------------------------------------------------------- */
	bool NonLinearSolverNewtonRaphson::testConvergence(
	const SolverVector & solver_vector) {
	AKANTU_DEBUG_IN();

	const auto & blocked_dofs = this->dof_manager.getBlockedDOFs();

	const Array<Real> & array(solver_vector);
	UInt nb_degree_of_freedoms = array.size();

	auto arr_it = array.begin();
	auto bld_it = blocked_dofs.begin();

	Real norm = 0.;
	for (UInt n = 0; n < nb_degree_of_freedoms; ++n, ++arr_it, ++bld_it) {
	bool is_local_node = this->dof_manager.isLocalOrMasterDOF(n);
	if ((!*bld_it) && is_local_node) {
	norm += arr_it *arr_it;
	}
	}

	dof_manager.getCommunicator().allReduce(norm, SynchronizerOperation::_sum);

	norm = std::sqrt(norm);

	AKANTU_DEBUG_ASSERT(!Math::isnan(norm),
	"Something went wrong in the solve phase");

	this->error = norm;

	return (error < this->convergence_criteria_normalized);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.hh b/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.hh
	index 6f53eeda0..6431c4963 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver_newton_raphson.hh
	@@ -1,111 +1,111 @@
	/**
	* @file non_linear_solver_newton_raphson.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 27 2019
	*
	* @brief Default implementation of NonLinearSolver, in case no external
	* library
	* is there to do the job
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_NEWTON_RAPHSON_HH_
	#define AKANTU_NON_LINEAR_SOLVER_NEWTON_RAPHSON_HH_

	namespace akantu {
	class DOFManagerDefault;
	class SparseSolverMumps;
	class SolverVector;
	} // namespace akantu

	namespace akantu {

	class NonLinearSolverNewtonRaphson : public NonLinearSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLinearSolverNewtonRaphson(
	DOFManagerDefault & dof_manager,
	const NonLinearSolverType & non_linear_solver_type,
	const ID & id = "non_linear_solver_newton_raphson");
	~NonLinearSolverNewtonRaphson() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Function that solve the non linear system described by the dof manager and
	/// the solver callback functions
	void solve(SolverCallback & solver_callback) override;

	AKANTU_GET_MACRO_NOT_CONST(Solver, *solver, SparseSolverMumps &);
	AKANTU_GET_MACRO(Solver, *solver, const SparseSolverMumps &);

	protected:
	/// test the convergence compare norm of array to convergence_criteria
	bool testConvergence(const SolverVector & solver_vector);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	DOFManagerDefault & dof_manager;

	/// Sparse solver used for the linear solves
	std::unique_ptr<SparseSolverMumps> solver;

	/// Type of convergence criteria
	SolveConvergenceCriteria convergence_criteria_type;

	/// convergence threshold
	Real convergence_criteria;

	/// convergence threshold
	Real convergence_criteria_normalized;

	/// Max number of iterations
	int max_iterations;

	/// Number of iterations at last solve call
	int n_iter{0};

	/// Convergence error at last solve call
	Real error{0.};

	/// Did the last call to solve reached convergence
	bool converged{false};

	/// Force a re-computation of the jacobian matrix
	bool force_linear_recompute{true};
	};

	} // namespace akantu

	#endif /* AKANTU_NON_LINEAR_SOLVER_NEWTON_RAPHSON_HH_ */
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_petsc.cc b/src/model/common/non_linear_solver/non_linear_solver_petsc.cc
	index 246922de5..c3351976e 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_petsc.cc
	+++ b/src/model/common/non_linear_solver/non_linear_solver_petsc.cc
	@@ -1,227 +1,227 @@
	/**
	* @file non_linear_solver_petsc.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Feb 03 2018
	* @date last modification: Sat May 23 2020
	*
	* @brief Interface to non linear solver of PETSc
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver_petsc.hh"
	#include "dof_manager_petsc.hh"
	#include "mpi_communicator_data.hh"
	#include "solver_callback.hh"
	#include "solver_vector_petsc.hh"
	#include "sparse_matrix_petsc.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscoptions.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	NonLinearSolverPETSc::NonLinearSolverPETSc(
	DOFManagerPETSc & dof_manager,
	const NonLinearSolverType & non_linear_solver_type, const ID & id)
	: NonLinearSolver(dof_manager, non_linear_solver_type, id),
	dof_manager(dof_manager) {
	std::unordered_map<NonLinearSolverType, SNESType>
	petsc_non_linear_solver_types{
	{NonLinearSolverType::_newton_raphson, SNESNEWTONLS},
	{NonLinearSolverType::_linear, SNESKSPONLY},
	{NonLinearSolverType::_gmres, SNESNGMRES},
	{NonLinearSolverType::_bfgs, SNESQN},
	{NonLinearSolverType::_cg, SNESNCG}};

	this->has_internal_set_param = true;

	for (const auto & pair : petsc_non_linear_solver_types) {
	supported_type.insert(pair.first);
	}

	this->checkIfTypeIsSupported();

	auto && mpi_comm = dof_manager.getMPIComm();

	PETSc_call(SNESCreate, mpi_comm, &snes);

	auto it = petsc_non_linear_solver_types.find(non_linear_solver_type);
	if (it != petsc_non_linear_solver_types.end()) {
	PETSc_call(SNESSetType, snes, it->second);
	}

	SNESSetFromOptions(snes);
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolverPETSc::~NonLinearSolverPETSc() {
	PETSc_call(SNESDestroy, &snes);
	}

	/* -------------------------------------------------------------------------- */
	class NonLinearSolverPETScCallback {
	public:
	NonLinearSolverPETScCallback(DOFManagerPETSc & dof_manager,
	SolverVectorPETSc & x)
	: dof_manager(dof_manager), x(x), x_prev(x, "previous_solution") {}

	void corrector() {
	auto & dx = dof_manager.getSolution();
	PETSc_call(VecWAXPY, dx, -1., x_prev, x);

	dof_manager.splitSolutionPerDOFs();
	callback->corrector();

	PETSc_call(VecCopy, x, x_prev);
	}

	void assembleResidual() {
	corrector();
	callback->assembleResidual();
	}

	void assembleJacobian() {
	// corrector();
	callback->assembleMatrix("J");
	}

	void setInitialSolution(SolverVectorPETSc & x) {
	PETSc_call(VecCopy, x, x_prev);
	}

	void setCallback(SolverCallback & callback) { this->callback = &callback; }

	private:
	// SNES & snes;
	SolverCallback * callback;
	DOFManagerPETSc & dof_manager;

	SolverVectorPETSc & x;
	SolverVectorPETSc x_prev;
	}; // namespace akantu

	/* -------------------------------------------------------------------------- */
	PetscErrorCode NonLinearSolverPETSc::FormFunction(SNES /snes/, Vec /dx/,
	Vec /f/, void * ctx) {
	auto * _this = reinterpret_cast<NonLinearSolverPETScCallback *>(ctx);
	_this->assembleResidual();
	return 0;
	}

	/* -------------------------------------------------------------------------- */
	PetscErrorCode NonLinearSolverPETSc::FormJacobian(SNES /snes/, Vec /dx/,
	Mat /J/, Mat /P/,
	void * ctx) {
	auto * _this = reinterpret_cast<NonLinearSolverPETScCallback *>(ctx);
	_this->assembleJacobian();
	return 0;
	}

	/* -------------------------------------------------------------------------- */
	void NonLinearSolverPETSc::solve(SolverCallback & callback) {
	callback.beforeSolveStep();
	this->dof_manager.updateGlobalBlockedDofs();

	callback.assembleMatrix("J");
	auto & global_x = dof_manager.getSolution();
	global_x.zero();

	if (not x) {
	x = std::make_unique<SolverVectorPETSc>(global_x, "temporary_solution");
	}

	*x = global_x;

	if (not ctx) {
	ctx = std::make_unique<NonLinearSolverPETScCallback>(dof_manager, *x);
	}

	ctx->setCallback(callback);
	ctx->setInitialSolution(global_x);

	auto & rhs = dof_manager.getResidual();
	auto & J = dof_manager.getMatrix("J");

	PETSc_call(SNESSetFunction, snes, rhs, NonLinearSolverPETSc::FormFunction,
	ctx.get());
	PETSc_call(SNESSetJacobian, snes, J, J, NonLinearSolverPETSc::FormJacobian,
	ctx.get());

	rhs.zero();

	callback.predictor();
	callback.assembleResidual();

	PETSc_call(SNESSolve, snes, nullptr, *x);
	PETSc_call(SNESGetConvergedReason, snes, &reason);
	PETSc_call(SNESGetIterationNumber, snes, &n_iter);

	PETSc_call(VecAXPY, global_x, -1.0, *x);

	dof_manager.splitSolutionPerDOFs();
	callback.corrector();

	bool converged = reason >= 0;
	callback.afterSolveStep(converged);

	if (not converged) {
	PetscReal atol;
	PetscReal rtol;
	PetscReal stol;
	PetscInt maxit;
	PetscInt maxf;

	PETSc_call(SNESGetTolerances, snes, &atol, &rtol, &stol, &maxit, &maxf);
	AKANTU_CUSTOM_EXCEPTION(debug::SNESNotConvergedException(
	this->reason, this->n_iter, stol, atol, rtol, maxit));
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLinearSolverPETSc::set_param(const ID & param,
	const std::string & value) {
	std::map<ID, ID> akantu_to_petsc_option = {{"max_iterations", "snes_max_it"},
	{"threshold", "snes_stol"}};

	auto it = akantu_to_petsc_option.find(param);
	auto p = it == akantu_to_petsc_option.end() ? param : it->second;

	PetscOptionsSetValue(nullptr, p.c_str(), value.c_str());
	SNESSetFromOptions(snes);
	PetscOptionsClear(nullptr);
	}

	/* -------------------------------------------------------------------------- */
	void NonLinearSolverPETSc::parseSection(const ParserSection & section) {
	auto parameters = section.getParameters();
	for (auto && param : range(parameters.first, parameters.second)) {
	PetscOptionsSetValue(nullptr, param.getName().c_str(),
	param.getValue().c_str());
	}
	SNESSetFromOptions(snes);
	PetscOptionsClear(nullptr);
	}

	} // namespace akantu
	diff --git a/src/model/common/non_linear_solver/non_linear_solver_petsc.hh b/src/model/common/non_linear_solver/non_linear_solver_petsc.hh
	index 21951a09c..585f39449 100644
	--- a/src/model/common/non_linear_solver/non_linear_solver_petsc.hh
	+++ b/src/model/common/non_linear_solver/non_linear_solver_petsc.hh
	@@ -1,111 +1,111 @@
	/**
	* @file non_linear_solver_petsc.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Feb 03 2018
	* @date last modification: Sat May 23 2020
	*
	* @brief Interface to non linear solver of PETSc
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscsnes.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LINEAR_SOLVER_PETSC_HH_
	#define AKANTU_NON_LINEAR_SOLVER_PETSC_HH_

	namespace akantu {
	class DOFManagerPETSc;
	class NonLinearSolverPETScCallback;
	class SolverVectorPETSc;
	} // namespace akantu

	namespace akantu {

	class NonLinearSolverPETSc : public NonLinearSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLinearSolverPETSc(DOFManagerPETSc & dof_manager,
	const NonLinearSolverType & non_linear_solver_type,
	const ID & id = "non_linear_solver_petsc");

	~NonLinearSolverPETSc() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// solve the system described by the jacobian matrix, and rhs contained in
	/// the dof manager
	void solve(SolverCallback & callback) override;

	/// parse the arguments from the input file
	void parseSection(const ParserSection & section) override;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	static PetscErrorCode FormFunction(SNES snes, Vec dx, Vec f, void * ctx);
	static PetscErrorCode FormJacobian(SNES snes, Vec dx, Mat J, Mat P,
	void * ctx);

	void set_param(const ID & param, const std::string & value) override;

	DOFManagerPETSc & dof_manager;

	/// PETSc non linear solver
	SNES snes;
	SNESConvergedReason reason;

	SolverCallback * callback{nullptr};

	std::unique_ptr<SolverVectorPETSc> x;
	std::unique_ptr<NonLinearSolverPETScCallback> ctx;

	Int n_iter{0};
	};

	namespace debug {
	class SNESNotConvergedException : public NLSNotConvergedException {
	public:
	SNESNotConvergedException(SNESConvergedReason reason, UInt niter,
	Real error, Real absolute_tolerance,
	Real relative_tolerance, UInt max_iterations)
	: NLSNotConvergedException(relative_tolerance, niter, error),
	reason(reason), absolute_tolerance(absolute_tolerance),
	max_iterations(max_iterations) {}
	SNESConvergedReason reason;
	Real absolute_tolerance;
	UInt max_iterations;
	};
	} // namespace debug

	} // namespace akantu

	#endif /* AKANTU_NON_LINEAR_SOLVER_PETSC_HH_ */
	diff --git a/src/model/common/non_local_toolbox/base_weight_function.hh b/src/model/common/non_local_toolbox/base_weight_function.hh
	index 99d294003..c9b94993c 100644
	--- a/src/model/common/non_local_toolbox/base_weight_function.hh
	+++ b/src/model/common/non_local_toolbox/base_weight_function.hh
	@@ -1,173 +1,173 @@
	/**
	* @file base_weight_function.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Base weight function for non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "model.hh"
	#include "non_local_manager.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BASE_WEIGHT_FUNCTION_HH_
	#define AKANTU_BASE_WEIGHT_FUNCTION_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Normal weight function */
	/* -------------------------------------------------------------------------- */
	class BaseWeightFunction : public Parsable, public DataAccessor<Element> {
	public:
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	BaseWeightFunction(NonLocalManager & manager,
	const std::string & type = "base")
	: Parsable(ParserType::_weight_function, "weight_function:" + type),
	manager(manager), type(type),
	spatial_dimension(manager.getModel().getMesh().getSpatialDimension()) {
	this->registerParam("update_rate", update_rate, UInt(1), _pat_parsmod,
	"Update frequency");
	}

	~BaseWeightFunction() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	/// initialize the weight function
	virtual inline void init();

	/// update the internal parameters
	virtual void updateInternals(){};

	/* ------------------------------------------------------------------------ */
	/// set the non-local radius
	inline void setRadius(Real radius);

	/* ------------------------------------------------------------------------ */
	/// compute the weight for a given distance between two quadrature points
	inline Real operator()(Real r, const IntegrationPoint & q1,
	const IntegrationPoint & q2) const;

	/// print function
	void printself(std::ostream & stream, int indent = 0) const override {
	std::string space;
	for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
	;
	}
	stream << space << "WeightFunction " << type << " [" << std::endl;
	Parsable::printself(stream, indent);
	stream << space << "]" << std::endl;
	}

	/* --------------------------------------------------------------------------
	*/
	/* Accessors */
	/* --------------------------------------------------------------------------
	*/

	public:
	/// get the radius
	Real getRadius() const { return R; }
	/// get the update rate
	UInt getUpdateRate() const { return update_rate; }

	public:
	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */

	UInt getNbData(const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override {
	return 0;
	}

	inline void packData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) const override {}

	inline void unpackData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) override {}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Type, type, const ID &);

	protected:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	/// reference to the non-local manager
	NonLocalManager & manager;

	/// the non-local radius
	Real R;

	/// the non-local radius squared
	Real R2;

	/// the update rate
	UInt update_rate;

	/// name of the type of weight function
	const std::string type;

	/// the spatial dimension
	UInt spatial_dimension;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const BaseWeightFunction & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "base_weight_function_inline_impl.hh"

	/* -------------------------------------------------------------------------- */
	/* Include all other weight function types */
	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_DAMAGE_NON_LOCAL)
	#include "damaged_weight_function.hh"
	#include "remove_damaged_weight_function.hh"
	#include "remove_damaged_with_damage_rate_weight_function.hh"
	#include "stress_based_weight_function.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_BASE_WEIGHT_FUNCTION_HH_ */
	diff --git a/src/model/common/non_local_toolbox/base_weight_function_inline_impl.hh b/src/model/common/non_local_toolbox/base_weight_function_inline_impl.hh
	index b116171d5..cf0216f96 100644
	--- a/src/model/common/non_local_toolbox/base_weight_function_inline_impl.hh
	+++ b/src/model/common/non_local_toolbox/base_weight_function_inline_impl.hh
	@@ -1,73 +1,73 @@
	/**
	* @file base_weight_function_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Wed Sep 01 2010
	* @date last modification: Wed Sep 27 2017
	*
	* @brief Implementation of inline function of base weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_BASE_WEIGHT_FUNCTION_INLINE_IMPL_HH_
	#define AKANTU_BASE_WEIGHT_FUNCTION_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline void BaseWeightFunction::init() {
	/// compute R^2 for a given non-local radius
	this->R2 = this->R * this->R;
	}

	/* -------------------------------------------------------------------------- */
	inline void BaseWeightFunction::setRadius(Real radius) {
	/// set the non-local radius and update R^2 accordingly
	this->R = radius;
	this->R2 = this->R * this->R;
	}

	/* -------------------------------------------------------------------------- */
	inline Real
	BaseWeightFunction::operator()(Real r, const IntegrationPoint & /* q1 */,
	const IntegrationPoint & /* q2 */) const {

	/// initialize the weight
	Real w = 0;
	/// compute weight for given r
	if (r <= this->R) {
	Real alpha = (1. - r * r / this->R2);
	w = alpha * alpha;
	// *weight = 1 - sqrt(r / radius);
	}

	return w;
	}

	} // namespace akantu
	#endif /* AKANTU_BASE_WEIGHT_FUNCTION_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/non_local_toolbox/neighborhood_base.cc b/src/model/common/non_local_toolbox/neighborhood_base.cc
	index 5f2b1f17a..1622cdba8 100644
	--- a/src/model/common/non_local_toolbox/neighborhood_base.cc
	+++ b/src/model/common/non_local_toolbox/neighborhood_base.cc
	@@ -1,305 +1,305 @@
	/**
	* @file neighborhood_base.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of generic neighborhood base
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "neighborhood_base.hh"
	#include "grid_synchronizer.hh"
	#include "mesh_accessor.hh"
	#include "model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	NeighborhoodBase::NeighborhoodBase(Model & model,
	const ElementTypeMapReal & quad_coordinates,
	const ID & id)
	: id(id), model(model), quad_coordinates(quad_coordinates),
	spatial_dimension(this->model.getMesh().getSpatialDimension()) {

	AKANTU_DEBUG_IN();

	this->registerDataAccessor(*this);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	NeighborhoodBase::~NeighborhoodBase() = default;

	/* -------------------------------------------------------------------------- */
	// void NeighborhoodBase::createSynchronizerRegistry(
	// DataAccessor<Element> * data_accessor) {
	// this->synch_registry = new SynchronizerRegistry(*data_accessor);
	// }

	/* -------------------------------------------------------------------------- */
	void NeighborhoodBase::initNeighborhood() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Creating the grid");
	this->createGrid();

	AKANTU_DEBUG_OUT();
	}

	/* ------------------------------------------------------------------------- */
	void NeighborhoodBase::createGrid() {
	AKANTU_DEBUG_IN();

	const Real safety_factor = 1.2; // for the cell grid spacing
	Mesh & mesh = this->model.getMesh();

	const auto & lower_bounds = mesh.getLocalLowerBounds();
	const auto & upper_bounds = mesh.getLocalUpperBounds();
	Vector<Real> center = 0.5 * (upper_bounds + lower_bounds);
	Vector<Real> spacing(spatial_dimension,
	this->neighborhood_radius * safety_factor);

	spatial_grid = std::make_unique<SpatialGrid<IntegrationPoint>>(
	spatial_dimension, spacing, center);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodBase::updatePairList() {
	AKANTU_DEBUG_IN();

	//// loop over all quads -> all cells
	for (auto && cell_id : *spatial_grid) {
	AKANTU_DEBUG_INFO("Looping on next cell");

	for (auto && q1 : spatial_grid->getCell(cell_id)) {
	if (q1.ghost_type == _ghost) {
	break;
	}
	auto coords_type_1_it = this->quad_coordinates(q1.type, q1.ghost_type)
	.begin(spatial_dimension);
	auto q1_coords = Vector<Real>(coords_type_1_it[q1.global_num]);

	AKANTU_DEBUG_INFO("Current quadrature point in this cell: " << q1);
	auto cell_id = spatial_grid->getCellID(q1_coords);

	/// loop over all the neighboring cells of the current quad
	for (auto && neighbor_cell : cell_id.neighbors()) {
	// loop over the quadrature point in the current neighboring cell
	for (auto && q2 : spatial_grid->getCell(neighbor_cell)) {
	auto coords_type_2_it = this->quad_coordinates(q2.type, q2.ghost_type)
	.begin(spatial_dimension);
	auto q2_coords = Vector<Real>(coords_type_2_it[q2.global_num]);

	Real distance = q1_coords.distance(q2_coords);

	if (distance <= this->neighborhood_radius + Math::getTolerance() &&
	(q2.ghost_type == _ghost \|\|
	(q2.ghost_type == _not_ghost &&
	q1.global_num <= q2.global_num))) { // storing only half lists
	pair_list[q2.ghost_type].push_back(std::make_pair(q1, q2));
	}
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodBase::savePairs(const std::string & filename) const {
	std::stringstream sstr;

	const Communicator & comm = model.getMesh().getCommunicator();
	Int prank = comm.whoAmI();
	sstr << filename << "." << prank;

	std::ofstream pout;
	pout.open(sstr.str().c_str());

	for (auto && ghost_type : ghost_types) {
	for (const auto & pair : pair_list[ghost_type]) {
	const auto & q1 = pair.first;
	const auto & q2 = pair.second;
	pout << q1 << " " << q2 << " " << std::endl;
	}
	}

	pout.close();

	if (comm.getNbProc() != 1) {
	return;
	}

	Mesh mesh_out(spatial_dimension);
	MeshAccessor mesh_accessor(mesh_out);
	auto & connectivity = mesh_accessor.getConnectivity(_segment_2);
	auto & tag = mesh_accessor.getData<UInt>("tag_1", _segment_2);
	auto & nodes = mesh_accessor.getNodes();

	std::map<IntegrationPoint, UInt> quad_to_nodes;
	UInt node = 0;

	IntegrationPoint q1;
	IntegrationPoint q2;
	bool inserted;
	for (auto && ghost_type : ghost_types) {
	for (const auto & pair : pair_list[ghost_type]) {
	std::tie(q1, q2) = pair;

	auto add_node = [&](auto && q) {
	std::tie(std::ignore, inserted) =
	quad_to_nodes.insert(std::make_pair(q, node));

	if (not inserted) {
	return;
	}

	auto coords_it = this->quad_coordinates(q.type, q.ghost_type)
	.begin(spatial_dimension);
	auto && coords = Vector<Real>(coords_it[q.global_num]);
	nodes.push_back(coords);
	++node;
	};

	add_node(q1);
	add_node(q2);
	}
	}

	for (auto && ghost_type : ghost_types) {
	for (const auto & pair : pair_list[ghost_type]) {
	std::tie(q1, q2) = pair;

	UInt node1 = quad_to_nodes[q1];
	UInt node2 = quad_to_nodes[q2];

	connectivity.push_back(Vector<UInt>{node1, node2});
	tag.push_back(node1 + 1);
	if (node1 != node2) {
	connectivity.push_back(Vector<UInt>{node2, node1});
	tag.push_back(node2 + 1);
	}
	}
	}

	mesh_out.write(filename + ".msh");
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodBase::saveNeighborCoords(const std::string & filename) const {
	// this function is not optimized and only used for tests on small meshes
	// @todo maybe optimize this function for better performance?
	IntegrationPoint q2;

	std::stringstream sstr;

	const Communicator & comm = model.getMesh().getCommunicator();
	Int prank = comm.whoAmI();
	sstr << filename << "." << prank;

	std::ofstream pout;
	pout.open(sstr.str().c_str());

	/// loop over all the quads and write the position of their neighbors
	for (auto && cell_id : *spatial_grid) {
	for (auto && q1 : spatial_grid->getCell(cell_id)) {
	auto coords_type_1_it = this->quad_coordinates(q1.type, q1.ghost_type)
	.begin(spatial_dimension);
	auto && q1_coords = Vector<Real>(coords_type_1_it[q1.global_num]);

	pout << "#neighbors for quad " << q1.global_num << std::endl;
	pout << q1_coords << std::endl;

	for (auto && ghost_type2 : ghost_types) {
	for (auto && pair : pair_list[ghost_type2]) {
	if (q1 == pair.first && pair.second != q1) {
	q2 = pair.second;
	} else if (q1 == pair.second && pair.first != q1) {
	q2 = pair.first;
	} else {
	continue;
	}

	auto coords_type_2_it = this->quad_coordinates(q2.type, q2.ghost_type)
	.begin(spatial_dimension);
	auto && q2_coords = Vector<Real>(coords_type_2_it[q2.global_num]);
	pout << q2_coords << std::endl;
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodBase::onElementsRemoved(
	const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) {
	AKANTU_DEBUG_IN();

	FEEngine & fem = this->model.getFEEngine();
	UInt nb_quad = 0;
	auto cleanPoint = [&](auto && q) {
	if (new_numbering.exists(q.type, q.ghost_type)) {
	UInt q_new_el = new_numbering(q.type, q.ghost_type)(q.element);
	AKANTU_DEBUG_ASSERT(q_new_el != UInt(-1),
	"A local quadrature_point "
	<< q
	<< " as been removed instead of "
	"just being renumbered: "
	<< id);
	q.element = q_new_el;
	nb_quad = fem.getNbIntegrationPoints(q.type, q.ghost_type);
	q.global_num = nb_quad * q.element + q.num_point;
	}
	};

	// Change the pairs in new global numbering
	for (auto ghost_type : ghost_types) {
	auto & pair_list = this->pair_list.at(ghost_type);
	for (auto && pair : pair_list) {
	if (pair.first.ghost_type == _ghost) {
	cleanPoint(pair.first);
	}
	if (pair.second.ghost_type == _ghost) {
	cleanPoint(pair.second);
	}
	}
	}

	this->grid_synchronizer->onElementsRemoved(element_list, new_numbering,
	event);
	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/common/non_local_toolbox/neighborhood_base.hh b/src/model/common/non_local_toolbox/neighborhood_base.hh
	index 5f39e7a45..5f1da3859 100644
	--- a/src/model/common/non_local_toolbox/neighborhood_base.hh
	+++ b/src/model/common/non_local_toolbox/neighborhood_base.hh
	@@ -1,153 +1,153 @@
	/**
	* @file neighborhood_base.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Generic neighborhood of quadrature points
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_NEIGHBORHOOD_BASE_HH_
	#define AKANTU_NEIGHBORHOOD_BASE_HH_
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "data_accessor.hh"
	#include "integration_point.hh"
	#include "synchronizer_registry.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class Model;
	template <class T> class SpatialGrid;
	class GridSynchronizer;
	class RemovedElementsEvent;
	} // namespace akantu

	namespace akantu {
	class NeighborhoodBase : public DataAccessor<Element>,
	public SynchronizerRegistry {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NeighborhoodBase(Model & model,
	const ElementTypeMapArray<Real> & quad_coordinates,
	const ID & id = "neighborhood");
	~NeighborhoodBase() override;

	using PairList = std::vector<std::pair<IntegrationPoint, IntegrationPoint>>;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */

	public:
	/// intialize the neighborhood
	virtual void initNeighborhood();

	// /// create a synchronizer registry
	// void createSynchronizerRegistry(DataAccessor * data_accessor);

	/// initialize the material computed parameter
	inline void insertIntegrationPoint(const IntegrationPoint & quad,
	const Vector<Real> & coords);

	/// create the pairs of quadrature points
	void updatePairList();

	/// save the pairs of quadrature points in a file
	void savePairs(const std::string & filename) const;

	/// save the coordinates of all neighbors of a quad
	void saveNeighborCoords(const std::string & filename) const;

	/// create grid synchronizer and exchange ghost cells
	virtual void createGridSynchronizer() = 0;
	virtual void synchronize(DataAccessor<Element> & data_accessor,
	const SynchronizationTag & tag) = 0;

	/// inherited function from MeshEventHandler
	virtual void
	onElementsRemoved(const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event);

	protected:
	/// create the grid
	void createGrid();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);
	AKANTU_GET_MACRO(Model, model, const Model &);
	/// return the object handling synchronizers
	const PairList & getPairLists(GhostType type) {
	return pair_list[type == _not_ghost ? 0 : 1];
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	/// the model to which the neighborhood belongs
	Model & model;

	/// Radius of impact: to determine if two quadrature points influence each
	/// other
	Real neighborhood_radius{0.};

	/**
	* the pairs of quadrature points
	* 0: not ghost to not ghost
	* 1: not ghost to ghost
	*/
	std::array<PairList, 2> pair_list;

	/// the regular grid to construct/update the pair lists
	std::unique_ptr<SpatialGrid<IntegrationPoint>> spatial_grid;

	bool is_creating_grid{false};

	/// the grid synchronizer for parallel computations
	std::unique_ptr<GridSynchronizer> grid_synchronizer;

	/// the quadrature point positions
	const ElementTypeMapArray<Real> & quad_coordinates;

	/// the spatial dimension of the problem
	const UInt spatial_dimension;
	};

	} // namespace akantu

	#include "neighborhood_base_inline_impl.hh"

	#endif /* AKANTU_NEIGHBORHOOD_BASE_HH_ */
	diff --git a/src/model/common/non_local_toolbox/neighborhood_base_inline_impl.hh b/src/model/common/non_local_toolbox/neighborhood_base_inline_impl.hh
	index a5e79c170..a3e09747e 100644
	--- a/src/model/common/non_local_toolbox/neighborhood_base_inline_impl.hh
	+++ b/src/model/common/non_local_toolbox/neighborhood_base_inline_impl.hh
	@@ -1,51 +1,51 @@
	/**
	* @file neighborhood_base_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Inline implementation of neighborhood base functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_grid_dynamic.hh"
	#include "neighborhood_base.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NEIGHBORHOOD_BASE_INLINE_IMPL_HH_
	#define AKANTU_NEIGHBORHOOD_BASE_INLINE_IMPL_HH_

	namespace akantu {

	inline void
	NeighborhoodBase::insertIntegrationPoint(const IntegrationPoint & quad,
	const Vector<Real> & coords) {
	this->spatial_grid->insert(quad, coords);
	}

	} // namespace akantu

	#endif /* AKANTU_NEIGHBORHOOD_BASE_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.cc b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.cc
	index 47e35297c..ac2e0d853 100644
	--- a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.cc
	+++ b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.cc
	@@ -1,292 +1,291 @@
	/**
	* @file neighborhood_max_criterion.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Thu Oct 15 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of class NeighborhoodMaxCriterion
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "neighborhood_max_criterion.hh"
	#include "grid_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NeighborhoodMaxCriterion::NeighborhoodMaxCriterion(
	Model & model, const ElementTypeMapReal & quad_coordinates,
	const ID & criterion_id, const ID & id)
	: NeighborhoodBase(model, quad_coordinates, id),
	- Parsable(ParserType::_non_local, id),
	- is_highest("is_highest", id),
	+ Parsable(ParserType::_non_local, id), is_highest("is_highest", id),
	criterion(criterion_id, id) {

	AKANTU_DEBUG_IN();

	this->registerParam("radius", neighborhood_radius, 100.,
	_pat_parsable \| _pat_readable, "Non local radius");

	Mesh & mesh = this->model.getMesh();
	/// allocate the element type map arrays for _not_ghosts: One entry per quad
	GhostType ghost_type = _not_ghost;
	for (auto type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	UInt new_size = this->quad_coordinates(type, ghost_type).size();
	this->is_highest.alloc(new_size, 1, type, ghost_type, true);
	this->criterion.alloc(new_size, 1, type, ghost_type, 1.);
	}

	/// criterion needs allocation also for ghost
	ghost_type = _ghost;
	for (auto type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	UInt new_size = this->quad_coordinates(type, ghost_type).size();
	this->criterion.alloc(new_size, 1, type, ghost_type, 1.);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	NeighborhoodMaxCriterion::~NeighborhoodMaxCriterion() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::initNeighborhood() {
	AKANTU_DEBUG_IN();

	/// parse the input parameter
	const Parser & parser = getStaticParser();
	const ParserSection & section_neighborhood =
	*(parser.getSubSections(ParserType::_neighborhood).first);
	this->parseSection(section_neighborhood);

	AKANTU_DEBUG_INFO("Creating the grid");
	this->createGrid();

	/// insert the non-ghost quads into the grid
	this->insertAllQuads(_not_ghost);

	/// store the number of current ghost elements for each type in the mesh
	ElementTypeMap<UInt> nb_ghost_protected;
	Mesh & mesh = this->model.getMesh();
	for (auto type : mesh.elementTypes(spatial_dimension, _ghost)) {
	nb_ghost_protected(mesh.getNbElement(type, _ghost), type, _ghost);
	}

	/// create the grid synchronizer
	this->createGridSynchronizer();

	/// insert the ghost quads into the grid
	this->insertAllQuads(_ghost);

	/// create the pair lists
	this->updatePairList();

	/// remove the unneccessary ghosts
	this->cleanupExtraGhostElements(nb_ghost_protected);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::createGridSynchronizer() {
	this->is_creating_grid = true;
	std::set<SynchronizationTag> tags;
	tags.insert(SynchronizationTag::_nh_criterion);

	std::stringstream sstr;
	sstr << id << ":grid_synchronizer";
	this->grid_synchronizer = std::make_unique<GridSynchronizer>(
	this->model.getMesh(), spatial_grid, this, tags, sstr.str(), false);
	this->is_creating_grid = false;
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::insertAllQuads(GhostType ghost_type) {
	IntegrationPoint q;
	q.ghost_type = ghost_type;
	Mesh & mesh = this->model.getMesh();

	for (auto type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt nb_quad =
	this->model.getFEEngine().getNbIntegrationPoints(type, ghost_type);

	const Array<Real> & quads = this->quad_coordinates(type, ghost_type);
	q.type = type;

	auto quad = quads.begin(spatial_dimension);

	for (UInt e = 0; e < nb_element; ++e) {
	q.element = e;
	for (UInt nq = 0; nq < nb_quad; ++nq) {
	q.num_point = nq;
	q.global_num = q.element * nb_quad + nq;
	spatial_grid->insert(q, *quad);
	++quad;
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::findMaxQuads(
	std::vector<IntegrationPoint> & max_quads) {
	AKANTU_DEBUG_IN();

	/// clear the element type maps
	this->is_highest.zero();
	this->criterion.zero();

	/// update the values of the criterion
	this->model.updateDataForNonLocalCriterion(criterion);

	/// start the exchange the value of the criterion on the ghost elements
	this->model.asynchronousSynchronize(SynchronizationTag::_nh_criterion);

	/// compare to not-ghost neighbors
	checkNeighbors(_not_ghost);

	/// finish the exchange
	this->model.waitEndSynchronize(SynchronizationTag::_nh_criterion);

	/// compare to ghost neighbors
	checkNeighbors(_ghost);

	/// extract the quads with highest criterion in their neighborhood
	IntegrationPoint quad;
	quad.ghost_type = _not_ghost;
	Mesh & mesh = this->model.getMesh();

	for (auto type : mesh.elementTypes(spatial_dimension, _not_ghost)) {
	quad.type = type;
	UInt nb_quadrature_points =
	this->model.getFEEngine().getNbIntegrationPoints(type, _not_ghost);

	/// loop over is_highest for the current element type
	for (auto data : enumerate(is_highest(type, _not_ghost))) {
	const auto & is_highest = std::get<1>(data);
	if (is_highest) {
	auto q = std::get<0>(data);
	/// gauss point has the highest stress in his neighbourhood
	quad.element = q / nb_quadrature_points;
	quad.global_num = q;
	quad.num_point = q % nb_quadrature_points;
	max_quads.push_back(quad);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::checkNeighbors(GhostType ghost_type2) {
	AKANTU_DEBUG_IN();

	// Compute the weights
	for (auto & pair : pair_list[ghost_type2]) {
	const auto & lq1 = pair.first;
	const auto & lq2 = pair.second;

	Array<bool> & has_highest_eq_stress_1 =
	is_highest(lq1.type, lq1.ghost_type);

	const Array<Real> & criterion_1 = this->criterion(lq1.type, lq1.ghost_type);
	const Array<Real> & criterion_2 = this->criterion(lq2.type, lq2.ghost_type);

	if (criterion_1(lq1.global_num) < criterion_2(lq2.global_num)) {
	has_highest_eq_stress_1(lq1.global_num) = false;
	} else if (ghost_type2 != _ghost) {
	Array<bool> & has_highest_eq_stress_2 =
	is_highest(lq2.type, lq2.ghost_type);
	has_highest_eq_stress_2(lq2.global_num) = false;
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NeighborhoodMaxCriterion::cleanupExtraGhostElements(
	const ElementTypeMap<UInt> & nb_ghost_protected) {

	Mesh & mesh = this->model.getMesh();
	/// create remove elements event
	RemovedElementsEvent remove_elem(mesh);
	/// create set of ghosts to keep
	std::set<Element> relevant_ghost_elements;
	for (auto & pair : pair_list[_ghost]) {
	const auto & q2 = pair.second;
	relevant_ghost_elements.insert(q2);
	}

	Array<Element> ghosts_to_erase(0);

	Element element;
	element.ghost_type = _ghost;
	auto end = relevant_ghost_elements.end();
	for (const auto & type : mesh.elementTypes(spatial_dimension, _ghost)) {
	element.type = type;
	UInt nb_ghost_elem = mesh.getNbElement(type, _ghost);
	UInt nb_ghost_elem_protected = 0;
	try {
	nb_ghost_elem_protected = nb_ghost_protected(type, _ghost);
	} catch (...) {
	}

	if (!remove_elem.getNewNumbering().exists(type, _ghost)) {
	remove_elem.getNewNumbering().alloc(nb_ghost_elem, 1, type, _ghost);
	} else {
	remove_elem.getNewNumbering(type, _ghost).resize(nb_ghost_elem);
	}
	Array<UInt> & new_numbering = remove_elem.getNewNumbering(type, _ghost);
	for (UInt g = 0; g < nb_ghost_elem; ++g) {
	element.element = g;
	if (element.element >= nb_ghost_elem_protected &&
	relevant_ghost_elements.find(element) == end) {
	ghosts_to_erase.push_back(element);
	new_numbering(element.element) = UInt(-1);
	}
	}
	/// renumber remaining ghosts
	UInt ng = 0;
	for (UInt g = 0; g < nb_ghost_elem; ++g) {
	if (new_numbering(g) != UInt(-1)) {
	new_numbering(g) = ng;
	++ng;
	}
	}
	}

	mesh.sendEvent(remove_elem);
	this->onElementsRemoved(ghosts_to_erase, remove_elem.getNewNumbering(),
	remove_elem);
	}

	} // namespace akantu
	diff --git a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.hh b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.hh
	index c58328575..4c7b751d2 100644
	--- a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.hh
	+++ b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion.hh
	@@ -1,115 +1,115 @@
	/**
	* @file neighborhood_max_criterion.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Neighborhood to find a maximum value in a neighborhood
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_NEIGHBORHOOD_MAX_CRITERION_BASE_HH_
	#define AKANTU_NEIGHBORHOOD_MAX_CRITERION_BASE_HH_
	/* -------------------------------------------------------------------------- */
	#include "neighborhood_base.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class NeighborhoodMaxCriterion : public NeighborhoodBase, public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NeighborhoodMaxCriterion(Model & model,
	const ElementTypeMapReal & quad_coordinates,
	const ID & criterion_id,
	const ID & id = "neighborhood_max_criterion");
	~NeighborhoodMaxCriterion() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */

	public:
	/// initialize the neighborhood
	void initNeighborhood() override;

	/// create grid synchronizer and exchange ghost cells
	void createGridSynchronizer() override;

	/// find the quads which have the maximum criterion in their neighborhood
	void findMaxQuads(std::vector<IntegrationPoint> & max_quads);

	protected:
	/// remove unneccessary ghost elements
	void
	cleanupExtraGhostElements(const ElementTypeMap<UInt> & nb_ghost_protected);

	/// insert the quadrature points in the grid
	void insertAllQuads(GhostType ghost_type);

	/// compare criterion with neighbors
	void checkNeighbors(GhostType ghost_type);

	/* --------------------------------------------------------------------------
	*/
	/* DataAccessor inherited members */
	/* --------------------------------------------------------------------------
	*/
	public:
	virtual inline UInt getNbDataForElements(const Array<Element> & elements,
	SynchronizationTag tag) const;

	virtual inline void packElementData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	SynchronizationTag tag) const;

	virtual inline void unpackElementData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	SynchronizationTag tag);

	/* -------------------------------------------------------------------------*/
	/* Accessors */
	/* -------------------------------------------------------------------------*/
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// a boolean to store the information if a quad has the max
	/// criterion in the neighborhood
	ElementTypeMapArray<bool> is_highest;

	/// an element type map to store the flattened internal of the criterion
	ElementTypeMapReal criterion;
	};

	} // namespace akantu

	#include "neighborhood_max_criterion_inline_impl.hh"

	#endif /* AKANTU_NEIGHBORHOOD_MAX_CRITERION_BASE_HH_ */
	diff --git a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion_inline_impl.hh b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion_inline_impl.hh
	index c48f43d6b..5cf323a24 100644
	--- a/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion_inline_impl.hh
	+++ b/src/model/common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion_inline_impl.hh
	@@ -1,83 +1,83 @@
	/**
	* @file neighborhood_max_criterion_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of inline functions for class NeighborhoodMaxCriterion
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "model.hh"
	#include "neighborhood_max_criterion.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NEIGHBORHOOD_MAX_CRITERION_INLINE_IMPL_HH_
	#define AKANTU_NEIGHBORHOOD_MAX_CRITERION_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt
	NeighborhoodMaxCriterion::getNbDataForElements(const Array<Element> & elements,
	SynchronizationTag tag) const {
	UInt nb_quadrature_points = this->model.getNbIntegrationPoints(elements);
	UInt size = 0;

	if (tag == SynchronizationTag::_nh_criterion) {
	size += sizeof(Real) * nb_quadrature_points;
	}

	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	NeighborhoodMaxCriterion::packElementData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	SynchronizationTag tag) const {
	if (tag == SynchronizationTag::_nh_criterion) {
	NeighborhoodMaxCriterion::packElementalDataHelper(
	criterion, buffer, elements, true, this->model.getFEEngine());
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	NeighborhoodMaxCriterion::unpackElementData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	SynchronizationTag tag) {
	if (tag == SynchronizationTag::_nh_criterion) {
	NeighborhoodMaxCriterion::unpackElementalDataHelper(
	criterion, buffer, elements, true, this->model.getFEEngine());
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_NEIGHBORHOOD_MAX_CRITERION_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_manager.cc b/src/model/common/non_local_toolbox/non_local_manager.cc
	index 84bf32562..6ff6af7b6 100644
	--- a/src/model/common/non_local_toolbox/non_local_manager.cc
	+++ b/src/model/common/non_local_toolbox/non_local_manager.cc
	@@ -1,654 +1,655 @@
	/**
	* @file non_local_manager.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of non-local manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_local_manager.hh"
	#include "grid_synchronizer.hh"
	#include "model.hh"
	#include "non_local_neighborhood.hh"
	/* -------------------------------------------------------------------------- */
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLocalManager::NonLocalManager(Model & model,
	NonLocalManagerCallback & callback,
	const ID & id)
	: Parsable(ParserType::_neighborhoods, id),
	- spatial_dimension(model.getMesh().getSpatialDimension()), id(id), model(model),
	+ spatial_dimension(model.getMesh().getSpatialDimension()), id(id),
	+ model(model),
	integration_points_positions("integration_points_positions", id),
	- volumes("volumes", id), compute_stress_calls(0),
	- dummy_registry(nullptr), dummy_grid(nullptr) {
	+ volumes("volumes", id), compute_stress_calls(0), dummy_registry(nullptr),
	+ dummy_grid(nullptr) {
	/// parse the neighborhood information from the input file
	const Parser & parser = getStaticParser();

	/// iterate over all the non-local sections and store them in a map
	std::pair<Parser::const_section_iterator, Parser::const_section_iterator>
	weight_sect = parser.getSubSections(ParserType::_non_local);
	Parser::const_section_iterator it = weight_sect.first;
	for (; it != weight_sect.second; ++it) {
	const ParserSection & section = *it;
	ID name = section.getName();
	this->weight_function_types[name] = section;
	}

	this->callback = &callback;
	}

	/* -------------------------------------------------------------------------- */
	NonLocalManager::~NonLocalManager() = default;

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::initialize() {
	volumes.initialize(this->model.getFEEngine(),
	_spatial_dimension = spatial_dimension);

	AKANTU_DEBUG_ASSERT(this->callback,
	"A callback should be registered prior to this call");
	this->callback->insertIntegrationPointsInNeighborhoods(_not_ghost);

	auto & mesh = this->model.getMesh();
	mesh.registerEventHandler(*this, _ehp_non_local_manager);

	/// store the number of current ghost elements for each type in the mesh
	// ElementTypeMap<UInt> nb_ghost_protected;
	// for (auto type : mesh.elementTypes(spatial_dimension, _ghost))
	// nb_ghost_protected(mesh.getNbElement(type, _ghost), type, _ghost);

	/// exchange the missing ghosts for the non-local neighborhoods
	this->createNeighborhoodSynchronizers();

	/// insert the ghost quadrature points of the non-local materials into the
	/// non-local neighborhoods
	this->callback->insertIntegrationPointsInNeighborhoods(_ghost);

	FEEngine & fee = this->model.getFEEngine();
	this->updatePairLists();

	/// cleanup the unneccessary ghost elements
	this->cleanupExtraGhostElements(); // nb_ghost_protected);

	this->callback->initializeNonLocal();

	this->setJacobians(fee, _ek_regular);

	this->initNonLocalVariables();
	this->computeWeights();
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::setJacobians(const FEEngine & fe_engine,
	ElementKind kind) {
	Mesh & mesh = this->model.getMesh();
	for (auto ghost_type : ghost_types) {
	for (auto type : mesh.elementTypes(spatial_dimension, ghost_type, kind)) {
	jacobians(type, ghost_type) =
	&fe_engine.getIntegratorInterface().getJacobians(type, ghost_type);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::createNeighborhood(const ID & weight_func,
	const ID & neighborhood_id) {

	AKANTU_DEBUG_IN();

	auto weight_func_it = this->weight_function_types.find(weight_func);
	AKANTU_DEBUG_ASSERT(weight_func_it != weight_function_types.end(),
	"No info found in the input file for the weight_function "
	<< weight_func << " in the neighborhood "
	<< neighborhood_id);

	const ParserSection & section = weight_func_it->second;
	const ID weight_func_type = section.getOption();
	/// create new neighborhood for given ID
	std::stringstream sstr;
	sstr << id << ":neighborhood:" << neighborhood_id;

	if (weight_func_type == "base_wf") {
	neighborhoods[neighborhood_id] =
	std::make_unique<NonLocalNeighborhood<BaseWeightFunction>>(
	*this, this->integration_points_positions, sstr.str());
	#if defined(AKANTU_DAMAGE_NON_LOCAL)
	} else if (weight_func_type == "remove_wf") {
	neighborhoods[neighborhood_id] =
	std::make_unique<NonLocalNeighborhood<RemoveDamagedWeightFunction>>(
	*this, this->integration_points_positions, sstr.str());
	} else if (weight_func_type == "stress_wf") {
	neighborhoods[neighborhood_id] =
	std::make_unique<NonLocalNeighborhood<StressBasedWeightFunction>>(
	*this, this->integration_points_positions, sstr.str());
	} else if (weight_func_type == "damage_wf") {
	neighborhoods[neighborhood_id] =
	std::make_unique<NonLocalNeighborhood<DamagedWeightFunction>>(
	*this, this->integration_points_positions, sstr.str());
	#endif
	} else {
	AKANTU_EXCEPTION("error in weight function type provided in material file");
	}

	neighborhoods[neighborhood_id]->parseSection(section);
	neighborhoods[neighborhood_id]->initNeighborhood();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::createNeighborhoodSynchronizers() {
	/// exchange all the neighborhood IDs, so that every proc knows how many
	/// neighborhoods exist globally
	/// First: Compute locally the maximum ID size
	UInt max_id_size = 0;
	UInt current_size = 0;
	NeighborhoodMap::const_iterator it;
	for (it = neighborhoods.begin(); it != neighborhoods.end(); ++it) {
	current_size = it->first.size();
	if (current_size > max_id_size) {
	max_id_size = current_size;
	}
	}

	/// get the global maximum ID size on each proc
	const Communicator & static_communicator = model.getMesh().getCommunicator();
	static_communicator.allReduce(max_id_size, SynchronizerOperation::_max);

	/// get the rank for this proc and the total nb proc
	UInt prank = static_communicator.whoAmI();
	UInt psize = static_communicator.getNbProc();

	/// exchange the number of neighborhoods on each proc
	Array<Int> nb_neighborhoods_per_proc(psize);
	nb_neighborhoods_per_proc(prank) = neighborhoods.size();
	static_communicator.allGather(nb_neighborhoods_per_proc);

	/// compute the total number of neighborhoods
	UInt nb_neighborhoods_global = std::accumulate(
	nb_neighborhoods_per_proc.begin(), nb_neighborhoods_per_proc.end(), 0);

	/// allocate an array of chars to store the names of all neighborhoods
	Array<char> buffer(nb_neighborhoods_global, max_id_size);

	/// starting index on this proc
	UInt starting_index =
	std::accumulate(nb_neighborhoods_per_proc.begin(),
	nb_neighborhoods_per_proc.begin() + prank, 0);

	it = neighborhoods.begin();
	/// store the names of local neighborhoods in the buffer
	for (UInt i = 0; i < neighborhoods.size(); ++i, ++it) {
	UInt c = 0;
	for (; c < it->first.size(); ++c) {
	buffer(i + starting_index, c) = it->first[c];
	}

	for (; c < max_id_size; ++c) {
	buffer(i + starting_index, c) = char(0);
	}
	}

	/// store the nb of data to send in the all gather
	Array<Int> buffer_size(nb_neighborhoods_per_proc);
	buffer_size *= max_id_size;
	/// exchange the names of all the neighborhoods with all procs
	static_communicator.allGatherV(buffer, buffer_size);

	for (UInt i = 0; i < nb_neighborhoods_global; ++i) {
	std::stringstream neighborhood_id;
	for (UInt c = 0; c < max_id_size; ++c) {
	if (buffer(i, c) == char(0)) {
	break;
	}
	neighborhood_id << buffer(i, c);
	}
	global_neighborhoods.insert(neighborhood_id.str());
	}

	/// this proc does not know all the neighborhoods -> create dummy
	/// grid so that this proc can participate in the all gather for
	/// detecting the overlap of neighborhoods this proc doesn't know
	Vector<Real> grid_center(this->spatial_dimension,
	std::numeric_limits<Real>::max());
	Vector<Real> spacing(this->spatial_dimension, 0.);

	dummy_grid = std::make_unique<SpatialGrid<IntegrationPoint>>(
	this->spatial_dimension, spacing, grid_center);

	for (const auto & neighborhood_id : global_neighborhoods) {
	it = neighborhoods.find(neighborhood_id);
	if (it != neighborhoods.end()) {
	it->second->createGridSynchronizer();
	} else {
	dummy_synchronizers[neighborhood_id] = std::make_unique<GridSynchronizer>(
	this->model.getMesh(), *dummy_grid,
	std::string(this->id + ":" + neighborhood_id + ":grid_synchronizer"),
	false);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::synchronize(DataAccessor<Element> & data_accessor,
	const SynchronizationTag & tag) {
	for (const auto & neighborhood_id : global_neighborhoods) {
	auto it = neighborhoods.find(neighborhood_id);
	if (it != neighborhoods.end()) {
	it->second->synchronize(data_accessor, tag);
	} else {
	auto synchronizer_it = dummy_synchronizers.find(neighborhood_id);
	if (synchronizer_it == dummy_synchronizers.end()) {
	continue;
	}

	synchronizer_it->second->synchronizeOnce(data_accessor, tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::averageInternals(GhostType ghost_type) {
	/// update the weights of the weight function
	if (ghost_type == _not_ghost) {
	this->computeWeights();
	}

	/// loop over all neighborhoods and compute the non-local variables
	for (auto & neighborhood : neighborhoods) {
	/// loop over all the non-local variables of the given neighborhood
	for (auto & non_local_variable : non_local_variables) {
	NonLocalVariable & non_local_var = *non_local_variable.second;
	neighborhood.second->weightedAverageOnNeighbours(
	non_local_var.local, non_local_var.non_local,
	non_local_var.nb_component, ghost_type);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::computeWeights() {
	AKANTU_DEBUG_IN();

	this->updateWeightFunctionInternals();
	this->volumes.zero();

	for (const auto & global_neighborhood : global_neighborhoods) {
	auto it = neighborhoods.find(global_neighborhood);

	if (it != neighborhoods.end()) {
	it->second->updateWeights();
	} else {
	dummy_synchronizers[global_neighborhood]->synchronize(
	dummy_accessor, SynchronizationTag::_mnl_weight);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::updatePairLists() {
	AKANTU_DEBUG_IN();

	integration_points_positions.initialize(
	this->model.getFEEngine(), _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension);

	/// compute the position of the quadrature points
	this->model.getFEEngine().computeIntegrationPointsCoordinates(
	integration_points_positions);

	for (auto & pair : neighborhoods) {
	pair.second->updatePairList();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::registerNonLocalVariable(const ID & variable_name,
	const ID & nl_variable_name,
	UInt nb_component) {

	AKANTU_DEBUG_IN();

	auto non_local_variable_it = non_local_variables.find(variable_name);

	if (non_local_variable_it == non_local_variables.end()) {
	non_local_variables[nl_variable_name] = std::make_unique<NonLocalVariable>(
	variable_name, nl_variable_name, this->id, nb_component);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ElementTypeMapReal &
	NonLocalManager::registerWeightFunctionInternal(const ID & field_name) {

	AKANTU_DEBUG_IN();

	auto it = this->weight_function_internals.find(field_name);
	if (it == weight_function_internals.end()) {
	weight_function_internals[field_name] =
	std::make_unique<ElementTypeMapReal>(field_name, this->id);
	}

	AKANTU_DEBUG_OUT();

	return *(weight_function_internals[field_name]);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::updateWeightFunctionInternals() {
	for (auto & pair : this->weight_function_internals) {
	auto & internals = *pair.second;
	internals.zero();
	for (auto ghost_type : ghost_types) {
	this->callback->updateLocalInternal(internals, ghost_type, _ek_regular);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::initNonLocalVariables() {
	/// loop over all the non-local variables
	for (auto & pair : non_local_variables) {
	auto & variable = *pair.second;
	variable.non_local.initialize(this->model.getFEEngine(),
	_nb_component = variable.nb_component,
	_spatial_dimension = spatial_dimension);
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::computeAllNonLocalStresses() {

	/// update the flattened version of the internals
	for (auto & pair : non_local_variables) {
	auto & variable = *pair.second;
	variable.local.zero();
	variable.non_local.zero();
	for (auto ghost_type : ghost_types) {
	this->callback->updateLocalInternal(variable.local, ghost_type,
	_ek_regular);
	}
	}

	this->volumes.zero();

	for (auto & pair : neighborhoods) {
	auto & neighborhood = *pair.second;
	neighborhood.asynchronousSynchronize(SynchronizationTag::_mnl_for_average);
	}

	this->averageInternals(_not_ghost);

	AKANTU_DEBUG_INFO("Wait distant non local stresses");

	for (auto & pair : neighborhoods) {
	auto & neighborhood = *pair.second;
	neighborhood.waitEndSynchronize(SynchronizationTag::_mnl_for_average);
	}

	this->averageInternals(_ghost);

	/// copy the results in the materials
	for (auto & pair : non_local_variables) {
	auto & variable = *pair.second;
	for (auto ghost_type : ghost_types) {
	this->callback->updateNonLocalInternal(variable.non_local, ghost_type,
	_ek_regular);
	}
	}

	this->callback->computeNonLocalStresses(_not_ghost);

	++this->compute_stress_calls;
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::cleanupExtraGhostElements() {
	// ElementTypeMap<UInt> & nb_ghost_protected) {

	using ElementSet = std::set<Element>;
	ElementSet relevant_ghost_elements;

	/// loop over all the neighborhoods and get their protected ghosts
	for (auto & pair : neighborhoods) {
	auto & neighborhood = *pair.second;
	ElementSet to_keep_per_neighborhood;

	neighborhood.getRelevantGhostElements(to_keep_per_neighborhood);
	relevant_ghost_elements.insert(to_keep_per_neighborhood.begin(),
	to_keep_per_neighborhood.end());
	}

	for (auto & pair : neighborhoods) {
	auto & neighborhood = *pair.second;
	neighborhood.cleanupExtraGhostElements(relevant_ghost_elements);
	}

	// /// remove all unneccessary ghosts from the mesh
	// /// Create list of element to remove and new numbering for element to keep
	// Mesh & mesh = this->model.getMesh();
	// ElementSet ghost_to_erase;

	// RemovedElementsEvent remove_elem(mesh);
	// auto & new_numberings = remove_elem.getNewNumbering();
	// Element element;
	// element.ghost_type = _ghost;

	// for (auto & type : mesh.elementTypes(spatial_dimension, _ghost)) {
	// element.type = type;
	// UInt nb_ghost_elem = mesh.getNbElement(type, _ghost);
	// // UInt nb_ghost_elem_protected = 0;
	// // try {
	// // nb_ghost_elem_protected = nb_ghost_protected(type, _ghost);
	// // } catch (...) {
	// // }

	// if (!new_numberings.exists(type, _ghost))
	// new_numberings.alloc(nb_ghost_elem, 1, type, _ghost);
	// else
	// new_numberings(type, _ghost).resize(nb_ghost_elem);

	// Array<UInt> & new_numbering = new_numberings(type, _ghost);
	// for (UInt g = 0; g < nb_ghost_elem; ++g) {
	// element.element = g;
	// if (element.element >= nb_ghost_elem_protected &&
	// relevant_ghost_elements.find(element) ==
	// relevant_ghost_elements.end()) {
	// remove_elem.getList().push_back(element);
	// new_numbering(element.element) = UInt(-1);
	// }
	// }
	// /// renumber remaining ghosts
	// UInt ng = 0;
	// for (UInt g = 0; g < nb_ghost_elem; ++g) {
	// if (new_numbering(g) != UInt(-1)) {
	// new_numbering(g) = ng;
	// ++ng;
	// }
	// }
	// }

	// for (auto & type : mesh.elementTypes(spatial_dimension, _not_ghost)) {
	// UInt nb_elem = mesh.getNbElement(type, _not_ghost);
	// if (!new_numberings.exists(type, _not_ghost))
	// new_numberings.alloc(nb_elem, 1, type, _not_ghost);
	// Array<UInt> & new_numbering = new_numberings(type, _not_ghost);
	// for (UInt e = 0; e < nb_elem; ++e) {
	// new_numbering(e) = e;
	// }
	// }
	// mesh.sendEvent(remove_elem);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::onElementsRemoved(
	const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	__attribute__((unused)) const RemovedElementsEvent & event) {

	FEEngine & fee = this->model.getFEEngine();
	NonLocalManager::removeIntegrationPointsFromMap(
	event.getNewNumbering(), spatial_dimension, integration_points_positions,
	fee, _ek_regular);
	NonLocalManager::removeIntegrationPointsFromMap(event.getNewNumbering(), 1,
	volumes, fee, _ek_regular);

	/// loop over all the neighborhoods and call onElementsRemoved
	auto global_neighborhood_it = global_neighborhoods.begin();
	NeighborhoodMap::iterator it;
	for (; global_neighborhood_it != global_neighborhoods.end();
	++global_neighborhood_it) {
	it = neighborhoods.find(*global_neighborhood_it);
	if (it != neighborhoods.end()) {
	it->second->onElementsRemoved(element_list, new_numbering, event);
	} else {
	dummy_synchronizers[*global_neighborhood_it]->onElementsRemoved(
	element_list, new_numbering, event);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::onElementsAdded(const Array<Element> & /unused/,
	const NewElementsEvent & /unused/) {
	this->resizeElementTypeMap(1, volumes, model.getFEEngine());
	this->resizeElementTypeMap(spatial_dimension, integration_points_positions,
	model.getFEEngine());
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::resizeElementTypeMap(UInt nb_component,
	ElementTypeMapReal & element_map,
	const FEEngine & fee,
	const ElementKind el_kind) {
	Mesh & mesh = this->model.getMesh();

	for (auto gt : ghost_types) {
	for (auto type : mesh.elementTypes(spatial_dimension, gt, el_kind)) {
	UInt nb_element = mesh.getNbElement(type, gt);
	UInt nb_quads = fee.getNbIntegrationPoints(type, gt);
	if (!element_map.exists(type, gt)) {
	element_map.alloc(nb_element * nb_quads, nb_component, type, gt);
	} else {
	element_map(type, gt).resize(nb_element * nb_quads);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::removeIntegrationPointsFromMap(
	const ElementTypeMapArray<UInt> & new_numbering, UInt nb_component,
	ElementTypeMapReal & element_map, const FEEngine & fee,
	const ElementKind el_kind) {

	for (auto gt : ghost_types) {
	for (auto type : new_numbering.elementTypes(_all_dimensions, gt, el_kind)) {
	if (element_map.exists(type, gt)) {
	const Array<UInt> & renumbering = new_numbering(type, gt);

	Array<Real> & vect = element_map(type, gt);
	UInt nb_quad_per_elem = fee.getNbIntegrationPoints(type, gt);
	Array<Real> tmp(renumbering.size() * nb_quad_per_elem, nb_component);

	AKANTU_DEBUG_ASSERT(
	tmp.size() == vect.size(),
	"Something strange append some mater was created or disappeared in "
	<< vect.getID() << "(" << vect.size() << "!=" << tmp.size()
	<< ") "
	"!!");

	UInt new_size = 0;
	for (UInt i = 0; i < renumbering.size(); ++i) {
	UInt new_i = renumbering(i);
	if (new_i != UInt(-1)) {
	memcpy(tmp.storage() + new_i * nb_component * nb_quad_per_elem,
	vect.storage() + i * nb_component * nb_quad_per_elem,
	nb_component * nb_quad_per_elem * sizeof(Real));
	++new_size;
	}
	}
	tmp.resize(new_size * nb_quad_per_elem);
	vect.copy(tmp);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	UInt NonLocalManager::getNbData(const Array<Element> & elements,
	const ID & id) const {
	UInt size = 0;
	UInt nb_quadrature_points = this->model.getNbIntegrationPoints(elements);
	auto it = non_local_variables.find(id);

	AKANTU_DEBUG_ASSERT(it != non_local_variables.end(),
	"The non-local variable " << id << " is not registered");

	size += it->second->nb_component * sizeof(Real) * nb_quadrature_points;
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & id) const {

	auto it = non_local_variables.find(id);

	AKANTU_DEBUG_ASSERT(it != non_local_variables.end(),
	"The non-local variable " << id << " is not registered");

	DataAccessor<Element>::packElementalDataHelper<Real>(
	it->second->local, buffer, elements, true, this->model.getFEEngine());
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalManager::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & id) const {
	auto it = non_local_variables.find(id);

	AKANTU_DEBUG_ASSERT(it != non_local_variables.end(),
	"The non-local variable " << id << " is not registered");

	DataAccessor<Element>::unpackElementalDataHelper<Real>(
	it->second->local, buffer, elements, true, this->model.getFEEngine());
	}

	} // namespace akantu
	diff --git a/src/model/common/non_local_toolbox/non_local_manager.hh b/src/model/common/non_local_toolbox/non_local_manager.hh
	index 700b39c69..e2753908e 100644
	--- a/src/model/common/non_local_toolbox/non_local_manager.hh
	+++ b/src/model/common/non_local_toolbox/non_local_manager.hh
	@@ -1,286 +1,287 @@
	/**
	* @file non_local_manager.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Classes that manages all the non-local neighborhoods
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_buffer.hh"
	#include "data_accessor.hh"
	#include "mesh_events.hh"
	#include "non_local_manager_callback.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	#include <set>
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_NON_LOCAL_MANAGER_HH_
	#define AKANTU_NON_LOCAL_MANAGER_HH_

	namespace akantu {
	class Model;
	class NonLocalNeighborhoodBase;
	class GridSynchronizer;
	class SynchronizerRegistry;
	class IntegrationPoint;
	template <typename T> class SpatialGrid;
	class FEEngine;
	} // namespace akantu

	namespace akantu {

	class NonLocalManager : public MeshEventHandler, public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLocalManager(Model & model, NonLocalManagerCallback & callback,
	const ID & id = "non_local_manager");
	~NonLocalManager() override;
	using NeighborhoodMap =
	std::map<ID, std::unique_ptr<NonLocalNeighborhoodBase>>;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ----------------------------------------------------------------------- */
	public:
	/// register a new internal needed for the weight computations
	ElementTypeMapReal & registerWeightFunctionInternal(const ID & field_name);

	/// register a non-local variable
	void registerNonLocalVariable(const ID & variable_name,
	const ID & nl_variable_name, UInt nb_component);

	/// register non-local neighborhood
	inline void registerNeighborhood(const ID & neighborhood,
	const ID & weight_func_id);

	// void registerNonLocalManagerCallback(NonLocalManagerCallback & callback);

	/// average the internals and compute the non-local stresses
	virtual void computeAllNonLocalStresses();

	/// initialize the non-local manager: compute pair lists and weights for all
	/// neighborhoods
	virtual void initialize();

	/// synchronize once on a given tag using the neighborhoods synchronizer
	void synchronize(DataAccessor<Element> & data_accessor,
	const SynchronizationTag & /tag/);

	protected:
	/// create the grid synchronizers for each neighborhood
	void createNeighborhoodSynchronizers();

	/// compute the weights in each neighborhood for non-local averaging
	void computeWeights();

	/// compute the weights in each neighborhood for non-local averaging
	void updatePairLists();

	/// average the non-local variables
	void averageInternals(GhostType ghost_type = _not_ghost);

	/// update the flattened version of the weight function internals
	void updateWeightFunctionInternals();

	protected:
	/// create a new neighborhood for a given domain ID
	void createNeighborhood(const ID & weight_func, const ID & neighborhood);

	/// set the values of the jacobians
	void setJacobians(const FEEngine & fe_engine, ElementKind kind);

	/// allocation of eelment type maps
	// void initElementTypeMap(UInt nb_component,
	// ElementTypeMapReal & element_map,
	// const FEEngine & fe_engine,
	// const ElementKind el_kind = _ek_regular);

	/// resizing of element type maps
	void resizeElementTypeMap(UInt nb_component, ElementTypeMapReal & element_map,
	const FEEngine & fee,
	ElementKind el_kind = _ek_regular);

	/// remove integration points from element type maps
	static void removeIntegrationPointsFromMap(
	const ElementTypeMapArray<UInt> & new_numbering, UInt nb_component,
	ElementTypeMapReal & element_map, const FEEngine & fee,
	ElementKind el_kind = _ek_regular);

	/// allocate the non-local variables
	void initNonLocalVariables();

	/// cleanup unneccessary ghosts
	void
	cleanupExtraGhostElements(); // ElementTypeMap<UInt> & nb_ghost_protected);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor kind of interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// get Nb data for synchronization in parallel
	UInt getNbData(const Array<Element> & elements, const ID & id) const;

	/// pack data for synchronization in parallel
	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const ID & id) const;

	/// unpack data for synchronization in parallel
	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const ID & id) const;

	/* ------------------------------------------------------------------------ */
	/* MeshEventHandler inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	void onElementsRemoved(const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) override;
	void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);
	AKANTU_GET_MACRO(Model, model, const Model &);
	AKANTU_GET_MACRO_NOT_CONST(Model, model, Model &);
	AKANTU_GET_MACRO_NOT_CONST(Volumes, volumes, ElementTypeMapReal &)
	AKANTU_GET_MACRO(NbStressCalls, compute_stress_calls, UInt);

	/// return the fem object associated with a provided name
	inline NonLocalNeighborhoodBase & getNeighborhood(const ID & name) const;

	inline const Array<Real> & getJacobians(ElementType type,
	GhostType ghost_type) {
	return *jacobians(type, ghost_type);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// the spatial dimension
	const UInt spatial_dimension;

	ID id;
	+
	protected:
	/// the non-local neighborhoods present
	NeighborhoodMap neighborhoods;

	/// list of all the non-local materials in the model
	// std::vector<ID> non_local_materials;

	struct NonLocalVariable {
	NonLocalVariable(const ID & variable_name, const ID & nl_variable_name,
	const ID & id, UInt nb_component)
	: local(variable_name, id), non_local(nl_variable_name, id),
	nb_component(nb_component) {}
	ElementTypeMapReal local;
	ElementTypeMapReal non_local;
	UInt nb_component;
	};

	/// the non-local variables associated to a certain neighborhood
	std::map<ID, std::unique_ptr<NonLocalVariable>> non_local_variables;

	/// reference to the model
	Model & model;

	/// jacobians for all the elements in the mesh
	ElementTypeMap<const Array<Real> *> jacobians;

	/// store the position of the quadrature points
	ElementTypeMapReal integration_points_positions;

	/// store the volume of each quadrature point for the non-local weight
	/// normalization
	ElementTypeMapReal volumes;

	/// counter for computeStress calls
	UInt compute_stress_calls;

	/// map to store weight function types from input file
	std::map<ID, ParserSection> weight_function_types;

	/// map to store the internals needed by the weight functions
	std::map<ID, std::unique_ptr<ElementTypeMapReal>> weight_function_internals;
	/* --------------------------------------------------------------------------
	*/
	/// the following are members needed to make this processor participate in the
	/// grid creation of neighborhoods he doesn't own as a member. For details see
	/// createGridSynchronizers function

	/// synchronizer registry for dummy grid synchronizers
	std::unique_ptr<SynchronizerRegistry> dummy_registry;

	/// map of dummy synchronizers
	std::map<ID, std::unique_ptr<GridSynchronizer>> dummy_synchronizers;

	/// dummy spatial grid
	std::unique_ptr<SpatialGrid<IntegrationPoint>> dummy_grid;

	/// create a set of all neighborhoods present in the simulation
	std::set<ID> global_neighborhoods;

	class DummyDataAccessor : public DataAccessor<Element> {
	public:
	inline UInt getNbData(const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override {
	return 0;
	};

	inline void packData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) const override{};

	inline void unpackData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) override{};
	};

	DummyDataAccessor dummy_accessor;

	/* ------------------------------------------------------------------------ */
	NonLocalManagerCallback * callback;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "non_local_manager_inline_impl.hh"

	#endif /* AKANTU_NON_LOCAL_MANAGER_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_manager_callback.hh b/src/model/common/non_local_toolbox/non_local_manager_callback.hh
	index b4be45854..acec2a05b 100644
	--- a/src/model/common/non_local_toolbox/non_local_manager_callback.hh
	+++ b/src/model/common/non_local_toolbox/non_local_manager_callback.hh
	@@ -1,69 +1,67 @@
	/**
	* @file non_local_manager_callback.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jul 21 2017
	* @date last modification: Tue Sep 19 2017
	*
	* @brief Callback functions for the non local manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LOCAL_MANAGER_CALLBACK_HH_
	#define AKANTU_NON_LOCAL_MANAGER_CALLBACK_HH_

	namespace akantu {
	class NonLocalManager;
	} // namespace akantu

	namespace akantu {

	class NonLocalManagerCallback {
	public:
	virtual void initializeNonLocal() {}

	/* ------------------------------------------------------------------------ */
	- virtual void
	- insertIntegrationPointsInNeighborhoods(GhostType ghost_type) = 0;
	+ virtual void insertIntegrationPointsInNeighborhoods(GhostType ghost_type) = 0;

	virtual void computeNonLocalStresses(GhostType ghost_type) = 0;

	/// update the values of the non local internal
	virtual void updateLocalInternal(ElementTypeMapReal & internal_flat,
	- GhostType ghost_type,
	- ElementKind kind) = 0;
	+ GhostType ghost_type, ElementKind kind) = 0;

	/// copy the results of the averaging in the materials
	virtual void updateNonLocalInternal(ElementTypeMapReal & internal_flat,
	GhostType ghost_type,
	ElementKind kind) = 0;
	};

	} // namespace akantu

	#endif /* AKANTU_NON_LOCAL_MANAGER_CALLBACK_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_manager_inline_impl.hh b/src/model/common/non_local_toolbox/non_local_manager_inline_impl.hh
	index 7b546740e..711c39502 100644
	--- a/src/model/common/non_local_toolbox/non_local_manager_inline_impl.hh
	+++ b/src/model/common/non_local_toolbox/non_local_manager_inline_impl.hh
	@@ -1,69 +1,69 @@
	/**
	* @file non_local_manager_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Mon Sep 11 2017
	*
	* @brief inline implementation of non-local manager functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "neighborhood_base.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LOCAL_MANAGER_INLINE_IMPL_HH_
	#define AKANTU_NON_LOCAL_MANAGER_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline void NonLocalManager::registerNeighborhood(const ID & neighborhood,
	const ID & weight_func_id) {

	/// check if neighborhood has already been created
	auto it = neighborhoods.find(neighborhood);
	if (it == neighborhoods.end()) {
	this->createNeighborhood(weight_func_id, neighborhood);
	}
	}

	/* -------------------------------------------------------------------------- */
	inline NonLocalNeighborhoodBase &
	NonLocalManager::getNeighborhood(const ID & name) const {
	AKANTU_DEBUG_IN();

	auto it = neighborhoods.find(name);

	AKANTU_DEBUG_ASSERT(it != neighborhoods.end(),
	"The neighborhood " << name << " is not registered");

	AKANTU_DEBUG_OUT();
	return *(it->second);
	}

	} // namespace akantu

	#endif /* AKANTU_NON_LOCAL_MANAGER_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_neighborhood.hh b/src/model/common/non_local_toolbox/non_local_neighborhood.hh
	index 6e9e94535..15dee5b72 100644
	--- a/src/model/common/non_local_toolbox/non_local_neighborhood.hh
	+++ b/src/model/common/non_local_toolbox/non_local_neighborhood.hh
	@@ -1,135 +1,134 @@
	/**
	* @file non_local_neighborhood.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Non-local neighborhood for non-local averaging based on
	* weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_NON_LOCAL_NEIGHBORHOOD_HH_
	#define AKANTU_NON_LOCAL_NEIGHBORHOOD_HH_
	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	#include "non_local_neighborhood_base.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class NonLocalManager;
	class BaseWeightFunction;
	} // namespace akantu

	namespace akantu {

	template <class WeightFunction = BaseWeightFunction>
	class NonLocalNeighborhood : public NonLocalNeighborhoodBase {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLocalNeighborhood(NonLocalManager & manager,
	const ElementTypeMapReal & quad_coordinates,
	const ID & id = "neighborhood");
	~NonLocalNeighborhood() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute the weights for non-local averaging
	void computeWeights() override;

	/// save the pair of weights in a file
	void saveWeights(const std::string & filename) const override;

	/// compute the non-local counter part for a given element type map
	// compute the non-local counter part for a given element type map
	- void
	- weightedAverageOnNeighbours(const ElementTypeMapReal & to_accumulate,
	- ElementTypeMapReal & accumulated,
	- UInt nb_degree_of_freedom,
	- GhostType ghost_type2) const override;
	+ void weightedAverageOnNeighbours(const ElementTypeMapReal & to_accumulate,
	+ ElementTypeMapReal & accumulated,
	+ UInt nb_degree_of_freedom,
	+ GhostType ghost_type2) const override;

	/// update the weights based on the weight function
	void updateWeights() override;

	/// register a new non-local variable in the neighborhood
	// void registerNonLocalVariable(const ID & id);
	protected:
	template <class Func>
	inline void foreach_weight(GhostType ghost_type, Func && func);

	template <class Func>
	inline void foreach_weight(GhostType ghost_type, Func && func) const;

	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Accessor */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(NonLocalManager, non_local_manager, const NonLocalManager &);
	AKANTU_GET_MACRO_NOT_CONST(NonLocalManager, non_local_manager,
	NonLocalManager &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// Pointer to non-local manager class
	NonLocalManager & non_local_manager;

	/// the weights associated to the pairs
	std::array<std::unique_ptr<Array<Real>>, 2> pair_weight;

	/// weight function
	std::unique_ptr<WeightFunction> weight_function;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* Implementation of template functions */
	/* -------------------------------------------------------------------------- */
	#include "non_local_neighborhood_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "non_local_neighborhood_inline_impl.hh"

	#endif /* AKANTU_NON_LOCAL_NEIGHBORHOOD_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_neighborhood_base.cc b/src/model/common/non_local_toolbox/non_local_neighborhood_base.cc
	index 75755ba81..f8b78a232 100644
	--- a/src/model/common/non_local_toolbox/non_local_neighborhood_base.cc
	+++ b/src/model/common/non_local_toolbox/non_local_neighborhood_base.cc
	@@ -1,126 +1,126 @@
	/**
	* @file non_local_neighborhood_base.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Jul 10 2020
	*
	* @brief Implementation of non-local neighborhood base
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_local_neighborhood_base.hh"
	#include "grid_synchronizer.hh"
	#include "model.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NonLocalNeighborhoodBase::NonLocalNeighborhoodBase(
	Model & model, const ElementTypeMapReal & quad_coordinates, const ID & id)
	: NeighborhoodBase(model, quad_coordinates, id),
	Parsable(ParserType::_non_local, id) {
	AKANTU_DEBUG_IN();

	this->registerParam("radius", neighborhood_radius, 100.,
	_pat_parsable \| _pat_readable, "Non local radius");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	NonLocalNeighborhoodBase::~NonLocalNeighborhoodBase() = default;

	/* -------------------------------------------------------------------------- */
	void NonLocalNeighborhoodBase::createGridSynchronizer() {
	this->is_creating_grid = true;

	this->grid_synchronizer = std::make_unique<GridSynchronizer>(
	this->model.getMesh(), spatial_grid, this,
	std::set<SynchronizationTag>{SynchronizationTag::_mnl_weight,
	SynchronizationTag::_mnl_for_average},
	std::string(id + ":grid_synchronizer"), false);

	this->is_creating_grid = false;
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalNeighborhoodBase::synchronize(
	DataAccessor<Element> & data_accessor, const SynchronizationTag & tag) {
	if (not grid_synchronizer) {
	return;
	}

	grid_synchronizer->synchronizeOnce(data_accessor, tag);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalNeighborhoodBase::getRelevantGhostElements(
	std::set<Element> & relevant_ghost_elements) {

	for (auto && ghost_type : ghost_type_t{}) {
	auto & pair_list = this->pair_list.at(ghost_type);
	for (auto && pair : pair_list) {
	if (pair.first.ghost_type == _ghost) {
	relevant_ghost_elements.insert(pair.first);
	}
	if (pair.second.ghost_type == _ghost) {
	relevant_ghost_elements.insert(pair.second);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalNeighborhoodBase::cleanupExtraGhostElements(
	std::set<Element> & relevant_ghost_elements) {

	Array<Element> ghosts_to_erase;
	auto & mesh = this->model.getMesh();

	auto end = relevant_ghost_elements.end();
	for (const auto & type : mesh.elementTypes(
	_spatial_dimension = spatial_dimension, _ghost_type = _ghost)) {
	auto nb_ghost_elem = mesh.getNbElement(type, _ghost);
	for (UInt g = 0; g < nb_ghost_elem; ++g) {
	Element element{type, g, _ghost};
	if (relevant_ghost_elements.find(element) == end) {
	ghosts_to_erase.push_back(element);
	}
	}
	}

	/// remove the unneccessary ghosts from the synchronizer
	mesh.eraseElements(ghosts_to_erase);
	}

	/* -------------------------------------------------------------------------- */
	void NonLocalNeighborhoodBase::registerNonLocalVariable(const ID & id) {
	this->non_local_variables.insert(id);
	}

	} // namespace akantu
	diff --git a/src/model/common/non_local_toolbox/non_local_neighborhood_base.hh b/src/model/common/non_local_toolbox/non_local_neighborhood_base.hh
	index ee68d9328..dce06713b 100644
	--- a/src/model/common/non_local_toolbox/non_local_neighborhood_base.hh
	+++ b/src/model/common/non_local_toolbox/non_local_neighborhood_base.hh
	@@ -1,136 +1,136 @@
	/**
	* @file non_local_neighborhood_base.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Non-local neighborhood base class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "neighborhood_base.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LOCAL_NEIGHBORHOOD_BASE_HH_
	#define AKANTU_NON_LOCAL_NEIGHBORHOOD_BASE_HH_

	namespace akantu {
	class Model;
	}
	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class NonLocalNeighborhoodBase : public NeighborhoodBase, public Parsable {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	NonLocalNeighborhoodBase(Model & model,
	const ElementTypeMapReal & quad_coordinates,
	const ID & id = "non_local_neighborhood");
	~NonLocalNeighborhoodBase() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// create grid synchronizer and exchange ghost cells
	void createGridSynchronizer() override;

	void synchronize(DataAccessor<Element> & data_accessor,
	const SynchronizationTag & tag) override;

	/// compute weights, for instance needed for non-local damage computation
	virtual void computeWeights(){};

	// compute the non-local counter part for a given element type map
	virtual void
	weightedAverageOnNeighbours(const ElementTypeMapReal & to_accumulate,
	ElementTypeMapReal & accumulated,
	UInt nb_degree_of_freedom,
	GhostType ghost_type2) const = 0;

	/// update the weights for the non-local averaging
	virtual void updateWeights() = 0;

	/// update the weights for the non-local averaging
	virtual void saveWeights(const std::string & /unused/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// register a new non-local variable in the neighborhood
	virtual void registerNonLocalVariable(const ID & id);

	/// clean up the unneccessary ghosts
	void cleanupExtraGhostElements(std::set<Element> & relevant_ghost_elements);

	/// list releveant ghosts
	void getRelevantGhostElements(std::set<Element> & relevant_ghost_elements);

	protected:
	/// create the grid
	void createGrid();

	/* --------------------------------------------------------------------------
	*/
	/* DataAccessor inherited members */
	/* --------------------------------------------------------------------------
	*/
	public:
	inline UInt getNbData(const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override {
	return 0;
	}

	inline void packData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) const override {}

	inline void unpackData(CommunicationBuffer & /buffer/,
	const Array<Element> & /element/,
	const SynchronizationTag & /tag/) override {}

	/* --------------------------------------------------------------------------
	*/
	/* Accessors */
	/* --------------------------------------------------------------------------
	*/
	public:
	AKANTU_GET_MACRO(NonLocalVariables, non_local_variables,
	const std::set<ID> &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// list of non-local variables associated to the neighborhood
	std::set<ID> non_local_variables;
	};

	} // namespace akantu

	#endif /* AKANTU_NON_LOCAL_NEIGHBORHOOD_BASE_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_neighborhood_inline_impl.hh b/src/model/common/non_local_toolbox/non_local_neighborhood_inline_impl.hh
	index aab11099e..f4534bdfb 100644
	--- a/src/model/common/non_local_toolbox/non_local_neighborhood_inline_impl.hh
	+++ b/src/model/common/non_local_toolbox/non_local_neighborhood_inline_impl.hh
	@@ -1,88 +1,88 @@
	/**
	* @file non_local_neighborhood_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Oct 06 2015
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Implementation of inline functions of non-local neighborhood class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_local_neighborhood.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LOCAL_NEIGHBORHOOD_INLINE_IMPL_HH_
	#define AKANTU_NON_LOCAL_NEIGHBORHOOD_INLINE_IMPL_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	inline UInt NonLocalNeighborhood<WeightFunction>::getNbData(
	const Array<Element> & elements, const SynchronizationTag & tag) const {
	UInt size = 0;

	if (tag == SynchronizationTag::_mnl_for_average) {
	for (auto & variable_id : non_local_variables) {
	size += this->non_local_manager.getNbData(elements, variable_id);
	}
	}

	size += this->weight_function->getNbData(elements, tag);

	return size;
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	inline void NonLocalNeighborhood<WeightFunction>::packData(
	CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	if (tag == SynchronizationTag::_mnl_for_average) {
	for (auto & variable_id : non_local_variables) {
	this->non_local_manager.packData(buffer, elements, variable_id);
	}
	}

	this->weight_function->packData(buffer, elements, tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	inline void NonLocalNeighborhood<WeightFunction>::unpackData(
	CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) {
	if (tag == SynchronizationTag::_mnl_for_average) {
	for (auto & variable_id : non_local_variables) {
	this->non_local_manager.unpackData(buffer, elements, variable_id);
	}
	}

	this->weight_function->unpackData(buffer, elements, tag);
	}

	} // namespace akantu

	#endif /* AKANTU_NON_LOCAL_NEIGHBORHOOD_INLINE_IMPL_HH_ */
	diff --git a/src/model/common/non_local_toolbox/non_local_neighborhood_tmpl.hh b/src/model/common/non_local_toolbox/non_local_neighborhood_tmpl.hh
	index 60dfd780a..e07deb731 100644
	--- a/src/model/common/non_local_toolbox/non_local_neighborhood_tmpl.hh
	+++ b/src/model/common/non_local_toolbox/non_local_neighborhood_tmpl.hh
	@@ -1,279 +1,281 @@
	/**
	* @file non_local_neighborhood_tmpl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Sep 28 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of class non-local neighborhood
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "non_local_manager.hh"
	#include "non_local_neighborhood.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NON_LOCAL_NEIGHBORHOOD_TMPL_HH_
	#define AKANTU_NON_LOCAL_NEIGHBORHOOD_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	template <class Func>
	-inline void NonLocalNeighborhood<WeightFunction>::foreach_weight(
	- GhostType ghost_type, Func && func) {
	+inline void
	+NonLocalNeighborhood<WeightFunction>::foreach_weight(GhostType ghost_type,
	+ Func && func) {
	auto weight_it =
	pair_weight[ghost_type]->begin(pair_weight[ghost_type]->getNbComponent());

	for (auto & pair : pair_list[ghost_type]) {
	std::forward<decltype(func)>(func)(pair.first, pair.second, *weight_it);
	++weight_it;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	template <class Func>
	-inline void NonLocalNeighborhood<WeightFunction>::foreach_weight(
	- GhostType ghost_type, Func && func) const {
	+inline void
	+NonLocalNeighborhood<WeightFunction>::foreach_weight(GhostType ghost_type,
	+ Func && func) const {
	auto weight_it =
	pair_weight[ghost_type]->begin(pair_weight[ghost_type]->getNbComponent());

	for (auto & pair : pair_list[ghost_type]) {
	std::forward<decltype(func)>(func)(pair.first, pair.second, *weight_it);
	++weight_it;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	NonLocalNeighborhood<WeightFunction>::NonLocalNeighborhood(
	NonLocalManager & manager, const ElementTypeMapReal & quad_coordinates,
	const ID & id)
	: NonLocalNeighborhoodBase(manager.getModel(), quad_coordinates, id),
	non_local_manager(manager) {
	AKANTU_DEBUG_IN();

	this->weight_function = std::make_unique<WeightFunction>(manager);

	this->registerSubSection(ParserType::_weight_function, "weight_parameter",
	*weight_function);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	NonLocalNeighborhood<WeightFunction>::~NonLocalNeighborhood() = default;

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	void NonLocalNeighborhood<WeightFunction>::computeWeights() {
	AKANTU_DEBUG_IN();

	this->weight_function->setRadius(this->neighborhood_radius);
	Vector<Real> q1_coord(this->spatial_dimension);
	Vector<Real> q2_coord(this->spatial_dimension);

	UInt nb_weights_per_pair = 2; /// w1: q1->q2, w2: q2->q1

	/// get the elementtypemap for the neighborhood volume for each quadrature
	/// point
	ElementTypeMapReal & quadrature_points_volumes =
	this->non_local_manager.getVolumes();

	/// update the internals of the weight function if applicable (not
	/// all the weight functions have internals and do noting in that
	/// case)
	weight_function->updateInternals();

	for (auto ghost_type : ghost_types) {
	/// allocate the array to store the weight, if it doesn't exist already
	if (!(pair_weight[ghost_type])) {
	pair_weight[ghost_type] =
	std::make_unique<Array<Real>>(0, nb_weights_per_pair);
	}

	/// resize the array to the correct size
	pair_weight[ghost_type]->resize(pair_list[ghost_type].size());
	/// set entries to zero
	pair_weight[ghost_type]->zero();

	/// loop over all pairs in the current pair list array and their
	/// corresponding weights
	auto first_pair = pair_list[ghost_type].begin();
	auto last_pair = pair_list[ghost_type].end();
	auto weight_it = pair_weight[ghost_type]->begin(nb_weights_per_pair);

	// Compute the weights
	for (; first_pair != last_pair; ++first_pair, ++weight_it) {
	Vector<Real> & weight = *weight_it;
	const IntegrationPoint & q1 = first_pair->first;
	const IntegrationPoint & q2 = first_pair->second;

	/// get the coordinates for the given pair of quads
	auto coords_type_1_it = this->quad_coordinates(q1.type, q1.ghost_type)
	.begin(this->spatial_dimension);
	q1_coord = coords_type_1_it[q1.global_num];
	auto coords_type_2_it = this->quad_coordinates(q2.type, q2.ghost_type)
	.begin(this->spatial_dimension);
	q2_coord = coords_type_2_it[q2.global_num];

	Array<Real> & quad_volumes_1 =
	quadrature_points_volumes(q1.type, q1.ghost_type);
	const Array<Real> & jacobians_2 =
	this->non_local_manager.getJacobians(q2.type, q2.ghost_type);
	const Real & q2_wJ = jacobians_2(q2.global_num);

	/// compute distance between the two quadrature points
	Real r = q1_coord.distance(q2_coord);

	/// compute the weight for averaging on q1 based on the distance
	Real w1 = this->weight_function->operator()(r, q1, q2);
	weight(0) = q2_wJ * w1;

	quad_volumes_1(q1.global_num) += weight(0);

	if (q2.ghost_type != _ghost && q1.global_num != q2.global_num) {
	const Array<Real> & jacobians_1 =
	this->non_local_manager.getJacobians(q1.type, q1.ghost_type);
	Array<Real> & quad_volumes_2 =
	quadrature_points_volumes(q2.type, q2.ghost_type);
	/// compute the weight for averaging on q2
	const Real & q1_wJ = jacobians_1(q1.global_num);
	Real w2 = this->weight_function->operator()(r, q2, q1);
	weight(1) = q1_wJ * w2;
	quad_volumes_2(q2.global_num) += weight(1);
	} else {
	weight(1) = 0.;
	}
	}
	}

	/// normalize the weights
	for (auto ghost_type : ghost_types) {
	foreach_weight(ghost_type, [&](const auto & q1, const auto & q2,
	auto & weight) {
	auto & quad_volumes_1 = quadrature_points_volumes(q1.type, q1.ghost_type);
	auto & quad_volumes_2 = quadrature_points_volumes(q2.type, q2.ghost_type);

	Real q1_volume = quad_volumes_1(q1.global_num);
	auto ghost_type2 = q2.ghost_type;
	weight(0) *= 1. / q1_volume;
	if (ghost_type2 != _ghost) {
	Real q2_volume = quad_volumes_2(q2.global_num);
	weight(1) *= 1. / q2_volume;
	}
	});
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	void NonLocalNeighborhood<WeightFunction>::saveWeights(
	const std::string & filename) const {
	std::ofstream pout;

	std::stringstream sstr;

	const Communicator & comm = model.getMesh().getCommunicator();

	Int prank = comm.whoAmI();
	sstr << filename << "." << prank;

	pout.open(sstr.str().c_str());

	for (UInt gt = _not_ghost; gt <= _ghost; ++gt) {
	auto ghost_type = (GhostType)gt;

	AKANTU_DEBUG_ASSERT((pair_weight[ghost_type]),
	"the weights have not been computed yet");

	Array<Real> & weights = *(pair_weight[ghost_type]);
	auto weights_it = weights.begin(2);
	for (UInt i = 0; i < weights.size(); ++i, ++weights_it) {
	pout << "w1: " << (weights_it)(0) << " w2: " << (weights_it)(1)
	<< std::endl;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	void NonLocalNeighborhood<WeightFunction>::weightedAverageOnNeighbours(
	const ElementTypeMapReal & to_accumulate, ElementTypeMapReal & accumulated,
	UInt nb_degree_of_freedom, GhostType ghost_type2) const {

	auto it = non_local_variables.find(accumulated.getName());
	// do averaging only for variables registered in the neighborhood
	if (it == non_local_variables.end()) {
	return;
	}

	foreach_weight(
	ghost_type2,
	[ghost_type2, nb_degree_of_freedom, &to_accumulate,
	&accumulated](const auto & q1, const auto & q2, auto & weight) {
	const Vector<Real> to_acc_1 =
	to_accumulate(q1.type, q1.ghost_type)
	.begin(nb_degree_of_freedom)[q1.global_num];
	const Vector<Real> to_acc_2 =
	to_accumulate(q2.type, q2.ghost_type)
	.begin(nb_degree_of_freedom)[q2.global_num];
	Vector<Real> acc_1 = accumulated(q1.type, q1.ghost_type)
	.begin(nb_degree_of_freedom)[q1.global_num];
	Vector<Real> acc_2 = accumulated(q2.type, q2.ghost_type)
	.begin(nb_degree_of_freedom)[q2.global_num];

	acc_1 += weight(0) * to_acc_2;

	if (ghost_type2 != _ghost) {
	acc_2 += weight(1) * to_acc_1;
	}
	});
	}

	/* -------------------------------------------------------------------------- */
	template <class WeightFunction>
	void NonLocalNeighborhood<WeightFunction>::updateWeights() {
	// Update the weights for the non local variable averaging
	if (this->weight_function->getUpdateRate() &&
	(this->non_local_manager.getNbStressCalls() %
	this->weight_function->getUpdateRate() ==
	0)) {
	SynchronizerRegistry::synchronize(SynchronizationTag::_mnl_weight);
	this->computeWeights();
	}
	}

	} // namespace akantu

	#endif /* __AKANTU_NON_LOCAL_NEIGHBORHOOD_TMPL__ */
	diff --git a/src/model/common/solver_callback.cc b/src/model/common/solver_callback.cc
	index 756203ab9..48f349228 100644
	--- a/src/model/common/solver_callback.cc
	+++ b/src/model/common/solver_callback.cc
	@@ -1,55 +1,55 @@
	/**
	* @file solver_callback.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Default behavior of solver_callbacks
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_callback.hh"
	#include "dof_manager.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SolverCallback::SolverCallback(DOFManager & dof_manager)
	: sc_dof_manager(&dof_manager) {}

	/* -------------------------------------------------------------------------- */
	SolverCallback::SolverCallback() = default;

	/* -------------------------------------------------------------------------- */
	SolverCallback::~SolverCallback() = default;

	/* -------------------------------------------------------------------------- */
	void SolverCallback::setDOFManager(DOFManager & dof_manager) {
	this->sc_dof_manager = &dof_manager;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/solver_callback.hh b/src/model/common/solver_callback.hh
	index 679eeeb08..b52267488 100644
	--- a/src/model/common/solver_callback.hh
	+++ b/src/model/common/solver_callback.hh
	@@ -1,110 +1,110 @@
	/**
	* @file solver_callback.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 27 2019
	*
	* @brief Class defining the interface for non_linear_solver callbacks
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_CALLBACK_HH_
	#define AKANTU_SOLVER_CALLBACK_HH_

	namespace akantu {
	class DOFManager;
	}

	namespace akantu {

	class SolverCallback {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	explicit SolverCallback(DOFManager & dof_manager);
	explicit SolverCallback();
	/* ------------------------------------------------------------------------ */
	virtual ~SolverCallback();

	protected:
	void setDOFManager(DOFManager & dof_manager);
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the type of matrix needed
	virtual MatrixType getMatrixType(const ID &) = 0;

	/// callback to assemble a Matrix
	virtual void assembleMatrix(const ID &) = 0;

	/// callback to assemble a lumped Matrix
	virtual void assembleLumpedMatrix(const ID &) = 0;

	/// callback to assemble the residual (rhs)
	virtual void assembleResidual() = 0;

	/// callback to assemble the rhs parts, (e.g. internal_forces +
	/// external_forces)
	virtual void assembleResidual(const ID & /residual_part/) {}

	/* ------------------------------------------------------------------------ */
	/* Dynamic simulations part */
	/* ------------------------------------------------------------------------ */
	/// callback for the predictor (in case of dynamic simulation)
	virtual void predictor() {}

	/// callback for the corrector (in case of dynamic simulation)
	virtual void corrector() {}

	/// tells if the residual can be computed in separated parts
	virtual bool canSplitResidual() { return false; }

	/* ------------------------------------------------------------------------ */
	/* management callbacks */
	/* ------------------------------------------------------------------------ */
	virtual void beforeSolveStep(){};
	virtual void afterSolveStep(bool /converged/ = true){};

	protected:
	/// DOFManager prefixed to avoid collision in multiple inheritance cases
	DOFManager * sc_dof_manager{nullptr};
	};

	namespace debug {
	class SolverCallbackResidualPartUnknown : public Exception {
	public:
	SolverCallbackResidualPartUnknown(const ID & residual_part)
	: Exception(residual_part + " is not known here.") {}
	};
	} // namespace debug

	} // namespace akantu

	#endif /* AKANTU_SOLVER_CALLBACK_HH_ */
	diff --git a/src/model/common/time_step_solvers/time_step_solver.cc b/src/model/common/time_step_solvers/time_step_solver.cc
	index 8f5c1fb92..42e69a0bb 100644
	--- a/src/model/common/time_step_solvers/time_step_solver.cc
	+++ b/src/model/common/time_step_solvers/time_step_solver.cc
	@@ -1,208 +1,208 @@
	/**
	* @file time_step_solver.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Implementation of common part of TimeStepSolvers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "time_step_solver.hh"
	#include "dof_manager.hh"
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	TimeStepSolver::TimeStepSolver(DOFManager & dof_manager,
	const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback, const ID & id)
	- : SolverCallback(dof_manager), id(id),
	- _dof_manager(dof_manager), type(type), time_step(0.),
	- solver_callback(&solver_callback), non_linear_solver(non_linear_solver) {
	+ : SolverCallback(dof_manager), id(id), _dof_manager(dof_manager),
	+ type(type), time_step(0.), solver_callback(&solver_callback),
	+ non_linear_solver(non_linear_solver) {
	this->registerSubRegistry("non_linear_solver", non_linear_solver);
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver::~TimeStepSolver() = default;

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::setIntegrationScheme(
	const ID & dof_id, const IntegrationSchemeType & type,
	IntegrationScheme::SolutionType solution_type) {
	auto scheme = this->getIntegrationSchemeInternal(dof_id, type, solution_type);
	this->setIntegrationScheme(dof_id, scheme, solution_type);
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::setIntegrationScheme(
	const ID & dof_id, std::unique_ptr<IntegrationScheme> & scheme,
	IntegrationScheme::SolutionType solution_type) {
	this->setIntegrationSchemeInternal(dof_id, scheme, solution_type);

	for (auto & pair : needed_matrices) {
	auto & mat_type = pair.second;
	const auto & name = pair.first;
	if (mat_type == _mt_not_defined) {
	mat_type = this->solver_callback->getMatrixType(name);
	}

	if (mat_type == _mt_not_defined) {
	continue;
	}

	if (not _dof_manager.hasMatrix(name)) {
	_dof_manager.getNewMatrix(name, mat_type);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	MatrixType TimeStepSolver::getCommonMatrixType() {
	MatrixType common_type = _mt_not_defined;
	for (auto & pair : needed_matrices) {
	auto & type = pair.second;
	common_type = std::min(common_type, type);
	}

	AKANTU_DEBUG_ASSERT(common_type != _mt_not_defined,
	"No type defined for the matrices");

	return common_type;
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::predictor() {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->solver_callback->predictor();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::corrector() {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->solver_callback->corrector();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::beforeSolveStep() {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->solver_callback->beforeSolveStep();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::afterSolveStep(bool converged) {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->solver_callback->afterSolveStep(converged);
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::assembleLumpedMatrix(const ID & matrix_id) {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	if (not _dof_manager.hasLumpedMatrix(matrix_id)) {
	_dof_manager.getNewLumpedMatrix(matrix_id);
	}

	this->solver_callback->assembleLumpedMatrix(matrix_id);
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::assembleMatrix(const ID & matrix_id) {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	auto common_type = this->getCommonMatrixType();

	if (matrix_id != "J") {
	auto type = needed_matrices[matrix_id];
	if (type == _mt_not_defined) {
	return;
	}

	if (not _dof_manager.hasMatrix(matrix_id)) {
	_dof_manager.getNewMatrix(matrix_id, type);
	}

	this->solver_callback->assembleMatrix(matrix_id);
	return;
	}

	if (not _dof_manager.hasMatrix("J")) {
	_dof_manager.getNewMatrix("J", common_type);
	}

	MatrixType type;
	ID name;
	for (auto & pair : needed_matrices) {
	std::tie(name, type) = pair;
	if (type == _mt_not_defined) {
	continue;
	}

	this->solver_callback->assembleMatrix(name);
	}
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::assembleResidual() {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->_dof_manager.zeroResidual();
	this->solver_callback->assembleResidual();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolver::assembleResidual(const ID & residual_part) {
	AKANTU_DEBUG_ASSERT(
	this->solver_callback != nullptr,
	"This function cannot be called if the solver_callback is not set");

	this->solver_callback->assembleResidual(residual_part);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/time_step_solvers/time_step_solver.hh b/src/model/common/time_step_solvers/time_step_solver.hh
	index 60c697896..8108b9616 100644
	--- a/src/model/common/time_step_solvers/time_step_solver.hh
	+++ b/src/model/common/time_step_solvers/time_step_solver.hh
	@@ -1,167 +1,167 @@
	/**
	* @file time_step_solver.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 08 2020
	*
	* @brief This corresponding to the time step evolution solver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "integration_scheme.hh"
	#include "parameter_registry.hh"
	#include "solver_callback.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TIME_STEP_SOLVER_HH_
	#define AKANTU_TIME_STEP_SOLVER_HH_

	namespace akantu {
	class DOFManager;
	class NonLinearSolver;
	} // namespace akantu

	namespace akantu {

	class TimeStepSolver : public ParameterRegistry, public SolverCallback {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	TimeStepSolver(DOFManager & dof_manager, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback, const ID & id);
	~TimeStepSolver() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// solves on step
	virtual void solveStep(SolverCallback & solver_callback) = 0;

	/// register an integration scheme for a given dof
	void setIntegrationScheme(const ID & dof_id,
	const IntegrationSchemeType & type,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined);
	/// register an integration scheme for a given dof
	void setIntegrationScheme(const ID & dof_id,
	std::unique_ptr<IntegrationScheme> & scheme,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined);

	protected:
	/// register an integration scheme for a given dof
	virtual std::unique_ptr<IntegrationScheme>
	getIntegrationSchemeInternal(const ID & dof_id,
	const IntegrationSchemeType & type,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined) = 0;

	virtual void
	setIntegrationSchemeInternal(const ID & dof_id,
	std::unique_ptr<IntegrationScheme> & scheme,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined) = 0;

	public:
	/// replies if a integration scheme has been set
	virtual bool hasIntegrationScheme(const ID & dof_id) const = 0;
	/* ------------------------------------------------------------------------ */
	/* Solver Callback interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// implementation of the SolverCallback::getMatrixType()
	MatrixType getMatrixType(const ID & /unused/) final {
	return _mt_not_defined;
	}
	/// implementation of the SolverCallback::predictor()
	void predictor() override;
	/// implementation of the SolverCallback::corrector()
	void corrector() override;
	/// implementation of the SolverCallback::assembleJacobian()
	void assembleMatrix(const ID & matrix_id) override;
	/// implementation of the SolverCallback::assembleJacobian()
	void assembleLumpedMatrix(const ID & matrix_id) override;
	/// implementation of the SolverCallback::assembleResidual()
	void assembleResidual() override;
	/// implementation of the SolverCallback::assembleResidual()
	void assembleResidual(const ID & residual_part) override;

	void beforeSolveStep() override;
	void afterSolveStep(bool converged = true) override;

	bool canSplitResidual() override {
	return solver_callback->canSplitResidual();
	}
	/* ------------------------------------------------------------------------ */
	/* Accessor */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(TimeStep, time_step, Real);
	AKANTU_SET_MACRO(TimeStep, time_step, Real);

	AKANTU_GET_MACRO(NonLinearSolver, non_linear_solver, const NonLinearSolver &);
	AKANTU_GET_MACRO_NOT_CONST(NonLinearSolver, non_linear_solver,
	NonLinearSolver &);

	protected:
	MatrixType getCommonMatrixType();

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	/// Underlying dof manager containing the dof to treat
	DOFManager & _dof_manager;

	/// Type of solver
	TimeStepSolverType type;

	/// The time step for this solver
	Real time_step;

	/// Temporary storage for solver callback
	SolverCallback * solver_callback;

	/// NonLinearSolver used by this tome step solver
	NonLinearSolver & non_linear_solver;

	/// List of required matrices
	std::map<std::string, MatrixType> needed_matrices;

	/// specifies if the solvers gives to full solution or just the increment of
	/// solution
	bool is_solution_increment{true};
	};

	} // namespace akantu

	#endif /* AKANTU_TIME_STEP_SOLVER_HH_ */
	diff --git a/src/model/common/time_step_solvers/time_step_solver_default.cc b/src/model/common/time_step_solvers/time_step_solver_default.cc
	index 6ef8bf6f6..f767800f6 100644
	--- a/src/model/common/time_step_solvers/time_step_solver_default.cc
	+++ b/src/model/common/time_step_solvers/time_step_solver_default.cc
	@@ -1,343 +1,344 @@
	/**
	* @file time_step_solver_default.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 15 2015
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Default implementation of the time step solver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "time_step_solver_default.hh"
	#include "dof_manager_default.hh"
	#include "integration_scheme_1st_order.hh"
	#include "integration_scheme_2nd_order.hh"
	#include "mesh.hh"
	#include "non_linear_solver.hh"
	#include "pseudo_time.hh"
	#include "sparse_matrix_aij.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	TimeStepSolverDefault::TimeStepSolverDefault(
	DOFManager & dof_manager, const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver, SolverCallback & solver_callback,
	const ID & id)
	- : TimeStepSolver(dof_manager, type, non_linear_solver, solver_callback, id) {
	+ : TimeStepSolver(dof_manager, type, non_linear_solver, solver_callback,
	+ id) {
	switch (type) {
	case TimeStepSolverType::_dynamic:
	break;
	case TimeStepSolverType::_dynamic_lumped:
	this->is_mass_lumped = true;
	break;
	case TimeStepSolverType::_static:
	/// initialize a static time solver for callback dofs
	break;
	default:
	AKANTU_TO_IMPLEMENT();
	}
	}

	/* -------------------------------------------------------------------------- */
	std::unique_ptr<IntegrationScheme>
	TimeStepSolverDefault::getIntegrationSchemeInternal(
	const ID & dof_id, const IntegrationSchemeType & type,
	IntegrationScheme::SolutionType /solution_type/) {
	std::unique_ptr<IntegrationScheme> integration_scheme;
	if (this->is_mass_lumped) {
	switch (type) {
	case IntegrationSchemeType::_forward_euler: {
	integration_scheme = std::make_unique<ForwardEuler>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_central_difference: {
	integration_scheme =
	std::make_unique<CentralDifference>(_dof_manager, dof_id);
	break;
	}
	default:
	AKANTU_EXCEPTION(
	"This integration scheme cannot be used in lumped dynamic");
	}
	} else {
	switch (type) {
	case IntegrationSchemeType::_pseudo_time: {
	integration_scheme = std::make_unique<PseudoTime>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_forward_euler: {
	integration_scheme = std::make_unique<ForwardEuler>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_trapezoidal_rule_1: {
	integration_scheme =
	std::make_unique<TrapezoidalRule1>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_backward_euler: {
	integration_scheme =
	std::make_unique<BackwardEuler>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_central_difference: {
	integration_scheme =
	std::make_unique<CentralDifference>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_fox_goodwin: {
	integration_scheme = std::make_unique<FoxGoodwin>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_trapezoidal_rule_2: {
	integration_scheme =
	std::make_unique<TrapezoidalRule2>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_linear_acceleration: {
	integration_scheme =
	std::make_unique<LinearAceleration>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_generalized_trapezoidal: {
	integration_scheme =
	std::make_unique<GeneralizedTrapezoidal>(_dof_manager, dof_id);
	break;
	}
	case IntegrationSchemeType::_newmark_beta:
	integration_scheme = std::make_unique<NewmarkBeta>(_dof_manager, dof_id);
	break;
	}
	}

	AKANTU_DEBUG_ASSERT(integration_scheme,
	"No integration scheme was found for the provided types");

	return integration_scheme;
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::setIntegrationSchemeInternal(
	const ID & dof_id, std::unique_ptr<IntegrationScheme> & integration_scheme,
	IntegrationScheme::SolutionType solution_type) {
	if (this->integration_schemes.find(dof_id) !=
	this->integration_schemes.end()) {
	AKANTU_EXCEPTION("Their DOFs "
	<< dof_id
	<< " have already an integration scheme associated");
	}

	auto && matrices_names = integration_scheme->getNeededMatrixList();
	for (auto && name : matrices_names) {
	needed_matrices.insert({name, _mt_not_defined});
	}

	this->integration_schemes[dof_id] = std::move(integration_scheme);
	this->solution_types[dof_id] = solution_type;

	this->integration_schemes_owner.insert(dof_id);
	}

	/* -------------------------------------------------------------------------- */
	bool TimeStepSolverDefault::hasIntegrationScheme(const ID & dof_id) const {
	return this->integration_schemes.find(dof_id) !=
	this->integration_schemes.end();
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolverDefault::~TimeStepSolverDefault() = default;

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::solveStep(SolverCallback & solver_callback) {
	this->solver_callback = &solver_callback;
	this->non_linear_solver.solve(*this);
	this->solver_callback = nullptr;
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::predictor() {
	TimeStepSolver::predictor();

	for (auto && pair : this->integration_schemes) {
	const auto & dof_id = pair.first;
	auto & integration_scheme = pair.second;

	if (this->_dof_manager.hasPreviousDOFs(dof_id)) {
	this->_dof_manager.savePreviousDOFs(dof_id);
	}

	/// integrator predictor
	integration_scheme->predictor(this->time_step);
	}
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::corrector() {
	AKANTU_DEBUG_IN();

	for (auto & pair : this->integration_schemes) {
	const auto & dof_id = pair.first;
	auto & integration_scheme = pair.second;

	const auto & solution_type = this->solution_types[dof_id];
	integration_scheme->corrector(solution_type, this->time_step);

	/// computing the increment of dof if needed
	if (this->_dof_manager.hasDOFsIncrement(dof_id)) {
	if (not this->_dof_manager.hasPreviousDOFs(dof_id)) {
	AKANTU_DEBUG_WARNING("In order to compute the increment of "
	<< dof_id << " a 'previous' has to be registered");
	continue;
	}

	auto & increment = this->_dof_manager.getDOFsIncrement(dof_id);
	auto & previous = this->_dof_manager.getPreviousDOFs(dof_id);

	auto dof_array_comp = this->_dof_manager.getDOFs(dof_id).getNbComponent();

	increment.copy(this->_dof_manager.getDOFs(dof_id));

	for (auto && data : zip(make_view(increment, dof_array_comp),
	make_view(previous, dof_array_comp))) {
	std::get<0>(data) -= std::get<1>(data);
	}
	}
	}

	TimeStepSolver::corrector();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::assembleMatrix(const ID & matrix_id) {
	AKANTU_DEBUG_IN();

	TimeStepSolver::assembleMatrix(matrix_id);

	if (matrix_id != "J") {
	return;
	}

	for_each_integrator([&](auto && dof_id, auto && integration_scheme) {
	const auto & solution_type = this->solution_types[dof_id];
	integration_scheme.assembleJacobian(solution_type, this->time_step);
	});

	this->_dof_manager.applyBoundary("J");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	// void TimeStepSolverDefault::assembleLumpedMatrix(const ID & matrix_id) {
	// AKANTU_DEBUG_IN();

	// TimeStepSolver::assembleLumpedMatrix(matrix_id);

	// if (matrix_id != "J")
	// return;

	// for (auto & pair : this->integration_schemes) {
	// auto & dof_id = pair.first;
	// auto & integration_scheme = pair.second;

	// const auto & solution_type = this->solution_types[dof_id];

	// integration_scheme->assembleJacobianLumped(solution_type,
	// this->time_step);
	// }

	// this->_dof_manager.applyBoundaryLumped("J");

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::assembleResidual() {
	if (this->needed_matrices.find("M") != needed_matrices.end()) {
	if (this->is_mass_lumped) {
	this->assembleLumpedMatrix("M");
	} else {
	this->assembleMatrix("M");
	}
	}

	TimeStepSolver::assembleResidual();

	for_each_integrator([&](auto && /unused/, auto && integration_scheme) {
	integration_scheme.assembleResidual(this->is_mass_lumped);
	});
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::assembleResidual(const ID & residual_part) {
	AKANTU_DEBUG_IN();

	if (this->needed_matrices.find("M") != needed_matrices.end()) {
	if (this->is_mass_lumped) {
	this->assembleLumpedMatrix("M");
	} else {
	this->assembleMatrix("M");
	}
	}

	if (residual_part != "inertial") {
	TimeStepSolver::assembleResidual(residual_part);
	}

	if (residual_part == "inertial") {
	for_each_integrator([&](auto && /unused/, auto && integration_scheme) {
	integration_scheme.assembleResidual(this->is_mass_lumped);
	});
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::beforeSolveStep() {
	TimeStepSolver::beforeSolveStep();
	for_each_integrator([&](auto && /unused/, auto && integration_scheme) {
	integration_scheme.store();
	});
	}

	/* -------------------------------------------------------------------------- */
	void TimeStepSolverDefault::afterSolveStep(bool converged) {
	if (not converged) {
	for_each_integrator([&](auto && /unused/, auto && integration_scheme) {
	integration_scheme.restore();
	});
	}

	TimeStepSolver::afterSolveStep(converged);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/common/time_step_solvers/time_step_solver_default.hh b/src/model/common/time_step_solvers/time_step_solver_default.hh
	index dab770873..a87cf2695 100644
	--- a/src/model/common/time_step_solvers/time_step_solver_default.hh
	+++ b/src/model/common/time_step_solvers/time_step_solver_default.hh
	@@ -1,135 +1,134 @@
	/**
	* @file time_step_solver_default.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Default implementation for the time stepper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integration_scheme.hh"
	#include "time_step_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	#include <set>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TIME_STEP_SOLVER_DEFAULT_HH_
	#define AKANTU_TIME_STEP_SOLVER_DEFAULT_HH_

	namespace akantu {
	class DOFManager;
	}

	namespace akantu {

	class TimeStepSolverDefault : public TimeStepSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	TimeStepSolverDefault(DOFManager & dof_manager,
	const TimeStepSolverType & type,
	NonLinearSolver & non_linear_solver,
	SolverCallback & solver_callback, const ID & id);

	~TimeStepSolverDefault() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// registers an integration scheme for a given dof
	std::unique_ptr<IntegrationScheme>
	getIntegrationSchemeInternal(const ID & dof_id,
	const IntegrationSchemeType & type,
	IntegrationScheme::SolutionType solution_type =
	IntegrationScheme::_not_defined) override;

	void setIntegrationSchemeInternal(
	- const ID & dof_id, std::unique_ptr<IntegrationScheme> & integration_scheme,
	- IntegrationScheme::SolutionType solution_type) override;
	+ const ID & dof_id,
	+ std::unique_ptr<IntegrationScheme> & integration_scheme,
	+ IntegrationScheme::SolutionType solution_type) override;

	public:
	bool hasIntegrationScheme(const ID & dof_id) const override;

	/// implementation of the TimeStepSolver::predictor()
	void predictor() override;
	/// implementation of the TimeStepSolver::corrector()
	void corrector() override;
	/// implementation of the TimeStepSolver::assembleMatrix()
	void assembleMatrix(const ID & matrix_id) override;

	// void assembleLumpedMatrix(const ID & matrix_id) override;
	/// implementation of the TimeStepSolver::assembleResidual()
	void assembleResidual() override;
	void assembleResidual(const ID & residual_part) override;

	void beforeSolveStep() override;
	void afterSolveStep(bool converged = true) override;

	/// implementation of the generic TimeStepSolver::solveStep()
	void solveStep(SolverCallback & solver_callback) override;

	private:
	-
	- template<class Func>
	- void for_each_integrator(Func && function) {
	+ template <class Func> void for_each_integrator(Func && function) {
	for (auto & pair : this->integration_schemes) {
	const auto & dof_id = pair.first;
	auto & integration_scheme = pair.second;
	function(dof_id, *integration_scheme);
	}
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	using DOFsIntegrationSchemes =
	std::map<ID, std::unique_ptr<IntegrationScheme>>;
	using DOFsIntegrationSchemesSolutionTypes =
	std::map<ID, IntegrationScheme::SolutionType>;
	using DOFsIntegrationSchemesOwner = std::set<ID>;

	/// Underlying integration scheme per dof, \todo check what happens in dynamic
	/// in case of coupled equations
	DOFsIntegrationSchemes integration_schemes;

	/// defines if the solver is owner of the memory or not
	DOFsIntegrationSchemesOwner integration_schemes_owner;

	/// Type of corrector to use
	DOFsIntegrationSchemesSolutionTypes solution_types;

	/// define if the mass matrix is lumped or not
	bool is_mass_lumped{false};
	};

	} // namespace akantu

	#endif /* AKANTU_TIME_STEP_SOLVER_DEFAULT_HH_ */
	diff --git a/src/model/common/time_step_solvers/time_step_solver_default_explicit.hh b/src/model/common/time_step_solvers/time_step_solver_default_explicit.hh
	index 6108e2023..871c605dc 100644
	--- a/src/model/common/time_step_solvers/time_step_solver_default_explicit.hh
	+++ b/src/model/common/time_step_solvers/time_step_solver_default_explicit.hh
	@@ -1,79 +1,78 @@
	/**
	* @file time_step_solver_default_explicit.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Default solver for explicit resolution
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TIME_STEP_SOLVER_DEFAULT_EXPLICIT_HH_
	#define AKANTU_TIME_STEP_SOLVER_DEFAULT_EXPLICIT_HH_

	namespace akantu {

	class TimeStepSolverDefaultExplicit : public TimeStepSolverDefault {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	TimeStepSolverDefaultExplicit();
	virtual ~TimeStepSolverDefaultExplicit();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void solveStep();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */

	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const TimeStepSolverDefaultExplicit & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	-
	//#include "time_step_solver_default_explicit_inline_impl.hh"

	#endif /* AKANTU_TIME_STEP_SOLVER_DEFAULT_EXPLICIT_HH_ */
	diff --git a/src/model/contact_mechanics/contact_detector.cc b/src/model/contact_mechanics/contact_detector.cc
	index d9dbfcc1c..f5c17d48d 100644
	--- a/src/model/contact_mechanics/contact_detector.cc
	+++ b/src/model/contact_mechanics/contact_detector.cc
	@@ -1,294 +1,295 @@
	/**
	* @file contact_detector.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Dec 05 2018
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Mother class for all detection algorithms
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_detector.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ContactDetector::ContactDetector(Mesh & mesh, const ID & id)
	: ContactDetector(mesh, mesh.getNodes(), id) {}

	/* -------------------------------------------------------------------------- */
	ContactDetector::ContactDetector(Mesh & mesh, Array<Real> positions,
	const ID & id)
	: Parsable(ParserType::_contact_detector, id), mesh(mesh),
	positions(0, mesh.getSpatialDimension()) {

	AKANTU_DEBUG_IN();

	this->spatial_dimension = mesh.getSpatialDimension();

	this->positions.copy(positions);

	const Parser & parser = getStaticParser();
	const ParserSection & section =
	*(parser.getSubSections(ParserType::_contact_detector).first);

	this->parseSection(section);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactDetector::parseSection(const ParserSection & section) {
	auto type = section.getParameterValue<std::string>("type");

	if (type == "implicit") {
	this->detection_type = _implicit;
	} else if (type == "explicit") {
	this->detection_type = _explicit;
	} else {
	AKANTU_ERROR("Unknown detection type : " << type);
	}

	this->projection_tolerance =
	section.getParameterValue<Real>("projection_tolerance");
	this->max_iterations = section.getParameterValue<Real>("max_iterations");
	this->extension_tolerance =
	section.getParameterValue<Real>("extension_tolerance");
	}

	/* -------------------------------------------------------------------------- */
	void ContactDetector::search(Array<ContactElement> & elements,
	Array<Real> & gaps, Array<Real> & normals,
	Array<Real> & tangents,
	Array<Real> & projections) {
	auto surface_dimension = spatial_dimension - 1;

	this->mesh.fillNodesToElements(surface_dimension);
	this->computeMaximalDetectionDistance();

	contact_pairs.clear();

	SpatialGrid<UInt> master_grid(spatial_dimension);
	SpatialGrid<UInt> slave_grid(spatial_dimension);

	this->globalSearch(slave_grid, master_grid);

	this->localSearch(slave_grid, master_grid);

	this->createContactElements(elements, gaps, normals, tangents, projections);
	}

	/* -------------------------------------------------------------------------- */
	void ContactDetector::globalSearch(SpatialGrid<UInt> & slave_grid,
	SpatialGrid<UInt> & master_grid) {
	auto & master_list = surface_selector->getMasterList();
	auto & slave_list = surface_selector->getSlaveList();

	BBox bbox_master(spatial_dimension);
	this->constructBoundingBox(bbox_master, master_list);

	BBox bbox_slave(spatial_dimension);
	this->constructBoundingBox(bbox_slave, slave_list);

	auto && bbox_intersection = bbox_master.intersection(bbox_slave);

	AKANTU_DEBUG_INFO("Intersection BBox " << bbox_intersection);

	Vector<Real> center(spatial_dimension);
	bbox_intersection.getCenter(center);

	Vector<Real> spacing(spatial_dimension);
	this->computeCellSpacing(spacing);

	master_grid.setCenter(center);
	master_grid.setSpacing(spacing);
	this->constructGrid(master_grid, bbox_intersection, master_list);

	slave_grid.setCenter(center);
	slave_grid.setSpacing(spacing);
	this->constructGrid(slave_grid, bbox_intersection, slave_list);

	// search slave grid nodes in contactelement array and if they exits
	// and still have orthogonal projection on its associated master
	// facetremove it from the spatial grid or do not consider it for
	// local search, maybe better option will be to have spatial grid of
	// type node info and one of the variable of node info should be
	// facet already exits
	// so contact elements will be updated based on the above
	// consideration , this means only those contact elements will be
	// keep whose slave node is still in intersection bbox and still has
	// projection in its master facet
	// also if slave node is already exists in contact element and
	// orthogonal projection does not exits then search the associated
	// master facets with the current master facets within a given
	// radius , this is subjected to computational cost as searching
	// neighbbor cells can be more effective.
	}

	/* -------------------------------------------------------------------------- */
	void ContactDetector::localSearch(SpatialGrid<UInt> & slave_grid,
	SpatialGrid<UInt> & master_grid) {
	// local search
	// out of these array check each cell for closet node in that cell
	// and neighbouring cells find the actual orthogonally closet
	// check the projection of slave node on master facets connected to
	// the closet master node, if yes update the contact element with
	// slave node and master node and master surfaces connected to the
	// master node
	// these master surfaces will be needed later to update contact
	// elements

	/// find the closet master node for each slave node
	for (auto && cell_id : slave_grid) {
	/// loop over all the slave nodes of the current cell
	for (auto && slave_node : slave_grid.getCell(cell_id)) {

	bool pair_exists = false;

	Vector<Real> pos(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	pos(s) = this->positions(slave_node, s);
	}

	Real closet_distance = std::numeric_limits<Real>::max();
	UInt closet_master_node;

	/// loop over all the neighboring cells of the current cell
	for (auto && neighbor_cell : cell_id.neighbors()) {
	/// loop over the data of neighboring cells from master grid
	for (auto && master_node : master_grid.getCell(neighbor_cell)) {

	/// check for self contact
	if (slave_node == master_node) {
	continue;
	}

	bool is_valid = true;
	Array<Element> elements;
	this->mesh.getAssociatedElements(slave_node, elements);

	for (auto & elem : elements) {
	if (elem.kind() != _ek_regular) {
	continue;
	}

	Vector<UInt> connectivity =
	const_cast<const Mesh &>(this->mesh).getConnectivity(elem);

	auto node_iter = std::find(connectivity.begin(), connectivity.end(),
	master_node);
	if (node_iter != connectivity.end()) {
	is_valid = false;
	break;
	}
	}

	Vector<Real> pos2(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	pos2(s) = this->positions(master_node, s);
	}

	Real distance = pos.distance(pos2);

	if (distance <= closet_distance and is_valid) {
	closet_master_node = master_node;
	closet_distance = distance;
	pair_exists = true;
	}
	}
	}

	if (pair_exists) {
	- contact_pairs.emplace_back(std::make_pair(slave_node, closet_master_node));
	+ contact_pairs.emplace_back(
	+ std::make_pair(slave_node, closet_master_node));
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactDetector::createContactElements(
	Array<ContactElement> & contact_elements, Array<Real> & gaps,
	Array<Real> & normals, Array<Real> & tangents, Array<Real> & projections) {
	auto surface_dimension = spatial_dimension - 1;

	Real alpha;
	switch (detection_type) {
	case _explicit: {
	alpha = 1.0;
	break;
	}
	case _implicit: {
	alpha = -1.0;
	break;
	}
	default:
	AKANTU_EXCEPTION(detection_type
	<< " is not a valid contact detection type");
	break;
	}

	for (auto & pairs : contact_pairs) {

	const auto & slave_node = pairs.first;

	Vector<Real> slave(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	slave(s) = this->positions(slave_node, s);
	}

	const auto & master_node = pairs.second;
	Array<Element> elements;
	this->mesh.getAssociatedElements(master_node, elements);

	auto & gap = gaps.begin()[slave_node];
	Vector<Real> normal(normals.begin(spatial_dimension)[slave_node]);
	Vector<Real> projection(projections.begin(surface_dimension)[slave_node]);
	Matrix<Real> tangent(
	tangents.begin(surface_dimension, spatial_dimension)[slave_node]);
	auto index = GeometryUtils::orthogonalProjection(
	mesh, positions, slave, elements, gap, projection, normal, tangent,
	alpha, this->max_iterations, this->projection_tolerance,
	this->extension_tolerance);

	// if a valid projection is not found on the patch of elements
	// index is -1 or if not a valid self contact, the contact element
	// is not created
	if (index == UInt(-1) or !isValidSelfContact(slave_node, gap, normal)) {
	gap *= 0;
	normal *= 0;
	projection *= 0;
	tangent *= 0;
	continue;
	}

	// create contact element
	contact_elements.push_back(ContactElement(slave_node, elements[index]));
	}

	contact_pairs.clear();
	}

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/contact_detector.hh b/src/model/contact_mechanics/contact_detector.hh
	index edadba8af..00f84dd66 100644
	--- a/src/model/contact_mechanics/contact_detector.hh
	+++ b/src/model/contact_mechanics/contact_detector.hh
	@@ -1,216 +1,218 @@
	/**
	* @file contact_detector.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Mother class for all detection algorithms
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_bbox.hh"
	#include "aka_common.hh"
	#include "aka_grid_dynamic.hh"
	#include "contact_element.hh"
	#include "element_class.hh"
	#include "element_group.hh"
	#include "fe_engine.hh"
	#include "geometry_utils.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "parsable.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_CONTACT_DETECTOR_HH__
	#define __AKANTU_CONTACT_DETECTOR_HH__

	namespace akantu {

	enum class Surface { master, slave };

	/* -------------------------------------------------------------------------- */

	class ContactDetector : public Parsable {

	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	- ContactDetector(Mesh &, const ID & id = "contact_detector");
	+ ContactDetector(Mesh & /mesh/, const ID & id = "contact_detector");

	- ContactDetector(Mesh &, Array<Real> positions,
	+ ContactDetector(Mesh & /mesh/, Array<Real> positions,
	const ID & id = "contact_detector");

	~ContactDetector() override = default;

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	public:
	/// performs all search steps
	void search(Array<ContactElement> & elements, Array<Real> & gaps,
	Array<Real> & normals, Array<Real> & tangents,
	Array<Real> & projections);

	/// performs global spatial search to construct spatial grids
	- void globalSearch(SpatialGrid<UInt> &, SpatialGrid<UInt> &);
	+ void globalSearch(SpatialGrid<UInt> & /slave_grid/,
	+ SpatialGrid<UInt> & /master_grid/);

	/// performs local search to find closet master node to a slave node
	- void localSearch(SpatialGrid<UInt> &, SpatialGrid<UInt> &);
	+ void localSearch(SpatialGrid<UInt> & /slave_grid/,
	+ SpatialGrid<UInt> & /master_grid/);

	/// create contact elements
	void createContactElements(Array<ContactElement> & elements,
	Array<Real> & gaps, Array<Real> & normals,
	Array<Real> & tangents, Array<Real> & projections);

	private:
	/// reads the input file to get contact detection options
	void parseSection(const ParserSection & section) override;

	/* ------------------------------------------------------------------------ */
	/* Inline Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// checks whether the natural projection is valid or not
	inline bool checkValidityOfProjection(Vector<Real> & projection) const;

	/// extracts the coordinates of an element
	inline void coordinatesOfElement(const Element & el,
	Matrix<Real> & coords) const;

	/// computes the optimal cell size for grid
	inline void computeCellSpacing(Vector<Real> & spacing) const;

	/// constructs a grid containing nodes lying within bounding box
	inline void constructGrid(SpatialGrid<UInt> & grid, BBox & bbox,
	const Array<UInt> & nodes_list) const;

	/// constructs the bounding box based on nodes list
	inline void constructBoundingBox(BBox & bbox,
	const Array<UInt> & nodes_list) const;

	/// computes the maximum in radius for a given mesh
	inline void computeMaximalDetectionDistance();

	/// constructs the connectivity for a contact element
	inline Vector<UInt> constructConnectivity(UInt & slave,
	const Element & master) const;

	/// computes normal on an element
	inline void computeNormalOnElement(const Element & element,
	Vector<Real> & normal) const;

	/// extracts vectors which forms the plane of element
	inline void vectorsAlongElement(const Element & el,
	Matrix<Real> & vectors) const;

	/// computes the gap between slave and its projection on master
	/// surface
	inline Real computeGap(const Vector<Real> & slave,
	const Vector<Real> & master) const;

	/// filter boundary elements
	inline void filterBoundaryElements(const Array<Element> & elements,
	Array<Element> & boundary_elements) const;

	/// checks whether self contact condition leads to a master element
	/// which is closet but not orthogonally opposite to slave surface
	inline bool isValidSelfContact(const UInt & slave_node, const Real & gap,
	const Vector<Real> & normal) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the mesh
	AKANTU_GET_MACRO(Mesh, mesh, Mesh &)

	/// returns the maximum detection distance
	AKANTU_GET_MACRO(MaximumDetectionDistance, max_dd, Real);
	AKANTU_SET_MACRO(MaximumDetectionDistance, max_dd, Real);

	/// returns the bounding box extension
	AKANTU_GET_MACRO(MaximumBoundingBox, max_bb, Real);
	AKANTU_SET_MACRO(MaximumBoundingBox, max_bb, Real);

	/// returns the minimum detection distance
	AKANTU_GET_MACRO(MinimumDetectionDistance, min_dd, Real);
	AKANTU_SET_MACRO(MinimumDetectionDistance, min_dd, Real);

	AKANTU_GET_MACRO_NOT_CONST(Positions, positions, Array<Real> &);
	AKANTU_SET_MACRO(Positions, positions, Array<Real>);

	AKANTU_GET_MACRO_NOT_CONST(SurfaceSelector, *surface_selector,
	SurfaceSelector &);
	AKANTU_SET_MACRO(SurfaceSelector, surface_selector,
	std::shared_ptr<SurfaceSelector>);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// maximal detection distance for grid spacing
	Real max_dd;

	/// minimal detection distance for grid spacing
	Real min_dd;

	/// maximal bounding box extension
	Real max_bb;

	/// tolerance for finding natural projection
	Real projection_tolerance;

	/// iterations for finding natural projection
	UInt max_iterations;

	/// tolerance for extending a master elements on all sides
	Real extension_tolerance;

	/// Mesh
	Mesh & mesh;

	/// dimension of the model
	UInt spatial_dimension{0};

	/// node selector for selecting master and slave nodes
	std::shared_ptr<SurfaceSelector> surface_selector;

	/// contact pair slave node to closet master node
	std::vector<std::pair<UInt, UInt>> contact_pairs;

	/// contains the updated positions of the nodes
	Array<Real> positions;

	/// type of detection explicit/implicit
	DetectionType detection_type;
	};

	} // namespace akantu

	#include "contact_detector_inline_impl.cc"

	#endif /* __AKANTU_CONTACT_DETECTOR_HH__ */
	diff --git a/src/model/contact_mechanics/contact_detector_inline_impl.cc b/src/model/contact_mechanics/contact_detector_inline_impl.cc
	index 29416fb7e..eaed7c983 100644
	--- a/src/model/contact_mechanics/contact_detector_inline_impl.cc
	+++ b/src/model/contact_mechanics/contact_detector_inline_impl.cc
	@@ -1,317 +1,316 @@
	/**
	* @file contact_detector_inline_impl.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed May 08 2019
	* @date last modification: Thu Jun 24 2021
	*
	* @brief inine implementation of the contact detector class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_detector.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_CONTACT_DETECTOR_INLINE_IMPL_CC__
	#define __AKANTU_CONTACT_DETECTOR_INLINE_IMPL_CC__

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline bool
	ContactDetector::checkValidityOfProjection(Vector<Real> & projection) const {
	Real tolerance = 1e-3;
	return std::all_of(projection.begin(), projection.end(),
	[&tolerance](auto && xi) {
	return (xi > -1.0 - tolerance) or (xi < 1.0 + tolerance);
	});
	}

	/* -------------------------------------------------------------------------- */
	inline void ContactDetector::coordinatesOfElement(const Element & el,
	Matrix<Real> & coords) const {

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(el.type);
	const Vector<UInt> connect = mesh.getConnectivity(el.type, _not_ghost)
	.begin(nb_nodes_per_element)[el.element];

	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connect[n];
	for (UInt s : arange(spatial_dimension)) {
	coords(s, n) = this->positions(node, s);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void ContactDetector::computeCellSpacing(Vector<Real> & spacing) const {
	for (UInt s : arange(spatial_dimension)) {
	spacing(s) = std::sqrt(2.0) * max_dd;
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	ContactDetector::constructGrid(SpatialGrid<UInt> & grid, BBox & bbox,
	const Array<UInt> & nodes_list) const {
	auto to_grid = [&](UInt node) {
	Vector<Real> pos(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	pos(s) = this->positions(node, s);
	}

	if (bbox.contains(pos)) {
	grid.insert(node, pos);
	}
	};

	std::for_each(nodes_list.begin(), nodes_list.end(), to_grid);
	}

	/* -------------------------------------------------------------------------- */
	inline void
	ContactDetector::constructBoundingBox(BBox & bbox,
	const Array<UInt> & nodes_list) const {
	auto to_bbox = [&](UInt node) {
	Vector<Real> pos(spatial_dimension);
	for (UInt s : arange(spatial_dimension)) {
	pos(s) = this->positions(node, s);
	}
	bbox += pos;
	};

	std::for_each(nodes_list.begin(), nodes_list.end(), to_bbox);

	auto & lower_bound = bbox.getLowerBounds();
	auto & upper_bound = bbox.getUpperBounds();

	lower_bound -= this->max_bb;
	upper_bound += this->max_bb;

	AKANTU_DEBUG_INFO("BBox" << bbox);
	}

	/* -------------------------------------------------------------------------- */
	inline void ContactDetector::computeMaximalDetectionDistance() {
	Real elem_size;
	Real max_elem_size = std::numeric_limits<Real>::min();
	Real min_elem_size = std::numeric_limits<Real>::max();

	auto & master_nodes = this->surface_selector->getMasterList();

	for (auto & master : master_nodes) {
	Array<Element> elements;
	this->mesh.getAssociatedElements(master, elements);

	for (auto element : elements) {
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element.type);
	Matrix<Real> elem_coords(spatial_dimension, nb_nodes_per_element);
	this->coordinatesOfElement(element, elem_coords);

	elem_size = FEEngine::getElementInradius(elem_coords, element.type);
	max_elem_size = std::max(max_elem_size, elem_size);
	min_elem_size = std::min(min_elem_size, elem_size);
	}
	}

	AKANTU_DEBUG_INFO("The maximum element size : " << max_elem_size);

	this->min_dd = min_elem_size;
	this->max_dd = max_elem_size;
	this->max_bb = max_elem_size;
	}

	/* -------------------------------------------------------------------------- */
	inline Vector<UInt>
	ContactDetector::constructConnectivity(UInt & slave,
	const Element & master) const {
	const Vector<UInt> master_conn = this->mesh.getConnectivity(master);

	Vector<UInt> elem_conn(master_conn.size() + 1);
	elem_conn[0] = slave;
	for (UInt i = 1; i < elem_conn.size(); ++i) {
	elem_conn[i] = master_conn[i - 1];
	}

	return elem_conn;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	ContactDetector::computeNormalOnElement(const Element & element,
	Vector<Real> & normal) const {
	Matrix<Real> vectors(spatial_dimension, spatial_dimension - 1);
	this->vectorsAlongElement(element, vectors);

	switch (this->spatial_dimension) {
	case 2: {
	Math::normal2(vectors.storage(), normal.storage());
	break;
	}
	case 3: {
	Math::normal3(vectors(0).storage(), vectors(1).storage(), normal.storage());
	break;
	}
	default: {
	AKANTU_ERROR("Unknown dimension : " << spatial_dimension);
	}
	}

	// to ensure that normal is always outwards from master surface
	const auto & element_to_subelement =
	mesh.getElementToSubelement(element.type)(element.element);

	Vector<Real> outside(spatial_dimension);
	mesh.getBarycenter(element, outside);

	// check if mesh facets exists for cohesive elements contact
	Vector<Real> inside(spatial_dimension);
	if (mesh.isMeshFacets()) {
	mesh.getMeshParent().getBarycenter(element_to_subelement[0], inside);
	} else {
	mesh.getBarycenter(element_to_subelement[0], inside);
	}

	Vector<Real> inside_to_outside = outside - inside;
	auto projection = inside_to_outside.dot(normal);

	if (projection < 0) {
	normal *= -1.0;
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void ContactDetector::vectorsAlongElement(const Element & el,
	Matrix<Real> & vectors) const {
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(el.type);

	Matrix<Real> coords(spatial_dimension, nb_nodes_per_element);
	this->coordinatesOfElement(el, coords);

	for (auto i : arange(spatial_dimension - 1)) {
	vectors(i) = Vector<Real>(coords(i + 1)) - Vector<Real>(coords(0));
	}
	}

	/* -------------------------------------------------------------------------- */
	inline Real ContactDetector::computeGap(const Vector<Real> & slave,
	const Vector<Real> & master) const {
	auto gap = (master - slave).norm();
	return gap;
	}

	/* -------------------------------------------------------------------------- */
	inline void ContactDetector::filterBoundaryElements(
	const Array<Element> & elements, Array<Element> & boundary_elements) const {
	for (auto elem : elements) {
	const auto & element_to_subelement =
	mesh.getElementToSubelement(elem.type)(elem.element);

	// for regular boundary elements
	if (element_to_subelement.size() == 1 and
	element_to_subelement[0].kind() == _ek_regular) {
	boundary_elements.push_back(elem);
	continue;
	}

	// for cohesive boundary elements
	UInt nb_subelements_regular = 0;
	for (auto subelem : element_to_subelement) {
	if (subelem == ElementNull) {
	continue;
	}

	if (subelem.kind() == _ek_regular) {
	++nb_subelements_regular;
	}
	}

	auto nb_subelements = element_to_subelement.size();

	if (nb_subelements_regular < nb_subelements) {
	boundary_elements.push_back(elem);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline bool
	ContactDetector::isValidSelfContact(const UInt & slave_node, const Real & gap,
	const Vector<Real> & normal) const {
	UInt master_node;

	// finding the master node corresponding to slave node
	for (auto && pair : contact_pairs) {
	if (pair.first == slave_node) {
	master_node = pair.second;
	break;
	}
	}

	Array<Element> slave_elements;
	this->mesh.getAssociatedElements(slave_node, slave_elements);

	// Check 1 : master node is not connected to elements connected to
	// slave node
	Vector<Real> slave_normal(spatial_dimension);
	for (auto & element : slave_elements) {
	if (element.kind() != _ek_regular) {
	continue;
	}

	- const Vector<UInt> connectivity =
	- this->mesh.getConnectivity(element);
	+ const Vector<UInt> connectivity = this->mesh.getConnectivity(element);

	// finding the normal at slave node by averaging of normals
	Vector<Real> normal(spatial_dimension);
	GeometryUtils::normal(mesh, positions, element, normal);
	slave_normal = slave_normal + normal;

	auto node_iter =
	std::find(connectivity.begin(), connectivity.end(), master_node);
	if (node_iter != connectivity.end()) {
	return false;
	}
	}

	// Check 2 : if gap is twice the size of smallest element
	if (std::abs(gap) > 2.0 * min_dd) {
	return false;
	}

	// Check 3 : check the directions of normal at slave node and at
	// master element, should be in opposite directions
	auto norm = slave_normal.norm();
	if (norm != 0) {
	slave_normal /= norm;
	}

	auto product = slave_normal.dot(normal);

	- return not (product >= 0);
	+ return not(product >= 0);
	}

	} // namespace akantu

	#endif /* __AKANTU_CONTACT_DETECTOR_INLINE_IMPL_CC__ */
	diff --git a/src/model/contact_mechanics/contact_element.hh b/src/model/contact_mechanics/contact_element.hh
	index cbe8db606..b97ae3c7d 100644
	--- a/src/model/contact_mechanics/contact_element.hh
	+++ b/src/model/contact_mechanics/contact_element.hh
	@@ -1,86 +1,87 @@
	/**
	* @file contact_element.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Tue Jun 08 2021
	*
	* @brief Mother class for all detection algorithms
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	-
	+#include "element.hh"
	+#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_CONTACT_ELEMENT_HH__
	#define __AKANTU_CONTACT_ELEMENT_HH__

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	using SlaveType = UInt;
	using MasterType = Element;

	class ContactElement {

	/* ------------------------------------------------------------------------ */
	/* Constructor/ Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ContactElement() = default;

	ContactElement(const SlaveType & slave, const MasterType & master)
	: slave(slave), master(master) {}

	~ContactElement() = default;

	bool operator==(const ContactElement & other) const {
	return slave == other.slave and master == other.master;
	}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbNodes() const {
	auto nb_master_nodes = Mesh::getNbNodesPerElement(master.type);
	return nb_master_nodes + 1;
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	public:
	/// slave node
	SlaveType slave;

	/// master element/node
	MasterType master;
	};

	} // namespace akantu

	#endif /* __AKANTU_CONTACT_ELEMENT_HH__ */
	diff --git a/src/model/contact_mechanics/contact_mechanics_model.cc b/src/model/contact_mechanics/contact_mechanics_model.cc
	index 3e7d69c31..a37223369 100644
	--- a/src/model/contact_mechanics/contact_mechanics_model.cc
	+++ b/src/model/contact_mechanics/contact_mechanics_model.cc
	@@ -1,708 +1,713 @@
	/**
	* @file contact_mechanics_model.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Jul 28 2021
	*
	* @brief Contact mechanics model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	#include "boundary_condition_functor.hh"
	#include "dumpable_inline_impl.hh"
	#include "group_manager_inline_impl.hh"
	#include "integrator_gauss.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ContactMechanicsModel::ContactMechanicsModel(
	Mesh & mesh, UInt dim, const ID & id,
	std::shared_ptr<DOFManager> dof_manager, const ModelType model_type)
	: Model(mesh, model_type, dof_manager, dim, id) {

	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<MyFEEngineType>("ContactMechanicsModel", mesh,
	Model::spatial_dimension);
	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("contact_mechanics", id, true);
	this->mesh.addDumpMeshToDumper("contact_mechanics", mesh,
	Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif

	this->registerDataAccessor(*this);

	this->detector =
	std::make_unique<ContactDetector>(this->mesh, id + ":contact_detector");

	registerFEEngineObject<MyFEEngineType>("ContactFacetsFEEngine", mesh,
	Model::spatial_dimension - 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ContactMechanicsModel::~ContactMechanicsModel() = default;

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::initFullImpl(const ModelOptions & options) {

	Model::initFullImpl(options);

	// initalize the resolutions
	if (not this->parser.getLastParsedFile().empty()) {
	this->instantiateResolutions();
	this->initResolutions();
	}

	this->initBC(this, displacement, displacement_increment, external_force);
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::instantiateResolutions() {
	ParserSection model_section;
	bool is_empty;
	std::tie(model_section, is_empty) = this->getParserSection();

	if (not is_empty) {
	auto model_resolutions =
	model_section.getSubSections(ParserType::_contact_resolution);
	for (const auto & section : model_resolutions) {
	this->registerNewResolution(section);
	}
	}

	auto sub_sections =
	this->parser.getSubSections(ParserType::_contact_resolution);
	for (const auto & section : sub_sections) {
	this->registerNewResolution(section);
	}

	- if (resolutions.empty())
	+ if (resolutions.empty()) {
	AKANTU_EXCEPTION("No contact resolutions where instantiated for the model"
	<< getID());
	+ }
	are_resolutions_instantiated = true;
	}

	/* -------------------------------------------------------------------------- */
	Resolution &
	ContactMechanicsModel::registerNewResolution(const ParserSection & section) {
	std::string res_name;
	std::string res_type = section.getName();
	std::string opt_param = section.getOption();

	try {
	std::string tmp = section.getParameter("name");
	res_name = tmp; /** this can seem weird, but there is an ambiguous operator
	* overload that i couldn't solve. @todo remove the
	* weirdness of this code
	*/
	} catch (debug::Exception &) {
	AKANTU_ERROR("A contact resolution of type \'"
	<< res_type
	<< "\' in the input file has been defined without a name!");
	}
	Resolution & res = this->registerNewResolution(res_name, res_type, opt_param);

	res.parseSection(section);

	return res;
	}

	/* -------------------------------------------------------------------------- */
	Resolution & ContactMechanicsModel::registerNewResolution(
	const ID & res_name, const ID & res_type, const ID & opt_param) {
	AKANTU_DEBUG_ASSERT(resolutions_names_to_id.find(res_name) ==
	resolutions_names_to_id.end(),
	"A resolution with this name '"
	<< res_name << "' has already been registered. "
	<< "Please use unique names for resolutions");

	UInt res_count = resolutions.size();
	resolutions_names_to_id[res_name] = res_count;

	std::stringstream sstr_res;
	sstr_res << this->id << ":" << res_count << ":" << res_type;
	ID res_id = sstr_res.str();

	std::unique_ptr<Resolution> resolution =
	ResolutionFactory::getInstance().allocate(res_type, spatial_dimension,
	opt_param, *this, res_id);

	resolutions.push_back(std::move(resolution));

	return *(resolutions.back());
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::initResolutions() {
	AKANTU_DEBUG_ASSERT(resolutions.size() != 0,
	"No resolutions to initialize !");

	if (!are_resolutions_instantiated) {
	instantiateResolutions();
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::initModel() {

	AKANTU_DEBUG_IN();

	getFEEngine("ContactMechanicsModel").initShapeFunctions(_not_ghost);
	getFEEngine("ContactMechanicsModel").initShapeFunctions(_ghost);

	getFEEngine("ContactFacetsFEEngine").initShapeFunctions(_not_ghost);
	getFEEngine("ContactFacetsFEEngine").initShapeFunctions(_ghost);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & ContactMechanicsModel::getFEEngineBoundary(const ID & name) {
	return dynamic_cast<FEEngine &>(
	getFEEngineClassBoundary<MyFEEngineType>(name));
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::initSolver(
	- TimeStepSolverType /time_step_solver_type/, NonLinearSolverType) {
	+ TimeStepSolverType /time_step_solver_type/,
	+ NonLinearSolverType /unused/) {

	// for alloc type of solvers
	this->allocNodalField(this->displacement, spatial_dimension, "displacement");
	this->allocNodalField(this->displacement_increment, spatial_dimension,
	"displacement_increment");
	this->allocNodalField(this->internal_force, spatial_dimension,
	"internal_force");
	this->allocNodalField(this->external_force, spatial_dimension,
	"external_force");
	this->allocNodalField(this->normal_force, spatial_dimension, "normal_force");
	this->allocNodalField(this->tangential_force, spatial_dimension,
	"tangential_force");

	this->allocNodalField(this->gaps, 1, "gaps");
	this->allocNodalField(this->nodal_area, 1, "areas");
	this->allocNodalField(this->blocked_dofs, 1, "blocked_dofs");
	this->allocNodalField(this->contact_state, 1, "contact_state");
	this->allocNodalField(this->previous_master_elements, 1,
	"previous_master_elements");

	this->allocNodalField(this->normals, spatial_dimension, "normals");

	auto surface_dimension = spatial_dimension - 1;
	this->allocNodalField(this->tangents, surface_dimension * spatial_dimension,
	"tangents");
	this->allocNodalField(this->projections, surface_dimension, "projections");
	this->allocNodalField(this->previous_projections, surface_dimension,
	"previous_projections");
	this->allocNodalField(this->previous_tangents,
	surface_dimension * spatial_dimension,
	"previous_tangents");
	this->allocNodalField(this->tangential_tractions, surface_dimension,
	"tangential_tractions");
	this->allocNodalField(this->previous_tangential_tractions, surface_dimension,
	"previous_tangential_tractions");

	// todo register multipliers as dofs for lagrange multipliers
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	ContactMechanicsModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _explicit_consistent_mass: {
	return std::make_tuple("explicit", TimeStepSolverType::_dynamic);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions ContactMechanicsModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type =
	NonLinearSolverType::_newton_raphson_contact;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["displacement"] = IntegrationScheme::_not_defined;
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	break;
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	/* ------------------------------------------------------------------------ */
	// computes the internal forces
	this->assembleInternalForces();

	/* ------------------------------------------------------------------------ */
	this->getDOFManager().assembleToResidual("displacement",
	*this->internal_force, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the contact forces");

	UInt nb_nodes = mesh.getNbNodes();
	this->internal_force->clear();
	this->normal_force->clear();
	this->tangential_force->clear();

	internal_force->resize(nb_nodes, 0.);
	normal_force->resize(nb_nodes, 0.);
	tangential_force->resize(nb_nodes, 0.);

	// assemble the forces due to contact
	auto assemble = [&](auto && ghost_type) {
	for (auto & resolution : resolutions) {
	resolution->assembleInternalForces(ghost_type);
	}
	};

	AKANTU_DEBUG_INFO("Assemble residual for local elements");
	assemble(_not_ghost);

	// assemble the stresses due to ghost elements
	// AKANTU_DEBUG_INFO("Assemble residual for ghost elements");
	// assemble(_ghost);

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::search() {

	// save the previous state
	this->savePreviousState();

	contact_elements.clear();

	// this needs to be resized if cohesive elements are added
	UInt nb_nodes = mesh.getNbNodes();

	auto resize_arrays = [&](auto & internal_array) {
	internal_array->resize(nb_nodes);
	internal_array->zero();
	};

	resize_arrays(gaps);
	resize_arrays(normals);
	resize_arrays(tangents);
	resize_arrays(projections);
	resize_arrays(tangential_tractions);
	resize_arrays(contact_state);
	resize_arrays(nodal_area);
	resize_arrays(external_force);

	this->detector->search(contact_elements, gaps, normals, *tangents,
	*projections);

	// intepenetration value must be positive for contact mechanics
	// model to work by default the gap value from detector is negative
	std::for_each((gaps).begin(), (gaps).end(), [](Real & gap) { gap *= -1.; });

	- if (contact_elements.size() != 0) {
	+ if (!contact_elements.empty()) {
	this->computeNodalAreas();
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::savePreviousState() {

	AKANTU_DEBUG_IN();

	// saving previous natural projections
	(previous_projections).copy(projections);

	// saving previous tangents
	(previous_tangents).copy(tangents);

	// saving previous tangential traction
	(previous_tangential_tractions).copy(tangential_tractions);

	previous_master_elements->clear();
	previous_master_elements->resize(projections->size());
	previous_master_elements->set(ElementNull);
	for (auto & element : contact_elements) {
	(*previous_master_elements)[element.slave] = element.master;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::computeNodalAreas(GhostType ghost_type) {

	UInt nb_nodes = mesh.getNbNodes();

	nodal_area->resize(nb_nodes);
	nodal_area->zero();

	external_force->resize(nb_nodes);
	external_force->zero();

	auto & fem_boundary =
	getFEEngineClassBoundary<MyFEEngineType>("ContactMechanicsModel");

	fem_boundary.initShapeFunctions(getPositions(), _not_ghost);
	fem_boundary.initShapeFunctions(getPositions(), _ghost);

	fem_boundary.computeNormalsOnIntegrationPoints(_not_ghost);
	fem_boundary.computeNormalsOnIntegrationPoints(_ghost);

	IntegrationPoint quad_point;
	quad_point.ghost_type = ghost_type;

	auto & group = mesh.getElementGroup("contact_surface");
	UInt nb_degree_of_freedom = external_force->getNbComponent();

	for (auto && type : group.elementTypes(spatial_dimension - 1, ghost_type)) {
	const auto & element_ids = group.getElements(type, ghost_type);

	UInt nb_quad_points = fem_boundary.getNbIntegrationPoints(type, ghost_type);
	UInt nb_elements = element_ids.size();

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	Array<Real> dual_before_integ(nb_elements * nb_quad_points,
	nb_degree_of_freedom, 0.);
	Array<Real> quad_coords(nb_elements * nb_quad_points, spatial_dimension);

	const auto & normals_on_quad =
	fem_boundary.getNormalsOnIntegrationPoints(type, ghost_type);

	auto normals_begin = normals_on_quad.begin(spatial_dimension);
	decltype(normals_begin) normals_iter;
	auto quad_coords_iter = quad_coords.begin(spatial_dimension);
	auto dual_iter = dual_before_integ.begin(nb_degree_of_freedom);

	quad_point.type = type;

	Element subelement;
	subelement.type = type;
	subelement.ghost_type = ghost_type;
	for (auto el : element_ids) {
	subelement.element = el;
	const auto & element_to_subelement =
	mesh.getElementToSubelement(type)(el);

	Vector<Real> outside(spatial_dimension);
	mesh.getBarycenter(subelement, outside);

	Vector<Real> inside(spatial_dimension);
	if (mesh.isMeshFacets()) {
	mesh.getMeshParent().getBarycenter(element_to_subelement[0], inside);
	} else {
	mesh.getBarycenter(element_to_subelement[0], inside);
	}

	Vector<Real> inside_to_outside(spatial_dimension);
	inside_to_outside = outside - inside;

	normals_iter = normals_begin + el * nb_quad_points;

	quad_point.element = el;
	for (auto q : arange(nb_quad_points)) {
	quad_point.num_point = q;
	auto ddot = inside_to_outside.dot(*normals_iter);
	Vector<Real> normal(*normals_iter);
	- if (ddot < 0)
	+ if (ddot < 0) {
	normal *= -1.0;
	+ }

	(*dual_iter)
	.mul<false>(Matrix<Real>::eye(spatial_dimension, 1), normal);
	++dual_iter;
	++quad_coords_iter;
	++normals_iter;
	}
	}

	Array<Real> dual_by_shapes(nb_elements * nb_quad_points,
	nb_degree_of_freedom * nb_nodes_per_element);

	fem_boundary.computeNtb(dual_before_integ, dual_by_shapes, type, ghost_type,
	element_ids);

	Array<Real> dual_by_shapes_integ(nb_elements, nb_degree_of_freedom *
	nb_nodes_per_element);
	fem_boundary.integrate(dual_by_shapes, dual_by_shapes_integ,
	nb_degree_of_freedom * nb_nodes_per_element, type,
	ghost_type, element_ids);

	this->getDOFManager().assembleElementalArrayLocalArray(
	dual_by_shapes_integ, *external_force, type, ghost_type, 1.,
	element_ids);
	}

	for (auto && tuple :
	zip(nodal_area, make_view(external_force, spatial_dimension))) {

	auto & area = std::get<0>(tuple);
	Vector<Real> force(std::get<1>(tuple));
	area = force.norm();
	}

	this->external_force->clear();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "Contact Mechanics Model [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + spatial dimension : " << Model::spatial_dimension
	<< std::endl;
	stream << space << " + fem [" << std::endl;
	getFEEngine().printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + resolutions [" << std::endl;
	- for (auto & resolution : resolutions) {
	+ for (const auto & resolution : resolutions) {
	resolution->printself(stream, indent + 1);
	}
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	MatrixType ContactMechanicsModel::getMatrixType(const ID & matrix_id) {
	- if (matrix_id == "K")
	+ if (matrix_id == "K") {
	return _symmetric;
	+ }

	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::assembleMatrix(const ID & matrix_id) {
	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	if (!this->getDOFManager().hasMatrix("K")) {
	this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
	}

	for (auto & resolution : resolutions) {
	resolution->assembleStiffnessMatrix(_not_ghost);
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::assembleLumpedMatrix(const ID & /matrix_id/) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::beforeSolveStep() {
	for (auto & resolution : resolutions) {
	resolution->beforeSolveStep();
	}
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::afterSolveStep(bool converged) {
	for (auto & resolution : resolutions) {
	resolution->afterSolveStep(converged);
	}
	}

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	-ContactMechanicsModel::createNodalFieldBool(const std::string &,
	- const std::string &, bool) {
	+ContactMechanicsModel::createNodalFieldBool(const std::string & /unused/,
	+ const std::string & /unused/,
	+ bool /unused/) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	ContactMechanicsModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {
	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["contact_force"] = this->internal_force.get();
	real_nodal_fields["normal_force"] = this->normal_force.get();
	real_nodal_fields["tangential_force"] = this->tangential_force.get();
	real_nodal_fields["blocked_dofs"] = this->blocked_dofs.get();
	real_nodal_fields["normals"] = this->normals.get();
	real_nodal_fields["tangents"] = this->tangents.get();
	real_nodal_fields["gaps"] = this->gaps.get();
	real_nodal_fields["areas"] = this->nodal_area.get();
	real_nodal_fields["tangential_traction"] = this->tangential_tractions.get();

	std::shared_ptr<dumpers::Field> field;
	if (padding_flag) {
	field = this->mesh.createNodalField(real_nodal_fields[field_name],
	group_name, 3);
	} else {
	field =
	this->mesh.createNodalField(real_nodal_fields[field_name], group_name);
	}
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	ContactMechanicsModel::createNodalFieldUInt(const std::string & field_name,
	const std::string & group_name,
	bool /padding_flag/) {
	std::shared_ptr<dumpers::Field> field;
	if (field_name == "contact_state") {
	auto && func =
	std::make_unique<dumpers::ComputeUIntFromEnum<ContactState>>();
	field = mesh.createNodalField(this->contact_state.get(), group_name);
	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, std::move(func));
	}
	return field;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	UInt ContactMechanicsModel::getNbData(
	const Array<Element> & elements, const SynchronizationTag & /tag/) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes_per_element = 0;

	for (const Element & el : elements) {
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::packData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::unpackData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt ContactMechanicsModel::getNbData(
	const Array<UInt> & dofs, const SynchronizationTag & /tag/) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;

	AKANTU_DEBUG_OUT();
	return size * dofs.size();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::packData(CommunicationBuffer & /buffer/,
	const Array<UInt> & /dofs/,
	const SynchronizationTag & /tag/) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ContactMechanicsModel::unpackData(CommunicationBuffer & /buffer/,
	const Array<UInt> & /dofs/,
	const SynchronizationTag & /tag/) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/contact_mechanics_model.hh b/src/model/contact_mechanics/contact_mechanics_model.hh
	index 201f93df0..b57d4472f 100644
	--- a/src/model/contact_mechanics/contact_mechanics_model.hh
	+++ b/src/model/contact_mechanics/contact_mechanics_model.hh
	@@ -1,373 +1,374 @@
	/**
	* @file contact_mechanics_model.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Model of Contact Mechanics
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition.hh"
	#include "contact_detector.hh"
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	#include "model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_CONTACT_MECHANICS_MODEL_HH__
	#define __AKANTU_CONTACT_MECHANICS_MODEL_HH__

	namespace akantu {
	class Resolution;
	template <ElementKind kind, class IntegrationOrderFunctor>
	class IntegratorGauss;
	template <ElementKind kind> class ShapeLagrange;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class ContactMechanicsModel : public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt>,
	public BoundaryCondition<ContactMechanicsModel> {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */

	using MyFEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	public:
	ContactMechanicsModel(
	- Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	+ Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "contact_mechanics_model",
	std::shared_ptr<DOFManager> dof_manager = nullptr,
	- const ModelType model_type = ModelType::_contact_mechanics_model);
	+ ModelType model_type = ModelType::_contact_mechanics_model);

	~ContactMechanicsModel() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize completely the model
	void initFullImpl(const ModelOptions & options) override;

	/// allocate all vectors
	- void initSolver(TimeStepSolverType, NonLinearSolverType) override;
	+ void initSolver(TimeStepSolverType /unused/,
	+ NonLinearSolverType /unused/) override;

	/// initialize all internal arrays for resolutions
	void initResolutions();

	/// initialize the modelType
	void initModel() override;

	/// call back for the solver, computes the force residual
	void assembleResidual() override;

	/// get the type of matrix needed
	MatrixType getMatrixType(const ID & matrix_id) override;

	/// callback for the solver, this assembles different matrices
	void assembleMatrix(const ID & matrix_id) override;

	/// callback for the solver, this assembles the stiffness matrix
	void assembleLumpedMatrix(const ID & matrix_id) override;

	/// get some default values for derived classes
	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;

	/// callback for the solver, this is called at beginning of solve
	void beforeSolveStep() override;

	/// callback for the solver, this is called at end of solve
	void afterSolveStep(bool converged = true) override;

	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Contact Detection */
	/* ------------------------------------------------------------------------ */
	public:
	void search();

	void computeNodalAreas(GhostType ghost_type = _not_ghost);

	/* ------------------------------------------------------------------------ */
	/* Contact Resolution */
	/* ------------------------------------------------------------------------ */
	public:
	/// register an empty contact resolution of a given type
	Resolution & registerNewResolution(const ID & res_name, const ID & res_type,
	const ID & opt_param);

	protected:
	/// register a resolution in the dynamic database
	Resolution & registerNewResolution(const ParserSection & res_section);

	/// read the resolution files to instantiate all the resolutions
	void instantiateResolutions();

	/// save the parameters from previous state
	void savePreviousState();

	/* ------------------------------------------------------------------------ */
	/* Solver Interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// assembles the contact stiffness matrix
	virtual void assembleStiffnessMatrix();

	/// assembles the contant internal forces
	virtual void assembleInternalForces();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	FEEngine & getFEEngineBoundary(const ID & name = "") override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	#if defined(AKANTU_USE_IOHELPER)
	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldUInt(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;
	#endif

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	UInt getNbData(const Array<UInt> & dofs,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	const SynchronizationTag & tag) override;

	protected:
	/// contact detection class
	friend class ContactDetector;

	/// contact resolution class
	friend class Resolution;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the ContactMechanicsModel::displacement vector
	AKANTU_GET_MACRO(Displacement, *displacement, Array<Real> &);

	/// get the ContactMechanicsModel::increment vector \warn only consistent
	/// if ContactMechanicsModel::setIncrementFlagOn has been called before
	AKANTU_GET_MACRO(Increment, *displacement_increment, Array<Real> &);

	/// get the ContactMechanics::internal_force vector (internal forces)
	AKANTU_GET_MACRO(InternalForce, *internal_force, Array<Real> &);

	/// get the ContactMechanicsModel::external_force vector (external forces)
	AKANTU_GET_MACRO(ExternalForce, *external_force, Array<Real> &);

	/// get the ContactMechanics::normal_force vector (normal forces)
	AKANTU_GET_MACRO(NormalForce, *normal_force, Array<Real> &);

	/// get the ContactMechanics::tangential_force vector (friction forces)
	AKANTU_GET_MACRO(TangentialForce, *tangential_force, Array<Real> &);

	/// get the ContactMechanics::traction vector (friction traction)
	AKANTU_GET_MACRO(TangentialTractions, *tangential_tractions, Array<Real> &);

	/// get the ContactMechanics::previous_tangential_tractions vector
	AKANTU_GET_MACRO(PreviousTangentialTractions, *previous_tangential_tractions,
	Array<Real> &);

	/// get the ContactMechanicsModel::force vector (external forces)
	Array<Real> & getForce() {
	AKANTU_DEBUG_WARNING("getForce was maintained for backward compatibility, "
	"use getExternalForce instead");
	return *external_force;
	}

	/// get the ContactMechanics::blocked_dofs vector
	AKANTU_GET_MACRO(BlockedDOFs, *blocked_dofs, Array<Real> &);

	/// get the ContactMechanics::gaps (contact gaps)
	AKANTU_GET_MACRO(Gaps, *gaps, Array<Real> &);

	/// get the ContactMechanics::normals (normals on slave nodes)
	AKANTU_GET_MACRO(Normals, *normals, Array<Real> &);

	/// get the ContactMechanics::tangents (tangents on slave nodes)
	AKANTU_GET_MACRO(Tangents, *tangents, Array<Real> &);

	/// get the ContactMechanics::previous_tangents (tangents on slave nodes)
	AKANTU_GET_MACRO(PreviousTangents, *previous_tangents, Array<Real> &);

	/// get the ContactMechanics::areas (nodal areas)
	AKANTU_GET_MACRO(NodalArea, *nodal_area, Array<Real> &);

	/// get the ContactMechanics::previous_projections (previous_projections)
	AKANTU_GET_MACRO(PreviousProjections, *previous_projections, Array<Real> &);

	/// get the ContactMechanics::projections (projections)
	AKANTU_GET_MACRO(Projections, *projections, Array<Real> &);

	/// get the ContactMechanics::contact_state vector (no_contact/stick/slip
	/// state)
	AKANTU_GET_MACRO(ContactState, *contact_state, Array<ContactState> &);

	/// get the ContactMechanics::previous_master_elements
	AKANTU_GET_MACRO(PreviousMasterElements, *previous_master_elements,
	Array<Element> &);

	/// get contact detector
	AKANTU_GET_MACRO_NOT_CONST(ContactDetector, *detector, ContactDetector &);

	/// get the contact elements
	inline const Array<ContactElement> & getContactElements() const {
	return contact_elements;
	}

	/// get the current positions of the nodes
	inline Array<Real> & getPositions() { return detector->getPositions(); }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// tells if the resolutions are instantiated
	bool are_resolutions_instantiated;

	/// displacements array
	std::unique_ptr<Array<Real>> displacement;

	/// increment of displacement
	std::unique_ptr<Array<Real>> displacement_increment;

	/// contact forces array
	std::unique_ptr<Array<Real>> internal_force;

	/// external forces array
	std::unique_ptr<Array<Real>> external_force;

	/// normal force array
	std::unique_ptr<Array<Real>> normal_force;

	/// friction force array
	std::unique_ptr<Array<Real>> tangential_force;

	/// friction traction array
	std::unique_ptr<Array<Real>> tangential_tractions;

	/// previous friction traction array
	std::unique_ptr<Array<Real>> previous_tangential_tractions;

	/// boundary vector
	std::unique_ptr<Array<Real>> blocked_dofs;

	/// array to store gap between slave and master
	std::unique_ptr<Array<Real>> gaps;

	/// array to store normals from master to slave
	std::unique_ptr<Array<Real>> normals;

	/// array to store tangents on the master element
	std::unique_ptr<Array<Real>> tangents;

	/// array to store previous tangents on the master element
	std::unique_ptr<Array<Real>> previous_tangents;

	/// array to store nodal areas
	std::unique_ptr<Array<Real>> nodal_area;

	/// array to store stick/slip state :
	std::unique_ptr<Array<ContactState>> contact_state;

	/// array to store previous projections in covariant basis
	std::unique_ptr<Array<Real>> previous_projections;

	// array to store projections in covariant basis
	std::unique_ptr<Array<Real>> projections;

	/// contact detection
	std::unique_ptr<ContactDetector> detector;

	/// list of contact resolutions
	std::vector<std::unique_ptr<Resolution>> resolutions;

	/// mapping between resolution name and resolution internal id
	std::map<std::string, UInt> resolutions_names_to_id;

	/// array to store contact elements
	Array<ContactElement> contact_elements;

	/// array to store previous master elements
	std::unique_ptr<Array<Element>> previous_master_elements;
	};

	} // namespace akantu

	/* ------------------------------------------------------------------------ */
	/* inline functions */
	/* ------------------------------------------------------------------------ */
	#include "parser.hh"
	#include "resolution.hh"
	/* ------------------------------------------------------------------------ */

	#endif /* __AKANTU_CONTACT_MECHANICS_MODEL_HH__ */
	diff --git a/src/model/contact_mechanics/geometry_utils.cc b/src/model/contact_mechanics/geometry_utils.cc
	index 94a5b0554..4b6683fef 100644
	--- a/src/model/contact_mechanics/geometry_utils.cc
	+++ b/src/model/contact_mechanics/geometry_utils.cc
	@@ -1,731 +1,731 @@
	/**
	* @file geometry_utils.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Oct 02 2019
	* @date last modification: Thu Jun 24 2021
	*
	* @brief Implementation of various utilities needed for contact geometry
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "geometry_utils.hh"
	#include "element_class_helper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::normal(const Mesh & mesh, const Array<Real> & positions,
	const Element & element, Vector<Real> & normal,
	bool outward) {

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt surface_dimension = spatial_dimension - 1;

	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(element.type);
	Matrix<Real> coords(spatial_dimension, nb_nodes_per_element);

	UInt * elem_val = mesh.getConnectivity(element.type, _not_ghost).storage();
	mesh.extractNodalValuesFromElement(positions, coords.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	Matrix<Real> vectors(spatial_dimension, surface_dimension);
	switch (spatial_dimension) {
	case 1: {
	normal[0] = 1;
	break;
	}
	case 2: {
	vectors(0) = Vector<Real>(coords(1)) - Vector<Real>(coords(0));
	Math::normal2(vectors.storage(), normal.storage());
	break;
	}
	case 3: {
	vectors(0) = Vector<Real>(coords(1)) - Vector<Real>(coords(0));
	vectors(1) = Vector<Real>(coords(2)) - Vector<Real>(coords(0));
	Math::normal3(vectors(0).storage(), vectors(1).storage(), normal.storage());
	break;
	}
	default: {
	AKANTU_ERROR("Unknown dimension : " << spatial_dimension);
	}
	}

	// to ensure that normal is always outwards from master surface
	if (outward) {

	const auto & element_to_subelement =
	mesh.getElementToSubelement(element.type)(element.element);

	Vector<Real> outside(spatial_dimension);
	mesh.getBarycenter(element, outside);

	// check if mesh facets exists for cohesive elements contact
	Vector<Real> inside(spatial_dimension);
	if (mesh.isMeshFacets()) {
	mesh.getMeshParent().getBarycenter(element_to_subelement[0], inside);
	} else {
	mesh.getBarycenter(element_to_subelement[0], inside);
	}

	Vector<Real> inside_to_outside = outside - inside;
	auto projection = inside_to_outside.dot(normal);

	if (projection < 0) {
	normal *= -1.0;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::normal(const Mesh & mesh, const Element & element,
	Matrix<Real> & tangents, Vector<Real> & normal,
	bool outward) {
	UInt spatial_dimension = mesh.getSpatialDimension();

	// to ensure that normal is always outwards from master surface we
	// compute a direction vector form inside of element attached to the
	// suurface element

	Vector<Real> inside_to_outside(spatial_dimension);
	if (outward) {

	const auto & element_to_subelement =
	mesh.getElementToSubelement(element.type)(element.element);

	Vector<Real> outside(spatial_dimension);
	mesh.getBarycenter(element, outside);

	// check if mesh facets exists for cohesive elements contact
	Vector<Real> inside(spatial_dimension);
	if (mesh.isMeshFacets()) {
	mesh.getMeshParent().getBarycenter(element_to_subelement[0], inside);
	} else {
	mesh.getBarycenter(element_to_subelement[0], inside);
	}

	inside_to_outside = outside - inside;
	// auto projection = inside_to_outside.dot(normal);

	// if (projection < 0) {
	// normal *= -1.0;
	//}
	}

	// to ensure that direction of tangents are correct, cross product
	// of tangents should give be in the same direction as of inside to outside
	switch (spatial_dimension) {
	case 2: {
	normal[0] = -tangents(0, 1);
	normal[1] = tangents(0, 0);

	auto ddot = inside_to_outside.dot(normal);
	if (ddot < 0) {
	tangents *= -1.0;
	normal *= -1.0;
	}

	break;
	}
	case 3: {
	auto tang_trans = tangents.transpose();
	auto tang1 = Vector<Real>(tang_trans(0));
	auto tang2 = Vector<Real>(tang_trans(1));

	auto tang1_cross_tang2 = tang1.crossProduct(tang2);
	normal = tang1_cross_tang2 / tang1_cross_tang2.norm();

	auto ddot = inside_to_outside.dot(normal);
	if (ddot < 0) {
	tang_trans(1) *= -1.0;
	normal *= -1.0;
	}

	tangents = tang_trans.transpose();

	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::covariantBasis(const Mesh & mesh,
	const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & normal,
	Vector<Real> & natural_coord,
	Matrix<Real> & tangents) {
	UInt spatial_dimension = mesh.getSpatialDimension();

	const ElementType type = element.type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(positions, nodes_coord.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	auto && dnds = ElementClassHelper<_ek_regular>::getDNDS(natural_coord, type);
	tangents.mul<false, true>(dnds, nodes_coord);

	auto temp_tangents = tangents.transpose();
	for (UInt i = 0; i < spatial_dimension - 1; ++i) {
	auto temp = Vector<Real>(temp_tangents(i));
	temp_tangents(i) = temp.normalize();
	}

	tangents = temp_tangents.transpose();

	// to ensure that direction of tangents are correct, cross product
	// of tangents should give the normal vector computed earlier
	switch (spatial_dimension) {
	case 2: {
	Vector<Real> e_z(3);
	e_z[0] = 0.;
	e_z[1] = 0.;
	e_z[2] = 1.;

	Vector<Real> tangent(3);
	tangent[0] = tangents(0, 0);
	tangent[1] = tangents(0, 1);
	tangent[2] = 0.;

	auto exp_normal = e_z.crossProduct(tangent);

	auto ddot = normal.dot(exp_normal);
	if (ddot < 0) {
	tangents *= -1.0;
	}
	break;
	}
	case 3: {
	auto tang_trans = tangents.transpose();
	auto tang1 = Vector<Real>(tang_trans(0));
	auto tang2 = Vector<Real>(tang_trans(1));

	auto tang1_cross_tang2 = tang1.crossProduct(tang2);
	auto exp_normal = tang1_cross_tang2 / tang1_cross_tang2.norm();

	auto ddot = normal.dot(exp_normal);
	if (ddot < 0) {
	tang_trans(1) *= -1.0;
	}

	tangents = tang_trans.transpose();
	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::covariantBasis(const Mesh & mesh,
	const Array<Real> & positions,
	const Element & element,
	Vector<Real> & natural_coord,
	Matrix<Real> & tangents) {

	UInt spatial_dimension = mesh.getSpatialDimension();

	const ElementType & type = element.type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(positions, nodes_coord.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	auto && dnds = ElementClassHelper<_ek_regular>::getDNDS(natural_coord, type);
	tangents.mul<false, true>(dnds, nodes_coord);

	auto temp_tangents = tangents.transpose();
	for (UInt i = 0; i < spatial_dimension - 1; ++i) {
	auto temp = Vector<Real>(temp_tangents(i));
	temp_tangents(i) = temp.normalize();
	}

	tangents = temp_tangents.transpose();
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::curvature(const Mesh & mesh, const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & natural_coord,
	Matrix<Real> & curvature) {
	UInt spatial_dimension = mesh.getSpatialDimension();
	const ElementType & type = element.type;

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();

	auto && d2nds2 =
	ElementClassHelper<_ek_regular>::getD2NDS2(natural_coord, type);

	Matrix<Real> coords(spatial_dimension, nb_nodes_per_element);
	mesh.extractNodalValuesFromElement(positions, coords.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	curvature.mul<false, true>(coords, d2nds2);
	}

	/* -------------------------------------------------------------------------- */
	UInt GeometryUtils::orthogonalProjection(
	const Mesh & mesh, const Array<Real> & positions,
	const Vector<Real> & slave, const Array<Element> & elements, Real & gap,
	Vector<Real> & natural_projection, Vector<Real> & normal, Real alpha,
	UInt max_iterations, Real projection_tolerance, Real extension_tolerance) {

	UInt index = UInt(-1);
	Real min_gap = std::numeric_limits<Real>::max();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt surface_dimension = spatial_dimension - 1;

	UInt nb_same_sides{0};
	UInt nb_boundary_elements{0};

	UInt counter{0};

	const auto & contact_group = mesh.getElementGroup("contact_surface");

	for (const auto & element : elements) {
	// filter out elements which are not there in the element group
	// contact surface created by the surface selector and is stored
	// in the mesh or mesh_facet, if a element is not there it
	// returnas UInt(-1)

	const auto & elements_of_type = contact_group.getElements(element.type);
	if (elements_of_type.find(element.element) == UInt(-1)) {
	continue;
	}

	nb_boundary_elements++;

	// find the natural coordinate corresponding to the minimum gap
	// between slave node and master element

	Vector<Real> master(spatial_dimension);

	Vector<Real> xi(natural_projection.size());
	GeometryUtils::naturalProjection(mesh, positions, element, slave, master,
	xi, max_iterations, projection_tolerance);

	Matrix<Real> tangent_ele(surface_dimension, spatial_dimension);
	GeometryUtils::covariantBasis(mesh, positions, element, xi, tangent_ele);

	Vector<Real> normal_ele(spatial_dimension);
	GeometryUtils::normal(mesh, element, tangent_ele, normal_ele);

	// if gap between master projection and slave point is zero, then
	// it means that slave point lies on the master element, hence the
	// normal from master to slave cannot be computed in that case

	auto master_to_slave = slave - master;
	Real temp_gap = master_to_slave.norm();

	if (temp_gap != 0) {
	master_to_slave /= temp_gap;
	}

	// also the slave point should lie inside the master surface in
	// case of explicit or outside in case of implicit, one way to
	// check that is by checking the dot product of normal at each
	// master element, if the values of all dot product is same then
	// the slave point lies on the same side of each master element

	// A alpha parameter is introduced which is 1 in case of explicit
	// and -1 in case of implicit, therefor the variation (dot product
	// + alpha) should be close to zero (within tolerance) for both
	// cases

	Real direction_tolerance = 1e-8;
	auto product = master_to_slave.dot(normal_ele);
	auto variation = std::abs(product + alpha);

	if (variation <= direction_tolerance and temp_gap <= min_gap and
	GeometryUtils::isValidProjection(xi, extension_tolerance)) {

	gap = -temp_gap;
	min_gap = temp_gap;
	index = counter;
	natural_projection = xi;
	normal = normal_ele;
	}

	if (temp_gap == 0 or variation <= direction_tolerance) {
	nb_same_sides++;
	}

	counter++;
	}

	// if point is not on the same side of all the boundary elements
	// than it is not consider even if the closet master element is
	// found
	if (nb_same_sides != nb_boundary_elements) {
	index = UInt(-1);
	}

	return index;
	}

	/* -------------------------------------------------------------------------- */
	UInt GeometryUtils::orthogonalProjection(
	const Mesh & mesh, const Array<Real> & positions,
	const Vector<Real> & slave, const Array<Element> & elements, Real & gap,
	Vector<Real> & natural_projection, Vector<Real> & normal,
	Matrix<Real> & tangent, Real /alpha/, UInt max_iterations,
	Real projection_tolerance, Real extension_tolerance) {

	UInt index = UInt(-1);
	Real min_gap = std::numeric_limits<Real>::max();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt surface_dimension = spatial_dimension - 1;

	const auto & contact_group = mesh.getElementGroup("contact_surface");

	for (auto && tuple : enumerate(elements)) {
	auto & counter = std::get<0>(tuple);
	const auto & element = std::get<1>(tuple);
	// filter out elements which are not there in the element group
	// contact surface created by the surface selector and is stored
	// in the mesh or mesh_facet, if a element is not there it
	// returnas UInt(-1)

	const auto & elements_of_type = contact_group.getElements(element.type);
	if (elements_of_type.find(element.element) == UInt(-1)) {
	continue;
	}

	Vector<Real> master(spatial_dimension);

	Vector<Real> xi_ele(natural_projection.size());
	GeometryUtils::naturalProjection(mesh, positions, element, slave, master,
	xi_ele, max_iterations,
	projection_tolerance);

	Matrix<Real> tangent_ele(surface_dimension, spatial_dimension);
	GeometryUtils::covariantBasis(mesh, positions, element, xi_ele,
	tangent_ele);

	Vector<Real> normal_ele(spatial_dimension);
	GeometryUtils::normal(mesh, element, tangent_ele, normal_ele);

	// if gap between master projection and slave point is zero, then
	// it means that slave point lies on the master element, hence the
	// normal from master to slave cannot be computed in that case

	auto master_to_slave = slave - master;
	Real temp_gap = master_to_slave.norm();

	if (temp_gap != 0) {
	master_to_slave /= temp_gap;
	}

	// A alpha parameter is introduced which is 1 in case of explicit
	// and -1 in case of implicit, therefor the variation (dot product
	// + alpha) should be close to zero (within tolerance) for both
	// cases

	auto product = master_to_slave.dot(normal_ele);

	if (product < 0 and temp_gap <= min_gap and
	GeometryUtils::isValidProjection(xi_ele, extension_tolerance)) {

	gap = -temp_gap;
	min_gap = temp_gap;
	index = counter;
	natural_projection = xi_ele;
	normal = normal_ele;
	tangent = tangent_ele;
	}
	}

	return index;
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::realProjection(const Mesh & mesh,
	const Array<Real> & positions,
	const Vector<Real> & slave,
	const Element & element,
	const Vector<Real> & normal,
	Vector<Real> & projection) {

	UInt spatial_dimension = mesh.getSpatialDimension();

	const ElementType & type = element.type;
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(element.type);

	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(positions, nodes_coord.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	Vector<Real> point(nodes_coord(0));
	Real alpha = (slave - point).dot(normal);

	projection = slave - alpha * normal;
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::realProjection(const Mesh & mesh,
	const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & natural_coord,
	Vector<Real> & projection) {

	auto spatial_dimension = mesh.getSpatialDimension();

	const auto & type = element.type;

	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(element.type);
	auto shapes =
	ElementClassHelper<_ek_regular>::getN(natural_coord, element.type);

	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
	mesh.extractNodalValuesFromElement(positions, nodes_coord.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	projection.mul<false>(nodes_coord, shapes);
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::naturalProjection(
	const Mesh & mesh, const Array<Real> & positions, const Element & element,
	const Vector<Real> & slave_coords, Vector<Real> & master_coords,
	Vector<Real> & natural_projection, UInt max_iterations,
	Real projection_tolerance) {

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt surface_dimension = spatial_dimension - 1;

	const ElementType & type = element.type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(positions, nodes_coord.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	// initial guess
	natural_projection.zero();

	// obhjective function computed on the natural_guess
	Matrix<Real> f(surface_dimension, 1);

	// jacobian matrix computed on the natural_guess
	Matrix<Real> J(surface_dimension, surface_dimension);

	// Jinv = J^{-1}
	Matrix<Real> Jinv(surface_dimension, surface_dimension);

	// dxi = \xi_{k+1} - \xi_{k} in the iterative process
	Matrix<Real> dxi(surface_dimension, 1);

	// gradient at natural projection
	Matrix<Real> gradient(surface_dimension, spatial_dimension);

	// second derivative at natural peojection
	Matrix<Real> double_gradient(surface_dimension, surface_dimension);

	// second derivative of shape function at natural projection
	Matrix<Real> d2nds2(surface_dimension * surface_dimension,
	nb_nodes_per_element);

	- auto compute_double_gradient =
	- [&d2nds2, &nodes_coord, surface_dimension,
	- spatial_dimension](UInt & alpha, UInt & beta) {
	- auto index = alpha * surface_dimension + beta;
	- Vector<Real> d_alpha_beta(spatial_dimension);
	+ auto compute_double_gradient = [&d2nds2, &nodes_coord, surface_dimension,
	+ spatial_dimension](UInt & alpha,
	+ UInt & beta) {
	+ auto index = alpha * surface_dimension + beta;
	+ Vector<Real> d_alpha_beta(spatial_dimension);

	- auto d2nds2_transpose = d2nds2.transpose();
	- Vector<Real> d2nds2_alpha_beta(d2nds2_transpose(index));
	+ auto d2nds2_transpose = d2nds2.transpose();
	+ Vector<Real> d2nds2_alpha_beta(d2nds2_transpose(index));

	- d_alpha_beta.mul<false>(nodes_coord, d2nds2_alpha_beta);
	+ d_alpha_beta.mul<false>(nodes_coord, d2nds2_alpha_beta);

	- return d_alpha_beta;
	- };
	+ return d_alpha_beta;
	+ };

	/* --------------------------- */
	/* init before iteration loop */
	/* --------------------------- */
	// do interpolation
	auto update_f = [&f, &master_coords, &natural_projection, &nodes_coord,
	&slave_coords, &gradient, surface_dimension,
	spatial_dimension, type]() {
	// compute real coords on natural projection
	auto && shapes =
	ElementClassHelper<_ek_regular>::getN(natural_projection, type);

	master_coords.mul<false>(nodes_coord, shapes);

	auto distance = slave_coords - master_coords;

	// first derivative of shape function at natural projection
	auto && dnds =
	ElementClassHelper<_ek_regular>::getDNDS(natural_projection, type);
	gradient.mul<false, true>(dnds, nodes_coord);

	// gradient transpose at natural projection
	Matrix<Real> gradient_transpose(surface_dimension, spatial_dimension);

	gradient_transpose = gradient.transpose();

	// loop over surface dimensions
	for (auto alpha : arange(surface_dimension)) {
	Vector<Real> gradient_alpha(gradient_transpose(alpha));
	f(alpha, 0) = -2. * gradient_alpha.dot(distance);
	}

	// compute initial error
	auto error = f.norm<L_2>();
	return error;
	};

	auto projection_error = update_f();

	/* --------------------------- */
	/* iteration loop */
	/* --------------------------- */
	UInt iterations{0};
	while (projection_tolerance < projection_error and
	iterations < max_iterations) {

	// compute covariant components of metric tensor
	auto a = GeometryUtils::covariantMetricTensor(gradient);

	// computing second derivative at natural projection
	d2nds2 =
	ElementClassHelper<_ek_regular>::getD2NDS2(natural_projection, type);

	// real coord - physical guess
	auto distance = slave_coords - master_coords;

	// computing Jacobian J
	for (auto alpha : arange(surface_dimension)) {
	for (auto beta : arange(surface_dimension)) {
	auto dgrad_alpha_beta = compute_double_gradient(alpha, beta);
	J(alpha, beta) = 2. * (a(alpha, beta) - dgrad_alpha_beta.dot(distance));
	}
	}

	Jinv.inverse(J);

	// compute increment
	dxi.mul<false, false>(Jinv, f, -1.0);

	// update our guess
	natural_projection += Vector<Real>(dxi(0));

	projection_error = update_f();
	iterations++;
	}
	}

	/* -------------------------------------------------------------------------- */
	void GeometryUtils::contravariantBasis(const Matrix<Real> & covariant,
	Matrix<Real> & contravariant) {

	auto inv_A = GeometryUtils::contravariantMetricTensor(covariant);
	contravariant.mul<false, false>(inv_A, covariant);
	}

	/* -------------------------------------------------------------------------- */
	Matrix<Real>
	GeometryUtils::covariantMetricTensor(const Matrix<Real> & covariant_bases) {
	Matrix<Real> A(covariant_bases.rows(), covariant_bases.rows());
	A.mul<false, true>(covariant_bases, covariant_bases);
	return A;
	}

	/* -------------------------------------------------------------------------- */
	Matrix<Real>
	GeometryUtils::contravariantMetricTensor(const Matrix<Real> & covariant_bases) {
	auto A = GeometryUtils::covariantMetricTensor(covariant_bases);
	auto inv_A = A.inverse();
	return inv_A;
	}

	/* -------------------------------------------------------------------------- */
	Matrix<Real> GeometryUtils::covariantCurvatureTensor(
	const Mesh & mesh, const Array<Real> & positions, const Element & element,
	const Vector<Real> & natural_coord, const Vector<Real> & normal) {

	UInt spatial_dimension = mesh.getSpatialDimension();
	auto surface_dimension = spatial_dimension - 1;

	const ElementType & type = element.type;
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt * elem_val = mesh.getConnectivity(type, _not_ghost).storage();

	auto && d2nds2 =
	ElementClassHelper<_ek_regular>::getD2NDS2(natural_coord, type);

	Matrix<Real> coords(spatial_dimension, nb_nodes_per_element);
	mesh.extractNodalValuesFromElement(positions, coords.storage(),
	elem_val +
	element.element * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	Matrix<Real> curvature(spatial_dimension,
	surface_dimension * surface_dimension);
	curvature.mul<false, true>(coords, d2nds2);

	Matrix<Real> H(surface_dimension, surface_dimension);

	UInt i = 0;
	for (auto alpha : arange(surface_dimension)) {
	for (auto beta : arange(surface_dimension)) {
	Vector<Real> temp(curvature(i));
	H(alpha, beta) = temp.dot(normal);
	i++;
	}
	}

	return H;
	}

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/geometry_utils.hh b/src/model/contact_mechanics/geometry_utils.hh
	index 089f42b24..a48a38ee9 100644
	--- a/src/model/contact_mechanics/geometry_utils.hh
	+++ b/src/model/contact_mechanics/geometry_utils.hh
	@@ -1,147 +1,150 @@
	/**
	* @file geometry_utils.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Oct 02 2019
	* @date last modification: Sat Dec 12 2020
	*
	* @brief class to compute geometry related quantities
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_GEOMETRY_UTILS_HH__
	#define __AKANTU_GEOMETRY_UTILS_HH__

	namespace akantu {

	class GeometryUtils {
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// computes the normal on an element (assuming elements is flat)
	static void normal(const Mesh & mesh, const Array<Real> & positions,
	const Element & element, Vector<Real> & normal,
	bool outward = true);

	// computes normal at given covariant basis
	static void normal(const Mesh & mesh, const Element & element,
	- Matrix<Real> & covariant_basis, Vector<Real> & normal,
	+ Matrix<Real> & tangents, Vector<Real> & normal,
	bool outward = true);

	/// computes the orthogonal projection on a set of elements and
	/// returns natural projection and normal gap and index of element
	static UInt
	orthogonalProjection(const Mesh & mesh, const Array<Real> & positions,
	const Vector<Real> & slave,
	const Array<Element> & elements, Real & gap,
	Vector<Real> & natural_projection, Vector<Real> & normal,
	Real alpha, UInt max_iterations = 100,
	Real tolerance = 1e-10, Real extension_tolerance = 1e-5);

	/// computes the orthogonal projection on a set of elements and
	/// returns natural projection and normal gap and index of element
	static UInt orthogonalProjection(
	const Mesh & mesh, const Array<Real> & positions,
	const Vector<Real> & slave, const Array<Element> & elements, Real & gap,
	Vector<Real> & natural_projection, Vector<Real> & normal,
	Matrix<Real> & tangent, Real alpha, UInt max_iterations = 100,
	Real tolerance = 1e-10, Real extension_tolerance = 1e-5);

	/// computes the natural projection on an element
	static void
	naturalProjection(const Mesh & mesh, const Array<Real> & positions,
	const Element & element, const Vector<Real> & slave_coords,
	Vector<Real> & master_coords,
	Vector<Real> & natural_projection,
	UInt max_iterations = 100, Real tolerance = 1e-10);

	/// computes the real projection on an element
	static void realProjection(const Mesh & mesh, const Array<Real> & positions,
	const Vector<Real> & slave,
	const Element & element,
	const Vector<Real> & normal,
	Vector<Real> & projection);

	/// computes the real projection from a natural coordinate
	static void realProjection(const Mesh & mesh, const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & natural_coord,
	Vector<Real> & projection);

	/// computes the covariant basis/ local surface basis/ tangents on projection
	/// point
	static void covariantBasis(const Mesh & mesh, const Array<Real> & positions,
	const Element & element,
	Vector<Real> & natural_coord,
	- Matrix<Real> & basis);
	+ Matrix<Real> & tangents);

	/// computes the covariant basis/ local surface basis/ tangents on projection
	/// point
	static void covariantBasis(const Mesh & mesh, const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & normal,
	Vector<Real> & natural_coord,
	- Matrix<Real> & basis);
	+ Matrix<Real> & tangents);

	// computes the curvature on projection
	static void curvature(const Mesh & mesh, const Array<Real> & positions,
	const Element & element,
	const Vector<Real> & natural_coord,
	Matrix<Real> & curvature);

	/// computes the contravariant basis on projection point
	static void contravariantBasis(const Matrix<Real> & covariant,
	Matrix<Real> & contravariant);

	/// computes metric tesnor with covariant components
	- static Matrix<Real> covariantMetricTensor(const Matrix<Real> &);
	+ static Matrix<Real>
	+ covariantMetricTensor(const Matrix<Real> & /covariant_bases/);

	/// computes metric tensor with contravariant components
	- static Matrix<Real> contravariantMetricTensor(const Matrix<Real> &);
	+ static Matrix<Real>
	+ contravariantMetricTensor(const Matrix<Real> & /covariant_bases/);

	// computes curvature tensor with convariant components
	- static Matrix<Real>
	- covariantCurvatureTensor(const Mesh &, const Array<Real> &, const Element &,
	- const Vector<Real> &, const Vector<Real> &);
	+ static Matrix<Real> covariantCurvatureTensor(
	+ const Mesh & /mesh/, const Array<Real> & /positions/,
	+ const Element & /element/, const Vector<Real> & /natural_coord/,
	+ const Vector<Real> & /normal/);

	/// checks if the element is truly a boundary element or not
	inline static bool isBoundaryElement(const Mesh & mesh,
	const Element & element);

	/// checks if the natural projection is valid for not
	inline static bool isValidProjection(const Vector<Real> & projection,
	Real extension_tolerance = 1e-5);
	};

	} // namespace akantu

	#include "geometry_utils_inline_impl.cc"

	#endif /* __AKANTU_GEOMETRY_UTILS_HH__ */
	diff --git a/src/model/contact_mechanics/geometry_utils_inline_impl.cc b/src/model/contact_mechanics/geometry_utils_inline_impl.cc
	index e41d380c2..276f1caef 100644
	--- a/src/model/contact_mechanics/geometry_utils_inline_impl.cc
	+++ b/src/model/contact_mechanics/geometry_utils_inline_impl.cc
	@@ -1,101 +1,98 @@
	/**
	* @file geometry_utils_inline_impl.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Oct 06 2019
	* @date last modification: Wed Sep 16 2020
	*
	* @brief Geometry utils
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "geometry_utils.hh"

	#ifndef __AKANTU_GEOMETRY_UTILS_INLINE_IMPL_CC__
	#define __AKANTU_GEOMETRY_UTILS_INLINE_IMPL_CC__

	-
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline bool GeometryUtils::isBoundaryElement(const Mesh & mesh,
	- const Element & subelement) {
	+ const Element & subelement) {

	const auto & element_to_subelement =
	- mesh.getElementToSubelement(subelement.type)(subelement.element);
	+ mesh.getElementToSubelement(subelement.type)(subelement.element);

	// for regular boundary elements when surfaceselector is set to
	// physical surfaces, the mesh contains only 1 element attached to a
	- // boundary subelement
	+ // boundary subelement
	if (element_to_subelement.size() == 1 and
	element_to_subelement[0].kind() == _ek_regular) {
	return true;
	}

	// for cohesive interface elements when surfaceSelector is set
	// either cohesive surface selector or all surface selector, in this
	// case mesh passed is actually mesh_facet and for boundary or
	// cohesive interface 2 elements are associated to a subelement
	// we want only one regular element attached to the subelement
	-
	+
	UInt nb_elements_regular = 0;
	UInt nb_elements_cohesive = 0;

	for (auto elem : element_to_subelement) {
	- if (elem == ElementNull)
	+ if (elem == ElementNull) {
	continue;
	-
	- if (elem.kind() == _ek_regular)
	+ }
	+
	+ if (elem.kind() == _ek_regular) {
	++nb_elements_regular;
	+ }

	- if (elem.kind() == _ek_cohesive)
	+ if (elem.kind() == _ek_cohesive) {
	++nb_elements_cohesive;
	+ }
	}

	auto nb_elements = element_to_subelement.size();
	- if (nb_elements_regular < nb_elements)
	- return true;
	-
	- return false;
	+ return nb_elements_regular < nb_elements;
	}

	/* -------------------------------------------------------------------------- */
	- inline bool GeometryUtils::isValidProjection(const Vector<Real> & projection,
	- Real extension_tolerance) {
	-
	+inline bool GeometryUtils::isValidProjection(const Vector<Real> & projection,
	+ Real extension_tolerance) {
	+
	UInt nb_xi_inside = 0;

	for (auto xi : projection) {
	- if (xi >= -1.0 - extension_tolerance and xi <= 1.0 + extension_tolerance)
	+ if (xi >= -1.0 - extension_tolerance and xi <= 1.0 + extension_tolerance) {
	nb_xi_inside++;
	+ }
	}

	- if (nb_xi_inside == projection.size())
	- return true;
	-
	- return false;
	+ return nb_xi_inside == projection.size();
	}

	-} //namespace akantu
	+} // namespace akantu

	#endif
	diff --git a/src/model/contact_mechanics/resolution.cc b/src/model/contact_mechanics/resolution.cc
	index 443388573..688b4db6e 100644
	--- a/src/model/contact_mechanics/resolution.cc
	+++ b/src/model/contact_mechanics/resolution.cc
	@@ -1,222 +1,222 @@
	/**
	* @file resolution.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Jan 17 2019
	* @date last modification: Wed Apr 07 2021
	*
	* @brief Implementation of common part of the contact resolution class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "resolution.hh"
	#include "contact_mechanics_model.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Resolution::Resolution(ContactMechanicsModel & model, const ID & id)
	- : Parsable(ParserType::_contact_resolution, id), id(id),
	+ : Parsable(ParserType::_contact_resolution, id), id(id),
	fem(model.getFEEngine()), model(model) {

	AKANTU_DEBUG_IN();

	spatial_dimension = model.getMesh().getSpatialDimension();
	this->initialize();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Resolution::~Resolution() = default;

	/* -------------------------------------------------------------------------- */
	void Resolution::initialize() {
	registerParam("name", name, std::string(), _pat_parsable \| _pat_readable);
	registerParam("mu", mu, Real(0.), _pat_parsable \| _pat_modifiable,
	"Friction Coefficient");
	registerParam("is_master_deformable", is_master_deformable, bool(false),
	_pat_parsable \| _pat_readable, "Is master surface deformable");
	}

	/* -------------------------------------------------------------------------- */
	void Resolution::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);
	std::string type = getID().substr(getID().find_last_of(':') + 1);

	stream << space << "Contact Resolution " << type << " [" << std::endl;
	Parsable::printself(stream, indent);
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void Resolution::assembleInternalForces(GhostType /ghost_type/) {
	AKANTU_DEBUG_IN();

	this->assembleInternalForces();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void Resolution::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	- for (auto & element : model.getContactElements()) {
	-
	- auto nb_nodes = element.getNbNodes();
	-
	+ for (const auto & element : model.getContactElements()) {
	+
	+ auto nb_nodes = element.getNbNodes();
	+
	Vector<Real> local_fn(nb_nodes * spatial_dimension);
	computeNormalForce(element, local_fn);

	- Vector<Real> local_ft(nb_nodes * spatial_dimension);
	+ Vector<Real> local_ft(nb_nodes * spatial_dimension);
	computeTangentialForce(element, local_ft);
	-
	+
	Vector<Real> local_fc(nb_nodes * spatial_dimension);
	local_fc = local_fn + local_ft;

	assembleLocalToGlobalArray(element, local_fn, model.getNormalForce());
	assembleLocalToGlobalArray(element, local_ft, model.getTangentialForce());
	assembleLocalToGlobalArray(element, local_fc, model.getInternalForce());
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void Resolution::assembleLocalToGlobalArray(const ContactElement & element,
	- Vector<Real> & local, Array<Real> & global) {
	+ Vector<Real> & local,
	+ Array<Real> & global) {

	auto get_connectivity = [&](auto & slave, auto & master) {
	Vector<UInt> master_conn =
	- const_cast<const Mesh &>(model.getMesh()).getConnectivity(master);
	+ const_cast<const Mesh &>(model.getMesh()).getConnectivity(master);
	Vector<UInt> elem_conn(master_conn.size() + 1);

	elem_conn[0] = slave;
	for (UInt i = 1; i < elem_conn.size(); ++i) {
	elem_conn[i] = master_conn[i - 1];
	}

	return elem_conn;
	};

	auto & surface_selector = model.getContactDetector().getSurfaceSelector();
	auto & slave_list = surface_selector.getSlaveList();
	auto & master_list = surface_selector.getMasterList();
	-
	+
	auto connectivity = get_connectivity(element.slave, element.master);
	-
	- UInt nb_dofs = global.getNbComponent();
	+
	+ UInt nb_dofs = global.getNbComponent();
	UInt nb_nodes = is_master_deformable ? connectivity.size() : 1;
	- Real alpha = is_master_deformable ? 0.5: 1.;
	-
	- for (UInt i : arange(nb_nodes)) {
	+ Real alpha = is_master_deformable ? 0.5 : 1.;
	+
	+ for (UInt i : arange(nb_nodes)) {
	UInt n = connectivity[i];

	auto slave_result = std::find(slave_list.begin(), slave_list.end(), n);
	auto master_result = std::find(master_list.begin(), master_list.end(), n);
	-
	+
	for (UInt j : arange(nb_dofs)) {
	UInt offset_node = n * nb_dofs + j;
	- global[offset_node] += alphalocal[i nb_dofs + j];
	+ global[offset_node] += alpha * local[i * nb_dofs + j];
	}
	}
	}
	-
	+
	/* -------------------------------------------------------------------------- */
	void Resolution::assembleStiffnessMatrix(GhostType /ghost_type/) {
	AKANTU_DEBUG_IN();

	auto & global_stiffness =
	const_cast<SparseMatrix &>(model.getDOFManager().getMatrix("K"));
	-
	- for (auto & element : model.getContactElements()) {

	- auto nb_nodes = element.getNbNodes();
	+ for (const auto & element : model.getContactElements()) {

	- Matrix<Real> local_kn(nb_nodes * spatial_dimension, nb_nodes * spatial_dimension);
	+ auto nb_nodes = element.getNbNodes();
	+
	+ Matrix<Real> local_kn(nb_nodes * spatial_dimension,
	+ nb_nodes * spatial_dimension);
	computeNormalModuli(element, local_kn);
	assembleLocalToGlobalMatrix(element, local_kn, global_stiffness);

	- Matrix<Real> local_kt(nb_nodes * spatial_dimension, nb_nodes * spatial_dimension);
	+ Matrix<Real> local_kt(nb_nodes * spatial_dimension,
	+ nb_nodes * spatial_dimension);
	computeTangentialModuli(element, local_kt);
	assembleLocalToGlobalMatrix(element, local_kt, global_stiffness);
	}

	AKANTU_DEBUG_OUT();
	}

	-
	/* -------------------------------------------------------------------------- */
	void Resolution::assembleLocalToGlobalMatrix(const ContactElement & element,
	- const Matrix<Real> & local, SparseMatrix & global) {
	+ const Matrix<Real> & local,
	+ SparseMatrix & global) {

	auto get_connectivity = [&](auto & slave, auto & master) {
	Vector<UInt> master_conn =
	- const_cast<const Mesh &>(model.getMesh()).getConnectivity(master);
	+ const_cast<const Mesh &>(model.getMesh()).getConnectivity(master);
	Vector<UInt> elem_conn(master_conn.size() + 1);

	elem_conn[0] = slave;
	for (UInt i = 1; i < elem_conn.size(); ++i) {
	elem_conn[i] = master_conn[i - 1];
	}

	return elem_conn;
	};

	auto connectivity = get_connectivity(element.slave, element.master);

	- auto nb_dofs = spatial_dimension;
	+ auto nb_dofs = spatial_dimension;
	UInt nb_nodes = is_master_deformable ? connectivity.size() : 1;
	UInt total_nb_dofs = nb_dofs * nb_nodes;
	-
	- std::vector<UInt> equations;
	+
	+ std::vector<UInt> equations;
	for (UInt i : arange(connectivity.size())) {
	UInt conn = connectivity[i];
	for (UInt j : arange(nb_dofs)) {
	equations.push_back(conn * nb_dofs + j);
	}
	}
	-
	+
	for (UInt i : arange(total_nb_dofs)) {
	UInt row = equations[i];
	for (UInt j : arange(total_nb_dofs)) {
	UInt col = equations[j];
	global.add(row, col, local(i, j));
	}
	}
	}

	-
	-
	/* -------------------------------------------------------------------------- */
	void Resolution::beforeSolveStep() {}

	/* -------------------------------------------------------------------------- */
	void Resolution::afterSolveStep(__attribute__((unused)) bool converged) {}
	-

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/resolution.hh b/src/model/contact_mechanics/resolution.hh
	index ab5e5e42d..eaef3d209 100644
	--- a/src/model/contact_mechanics/resolution.hh
	+++ b/src/model/contact_mechanics/resolution.hh
	@@ -1,235 +1,236 @@
	/**
	* @file resolution.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Apr 07 2021
	*
	* @brief Mother class for all contact resolutions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_factory.hh"
	+#include "contact_element.hh"
	+#include "fe_engine.hh"
	+#include "geometry_utils.hh"
	#include "parsable.hh"
	#include "parser.hh"
	-#include "fe_engine.hh"
	-#include "contact_element.hh"
	#include "resolution_utils.hh"
	-#include "geometry_utils.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_RESOLUTION_HH__
	#define __AKANTU_RESOLUTION_HH__

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	- class Model;
	- class ContactMechanicsModel;
	+class Model;
	+class ContactMechanicsModel;
	} // namespace akantu

	-
	namespace akantu {

	/**
	* Interface of all contact resolutions
	* Prerequisites for a new resolution
	* - inherit from this class
	* - implement the following methods:
	* \code
	*
	* virtual void computeNormalForce();
	* virtual void computeTangentialForce();
	* virtual void computeNormalModuli();
	* virtual void computeTangentialModuli();
	*
	* \endcode
	*
	*/
	class Resolution : public Parsable {

	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructor */
	/* ------------------------------------------------------------------------ */
	public:
	/// instantiate contact resolution with defaults
	Resolution(ContactMechanicsModel & model, const ID & id = "");

	/// Destructor
	~Resolution() override;

	protected:
	void initialize();

	/// computes coordinates of a given element
	- void computeCoordinates(const Element & , Matrix<Real> &);
	+ void computeCoordinates(const Element &, Matrix<Real> &);

	/* ------------------------------------------------------------------------ */
	/* Functions that resolutions should reimplement for force */
	/* ------------------------------------------------------------------------ */
	public:
	/// computes the force vector due to normal traction
	- virtual void computeNormalForce(__attribute__((unused)) const ContactElement &,
	- __attribute__((unused)) Vector<Real> &) {
	+ virtual void computeNormalForce(__attribute__((unused))
	+ const ContactElement & /unused/,
	+ __attribute__((unused))
	+ Vector<Real> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// computes the tangential force vector due to frictional traction
	- virtual void computeTangentialForce(__attribute__((unused)) const ContactElement &,
	- __attribute__((unused)) Vector<Real> &) {
	+ virtual void computeTangentialForce(__attribute__((unused))
	+ const ContactElement & /unused/,
	+ __attribute__((unused))
	+ Vector<Real> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/* ------------------------------------------------------------------------ */
	/* Functions that resolutions should reimplement for stiffness */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute the normal moduli due to normal traction
	- virtual void computeNormalModuli(__attribute__((unused)) const ContactElement &,
	- __attribute__((unused)) Matrix<Real> & ) {
	+ virtual void computeNormalModuli(__attribute__((unused))
	+ const ContactElement & /unused/,
	+ __attribute__((unused))
	+ Matrix<Real> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the tangent moduli due to tangential traction
	- virtual void computeTangentialModuli(__attribute__((unused)) const ContactElement &,
	- __attribute__((unused)) Matrix<Real> & ) {
	+ virtual void computeTangentialModuli(__attribute__((unused))
	+ const ContactElement & /unused/,
	+ __attribute__((unused))
	+ Matrix<Real> & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	-
	/* ------------------------------------------------------------------------ */
	/* Methods */
	- /* ------------------------------------------------------------------------ */
	+ /* ------------------------------------------------------------------------ */
	public:
	/// assemble the residual for this resolution
	void assembleInternalForces(GhostType ghost_type);

	/// assemble the stiffness matrix for this resolution
	void assembleStiffnessMatrix(GhostType ghost_type);

	private:
	- /// assemble the residual for this resolution
	+ /// assemble the residual for this resolution
	void assembleInternalForces();

	/// assemble the local array to global array for a contact element
	- void assembleLocalToGlobalArray(const ContactElement & , Vector<Real> & , Array<Real> & );
	+ void assembleLocalToGlobalArray(const ContactElement & /element/,
	+ Vector<Real> & /local/,
	+ Array<Real> & /global/);

	/// assemble the local stiffness to global stiffness for a contact element
	- void assembleLocalToGlobalMatrix(const ContactElement &, const Matrix<Real> &, SparseMatrix &);
	+ void assembleLocalToGlobalMatrix(const ContactElement & /element/,
	+ const Matrix<Real> & /local/,
	+ SparseMatrix & /global/);

	public:
	virtual void beforeSolveStep();

	virtual void afterSolveStep(bool converged = true);
	-

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(ID, id, const ID &);

	-
	public:
	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	/// friction coefficient : mu
	Real mu;
	-
	+
	/// spatial dimension
	UInt spatial_dimension;

	/// is master surface deformable
	bool is_master_deformable;
	-
	+
	/// Link to the fe engine object in the model
	FEEngine & fem;
	-
	+
	/// resolution name
	std::string name;
	-
	+
	/// model to which the resolution belong
	ContactMechanicsModel & model;
	-
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const Resolution & _this) {
	_this.printself(stream);
	return stream;
	}

	-
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	-using ResolutionFactory =
	- Factory<Resolution, ID, UInt, const ID &, ContactMechanicsModel &, const ID &>;
	+using ResolutionFactory = Factory<Resolution, ID, UInt, const ID &,
	+ ContactMechanicsModel &, const ID &>;

	-/// macaulay bracket to convert positive gap to zero
	-template <typename T>
	-T macaulay(T var) {return var < 0 ? 0 : var; }
	+/// macaulay bracket to convert positive gap to zero
	+template <typename T> T macaulay(T var) { return var < 0 ? 0 : var; }

	-template <typename T>
	-T heaviside(T var) {return var < 0 ? 0 : 1.0; }
	+template <typename T> T heaviside(T var) { return var < 0 ? 0 : 1.0; }
	} // namespace akantu

	-#define INSTANTIATE_RESOLUTION_ONLY(res_name) \
	- class res_name
	-
	-#define RESOLUTION_DEFAULT_PER_DIM_ALLOCATOR(id, res_name) \
	- [](UInt dim, const ID &, ContactMechanicsModel & model, \
	- const ID & id) -> std::unique_ptr<Resolution> { \
	- switch (dim) { \
	- case 1: \
	- return std::make_unique<res_name>(model, id); \
	- case 2: \
	- return std::make_unique<res_name>(model, id); \
	- case 3: \
	- return std::make_unique<res_name>(model, id); \
	- default: \
	- AKANTU_EXCEPTION("The dimension " \
	- << dim << "is not a valid dimension for the contact resolution " \
	- << #id); \
	- } \
	+#define INSTANTIATE_RESOLUTION_ONLY(res_name) class res_name
	+
	+#define RESOLUTION_DEFAULT_PER_DIM_ALLOCATOR(id, res_name) \
	+ [](UInt dim, const ID &, ContactMechanicsModel & model, \
	+ const ID & id) -> std::unique_ptr<Resolution> { \
	+ switch (dim) { \
	+ case 1: \
	+ return std::make_unique<res_name>(model, id); \
	+ case 2: \
	+ return std::make_unique<res_name>(model, id); \
	+ case 3: \
	+ return std::make_unique<res_name>(model, id); \
	+ default: \
	+ AKANTU_EXCEPTION( \
	+ "The dimension " \
	+ << dim << "is not a valid dimension for the contact resolution " \
	+ << #id); \
	+ } \
	}

	-
	-#define INSTANTIATE_RESOLUTION(id, res_name) \
	- INSTANTIATE_RESOLUTION_ONLY(res_name); \
	- static bool resolution_is_alocated_##id[[gnu::unused]] = \
	- ResolutionFactory::getInstance().registerAllocator( \
	+#define INSTANTIATE_RESOLUTION(id, res_name) \
	+ INSTANTIATE_RESOLUTION_ONLY(res_name); \
	+ static bool resolution_is_alocated_##id [[gnu::unused]] = \
	+ ResolutionFactory::getInstance().registerAllocator( \
	#id, RESOLUTION_DEFAULT_PER_DIM_ALLOCATOR(id, res_name))

	#endif /* __AKANTU_RESOLUTION_HH__ */
	-
	-
	diff --git a/src/model/contact_mechanics/resolution_utils.cc b/src/model/contact_mechanics/resolution_utils.cc
	index 528318aa4..88a839c9a 100644
	--- a/src/model/contact_mechanics/resolution_utils.cc
	+++ b/src/model/contact_mechanics/resolution_utils.cc
	@@ -1,71 +1,70 @@
	/**
	* @file resolution_utils.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon May 20 2019
	* @date last modification: Sun Jun 06 2021
	*
	* @brief Implementation of various utilities neede for resolution class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "resolution_utils.hh"
	#include "element_class_helper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	void ResolutionUtils::computeShapeFunctionMatric(
	const ContactElement & element, const Vector<Real> & projection,
	Matrix<Real> & shape_matric) {

	shape_matric.zero();

	const ElementType & type = element.master.type;

	auto surface_dimension = Mesh::getSpatialDimension(type);
	auto spatial_dimension = surface_dimension + 1;
	UInt nb_nodes_per_contact = element.getNbNodes();

	AKANTU_DEBUG_ASSERT(spatial_dimension == shape_matric.rows() &&
	spatial_dimension * nb_nodes_per_contact ==
	shape_matric.cols(),
	"Shape Matric dimensions are not correct");

	- auto && shapes =
	- ElementClassHelper<_ek_regular>::getN(projection, type);
	+ auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	shape_matric(j, i * spatial_dimension + j) = 1;
	continue;
	}
	shape_matric(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}
	}

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/resolution_utils.hh b/src/model/contact_mechanics/resolution_utils.hh
	index ba2a89101..d42beacc6 100644
	--- a/src/model/contact_mechanics/resolution_utils.hh
	+++ b/src/model/contact_mechanics/resolution_utils.hh
	@@ -1,63 +1,61 @@
	/**
	* @file resolution_utils.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon May 20 2019
	* @date last modification: Sun Jun 06 2021
	*
	* @brief All resolution utils necessary for various tasks
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	-#include "contact_mechanics_model.hh"
	#include "contact_element.hh"
	+#include "contact_mechanics_model.hh"
	#include "fe_engine.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_RESOLUTION_UTILS_HH__
	#define __AKANTU_RESOLUTION_UTILS_HH__

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class ResolutionUtils {
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	-
	/// computes the shape function matric for the contact element (@f$A
	/// @f$) where row is equal to spatial dimension and cols is equal
	/// to spatial dimension times number of nodes in contact element
	- static void computeShapeFunctionMatric(const ContactElement &,
	- const Vector<Real> &,
	- Matrix<Real> &);
	-
	+ static void computeShapeFunctionMatric(const ContactElement & /element/,
	+ const Vector<Real> & /projection/,
	+ Matrix<Real> & /shape_matric/);
	};

	} // namespace akantu

	#endif /* __AKANTU_RESOLUTION_UTILS_HH__ */
	diff --git a/src/model/contact_mechanics/resolutions/resolution_penalty.cc b/src/model/contact_mechanics/resolutions/resolution_penalty.cc
	index 3c4e0bc86..eb6ee0d98 100644
	--- a/src/model/contact_mechanics/resolutions/resolution_penalty.cc
	+++ b/src/model/contact_mechanics/resolutions/resolution_penalty.cc
	@@ -1,840 +1,844 @@
	/**
	* @file resolution_penalty.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Jan 17 2019
	* @date last modification: Wed Jun 09 2021
	*
	* @brief Specialization of the resolution class for the penalty method
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "resolution_penalty.hh"
	#include "element_class_helper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ResolutionPenalty::ResolutionPenalty(ContactMechanicsModel & model,
	const ID & id)
	: Resolution(model, id) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::initialize() {
	this->registerParam("epsilon_n", epsilon_n, Real(0.),
	_pat_parsable \| _pat_modifiable,
	"Normal penalty parameter");
	this->registerParam("epsilon_t", epsilon_t, Real(0.),
	_pat_parsable \| _pat_modifiable,
	"Tangential penalty parameter");
	}

	/* -------------------------------------------------------------------------- */
	-Real ResolutionPenalty::computeNormalTraction(Real & gap) {
	+Real ResolutionPenalty::computeNormalTraction(Real & gap) const {
	return epsilon_n * macaulay(gap);
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeNormalForce(const ContactElement & element,
	Vector<Real> & force) {

	force.zero();

	auto & gaps = model.getGaps();
	auto & projections = model.getProjections();
	auto & normals = model.getNormals();

	auto surface_dimension = spatial_dimension - 1;

	Real gap(gaps.begin()[element.slave]);
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_area = const_cast<Array<Real> &>(model.getNodalArea());

	// compute normal traction
	Real p_n = computeNormalTraction(gap);
	p_n *= nodal_area[element.slave];

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> shape_matric(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	ResolutionUtils::computeShapeFunctionMatric(element, projection,
	shape_matric);

	force.mul<true>(shape_matric, normal, p_n);
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeTangentialForce(const ContactElement & element,
	Vector<Real> & force) {

	- if (mu == 0)
	+ if (mu == 0) {
	return;
	+ }

	force.zero();

	UInt surface_dimension = spatial_dimension - 1;

	// compute covariant basis
	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	// check for no-contact to contact condition
	// need a better way to check if new node added is not presnt in the
	// previous master elemets
	auto & previous_master_elements = model.getPreviousMasterElements();
	- if (element.slave >= previous_master_elements.size())
	+ if (element.slave >= previous_master_elements.size()) {
	return;
	+ }

	auto & previous_element = previous_master_elements[element.slave];
	- if (previous_element.type == _not_defined)
	+ if (previous_element.type == _not_defined) {
	return;
	+ }

	// compute tangential traction using return map algorithm
	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);
	this->computeTangentialTraction(element, covariant_basis,
	tangential_traction);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> shape_matric(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	ResolutionUtils::computeShapeFunctionMatric(element, projection,
	shape_matric);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	auto & nodal_area = const_cast<Array<Real> &>(model.getNodalArea());

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);
	for (auto && values2 : enumerate(tangential_traction)) {
	auto & beta = std::get<0>(values2);
	auto & traction_beta = std::get<1>(values2);
	Vector<Real> tmp(force.size());
	tmp.mul<true>(shape_matric, tangent_alpha, traction_beta);
	tmp *=
	contravariant_metric_tensor(alpha, beta) * nodal_area[element.slave];
	force += tmp;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction_tangential) {

	UInt surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	auto & gap = gaps.begin()[element.slave];

	// Return map algorithm is employed
	// compute trial traction
	Vector<Real> traction_trial(surface_dimension);
	this->computeTrialTangentialTraction(element, covariant_basis,
	traction_trial);

	// compute norm of trial traction
	Real traction_trial_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);
	for (auto i : arange(surface_dimension)) {
	for (auto j : arange(surface_dimension)) {
	traction_trial_norm += traction_trial[i] * traction_trial[j] *
	contravariant_metric_tensor(i, j);
	}
	}
	traction_trial_norm = sqrt(traction_trial_norm);

	// check stick or slip condition
	auto & contact_state = model.getContactState();
	auto & state = contact_state.begin()[element.slave];

	Real p_n = computeNormalTraction(gap);
	bool stick = (traction_trial_norm <= mu * p_n);

	if (stick) {
	state = ContactState::_stick;
	computeStickTangentialTraction(element, traction_trial,
	traction_tangential);
	} else {
	state = ContactState::_slip;
	computeSlipTangentialTraction(element, covariant_basis, traction_trial,
	traction_tangential);
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeTrialTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction) {

	UInt surface_dimension = spatial_dimension - 1;

	auto & projections = model.getProjections();
	Vector<Real> current_projection(
	projections.begin(surface_dimension)[element.slave]);

	auto & previous_projections = model.getPreviousProjections();
	Vector<Real> previous_projection(
	previous_projections.begin(surface_dimension)[element.slave]);

	// method from Laursen et. al.
	/*auto covariant_metric_tensor =
	GeometryUtils::covariantMetricTensor(covariant_basis); auto
	increment_projection = current_projection - previous_projection;

	traction.mul<false>(covariant_metric_tensor, increment_projection, epsilon_t);

	auto & previous_tangential_tractions = model.getPreviousTangentialTractions();
	Vector<Real>
	previous_traction(previous_tangential_tractions.begin(surface_dimension)[element.slave]);
	traction = previous_traction + traction;*/

	// method from Schweizerhof
	auto covariant_metric_tensor =
	GeometryUtils::covariantMetricTensor(covariant_basis);

	auto & previous_tangential_tractions = model.getPreviousTangentialTractions();
	Vector<Real> previous_traction(
	previous_tangential_tractions.begin(surface_dimension)[element.slave]);

	auto & previous_tangents = model.getPreviousTangents();
	Matrix<Real> previous_covariant_basis(previous_tangents.begin(
	surface_dimension, spatial_dimension)[element.slave]);
	auto previous_contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(previous_covariant_basis);

	auto current_tangent = covariant_basis.transpose();
	auto previous_tangent = previous_covariant_basis.transpose();

	for (auto alpha : arange(surface_dimension)) {
	Vector<Real> tangent_alpha(current_tangent(alpha));
	for (auto gamma : arange(surface_dimension)) {
	for (auto beta : arange(surface_dimension)) {
	Vector<Real> tangent_beta(previous_tangent(beta));
	auto t_alpha_t_beta = tangent_beta.dot(tangent_alpha);
	traction[alpha] += previous_traction[gamma] *
	previous_contravariant_metric_tensor(gamma, beta) *
	t_alpha_t_beta;
	}
	}
	}

	auto & previous_master_elements = model.getPreviousMasterElements();
	auto & previous_element = previous_master_elements[element.slave];

	Vector<Real> previous_real_projection(spatial_dimension);
	GeometryUtils::realProjection(
	model.getMesh(), model.getContactDetector().getPositions(),
	previous_element, previous_projection, previous_real_projection);

	Vector<Real> current_real_projection(spatial_dimension);
	GeometryUtils::realProjection(
	model.getMesh(), model.getContactDetector().getPositions(),
	element.master, current_projection, current_real_projection);

	auto increment_real = current_real_projection - previous_real_projection;
	Vector<Real> increment_xi(surface_dimension);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// increment in natural coordinate
	for (auto beta : arange(surface_dimension)) {
	for (auto gamma : arange(surface_dimension)) {
	auto temp = increment_real.dot(current_tangent(gamma));
	temp *= contravariant_metric_tensor(beta, gamma);
	increment_xi[beta] += temp;
	}
	}

	Vector<Real> temp(surface_dimension);
	temp.mul<false>(covariant_metric_tensor, increment_xi, epsilon_t);

	traction -= temp;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeStickTangentialTraction(
	const ContactElement & /element/, Vector<Real> & traction_trial,
	Vector<Real> & traction_tangential) {
	traction_tangential = traction_trial;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeSlipTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction_trial, Vector<Real> & traction_tangential) {
	UInt surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	auto & gap = gaps.begin()[element.slave];

	// compute norm of trial traction
	Real traction_trial_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	for (auto alpha : arange(surface_dimension)) {
	for (auto beta : arange(surface_dimension)) {
	traction_trial_norm += traction_trial[alpha] * traction_trial[beta] *
	contravariant_metric_tensor(alpha, beta);
	}
	}
	traction_trial_norm = sqrt(traction_trial_norm);

	auto slip_direction = traction_trial;
	slip_direction /= traction_trial_norm;

	Real p_n = computeNormalTraction(gap);
	traction_tangential = slip_direction;
	traction_tangential = mu p_n;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeNormalModuli(const ContactElement & element,
	Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	Real gap(gaps.begin()[element.slave]);

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// construct the main part of normal matrix
	Matrix<Real> k_main(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_n(normal.storage(), normal.size(), 1.);
	n_outer_n.mul<false, true>(mat_n, mat_n);

	Matrix<Real> tmp(spatial_dimension, spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(n_outer_n, A);

	k_main.mul<true, false>(A, tmp);
	k_main = epsilon_n heaviside(gap) * nodal_area;

	// construct the rotational part of the normal matrix
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	// consists of 2 rotational parts
	Matrix<Real> k_rot1(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_rot2(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent = std::get<1>(values1);

	Matrix<Real> n_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t(tangent.storage(), tangent.size(), 1.);
	n_outer_t.mul<false, true>(mat_n, mat_t);

	Matrix<Real> t_outer_n(spatial_dimension, spatial_dimension);
	t_outer_n.mul<false, true>(mat_t, mat_n);

	for (auto && values2 : enumerate(shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & dnds = std::get<1>(values2);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(n_outer_t, A);
	tmp1.mul<true, false>(Aj, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_rot1 += tmp1;

	tmp.mul<false, false>(t_outer_n, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_rot2 += tmp1;
	}
	}

	k_rot1 = -epsilon_n heaviside(gap) * gap * nodal_area;
	k_rot2 = -epsilon_n heaviside(gap) * gap * nodal_area;

	stiffness += k_main + k_rot1 + k_rot2;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeTangentialModuli(const ContactElement & element,
	Matrix<Real> & stiffness) {
	if (mu == 0) {
	return;
	}

	stiffness.zero();

	auto & contact_state = model.getContactState();
	auto state = contact_state.begin()[element.slave];

	switch (state) {
	case ContactState::_stick: {
	computeStickModuli(element, stiffness);
	break;
	}
	case ContactState::_slip: {
	computeSlipModuli(element, stiffness);
	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeStickModuli(const ContactElement & element,
	Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	// tangents should have been calculated in normal modulii
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// construct 1st part of the stick modulii
	Matrix<Real> k_main(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);

	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t_alpha(tangent_alpha.storage(), tangent_alpha.size(), 1.);

	for (auto && values2 : enumerate(covariant_basis.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & tangent_beta = std::get<1>(values2);

	Matrix<Real> mat_t_beta(tangent_beta.storage(), tangent_beta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_alpha, mat_t_beta);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_main += tmp1;
	}
	}

	k_main *= -epsilon_t;

	// construct 2nd part of the stick modulii
	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);

	Matrix<Real> k_second(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto alpha : arange(surface_dimension)) {

	Matrix<Real> k_sum(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values1);
	auto & dnds = std::get<1>(values1);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);
	for (auto && values2 : enumerate(covariant_basis.transpose())) {
	auto & gamma = std::get<0>(values2);
	auto & tangent_gamma = std::get<1>(values2);

	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t_gamma(tangent_gamma.storage(), tangent_gamma.size(),
	1.);

	for (auto && values3 : enumerate(covariant_basis.transpose())) {
	auto & theta = std::get<0>(values3);
	auto & tangent_theta = std::get<1>(values3);

	Matrix<Real> mat_t_theta(tangent_theta.storage(),
	tangent_theta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_gamma, mat_t_theta);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_t, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 = contravariant_metric_tensor(alpha, theta)
	contravariant_metric_tensor(beta, gamma);

	Matrix<Real> tmp2(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp3(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp2.mul<false, false>(t_outer_t, A);
	tmp3.mul<true, false>(Aj, tmp2);
	tmp3 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);

	k_sum += tmp1 + tmp3;
	}
	}
	}

	k_second += tangential_traction[alpha] * k_sum;
	}

	stiffness += k_main * nodal_area - k_second * nodal_area;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::computeSlipModuli(const ContactElement & element,
	Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	Real gap(gaps.begin()[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	// compute normal traction
	Real p_n = computeNormalTraction(gap);

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	// restructure normal as a matrix for an outer product
	Matrix<Real> mat_n(normal.storage(), normal.size(), 1.);

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	// tangents should have been calculated in normal modulii
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);

	// compute norm of trial traction
	Real traction_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	for (auto i : arange(surface_dimension)) {
	for (auto j : arange(surface_dimension)) {
	traction_norm += tangential_traction[i] * tangential_traction[j] *
	contravariant_metric_tensor(i, j);
	}
	}
	traction_norm = sqrt(traction_norm);

	// construct four parts of stick modulii (eq 107,107a-c)
	Matrix<Real> k_first(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_second(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_third(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_fourth(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);

	Matrix<Real> mat_t_alpha(tangent_alpha.storage(), tangent_alpha.size(), 1.);

	Matrix<Real> t_outer_n(spatial_dimension, spatial_dimension);
	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);

	for (auto && values2 :
	zip(arange(surface_dimension), covariant_basis.transpose(),
	shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & tangent_beta = std::get<1>(values2);
	auto & dnds = std::get<2>(values2);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);

	// eq 107
	Matrix<Real> mat_t_beta(tangent_beta.storage(), tangent_beta.size(), 1.);
	t_outer_n.mul<false, true>(mat_t_beta, mat_n);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_n, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_n mu * tangential_traction[alpha] *
	contravariant_metric_tensor(alpha, beta);
	tmp1 /= traction_norm;

	k_first += tmp1 * nodal_area;

	// eq 107a
	t_outer_t.mul<false, true>(mat_t_alpha, mat_t_beta);

	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_t mu * p_n * contravariant_metric_tensor(alpha, beta);
	tmp1 /= traction_norm;

	k_second += tmp1 * nodal_area;

	for (auto && values3 : enumerate(covariant_basis.transpose())) {
	auto & gamma = std::get<0>(values3);
	auto & tangent_gamma = std::get<1>(values3);

	Matrix<Real> mat_t_gamma(tangent_gamma.storage(), tangent_gamma.size(),
	1.);

	for (auto && values4 : enumerate(covariant_basis.transpose())) {
	auto & theta = std::get<0>(values4);
	auto & tangent_theta = std::get<1>(values4);

	Matrix<Real> mat_t_theta(tangent_theta.storage(),
	tangent_theta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_gamma, mat_t_theta);

	// eq 107b
	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_t mu * p_n * tangential_traction[alpha] *
	tangential_traction[beta];
	tmp1 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);
	tmp1 /= pow(traction_norm, 3);

	k_third += tmp1 * nodal_area;

	// eq 107c
	tmp.mul<false, false>(t_outer_t, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 = contravariant_metric_tensor(alpha, theta)
	contravariant_metric_tensor(beta, gamma);
	tmp1 = mu p_n * tangential_traction[alpha];
	tmp1 /= traction_norm;

	Matrix<Real> tmp2(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp3(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp2.mul<false, false>(t_outer_t, A);
	tmp3.mul<true, false>(Aj, tmp2);
	tmp3 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);
	tmp3 = mu p_n * tangential_traction[alpha];
	tmp3 /= traction_norm;

	k_fourth += (tmp1 + tmp3) * nodal_area;
	}
	}
	}
	}

	stiffness += k_third + k_fourth - k_first - k_second;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenalty::beforeSolveStep() {}

	/* -------------------------------------------------------------------------- */
	-void ResolutionPenalty::afterSolveStep(__attribute__((unused)) bool converged) {}
	+void ResolutionPenalty::afterSolveStep(__attribute__((unused)) bool converged) {
	+}

	INSTANTIATE_RESOLUTION(penalty_linear, ResolutionPenalty);

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/resolutions/resolution_penalty.hh b/src/model/contact_mechanics/resolutions/resolution_penalty.hh
	index bb8e0d91d..3242f0567 100644
	--- a/src/model/contact_mechanics/resolutions/resolution_penalty.hh
	+++ b/src/model/contact_mechanics/resolutions/resolution_penalty.hh
	@@ -1,123 +1,133 @@
	/**
	* @file resolution_penalty.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jun 09 2021
	*
	* @brief Linear Penalty Resolution for Contact Mechanics Model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "resolution.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_RESOLUTION_PENALTY_HH__
	#define __AKANTU_RESOLUTION_PENALTY_HH__

	namespace akantu {
	class ResolutionPenalty : public Resolution {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ResolutionPenalty(ContactMechanicsModel & model, const ID & id = "");

	~ResolutionPenalty() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize the resolution
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods for stiffness computation */
	/* ------------------------------------------------------------------------ */
	protected:
	/// local computaion of stiffness matrix due to stick state
	- void computeStickModuli(const ContactElement &, Matrix<Real> &);
	+ void computeStickModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/);

	/// local computation of stiffness matrix due to slip state
	- void computeSlipModuli(const ContactElement &, Matrix<Real> &);
	+ void computeSlipModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/);

	public:
	/// local computation of tangent moduli due to normal traction
	- void computeNormalModuli(const ContactElement &, Matrix<Real> &) override;
	+ void computeNormalModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/) override;

	/// local computation of tangent moduli due to tangential traction
	- void computeTangentialModuli(const ContactElement &, Matrix<Real> &) override;
	+ void computeTangentialModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/) override;

	/* ------------------------------------------------------------------------ */
	/* Methods for force computation */
	/* ------------------------------------------------------------------------ */
	public:
	/// local computation of normal force due to normal contact
	- void computeNormalForce(const ContactElement &, Vector<Real> &) override;
	+ void computeNormalForce(const ContactElement & /element/,
	+ Vector<Real> & /force/) override;

	/// local computation of tangential force due to frictional traction
	- void computeTangentialForce(const ContactElement &, Vector<Real> &) override;
	+ void computeTangentialForce(const ContactElement & /element/,
	+ Vector<Real> & /force/) override;

	protected:
	/// local computation of normal traction due to penetration
	- Real computeNormalTraction(Real &);
	+ Real computeNormalTraction(Real & /gap/) const;

	/// local computation of trial tangential traction due to friction
	- void computeTrialTangentialTraction(const ContactElement &,
	- const Matrix<Real> &, Vector<Real> &);
	+ void computeTrialTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction/);

	/// local computation of tangential traction due to stick
	- void computeStickTangentialTraction(const ContactElement &, Vector<Real> &,
	- Vector<Real> &);
	+ void computeStickTangentialTraction(const ContactElement & /unused/,
	+ Vector<Real> & /traction_trial/,
	+ Vector<Real> & /traction_tangential/);

	/// local computation of tangential traction due to slip
	- void computeSlipTangentialTraction(const ContactElement &,
	- const Matrix<Real> &, Vector<Real> &,
	- Vector<Real> &);
	+ void computeSlipTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction_trial/,
	+ Vector<Real> & /traction_tangential/);

	/// local computation of tangential traction due to friction
	- void computeTangentialTraction(const ContactElement &, const Matrix<Real> &,
	- Vector<Real> &);
	+ void computeTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction_tangential/);

	public:
	void beforeSolveStep() override;

	void afterSolveStep(bool converged = true) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// penalty parameter for normal traction
	Real epsilon_n;

	/// penalty parameter for tangential traction
	Real epsilon_t;
	};

	} // namespace akantu

	#endif /* __AKANTU_RESOLUTION_PENALTY_HH__ */
	diff --git a/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.cc b/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.cc
	index 95f64dc3e..0849b48a6 100644
	--- a/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.cc
	+++ b/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.cc
	@@ -1,833 +1,836 @@
	/**
	* @file resolution_penalty_quadratic.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Jan 17 2019
	* @date last modification: Wed Jun 09 2021
	*
	* @brief Specialization of the resolution class for the quadratic penalty
	* method
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "resolution_penalty_quadratic.hh"
	#include "element_class_helper.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ResolutionPenaltyQuadratic::ResolutionPenaltyQuadratic(
	ContactMechanicsModel & model, const ID & id)
	: Parent(model, id) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::initialize() {}

	/* -------------------------------------------------------------------------- */
	Real ResolutionPenaltyQuadratic::computeNormalTraction(Real & gap) {
	return epsilon_n * (macaulay(gap) * macaulay(gap) + macaulay(gap));
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeNormalForce(
	const ContactElement & element, Vector<Real> & force) {
	force.zero();

	auto & gaps = model.getGaps();
	auto & projections = model.getProjections();
	auto & normals = model.getNormals();

	auto surface_dimension = spatial_dimension - 1;

	Real gap(gaps.begin()[element.slave]);
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_area = const_cast<Array<Real> &>(model.getNodalArea());

	// compute normal traction
	Real p_n = computeNormalTraction(gap);
	p_n *= nodal_area[element.slave];

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> shape_matric(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	ResolutionUtils::computeShapeFunctionMatric(element, projection,
	shape_matric);

	force.mul<true>(shape_matric, normal, p_n);
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeTangentialForce(
	const ContactElement & element, Vector<Real> & force) {

	- if (mu == 0)
	+ if (mu == 0) {
	return;
	+ }

	force.zero();

	UInt surface_dimension = spatial_dimension - 1;

	// compute tangents
	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	// check for no-contact to contact condition
	// need a better way to check if new node added is not presnt in the
	// previous master elemets
	auto & previous_master_elements = model.getPreviousMasterElements();
	- if (element.slave >= previous_master_elements.size())
	+ if (element.slave >= previous_master_elements.size()) {
	return;
	+ }

	auto & previous_element = previous_master_elements[element.slave];
	- if (previous_element.type == _not_defined)
	+ if (previous_element.type == _not_defined) {
	return;
	+ }

	// compute tangential traction using return map algorithm
	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);
	this->computeTangentialTraction(element, covariant_basis,
	tangential_traction);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> shape_matric(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	ResolutionUtils::computeShapeFunctionMatric(element, projection,
	shape_matric);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	auto & nodal_area = const_cast<Array<Real> &>(model.getNodalArea());

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);
	for (auto && values2 : enumerate(tangential_traction)) {
	auto & beta = std::get<0>(values2);
	auto & traction_beta = std::get<1>(values2);
	Vector<Real> tmp(force.size());
	tmp.mul<true>(shape_matric, tangent_alpha, traction_beta);
	tmp *=
	contravariant_metric_tensor(alpha, beta) * nodal_area[element.slave];
	force += tmp;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction_tangential) {

	UInt surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	auto & gap = gaps.begin()[element.slave];

	// Return map algorithm is employed
	// compute trial traction
	Vector<Real> traction_trial(surface_dimension);
	this->computeTrialTangentialTraction(element, covariant_basis,
	traction_trial);

	// compute norm of trial traction
	Real traction_trial_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);
	for (auto i : arange(surface_dimension)) {
	for (auto j : arange(surface_dimension)) {
	traction_trial_norm += traction_trial[i] * traction_trial[j] *
	contravariant_metric_tensor(i, j);
	}
	}
	traction_trial_norm = sqrt(traction_trial_norm);

	// check stick or slip condition
	auto & contact_state = model.getContactState();
	auto & state = contact_state.begin()[element.slave];

	Real p_n = computeNormalTraction(gap);
	- bool stick = (traction_trial_norm <= mu * p_n) ? true : false;
	+ bool stick = traction_trial_norm <= mu * p_n;

	if (stick) {
	state = ContactState::_stick;
	computeStickTangentialTraction(element, traction_trial,
	traction_tangential);
	} else {
	state = ContactState::_slip;
	computeSlipTangentialTraction(element, covariant_basis, traction_trial,
	traction_tangential);
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeTrialTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction) {

	UInt surface_dimension = spatial_dimension - 1;

	auto & projections = model.getProjections();
	Vector<Real> current_projection(
	projections.begin(surface_dimension)[element.slave]);

	auto & previous_projections = model.getPreviousProjections();
	Vector<Real> previous_projection(
	previous_projections.begin(surface_dimension)[element.slave]);

	// method from Laursen et. al.
	/*auto covariant_metric_tensor =
	GeometryUtils::covariantMetricTensor(covariant_basis); auto
	increment_projection = current_projection - previous_projection;

	traction.mul<false>(covariant_metric_tensor, increment_projection, epsilon_t);

	auto & previous_tangential_tractions = model.getPreviousTangentialTractions();
	Vector<Real>
	previous_traction(previous_tangential_tractions.begin(surface_dimension)[element.slave]);
	traction = previous_traction + traction;*/

	// method from Schweizerhof
	auto covariant_metric_tensor =
	GeometryUtils::covariantMetricTensor(covariant_basis);

	auto & previous_tangential_tractions = model.getPreviousTangentialTractions();
	Vector<Real> previous_traction(
	previous_tangential_tractions.begin(surface_dimension)[element.slave]);

	auto & previous_tangents = model.getPreviousTangents();
	Matrix<Real> previous_covariant_basis(previous_tangents.begin(
	surface_dimension, spatial_dimension)[element.slave]);
	auto previous_contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(previous_covariant_basis);

	auto current_tangent = covariant_basis.transpose();
	auto previous_tangent = previous_covariant_basis.transpose();

	for (auto alpha : arange(surface_dimension)) {
	Vector<Real> tangent_alpha(current_tangent(alpha));
	for (auto gamma : arange(surface_dimension)) {
	for (auto beta : arange(surface_dimension)) {
	Vector<Real> tangent_beta(previous_tangent(beta));
	auto t_alpha_t_beta = tangent_beta.dot(tangent_alpha);
	traction[alpha] += previous_traction[gamma] *
	previous_contravariant_metric_tensor(gamma, beta) *
	t_alpha_t_beta;
	}
	}
	}

	auto & previous_master_elements = model.getPreviousMasterElements();
	auto & previous_element = previous_master_elements[element.slave];

	Vector<Real> previous_real_projection(spatial_dimension);
	GeometryUtils::realProjection(
	model.getMesh(), model.getContactDetector().getPositions(),
	previous_element, previous_projection, previous_real_projection);

	Vector<Real> current_real_projection(spatial_dimension);
	GeometryUtils::realProjection(
	model.getMesh(), model.getContactDetector().getPositions(),
	element.master, current_projection, current_real_projection);

	auto increment_real = current_real_projection - previous_real_projection;
	Vector<Real> increment_xi(surface_dimension);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// increment in natural coordinate
	for (auto beta : arange(surface_dimension)) {
	for (auto gamma : arange(surface_dimension)) {
	auto temp = increment_real.dot(current_tangent(gamma));
	temp *= contravariant_metric_tensor(beta, gamma);
	increment_xi[beta] += temp;
	}
	}

	Vector<Real> temp(surface_dimension);
	temp.mul<false>(covariant_metric_tensor, increment_xi, epsilon_t);

	traction -= temp;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeStickTangentialTraction(
	const ContactElement & /element/, Vector<Real> & traction_trial,
	Vector<Real> & traction_tangential) {
	traction_tangential = traction_trial;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeSlipTangentialTraction(
	const ContactElement & element, const Matrix<Real> & covariant_basis,
	Vector<Real> & traction_trial, Vector<Real> & traction_tangential) {
	UInt surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	auto & gap = gaps.begin()[element.slave];

	// compute norm of trial traction
	Real traction_trial_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);
	for (auto i : arange(surface_dimension)) {
	for (auto j : arange(surface_dimension)) {
	traction_trial_norm += traction_trial[i] * traction_trial[j] *
	contravariant_metric_tensor(i, j);
	}
	}
	traction_trial_norm = sqrt(traction_trial_norm);

	auto slip_direction = traction_trial;
	slip_direction /= traction_trial_norm;

	Real p_n = computeNormalTraction(gap);
	traction_tangential = slip_direction;
	traction_tangential = mu p_n;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeNormalModuli(
	const ContactElement & element, Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	Real gap(gaps.begin()[element.slave]);

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// construct the main part of normal matrix
	Matrix<Real> k_main(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_n(normal.storage(), normal.size(), 1.);
	n_outer_n.mul<false, true>(mat_n, mat_n);

	Matrix<Real> tmp(spatial_dimension, spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(n_outer_n, A);

	k_main.mul<true, false>(A, tmp);
	k_main = epsilon_n heaviside(gap) * (2 * gap + 1) * nodal_area;

	// construct the rotational part of the normal matrix
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	// consists of 2 rotational parts
	Matrix<Real> k_rot1(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_rot2(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent = std::get<1>(values1);

	Matrix<Real> n_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t(tangent.storage(), tangent.size(), 1.);
	n_outer_t.mul<false, true>(mat_n, mat_t);

	Matrix<Real> t_outer_n(spatial_dimension, spatial_dimension);
	t_outer_n.mul<false, true>(mat_t, mat_n);

	for (auto && values2 : enumerate(shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & dnds = std::get<1>(values2);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(n_outer_t, A);
	tmp1.mul<true, false>(Aj, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_rot1 += tmp1;

	tmp.mul<false, false>(t_outer_n, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_rot2 += tmp1;
	}
	}

	k_rot1 = -epsilon_n heaviside(gap) * (gap * gap + gap) * nodal_area;
	k_rot2 = -epsilon_n heaviside(gap) * (gap * gap + gap) * nodal_area;

	stiffness += k_main + k_rot1 + k_rot2;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeTangentialModuli(
	const ContactElement & element, Matrix<Real> & stiffness) {
	if (mu == 0) {
	return;
	}

	stiffness.zero();

	auto & contact_state = model.getContactState();
	auto state = contact_state.begin()[element.slave];

	switch (state) {
	case ContactState::_stick: {
	computeStickModuli(element, stiffness);
	break;
	}
	case ContactState::_slip: {
	computeSlipModuli(element, stiffness);
	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeStickModuli(
	const ContactElement & element, Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	// tangents should have been calculated in normal modulii
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	// construct 1st part of the stick modulii
	Matrix<Real> k_main(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);

	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t_alpha(tangent_alpha.storage(), tangent_alpha.size(), 1.);

	for (auto && values2 : enumerate(covariant_basis.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & tangent_beta = std::get<1>(values2);

	Matrix<Real> mat_t_beta(tangent_beta.storage(), tangent_beta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_alpha, mat_t_beta);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);
	tmp1 *= contravariant_metric_tensor(alpha, beta);
	k_main += tmp1;
	}
	}

	k_main *= -epsilon_t;

	// construct 2nd part of the stick modulii
	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);

	Matrix<Real> k_second(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto alpha : arange(surface_dimension)) {

	Matrix<Real> k_sum(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values1);
	auto & dnds = std::get<1>(values1);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);
	for (auto && values2 : enumerate(covariant_basis.transpose())) {
	auto & gamma = std::get<0>(values2);
	auto & tangent_gamma = std::get<1>(values2);

	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);
	Matrix<Real> mat_t_gamma(tangent_gamma.storage(), tangent_gamma.size(),
	1.);

	for (auto && values3 : enumerate(covariant_basis.transpose())) {
	auto & theta = std::get<0>(values3);
	auto & tangent_theta = std::get<1>(values3);

	Matrix<Real> mat_t_theta(tangent_theta.storage(),
	tangent_theta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_gamma, mat_t_theta);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_t, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 = contravariant_metric_tensor(alpha, theta)
	contravariant_metric_tensor(beta, gamma);

	Matrix<Real> tmp2(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp3(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp2.mul<false, false>(t_outer_t, A);
	tmp3.mul<true, false>(Aj, tmp2);
	tmp3 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);

	k_sum += tmp1 + tmp3;
	}
	}
	}

	k_second += tangential_traction[alpha] * k_sum;
	}

	stiffness += k_main * nodal_area - k_second * nodal_area;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::computeSlipModuli(
	const ContactElement & element, Matrix<Real> & stiffness) {

	auto surface_dimension = spatial_dimension - 1;

	auto & gaps = model.getGaps();
	Real gap(gaps.begin()[element.slave]);

	auto & nodal_areas = model.getNodalArea();
	auto & nodal_area = nodal_areas.begin()[element.slave];

	// compute normal traction
	Real p_n = computeNormalTraction(gap);

	auto & projections = model.getProjections();
	Vector<Real> projection(projections.begin(surface_dimension)[element.slave]);

	auto & normals = model.getNormals();
	Vector<Real> normal(normals.begin(spatial_dimension)[element.slave]);

	// restructure normal as a matrix for an outer product
	Matrix<Real> mat_n(normal.storage(), normal.size(), 1.);

	// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
	// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3

	// construct A matrix
	const ElementType & type = element.master.type;
	auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);

	UInt nb_nodes_per_contact = element.getNbNodes();
	Matrix<Real> A(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	A(j, i * spatial_dimension + j) = 1;
	continue;
	}
	A(j, i * spatial_dimension + j) = -shapes[i - 1];
	}
	}

	// computing shape derivatives
	auto && shape_derivatives =
	ElementClassHelper<_ek_regular>::getDNDS(projection, type);

	Matrix<Real> Aj(spatial_dimension, spatial_dimension * nb_nodes_per_contact);

	auto construct_Aj = [&](auto && dnds) {
	for (auto i : arange(nb_nodes_per_contact)) {
	for (auto j : arange(spatial_dimension)) {
	if (i == 0) {
	Aj(j, i * spatial_dimension + j) = 0;
	continue;
	}
	Aj(j, i * spatial_dimension + j) = dnds(i - 1);
	}
	}
	};

	// tangents should have been calculated in normal modulii
	auto & tangents = model.getTangents();
	Matrix<Real> covariant_basis(
	tangents.begin(surface_dimension, spatial_dimension)[element.slave]);

	auto & tangential_tractions = model.getTangentialTractions();
	Vector<Real> tangential_traction(
	tangential_tractions.begin(surface_dimension)[element.slave]);

	// compute norm of trial traction
	Real traction_norm = 0;
	auto contravariant_metric_tensor =
	GeometryUtils::contravariantMetricTensor(covariant_basis);

	for (auto i : arange(surface_dimension)) {
	for (auto j : arange(surface_dimension)) {
	traction_norm += tangential_traction[i] * tangential_traction[j] *
	contravariant_metric_tensor(i, j);
	}
	}
	traction_norm = sqrt(traction_norm);

	// construct four parts of stick modulii (eq 107,107a-c)
	Matrix<Real> k_first(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_second(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_third(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);
	Matrix<Real> k_fourth(nb_nodes_per_contact * spatial_dimension,
	nb_nodes_per_contact * spatial_dimension);

	for (auto && values1 : enumerate(covariant_basis.transpose())) {
	auto & alpha = std::get<0>(values1);
	auto & tangent_alpha = std::get<1>(values1);

	Matrix<Real> mat_t_alpha(tangent_alpha.storage(), tangent_alpha.size(), 1.);

	Matrix<Real> t_outer_n(spatial_dimension, spatial_dimension);
	Matrix<Real> t_outer_t(spatial_dimension, spatial_dimension);

	for (auto && values2 :
	zip(arange(surface_dimension), covariant_basis.transpose(),
	shape_derivatives.transpose())) {
	auto & beta = std::get<0>(values2);
	auto & tangent_beta = std::get<1>(values2);
	auto & dnds = std::get<2>(values2);
	// construct Aj from shape function wrt to jth natural
	// coordinate
	construct_Aj(dnds);

	// eq 107
	Matrix<Real> mat_t_beta(tangent_beta.storage(), tangent_beta.size(), 1.);
	t_outer_n.mul<false, true>(mat_t_beta, mat_n);

	Matrix<Real> tmp(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp1(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp.mul<false, false>(t_outer_n, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_n mu * tangential_traction[alpha] *
	contravariant_metric_tensor(alpha, beta);
	tmp1 /= traction_norm;

	k_first += tmp1 * nodal_area;

	// eq 107a
	t_outer_t.mul<false, true>(mat_t_alpha, mat_t_beta);

	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_t mu * p_n * contravariant_metric_tensor(alpha, beta);
	tmp1 /= traction_norm;

	k_second += tmp1 * nodal_area;

	for (auto && values3 : enumerate(covariant_basis.transpose())) {
	auto & gamma = std::get<0>(values3);
	auto & tangent_gamma = std::get<1>(values3);

	Matrix<Real> mat_t_gamma(tangent_gamma.storage(), tangent_gamma.size(),
	1.);

	for (auto && values4 : enumerate(covariant_basis.transpose())) {
	auto & theta = std::get<0>(values4);
	auto & tangent_theta = std::get<1>(values4);

	Matrix<Real> mat_t_theta(tangent_theta.storage(),
	tangent_theta.size(), 1.);
	t_outer_t.mul<false, true>(mat_t_gamma, mat_t_theta);

	// eq 107b
	tmp.mul<false, false>(t_outer_t, A);
	tmp1.mul<true, false>(A, tmp);

	tmp1 = epsilon_t mu * p_n * tangential_traction[alpha] *
	tangential_traction[beta];
	tmp1 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);
	tmp1 /= pow(traction_norm, 3);

	k_third += tmp1 * nodal_area;

	// eq 107c
	tmp.mul<false, false>(t_outer_t, Aj);
	tmp1.mul<true, false>(A, tmp);
	tmp1 = contravariant_metric_tensor(alpha, theta)
	contravariant_metric_tensor(beta, gamma);
	tmp1 = mu p_n * tangential_traction[alpha];
	tmp1 /= traction_norm;

	Matrix<Real> tmp2(spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	Matrix<Real> tmp3(nb_nodes_per_contact * spatial_dimension,
	spatial_dimension * nb_nodes_per_contact);
	tmp2.mul<false, false>(t_outer_t, A);
	tmp3.mul<true, false>(Aj, tmp2);
	tmp3 = contravariant_metric_tensor(alpha, gamma)
	contravariant_metric_tensor(beta, theta);
	tmp3 = mu p_n * tangential_traction[alpha];
	tmp3 /= traction_norm;

	k_fourth += (tmp1 + tmp3) * nodal_area;
	}
	}
	}
	}

	stiffness += k_third + k_fourth - k_first - k_second;
	}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::beforeSolveStep() {}

	/* -------------------------------------------------------------------------- */
	void ResolutionPenaltyQuadratic::afterSolveStep(
	__attribute__((unused)) bool converged) {}

	INSTANTIATE_RESOLUTION(penalty_quadratic, ResolutionPenaltyQuadratic);

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.hh b/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.hh
	index 16756ed47..363bade8a 100644
	--- a/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.hh
	+++ b/src/model/contact_mechanics/resolutions/resolution_penalty_quadratic.hh
	@@ -1,125 +1,130 @@
	/**
	* @file resolution_penalty_quadratic.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Mon Aug 10 2020
	*
	* @brief Quadratic Penalty Resolution for Contact Mechanics Model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "resolution_penalty.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_RESOLUTION_PENALTY_QUADRATIC_HH__
	#define __AKANTU_RESOLUTION_PENALTY_QUADRATIC_HH__

	namespace akantu {

	class ResolutionPenaltyQuadratic : public ResolutionPenalty {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	private:
	using Parent = ResolutionPenalty;
	-
	+
	public:
	ResolutionPenaltyQuadratic(ContactMechanicsModel & model, const ID & id = "");

	~ResolutionPenaltyQuadratic() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize the resolution
	void initialize();

	-
	/* ------------------------------------------------------------------------ */
	/* Methods for stiffness computation */
	/* ------------------------------------------------------------------------ */
	protected:
	-
	/// local computaion of stiffness matrix due to stick state
	- void computeStickModuli(const ContactElement &, Matrix<Real> &);
	+ void computeStickModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/);

	- /// local computation of stiffness matrix due to slip state
	- void computeSlipModuli(const ContactElement &, Matrix<Real> &);
	+ /// local computation of stiffness matrix due to slip state
	+ void computeSlipModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/);

	/* ------------------------------------------------------------------------ */
	/* Methods for stiffness computation */
	/* ------------------------------------------------------------------------ */
	public:
	/// local computation of tangent moduli due to normal traction
	- void computeNormalModuli(const ContactElement &, Matrix<Real> &) override;
	-
	+ void computeNormalModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/) override;
	+
	/// local computation of tangent moduli due to tangential traction
	- void computeTangentialModuli(const ContactElement &, Matrix<Real> &) override;
	+ void computeTangentialModuli(const ContactElement & /element/,
	+ Matrix<Real> & /stiffness/) override;

	-
	/* ------------------------------------------------------------------------ */
	/* Methods for force computation */
	/* ------------------------------------------------------------------------ */
	public:
	/// local computation of normal force due to normal contact
	- void computeNormalForce(const ContactElement &, Vector<Real> &) override;
	-
	- /// local computation of tangential force due to frictional traction
	- void computeTangentialForce(const ContactElement &, Vector<Real> &) override;
	+ void computeNormalForce(const ContactElement & /element/,
	+ Vector<Real> & /force/) override;
	+
	+ /// local computation of tangential force due to frictional traction
	+ void computeTangentialForce(const ContactElement & /element/,
	+ Vector<Real> & /force/) override;

	protected:
	/// local computation of normal traction due to penetration
	- Real computeNormalTraction(Real &);
	-
	+ Real computeNormalTraction(Real & /gap/);
	+
	/// local computation of trial tangential traction due to friction
	- void computeTrialTangentialTraction(const ContactElement &, const Matrix<Real> &,
	- Vector<Real> &);
	+ void computeTrialTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction/);

	- /// local computation of tangential traction due to stick
	- void computeStickTangentialTraction(const ContactElement &, Vector<Real> &,
	- Vector<Real> &);
	+ /// local computation of tangential traction due to stick
	+ void computeStickTangentialTraction(const ContactElement & /unused/,
	+ Vector<Real> & /traction_trial/,
	+ Vector<Real> & /traction_tangential/);

	/// local computation of tangential traction due to slip
	- void computeSlipTangentialTraction(const ContactElement &, const Matrix<Real> &,
	- Vector<Real> &, Vector<Real> &);
	+ void computeSlipTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction_trial/,
	+ Vector<Real> & /traction_tangential/);

	/// local computation of tangential traction due to friction
	- void computeTangentialTraction(const ContactElement &, const Matrix<Real> &,
	- Vector<Real> &);
	+ void computeTangentialTraction(const ContactElement & /element/,
	+ const Matrix<Real> & /covariant_basis/,
	+ Vector<Real> & /traction_tangential/);

	public:
	-
	void beforeSolveStep() override;

	- void afterSolveStep(bool converged = true) override;
	+ void afterSolveStep(bool converged = true) override;
	};

	-} // akantu
	-
	-
	+} // namespace akantu

	#endif /* __AKANTU_RESOLUTION_PENALTY_QUADRATIC_HH__ */
	diff --git a/src/model/contact_mechanics/surface_selector.cc b/src/model/contact_mechanics/surface_selector.cc
	index 668c84d36..ec709e97b 100644
	--- a/src/model/contact_mechanics/surface_selector.cc
	+++ b/src/model/contact_mechanics/surface_selector.cc
	@@ -1,287 +1,223 @@
	/**
	* @file surface_selector.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 30 2019
	* @date last modification: Fri Sep 18 2020
	*
	* @brief Surface selector for contact detector
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "surface_selector.hh"
	-#include "model.hh"
	#include "geometry_utils.hh"
	+#include "model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SurfaceSelector::SurfaceSelector(Mesh & mesh)
	: Parsable(ParserType::_contact_detector), mesh(mesh) {}

	-
	/* -------------------------------------------------------------------------- */
	/**
	- * class that selects contact surface from physical names
	+ * class that selects contact surface from physical names
	*/
	PhysicalSurfaceSelector::PhysicalSurfaceSelector(Mesh & mesh)
	: SurfaceSelector(mesh) {

	const Parser & parser = getStaticParser();

	const ParserSection & section =
	*(parser.getSubSections(ParserType::_contact_detector).first);
	-
	+
	master = section.getParameterValue<std::string>("master");
	slave = section.getParameterValue<std::string>("slave");

	UInt surface_dimension = mesh.getSpatialDimension() - 1;
	- auto & group = mesh.createElementGroup("contact_surface",
	- surface_dimension);
	+ auto & group = mesh.createElementGroup("contact_surface", surface_dimension);
	group.append(mesh.getElementGroup(master));
	group.append(mesh.getElementGroup(slave));

	group.optimize();
	}

	/* -------------------------------------------------------------------------- */
	Array<UInt> & PhysicalSurfaceSelector::getMasterList() {
	return mesh.getElementGroup(master).getNodeGroup().getNodes();
	}

	/* -------------------------------------------------------------------------- */
	Array<UInt> & PhysicalSurfaceSelector::getSlaveList() {
	return mesh.getElementGroup(slave).getNodeGroup().getNodes();
	}

	-
	/* -------------------------------------------------------------------------- */
	/**
	* class that selects contact surface from cohesive elements
	*/
	#if defined(AKANTU_COHESIVE_ELEMENT)
	/* -------------------------------------------------------------------------- */
	CohesiveSurfaceSelector::CohesiveSurfaceSelector(Mesh & mesh)
	: SurfaceSelector(mesh), mesh_facets(mesh.getMeshFacets()) {
	this->mesh.registerEventHandler(*this, _ehp_lowest);

	UInt surface_dimension = mesh.getSpatialDimension() - 1;
	- mesh_facets.createElementGroup("contact_surface",
	- surface_dimension, true);
	-
	+ mesh_facets.createElementGroup("contact_surface", surface_dimension, true);
	}

	/* -------------------------------------------------------------------------- */
	-void CohesiveSurfaceSelector::onElementsAdded(const Array<Element> & element_list,
	- __attribute__((unused)) const NewElementsEvent & event) {
	-
	+void CohesiveSurfaceSelector::onElementsAdded(
	+ const Array<Element> & element_list,
	+ __attribute__((unused)) const NewElementsEvent & event) {
	+
	auto & group = mesh_facets.getElementGroup("contact_surface");
	-
	- for(auto elem : element_list) {
	- if(elem.kind() != _ek_cohesive)
	+
	+ for (auto elem : element_list) {
	+ if (elem.kind() != _ek_cohesive) {
	continue;
	+ }

	const auto & subelement_to_element =
	- mesh_facets.getSubelementToElement(elem.type);
	-
	+ mesh_facets.getSubelementToElement(elem.type);
	+
	auto && facets = Vector<Element>(
	- make_view(subelement_to_element,
	- subelement_to_element.getNbComponent())
	- .begin()[elem.element]);
	+ make_view(subelement_to_element, subelement_to_element.getNbComponent())
	+ .begin()[elem.element]);

	-
	- for(auto facet : facets) {
	+ for (auto facet : facets) {
	group.add(facet, true);
	}
	}

	group.optimize();
	}
	-
	+
	/* -------------------------------------------------------------------------- */
	-void CohesiveSurfaceSelector::onNodesAdded(__attribute__((unused)) const Array<UInt> & new_nodes,
	+void CohesiveSurfaceSelector::onNodesAdded(const Array<UInt> & /nodes_list/,
	const NewNodesEvent & event) {

	- if (not aka::is_of_type<CohesiveNewNodesEvent>(event))
	+ if (not aka::is_of_type<CohesiveNewNodesEvent>(event)) {
	return;
	-
	- /*const auto & cohesive_event = aka::as_type<CohesiveNewNodesEvent>(event);
	- const auto & old_nodes = cohesive_event.getOldNodesList();
	-
	- UInt nb_new_nodes = new_nodes.size();
	- UInt nb_old_nodes = old_nodes.size();
	-
	- for (auto n : arange(nb_new_nodes)) {
	- new_nodes_list.push_back(new_nodes(n));
	}

	- for (auto n : arange(nb_old_nodes)) {
	- new_nodes_list.push_back(old_nodes(n));
	- }*/
	-
	mesh_facets.fillNodesToElements(mesh.getSpatialDimension() - 1);
	-
	- /*UInt surface_dimension = mesh.getSpatialDimension() - 1;
	- auto & group = mesh_facets.createElementGroup("contact_surface",
	- surface_dimension, true);
	-
	- for (auto node : new_nodes_list) {
	- Array<Element> all_elements;
	- mesh_facets.getAssociatedElements(node, all_elements);
	-
	- Array<Element> mesh_facet_elements;
	- this->filterBoundaryElements(all_elements, mesh_facet_elements);
	-
	- for (auto nb_elem : arange(mesh_facet_elements.size()))
	- group.add(mesh_facet_elements[nb_elem], true);
	- }
	- group.optimize();*/
	-
	-
	}

	-/* -------------------------------------------------------------------------- */
	-//void CohesiveSurfaceSelector::filterBoundaryElements(
	-// Array<Element> & subelements, Array<Element> & boundary_elements) {
	-
	-// for (auto subelem : subelements) {
	-// if(GeometryUtils::isBoundaryElement(mesh_facets, subelem))
	-// boundary_elements.push_back(subelem);
	-// }
	-//}
	-
	/* -------------------------------------------------------------------------- */
	Array<UInt> & CohesiveSurfaceSelector::getMasterList() {
	- return mesh_facets.getElementGroup("contact_surface").getNodeGroup().getNodes();
	+ return mesh_facets.getElementGroup("contact_surface")
	+ .getNodeGroup()
	+ .getNodes();
	}

	/* -------------------------------------------------------------------------- */
	Array<UInt> & CohesiveSurfaceSelector::getSlaveList() {
	- return mesh_facets.getElementGroup("contact_surface").getNodeGroup().getNodes();
	+ return mesh_facets.getElementGroup("contact_surface")
	+ .getNodeGroup()
	+ .getNodes();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* class that selects contact surface from both cohesive elements and
	* physical names
	*/
	AllSurfaceSelector::AllSurfaceSelector(Mesh & mesh)
	: SurfaceSelector(mesh), mesh_facets(mesh.getMeshFacets()) {
	this->mesh.registerEventHandler(*this, _ehp_lowest);

	const Parser & parser = getStaticParser();

	const ParserSection & section =
	*(parser.getSubSections(ParserType::_contact_detector).first);

	master = section.getParameterValue<std::string>("master");
	slave = section.getParameterValue<std::string>("slave");

	UInt surface_dimension = this->mesh.getSpatialDimension() - 1;
	- auto & group = mesh_facets.createElementGroup("contact_surface",
	- surface_dimension);
	+ auto & group =
	+ mesh_facets.createElementGroup("contact_surface", surface_dimension);
	group.append(mesh_facets.getElementGroup(master));
	group.append(mesh_facets.getElementGroup(slave));

	group.optimize();
	}

	/* -------------------------------------------------------------------------- */
	void AllSurfaceSelector::onElementsAdded(const Array<Element> & element_list,
	- __attribute__((unused)) const NewElementsEvent & event) {
	-
	+ __attribute__((unused))
	+ const NewElementsEvent & event) {
	+
	auto & group = mesh_facets.getElementGroup("contact_surface");

	- for(auto elem : element_list) {
	- if(elem.kind() != _ek_cohesive)
	+ for (auto elem : element_list) {
	+ if (elem.kind() != _ek_cohesive) {
	continue;
	+ }

	const auto & subelement_to_element =
	- mesh_facets.getSubelementToElement(elem.type);
	-
	+ mesh_facets.getSubelementToElement(elem.type);
	+
	auto && facets = Vector<Element>(
	- make_view(subelement_to_element,
	- subelement_to_element.getNbComponent()).begin()[elem.element]);
	-
	- for(auto facet : facets) {
	+ make_view(subelement_to_element, subelement_to_element.getNbComponent())
	+ .begin()[elem.element]);
	+
	+ for (auto facet : facets) {
	group.add(facet, true);
	}
	}

	group.optimize();
	-}
	+}

	/* -------------------------------------------------------------------------- */
	-void AllSurfaceSelector::onNodesAdded(__attribute__((unused)) const Array<UInt> & new_nodes,
	- const NewNodesEvent & event) {
	+void AllSurfaceSelector::onNodesAdded(const Array<UInt> & /* nodes_list */,
	+ const NewNodesEvent & event) {

	- if (not aka::is_of_type<CohesiveNewNodesEvent>(event))
	+ if (not aka::is_of_type<CohesiveNewNodesEvent>(event)) {
	return;
	-
	- /*const auto & cohesive_event = aka::as_type<CohesiveNewNodesEvent>(event);
	- const auto & old_nodes = cohesive_event.getOldNodesList();
	-
	- UInt nb_new_nodes = new_nodes.size();
	- UInt nb_old_nodes = old_nodes.size();
	-
	- for (auto n : arange(nb_new_nodes)) {
	- new_nodes_list.push_back(new_nodes(n));
	}

	- for (auto n : arange(nb_old_nodes)) {
	- new_nodes_list.push_back(old_nodes(n));
	- }*/
	-
	mesh_facets.fillNodesToElements(mesh.getSpatialDimension() - 1);
	-
	- /*auto & group = mesh_facets.getElementGroup("contact_surface");
	-
	- for (auto node : new_nodes_list) {
	- Array<Element> all_elements;
	- mesh_facets.getAssociatedElements(node, all_elements);
	-
	- Array<Element> mesh_facet_elements;
	- this->filterBoundaryElements(all_elements, mesh_facet_elements);
	-
	- for (auto nb_elem : arange(mesh_facet_elements.size()))
	- group.add(mesh_facet_elements[nb_elem], true);
	- }
	-
	- group.optimize();*/
	}

	/* -------------------------------------------------------------------------- */
	Array<UInt> & AllSurfaceSelector::getMasterList() {
	- return mesh_facets.getElementGroup("contact_surface").getNodeGroup().getNodes();
	+ return mesh_facets.getElementGroup("contact_surface")
	+ .getNodeGroup()
	+ .getNodes();
	}

	/* -------------------------------------------------------------------------- */
	Array<UInt> & AllSurfaceSelector::getSlaveList() {
	- return mesh_facets.getElementGroup("contact_surface").getNodeGroup().getNodes();
	+ return mesh_facets.getElementGroup("contact_surface")
	+ .getNodeGroup()
	+ .getNodes();
	}

	#endif

	} // namespace akantu
	diff --git a/src/model/contact_mechanics/surface_selector.hh b/src/model/contact_mechanics/surface_selector.hh
	index e16759b32..cef245726 100644
	--- a/src/model/contact_mechanics/surface_selector.hh
	+++ b/src/model/contact_mechanics/surface_selector.hh
	@@ -1,150 +1,150 @@
	/**
	* @file surface_selector.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 30 2019
	* @date last modification: Sun Jun 06 2021
	*
	* @brief Node selectors for contact detection
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	#include "mesh_utils.hh"
	#include "parsable.hh"
	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "cohesive_element_inserter.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_SURFACE_SELECTOR_HH__
	#define __AKANTU_SURFACE_SELECTOR_HH__

	namespace akantu {
	class Model;
	class GlobalIdsUpdater;
	} // namespace akantu

	namespace akantu {

	/**
	* main class to assign surfaces for contact detection
	*/
	class SurfaceSelector : public MeshEventHandler, public Parsable {
	public:
	SurfaceSelector(Mesh & mesh);
	- virtual ~SurfaceSelector() = default;
	+ ~SurfaceSelector() override = default;

	public:
	- virtual Array<UInt> & getMasterList() { AKANTU_TO_IMPLEMENT();}
	- virtual Array<UInt> & getSlaveList() { AKANTU_TO_IMPLEMENT();}
	+ virtual Array<UInt> & getMasterList() { AKANTU_TO_IMPLEMENT(); }
	+ virtual Array<UInt> & getSlaveList() { AKANTU_TO_IMPLEMENT(); }

	protected:
	Mesh & mesh;
	};

	/* -------------------------------------------------------------------------- */
	/**
	- * class that selects contact surface from physical names
	+ * class that selects contact surface from physical names
	*/
	class PhysicalSurfaceSelector : public SurfaceSelector {
	public:
	PhysicalSurfaceSelector(Mesh & mesh);

	public:
	Array<UInt> & getMasterList() override;
	Array<UInt> & getSlaveList() override;

	protected:
	std::string master;
	std::string slave;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class that selects contact surface from cohesive elements
	*/
	#if defined(AKANTU_COHESIVE_ELEMENT)
	class CohesiveSurfaceSelector : public SurfaceSelector {
	public:
	CohesiveSurfaceSelector(Mesh & mesh);

	protected:
	void onElementsAdded(const Array<Element> & element_list,
	- const NewElementsEvent & event) override;
	-
	+ const NewElementsEvent & event) override;
	+
	void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) override;

	public:
	Array<UInt> & getMasterList() override;
	Array<UInt> & getSlaveList() override;

	AKANTU_GET_MACRO_NOT_CONST(NewNodesList, new_nodes_list, Array<UInt> &);
	AKANTU_GET_MACRO(NewNodesList, new_nodes_list, const Array<UInt> &);

	protected:
	Mesh & mesh_facets;
	Array<UInt> new_nodes_list;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class that selects contact surface from both cohesive elements and
	* physical names
	*/
	-class AllSurfaceSelector : public SurfaceSelector {
	+class AllSurfaceSelector : public SurfaceSelector {
	public:
	AllSurfaceSelector(Mesh & mesh);

	protected:
	void onElementsAdded(const Array<Element> & element_list,
	- const NewElementsEvent & event) override;
	-
	+ const NewElementsEvent & event) override;
	+
	void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) override;

	public:
	Array<UInt> & getMasterList() override;

	Array<UInt> & getSlaveList() override;

	AKANTU_GET_MACRO_NOT_CONST(NewNodesList, new_nodes_list, Array<UInt> &);
	AKANTU_GET_MACRO(NewNodesList, new_nodes_list, const Array<UInt> &);

	protected:
	std::string master;
	std::string slave;
	Mesh & mesh_facets;
	Array<UInt> new_nodes_list;
	};

	#endif

	} // namespace akantu

	#endif /* __AKANTU_SURFACE_SELECTOR_HH__ */
	diff --git a/src/model/heat_transfer/heat_transfer_model.cc b/src/model/heat_transfer/heat_transfer_model.cc
	index 87856f4ba..f282187b1 100644
	--- a/src/model/heat_transfer/heat_transfer_model.cc
	+++ b/src/model/heat_transfer/heat_transfer_model.cc
	@@ -1,919 +1,919 @@
	/**
	* @file heat_transfer_model.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Srinivasa Babu Ramisetti <srinivasa.ramisetti@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Rui Wang <rui.wang@epfl.ch>
	*
	* @date creation: Sun May 01 2011
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of HeatTransferModel class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "heat_transfer_model.hh"
	#include "dumpable_inline_impl.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "generalized_trapezoidal.hh"
	#include "group_manager_inline_impl.hh"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "parser.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_element_partition.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	namespace heat_transfer {
	namespace details {
	class ComputeRhoFunctor {
	public:
	ComputeRhoFunctor(const HeatTransferModel & model) : model(model){};

	void operator()(Matrix<Real> & rho, const Element & /unused/) {
	rho.set(model.getCapacity() * model.getDensity());
	}

	private:
	const HeatTransferModel & model;
	};
	} // namespace details
	} // namespace heat_transfer

	/* -------------------------------------------------------------------------- */
	HeatTransferModel::HeatTransferModel(Mesh & mesh, UInt dim, const ID & id,
	std::shared_ptr<DOFManager> dof_manager)
	: Model(mesh, ModelType::_heat_transfer_model, dof_manager, dim, id),
	temperature_gradient("temperature_gradient", id),
	temperature_on_qpoints("temperature_on_qpoints", id),
	conductivity_on_qpoints("conductivity_on_qpoints", id),
	k_gradt_on_qpoints("k_gradt_on_qpoints", id) {
	AKANTU_DEBUG_IN();

	conductivity = Matrix<Real>(this->spatial_dimension, this->spatial_dimension);

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer,
	SynchronizationTag::_htm_temperature);
	this->registerSynchronizer(synchronizer,
	SynchronizationTag::_htm_gradient_temperature);
	}

	registerFEEngineObject<FEEngineType>(id + ":fem", mesh, spatial_dimension);

	#ifdef AKANTU_USE_IOHELPER
	this->mesh.registerDumper<DumperParaview>("heat_transfer", id, true);
	this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_regular);
	#endif

	this->registerParam("conductivity", conductivity, _pat_parsmod);
	this->registerParam("conductivity_variation", conductivity_variation, 0.,
	_pat_parsmod);
	this->registerParam("temperature_reference", T_ref, 0., _pat_parsmod);
	this->registerParam("capacity", capacity, _pat_parsmod);
	this->registerParam("density", density, _pat_parsmod);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::initModel() {
	auto & fem = this->getFEEngine();
	fem.initShapeFunctions(_not_ghost);
	fem.initShapeFunctions(_ghost);

	temperature_on_qpoints.initialize(fem, _nb_component = 1);
	temperature_gradient.initialize(fem, _nb_component = spatial_dimension);
	conductivity_on_qpoints.initialize(fem, _nb_component = spatial_dimension *
	spatial_dimension);
	k_gradt_on_qpoints.initialize(fem, _nb_component = spatial_dimension);
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & HeatTransferModel::getFEEngineBoundary(const ID & name) {
	return aka::as_type<FEEngine>(getFEEngineClassBoundary<FEEngineType>(name));
	}

	/* -------------------------------------------------------------------------- */
	HeatTransferModel::~HeatTransferModel() = default;

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleCapacityLumped(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem = getFEEngineClass<FEEngineType>();
	heat_transfer::details::ComputeRhoFunctor compute_rho(*this);

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldLumped(compute_rho, "M", "temperature",
	this->getDOFManager(), type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MatrixType HeatTransferModel::getMatrixType(const ID & matrix_id) {
	if (matrix_id == "K" or matrix_id == "M") {
	return _symmetric;
	}

	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleMatrix(const ID & matrix_id) {
	if (matrix_id == "K") {
	this->assembleConductivityMatrix();
	} else if (matrix_id == "M" and need_to_reassemble_capacity) {
	this->assembleCapacity();
	}
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleLumpedMatrix(const ID & matrix_id) {
	if (matrix_id == "M" and need_to_reassemble_capacity) {
	this->assembleCapacityLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	this->assembleInternalHeatRate();

	this->getDOFManager().assembleToResidual("temperature",
	*this->external_heat_rate, 1);
	this->getDOFManager().assembleToResidual("temperature",
	*this->internal_heat_rate, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::predictor() { ++temperature_release; }

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleCapacityLumped() {
	AKANTU_DEBUG_IN();

	if (!this->getDOFManager().hasLumpedMatrix("M")) {
	this->getDOFManager().getNewLumpedMatrix("M");
	}

	this->getDOFManager().zeroLumpedMatrix("M");

	assembleCapacityLumped(_not_ghost);
	assembleCapacityLumped(_ghost);

	need_to_reassemble_capacity_lumped = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType /unused/) {
	DOFManager & dof_manager = this->getDOFManager();

	this->allocNodalField(this->temperature, 1, "temperature");
	this->allocNodalField(this->external_heat_rate, 1, "external_heat_rate");
	this->allocNodalField(this->internal_heat_rate, 1, "internal_heat_rate");
	this->allocNodalField(this->blocked_dofs, 1, "blocked_dofs");

	if (!dof_manager.hasDOFs("temperature")) {
	dof_manager.registerDOFs("temperature", *this->temperature, _dst_nodal);
	dof_manager.registerBlockedDOFs("temperature", *this->blocked_dofs);
	}

	if (time_step_solver_type == TimeStepSolverType::_dynamic \|\|
	time_step_solver_type == TimeStepSolverType::_dynamic_lumped) {
	this->allocNodalField(this->temperature_rate, 1, "temperature_rate");

	if (!dof_manager.hasDOFsDerivatives("temperature", 1)) {
	dof_manager.registerDOFsDerivative("temperature", 1,
	*this->temperature_rate);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	HeatTransferModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions HeatTransferModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["temperature"] =
	IntegrationSchemeType::_forward_euler;
	options.solution_type["temperature"] = IntegrationScheme::_temperature_rate;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["temperature"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["temperature"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	if (this->method == _explicit_consistent_mass) {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["temperature"] =
	IntegrationSchemeType::_forward_euler;
	options.solution_type["temperature"] =
	IntegrationScheme::_temperature_rate;
	} else {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["temperature"] =
	IntegrationSchemeType::_backward_euler;
	options.solution_type["temperature"] = IntegrationScheme::_temperature;
	}
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleConductivityMatrix() {
	AKANTU_DEBUG_IN();

	this->computeConductivityOnQuadPoints(_not_ghost);

	if (conductivity_release[_not_ghost] == conductivity_matrix_release) {
	return;
	}

	AKANTU_DEBUG_ASSERT(this->getDOFManager().hasMatrix("K"),
	"The K matrix has not been initialized yet.");

	this->getDOFManager().zeroMatrix("K");

	auto & fem = this->getFEEngine();

	for (auto && type : mesh.elementTypes(spatial_dimension)) {
	auto nb_element = mesh.getNbElement(type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type);

	auto bt_d_b = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "B^tDB");

	fem.computeBtDB(conductivity_on_qpoints(type), *bt_d_b, 2, type);

	/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
	auto K_e = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_e");

	fem.integrate(bt_d_b, K_e, nb_nodes_per_element * nb_nodes_per_element,
	type);

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "temperature", *K_e, type, _not_ghost, _symmetric);
	}

	conductivity_matrix_release = conductivity_release[_not_ghost];

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::computeConductivityOnQuadPoints(GhostType ghost_type) {
	// if already computed once check if need to compute
	if (not initial_conductivity[ghost_type]) {
	// if temperature did not change, conductivity will not vary
	if (temperature_release == conductivity_release[ghost_type]) {
	return;
	}
	// if conductivity_variation is 0 no need to recompute
	if (conductivity_variation == 0.) {
	return;
	}
	}

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	auto & temperature_interpolated = temperature_on_qpoints(type, ghost_type);

	// compute the temperature on quadrature points
	this->getFEEngine().interpolateOnIntegrationPoints(
	*temperature, temperature_interpolated, 1, type, ghost_type);

	auto & cond = conductivity_on_qpoints(type, ghost_type);
	for (auto && tuple :
	zip(make_view(cond, spatial_dimension, spatial_dimension),
	temperature_interpolated)) {
	auto & C = std::get<0>(tuple);
	auto & T = std::get<1>(tuple);
	C = conductivity;

	Matrix<Real> variation(spatial_dimension, spatial_dimension,
	conductivity_variation * (T - T_ref));
	// @TODO: Guillaume are you sure ? why due you compute variation then ?
	C += conductivity_variation;
	}
	}

	conductivity_release[ghost_type] = temperature_release;
	initial_conductivity[ghost_type] = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::computeKgradT(GhostType ghost_type) {
	computeConductivityOnQuadPoints(ghost_type);

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	auto & gradient = temperature_gradient(type, ghost_type);
	this->getFEEngine().gradientOnIntegrationPoints(*temperature, gradient, 1,
	type, ghost_type);

	for (auto && values :
	zip(make_view(conductivity_on_qpoints(type, ghost_type),
	spatial_dimension, spatial_dimension),
	make_view(gradient, spatial_dimension),
	make_view(k_gradt_on_qpoints(type, ghost_type),
	spatial_dimension))) {
	const auto & C = std::get<0>(values);
	const auto & BT = std::get<1>(values);
	auto & k_BT = std::get<2>(values);

	k_BT.mul<false>(C, BT);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleInternalHeatRate() {
	AKANTU_DEBUG_IN();

	this->internal_heat_rate->zero();

	this->synchronize(SynchronizationTag::_htm_temperature);
	auto & fem = this->getFEEngine();

	for (auto ghost_type : ghost_types) {
	// compute k \grad T
	computeKgradT(ghost_type);

	for (auto type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto & k_gradt_on_qpoints_vect = k_gradt_on_qpoints(type, ghost_type);

	UInt nb_quad_points = k_gradt_on_qpoints_vect.size();
	Array<Real> bt_k_gT(nb_quad_points, nb_nodes_per_element);
	fem.computeBtD(k_gradt_on_qpoints_vect, bt_k_gT, type, ghost_type);

	UInt nb_elements = mesh.getNbElement(type, ghost_type);
	Array<Real> int_bt_k_gT(nb_elements, nb_nodes_per_element);

	fem.integrate(bt_k_gT, int_bt_k_gT, nb_nodes_per_element, type,
	ghost_type);

	this->getDOFManager().assembleElementalArrayLocalArray(
	int_bt_k_gT, *this->internal_heat_rate, type, ghost_type, -1);
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::getStableTimeStep() {
	AKANTU_DEBUG_IN();

	Real el_size;
	Real min_el_size = std::numeric_limits<Real>::max();
	Real conductivitymax = conductivity(0, 0);

	// get the biggest parameter from k11 until k33//
	for (UInt i = 0; i < spatial_dimension; i++) {
	for (UInt j = 0; j < spatial_dimension; j++) {
	conductivitymax = std::max(conductivity(i, j), conductivitymax);
	}
	}
	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	Array<Real> coord(0, nb_nodes_per_element * spatial_dimension);
	FEEngine::extractNodalToElementField(mesh, mesh.getNodes(), coord, type,
	_not_ghost);

	auto el_coord = coord.begin(spatial_dimension, nb_nodes_per_element);
	UInt nb_element = mesh.getNbElement(type);

	for (UInt el = 0; el < nb_element; ++el, ++el_coord) {
	el_size = getFEEngine().getElementInradius(*el_coord, type);
	min_el_size = std::min(min_el_size, el_size);
	}

	AKANTU_DEBUG_INFO("The minimum element size : "
	<< min_el_size
	<< " and the max conductivity is : " << conductivitymax);
	}

	Real min_dt = 2. * min_el_size * min_el_size / 4. * density * capacity /
	conductivitymax;

	mesh.getCommunicator().allReduce(min_dt, SynchronizerOperation::_min);

	AKANTU_DEBUG_OUT();

	return min_dt;
	}
	/* -------------------------------------------------------------------------- */

	void HeatTransferModel::setTimeStep(Real time_step, const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper("heat_transfer").setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::readMaterials() {
	auto sect = this->getParserSection();

	if (not std::get<1>(sect)) {
	const auto & section = std::get<0>(sect);
	this->parseSection(section);
	}

	conductivity_on_qpoints.set(conductivity);
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::initFullImpl(const ModelOptions & options) {
	Model::initFullImpl(options);

	readMaterials();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::assembleCapacity() {
	AKANTU_DEBUG_IN();
	auto ghost_type = _not_ghost;

	this->getDOFManager().zeroMatrix("M");

	auto & fem = getFEEngineClass<FEEngineType>();

	heat_transfer::details::ComputeRhoFunctor rho_functor(*this);

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldMatrix(rho_functor, "M", "temperature",
	this->getDOFManager(), type, ghost_type);
	}

	need_to_reassemble_capacity = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void HeatTransferModel::computeRho(Array<Real> & rho, ElementType type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	FEEngine & fem = this->getFEEngine();
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	rho.resize(nb_element * nb_quadrature_points);
	rho.set(this->capacity);

	// Real * rho_1_val = rho.storage();
	// /// compute @f$ rho @f$ for each nodes of each element
	// for (UInt el = 0; el < nb_element; ++el) {
	// for (UInt n = 0; n < nb_quadrature_points; ++n) {
	// *rho_1_val++ = this->capacity;
	// }
	// }

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::computeThermalEnergyByNode() {
	AKANTU_DEBUG_IN();

	Real ethermal = 0.;

	for (auto && pair : enumerate(make_view(
	*internal_heat_rate, internal_heat_rate->getNbComponent()))) {
	auto n = std::get<0>(pair);
	auto & heat_rate = std::get<1>(pair);

	Real heat = 0.;
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	bool count_node = is_local_node;

	for (UInt i = 0; i < heat_rate.size(); ++i) {
	if (count_node) {
	heat += heat_rate[i] * time_step;
	}
	}
	ethermal += heat;
	}

	mesh.getCommunicator().allReduce(ethermal, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return ethermal;
	}

	/* -------------------------------------------------------------------------- */
	template <class iterator>
	void HeatTransferModel::getThermalEnergy(
	iterator Eth, Array<Real>::const_iterator<Real> T_it,
	const Array<Real>::const_iterator<Real> & T_end) const {
	for (; T_it != T_end; ++T_it, ++Eth) {
	Eth = capacity density * *T_it;
	}
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::getThermalEnergy(ElementType type, UInt index) {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
	Vector<Real> Eth_on_quarature_points(nb_quadrature_points);

	auto T_it = this->temperature_on_qpoints(type).begin();
	T_it += index * nb_quadrature_points;

	auto T_end = T_it + nb_quadrature_points;

	getThermalEnergy(Eth_on_quarature_points.storage(), T_it, T_end);

	return getFEEngine().integrate(Eth_on_quarature_points, type, index);
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::getThermalEnergy() {
	Real Eth = 0;

	auto & fem = getFEEngine();

	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {
	auto nb_element = mesh.getNbElement(type, _not_ghost);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, _not_ghost);
	Array<Real> Eth_per_quad(nb_element * nb_quadrature_points, 1);

	auto & temperature_interpolated = temperature_on_qpoints(type);

	// compute the temperature on quadrature points
	this->getFEEngine().interpolateOnIntegrationPoints(
	*temperature, temperature_interpolated, 1, type);

	auto T_it = temperature_interpolated.begin();
	auto T_end = temperature_interpolated.end();
	getThermalEnergy(Eth_per_quad.begin(), T_it, T_end);

	Eth += fem.integrate(Eth_per_quad, type);
	}

	return Eth;
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::getEnergy(const std::string & id) {
	AKANTU_DEBUG_IN();
	Real energy = 0;

	if (id == "thermal") {
	energy = getThermalEnergy();
	}
	// reduction sum over all processors
	mesh.getCommunicator().allReduce(energy, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	Real HeatTransferModel::getEnergy(const std::string & id, ElementType type,
	UInt index) {
	AKANTU_DEBUG_IN();

	Real energy = 0.;

	if (id == "thermal") {
	energy = getThermalEnergy(type, index);
	}

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	std::shared_ptr<dumpers::Field> HeatTransferModel::createNodalFieldBool(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs.get();

	auto field = mesh.createNodalField(uint_nodal_fields[field_name], group_name);
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> HeatTransferModel::createNodalFieldReal(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	if (field_name == "capacity_lumped") {
	AKANTU_EXCEPTION(
	"Capacity lumped is a nodal field now stored in the DOF manager."
	"Therefore it cannot be used by a dumper anymore");
	}

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["temperature"] = temperature.get();
	real_nodal_fields["temperature_rate"] = temperature_rate.get();
	real_nodal_fields["external_heat_rate"] = external_heat_rate.get();
	real_nodal_fields["internal_heat_rate"] = internal_heat_rate.get();
	real_nodal_fields["increment"] = increment.get();

	std::shared_ptr<dumpers::Field> field =
	mesh.createNodalField(real_nodal_fields[field_name], group_name);

	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> HeatTransferModel::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool /padding_flag/, UInt /spatial_dimension/,
	ElementKind element_kind) {

	std::shared_ptr<dumpers::Field> field;

	if (field_name == "partitions") {
	field = mesh.createElementalField<UInt, dumpers::ElementPartitionField>(
	mesh.getConnectivities(), group_name, this->spatial_dimension,
	element_kind);
	} else if (field_name == "temperature_gradient") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(temperature_gradient);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	temperature_gradient, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);
	} else if (field_name == "conductivity") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(conductivity_on_qpoints);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	conductivity_on_qpoints, group_name, this->spatial_dimension,
	element_kind, nb_data_per_elem);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> HeatTransferModel::createElementalField(
	const std::string & /* field_name/, const std::string & /group_name*/,
	bool /padding_flag/, ElementKind /element_kind/) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	HeatTransferModel::createNodalFieldBool(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	HeatTransferModel::createNodalFieldReal(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	inline UInt HeatTransferModel::getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes = indexes.size();

	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	size += nb_nodes * sizeof(Real);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void HeatTransferModel::packData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	buffer << (*temperature)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline void HeatTransferModel::unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	buffer >> (*temperature)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt HeatTransferModel::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes_per_element = 0;
	Array<Element>::const_iterator<Element> it = elements.begin();
	Array<Element>::const_iterator<Element> end = elements.end();
	for (; it != end; ++it) {
	const Element & el = *it;
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	size += nb_nodes_per_element * sizeof(Real); // temperature
	break;
	}
	case SynchronizationTag::_htm_gradient_temperature: {
	// temperature gradient
	size += getNbIntegrationPoints(elements) * spatial_dimension * sizeof(Real);
	size += nb_nodes_per_element * sizeof(Real); // nodal temperatures
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void HeatTransferModel::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	packNodalDataHelper(*temperature, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_htm_gradient_temperature: {
	packElementalDataHelper(temperature_gradient, buffer, elements, true,
	getFEEngine());
	packNodalDataHelper(*temperature, buffer, elements, mesh);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void HeatTransferModel::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	switch (tag) {
	case SynchronizationTag::_htm_temperature: {
	unpackNodalDataHelper(*temperature, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_htm_gradient_temperature: {
	unpackElementalDataHelper(temperature_gradient, buffer, elements, true,
	getFEEngine());
	unpackNodalDataHelper(*temperature, buffer, elements, mesh);

	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/model/heat_transfer/heat_transfer_model.hh b/src/model/heat_transfer/heat_transfer_model.hh
	index ec41cbc8b..925f26428 100644
	--- a/src/model/heat_transfer/heat_transfer_model.hh
	+++ b/src/model/heat_transfer/heat_transfer_model.hh
	@@ -1,316 +1,316 @@
	/**
	* @file heat_transfer_model.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Srinivasa Babu Ramisetti <srinivasa.ramisetti@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Rui Wang <rui.wang@epfl.ch>
	*
	* @date creation: Sun May 01 2011
	* @date last modification: Mon Mar 15 2021
	*
	* @brief Model of Heat Transfer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	#include "model.hh"
	/* -------------------------------------------------------------------------- */
	#include <array>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_HEAT_TRANSFER_MODEL_HH_
	#define AKANTU_HEAT_TRANSFER_MODEL_HH_

	namespace akantu {
	template <ElementKind kind, class IntegrationOrderFunctor>
	class IntegratorGauss;
	template <ElementKind kind> class ShapeLagrange;
	} // namespace akantu

	namespace akantu {

	class HeatTransferModel : public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using FEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	HeatTransferModel(Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "heat_transfer_model",
	std::shared_ptr<DOFManager> dof_manager = nullptr);

	~HeatTransferModel() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// generic function to initialize everything ready for explicit dynamics
	void initFullImpl(const ModelOptions & options) override;

	/// read one material file to instantiate all the materials
	void readMaterials();

	/// allocate all vectors
	void initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type) override;

	/// initialize the model
	void initModel() override;

	void predictor() override;

	/// compute the heat flux
	void assembleResidual() override;

	/// get the type of matrix needed
	MatrixType getMatrixType(const ID & matrix_id) override;

	/// callback to assemble a Matrix
	void assembleMatrix(const ID & matrix_id) override;

	/// callback to assemble a lumped Matrix
	void assembleLumpedMatrix(const ID & matrix_id) override;

	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;
	/* ------------------------------------------------------------------------ */
	/* Methods for explicit */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute and get the stable time step
	Real getStableTimeStep();

	/// set the stable timestep
	void setTimeStep(Real time_step, const ID & solver_id = "") override;

	// temporary protection to prevent bad usage: should check for bug
	protected:
	/// compute the internal heat flux \todo Need code review: currently not
	/// public method
	void assembleInternalHeatRate();

	public:
	/// calculate the lumped capacity vector for heat transfer problem
	void assembleCapacityLumped();

	public:
	/// assemble the conductivity matrix
	void assembleConductivityMatrix();

	/// assemble the conductivity matrix
	void assembleCapacity();

	/// compute the capacity on quadrature points
	void computeRho(Array<Real> & rho, ElementType type, GhostType ghost_type);

	private:
	/// calculate the lumped capacity vector for heat transfer problem (w
	/// ghost type)
	void assembleCapacityLumped(GhostType ghost_type);

	/// compute the conductivity tensor for each quadrature point in an array
	void computeConductivityOnQuadPoints(GhostType ghost_type);

	/// compute vector \f[k \grad T\f] for each quadrature point
	void computeKgradT(GhostType ghost_type);

	/// compute the thermal energy
	Real computeThermalEnergyByNode();

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;
	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;
	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	inline UInt getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const override;
	inline void packData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) const override;
	inline void unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createElementalField(const std::string & field_name,
	const std::string & group_name, bool padding_flag,
	UInt spatial_dimension, ElementKind kind) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Density, density, Real);
	AKANTU_GET_MACRO(Capacity, capacity, Real);
	/// get the current value of the time step
	AKANTU_GET_MACRO(TimeStep, time_step, Real);
	/// get the assembled heat flux
	AKANTU_GET_MACRO(InternalHeatRate, *internal_heat_rate, Array<Real> &);
	/// get the boundary vector
	AKANTU_GET_MACRO(BlockedDOFs, *blocked_dofs, Array<bool> &);
	/// get the external heat rate vector
	AKANTU_GET_MACRO(ExternalHeatRate, *external_heat_rate, Array<Real> &);
	/// get the temperature gradient
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(TemperatureGradient,
	temperature_gradient, Real);
	/// get the conductivity on q points
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ConductivityOnQpoints,
	conductivity_on_qpoints, Real);
	/// get the conductivity on q points
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(TemperatureOnQpoints,
	temperature_on_qpoints, Real);
	/// internal variables
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(KgradT, k_gradt_on_qpoints, Real);
	/// get the temperature
	AKANTU_GET_MACRO(Temperature, *temperature, Array<Real> &);
	/// get the temperature derivative
	AKANTU_GET_MACRO(TemperatureRate, *temperature_rate, Array<Real> &);

	/// get the energy denominated by thermal
	Real getEnergy(const std::string & energy_id, ElementType type, UInt index);
	/// get the energy denominated by thermal
	Real getEnergy(const std::string & energy_id);

	/// get the thermal energy for a given element
	Real getThermalEnergy(ElementType type, UInt index);
	/// get the thermal energy for a given element
	Real getThermalEnergy();

	protected:
	/* ------------------------------------------------------------------------ */
	FEEngine & getFEEngineBoundary(const ID & name = "") override;

	/* ----------------------------------------------------------------------- */
	template <class iterator>
	void getThermalEnergy(iterator Eth, Array<Real>::const_iterator<Real> T_it,
	const Array<Real>::const_iterator<Real> & T_end) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// time step
	Real time_step;

	/// temperatures array
	std::unique_ptr<Array<Real>> temperature;

	/// temperatures derivatives array
	std::unique_ptr<Array<Real>> temperature_rate;

	/// increment array (@f$\delta \dot T@f$ or @f$\delta T@f$)
	std::unique_ptr<Array<Real>> increment;

	/// the density
	Real density;

	/// the speed of the changing temperature
	ElementTypeMapArray<Real> temperature_gradient;

	/// temperature field on quadrature points
	ElementTypeMapArray<Real> temperature_on_qpoints;

	/// conductivity tensor on quadrature points
	ElementTypeMapArray<Real> conductivity_on_qpoints;

	/// vector \f[k \grad T\f] on quad points
	ElementTypeMapArray<Real> k_gradt_on_qpoints;

	/// external flux vector
	std::unique_ptr<Array<Real>> external_heat_rate;

	/// residuals array
	std::unique_ptr<Array<Real>> internal_heat_rate;

	/// boundary vector
	std::unique_ptr<Array<bool>> blocked_dofs;

	// realtime
	// Real time;

	/// capacity
	Real capacity;

	// conductivity matrix
	Matrix<Real> conductivity;

	// linear variation of the conductivity (for temperature dependent
	// conductivity)
	Real conductivity_variation;

	// reference temperature for the interpretation of temperature variation
	Real T_ref;

	// the biggest parameter of conductivity matrix
	// Real conductivitymax;

	bool need_to_reassemble_capacity{true};
	bool need_to_reassemble_capacity_lumped{true};
	UInt temperature_release{0};
	UInt conductivity_matrix_release{UInt(-1)};
	std::unordered_map<GhostType, bool> initial_conductivity{{_not_ghost, true},
	{_ghost, true}};
	std::unordered_map<GhostType, UInt> conductivity_release{{_not_ghost, 0},
	{_ghost, 0}};
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "heat_transfer_model_inline_impl.hh"

	#endif /* AKANTU_HEAT_TRANSFER_MODEL_HH_ */
	diff --git a/src/model/heat_transfer/heat_transfer_model_inline_impl.hh b/src/model/heat_transfer/heat_transfer_model_inline_impl.hh
	index 928571565..6c6a2cc24 100644
	--- a/src/model/heat_transfer/heat_transfer_model_inline_impl.hh
	+++ b/src/model/heat_transfer/heat_transfer_model_inline_impl.hh
	@@ -1,43 +1,43 @@
	/**
	* @file heat_transfer_model_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Srinivasa Babu Ramisetti <srinivasa.ramisetti@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Aug 20 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Implementation of the inline functions of the HeatTransferModel class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKANTU_HEAT_TRANSFER_MODEL_INLINE_IMPL_HH_
	#define AKANTU_HEAT_TRANSFER_MODEL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_HEAT_TRANSFER_MODEL_INLINE_IMPL_HH_ */
	diff --git a/src/model/model.cc b/src/model/model.cc
	index d2765097c..e90d3cf35 100644
	--- a/src/model/model.cc
	+++ b/src/model/model.cc
	@@ -1,367 +1,367 @@
	/**
	* @file model.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Oct 03 2011
	* @date last modification: Fri Apr 09 2021
	*
	* @brief implementation of model common parts
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "model.hh"
	#include "communicator.hh"
	#include "data_accessor.hh"
	#include "element_group.hh"
	#include "element_synchronizer.hh"
	#include "synchronizer_registry.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Model::Model(Mesh & mesh, const ModelType & type,
	std::shared_ptr<DOFManager> dof_manager, UInt dim, const ID & id)
	: ModelSolver(mesh, type, id, std::move(dof_manager)), mesh(mesh),
	spatial_dimension(dim == _all_dimensions ? mesh.getSpatialDimension()
	: dim),
	parser(getStaticParser()) {
	this->mesh.registerEventHandler(*this, _ehp_model);
	}

	/* -------------------------------------------------------------------------- */
	Model::Model(Mesh & mesh, const ModelType & type, UInt dim, const ID & id)
	: ModelSolver(mesh, type, id), mesh(mesh),
	spatial_dimension(dim == _all_dimensions ? mesh.getSpatialDimension()
	: dim),
	parser(getStaticParser()) {
	this->mesh.registerEventHandler(*this, _ehp_model);
	}

	/* -------------------------------------------------------------------------- */
	Model::~Model() = default;

	/* -------------------------------------------------------------------------- */
	void Model::initFullImpl(const ModelOptions & options) {
	AKANTU_DEBUG_IN();

	method = options.analysis_method;
	if (!this->hasDefaultSolver()) {
	this->initNewSolver(this->method);
	}

	initModel();

	initFEEngineBoundary();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void Model::initNewSolver(const AnalysisMethod & method) {
	ID solver_name;
	TimeStepSolverType tss_type;
	std::tie(solver_name, tss_type) = this->getDefaultSolverID(method);

	if (not this->hasSolver(solver_name)) {
	ModelSolverOptions options = this->getDefaultSolverOptions(tss_type);
	this->getNewSolver(solver_name, tss_type, options.non_linear_solver_type);

	for (auto && is_type : options.integration_scheme_type) {
	if (!this->hasIntegrationScheme(solver_name, is_type.first)) {
	this->setIntegrationScheme(solver_name, is_type.first, is_type.second,
	options.solution_type[is_type.first]);
	}
	}
	}

	this->method = method;
	this->setDefaultSolver(solver_name);
	}

	/* -------------------------------------------------------------------------- */
	void Model::initFEEngineBoundary() {
	try {
	FEEngine & fem_boundary = getFEEngineBoundary();
	fem_boundary.initShapeFunctions(_not_ghost);
	fem_boundary.initShapeFunctions(_ghost);

	fem_boundary.computeNormalsOnIntegrationPoints(_not_ghost);
	fem_boundary.computeNormalsOnIntegrationPoints(_ghost);
	} catch (debug::Exception & /e/) {
	}
	}

	/* -------------------------------------------------------------------------- */
	void Model::dumpGroup(const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	group.dump();
	}

	/* -------------------------------------------------------------------------- */
	void Model::dumpGroup(const std::string & group_name,
	const std::string & dumper_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	group.dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	void Model::dumpGroup() {
	for (auto & group : mesh.iterateElementGroups()) {
	group.dump();
	}
	}

	/* -------------------------------------------------------------------------- */
	void Model::setGroupDirectory(const std::string & directory) {
	for (auto & group : mesh.iterateElementGroups()) {
	group.setDirectory(directory);
	}
	}

	/* -------------------------------------------------------------------------- */
	void Model::setGroupDirectory(const std::string & directory,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	group.setDirectory(directory);
	}

	/* -------------------------------------------------------------------------- */
	void Model::setGroupBaseName(const std::string & basename,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	group.setBaseName(basename);
	}

	/* -------------------------------------------------------------------------- */
	DumperIOHelper & Model::getGroupDumper(const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	return group.getDumper();
	}

	/* -------------------------------------------------------------------------- */
	// DUMPER stuff
	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupFieldToDumper(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field,
	DumperIOHelper & dumper) {
	#ifdef AKANTU_USE_IOHELPER
	dumper.registerField(field_id, std::move(field));
	#endif
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpField(const std::string & field_id) {
	this->addDumpFieldToDumper(mesh.getDefaultDumperName(), field_id);
	}
	/* -------------------------------------------------------------------------- */

	void Model::addDumpFieldVector(const std::string & field_id) {
	this->addDumpFieldVectorToDumper(mesh.getDefaultDumperName(), field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpFieldTensor(const std::string & field_id) {
	this->addDumpFieldTensorToDumper(mesh.getDefaultDumperName(), field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Model::setBaseName(const std::string & field_id) {
	mesh.setBaseName(field_id);
	}
	/* -------------------------------------------------------------------------- */

	void Model::setBaseNameToDumper(const std::string & dumper_name,
	const std::string & basename) {
	mesh.setBaseNameToDumper(dumper_name, basename);
	}
	/* -------------------------------------------------------------------------- */

	void Model::addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	this->addDumpGroupFieldToDumper(dumper_name, field_id, "all",
	dumper_default_element_kind, false);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupField(const std::string & field_id,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	this->addDumpGroupFieldToDumper(group.getDefaultDumperName(), field_id,
	group_name, dumper_default_element_kind,
	false);
	}

	/* -------------------------------------------------------------------------- */
	void Model::removeDumpGroupField(const std::string & field_id,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	this->removeDumpGroupFieldFromDumper(group.getDefaultDumperName(), field_id,
	group_name);
	}

	/* -------------------------------------------------------------------------- */
	void Model::removeDumpGroupFieldFromDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	group.removeDumpFieldFromDumper(dumper_name, field_id);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpFieldVectorToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	this->addDumpGroupFieldToDumper(dumper_name, field_id, "all",
	dumper_default_element_kind, true);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupFieldVector(const std::string & field_id,
	const std::string & group_name) {
	ElementGroup & group = mesh.getElementGroup(group_name);
	this->addDumpGroupFieldVectorToDumper(group.getDefaultDumperName(), field_id,
	group_name);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupFieldVectorToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name) {
	this->addDumpGroupFieldToDumper(dumper_name, field_id, group_name,
	dumper_default_element_kind, true);
	}
	/* -------------------------------------------------------------------------- */

	void Model::addDumpFieldTensorToDumper(const std::string & dumper_name,
	const std::string & field_id) {
	this->addDumpGroupFieldToDumper(dumper_name, field_id, "all",
	dumper_default_element_kind, true);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind,
	bool padding_flag) {
	this->addDumpGroupFieldToDumper(dumper_name, field_id, group_name,
	this->spatial_dimension, element_kind,
	padding_flag);
	}

	/* -------------------------------------------------------------------------- */
	void Model::addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	UInt spatial_dimension,
	ElementKind element_kind,
	bool padding_flag) {
	#ifdef AKANTU_USE_IOHELPER
	std::shared_ptr<dumpers::Field> field;

	if (!field) {
	field = this->createNodalFieldReal(field_id, group_name, padding_flag);
	}
	if (!field) {
	field = this->createNodalFieldUInt(field_id, group_name, padding_flag);
	}
	if (!field) {
	field = this->createNodalFieldBool(field_id, group_name, padding_flag);
	}
	if (!field) {
	field = this->createElementalField(field_id, group_name, padding_flag,
	spatial_dimension, element_kind);
	}
	if (!field) {
	field = this->mesh.createFieldFromAttachedData<UInt>(field_id, group_name,
	element_kind);
	}
	if (!field) {
	field = this->mesh.createFieldFromAttachedData<Real>(field_id, group_name,
	element_kind);
	}

	#ifndef AKANTU_NDEBUG
	if (!field) {
	AKANTU_DEBUG_WARNING("No field could be found based on name: " << field_id);
	}
	#endif
	if (field) {
	DumperIOHelper & dumper = mesh.getGroupDumper(dumper_name, group_name);
	this->addDumpGroupFieldToDumper(field_id, field, dumper);
	}

	#endif
	}

	/* -------------------------------------------------------------------------- */
	void Model::dump(const std::string & dumper_name) { mesh.dump(dumper_name); }

	/* -------------------------------------------------------------------------- */
	void Model::dump(const std::string & dumper_name, UInt step) {
	mesh.dump(dumper_name, step);
	}

	/* ------------------------------------------------------------------------- */
	void Model::dump(const std::string & dumper_name, Real time, UInt step) {
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void Model::dump() {
	auto default_dumper = mesh.getDefaultDumperName();
	this->dump(default_dumper);
	}

	/* -------------------------------------------------------------------------- */
	void Model::dump(UInt step) {
	auto default_dumper = mesh.getDefaultDumperName();
	this->dump(default_dumper, step);
	}

	/* -------------------------------------------------------------------------- */
	void Model::dump(Real time, UInt step) {
	auto default_dumper = mesh.getDefaultDumperName();
	this->dump(default_dumper, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void Model::setDirectory(const std::string & directory) {
	mesh.setDirectory(directory);
	}

	/* -------------------------------------------------------------------------- */
	void Model::setDirectoryToDumper(const std::string & dumper_name,
	const std::string & directory) {
	mesh.setDirectoryToDumper(dumper_name, directory);
	}

	/* -------------------------------------------------------------------------- */
	void Model::setTextModeToDumper() { mesh.setTextModeToDumper(); }

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/model.hh b/src/model/model.hh
	index c7b75fe07..d0040fe98 100644
	--- a/src/model/model.hh
	+++ b/src/model/model.hh
	@@ -1,391 +1,390 @@
	/**
	* @file model.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Interface of a model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_named_argument.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "model_options.hh"
	#include "model_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <typeindex>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MODEL_HH_
	#define AKANTU_MODEL_HH_

	namespace akantu {
	class SynchronizerRegistry;
	class Parser;
	class DumperIOHelper;
	class DOFManager;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class Model : public ModelSolver, public MeshEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Normal constructor where the DOFManager is created internally
	Model(Mesh & mesh, const ModelType & type, UInt dim = _all_dimensions,
	const ID & id = "model");

	/// Model constructor the the dof manager is created externally, for example
	/// in a ModelCoupler
	Model(Mesh & mesh, const ModelType & type,
	std::shared_ptr<DOFManager> dof_manager, UInt dim = _all_dimensions,
	const ID & id = "model");

	~Model() override;

	using FEEngineMap = std::map<std::string, std::unique_ptr<FEEngine>>;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	virtual void initFullImpl(const ModelOptions & options);

	public:
	template <typename... pack>
	std::enable_if_t<are_named_argument<pack...>::value>
	initFull(pack &&... _pack) {
	switch (this->model_type) {
	#ifdef AKANTU_SOLID_MECHANICS
	case ModelType::_solid_mechanics_model:
	this->initFullImpl(SolidMechanicsModelOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	#ifdef AKANTU_COHESIVE_ELEMENT
	case ModelType::_solid_mechanics_model_cohesive:
	this->initFullImpl(SolidMechanicsModelCohesiveOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	#ifdef AKANTU_HEAT_TRANSFER
	case ModelType::_heat_transfer_model:
	this->initFullImpl(HeatTransferModelOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	#ifdef AKANTU_PHASE_FIELD
	case ModelType::_phase_field_model:
	this->initFullImpl(PhaseFieldModelOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	-#endif
	+#endif
	#ifdef AKANTU_EMBEDDED
	case ModelType::_embedded_model:
	this->initFullImpl(EmbeddedInterfaceModelOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	#ifdef AKANTU_CONTACT_MECHANICS
	case ModelType::_contact_mechanics_model:
	this->initFullImpl(ContactMechanicsModelOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	#ifdef AKANTU_MODEL_COUPLERS
	case ModelType::_coupler_solid_contact:
	this->initFullImpl(CouplerSolidContactOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	case ModelType::_coupler_solid_cohesive_contact:
	this->initFullImpl(CouplerSolidCohesiveContactOptions{
	use_named_args, std::forward<decltype(_pack)>(_pack)...});
	break;
	#endif
	default:
	this->initFullImpl(ModelOptions{use_named_args,
	std::forward<decltype(_pack)>(_pack)...});
	}
	}

	template <typename... pack>
	std::enable_if_t<not are_named_argument<pack...>::value>
	initFull(pack &&... _pack) {
	this->initFullImpl(std::forward<decltype(_pack)>(_pack)...);
	}

	/// initialize a new solver if needed
	void initNewSolver(const AnalysisMethod & method);

	protected:
	/// get some default values for derived classes
	virtual std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) = 0;

	- virtual void initModel() {};
	+ virtual void initModel(){};

	virtual void initFEEngineBoundary();

	/// function to print the containt of the class
	void printself(std::ostream & /stream/,
	int /indent/ = 0) const override{};

	public:
	/* ------------------------------------------------------------------------ */
	/* Access to the dumpable interface of the boundaries */
	/* ------------------------------------------------------------------------ */
	/// Dump the data for a given group
	void dumpGroup(const std::string & group_name);
	void dumpGroup(const std::string & group_name,
	const std::string & dumper_name);
	/// Dump the data for all boundaries
	void dumpGroup();
	/// Set the directory for a given group
	void setGroupDirectory(const std::string & directory,
	const std::string & group_name);
	/// Set the directory for all boundaries
	void setGroupDirectory(const std::string & directory);
	/// Set the base name for a given group
	void setGroupBaseName(const std::string & basename,
	const std::string & group_name);
	/// Get the internal dumper of a given group
	DumperIOHelper & getGroupDumper(const std::string & group_name);

	/* ------------------------------------------------------------------------ */
	/* Function for non local capabilities */
	/* ------------------------------------------------------------------------ */
	virtual void updateDataForNonLocalCriterion(__attribute__((unused))
	ElementTypeMapReal & criterion) {
	AKANTU_TO_IMPLEMENT();
	}

	protected:
	template <typename T>
	void allocNodalField(std::unique_ptr<Array<T>> & array, UInt nb_component,
	const ID & name) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get id of model
	AKANTU_GET_MACRO(ID, id, const ID &)

	/// get the number of surfaces
	AKANTU_GET_MACRO(Mesh, mesh, Mesh &)

	/// synchronize the boundary in case of parallel run
	virtual void synchronizeBoundaries(){};

	/// return the fem object associated with a provided name
	inline FEEngine & getFEEngine(const ID & name = "") const;

	/// return the fem boundary object associated with a provided name
	virtual FEEngine & getFEEngineBoundary(const ID & name = "");

	inline bool hasFEEngineBoundary(const ID & name = "");

	/// register a fem object associated with name
	template <typename FEEngineClass>
	inline void registerFEEngineObject(const std::string & name, Mesh & mesh,
	UInt spatial_dimension);
	/// unregister a fem object associated with name
	inline void unRegisterFEEngineObject(const std::string & name);

	/// return the synchronizer registry
	SynchronizerRegistry & getSynchronizerRegistry();

	/// return the fem object associated with a provided name
	template <typename FEEngineClass>
	inline FEEngineClass & getFEEngineClass(std::string name = "") const;

	/// return the fem boundary object associated with a provided name
	template <typename FEEngineClass>
	inline FEEngineClass & getFEEngineClassBoundary(std::string name = "");

	/// Get the type of analysis method used
	AKANTU_GET_MACRO(AnalysisMethod, method, AnalysisMethod);

	/// return the dimension of the system space
	AKANTU_GET_MACRO(SpatialDimension, Model::spatial_dimension, UInt);

	/* ------------------------------------------------------------------------ */
	- /* Pack and unpack hexlper functions */
	+ /* Pack and unpack hexlper functions */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbIntegrationPoints(const Array<Element> & elements,
	const ID & fem_id = ID()) const;

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface (kept for convenience) and dumper relative functions */
	/* ------------------------------------------------------------------------ */
	void setTextModeToDumper();

	virtual void addDumpGroupFieldToDumper(const std::string & field_id,
	std::shared_ptr<dumpers::Field> field,
	DumperIOHelper & dumper);

	virtual void addDumpField(const std::string & field_id);

	virtual void addDumpFieldVector(const std::string & field_id);

	virtual void addDumpFieldToDumper(const std::string & dumper_name,
	const std::string & field_id);

	virtual void addDumpFieldVectorToDumper(const std::string & dumper_name,
	const std::string & field_id);

	virtual void addDumpFieldTensorToDumper(const std::string & dumper_name,
	const std::string & field_id);

	virtual void addDumpFieldTensor(const std::string & field_id);

	virtual void setBaseName(const std::string & field_id);

	virtual void setBaseNameToDumper(const std::string & dumper_name,
	const std::string & basename);

	virtual void addDumpGroupField(const std::string & field_id,
	const std::string & group_name);

	virtual void addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind,
	bool padding_flag);

	virtual void addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	UInt spatial_dimension,
	ElementKind element_kind,
	bool padding_flag);

	virtual void removeDumpGroupField(const std::string & field_id,
	const std::string & group_name);
	virtual void removeDumpGroupFieldFromDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name);

	virtual void addDumpGroupFieldVector(const std::string & field_id,
	const std::string & group_name);

	virtual void addDumpGroupFieldVectorToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name);

	virtual std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}

	virtual std::shared_ptr<dumpers::Field>
	createNodalFieldUInt(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}

	virtual std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & /field_name/,
	const std::string & /group_name/,
	bool /padding_flag/) {
	return nullptr;
	}

	virtual std::shared_ptr<dumpers::Field> createElementalField(
	const std::string & /field_name/, const std::string & /group_name/,
	bool /padding_flag/, UInt /spatial_dimension/, ElementKind /kind/) {
	return nullptr;
	}

	void setDirectory(const std::string & directory);
	void setDirectoryToDumper(const std::string & dumper_name,
	const std::string & directory);

	-
	/* ------------------------------------------------------------------------ */
	virtual void dump(const std::string & dumper_name);
	virtual void dump(const std::string & dumper_name, UInt step);
	virtual void dump(const std::string & dumper_name, Real time, UInt step);
	/* ------------------------------------------------------------------------ */
	virtual void dump();
	virtual void dump(UInt step);
	virtual void dump(Real time, UInt step);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	friend std::ostream & operator<<(std::ostream & /stream/,
	const Model & /_this/);

	ID id;

	/// analysis method check the list in akantu::AnalysisMethod
	AnalysisMethod method;

	/// Mesh
	Mesh & mesh;

	/// Spatial dimension of the problem
	UInt spatial_dimension;

	/// the main fem object present in all models
	FEEngineMap fems;

	/// the fem object present in all models for boundaries
	FEEngineMap fems_boundary;

	/// default fem object
	std::string default_fem;

	/// parser to the pointer to use
	Parser & parser;

	/// default ElementKind for dumper
	ElementKind dumper_default_element_kind{_ek_regular};
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream, const Model & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "model_inline_impl.hh"

	#endif /* AKANTU_MODEL_HH_ */
	diff --git a/src/model/model_couplers/cohesive_contact_solvercallback.cc b/src/model/model_couplers/cohesive_contact_solvercallback.cc
	index f38138028..445fc895c 100644
	--- a/src/model/model_couplers/cohesive_contact_solvercallback.cc
	+++ b/src/model/model_couplers/cohesive_contact_solvercallback.cc
	@@ -1,141 +1,141 @@
	/**
	* @file cohesive_contact_solvercallback.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 06 2021
	* @date last modification: Sun Jun 06 2021
	*
	* @brief class for coupling of solid mechanics cohesive and contact mechanics
	* model via solvercallback
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_contact_solvercallback.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	CohesiveContactSolverCallback::CohesiveContactSolverCallback(
	SolidMechanicsModelCohesive & solid, ContactMechanicsModel & contact,
	AnalysisMethod & method)
	- : SolverCallback(), solid(solid), contact(contact), method(method) {}
	+ : solid(solid), contact(contact), method(method) {}

	void CohesiveContactSolverCallback::assembleMatrix(const ID & matrix_id) {

	if (matrix_id == "K") {
	solid.assembleStiffnessMatrix();

	switch (method) {
	case _static:
	case _implicit_dynamic: {
	contact.assembleStiffnessMatrix();
	break;
	}
	default:
	break;
	}

	} else if (matrix_id == "M") {
	solid.assembleMass();
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::assembleLumpedMatrix(const ID & matrix_id) {
	if (matrix_id == "M") {
	solid.assembleMassLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::assembleResidual() {
	// computes the internal forces

	switch (method) {
	case _explicit_lumped_mass: {
	auto & current_positions = contact.getContactDetector().getPositions();
	current_positions.copy(solid.getCurrentPosition());
	contact.search();
	break;
	}
	default:
	break;
	}

	solid.assembleInternalForces();
	contact.assembleInternalForces();

	auto & internal_force = solid.getInternalForce();
	auto & external_force = solid.getExternalForce();

	auto & contact_force = contact.getInternalForce();

	solid.getDOFManager().assembleToResidual("displacement", external_force, 1);
	solid.getDOFManager().assembleToResidual("displacement", internal_force, 1);
	solid.getDOFManager().assembleToResidual("displacement", contact_force, 1);
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::predictor() {
	auto & solid_model_solver = aka::as_type<ModelSolver>(solid);
	solid_model_solver.predictor();
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::beforeSolveStep() {
	auto & solid_model_solver = aka::as_type<ModelSolver>(solid);
	solid_model_solver.beforeSolveStep();
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::afterSolveStep(bool converged) {
	auto & solid_model_solver = aka::as_type<ModelSolver>(solid);
	solid_model_solver.afterSolveStep(converged);
	}

	/* -------------------------------------------------------------------------- */
	void CohesiveContactSolverCallback::corrector() {
	auto & solid_model_solver = aka::as_type<ModelSolver>(solid);
	solid_model_solver.corrector();

	switch (method) {
	case _static:
	case _implicit_dynamic: {
	auto & current_positions = contact.getContactDetector().getPositions();
	current_positions.copy(solid.getCurrentPosition());
	contact.search();
	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	MatrixType
	CohesiveContactSolverCallback::getMatrixType(const ID & /matrix_id/) {
	return _symmetric;
	}

	} // namespace akantu
	diff --git a/src/model/model_couplers/cohesive_contact_solvercallback.hh b/src/model/model_couplers/cohesive_contact_solvercallback.hh
	index 02dcd7399..078e56e19 100644
	--- a/src/model/model_couplers/cohesive_contact_solvercallback.hh
	+++ b/src/model/model_couplers/cohesive_contact_solvercallback.hh
	@@ -1,92 +1,90 @@
	/**
	* @file cohesive_contact_solvercallback.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 06 2021
	* @date last modification: Wed Jul 28 2021
	*
	* @brief class for coupling of solid mechanics and conatct mechanics
	* model via solvercallback
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	+#include "contact_mechanics_model.hh"
	#include "mesh_iterators.hh"
	#include "non_linear_solver.hh"
	-#include "contact_mechanics_model.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	-
	#ifndef __AKANTU_COHESIVE_CONTACT_SOLVERCALLBACK_HH__
	#define __AKANTU_COHESIVE_CONTACT_SOLVERCALLBACK_HH__

	-namespace akantu{
	-
	+namespace akantu {

	class CohesiveContactSolverCallback : public SolverCallback {

	public:
	- CohesiveContactSolverCallback(SolidMechanicsModelCohesive &,
	- ContactMechanicsModel &, AnalysisMethod &);
	+ CohesiveContactSolverCallback(SolidMechanicsModelCohesive & /solid/,
	+ ContactMechanicsModel & /contact/,
	+ AnalysisMethod & /method/);

	public:
	-
	/// implementation of SolverCallback::assembleMatrix
	- void assembleMatrix(const ID &) override;
	+ void assembleMatrix(const ID & /matrix_id/) override;

	/// implementation of SolverCallback::assembleResidual
	void assembleResidual() override;

	/// implementation of SolverCallback::assembleLumpedMatrix
	- void assembleLumpedMatrix(const ID &) override;
	+ void assembleLumpedMatrix(const ID & /matrix_id/) override;

	/// implementation of SolverCallback::getMatrixType
	- MatrixType getMatrixType(const ID &) override;
	+ MatrixType getMatrixType(const ID & /unused/) override;

	/// implementation of SolverCallback::predictor
	void predictor() override;

	/// implementation of SolverCallback::corrector
	void corrector() override;

	/// implementation of SolverCallback::beforeSolveStep
	void beforeSolveStep() override;

	/// implementation of SolverCallback::afterSolveStep
	- void afterSolveStep(bool converged=true) override;
	+ void afterSolveStep(bool converged = true) override;

	private:
	/// model for the solid mechanics part of the coupling
	SolidMechanicsModelCohesive & solid;

	/// model for the contact resoluion of the coupling
	ContactMechanicsModel & contact;

	/// Method of resolution for the coupling solver
	AnalysisMethod & method;
	};

	-}
	-
	+} // namespace akantu
	+
	#endif
	diff --git a/src/model/model_couplers/coupler_solid_cohesive_contact.cc b/src/model/model_couplers/coupler_solid_cohesive_contact.cc
	index 34953b99a..aca99f73f 100644
	--- a/src/model/model_couplers/coupler_solid_cohesive_contact.cc
	+++ b/src/model/model_couplers/coupler_solid_cohesive_contact.cc
	@@ -1,78 +1,78 @@
	/**
	* @file coupler_solid_cohesive_contact.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jan 21 2019
	* @date last modification: Wed Jun 23 2021
	*
	* @brief class for coupling of solid mechanics cohesive and conatct mechanics
	* model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_cohesive_contact.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <>
	CouplerSolidContactTemplate<SolidMechanicsModelCohesive>::
	CouplerSolidContactTemplate(Mesh & mesh, UInt dim, const ID & id,
	std::shared_ptr<DOFManager> dof_manager,
	ModelType model_type)
	: Model(mesh, model_type, dof_manager, dim, id) {
	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("coupler_solid_cohesive_contact",
	id, true);
	this->mesh.addDumpMeshToDumper("coupler_solid_cohesive_contact", mesh,
	Model::spatial_dimension, _not_ghost,
	_ek_cohesive);
	#endif

	this->registerDataAccessor(*this);

	solid = std::make_unique<SolidMechanicsModelCohesive>(
	mesh, Model::spatial_dimension, "solid_mechanics_model_cohesive",
	this->dof_manager);
	contact = std::make_unique<ContactMechanicsModel>(mesh.getMeshFacets(),
	Model::spatial_dimension,
	"contact_mechanics_model");
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void CouplerSolidContactTemplate<SolidMechanicsModelCohesive>::initFullImpl(
	const ModelOptions & options) {
	Model::initFullImpl(options);

	const auto & cscc_options =
	aka::as_type<CouplerSolidCohesiveContactOptions>(options);

	solid->initFull(_analysis_method = cscc_options.analysis_method,
	_is_extrinsic = cscc_options.is_extrinsic);
	contact->initFull(_analysis_method = cscc_options.analysis_method);
	}

	} // namespace akantu
	diff --git a/src/model/model_couplers/coupler_solid_cohesive_contact.hh b/src/model/model_couplers/coupler_solid_cohesive_contact.hh
	index 099a59b28..4578c6b6b 100644
	--- a/src/model/model_couplers/coupler_solid_cohesive_contact.hh
	+++ b/src/model/model_couplers/coupler_solid_cohesive_contact.hh
	@@ -1,52 +1,52 @@
	/**
	* @file coupler_solid_cohesive_contact.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jul 28 2021
	*
	* @brief class for coupling of solid mechanics and conatct mechanics
	* model in explicit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_contact.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_COUPLER_SOLID_COHESIVE_CONTACT_HH__
	#define __AKANTU_COUPLER_SOLID_COHESIVE_CONTACT_HH__

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	using CouplerSolidCohesiveContact =
	CouplerSolidContactTemplate<SolidMechanicsModelCohesive>;

	} // namespace akantu

	#endif /* __COUPLER_SOLID_CONTACT_HH__ */
	diff --git a/src/model/model_couplers/coupler_solid_contact.cc b/src/model/model_couplers/coupler_solid_contact.cc
	index 37d11add6..8cc5a5c5b 100644
	--- a/src/model/model_couplers/coupler_solid_contact.cc
	+++ b/src/model/model_couplers/coupler_solid_contact.cc
	@@ -1,71 +1,71 @@
	/**
	* @file coupler_solid_contact.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jan 21 2019
	* @date last modification: Wed Jun 23 2021
	*
	* @brief class for coupling of solid mechanics and conatct mechanics
	* model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_contact.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <>
	CouplerSolidContactTemplate<SolidMechanicsModel>::CouplerSolidContactTemplate(
	Mesh & mesh, UInt dim, const ID & id,
	std::shared_ptr<DOFManager> dof_manager, ModelType model_type)
	: Model(mesh, model_type, dof_manager, dim, id) {
	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("coupler_solid_contact", id, true);
	this->mesh.addDumpMeshToDumper("coupler_solid_contact", mesh,
	Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif
	this->registerDataAccessor(*this);

	solid = std::make_unique<SolidMechanicsModel>(mesh, Model::spatial_dimension,
	"solid_mechanics_model",
	this->dof_manager);
	contact = std::make_unique<ContactMechanicsModel>(
	mesh, Model::spatial_dimension, "contact_mechanics_model",
	this->dof_manager);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void CouplerSolidContactTemplate<SolidMechanicsModel>::initFullImpl(
	const ModelOptions & options) {
	Model::initFullImpl(options);

	solid->initFull(_analysis_method = this->method);
	contact->initFull(_analysis_method = this->method);
	}

	} // namespace akantu
	diff --git a/src/model/model_couplers/coupler_solid_contact.hh b/src/model/model_couplers/coupler_solid_contact.hh
	index 4fa8898a2..a6a99e77e 100644
	--- a/src/model/model_couplers/coupler_solid_contact.hh
	+++ b/src/model/model_couplers/coupler_solid_contact.hh
	@@ -1,282 +1,282 @@
	/**
	* @file coupler_solid_contact.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Sat Jun 26 2021
	*
	* @brief class for coupling of solid mechanics and conatct mechanics
	* model in explicit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	#include "solid_mechanics_model.hh"
	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "solid_mechanics_model_cohesive.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_COUPLER_SOLID_CONTACT_HH__
	#define __AKANTU_COUPLER_SOLID_CONTACT_HH__

	/* ------------------------------------------------------------------------ */
	/* Coupling : Solid Mechanics / Contact Mechanics */
	/* ------------------------------------------------------------------------ */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	class CouplerSolidContactTemplate : public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt> {
	static_assert(
	std::is_base_of<SolidMechanicsModel, SolidMechanicsModelType>::value,
	"SolidMechanicsModelType should be derived from SolidMechanicsModel");
	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructor */
	/* ------------------------------------------------------------------------ */
	public:
	CouplerSolidContactTemplate(
	Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "coupler_solid_contact",
	std::shared_ptr<DOFManager> dof_manager = nullptr,
	ModelType model_type = std::is_same<SolidMechanicsModelType,
	SolidMechanicsModelCohesive>::value
	? ModelType::_coupler_solid_cohesive_contact
	: ModelType::_coupler_solid_contact);

	~CouplerSolidContactTemplate() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize completely the model
	void initFullImpl(const ModelOptions & options) override;

	/// get some default values for derived classes
	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	/* ------------------------------------------------------------------------ */
	/* Solver Interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// assembles the contact stiffness matrix
	virtual void assembleStiffnessMatrix();

	/// assembles the contant internal forces
	virtual void assembleInternalForces();

	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <class Model_ = SolidMechanicsModelType,
	std::enable_if_t<std::is_same<
	Model_, SolidMechanicsModelCohesive>::value> * = nullptr>
	UInt checkCohesiveStress() {
	return solid->checkCohesiveStress();
	}
	#endif

	template <typename FunctorType>
	inline void applyBC(const FunctorType & func) {
	solid->applyBC(func);
	}

	template <class FunctorType>
	inline void applyBC(const FunctorType & func,
	const std::string & group_name) {
	solid->applyBC(func, group_name);
	}

	template <class FunctorType>
	inline void applyBC(const FunctorType & func,
	const ElementGroup & element_group) {
	solid->applyBC(func, element_group);
	}

	protected:
	/// callback for the solver, this adds f_{ext} - f_{int} to the residual
	void assembleResidual() override;

	/// callback for the solver, this adds f_{ext} or f_{int} to the residual
	void assembleResidual(const ID & residual_part) override;
	bool canSplitResidual() override { return true; }

	/// get the type of matrix needed
	MatrixType getMatrixType(const ID & matrix_id) override;

	/// callback for the solver, this assembles different matrices
	void assembleMatrix(const ID & matrix_id) override;

	/// callback for the solver, this assembles the stiffness matrix
	void assembleLumpedMatrix(const ID & matrix_id) override;

	/// callback for the solver, this is called at beginning of solve
	void predictor() override;

	/// callback for the solver, this is called at end of solve
	void corrector() override;

	/// callback for the solver, this is called at beginning of solve
	void beforeSolveStep() override;

	/// callback for the solver, this is called at end of solve
	void afterSolveStep(bool converged = true) override;

	/// callback for the model to instantiate the matricess when needed
	void initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type) override;

	/* ------------------------------------------------------------------------ */
	/* Mass matrix for solid mechanics model */
	/* ------------------------------------------------------------------------ */
	public:
	/// assemble the lumped mass matrix
	void assembleMassLumped();

	/// assemble the mass matrix for consistent mass resolutions
	void assembleMass();

	protected:
	/// assemble the lumped mass matrix for local and ghost elements
	void assembleMassLumped(GhostType ghost_type);

	/// assemble the mass matrix for either _ghost or _not_ghost elements
	void assembleMass(GhostType ghost_type);

	protected:
	/* ------------------------------------------------------------------------ */
	TimeStepSolverType getDefaultSolverType() const override;
	/* ------------------------------------------------------------------------ */
	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;

	public:
	bool isDefaultSolverExplicit() { return method == _explicit_lumped_mass; }

	/* ------------------------------------------------------------------------ */
	public:
	// DataAccessor<Element>
	UInt getNbData(const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override {
	return 0;
	}
	void packData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override {}
	void unpackData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) override {}

	// DataAccessor<UInt> nodes
	UInt getNbData(const Array<UInt> & /nodes/,
	const SynchronizationTag & /tag/) const override {
	return 0;
	}
	void packData(CommunicationBuffer & /buffer/, const Array<UInt> & /nodes/,
	const SynchronizationTag & /tag/) const override {}
	void unpackData(CommunicationBuffer & /buffer/,
	const Array<UInt> & /nodes/,
	const SynchronizationTag & /tag/) override {}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the solid mechanics model
	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <class Model_ = SolidMechanicsModelType,
	std::enable_if_t<std::is_same<
	Model_, SolidMechanicsModelCohesive>::value> * = nullptr>
	SolidMechanicsModelCohesive & getSolidMechanicsModelCohesive() {
	return *solid;
	}
	#endif
	template <class Model_ = SolidMechanicsModelType,
	std::enable_if_t<
	std::is_same<Model_, SolidMechanicsModel>::value> * = nullptr>
	SolidMechanicsModelType & getSolidMechanicsModel() {
	return *solid;
	}

	/// get the contact mechanics model
	AKANTU_GET_MACRO(ContactMechanicsModel, *contact, ContactMechanicsModel &)

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	#if defined(AKANTU_USE_IOHELPER)
	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldUInt(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createElementalField(const std::string & field_name,
	const std::string & group_name, bool padding_flag,
	UInt spatial_dimension, ElementKind kind) override;
	#endif

	void dump(const std::string & dumper_name) override;
	void dump(const std::string & dumper_name, UInt step) override;
	void dump(const std::string & dumper_name, Real time, UInt step) override;

	void dump() override;

	void dump(UInt step) override;
	void dump(Real time, UInt step) override;

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// solid mechanics model
	std::unique_ptr<SolidMechanicsModelType> solid;

	/// contact mechanics model
	std::unique_ptr<ContactMechanicsModel> contact;

	UInt step;
	};

	using CouplerSolidContact = CouplerSolidContactTemplate<SolidMechanicsModel>;

	} // namespace akantu

	#include "coupler_solid_contact_tmpl.hh"

	#endif /* __COUPLER_SOLID_CONTACT_HH__ */
	diff --git a/src/model/model_couplers/coupler_solid_contact_tmpl.hh b/src/model/model_couplers/coupler_solid_contact_tmpl.hh
	index dd349e195..76d14ae35 100644
	--- a/src/model/model_couplers/coupler_solid_contact_tmpl.hh
	+++ b/src/model/model_couplers/coupler_solid_contact_tmpl.hh
	@@ -1,400 +1,401 @@
	/**
	* @file coupler_solid_contact_tmpl.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jan 21 2019
	* @date last modification: Wed Jun 23 2021
	*
	* @brief class for coupling of solid mechanics and conatct mechanics
	* model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_contact.hh"
	#include "dumpable_inline_impl.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_iohelper_paraview.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	CouplerSolidContactTemplate<
	SolidMechanicsModelType>::~CouplerSolidContactTemplate() = default;

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::initSolver(
	TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type) {
	auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	solid_model_solver.initSolver(time_step_solver_type, non_linear_solver_type);

	auto & contact_model_solver = aka::as_type<ModelSolver>(*contact);
	contact_model_solver.initSolver(time_step_solver_type,
	non_linear_solver_type);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	std::tuple<ID, TimeStepSolverType>
	CouplerSolidContactTemplate<SolidMechanicsModelType>::getDefaultSolverID(
	const AnalysisMethod & method) {
	return solid->getDefaultSolverID(method);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	TimeStepSolverType
	CouplerSolidContactTemplate<SolidMechanicsModelType>::getDefaultSolverType()
	const {
	return solid->getDefaultSolverType();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	ModelSolverOptions
	CouplerSolidContactTemplate<SolidMechanicsModelType>::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	return solid->getDefaultSolverOptions(type);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleResidual() {
	// computes the internal forces
	switch (method) {
	case _explicit_lumped_mass: {
	auto & current_positions = contact->getContactDetector().getPositions();
	current_positions.copy(solid->getCurrentPosition());
	contact->search();
	break;
	}
	default:
	break;
	}

	this->assembleInternalForces();

	auto & internal_force = solid->getInternalForce();
	auto & external_force = solid->getExternalForce();

	auto & contact_force = contact->getInternalForce();

	/* ------------------------------------------------------------------------ */
	this->getDOFManager().assembleToResidual("displacement", external_force, 1);
	this->getDOFManager().assembleToResidual("displacement", internal_force, 1);
	this->getDOFManager().assembleToResidual("displacement", contact_force, 1);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleResidual(
	const ID & residual_part) {
	AKANTU_DEBUG_IN();

	// contact->assembleInternalForces();

	auto & internal_force = solid->getInternalForce();
	auto & external_force = solid->getExternalForce();
	auto & contact_force = contact->getInternalForce();

	if ("external" == residual_part) {
	this->getDOFManager().assembleToResidual("displacement", external_force, 1);
	this->getDOFManager().assembleToResidual("displacement", contact_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	if ("internal" == residual_part) {
	this->getDOFManager().assembleToResidual("displacement", internal_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	AKANTU_CUSTOM_EXCEPTION(
	debug::SolverCallbackResidualPartUnknown(residual_part));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::predictor() {
	auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	solid_model_solver.predictor();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::corrector() {
	auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	solid_model_solver.corrector();

	switch (method) {
	case _static:
	case _implicit_dynamic: {
	auto & current_positions = contact->getContactDetector().getPositions();
	current_positions.copy(solid->getCurrentPosition());
	contact->search();
	break;
	}
	default:
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	MatrixType CouplerSolidContactTemplate<SolidMechanicsModelType>::getMatrixType(
	const ID & matrix_id) {
	- if (matrix_id == "K")
	+ if (matrix_id == "K") {
	return _symmetric;
	+ }
	if (matrix_id == "M") {
	return _symmetric;
	}
	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleMatrix(
	const ID & matrix_id) {
	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	} else if (matrix_id == "M") {
	solid->assembleMass();
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleLumpedMatrix(
	const ID & matrix_id) {
	if (matrix_id == "M") {
	solid->assembleMassLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::beforeSolveStep() {
	auto & solid_solver_callback = aka::as_type<SolverCallback>(*solid);
	solid_solver_callback.beforeSolveStep();

	auto & contact_solver_callback = aka::as_type<SolverCallback>(*contact);
	contact_solver_callback.beforeSolveStep();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::afterSolveStep(
	bool converged) {
	auto & solid_solver_callback = aka::as_type<SolverCallback>(*solid);
	solid_solver_callback.afterSolveStep(converged);

	auto & contact_solver_callback = aka::as_type<SolverCallback>(*contact);
	contact_solver_callback.afterSolveStep(converged);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<
	SolidMechanicsModelType>::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the internal forces");

	solid->assembleInternalForces();
	contact->assembleInternalForces();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<
	SolidMechanicsModelType>::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	solid->assembleStiffnessMatrix(true);

	switch (method) {
	case _static:
	case _implicit_dynamic: {
	contact->assembleStiffnessMatrix();
	break;
	}
	default:
	break;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<
	SolidMechanicsModelType>::assembleMassLumped() {
	solid->assembleMassLumped();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleMass() {
	solid->assembleMass();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleMassLumped(
	GhostType ghost_type) {
	solid->assembleMassLumped(ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::assembleMass(
	GhostType ghost_type) {
	solid->assembleMass(ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	std::shared_ptr<dumpers::Field>
	CouplerSolidContactTemplate<SolidMechanicsModelType>::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool padding_flag, UInt spatial_dimension, ElementKind kind) {

	std::shared_ptr<dumpers::Field> field;
	field = contact->createElementalField(field_name, group_name, padding_flag,
	spatial_dimension, kind);
	if (not field) {
	field = solid->createElementalField(field_name, group_name, padding_flag,
	spatial_dimension, kind);
	}
	return field;
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	std::shared_ptr<dumpers::Field>
	CouplerSolidContactTemplate<SolidMechanicsModelType>::createNodalFieldReal(
	const std::string & field_name, const std::string & group_name,
	bool padding_flag) {

	std::shared_ptr<dumpers::Field> field;
	field = contact->createNodalFieldReal(field_name, group_name, padding_flag);
	if (not field) {
	field = solid->createNodalFieldReal(field_name, group_name, padding_flag);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	std::shared_ptr<dumpers::Field>
	CouplerSolidContactTemplate<SolidMechanicsModelType>::createNodalFieldUInt(
	const std::string & field_name, const std::string & group_name,
	bool padding_flag) {
	std::shared_ptr<dumpers::Field> field;
	field = contact->createNodalFieldUInt(field_name, group_name, padding_flag);
	if (not field) {
	field = solid->createNodalFieldUInt(field_name, group_name, padding_flag);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	std::shared_ptr<dumpers::Field>
	CouplerSolidContactTemplate<SolidMechanicsModelType>::createNodalFieldBool(
	const std::string & field_name, const std::string & group_name,
	bool padding_flag) {
	std::shared_ptr<dumpers::Field> field;
	field = contact->createNodalFieldBool(field_name, group_name, padding_flag);
	if (not field) {
	field = solid->createNodalFieldBool(field_name, group_name, padding_flag);
	}
	return field;
	}

	#endif

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump(
	const std::string & dumper_name) {
	solid->onDump();
	Model::dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump(
	const std::string & dumper_name, UInt step) {
	solid->onDump();
	Model::dump(dumper_name, step);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump(
	const std::string & dumper_name, Real time, UInt step) {
	solid->onDump();
	Model::dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump() {
	solid->onDump();
	Model::dump();
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump(UInt step) {
	solid->onDump();
	Model::dump(step);
	}

	/* -------------------------------------------------------------------------- */
	template <class SolidMechanicsModelType>
	void CouplerSolidContactTemplate<SolidMechanicsModelType>::dump(Real time,
	UInt step) {
	solid->onDump();
	Model::dump(time, step);
	}

	} // namespace akantu
	diff --git a/src/model/model_couplers/coupler_solid_phasefield.cc b/src/model/model_couplers/coupler_solid_phasefield.cc
	index c6d05310e..3438f6798 100644
	--- a/src/model/model_couplers/coupler_solid_phasefield.cc
	+++ b/src/model/model_couplers/coupler_solid_phasefield.cc
	@@ -1,642 +1,630 @@
	/**
	* @file coupler_solid_phasefield.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Jun 24 2019
	* @date last modification: Fri Apr 02 2021
	*
	* @brief class for coupling of solid mechancis and phase model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_phasefield.hh"
	#include "dumpable_inline_impl.hh"
	+#include "element_synchronizer.hh"
	#include "integrator_gauss.hh"
	#include "shape_lagrange.hh"
	-#include "element_synchronizer.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_iohelper_paraview.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	-

	CouplerSolidPhaseField::CouplerSolidPhaseField(Mesh & mesh, UInt dim,
	const ID & id,
	- const ModelType model_type)
	+ const ModelType model_type)
	: Model(mesh, model_type, dim, id) {

	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<MyFEEngineType>("CouplerSolidPhaseField", mesh,
	Model::spatial_dimension);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("coupler_solid_phasefield", id,
	true);
	this->mesh.addDumpMeshToDumper("coupler_solid_phasefield", mesh,
	Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif

	this->registerDataAccessor(*this);

	solid = new SolidMechanicsModel(mesh, Model::spatial_dimension,
	"solid_mechanics_model");
	- phase = new PhaseFieldModel(mesh, Model::spatial_dimension,
	- "phase_field_model");
	+ phase =
	+ new PhaseFieldModel(mesh, Model::spatial_dimension, "phase_field_model");

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, SynchronizationTag::_csp_damage);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_csp_strain);
	-
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	-CouplerSolidPhaseField::~CouplerSolidPhaseField() {}
	+CouplerSolidPhaseField::~CouplerSolidPhaseField() = default;

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::initFullImpl(const ModelOptions & options) {

	Model::initFullImpl(options);

	this->initBC(this, displacement, displacement_increment, external_force);
	- solid->initFull( _analysis_method = this->method);
	- phase->initFull( _analysis_method = this->method);
	+ solid->initFull(_analysis_method = this->method);
	+ phase->initFull(_analysis_method = this->method);
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::initModel() {

	getFEEngine().initShapeFunctions(_not_ghost);
	getFEEngine().initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & CouplerSolidPhaseField::getFEEngineBoundary(const ID & name) {
	return dynamic_cast<FEEngine &>(
	getFEEngineClassBoundary<MyFEEngineType>(name));
	}

	/* -------------------------------------------------------------------------- */
	-void CouplerSolidPhaseField::initSolver(TimeStepSolverType time_step_solver_type,
	- NonLinearSolverType non_linear_solver_type) {
	+void CouplerSolidPhaseField::initSolver(
	+ TimeStepSolverType time_step_solver_type,
	+ NonLinearSolverType non_linear_solver_type) {

	- auto & solid_model_solver =
	- aka::as_type<ModelSolver>(*solid);
	- solid_model_solver.initSolver(time_step_solver_type, non_linear_solver_type);
	+ auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	+ solid_model_solver.initSolver(time_step_solver_type, non_linear_solver_type);

	- auto & phase_model_solver =
	- aka::as_type<ModelSolver>(*phase);
	- phase_model_solver.initSolver(time_step_solver_type, non_linear_solver_type);
	+ auto & phase_model_solver = aka::as_type<ModelSolver>(*phase);
	+ phase_model_solver.initSolver(time_step_solver_type, non_linear_solver_type);
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	CouplerSolidPhaseField::getDefaultSolverID(const AnalysisMethod & method) {

	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _explicit_consistent_mass: {
	return std::make_tuple("explicit", TimeStepSolverType::_dynamic);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	- }
	+ }
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolverType CouplerSolidPhaseField::getDefaultSolverType() const {
	return TimeStepSolverType::_dynamic_lumped;
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions CouplerSolidPhaseField::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_linear;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["displacement"] = IntegrationScheme::_not_defined;
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	break;
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleResidual() {

	// computes the internal forces
	this->assembleInternalForces();

	auto & solid_internal_force = solid->getInternalForce();
	auto & solid_external_force = solid->getExternalForce();

	auto & phasefield_internal_force = phase->getInternalForce();
	auto & phasefield_external_force = phase->getExternalForce();

	/* ------------------------------------------------------------------------ */
	this->getDOFManager().assembleToResidual("displacement", solid_external_force,
	1);
	this->getDOFManager().assembleToResidual("displacement", solid_internal_force,
	1);
	this->getDOFManager().assembleToResidual("damage", phasefield_external_force,
	1);
	this->getDOFManager().assembleToResidual("damage", phasefield_internal_force,
	1);
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleResidual(const ID & residual_part) {
	AKANTU_DEBUG_IN();

	auto & solid_internal_force = solid->getInternalForce();
	auto & solid_external_force = solid->getExternalForce();

	auto & phasefield_internal_force = phase->getInternalForce();
	auto & phasefield_external_force = phase->getExternalForce();

	if ("external" == residual_part) {
	this->getDOFManager().assembleToResidual("displacement",
	solid_external_force, 1);
	this->getDOFManager().assembleToResidual("displacement",
	solid_internal_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	if ("internal" == residual_part) {
	this->getDOFManager().assembleToResidual("damage",
	phasefield_external_force, 1);
	this->getDOFManager().assembleToResidual("damage",
	phasefield_internal_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	AKANTU_CUSTOM_EXCEPTION(
	debug::SolverCallbackResidualPartUnknown(residual_part));

	AKANTU_DEBUG_OUT();
	}

	-
	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::predictor() {

	- auto & solid_model_solver =
	- aka::as_type<ModelSolver>(*solid);
	+ auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	solid_model_solver.predictor();
	-
	- auto & phase_model_solver =
	- aka::as_type<ModelSolver>(*phase);
	+
	+ auto & phase_model_solver = aka::as_type<ModelSolver>(*phase);
	phase_model_solver.predictor();
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::corrector() {

	- auto & solid_model_solver =
	- aka::as_type<ModelSolver>(*solid);
	+ auto & solid_model_solver = aka::as_type<ModelSolver>(*solid);
	solid_model_solver.corrector();
	-
	- auto & phase_model_solver =
	- aka::as_type<ModelSolver>(*phase);
	+
	+ auto & phase_model_solver = aka::as_type<ModelSolver>(*phase);
	phase_model_solver.corrector();
	}
	-
	-

	/* -------------------------------------------------------------------------- */
	MatrixType CouplerSolidPhaseField::getMatrixType(const ID & matrix_id) {

	- if (matrix_id == "K")
	+ if (matrix_id == "K") {
	return _symmetric;
	+ }
	if (matrix_id == "M") {
	return _symmetric;
	}
	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleMatrix(const ID & matrix_id) {

	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	} else if (matrix_id == "M") {
	solid->assembleMass();
	}
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleLumpedMatrix(const ID & matrix_id) {
	if (matrix_id == "M") {
	solid->assembleMassLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::beforeSolveStep() {
	- auto & solid_solver_callback =
	- aka::as_type<SolverCallback>(*solid);
	+ auto & solid_solver_callback = aka::as_type<SolverCallback>(*solid);
	solid_solver_callback.beforeSolveStep();
	-
	- auto & phase_solver_callback =
	- aka::as_type<SolverCallback>(*phase);
	+
	+ auto & phase_solver_callback = aka::as_type<SolverCallback>(*phase);
	phase_solver_callback.beforeSolveStep();
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::afterSolveStep(bool converged) {
	- auto & solid_solver_callback =
	- aka::as_type<SolverCallback>(*solid);
	+ auto & solid_solver_callback = aka::as_type<SolverCallback>(*solid);
	solid_solver_callback.afterSolveStep(converged);
	-
	- auto & phase_solver_callback =
	- aka::as_type<SolverCallback>(*phase);
	+
	+ auto & phase_solver_callback = aka::as_type<SolverCallback>(*phase);
	phase_solver_callback.afterSolveStep(converged);
	}
	-

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the internal forces");

	solid->assembleInternalForces();
	phase->assembleInternalForces();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	solid->assembleStiffnessMatrix();
	phase->assembleStiffnessMatrix();
	-
	+
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	-void CouplerSolidPhaseField::assembleMassLumped() { solid->assembleMassLumped(); }
	+void CouplerSolidPhaseField::assembleMassLumped() {
	+ solid->assembleMassLumped();
	+}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleMass() { solid->assembleMass(); }

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleMassLumped(GhostType ghost_type) {
	solid->assembleMassLumped(ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::assembleMass(GhostType ghost_type) {
	solid->assembleMass(ghost_type);
	}

	/* ------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::computeDamageOnQuadPoints(
	const GhostType & ghost_type) {

	AKANTU_DEBUG_IN();

	auto & fem = phase->getFEEngine();
	auto & mesh = phase->getMesh();

	- auto nb_materials = solid->getNbMaterials();
	+ auto nb_materials = solid->getNbMaterials();
	auto nb_phasefields = phase->getNbPhaseFields();
	-
	- AKANTU_DEBUG_ASSERT(nb_phasefields == nb_materials,
	- "The number of phasefields and materials should be equal" );
	-
	- for(auto index : arange(nb_materials)) {
	+
	+ AKANTU_DEBUG_ASSERT(
	+ nb_phasefields == nb_materials,
	+ "The number of phasefields and materials should be equal");
	+
	+ for (auto index : arange(nb_materials)) {
	auto & material = solid->getMaterial(index);
	-
	- for(auto index2 : arange(nb_phasefields)) {
	+
	+ for (auto index2 : arange(nb_phasefields)) {
	auto & phasefield = phase->getPhaseField(index2);
	-
	- if(phasefield.getName() == material.getName()){
	-
	- switch (spatial_dimension) {
	- case 1: {
	- auto & mat = static_cast<MaterialPhaseField<1> &>(material);
	- auto & damage = mat.getDamage();
	- for (auto & type :
	- mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	- auto & damage_on_qpoints_vect = damage(type, ghost_type);
	- fem.interpolateOnIntegrationPoints(phase->getDamage(), damage_on_qpoints_vect,
	- 1, type, ghost_type);
	- }
	- break;
	- }
	-
	- case 2: {
	- auto & mat = static_cast<MaterialPhaseField<2> &>(material);
	- auto & damage = mat.getDamage();
	-
	- for (auto & type :
	- mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	- auto & damage_on_qpoints_vect = damage(type, ghost_type);
	- fem.interpolateOnIntegrationPoints(phase->getDamage(), damage_on_qpoints_vect,
	- 1, type, ghost_type);
	- }
	- break;
	- }
	- default:
	- auto & mat = static_cast<MaterialPhaseField<3> &>(material);
	- auto & damage = mat.getDamage();
	-
	- for (auto & type :
	- mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	- auto & damage_on_qpoints_vect = damage(type, ghost_type);
	- fem.interpolateOnIntegrationPoints(phase->getDamage(), damage_on_qpoints_vect,
	- 1, type, ghost_type);
	- }
	- break;
	- }
	+
	+ if (phasefield.getName() == material.getName()) {
	+
	+ switch (spatial_dimension) {
	+ case 1: {
	+ auto & mat = static_cast<MaterialPhaseField<1> &>(material);
	+ auto & damage = mat.getDamage();
	+ for (const auto & type :
	+ mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	+ auto & damage_on_qpoints_vect = damage(type, ghost_type);
	+ fem.interpolateOnIntegrationPoints(phase->getDamage(),
	+ damage_on_qpoints_vect, 1, type,
	+ ghost_type);
	+ }
	+ break;
	+ }
	+
	+ case 2: {
	+ auto & mat = static_cast<MaterialPhaseField<2> &>(material);
	+ auto & damage = mat.getDamage();
	+
	+ for (const auto & type :
	+ mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	+ auto & damage_on_qpoints_vect = damage(type, ghost_type);
	+ fem.interpolateOnIntegrationPoints(phase->getDamage(),
	+ damage_on_qpoints_vect, 1, type,
	+ ghost_type);
	+ }
	+ break;
	+ }
	+ default:
	+ auto & mat = static_cast<MaterialPhaseField<3> &>(material);
	+ auto & damage = mat.getDamage();
	+
	+ for (const auto & type :
	+ mesh.elementTypes(Model::spatial_dimension, ghost_type)) {
	+ auto & damage_on_qpoints_vect = damage(type, ghost_type);
	+ fem.interpolateOnIntegrationPoints(phase->getDamage(),
	+ damage_on_qpoints_vect, 1, type,
	+ ghost_type);
	+ }
	+ break;
	+ }
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* ------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::computeStrainOnQuadPoints(
	const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	-
	auto & mesh = solid->getMesh();

	- auto nb_materials = solid->getNbMaterials();
	+ auto nb_materials = solid->getNbMaterials();
	auto nb_phasefields = phase->getNbPhaseFields();
	-
	- AKANTU_DEBUG_ASSERT(nb_phasefields == nb_materials,
	- "The number of phasefields and materials should be equal" );

	+ AKANTU_DEBUG_ASSERT(
	+ nb_phasefields == nb_materials,
	+ "The number of phasefields and materials should be equal");

	- for(auto index : arange(nb_materials)) {
	+ for (auto index : arange(nb_materials)) {
	auto & material = solid->getMaterial(index);
	-
	- for(auto index2 : arange(nb_phasefields)) {
	+
	+ for (auto index2 : arange(nb_phasefields)) {
	auto & phasefield = phase->getPhaseField(index2);
	-
	- if(phasefield.getName() == material.getName()){
	-
	- auto & strain_on_qpoints = phasefield.getStrain();
	- auto & gradu_on_qpoints = material.getGradU();
	-
	- for (auto & type: mesh.elementTypes(spatial_dimension, ghost_type)) {
	- auto & strain_on_qpoints_vect = strain_on_qpoints(type, ghost_type);
	- auto & gradu_on_qpoints_vect = gradu_on_qpoints(type, ghost_type);
	- for (auto && values:
	- zip(make_view(strain_on_qpoints_vect, spatial_dimension, spatial_dimension),
	- make_view(gradu_on_qpoints_vect, spatial_dimension, spatial_dimension))) {
	- auto & strain = std::get<0>(values);
	- auto & grad_u = std::get<1>(values);
	- gradUToEpsilon(grad_u, strain);
	- }
	- }
	-
	- break;
	+
	+ if (phasefield.getName() == material.getName()) {
	+
	+ auto & strain_on_qpoints = phasefield.getStrain();
	+ const auto & gradu_on_qpoints = material.getGradU();
	+
	+ for (const auto & type :
	+ mesh.elementTypes(spatial_dimension, ghost_type)) {
	+ auto & strain_on_qpoints_vect = strain_on_qpoints(type, ghost_type);
	+ const auto & gradu_on_qpoints_vect =
	+ gradu_on_qpoints(type, ghost_type);
	+ for (auto && values :
	+ zip(make_view(strain_on_qpoints_vect, spatial_dimension,
	+ spatial_dimension),
	+ make_view(gradu_on_qpoints_vect, spatial_dimension,
	+ spatial_dimension))) {
	+ auto & strain = std::get<0>(values);
	+ const auto & grad_u = std::get<1>(values);
	+ gradUToEpsilon(grad_u, strain);
	+ }
	+ }
	+
	+ break;
	}
	-
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* ------------------------------------------------------------------------- */
	-void CouplerSolidPhaseField::solve(const ID & solid_solver_id, const ID & phase_solver_id) {
	+void CouplerSolidPhaseField::solve(const ID & solid_solver_id,
	+ const ID & phase_solver_id) {

	solid->solveStep(solid_solver_id);
	this->computeStrainOnQuadPoints(_not_ghost);

	phase->solveStep(phase_solver_id);
	this->computeDamageOnQuadPoints(_not_ghost);

	solid->assembleInternalForces();
	}

	/* ------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::gradUToEpsilon(const Matrix<Real> & grad_u,
	Matrix<Real> & epsilon) {
	for (UInt i = 0; i < Model::spatial_dimension; ++i) {
	- for (UInt j = 0; j < Model::spatial_dimension; ++j)
	+ for (UInt j = 0; j < Model::spatial_dimension; ++j) {
	epsilon(i, j) = 0.5 * (grad_u(i, j) + grad_u(j, i));
	+ }
	}
	}

	/* ------------------------------------------------------------------------- */
	bool CouplerSolidPhaseField::checkConvergence(Array<Real> & u_new,
	Array<Real> & u_old,
	Array<Real> & d_new,
	Array<Real> & d_old) {

	const Array<bool> & blocked_dofs = solid->getBlockedDOFs();
	UInt nb_degree_of_freedom = u_new.size();

	auto u_n_it = u_new.begin();
	auto u_o_it = u_old.begin();
	auto bld_it = blocked_dofs.begin();

	Real norm = 0;
	for (UInt n = 0; n < nb_degree_of_freedom;
	++n, ++u_n_it, ++u_o_it, ++bld_it) {
	if ((!*bld_it)) {
	norm += (u_n_it - u_o_it) * (u_n_it - u_o_it);
	}
	}

	norm = std::sqrt(norm);

	auto d_n_it = d_new.begin();
	auto d_o_it = d_old.begin();
	nb_degree_of_freedom = d_new.size();

	Real norm2 = 0;
	for (UInt i = 0; i < nb_degree_of_freedom; ++i) {
	norm2 += (d_n_it - d_o_it);
	}

	norm2 = std::sqrt(norm2);

	Real error = std::max(norm, norm2);

	Real tolerance = 1e-8;
	- if (error < tolerance) {
	-
	- return true;
	- }
	-
	- return false;
	+ return error < tolerance;
	}

	-
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> CouplerSolidPhaseField::createElementalField(
	const std::string & field_name, const std::string & group_name,
	- bool padding_flag, UInt spatial_dimension,
	- ElementKind kind) {
	+ bool padding_flag, UInt spatial_dimension, ElementKind kind) {

	return solid->createElementalField(field_name, group_name, padding_flag,
	spatial_dimension, kind);

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	CouplerSolidPhaseField::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	return solid->createNodalFieldReal(field_name, group_name, padding_flag);

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	CouplerSolidPhaseField::createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	return solid->createNodalFieldBool(field_name, group_name, padding_flag);

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	#else

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> CouplerSolidPhaseField::createElementalField(
	- const std::string &, const std::string &, bool, UInt ,
	- ElementKind) {
	+ const std::string &, const std::string &, bool, UInt, ElementKind) {
	return nullptr;
	}

	/* ----------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	CouplerSolidPhaseField::createNodalFieldReal(const std::string &,
	const std::string &, bool) {
	return nullptr;
	}

	/-------------------------------------------------------------------/
	std::shared_ptr<dumpers::Field>
	CouplerSolidPhaseField::createNodalFieldBool(const std::string &,
	const std::string &, bool) {
	return nullptr;
	}

	#endif

	/* -----------------------------------------------------------------------*/
	void CouplerSolidPhaseField::dump(const std::string & dumper_name) {
	solid->onDump();
	mesh.dump(dumper_name);
	}

	/* ------------------------------------------------------------------------*/
	void CouplerSolidPhaseField::dump(const std::string & dumper_name, UInt step) {
	solid->onDump();
	mesh.dump(dumper_name, step);
	}

	/* ----------------------------------------------------------------------- */
	void CouplerSolidPhaseField::dump(const std::string & dumper_name, Real time,
	UInt step) {
	solid->onDump();
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::dump() {
	solid->onDump();
	mesh.dump();
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::dump(UInt step) {
	solid->onDump();
	mesh.dump(step);
	}

	/* -------------------------------------------------------------------------- */
	void CouplerSolidPhaseField::dump(Real time, UInt step) {
	solid->onDump();
	mesh.dump(time, step);
	}

	} // namespace akantu
	diff --git a/src/model/model_couplers/coupler_solid_phasefield.hh b/src/model/model_couplers/coupler_solid_phasefield.hh
	index 1726dfa94..38503760a 100644
	--- a/src/model/model_couplers/coupler_solid_phasefield.hh
	+++ b/src/model/model_couplers/coupler_solid_phasefield.hh
	@@ -1,289 +1,294 @@
	/**
	* @file coupler_solid_phasefield.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Jun 24 2019
	* @date last modification: Wed Jun 23 2021
	*
	* @brief class for coupling of solid mechancis and phasefield model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition.hh"
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	#include "material.hh"
	#include "material_phasefield.hh"
	#include "model.hh"
	#include "phase_field_model.hh"
	#include "solid_mechanics_model.hh"
	#include "sparse_matrix.hh"
	#include "time_step_solver.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_COUPLER_SOLID_PHASEFIELD_HH__
	#define __AKANTU_COUPLER_SOLID_PHASEFIELD_HH__

	/* ------------------------------------------------------------------------ */
	/* Coupling : Solid Mechanics / PhaseField */
	/* ------------------------------------------------------------------------ */
	namespace akantu {
	template <ElementKind kind, class IntegrationOrderFunctor>
	class IntegratorGauss;
	template <ElementKind kind> class ShapeLagrange;
	class DOFManager;
	} // namespace akantu

	namespace akantu {

	class CouplerSolidPhaseField
	: public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt>,
	public BoundaryCondition<CouplerSolidPhaseField> {

	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructors */
	/* ------------------------------------------------------------------------ */

	using MyFEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	public:
	CouplerSolidPhaseField(
	- Mesh & mesh, UInt spatial_dimension = _all_dimensions,
	+ Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "coupler_solid_phasefield",
	- const ModelType model_type = ModelType::_coupler_solid_phasefield);
	+ ModelType model_type = ModelType::_coupler_solid_phasefield);

	~CouplerSolidPhaseField() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize the complete model
	void initFullImpl(const ModelOptions & options) override;

	/// initialize the modelType
	void initModel() override;

	/// get some default values for derived classes
	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	/* ------------------------------------------------------------------------ */
	/* Solver Interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// assembles the contact stiffness matrix
	virtual void assembleStiffnessMatrix();

	/// assembles the contant internal forces
	virtual void assembleInternalForces();

	public:
	/// computes damage on quad points for solid mechanics model from
	/// damage array from phasefield model
	- void computeDamageOnQuadPoints(const GhostType &);
	+ void computeDamageOnQuadPoints(const GhostType & /ghost_type/);

	/// computes strain on quadrature points for phasefield model from
	/// displacement gradient from solid mechanics model
	void computeStrainOnQuadPoints(const GhostType & ghost_type);

	/// solve the coupled model
	void solve(const ID & solid_solver_id = "", const ID & phase_solver_id = "");

	private:
	/// computes small strain from displacement gradient
	void gradUToEpsilon(const Matrix<Real> & grad_u, Matrix<Real> & epsilon);

	/// test the convergence criteria
	- bool checkConvergence(Array<Real> &, Array<Real> &, Array<Real> &,
	- Array<Real> &);
	+ bool checkConvergence(Array<Real> & /u_new/, Array<Real> & /u_old/,
	+ Array<Real> & /d_new/, Array<Real> & /d_old/);

	protected:
	/// callback for the solver, this adds f_{ext} - f_{int} to the residual
	void assembleResidual() override;

	/// callback for the solver, this adds f_{ext} or f_{int} to the residual
	void assembleResidual(const ID & residual_part) override;
	bool canSplitResidual() override { return true; }

	/// get the type of matrix needed
	MatrixType getMatrixType(const ID & matrix_id) override;

	/// callback for the solver, this assembles different matrices
	void assembleMatrix(const ID & matrix_id) override;

	/// callback for the solver, this assembles the stiffness matrix
	void assembleLumpedMatrix(const ID & matrix_id) override;

	/// callback for the model to instantiate the matricess when needed
	- void initSolver(TimeStepSolverType, NonLinearSolverType) override;
	-
	+ void initSolver(TimeStepSolverType /time_step_solver_type/,
	+ NonLinearSolverType /non_linear_solver_type/) override;
	+
	/// callback for the solver, this is called at beginning of solve
	void predictor() override;

	/// callback for the solver, this is called at end of solve
	void corrector() override;

	/// callback for the solver, this is called at beginning of solve
	void beforeSolveStep() override;

	/// callback for the solver, this is called at end of solve
	void afterSolveStep(bool converged = true) override;
	-
	+
	/// solve the coupled model
	- //void solveStep(const ID & solver_id = "") override;
	+ // void solveStep(const ID & solver_id = "") override;

	/// solve a step using a given pre instantiated time step solver and
	/// non linear solver with a user defined callback instead of the
	/// model itself /!\ This can mess up everything
	- //void solveStep(SolverCallback & callback, const ID & solver_id = "") override;
	+ // void solveStep(SolverCallback & callback, const ID & solver_id = "")
	+ // override;

	/* ------------------------------------------------------------------------ */
	/* Mass matrix for solid mechanics model */
	/* ------------------------------------------------------------------------ */
	public:
	/// assemble the lumped mass matrix
	void assembleMassLumped();

	/// assemble the mass matrix for consistent mass resolutions
	void assembleMass();

	protected:
	/// assemble the lumped mass matrix for local and ghost elements
	void assembleMassLumped(GhostType ghost_type);

	/// assemble the mass matrix for either _ghost or _not_ghost elements
	void assembleMass(GhostType ghost_type);

	protected:
	/* --------------------------------------------------------------------------
	*/
	TimeStepSolverType getDefaultSolverType() const override;
	/* --------------------------------------------------------------------------
	*/
	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;

	public:
	bool isDefaultSolverExplicit() { return method == _explicit_lumped_mass; }

	/* ------------------------------------------------------------------------ */
	public:
	// DataAccessor<Element>
	-
	- UInt getNbData(const Array<Element> &,
	- const SynchronizationTag &) const override {
	+
	+ UInt getNbData(const Array<Element> & /elements/,
	+ const SynchronizationTag & /tag/) const override {
	return 0;
	}
	- void packData(CommunicationBuffer &, const Array<Element> &,
	- const SynchronizationTag &) const override {}
	- void unpackData(CommunicationBuffer &, const Array<Element> &,
	- const SynchronizationTag &) override {}
	-
	+ void packData(CommunicationBuffer & /buffer/,
	+ const Array<Element> & /element/,
	+ const SynchronizationTag & /tag/) const override {}
	+ void unpackData(CommunicationBuffer & /buffer/,
	+ const Array<Element> & /element/,
	+ const SynchronizationTag & /tag/) override {}
	+
	UInt getNbData(__attribute__((unused)) const Array<UInt> & indexes,
	- __attribute__((unused)) const SynchronizationTag & tag) const override {
	+ __attribute__((unused))
	+ const SynchronizationTag & tag) const override {
	return 0;
	}

	void packData(__attribute__((unused)) CommunicationBuffer & buffer,
	- __attribute__((unused)) const Array<UInt> & dofs,
	- __attribute__((unused)) const SynchronizationTag & tag) const override{}
	+ __attribute__((unused)) const Array<UInt> & dofs,
	+ __attribute__((unused))
	+ const SynchronizationTag & tag) const override {}

	void unpackData(__attribute__((unused)) CommunicationBuffer & buffer,
	- __attribute__((unused)) const Array<UInt> & dofs,
	- __attribute__((unused)) const SynchronizationTag & tag) override {}
	-
	+ __attribute__((unused)) const Array<UInt> & dofs,
	+ __attribute__((unused))
	+ const SynchronizationTag & tag) override {}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	FEEngine & getFEEngineBoundary(const ID & name = "") override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the solid mechanics model
	AKANTU_GET_MACRO(SolidMechanicsModel, *solid, SolidMechanicsModel &);

	/// get the contact mechanics model
	AKANTU_GET_MACRO(PhaseFieldModel, *phase, PhaseFieldModel &);

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createElementalField(const std::string & field_name,
	const std::string & group_name, bool padding_flag,
	- UInt spatial_dimension,
	- ElementKind kind) override;
	+ UInt spatial_dimension, ElementKind kind) override;

	- virtual void dump(const std::string & dumper_name) override;
	+ void dump(const std::string & dumper_name) override;

	- virtual void dump(const std::string & dumper_name, UInt step) override;
	+ void dump(const std::string & dumper_name, UInt step) override;

	- virtual void dump(const std::string & dumper_name, Real time, UInt step) override;
	+ void dump(const std::string & dumper_name, Real time, UInt step) override;

	void dump() override;

	- virtual void dump(UInt step) override;
	+ void dump(UInt step) override;

	- virtual void dump(Real time, UInt step) override;
	+ void dump(Real time, UInt step) override;

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// solid mechanics model
	SolidMechanicsModel * solid{nullptr};

	/// phasefield model
	PhaseFieldModel * phase{nullptr};

	Array<Real> * displacement{nullptr};

	///
	Array<Real> * displacement_increment{nullptr};

	/// external forces array
	Array<Real> * external_force{nullptr};
	};

	} // namespace akantu

	#endif /* __AKANTU_COUPLER_SOLID_PHASEFIELD_HH__ */
	diff --git a/src/model/model_inline_impl.hh b/src/model/model_inline_impl.hh
	index 1563a3a2a..1f1e8572c 100644
	--- a/src/model/model_inline_impl.hh
	+++ b/src/model/model_inline_impl.hh
	@@ -1,177 +1,177 @@
	/**
	* @file model_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 25 2010
	* @date last modification: Wed Mar 10 2021
	*
	* @brief inline implementation of the model class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MODEL_INLINE_IMPL_HH_
	#define AKANTU_MODEL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename FEEngineClass>
	inline FEEngineClass & Model::getFEEngineClassBoundary(std::string name) {
	if (name.empty()) {
	name = default_fem;
	}

	auto it_boun = fems_boundary.find(name);

	if (it_boun == fems_boundary.end()) {
	AKANTU_DEBUG_INFO("Creating FEEngine boundary " << name);

	auto it = fems.find(name);
	if (it == fems.end()) {
	AKANTU_EXCEPTION("The FEEngine " << name << " is not registered");
	}

	auto spatial_dimension = it->second->getElementDimension();
	fems_boundary[name] = std::make_unique<FEEngineClass>(
	it->second->getMesh(), spatial_dimension - 1,
	id + ":fem_boundary:" + name);
	}

	return aka::as_type<FEEngineClass>(*fems_boundary[name]);
	}

	/* -------------------------------------------------------------------------- */
	template <typename FEEngineClass>
	inline FEEngineClass & Model::getFEEngineClass(std::string name) const {
	if (name.empty()) {
	name = default_fem;
	}

	auto it = fems.find(name);
	if (it == fems.end()) {
	AKANTU_EXCEPTION("The FEEngine " << name << " is not registered");
	}

	return aka::as_type<FEEngineClass>(*(it->second));
	}

	/* -------------------------------------------------------------------------- */
	inline void Model::unRegisterFEEngineObject(const std::string & name) {
	auto it = fems.find(name);
	if (it == fems.end()) {
	AKANTU_EXCEPTION("FEEngine object with name " << name << " was not found");
	}

	fems.erase(it);
	if (not fems.empty() and default_fem == name) {
	default_fem = (*fems.begin()).first;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename FEEngineClass>
	inline void Model::registerFEEngineObject(const std::string & name, Mesh & mesh,
	UInt spatial_dimension) {
	if (fems.empty()) {
	default_fem = name;
	}

	auto it = fems.find(name);
	if (it != fems.end()) {
	AKANTU_EXCEPTION("FEEngine object with name " << name
	<< " was already created");
	}

	- fems[name] = std::make_unique<FEEngineClass>(
	- mesh, spatial_dimension, id + ":fem:" + name);
	+ fems[name] = std::make_unique<FEEngineClass>(mesh, spatial_dimension,
	+ id + ":fem:" + name);
	}

	/* -------------------------------------------------------------------------- */
	inline FEEngine & Model::getFEEngine(const ID & name) const {
	ID tmp_name = (name.empty()) ? default_fem : name;

	auto it = fems.find(tmp_name);

	if (it == fems.end()) {
	AKANTU_EXCEPTION("The FEEngine " << tmp_name << " is not registered");
	}
	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	inline FEEngine & Model::getFEEngineBoundary(const ID & name) {
	ID tmp_name = (name.empty()) ? default_fem : name;

	auto it = fems_boundary.find(tmp_name);
	if (it == fems_boundary.end()) {
	AKANTU_EXCEPTION("The FEEngine boundary " << tmp_name
	<< " is not registered");
	}
	AKANTU_DEBUG_ASSERT(it->second != nullptr, "The FEEngine boundary "
	<< tmp_name
	<< " was not created");
	return *(it->second);
	}

	/* -------------------------------------------------------------------------- */
	inline bool Model::hasFEEngineBoundary(const ID & name) {
	ID tmp_name = (name.empty()) ? default_fem : name;
	auto it = fems_boundary.find(tmp_name);
	return (it != fems_boundary.end());
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Model::allocNodalField(std::unique_ptr<Array<T>> & array,
	UInt nb_component, const ID & name) const {
	if (array) {
	return;
	}

	UInt nb_nodes = mesh.getNbNodes();
	array =
	std::make_unique<Array<T>>(nb_nodes, nb_component, T(), id + ":" + name);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Model::getNbIntegrationPoints(const Array<Element> & elements,
	const ID & fem_id) const {
	UInt nb_quad = 0;
	for (auto && el : elements) {
	nb_quad +=
	getFEEngine(fem_id).getNbIntegrationPoints(el.type, el.ghost_type);
	}
	return nb_quad;
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_MODEL_INLINE_IMPL_HH_ */
	diff --git a/src/model/model_options.hh b/src/model/model_options.hh
	index b9f462c99..77128acc7 100644
	--- a/src/model/model_options.hh
	+++ b/src/model/model_options.hh
	@@ -1,204 +1,205 @@
	/**
	* @file model_options.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 04 2017
	* @date last modification: Fri Jun 12 2020
	*
	* @brief Description of the model options
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_named_argument.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MODEL_OPTIONS_HH_
	#define AKANTU_MODEL_OPTIONS_HH_

	namespace akantu {

	namespace {
	DECLARE_NAMED_ARGUMENT(analysis_method);
	}

	struct ModelOptions {
	explicit ModelOptions(AnalysisMethod analysis_method = _static)
	: analysis_method(analysis_method) {}

	template <typename... pack>
	ModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: ModelOptions(OPTIONAL_NAMED_ARG(analysis_method, _static)) {}

	virtual ~ModelOptions() = default;

	AnalysisMethod analysis_method;
	};

	#ifdef AKANTU_SOLID_MECHANICS
	/* -------------------------------------------------------------------------- */
	struct SolidMechanicsModelOptions : public ModelOptions {
	explicit SolidMechanicsModelOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass)
	: ModelOptions(analysis_method) {}

	template <typename... pack>
	SolidMechanicsModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: SolidMechanicsModelOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass)) {}
	};
	#endif

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_COHESIVE_ELEMENT
	namespace {
	DECLARE_NAMED_ARGUMENT(is_extrinsic);
	}
	/* -------------------------------------------------------------------------- */
	struct SolidMechanicsModelCohesiveOptions : public SolidMechanicsModelOptions {
	SolidMechanicsModelCohesiveOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass,
	bool extrinsic = false)
	- : SolidMechanicsModelOptions(analysis_method), is_extrinsic(extrinsic) {}
	+ : SolidMechanicsModelOptions(analysis_method), is_extrinsic(extrinsic) {}

	template <typename... pack>
	SolidMechanicsModelCohesiveOptions(use_named_args_t /unused/,
	pack &&... _pack)
	: SolidMechanicsModelCohesiveOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass),
	OPTIONAL_NAMED_ARG(is_extrinsic, false)) {}

	bool is_extrinsic{false};
	};
	-
	+
	#endif

	#ifdef AKANTU_HEAT_TRANSFER
	/* -------------------------------------------------------------------------- */
	struct HeatTransferModelOptions : public ModelOptions {
	explicit HeatTransferModelOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass)
	: ModelOptions(analysis_method) {}

	template <typename... pack>
	HeatTransferModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: HeatTransferModelOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass)) {}
	};
	#endif

	#ifdef AKANTU_PHASE_FIELD
	/* -------------------------------------------------------------------------- */
	struct PhaseFieldModelOptions : public ModelOptions {
	explicit PhaseFieldModelOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass)
	: ModelOptions(analysis_method) {}

	template <typename... pack>
	- PhaseFieldModelOptions(use_named_args_t, pack &&... _pack)
	+ PhaseFieldModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: PhaseFieldModelOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass)) {}
	};
	#endif

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_EMBEDDED

	namespace {
	DECLARE_NAMED_ARGUMENT(init_intersections);
	}
	/* -------------------------------------------------------------------------- */
	struct EmbeddedInterfaceModelOptions : SolidMechanicsModelOptions {
	/**
	* @brief Constructor for EmbeddedInterfaceModelOptions
	* @param analysis_method see SolidMechanicsModelOptions
	* @param init_intersections compute intersections
	*/
	EmbeddedInterfaceModelOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass,
	bool init_intersections = true)
	: SolidMechanicsModelOptions(analysis_method),
	has_intersections(init_intersections) {}

	template <typename... pack>
	EmbeddedInterfaceModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: EmbeddedInterfaceModelOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass),
	OPTIONAL_NAMED_ARG(init_intersections, true)) {}

	/// Should consider reinforcements
	bool has_intersections;
	};
	#endif

	#ifdef AKANTU_CONTACT_MECHANICS
	/* -------------------------------------------------------------------------- */
	struct ContactMechanicsModelOptions : public ModelOptions {
	explicit ContactMechanicsModelOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass)
	: ModelOptions(analysis_method) {}

	template <typename... pack>
	- ContactMechanicsModelOptions(use_named_args_t, pack &&... _pack)
	+ ContactMechanicsModelOptions(use_named_args_t /unused/, pack &&... _pack)
	: ContactMechanicsModelOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass)) {}
	};
	#endif

	#ifdef AKANTU_MODEL_COUPLERS
	/* -------------------------------------------------------------------------- */
	struct CouplerSolidContactOptions : public ModelOptions {
	explicit CouplerSolidContactOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass)
	: ModelOptions(analysis_method) {}

	template <typename... pack>
	- CouplerSolidContactOptions(use_named_args_t, pack &&... _pack)
	+ CouplerSolidContactOptions(use_named_args_t /unused/, pack &&... _pack)
	: CouplerSolidContactOptions(
	OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass)) {}
	};

	/* -------------------------------------------------------------------------- */
	struct CouplerSolidCohesiveContactOptions : public ModelOptions {
	CouplerSolidCohesiveContactOptions(
	AnalysisMethod analysis_method = _explicit_lumped_mass,
	bool extrinsic = false)
	- : ModelOptions(analysis_method), is_extrinsic(extrinsic) {}
	-
	- template<typename... pack>
	- CouplerSolidCohesiveContactOptions(use_named_args_t, pack &&... _pack)
	- : CouplerSolidCohesiveContactOptions(
	- OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass),
	- OPTIONAL_NAMED_ARG(is_extrinsic, false)) {}
	-
	+ : ModelOptions(analysis_method), is_extrinsic(extrinsic) {}
	+
	+ template <typename... pack>
	+ CouplerSolidCohesiveContactOptions(use_named_args_t /unused/,
	+ pack &&... _pack)
	+ : CouplerSolidCohesiveContactOptions(
	+ OPTIONAL_NAMED_ARG(analysis_method, _explicit_lumped_mass),
	+ OPTIONAL_NAMED_ARG(is_extrinsic, false)) {}
	+
	bool is_extrinsic{false};
	};
	-
	+
	#endif

	} // namespace akantu

	#endif /* AKANTU_MODEL_OPTIONS_HH_ */
	diff --git a/src/model/phase_field/phase_field_model.cc b/src/model/phase_field/phase_field_model.cc
	index 22465d450..fadfd6ffe 100644
	--- a/src/model/phase_field/phase_field_model.cc
	+++ b/src/model/phase_field/phase_field_model.cc
	@@ -1,633 +1,635 @@
	/**
	* @file phase_field_model.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Tue Sep 04 2018
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Implementation of PhaseFieldModel class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phase_field_model.hh"
	#include "dumpable_inline_impl.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "generalized_trapezoidal.hh"
	#include "group_manager_inline_impl.hh"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "parser.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_element_partition.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	PhaseFieldModel::PhaseFieldModel(Mesh & mesh, UInt dim, const ID & id,
	ModelType model_type)
	: Model(mesh, model_type, dim, id),
	phasefield_index("phasefield index", id),
	phasefield_local_numbering("phasefield local numbering", id) {

	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<FEEngineType>("PhaseFieldFEEngine", mesh,
	Model::spatial_dimension);

	#ifdef AKANTU_USE_IOHELPER
	this->mesh.registerDumper<DumperParaview>("phase_field", id, true);
	this->mesh.addDumpMesh(mesh, Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif // AKANTU_USE_IOHELPER

	phasefield_selector =
	std::make_shared<DefaultPhaseFieldSelector>(phasefield_index);

	this->initDOFManager();

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, SynchronizationTag::_pfm_damage);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_pfm_driving);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_pfm_history);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_pfm_energy);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	PhaseFieldModel::~PhaseFieldModel() = default;

	/* -------------------------------------------------------------------------- */
	MatrixType PhaseFieldModel::getMatrixType(const ID & matrix_id) {
	if (matrix_id == "K") {
	return _symmetric;
	}
	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initModel() {
	auto & fem = this->getFEEngine();
	fem.initShapeFunctions(_not_ghost);
	fem.initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initFullImpl(const ModelOptions & options) {
	phasefield_index.initialize(mesh, _element_kind = _ek_not_defined,
	_default_value = UInt(-1),
	_with_nb_element = true);
	phasefield_local_numbering.initialize(mesh, _element_kind = _ek_not_defined,
	_with_nb_element = true);

	Model::initFullImpl(options);

	// initialize the phasefields
	- if (this->parser.getLastParsedFile() != "") {
	+ if (!this->parser.getLastParsedFile().empty()) {
	this->instantiatePhaseFields();
	this->initPhaseFields();
	}

	this->initBC(this, damage, *external_force);
	}

	/* -------------------------------------------------------------------------- */
	PhaseField &
	PhaseFieldModel::registerNewPhaseField(const ParserSection & section) {
	std::string phase_name;
	std::string phase_type = section.getName();
	std::string opt_param = section.getOption();

	try {
	std::string tmp = section.getParameter("name");
	phase_name = tmp; /** this can seam weird, but there is an ambiguous
	* operator overload that i couldn't solve. @todo remove
	* the weirdness of this code
	*/
	} catch (debug::Exception &) {
	AKANTU_ERROR("A phasefield of type \'"
	<< phase_type
	<< "\' in the input file has been defined without a name!");
	}
	PhaseField & phase =
	this->registerNewPhaseField(phase_name, phase_type, opt_param);

	phase.parseSection(section);

	return phase;
	}

	/* -------------------------------------------------------------------------- */
	PhaseField & PhaseFieldModel::registerNewPhaseField(const ID & phase_name,
	const ID & phase_type,
	const ID & opt_param) {
	AKANTU_DEBUG_ASSERT(phasefields_names_to_id.find(phase_name) ==
	phasefields_names_to_id.end(),
	"A phasefield with this name '"
	<< phase_name << "' has already been registered. "
	<< "Please use unique names for phasefields");

	UInt phase_count = phasefields.size();
	phasefields_names_to_id[phase_name] = phase_count;

	std::stringstream sstr_phase;
	sstr_phase << this->id << ":" << phase_count << ":" << phase_type;
	ID mat_id = sstr_phase.str();

	std::unique_ptr<PhaseField> phase = PhaseFieldFactory::getInstance().allocate(
	phase_type, opt_param, *this, mat_id);

	phasefields.push_back(std::move(phase));

	return *(phasefields.back());
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::instantiatePhaseFields() {

	ParserSection model_section;
	bool is_empty;
	std::tie(model_section, is_empty) = this->getParserSection();

	if (not is_empty) {
	auto model_phasefields =
	model_section.getSubSections(ParserType::_phasefield);
	for (const auto & section : model_phasefields) {
	this->registerNewPhaseField(section);
	}
	}

	auto sub_sections = this->parser.getSubSections(ParserType::_phasefield);
	for (const auto & section : sub_sections) {
	this->registerNewPhaseField(section);
	}

	- if (phasefields.empty())
	+ if (phasefields.empty()) {
	AKANTU_EXCEPTION("No phasefields where instantiated for the model"
	<< getID());
	+ }
	are_phasefields_instantiated = true;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initPhaseFields() {
	AKANTU_DEBUG_ASSERT(phasefields.size() != 0, "No phasefield to initialize !");

	- if (!are_phasefields_instantiated)
	+ if (!are_phasefields_instantiated) {
	instantiatePhaseFields();
	+ }

	this->assignPhaseFieldToElements();

	for (auto & phasefield : phasefields) {
	/// init internals properties
	phasefield->initPhaseField();
	}

	this->synchronize(SynchronizationTag::_smm_init_mat);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assignPhaseFieldToElements(
	const ElementTypeMapArray<UInt> * filter) {

	for_each_element(
	mesh,
	[&](auto && element) {
	UInt phase_index = (*phasefield_selector)(element);
	AKANTU_DEBUG_ASSERT(
	phase_index < phasefields.size(),
	"The phasefield selector returned an index that does not exists");
	phasefield_index(element) = phase_index;
	},
	_element_filter = filter, _ghost_type = _not_ghost);

	for_each_element(
	mesh,
	[&](auto && element) {
	auto phase_index = phasefield_index(element);
	auto index = phasefields[phase_index]->addElement(element);
	phasefield_local_numbering(element) = index;
	},
	_element_filter = filter, _ghost_type = _not_ghost);

	// synchronize the element phasefield arrays
	this->synchronize(SynchronizationTag::_material_id);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleMatrix(const ID & matrix_id) {

	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	} else {
	AKANTU_ERROR("Unknown Matrix ID for PhaseFieldModel : " << matrix_id);
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::predictor() {
	// AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::corrector() {
	// AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::initSolver(TimeStepSolverType time_step_solver_type,
	- NonLinearSolverType) {
	+ NonLinearSolverType /unused/) {
	DOFManager & dof_manager = this->getDOFManager();

	this->allocNodalField(this->damage, 1, "damage");
	this->allocNodalField(this->external_force, 1, "external_force");
	this->allocNodalField(this->internal_force, 1, "internal_force");
	this->allocNodalField(this->blocked_dofs, 1, "blocked_dofs");
	this->allocNodalField(this->previous_damage, 1, "previous_damage");

	if (!dof_manager.hasDOFs("damage")) {
	dof_manager.registerDOFs("damage", *this->damage, _dst_nodal);
	dof_manager.registerBlockedDOFs("damage", *this->blocked_dofs);
	dof_manager.registerDOFsPrevious("damage", *this->previous_damage);
	}

	if (time_step_solver_type == TimeStepSolverType::_dynamic) {
	AKANTU_TO_IMPLEMENT();
	}
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & PhaseFieldModel::getFEEngineBoundary(const ID & name) {
	return dynamic_cast<FEEngine &>(getFEEngineClassBoundary<FEEngineType>(name));
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	PhaseFieldModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _explicit_consistent_mass: {
	return std::make_tuple("explicit", TimeStepSolverType::_dynamic);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions PhaseFieldModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["damage"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["damage"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_linear;
	options.integration_scheme_type["damage"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["damage"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["damage"] =
	IntegrationSchemeType::_backward_euler;
	options.solution_type["damage"] = IntegrationScheme::_damage;
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::beforeSolveStep() {
	for (auto & phasefield : phasefields) {
	phasefield->beforeSolveStep();
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::afterSolveStep(bool converged) {
	- if (not converged)
	+ if (not converged) {
	return;
	+ }

	for (auto && values : zip(damage, previous_damage)) {
	auto & dam = std::get<0>(values);
	auto & prev_dam = std::get<1>(values);

	dam -= prev_dam;
	prev_dam = dam;
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	if (!this->getDOFManager().hasMatrix("K")) {
	this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
	}

	this->getDOFManager().zeroMatrix("K");

	for (auto & phasefield : phasefields) {
	phasefield->assembleStiffnessMatrix(_not_ghost);
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleResidual() {
	this->assembleInternalForces();

	this->getDOFManager().assembleToResidual("damage", *this->external_force, 1);
	this->getDOFManager().assembleToResidual("damage", *this->internal_force, 1);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleInternalForces() {
	AKANTU_DEBUG_INFO("Assemble the internal forces");

	this->internal_force->zero();

	// communicate the driving forces
	AKANTU_DEBUG_INFO("Send data for residual assembly");
	this->asynchronousSynchronize(SynchronizationTag::_pfm_driving);

	// assemble the forces due to local driving forces
	AKANTU_DEBUG_INFO("Assemble residual for local elements");
	for (auto & phasefield : phasefields) {
	phasefield->assembleInternalForces(_not_ghost);
	}

	// finalize communications
	AKANTU_DEBUG_INFO("Wait distant driving forces");
	this->waitEndSynchronize(SynchronizationTag::_pfm_driving);

	// assemble the residual due to ghost elements
	AKANTU_DEBUG_INFO("Assemble residual for ghost elements");
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::assembleLumpedMatrix(const ID & /matrix_id/) {}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::setTimeStep(Real time_step, const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper("phase_field").setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	UInt PhaseFieldModel::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	UInt size = 0;
	UInt nb_nodes_per_element = 0;

	for (const Element & el : elements) {
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	size += nb_nodes_per_element * sizeof(Real); // damage
	break;
	}
	case SynchronizationTag::_pfm_driving: {
	size += getNbIntegrationPoints(elements) * sizeof(Real);
	break;
	}
	case SynchronizationTag::_pfm_history: {
	size += getNbIntegrationPoints(elements) * sizeof(Real);
	break;
	}
	case SynchronizationTag::_pfm_energy: {
	size += getNbIntegrationPoints(elements) * sizeof(Real);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	return size;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::packData(__attribute__((unused))
	CommunicationBuffer & buffer,
	__attribute__((unused))
	const Array<Element> & elements,
	__attribute__((unused))
	const SynchronizationTag & tag) const {}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::unpackData(__attribute__((unused))
	CommunicationBuffer & buffer,
	__attribute__((unused))
	const Array<Element> & elements,
	__attribute__((unused))
	const SynchronizationTag & tag) {}

	/* -------------------------------------------------------------------------- */
	UInt PhaseFieldModel::getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	UInt size = 0;
	UInt nb_nodes = indexes.size();

	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	size += nb_nodes * sizeof(Real);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::packData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	buffer << (*damage)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) {
	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_pfm_damage: {
	buffer >> (*damage)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	std::shared_ptr<dumpers::Field>
	PhaseFieldModel::createNodalFieldBool(const std::string & field_name,
	- const std::string & group_name, bool) {
	+ const std::string & group_name,
	+ bool /unused/) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs.get();

	return mesh.createNodalField(uint_nodal_fields[field_name], group_name);

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	PhaseFieldModel::createNodalFieldReal(const std::string & field_name,
	- const std::string & group_name, bool) {
	+ const std::string & group_name,
	+ bool /unused/) {

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["damage"] = damage.get();
	real_nodal_fields["external_force"] = external_force.get();
	real_nodal_fields["internal_force"] = internal_force.get();

	return mesh.createNodalField(real_nodal_fields[field_name], group_name);

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	-std::shared_ptr<dumpers::Field>
	-PhaseFieldModel::createElementalField(const std::string & field_name,
	- const std::string & group_name, bool,
	- UInt, ElementKind element_kind) {
	+std::shared_ptr<dumpers::Field> PhaseFieldModel::createElementalField(
	+ const std::string & field_name, const std::string & group_name,
	+ bool /unused/, UInt /unused/, ElementKind element_kind) {

	if (field_name == "partitions") {
	return mesh.createElementalField<UInt, dumpers::ElementPartitionField>(
	mesh.getConnectivities(), group_name, this->spatial_dimension,
	element_kind);
	}

	std::shared_ptr<dumpers::Field> field;
	return field;
	}

	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	PhaseFieldModel::createElementalField(const std::string &, const std::string &,
	bool, const UInt &, ElementKind) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	PhaseFieldModel::createNodalFieldReal(const std::string &, const std::string &,
	bool) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	PhaseFieldModel::createNodalFieldBool(const std::string &, const std::string &,
	bool) {
	return nullptr;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	void PhaseFieldModel::printself(std::ostream & stream, int indent) const {
	- std::string space;
	- for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
	- ;
	+ std::string space(indent, AKANTU_INDENT);

	stream << space << "Phase Field Model [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + spatial dimension : " << Model::spatial_dimension
	<< std::endl;
	stream << space << " + fem [" << std::endl;
	getFEEngine().printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;
	stream << space << " + nodals information [" << std::endl;
	damage->printself(stream, indent + 2);
	external_force->printself(stream, indent + 2);
	internal_force->printself(stream, indent + 2);
	blocked_dofs->printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + phasefield information [" << std::endl;
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << "]" << std::endl;
	}

	} // namespace akantu
	diff --git a/src/model/phase_field/phase_field_model.hh b/src/model/phase_field/phase_field_model.hh
	index 28cdafa61..c9c90a530 100644
	--- a/src/model/phase_field/phase_field_model.hh
	+++ b/src/model/phase_field/phase_field_model.hh
	@@ -1,336 +1,338 @@
	/**
	* @file phase_field_model.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Tue Sep 04 2018
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Model class for Phase Field problem
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition.hh"
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	#include "model.hh"
	/* -------------------------------------------------------------------------- */
	#include <array>
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASE_FIELD_MODEL_HH__
	#define __AKANTU_PHASE_FIELD_MODEL_HH__

	namespace akantu {
	class PhaseField;
	class PhaseFieldSelector;
	template <ElementKind kind, class IntegrationOrderFuntor> class IntegratorGauss;
	template <ElementKind kind> class ShapeLagrange;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class PhaseFieldModel : public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt>,
	public BoundaryCondition<PhaseFieldModel> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using FEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	PhaseFieldModel(Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "phase_field_model",
	ModelType model_type = ModelType::_phase_field_model);

	~PhaseFieldModel() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// generic function to initialize everything ready for explicit dynamics
	void initFullImpl(const ModelOptions & options) override;

	/// initialize all internal array for phasefields
	void initPhaseFields();

	/// allocate all vectors
	- void initSolver(TimeStepSolverType, NonLinearSolverType) override;
	+ void initSolver(TimeStepSolverType /unused/,
	+ NonLinearSolverType /unused/) override;

	/// initialize the model
	void initModel() override;

	/// predictor
	void predictor() override;

	/// corrector
	void corrector() override;

	/// compute the heat flux
	void assembleResidual() override;

	/// get the type of matrix needed
	- MatrixType getMatrixType(const ID &) override;
	+ MatrixType getMatrixType(const ID & /unused/) override;

	/// callback to assemble a Matrix
	- void assembleMatrix(const ID &) override;
	+ void assembleMatrix(const ID & /unused/) override;

	/// callback to assemble a lumped Matrix
	- void assembleLumpedMatrix(const ID &) override;
	+ void assembleLumpedMatrix(const ID & /unused/) override;

	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;

	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/* ------------------------------------------------------------------------ */
	/* Materials (phase_field_model.cc) */
	/* ------------------------------------------------------------------------ */
	public:
	/// register an empty phasefield of a given type
	- PhaseField & registerNewPhaseField(const ID & mat_name, const ID & mat_type,
	+ PhaseField & registerNewPhaseField(const ID & phase_name,
	+ const ID & phase_type,
	const ID & opt_param);

	/// reassigns phasefields depending on the phasefield selector
	void reassignPhaseField();

	protected:
	/// register a phasefield in the dynamic database
	PhaseField & registerNewPhaseField(const ParserSection & phase_section);

	/// read the phasefield files to instantiate all the phasefields
	void instantiatePhaseFields();

	/// set the element_id_by_phasefield and add the elements to the good
	/// phasefields
	void assignPhaseFieldToElements(
	const ElementTypeMapArray<UInt> * filter = nullptr);

	/* ------------------------------------------------------------------------ */
	/* Methods for static */
	/* ------------------------------------------------------------------------ */
	public:
	/// assembles the phasefield stiffness matrix
	virtual void assembleStiffnessMatrix();

	/// compute the internal forces
	virtual void assembleInternalForces();

	// compute the internal forces
	void assembleInternalForces(const GhostType & ghost_type);

	/* ------------------------------------------------------------------------ */
	/* Methods for dynamic */
	/* ------------------------------------------------------------------------ */
	public:
	/// set the stable timestep
	void setTimeStep(Real time_step, const ID & solver_id = "") override;

	protected:
	/// callback for the solver, this is called at beginning of solve
	void beforeSolveStep() override;
	/// callback for the solver, this is called at end of solve
	void afterSolveStep(bool converged = true) override;

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	UInt getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const override;

	- void packData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	+ void packData(CommunicationBuffer & buffer, const Array<UInt> & indexes,
	const SynchronizationTag & tag) const override;

	- void unpackData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	+ void unpackData(CommunicationBuffer & buffer, const Array<UInt> & indexes,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// return the damage array
	AKANTU_GET_MACRO_DEREF_PTR(Damage, damage);

	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(Damage, damage);

	/// get the PhaseFieldModel::internal_force vector (internal forces)
	AKANTU_GET_MACRO_DEREF_PTR(InternalForce, internal_force);

	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(InternalForce, internal_force);

	/// get the PhaseFieldModel::external_force vector (external forces)
	AKANTU_GET_MACRO_DEREF_PTR(ExternalForce, external_force);

	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(ExternalForce, external_force);

	/// get the PhaseFieldModel::force vector (external forces)
	Array<Real> & getForce() {
	AKANTU_DEBUG_WARNING("getForce was maintained for backward compatibility, "
	"use getExternalForce instead");
	return *external_force;
	}

	/// get the PhaseFieldModel::blocked_dofs vector
	AKANTU_GET_MACRO_DEREF_PTR(BlockedDOFs, blocked_dofs);

	/// get an iterable on the phasefields
	inline decltype(auto) getPhaseFields();

	/// get an iterable on the phasefields
	inline decltype(auto) getPhaseFields() const;

	/// get a particular phasefield (by phasefield index)
	inline PhaseField & getPhaseField(UInt mat_index);

	/// get a particular phasefield (by phasefield index)
	inline const PhaseField & getPhaseField(UInt mat_index) const;

	/// get a particular phasefield (by phasefield name)
	inline PhaseField & getPhaseField(const std::string & name);

	/// get a particular phasefield (by phasefield name)
	inline const PhaseField & getPhaseField(const std::string & name) const;

	/// get a particular phasefield id from is name
	inline UInt getPhaseFieldIndex(const std::string & name) const;

	/// give the number of phasefields
	inline UInt getNbPhaseFields() const { return phasefields.size(); }

	/// give the phasefield internal index from its id
	Int getInternalIndexFromID(const ID & id) const;

	AKANTU_GET_MACRO(PhaseFieldByElement, phasefield_index,
	const ElementTypeMapArray<UInt> &);
	AKANTU_GET_MACRO(PhaseFieldLocalNumbering, phasefield_local_numbering,
	const ElementTypeMapArray<UInt> &);

	/// vectors containing local material element index for each global element
	/// index
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(PhaseFieldByElement, phasefield_index,
	UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(PhaseFieldByElement, phasefield_index, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(PhaseFieldLocalNumbering,
	phasefield_local_numbering, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(PhaseFieldLocalNumbering,
	phasefield_local_numbering, UInt);

	AKANTU_GET_MACRO_NOT_CONST(PhaseFieldSelector, *phasefield_selector,
	PhaseFieldSelector &);

	AKANTU_SET_MACRO(PhaseFieldSelector, phasefield_selector,
	std::shared_ptr<PhaseFieldSelector>);

	FEEngine & getFEEngineBoundary(const ID & name = "") override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable Interface */
	/* ------------------------------------------------------------------------ */
	public:
	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createElementalField(const std::string & field_name,
	const std::string & group_name, bool padding_flag,
	UInt spatial_dimension, ElementKind kind) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// number of iterations
	UInt n_iter;

	/// damage array
	std::unique_ptr<Array<Real>> damage;

	/// damage array at the previous time step
	std::unique_ptr<Array<Real>> previous_damage;

	/// boundary vector
	std::unique_ptr<Array<bool>> blocked_dofs;

	/// external force vector
	std::unique_ptr<Array<Real>> external_force;

	/// residuals array
	std::unique_ptr<Array<Real>> internal_force;

	/// Arrays containing the phasefield index for each element
	ElementTypeMapArray<UInt> phasefield_index;

	/// Arrays containing the position in the element filter of the phasefield
	/// (phasefield's local numbering)
	ElementTypeMapArray<UInt> phasefield_local_numbering;

	/// class defining of to choose a phasefield
	std::shared_ptr<PhaseFieldSelector> phasefield_selector;

	/// mapping between phasefield name and phasefield internal id
	std::map<std::string, UInt> phasefields_names_to_id;

	/// list of used phasefields
	std::vector<std::unique_ptr<PhaseField>> phasefields;

	/// tells if the phasefield are instantiated
	bool are_phasefields_instantiated{false};
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "parser.hh"
	#include "phasefield.hh"

	#include "phase_field_model_inline_impl.cc"
	/* -------------------------------------------------------------------------- */

	#endif
	diff --git a/src/model/phase_field/phase_field_model_inline_impl.cc b/src/model/phase_field/phase_field_model_inline_impl.cc
	index 5b06aadab..8d9288c1e 100644
	--- a/src/model/phase_field/phase_field_model_inline_impl.cc
	+++ b/src/model/phase_field/phase_field_model_inline_impl.cc
	@@ -1,100 +1,103 @@
	/**
	* @file phase_field_model_inline_impl.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Jun 19 2020
	*
	* @brief Phase field implementation of inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_named_argument.hh"
	#include "phasefield_selector.hh"
	#include "phasefield_selector_tmpl.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASE_FIELD_MODEL_INLINE_IMPL_CC__
	#define __AKANTU_PHASE_FIELD_MODEL_INLINE_IMPL_CC__

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline decltype(auto) PhaseFieldModel::getPhaseFields() {
	return make_dereference_adaptor(phasefields);
	}

	/* -------------------------------------------------------------------------- */
	inline decltype(auto) PhaseFieldModel::getPhaseFields() const {
	return make_dereference_adaptor(phasefields);
	}

	/* -------------------------------------------------------------------------- */
	inline PhaseField & PhaseFieldModel::getPhaseField(UInt mat_index) {
	AKANTU_DEBUG_ASSERT(mat_index < phasefields.size(),
	"The model " << id << " has no phasefield no "
	<< mat_index);
	return *phasefields[mat_index];
	}

	/* -------------------------------------------------------------------------- */
	inline const PhaseField & PhaseFieldModel::getPhaseField(UInt mat_index) const {
	AKANTU_DEBUG_ASSERT(mat_index < phasefields.size(),
	"The model " << id << " has no phasefield no "
	<< mat_index);
	return *phasefields[mat_index];
	}

	/* -------------------------------------------------------------------------- */
	inline PhaseField & PhaseFieldModel::getPhaseField(const std::string & name) {
	std::map<std::string, UInt>::const_iterator it =
	phasefields_names_to_id.find(name);
	AKANTU_DEBUG_ASSERT(it != phasefields_names_to_id.end(),
	- "The model " << id << " has no phasefield named " << name);
	+ "The model " << id << " has no phasefield named "
	+ << name);
	return *phasefields[it->second];
	}

	/* -------------------------------------------------------------------------- */
	inline UInt
	PhaseFieldModel::getPhaseFieldIndex(const std::string & name) const {
	auto it = phasefields_names_to_id.find(name);
	AKANTU_DEBUG_ASSERT(it != phasefields_names_to_id.end(),
	- "The model " << id << " has no phasefield named " << name);
	+ "The model " << id << " has no phasefield named "
	+ << name);
	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	inline const PhaseField &
	PhaseFieldModel::getPhaseField(const std::string & name) const {
	auto it = phasefields_names_to_id.find(name);
	AKANTU_DEBUG_ASSERT(it != phasefields_names_to_id.end(),
	- "The model " << id << " has no phasefield named " << name);
	+ "The model " << id << " has no phasefield named "
	+ << name);
	return *phasefields[it->second];
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* __AKANTU_PHASE_FIELD_MODEL_INLINE_IMPL_CC__ */
	diff --git a/src/model/phase_field/phasefield.cc b/src/model/phase_field/phasefield.cc
	index f3fa89f96..7f73f21b9 100644
	--- a/src/model/phase_field/phasefield.cc
	+++ b/src/model/phase_field/phasefield.cc
	@@ -1,299 +1,299 @@
	/**
	* @file phasefield.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 19 2020
	* @date last modification: Fri May 14 2021
	*
	* @brief Implementation of the common part of the phasefield class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phasefield.hh"
	#include "phase_field_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	PhaseField::PhaseField(PhaseFieldModel & model, const ID & id)
	: Parsable(ParserType::_phasefield, id), id(id), fem(model.getFEEngine()),
	model(model), spatial_dimension(this->model.getSpatialDimension()),
	element_filter("element_filter", id), damage("damage", *this),
	phi("phi", this), strain("strain", this),
	driving_force("driving_force", *this),
	damage_energy("damage_energy", *this),
	damage_energy_density("damage_energy_density", *this) {

	AKANTU_DEBUG_IN();

	/// for each connectivity types allocate the element filer array of the
	/// material
	element_filter.initialize(model.getMesh(),
	_spatial_dimension = spatial_dimension,
	_element_kind = _ek_regular);
	this->initialize();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	PhaseField::PhaseField(PhaseFieldModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id)
	: Parsable(ParserType::_phasefield, id), id(id), fem(fe_engine),
	model(model), spatial_dimension(this->model.getSpatialDimension()),
	element_filter("element_filter", id),
	damage("damage", *this, dim, fe_engine, this->element_filter),
	phi("phi", *this, dim, fe_engine, this->element_filter),
	strain("strain", *this, dim, fe_engine, this->element_filter),
	driving_force("driving_force", *this, dim, fe_engine,
	this->element_filter),
	damage_energy("damage_energy", *this, dim, fe_engine,
	this->element_filter),
	damage_energy_density("damage_energy_density", *this, dim, fe_engine,
	this->element_filter) {

	AKANTU_DEBUG_IN();

	/// for each connectivity types allocate the element filer array of the
	/// material
	element_filter.initialize(mesh, _spatial_dimension = spatial_dimension,
	_element_kind = _ek_regular);
	this->initialize();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	PhaseField::~PhaseField() = default;

	/* -------------------------------------------------------------------------- */
	void PhaseField::initialize() {
	registerParam("name", name, std::string(), _pat_parsable \| _pat_readable);
	registerParam("l0", l0, Real(0.), _pat_parsable \| _pat_readable,
	"length scale parameter");
	registerParam("gc", g_c, _pat_parsable \| _pat_readable,
	"critical local fracture energy density");
	registerParam("E", E, _pat_parsable \| _pat_readable, "Young's modulus");
	registerParam("nu", nu, _pat_parsable \| _pat_readable, "Poisson ratio");

	damage.initialize(1);

	phi.initialize(1);
	driving_force.initialize(1);

	strain.initialize(spatial_dimension * spatial_dimension);
	damage_energy_density.initialize(1);
	damage_energy.initialize(spatial_dimension * spatial_dimension);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::initPhaseField() {
	AKANTU_DEBUG_IN();

	this->phi.initializeHistory();

	this->resizeInternals();

	updateInternalParameters();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::resizeInternals() {
	AKANTU_DEBUG_IN();
	for (auto it = internal_vectors_real.begin();
	it != internal_vectors_real.end(); ++it) {
	it->second->resize();
	}

	for (auto it = internal_vectors_uint.begin();
	it != internal_vectors_uint.end(); ++it) {
	it->second->resize();
	}

	for (auto it = internal_vectors_bool.begin();
	it != internal_vectors_bool.end(); ++it) {
	it->second->resize();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::updateInternalParameters() {
	this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - 2 * this->nu));
	this->mu = this->E / (2 * (1 + this->nu));
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::computeAllDrivingForces(GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();

	for (const auto & type :
	element_filter.elementTypes(spatial_dimension, ghost_type)) {
	auto & elem_filter = element_filter(type, ghost_type);

	if (elem_filter.empty()) {
	continue;
	}

	computeDrivingForce(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::assembleInternalForces(GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	Array<Real> & internal_force = model.getInternalForce();

	for (auto type : element_filter.elementTypes(_ghost_type = ghost_type)) {
	auto & elem_filter = element_filter(type, ghost_type);
	if (elem_filter.empty()) {
	continue;
	}

	auto nb_element = elem_filter.size();
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	Array<Real> nt_driving_force(nb_quadrature_points, nb_nodes_per_element);
	fem.computeNtb(driving_force(type, ghost_type), nt_driving_force, type,
	ghost_type, elem_filter);

	Array<Real> int_nt_driving_force(nb_element, nb_nodes_per_element);
	fem.integrate(nt_driving_force, int_nt_driving_force, nb_nodes_per_element,
	type, ghost_type, elem_filter);

	model.getDOFManager().assembleElementalArrayLocalArray(
	int_nt_driving_force, internal_force, type, ghost_type, 1, elem_filter);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::assembleStiffnessMatrix(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix");

	for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type)) {
	auto & elem_filter = element_filter(type, ghost_type);
	if (elem_filter.empty()) {
	AKANTU_DEBUG_OUT();
	return;
	}

	auto nb_element = elem_filter.size();
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	auto nt_b_n = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "N^tbN");

	auto bt_d_b = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "B^tDB");

	// damage_energy_density_on_qpoints = gc/l0 + phi = scalar
	auto & damage_energy_density_vect = damage_energy_density(type, ghost_type);

	// damage_energy_on_qpoints = gc*l0 = scalar
	auto & damage_energy_vect = damage_energy(type, ghost_type);

	fem.computeBtDB(damage_energy_vect, *bt_d_b, 2, type, ghost_type,
	elem_filter);

	fem.computeNtbN(damage_energy_density_vect, *nt_b_n, type, ghost_type,
	elem_filter);

	/// compute @f$ K_{\grad d} = \int_e \mathbf{N}^t * \mathbf{w} *
	/// \mathbf{N}@f$
	auto K_n = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_n");

	fem.integrate(nt_b_n, K_n, nb_nodes_per_element * nb_nodes_per_element,
	type, ghost_type, elem_filter);

	model.getDOFManager().assembleElementalMatricesToMatrix(
	"K", "damage", *K_n, type, _not_ghost, _symmetric, elem_filter);

	/// compute @f$ K_{\grad d} = \int_e \mathbf{B}^t * \mathbf{W} *
	/// \mathbf{B}@f$
	auto K_b = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_b");

	fem.integrate(bt_d_b, K_b, nb_nodes_per_element * nb_nodes_per_element,
	type, ghost_type, elem_filter);

	model.getDOFManager().assembleElementalMatricesToMatrix(
	"K", "damage", *K_b, type, _not_ghost, _symmetric, elem_filter);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::beforeSolveStep() {
	this->savePreviousState();
	this->computeAllDrivingForces(_not_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::afterSolveStep() {}

	/* -------------------------------------------------------------------------- */
	void PhaseField::savePreviousState() {
	AKANTU_DEBUG_IN();

	for (auto pair : internal_vectors_real) {
	if (pair.second->hasHistory()) {
	pair.second->saveCurrentValues();
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void PhaseField::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);
	std::string type = getID().substr(getID().find_last_of(':') + 1);

	stream << space << "PhaseField Material " << type << " [" << std::endl;
	Parsable::printself(stream, indent);
	stream << space << "]" << std::endl;
	}

	} // namespace akantu
	diff --git a/src/model/phase_field/phasefield.hh b/src/model/phase_field/phasefield.hh
	index 1b13f132d..5c74b5621 100644
	--- a/src/model/phase_field/phasefield.hh
	+++ b/src/model/phase_field/phasefield.hh
	@@ -1,300 +1,300 @@
	/**
	* @file phasefield.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 19 2020
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Mother class for all phasefield laws
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_factory.hh"
	#include "data_accessor.hh"
	#include "parsable.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */
	#include "internal_field.hh"
	#include "random_internal_field.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASEFIELD_HH__
	#define __AKANTU_PHASEFIELD_HH__

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class Model;
	class PhaseFieldModel;
	class PhaseField;
	} // namespace akantu

	namespace akantu {

	template <typename T>
	using InternalPhaseField = InternalFieldTmpl<PhaseField, T>;

	using PhaseFieldFactory =
	Factory<PhaseField, ID, const ID &, PhaseFieldModel &, const ID &>;

	class PhaseField : public DataAccessor<Element>, public Parsable {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	PhaseField(const PhaseField & phase) = delete;
	PhaseField & operator=(const PhaseField & phase) = delete;

	/// Initialize phasefield with defaults
	PhaseField(PhaseFieldModel & model, const ID & id = "");

	/// Initialize phasefield with custom mesh & fe_engine
	PhaseField(PhaseFieldModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id = "");

	/// Destructor
	~PhaseField() override;

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	template <typename T>
	void registerInternal(InternalPhaseField<T> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	}

	template <typename T>
	void unregisterInternal(InternalPhaseField<T> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// initialize the phasefield computed parameter
	virtual void initPhaseField();

	///
	virtual void beforeSolveStep();

	///
	virtual void afterSolveStep();

	/// assemble the residual for this phasefield
	virtual void assembleInternalForces(GhostType ghost_type);

	/// assemble the stiffness matrix for this phasefield
	virtual void assembleStiffnessMatrix(GhostType ghost_type);

	/// compute the driving force for this phasefield
	virtual void computeAllDrivingForces(GhostType ghost_type = _not_ghost);

	/// save the phi in the phi internal field if needed
	virtual void savePreviousState();

	/// add an element to the local mesh filter
	inline UInt addElement(const ElementType & type, UInt element,
	const GhostType & ghost_type);
	inline UInt addElement(const Element & element);

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	/// resize the internals arrrays
	virtual void resizeInternals();

	/// function called to updatet the internal parameters when the
	/// modifiable parameters are modified
	virtual void updateInternalParameters();

	// constitutive law for driving force
	virtual void computeDrivingForce(const ElementType & /* el_type */,
	GhostType /* ghost_type */ = _not_ghost) {
	AKANTU_TO_IMPLEMENT();
	}

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	template <typename T>
	inline void packElementDataHelper(const ElementTypeMapArray<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & fem_id = ID()) const;

	template <typename T>
	inline void unpackElementDataHelper(ElementTypeMapArray<T> & data_to_unpack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & fem_id = ID());

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Name, name, const std::string &);

	AKANTU_GET_MACRO(Model, model, const PhaseFieldModel &)

	AKANTU_GET_MACRO(ID, id, const ID &);

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Strain, strain, Real);

	AKANTU_GET_MACRO(Strain, strain, const ElementTypeMapArray<Real> &);

	AKANTU_GET_MACRO_NOT_CONST(Strain, strain, ElementTypeMapArray<Real> &);

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real);

	AKANTU_GET_MACRO_NOT_CONST(Damage, damage, ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO(Damage, damage, const ElementTypeMapArray<Real> &);

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ElementFilter, element_filter, UInt);

	AKANTU_GET_MACRO(ElementFilter, element_filter,
	const ElementTypeMapArray<UInt> &);

	template <typename T>
	const InternalPhaseField<T> & getInternal(const ID & id) const;
	template <typename T> InternalPhaseField<T> & getInternal(const ID & id);

	template <typename T>
	inline bool isInternal(const ID & id, const ElementKind & element_kind) const;

	template <typename T> inline void setParam(const ID & param, T value);
	inline const Parameter & getParam(const ID & param) const;

	template <typename T>
	void flattenInternal(const std::string & field_id,
	ElementTypeMapArray<T> & internal_flat,
	- const GhostType ghost_type = _not_ghost,
	+ GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// boolean to know if the material has been initialized
	bool is_init;

	std::map<ID, InternalPhaseField<Real> *> internal_vectors_real;
	std::map<ID, InternalPhaseField<UInt> *> internal_vectors_uint;
	std::map<ID, InternalPhaseField<bool> *> internal_vectors_bool;

	protected:
	ID id;

	/// Link to the fem object in the model
	FEEngine & fem;

	/// phasefield name
	std::string name;

	/// The model to whch the phasefield belong
	PhaseFieldModel & model;

	/// length scale parameter
	Real l0;

	/// critical energy release rate
	Real g_c;

	/// Young's modulus
	Real E;

	/// Poisson ratio
	Real nu;

	/// Lame's first parameter
	Real lambda;

	/// Lame's second paramter
	Real mu;

	/// spatial dimension
	UInt spatial_dimension;

	/// list of element handled by the phasefield
	ElementTypeMapArray<UInt> element_filter;

	/// damage arrays ordered by element types
	InternalPhaseField<Real> damage;

	/// phi arrays ordered by element types
	InternalPhaseField<Real> phi;

	/// strain arrays ordered by element types
	InternalPhaseField<Real> strain;

	/// driving force ordered by element types
	InternalPhaseField<Real> driving_force;

	/// damage energy ordered by element types
	InternalPhaseField<Real> damage_energy;

	/// damage energy density ordered by element types
	InternalPhaseField<Real> damage_energy_density;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const PhaseField & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "phasefield_inline_impl.cc"

	#include "internal_field_tmpl.hh"
	#include "random_internal_field_tmpl.hh"

	/* -------------------------------------------------------------------------- */
	#define PHASEFIELD_DEFAULT_ALLOCATOR(id, phase_name) \
	[](const ID &, PhaseFieldModel & model, \
	const ID & id) -> std::unique_ptr<PhaseField> { \
	return std::make_unique<phase_name>(model, id); \
	}

	#define INSTANTIATE_PHASEFIELD(id, phase_name) \
	static bool phasefield_is_alocated_##id [[gnu::unused]] = \
	PhaseFieldFactory::getInstance().registerAllocator( \
	#id, PHASEFIELD_DEFAULT_ALLOCATOR(id, phase_name))

	#endif
	diff --git a/src/model/phase_field/phasefield_inline_impl.cc b/src/model/phase_field/phasefield_inline_impl.cc
	index 6f4f79413..f87db2f0d 100644
	--- a/src/model/phase_field/phasefield_inline_impl.cc
	+++ b/src/model/phase_field/phasefield_inline_impl.cc
	@@ -1,159 +1,163 @@
	/**
	* @file phasefield_inline_impl.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 19 2020
	* @date last modification: Fri Apr 02 2021
	*
	* @brief Phase field implementation of inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phase_field_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASEFIELD_INLINE_IMPL_CC__
	#define __AKANTU_PHASEFIELD_INLINE_IMPL_CC__

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt PhaseField::addElement(const ElementType & type, UInt element,
	- const GhostType & ghost_type) {
	+ const GhostType & ghost_type) {
	Array<UInt> & el_filter = this->element_filter(type, ghost_type);
	el_filter.push_back(element);
	return el_filter.size() - 1;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt PhaseField::addElement(const Element & element) {
	return this->addElement(element.type, element.element, element.ghost_type);
	}

	-
	/* -------------------------------------------------------------------------- */
	template <>
	-inline void PhaseField::registerInternal<Real>(InternalPhaseField<Real> & vect) {
	+inline void
	+PhaseField::registerInternal<Real>(InternalPhaseField<Real> & vect) {
	internal_vectors_real[vect.getID()] = &vect;
	}

	template <>
	-inline void PhaseField::registerInternal<UInt>(InternalPhaseField<UInt> & vect) {
	+inline void
	+PhaseField::registerInternal<UInt>(InternalPhaseField<UInt> & vect) {
	internal_vectors_uint[vect.getID()] = &vect;
	}

	template <>
	-inline void PhaseField::registerInternal<bool>(InternalPhaseField<bool> & vect) {
	+inline void
	+PhaseField::registerInternal<bool>(InternalPhaseField<bool> & vect) {
	internal_vectors_bool[vect.getID()] = &vect;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	-inline void PhaseField::unregisterInternal<Real>(InternalPhaseField<Real> & vect) {
	+inline void
	+PhaseField::unregisterInternal<Real>(InternalPhaseField<Real> & vect) {
	internal_vectors_real.erase(vect.getID());
	}

	template <>
	-inline void PhaseField::unregisterInternal<UInt>(InternalPhaseField<UInt> & vect) {
	+inline void
	+PhaseField::unregisterInternal<UInt>(InternalPhaseField<UInt> & vect) {
	internal_vectors_uint.erase(vect.getID());
	}

	template <>
	-inline void PhaseField::unregisterInternal<bool>(InternalPhaseField<bool> & vect) {
	+inline void
	+PhaseField::unregisterInternal<bool>(InternalPhaseField<bool> & vect) {
	internal_vectors_bool.erase(vect.getID());
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline bool PhaseField::isInternal(__attribute__((unused)) const ID & id,
	- __attribute__((unused))
	- const ElementKind & element_kind) const {
	+ __attribute__((unused))
	+ const ElementKind & element_kind) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <>
	-inline bool PhaseField::isInternal<Real>(const ID & id,
	- const ElementKind & element_kind) const {
	+inline bool
	+PhaseField::isInternal<Real>(const ID & id,
	+ const ElementKind & element_kind) const {
	auto internal_array = internal_vectors_real.find(this->getID() + ":" + id);

	- if (internal_array == internal_vectors_real.end() \|\|
	- internal_array->second->getElementKind() != element_kind)
	- return false;
	- return true;
	+ return !(internal_array == internal_vectors_real.end() \|\|
	+ internal_array->second->getElementKind() != element_kind);
	}

	-
	/* -------------------------------------------------------------------------- */
	-inline UInt PhaseField::getNbData(__attribute__((unused)) const Array<Element> & elements,
	- __attribute__((unused)) const SynchronizationTag & tag) const {
	+inline UInt PhaseField::getNbData(__attribute__((unused))
	+ const Array<Element> & elements,
	+ __attribute__((unused))
	+ const SynchronizationTag & tag) const {
	return 0;
	}

	/* -------------------------------------------------------------------------- */
	-inline void PhaseField::packData(__attribute__((unused)) CommunicationBuffer & buffer,
	- __attribute__((unused)) const Array<Element> & elements,
	- __attribute__((unused)) const SynchronizationTag & tag) const {
	-}
	+inline void PhaseField::packData(__attribute__((unused))
	+ CommunicationBuffer & buffer,
	+ __attribute__((unused))
	+ const Array<Element> & elements,
	+ __attribute__((unused))
	+ const SynchronizationTag & tag) const {}

	/* -------------------------------------------------------------------------- */
	-inline void PhaseField::unpackData(__attribute__((unused)) CommunicationBuffer & buffer,
	- __attribute__((unused)) const Array<Element> & elements,
	- __attribute__((unused)) const SynchronizationTag & tag) {
	+inline void
	+PhaseField::unpackData(__attribute__((unused)) CommunicationBuffer & buffer,
	+ __attribute__((unused)) const Array<Element> & elements,
	+ __attribute__((unused)) const SynchronizationTag & tag) {
	}

	-
	- /* -------------------------------------------------------------------------- */
	+/* -------------------------------------------------------------------------- */
	inline const Parameter & PhaseField::getParam(const ID & param) const {
	try {
	return get(param);
	} catch (...) {
	AKANTU_EXCEPTION("No parameter " << param << " in the material "
	<< getID());
	}
	}

	-
	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void PhaseField::packElementDataHelper(
	const ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & elements, const ID & fem_id) const {
	DataAccessor::packElementalDataHelper<T>(data_to_pack, buffer, elements, true,
	model.getFEEngine(fem_id));
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void PhaseField::unpackElementDataHelper(
	ElementTypeMapArray<T> & data_to_unpack, CommunicationBuffer & buffer,
	const Array<Element> & elements, const ID & fem_id) {
	DataAccessor::unpackElementalDataHelper<T>(data_to_unpack, buffer, elements,
	true, model.getFEEngine(fem_id));
	}
	-
	-

	-}
	+} // namespace akantu

	-#endif
	+#endif
	diff --git a/src/model/phase_field/phasefield_selector.hh b/src/model/phase_field/phasefield_selector.hh
	index ac46bb05c..a681b72d4 100644
	--- a/src/model/phase_field/phasefield_selector.hh
	+++ b/src/model/phase_field/phasefield_selector.hh
	@@ -1,169 +1,169 @@
	/**
	* @file phasefield_selector.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri May 14 2021
	*
	* @brief class describing how to choose a phasefield variable
	* function for a given element
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASEFIELD_SELECTOR_HH__
	#define __AKANTU_PHASEFIELD_SELECTOR_HH__

	namespace akantu {
	class PhaseFieldModel;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/**
	* main class to assign same or different phasefield constitutive laws to
	* different elements
	*/
	class PhaseFieldSelector
	: public std::enable_shared_from_this<PhaseFieldSelector> {
	public:
	PhaseFieldSelector() = default;
	virtual ~PhaseFieldSelector() = default;
	virtual inline UInt operator()(const Element & element) {
	if (fallback_selector) {
	return (*fallback_selector)(element);
	}

	return fallback_value;
	}

	inline void setFallback(UInt f) { fallback_value = f; }
	inline void
	setFallback(const std::shared_ptr<PhaseFieldSelector> & fallback_selector) {
	this->fallback_selector = fallback_selector;
	}

	inline void setFallback(PhaseFieldSelector & fallback_selector) {
	this->fallback_selector = fallback_selector.shared_from_this();
	}

	inline std::shared_ptr<PhaseFieldSelector> & getFallbackSelector() {
	return this->fallback_selector;
	}

	inline UInt getFallbackValue() const { return this->fallback_value; }

	protected:
	UInt fallback_value{0};
	std::shared_ptr<PhaseFieldSelector> fallback_selector;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class that assigns the first phasefield to regular elements by default
	*/
	class DefaultPhaseFieldSelector : public PhaseFieldSelector {
	public:
	explicit DefaultPhaseFieldSelector(
	const ElementTypeMapArray<UInt> & phasefield_index)
	: phasefield_index(phasefield_index) {}

	UInt operator()(const Element & element) override {
	if (not phasefield_index.exists(element.type, element.ghost_type)) {
	return PhaseFieldSelector::operator()(element);
	}

	const auto & phase_indexes =
	phasefield_index(element.type, element.ghost_type);
	if (element.element < phase_indexes.size()) {
	auto && tmp_phase = phase_indexes(element.element);
	if (tmp_phase != UInt(-1)) {
	return tmp_phase;
	}
	}

	return PhaseFieldSelector::operator()(element);
	}

	private:
	const ElementTypeMapArray<UInt> & phasefield_index;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* Use elemental data to assign phasefields
	*/
	template <typename T>
	class ElementDataPhaseFieldSelector : public PhaseFieldSelector {
	public:
	ElementDataPhaseFieldSelector(const ElementTypeMapArray<T> & element_data,
	const PhaseFieldModel & model,
	UInt first_index = 1)
	: element_data(element_data), model(model), first_index(first_index) {}

	inline T elementData(const Element & element) {
	DebugLevel dbl = debug::getDebugLevel();
	debug::setDebugLevel(dblError);
	T data = element_data(element.type, element.ghost_type)(element.element);
	debug::setDebugLevel(dbl);
	return data;
	}

	inline UInt operator()(const Element & element) override {
	return PhaseFieldSelector::operator()(element);
	}

	protected:
	/// list of element with the specified data (i.e. tag value)
	const ElementTypeMapArray<T> & element_data;

	/// the model that the materials belong
	const PhaseFieldModel & model;

	/// first phasefield index: equal to 1 if none specified
	UInt first_index;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class to use mesh data information to assign different phasefields
	* where name is the tag value: tag_0, tag_1
	*/
	template <typename T>
	class MeshDataPhaseFieldSelector : public ElementDataPhaseFieldSelector<T> {
	public:
	MeshDataPhaseFieldSelector(const std::string & name,
	const PhaseFieldModel & model,
	UInt first_index = 1);
	};

	} // namespace akantu

	#endif /* __AKANTU_PHASEFIELD_SELECTOR_HH__ */
	diff --git a/src/model/phase_field/phasefield_selector_tmpl.hh b/src/model/phase_field/phasefield_selector_tmpl.hh
	index fca2db9eb..116d2a192 100644
	--- a/src/model/phase_field/phasefield_selector_tmpl.hh
	+++ b/src/model/phase_field/phasefield_selector_tmpl.hh
	@@ -1,74 +1,73 @@
	/**
	* @file phasefield_selector_tmpl.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Jun 19 2020
	*
	* @brief Implementation of the template PhaseFieldSelector
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phasefield_selector.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASEFIELD_SELECTOR_TMPL_HH__
	#define __AKANTU_PHASEFIELD_SELECTOR_TMPL_HH__

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	-inline UInt ElementDataPhaseFieldSelector<std::string>::
	-operator()(const Element & element) {
	+inline UInt ElementDataPhaseFieldSelector<std::string>::operator()(
	+ const Element & element) {
	try {
	std::string material_name = this->elementData(element);
	return model.getPhaseFieldIndex(material_name);
	} catch (...) {
	return PhaseFieldSelector::operator()(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	-inline UInt ElementDataPhaseFieldSelector<UInt>::
	-operator()(const Element & element) {
	+inline UInt
	+ElementDataPhaseFieldSelector<UInt>::operator()(const Element & element) {
	try {
	return this->elementData(element) - first_index;
	} catch (...) {
	return PhaseFieldSelector::operator()(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	MeshDataPhaseFieldSelector<T>::MeshDataPhaseFieldSelector(
	- const std::string & name, const PhaseFieldModel & model,
	- UInt first_index)
	+ const std::string & name, const PhaseFieldModel & model, UInt first_index)
	: ElementDataPhaseFieldSelector<T>(model.getMesh().getData<T>(name), model,
	- first_index) {}
	+ first_index) {}

	} // namespace akantu

	#endif /* __AKANTU_PHASEFIELD_SELECTOR_TMPL_HH__ */
	diff --git a/src/model/phase_field/phasefields/phasefield_exponential.cc b/src/model/phase_field/phasefields/phasefield_exponential.cc
	index e8def49b8..8fd639e64 100644
	--- a/src/model/phase_field/phasefields/phasefield_exponential.cc
	+++ b/src/model/phase_field/phasefields/phasefield_exponential.cc
	@@ -1,70 +1,70 @@
	/**
	* @file phasefield_exponential.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 19 2020
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Specialization of the phasefield law class for exponential type
	* law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phasefield_exponential.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	PhaseFieldExponential::PhaseFieldExponential(PhaseFieldModel & model,
	const ID & id)
	: PhaseField(model, id) {}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldExponential::updateInternalParameters() {
	PhaseField::updateInternalParameters();

	Matrix<Real> d(spatial_dimension, spatial_dimension);
	d.eye(this->g_c * this->l0);
	damage_energy.set(d);
	}

	/* -------------------------------------------------------------------------- */
	void PhaseFieldExponential::computeDrivingForce(const ElementType & el_type,
	GhostType ghost_type) {
	for (auto && tuple : zip(this->phi(el_type, ghost_type),
	this->phi.previous(el_type, ghost_type),
	this->driving_force(el_type, ghost_type),
	this->damage_energy_density(el_type, ghost_type),
	make_view(this->strain(el_type, ghost_type),
	spatial_dimension, spatial_dimension))) {
	computePhiOnQuad(std::get<4>(tuple), std::get<0>(tuple),
	std::get<1>(tuple));
	computeDamageEnergyDensityOnQuad(std::get<0>(tuple), std::get<3>(tuple));
	computeDrivingForceOnQuad(std::get<0>(tuple), std::get<2>(tuple));
	}
	}

	INSTANTIATE_PHASEFIELD(exponential, PhaseFieldExponential);

	} // namespace akantu
	diff --git a/src/model/phase_field/phasefields/phasefield_exponential.hh b/src/model/phase_field/phasefields/phasefield_exponential.hh
	index 77f1358ab..bba5414ea 100644
	--- a/src/model/phase_field/phasefields/phasefield_exponential.hh
	+++ b/src/model/phase_field/phasefields/phasefield_exponential.hh
	@@ -1,135 +1,140 @@
	/**
	* @file phasefield_exponential.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 19 2020
	* @date last modification: Wed Jun 23 2021
	*
	* @brief Phasefield law for approximating discrete crack as an exponential
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "phasefield.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_PHASEFIELD_EXPONENTIAL_HH__
	#define __AKANTU_PHASEFIELD_EXPONENTIAL_HH__

	namespace akantu {
	class PhaseFieldExponential : public PhaseField {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	PhaseFieldExponential(PhaseFieldModel & model, const ID & id = "");

	~PhaseFieldExponential() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	- void computePhiOnQuad(const Matrix<Real> &, Real &, Real &);
	+ void computePhiOnQuad(const Matrix<Real> & /strain_quad/,
	+ Real & /phi_quad/, Real & /phi_hist_quad/);

	- void computeDrivingForce(const ElementType &, GhostType) override;
	+ void computeDrivingForce(const ElementType & /el_type/,
	+ GhostType /ghost_type/) override;

	- inline void computeDrivingForceOnQuad(const Real &, Real &);
	+ inline void computeDrivingForceOnQuad(const Real & /phi_quad/,
	+ Real & /driving_force_quad/);

	- inline void computeDamageEnergyDensityOnQuad(const Real &, Real &);
	+ inline void computeDamageEnergyDensityOnQuad(const Real & /phi_quad/,
	+ Real & /dam_energy_quad/);

	public:
	void updateInternalParameters() override;
	};

	/* -------------------------------------------------------------------------- */
	inline void
	PhaseFieldExponential::computeDrivingForceOnQuad(const Real & phi_quad,
	Real & driving_force_quad) {
	driving_force_quad = 2.0 * phi_quad;
	}

	/* -------------------------------------------------------------------------- */
	inline void PhaseFieldExponential::computeDamageEnergyDensityOnQuad(
	const Real & phi_quad, Real & dam_energy_quad) {
	dam_energy_quad = 2.0 * phi_quad + this->g_c / this->l0;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	PhaseFieldExponential::computePhiOnQuad(const Matrix<Real> & strain_quad,
	Real & phi_quad, Real & phi_hist_quad) {

	Matrix<Real> strain_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_minus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_dir(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_diag_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_diag_minus(spatial_dimension, spatial_dimension);

	Vector<Real> strain_values(spatial_dimension);

	Real trace_plus, trace_minus;

	strain_plus.zero();
	strain_minus.zero();
	strain_dir.zero();
	strain_values.zero();
	strain_diag_plus.zero();
	strain_diag_minus.zero();

	strain_quad.eig(strain_values, strain_dir);

	for (UInt i = 0; i < spatial_dimension; i++) {
	strain_diag_plus(i, i) = std::max(Real(0.), strain_values(i));
	strain_diag_minus(i, i) = std::min(Real(0.), strain_values(i));
	}

	Matrix<Real> mat_tmp(spatial_dimension, spatial_dimension);
	Matrix<Real> sigma_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> sigma_minus(spatial_dimension, spatial_dimension);

	mat_tmp.mul<false, true>(strain_diag_plus, strain_dir);
	strain_plus.mul<false, false>(strain_dir, mat_tmp);
	mat_tmp.mul<false, true>(strain_diag_minus, strain_dir);
	strain_minus.mul<false, true>(strain_dir, mat_tmp);

	trace_plus = std::max(Real(0.), strain_quad.trace());
	trace_minus = std::min(Real(0.), strain_quad.trace());

	for (UInt i = 0; i < spatial_dimension; i++) {
	for (UInt j = 0; j < spatial_dimension; j++) {
	- sigma_plus(i, j) =
	- (i == j) * lambda * trace_plus + 2 * mu * strain_plus(i, j);
	- sigma_minus(i, j) =
	- (i == j) * lambda * trace_minus + 2 * mu * strain_minus(i, j);
	+ sigma_plus(i, j) = static_cast<double>(i == j) * lambda * trace_plus +
	+ 2 * mu * strain_plus(i, j);
	+ sigma_minus(i, j) = static_cast<double>(i == j) * lambda * trace_minus +
	+ 2 * mu * strain_minus(i, j);
	}
	}

	phi_quad = 0.5 * sigma_plus.doubleDot(strain_quad);
	- if (phi_quad < phi_hist_quad)
	+ if (phi_quad < phi_hist_quad) {
	phi_quad = phi_hist_quad;
	+ }
	}

	} // namespace akantu

	#endif
	diff --git a/src/model/solid_mechanics/material.hh b/src/model/solid_mechanics/material.hh
	index 4cc050413..ae028bb11 100644
	--- a/src/model/solid_mechanics/material.hh
	+++ b/src/model/solid_mechanics/material.hh
	@@ -1,712 +1,713 @@
	/**
	* @file material.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Mother class for all materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_factory.hh"
	#include "aka_voigthelper.hh"
	#include "data_accessor.hh"
	#include "integration_point.hh"
	#include "parsable.hh"
	#include "parser.hh"
	/* -------------------------------------------------------------------------- */
	#include "internal_field.hh"
	#include "random_internal_field.hh"
	/* -------------------------------------------------------------------------- */
	#include "mesh_events.hh"
	#include "solid_mechanics_model_event_handler.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_HH_
	#define AKANTU_MATERIAL_HH_

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class Model;
	class SolidMechanicsModel;
	class Material;
	} // namespace akantu

	namespace akantu {

	using MaterialFactory =
	Factory<Material, ID, UInt, const ID &, SolidMechanicsModel &, const ID &>;

	/**
	* Interface of all materials
	* Prerequisites for a new material
	* - inherit from this class
	* - implement the following methods:
	* \code
	* virtual Real getStableTimeStep(Real h, const Element & element =
	* ElementNull);
	*
	* virtual void computeStress(ElementType el_type,
	* GhostType ghost_type = _not_ghost);
	*
	* virtual void computeTangentStiffness(ElementType el_type,
	* Array<Real> & tangent_matrix,
	* GhostType ghost_type = _not_ghost);
	* \endcode
	*
	*/
	class Material : public DataAccessor<Element>,
	public Parsable,
	public MeshEventHandler,
	protected SolidMechanicsModelEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Material(const Material & mat) = delete;
	Material & operator=(const Material & mat) = delete;

	/// Initialize material with defaults
	Material(SolidMechanicsModel & model, const ID & id = "");

	/// Initialize material with custom mesh & fe_engine
	Material(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id = "");

	/// Destructor
	~Material() override;

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Function that materials can/should reimplement */
	/* ------------------------------------------------------------------------ */
	protected:
	/// constitutive law
	virtual void computeStress(ElementType /* el_type */,
	GhostType /* ghost_type */ = _not_ghost) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the tangent stiffness matrix
	virtual void computeTangentModuli(ElementType /el_type/,
	Array<Real> & /tangent_matrix/,
	GhostType /ghost_type/ = _not_ghost) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the potential energy
	virtual void computePotentialEnergy(ElementType el_type);

	/// compute the potential energy for an element
	virtual void
	computePotentialEnergyByElement(ElementType /type/, UInt /index/,
	Vector<Real> & /epot_on_quad_points/) {
	AKANTU_TO_IMPLEMENT();
	}

	virtual void updateEnergies(ElementType /el_type/) {}

	virtual void updateEnergiesAfterDamage(ElementType /el_type/) {}

	/// set the material to steady state (to be implemented for materials that
	/// need it)
	virtual void setToSteadyState(ElementType /el_type/,
	GhostType /ghost_type/ = _not_ghost) {}

	/// function called to update the internal parameters when the modifiable
	/// parameters are modified
	virtual void updateInternalParameters() {}

	public:
	/// extrapolate internal values
	virtual void extrapolateInternal(const ID & id, const Element & element,
	const Matrix<Real> & points,
	Matrix<Real> & extrapolated);

	/// compute the p-wave speed in the material
	virtual Real getPushWaveSpeed(const Element & /element/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the s-wave speed in the material
	virtual Real getShearWaveSpeed(const Element & /element/) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// get a material celerity to compute the stable time step (default: is the
	/// push wave speed)
	virtual Real getCelerity(const Element & element) const {
	return getPushWaveSpeed(element);
	}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	template <typename T> void registerInternal(InternalField<T> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	}

	template <typename T> void unregisterInternal(InternalField<T> & /vect/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// initialize the material computed parameter
	virtual void initMaterial();

	/// compute the residual for this material
	// virtual void updateResidual(GhostType ghost_type = _not_ghost);

	/// assemble the residual for this material
	virtual void assembleInternalForces(GhostType ghost_type);

	/// save the stress in the previous_stress if needed
	virtual void savePreviousState();

	/// restore the stress from previous_stress if needed
	virtual void restorePreviousState();

	/// compute the stresses for this material
	virtual void computeAllStresses(GhostType ghost_type = _not_ghost);
	// virtual void
	// computeAllStressesFromTangentModuli(GhostType ghost_type = _not_ghost);
	virtual void computeAllCauchyStresses(GhostType ghost_type = _not_ghost);

	/// set material to steady state
	void setToSteadyState(GhostType ghost_type = _not_ghost);

	/// compute the stiffness matrix
	virtual void assembleStiffnessMatrix(GhostType ghost_type);

	/// add an element to the local mesh filter
	inline UInt addElement(ElementType type, UInt element, GhostType ghost_type);
	inline UInt addElement(const Element & element);

	/// add many elements at once
	void addElements(const Array<Element> & elements_to_add);

	/// remove many element at once
	void removeElements(const Array<Element> & elements_to_remove);

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/**
	* interpolate stress on given positions for each element by means
	* of a geometrical interpolation on quadrature points
	*/
	void interpolateStress(ElementTypeMapArray<Real> & result,
	GhostType ghost_type = _not_ghost);

	/**
	* interpolate stress on given positions for each element by means
	* of a geometrical interpolation on quadrature points and store the
	* results per facet
	*/
	void interpolateStressOnFacets(ElementTypeMapArray<Real> & result,
	ElementTypeMapArray<Real> & by_elem_result,
	GhostType ghost_type = _not_ghost);

	/**
	* function to initialize the elemental field interpolation
	* function by inverting the quadrature points' coordinates
	*/
	void initElementalFieldInterpolation(
	const ElementTypeMapArray<Real> & interpolation_points_coordinates);

	/* ------------------------------------------------------------------------ */
	/* Common part */
	/* ------------------------------------------------------------------------ */
	protected:
	/* ------------------------------------------------------------------------ */
	static inline UInt getTangentStiffnessVoigtSize(UInt dim);

	/// compute the potential energy by element
	void computePotentialEnergyByElements();

	/// resize the intenals arrays
	virtual void resizeInternals();

	/* ------------------------------------------------------------------------ */
	/* Finite deformation functions */
	/* This functions area implementing what is described in the paper of Bathe */
	/* et al, in IJNME, Finite Element Formulations For Large Deformation */
	/* Dynamic Analysis, Vol 9, 353-386, 1975 */
	/* ------------------------------------------------------------------------ */
	protected:
	/// assemble the residual
	template <UInt dim> void assembleInternalForces(GhostType ghost_type);

	template <UInt dim>
	void computeAllStressesFromTangentModuli(ElementType type,
	GhostType ghost_type);

	template <UInt dim>
	void assembleStiffnessMatrix(ElementType type, GhostType ghost_type);

	/// assembling in finite deformation
	template <UInt dim>
	void assembleStiffnessMatrixNL(ElementType type, GhostType ghost_type);

	template <UInt dim>
	void assembleStiffnessMatrixL2(ElementType type, GhostType ghost_type);

	/* ------------------------------------------------------------------------ */
	/* Conversion functions */
	/* ------------------------------------------------------------------------ */
	public:
	/// Size of the Stress matrix for the case of finite deformation see: Bathe et
	/// al, IJNME, Vol 9, 353-386, 1975
	static inline UInt getCauchyStressMatrixSize(UInt dim);

	/// Sets the stress matrix according to Bathe et al, IJNME, Vol 9, 353-386,
	/// 1975
	template <UInt dim>
	static inline void setCauchyStressMatrix(const Matrix<Real> & S_t,
	Matrix<Real> & sigma);

	/// write the stress tensor in the Voigt notation.
	template <UInt dim>
	static inline decltype(auto) stressToVoigt(const Matrix<Real> & stress) {
	return VoigtHelper<dim>::matrixToVoigt(stress);
	}

	/// write the strain tensor in the Voigt notation.
	template <UInt dim>
	static inline decltype(auto) strainToVoigt(const Matrix<Real> & strain) {
	return VoigtHelper<dim>::matrixToVoigtWithFactors(strain);
	}

	/// write a voigt vector to stress
	template <UInt dim>
	static inline void voigtToStress(const Vector<Real> & voigt,
	Matrix<Real> & stress) {
	VoigtHelper<dim>::voigtToMatrix(voigt, stress);
	}

	/// Computation of Cauchy stress tensor in the case of finite deformation from
	/// the 2nd Piola-Kirchhoff for a given element type
	template <UInt dim>
	void StoCauchy(ElementType el_type, GhostType ghost_type = _not_ghost);

	/// Computation the Cauchy stress the 2nd Piola-Kirchhoff and the deformation
	/// gradient
	template <UInt dim>
	inline void StoCauchy(const Matrix<Real> & F, const Matrix<Real> & S,
	Matrix<Real> & sigma, const Real & C33 = 1.0) const;

	template <UInt dim>
	static inline void gradUToF(const Matrix<Real> & grad_u, Matrix<Real> & F);

	template <UInt dim>
	static inline decltype(auto) gradUToF(const Matrix<Real> & grad_u);

	static inline void rightCauchy(const Matrix<Real> & F, Matrix<Real> & C);
	static inline void leftCauchy(const Matrix<Real> & F, Matrix<Real> & B);

	template <UInt dim>
	static inline void gradUToEpsilon(const Matrix<Real> & grad_u,
	Matrix<Real> & epsilon);
	template <UInt dim>
	static inline decltype(auto) gradUToEpsilon(const Matrix<Real> & grad_u);

	template <UInt dim>
	static inline void gradUToE(const Matrix<Real> & grad_u,
	Matrix<Real> & epsilon);

	template <UInt dim>
	static inline decltype(auto) gradUToE(const Matrix<Real> & grad_u);

	static inline Real stressToVonMises(const Matrix<Real> & stress);

	protected:
	/// converts global element to local element
	inline Element convertToLocalElement(const Element & global_element) const;
	/// converts local element to global element
	inline Element convertToGlobalElement(const Element & local_element) const;

	/// converts global quadrature point to local quadrature point
	inline IntegrationPoint
	convertToLocalPoint(const IntegrationPoint & global_point) const;
	/// converts local quadrature point to global quadrature point
	inline IntegrationPoint
	convertToGlobalPoint(const IntegrationPoint & local_point) const;

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	template <typename T>
	inline void packElementDataHelper(const ElementTypeMapArray<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & fem_id = ID()) const;

	template <typename T>
	inline void unpackElementDataHelper(ElementTypeMapArray<T> & data_to_unpack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const ID & fem_id = ID());

	/* ------------------------------------------------------------------------ */
	/* MeshEventHandler inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	void onNodesAdded(const Array<UInt> & /unused/,
	const NewNodesEvent & /unused/) override{};
	void onNodesRemoved(const Array<UInt> & /unused/,
	const Array<UInt> & /unused/,
	const RemovedNodesEvent & /unused/) override{};
	void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) override;
	void onElementsRemoved(const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) override;
	void onElementsChanged(const Array<Element> & /unused/,
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) override{};

	/* ------------------------------------------------------------------------ */
	/* SolidMechanicsModelEventHandler inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	virtual void beforeSolveStep();
	virtual void afterSolveStep(bool converged = true);

	void onDamageIteration() override;
	void onDamageUpdate() override;
	void onDump() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Name, name, const std::string &);

	AKANTU_GET_MACRO(Model, model, const SolidMechanicsModel &)

	AKANTU_GET_MACRO(ID, id, const ID &);
	AKANTU_GET_MACRO(Rho, rho, Real);
	AKANTU_SET_MACRO(Rho, rho, Real);

	AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);

	/// return the potential energy for the subset of elements contained by the
	/// material
	Real getPotentialEnergy();
	/// return the potential energy for the provided element
	Real getPotentialEnergy(ElementType & type, UInt index);

	/// return the energy (identified by id) for the subset of elements contained
	/// by the material
	virtual Real getEnergy(const std::string & type);
	/// return the energy (identified by id) for the provided element
	virtual Real getEnergy(const std::string & energy_id, ElementType type,
	UInt index);

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ElementFilter, element_filter, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(GradU, gradu, Real);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Stress, stress, Real);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(PotentialEnergy, potential_energy,
	Real);
	AKANTU_GET_MACRO(GradU, gradu, const ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO(Stress, stress, const ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO(ElementFilter, element_filter,
	const ElementTypeMapArray<UInt> &);
	AKANTU_GET_MACRO(FEEngine, fem, FEEngine &);

	bool isNonLocal() const { return is_non_local; }

	template <typename T>
	const Array<T> & getArray(const ID & id, ElementType type,
	GhostType ghost_type = _not_ghost) const;
	template <typename T>
	Array<T> & getArray(const ID & id, ElementType type,
	GhostType ghost_type = _not_ghost);

	template <typename T>
	const InternalField<T> & getInternal(const ID & id) const;
	template <typename T> InternalField<T> & getInternal(const ID & id);

	template <typename T>
	inline bool isInternal(const ID & id, ElementKind element_kind) const;

	template <typename T>
	ElementTypeMap<UInt> getInternalDataPerElem(const ID & id,
	ElementKind element_kind) const;

	bool isFiniteDeformation() const { return finite_deformation; }
	bool isInelasticDeformation() const { return inelastic_deformation; }

	template <typename T> inline void setParam(const ID & param, T value);
	inline const Parameter & getParam(const ID & param) const;

	template <typename T>
	void flattenInternal(const std::string & field_id,
	ElementTypeMapArray<T> & internal_flat,
	GhostType ghost_type = _not_ghost,
	ElementKind element_kind = _ek_not_defined) const;

	/// apply a constant eigengrad_u everywhere in the material
	virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
	GhostType /ghost_type/ = _not_ghost);

	bool hasMatrixChanged(const ID & id) {
	if (id == "K") {
	return hasStiffnessMatrixChanged() or finite_deformation;
	}

	return true;
	}

	MatrixType getMatrixType(const ID & id) {
	if (id == "K") {
	return getTangentType();
	}

	if (id == "M") {
	return _symmetric;
	}

	return _mt_not_defined;
	}

	/// specify if the matrix need to be recomputed for this material
	virtual bool hasStiffnessMatrixChanged() { return true; }

	/// specify the type of matrix, if not overloaded the material is not valid
	/// for static or implicit computations
	virtual MatrixType getTangentType() { return _mt_not_defined; }

	/// static method to reteive the material factory
	static MaterialFactory & getFactory();

	protected:
	bool isInit() const { return is_init; }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// boolean to know if the material has been initialized
	bool is_init{false};

	std::map<ID, InternalField<Real> *> internal_vectors_real;
	std::map<ID, InternalField<UInt> *> internal_vectors_uint;
	std::map<ID, InternalField<bool> *> internal_vectors_bool;

	protected:
	ID id;

	/// Link to the fem object in the model
	FEEngine & fem;

	/// Finite deformation
	bool finite_deformation{false};

	/// Finite deformation
	bool inelastic_deformation{false};

	/// material name
	std::string name;

	/// The model to witch the material belong
	SolidMechanicsModel & model;

	/// density : rho
	Real rho{0.};

	/// spatial dimension
	UInt spatial_dimension;

	/// list of element handled by the material
	ElementTypeMapArray<UInt> element_filter;

	/// stresses arrays ordered by element types
	InternalField<Real> stress;

	/// eigengrad_u arrays ordered by element types
	InternalField<Real> eigengradu;

	/// grad_u arrays ordered by element types
	InternalField<Real> gradu;

	/// Green Lagrange strain (Finite deformation)
	InternalField<Real> green_strain;

	/// Second Piola-Kirchhoff stress tensor arrays ordered by element types
	/// (Finite deformation)
	InternalField<Real> piola_kirchhoff_2;

	/// potential energy by element
	InternalField<Real> potential_energy;

	/// tell if using in non local mode or not
	bool is_non_local{false};

	/// tell if the material need the previous stress state
	bool use_previous_stress{false};

	/// tell if the material need the previous strain state
	bool use_previous_gradu{false};

	/// elemental field interpolation coordinates
	InternalField<Real> interpolation_inverse_coordinates;

	/// elemental field interpolation points
	InternalField<Real> interpolation_points_matrices;

	/// vector that contains the names of all the internals that need to
	/// be transferred when material interfaces move
	std::vector<ID> internals_to_transfer;
	+
	private:
	/// eigen_grad_u for the parser
	Matrix<Real> eigen_grad_u;
	};

	/// standard output stream operator
	inline std::ostream & operator<<(std::ostream & stream,
	const Material & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "material_inline_impl.hh"

	#include "internal_field_tmpl.hh"
	#include "random_internal_field_tmpl.hh"

	/* -------------------------------------------------------------------------- */
	/* Auto loop */
	/* -------------------------------------------------------------------------- */
	/// This can be used to automatically write the loop on quadrature points in
	/// functions such as computeStress. This macro in addition to write the loop
	/// provides two tensors (matrices) sigma and grad_u
	#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type) \
	auto && grad_u_view = \
	make_view(this->gradu(el_type, ghost_type), this->spatial_dimension, \
	this->spatial_dimension); \
	\
	auto stress_view = \
	make_view(this->stress(el_type, ghost_type), this->spatial_dimension, \
	this->spatial_dimension); \
	\
	if (this->isFiniteDeformation()) { \
	stress_view = make_view(this->piola_kirchhoff_2(el_type, ghost_type), \
	this->spatial_dimension, this->spatial_dimension); \
	} \
	\
	for (auto && data : zip(grad_u_view, stress_view)) { \
	[[gnu::unused]] Matrix<Real> & grad_u = std::get<0>(data); \
	[[gnu::unused]] Matrix<Real> & sigma = std::get<1>(data)

	#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END }

	/// This can be used to automatically write the loop on quadrature points in
	/// functions such as computeTangentModuli. This macro in addition to write the
	/// loop provides two tensors (matrices) sigma_tensor, grad_u, and a matrix
	/// where the elemental tangent moduli should be stored in Voigt Notation
	#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_mat) \
	auto && grad_u_view = \
	make_view(this->gradu(el_type, ghost_type), this->spatial_dimension, \
	this->spatial_dimension); \
	\
	auto && stress_view = \
	make_view(this->stress(el_type, ghost_type), this->spatial_dimension, \
	this->spatial_dimension); \
	\
	auto tangent_size = \
	this->getTangentStiffnessVoigtSize(this->spatial_dimension); \
	\
	auto && tangent_view = make_view(tangent_mat, tangent_size, tangent_size); \
	\
	for (auto && data : zip(grad_u_view, stress_view, tangent_view)) { \
	[[gnu::unused]] Matrix<Real> & grad_u = std::get<0>(data); \
	[[gnu::unused]] Matrix<Real> & sigma = std::get<1>(data); \
	Matrix<Real> & tangent = std::get<2>(data);

	#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END }

	/* -------------------------------------------------------------------------- */

	#define INSTANTIATE_MATERIAL_ONLY(mat_name) \
	template class mat_name<1>; /* NOLINT */ \
	template class mat_name<2>; /* NOLINT */ \
	template class mat_name<3> /* NOLINT */

	#define MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name) \
	[](UInt dim, const ID &, SolidMechanicsModel & model, \
	const ID & id) /* NOLINT */ \
	-> std::unique_ptr< \
	Material> { /* NOLINT */ \
	switch (dim) { \
	case 1: \
	return std::make_unique<mat_name<1>>(/* NOLINT */ \
	model, id); \
	case 2: \
	return std::make_unique<mat_name<2>>(/* NOLINT */ \
	model, id); \
	case 3: \
	return std::make_unique<mat_name<3>>(/* NOLINT */ \
	model, id); \
	default: \
	AKANTU_EXCEPTION( \
	"The dimension " \
	<< dim \
	<< "is not a valid dimension for the material " \
	<< #id); \
	} \
	}

	#define INSTANTIATE_MATERIAL(id, mat_name) \
	INSTANTIATE_MATERIAL_ONLY(mat_name); \
	static bool material_is_alocated_##id [[gnu::unused]] = \
	MaterialFactory::getInstance().registerAllocator( \
	#id, MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name))

	#endif /* AKANTU_MATERIAL_HH_ */
	diff --git a/src/model/solid_mechanics/material_inline_impl.hh b/src/model/solid_mechanics/material_inline_impl.hh
	index c9b47c3e4..be0aac162 100644
	--- a/src/model/solid_mechanics/material_inline_impl.hh
	+++ b/src/model/solid_mechanics/material_inline_impl.hh
	@@ -1,551 +1,551 @@
	/**
	* @file material_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Jul 27 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of the inline functions of the class material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_INLINE_IMPL_HH_
	#define AKANTU_MATERIAL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt Material::addElement(ElementType type, UInt element,
	GhostType ghost_type) {
	Array<UInt> & el_filter = this->element_filter(type, ghost_type);
	el_filter.push_back(element);
	return el_filter.size() - 1;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Material::addElement(const Element & element) {
	return this->addElement(element.type, element.element, element.ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Material::getTangentStiffnessVoigtSize(UInt dim) {
	return (dim * (dim - 1) / 2 + dim);
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Material::getCauchyStressMatrixSize(UInt dim) {
	return (dim * dim);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void Material::gradUToF(const Matrix<Real> & grad_u, Matrix<Real> & F) {
	AKANTU_DEBUG_ASSERT(F.size() >= grad_u.size() && grad_u.size() == dim * dim,
	"The dimension of the tensor F should be greater or "
	"equal to the dimension of the tensor grad_u.");
	F.eye();

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	F(i, j) += grad_u(i, j);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline decltype(auto) Material::gradUToF(const Matrix<Real> & grad_u) {
	Matrix<Real> F(dim, dim);
	gradUToF<dim>(grad_u, F);
	return F;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void Material::StoCauchy(const Matrix<Real> & F, const Matrix<Real> & S,
	Matrix<Real> & sigma, const Real & C33) const {
	Real J = F.det() * sqrt(C33);

	Matrix<Real> F_S(dim, dim);
	F_S = F * S;
	Real constant = J ? 1. / J : 0;
	sigma.mul<false, true>(F_S, F, constant);
	}

	/* -------------------------------------------------------------------------- */
	inline void Material::rightCauchy(const Matrix<Real> & F, Matrix<Real> & C) {
	C.mul<true, false>(F, F);
	}

	/* -------------------------------------------------------------------------- */
	inline void Material::leftCauchy(const Matrix<Real> & F, Matrix<Real> & B) {
	B.mul<false, true>(F, F);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void Material::gradUToEpsilon(const Matrix<Real> & grad_u,
	Matrix<Real> & epsilon) {
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	epsilon(i, j) = 0.5 * (grad_u(i, j) + grad_u(j, i));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline decltype(auto) Material::gradUToEpsilon(const Matrix<Real> & grad_u) {
	Matrix<Real> epsilon(dim, dim);
	Material::template gradUToEpsilon<dim>(grad_u, epsilon);
	return epsilon;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void Material::gradUToE(const Matrix<Real> & grad_u, Matrix<Real> & E) {
	E.mul<true, false>(grad_u, grad_u, .5);

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	E(i, j) += 0.5 * (grad_u(i, j) + grad_u(j, i));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline decltype(auto) Material::gradUToE(const Matrix<Real> & grad_u) {
	Matrix<Real> E(dim, dim);
	gradUToE<dim>(grad_u, E);
	return E;
	}

	/* -------------------------------------------------------------------------- */
	inline Real Material::stressToVonMises(const Matrix<Real> & stress) {
	// compute deviatoric stress
	UInt dim = stress.cols();
	Matrix<Real> deviatoric_stress =
	Matrix<Real>::eye(dim, -1. * stress.trace() / 3.);

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	deviatoric_stress(i, j) += stress(i, j);
	}
	}

	// return Von Mises stress
	return std::sqrt(3. * deviatoric_stress.doubleDot(deviatoric_stress) / 2.);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void Material::setCauchyStressMatrix(const Matrix<Real> & S_t,
	Matrix<Real> & sigma) {
	AKANTU_DEBUG_IN();

	sigma.zero();

	/// see Finite ekement formulations for large deformation dynamic analysis,
	/// Bathe et al. IJNME vol 9, 1975, page 364 ^t \f$\tau\f$
	for (UInt i = 0; i < dim; ++i) {
	for (UInt m = 0; m < dim; ++m) {
	for (UInt n = 0; n < dim; ++n) {
	sigma(i * dim + m, i * dim + n) = S_t(m, n);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline Element
	Material::convertToLocalElement(const Element & global_element) const {
	UInt ge = global_element.element;
	#ifndef AKANTU_NDEBUG
	UInt model_mat_index = this->model.getMaterialByElement(
	global_element.type, global_element.ghost_type)(ge);

	UInt mat_index = this->model.getMaterialIndex(this->name);
	AKANTU_DEBUG_ASSERT(model_mat_index == mat_index,
	"Conversion of a global element in a local element for "
	"the wrong material "
	<< this->name << std::endl);
	#endif
	UInt le = this->model.getMaterialLocalNumbering(
	global_element.type, global_element.ghost_type)(ge);

	Element tmp_quad{global_element.type, le, global_element.ghost_type};
	return tmp_quad;
	}

	/* -------------------------------------------------------------------------- */
	inline Element
	Material::convertToGlobalElement(const Element & local_element) const {
	UInt le = local_element.element;
	UInt ge =
	this->element_filter(local_element.type, local_element.ghost_type)(le);

	Element tmp_quad{local_element.type, ge, local_element.ghost_type};
	return tmp_quad;
	}

	/* -------------------------------------------------------------------------- */
	inline IntegrationPoint
	Material::convertToLocalPoint(const IntegrationPoint & global_point) const {
	const FEEngine & fem = this->model.getFEEngine();
	UInt nb_quad = fem.getNbIntegrationPoints(global_point.type);
	Element el =
	this->convertToLocalElement(static_cast<const Element &>(global_point));
	IntegrationPoint tmp_quad(el, global_point.num_point, nb_quad);
	return tmp_quad;
	}

	/* -------------------------------------------------------------------------- */
	inline IntegrationPoint
	Material::convertToGlobalPoint(const IntegrationPoint & local_point) const {
	const FEEngine & fem = this->model.getFEEngine();
	UInt nb_quad = fem.getNbIntegrationPoints(local_point.type);
	Element el =
	this->convertToGlobalElement(static_cast<const Element &>(local_point));
	IntegrationPoint tmp_quad(el, local_point.num_point, nb_quad);
	return tmp_quad;
	}

	/* -------------------------------------------------------------------------- */
	inline UInt Material::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	if (tag == SynchronizationTag::_smm_stress) {
	return (this->isFiniteDeformation() ? 3 : 1) * spatial_dimension *
	spatial_dimension * sizeof(Real) *
	this->getModel().getNbIntegrationPoints(elements);
	}
	return 0;
	}

	/* -------------------------------------------------------------------------- */
	inline void Material::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	if (tag == SynchronizationTag::_smm_stress) {
	if (this->isFiniteDeformation()) {
	packElementDataHelper(piola_kirchhoff_2, buffer, elements);
	packElementDataHelper(gradu, buffer, elements);
	}
	packElementDataHelper(stress, buffer, elements);
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void Material::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	if (tag == SynchronizationTag::_smm_stress) {
	if (this->isFiniteDeformation()) {
	unpackElementDataHelper(piola_kirchhoff_2, buffer, elements);
	unpackElementDataHelper(gradu, buffer, elements);
	}
	unpackElementDataHelper(stress, buffer, elements);
	}
	}

	/* -------------------------------------------------------------------------- */
	inline const Parameter & Material::getParam(const ID & param) const {
	try {
	return get(param);
	} catch (...) {
	AKANTU_EXCEPTION("No parameter " << param << " in the material "
	<< getID());
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Material::setParam(const ID & param, T value) {
	try {
	set<T>(param, value);
	} catch (...) {
	AKANTU_EXCEPTION("No parameter " << param << " in the material "
	<< getID());
	}
	updateInternalParameters();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Material::packElementDataHelper(
	const ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & elements, const ID & fem_id) const {
	DataAccessor::packElementalDataHelper<T>(data_to_pack, buffer, elements, true,
	model.getFEEngine(fem_id));
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline void Material::unpackElementDataHelper(
	ElementTypeMapArray<T> & data_to_unpack, CommunicationBuffer & buffer,
	const Array<Element> & elements, const ID & fem_id) {
	DataAccessor::unpackElementalDataHelper<T>(data_to_unpack, buffer, elements,
	true, model.getFEEngine(fem_id));
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void Material::registerInternal<Real>(InternalField<Real> & vect) {
	internal_vectors_real[vect.getID()] = &vect;
	}

	template <>
	inline void Material::registerInternal<UInt>(InternalField<UInt> & vect) {
	internal_vectors_uint[vect.getID()] = &vect;
	}

	template <>
	inline void Material::registerInternal<bool>(InternalField<bool> & vect) {
	internal_vectors_bool[vect.getID()] = &vect;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void Material::unregisterInternal<Real>(InternalField<Real> & vect) {
	internal_vectors_real.erase(vect.getID());
	}

	template <>
	inline void Material::unregisterInternal<UInt>(InternalField<UInt> & vect) {
	internal_vectors_uint.erase(vect.getID());
	}

	template <>
	inline void Material::unregisterInternal<bool>(InternalField<bool> & vect) {
	internal_vectors_bool.erase(vect.getID());
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline bool Material::isInternal(const ID & /id/,
	ElementKind /element_kind/) const {
	AKANTU_TO_IMPLEMENT();
	}

	template <>
	inline bool Material::isInternal<Real>(const ID & id,
	ElementKind element_kind) const {
	auto internal_array = internal_vectors_real.find(this->getID() + ":" + id);

	return not(internal_array == internal_vectors_real.end() \|\|
	internal_array->second->getElementKind() != element_kind);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline ElementTypeMap<UInt>
	Material::getInternalDataPerElem(const ID & field_id,
	ElementKind element_kind) const {

	if (!this->template isInternal<T>(field_id, element_kind)) {
	AKANTU_EXCEPTION("Cannot find internal field " << id << " in material "
	<< this->name);
	}

	const InternalField<T> & internal_field =
	this->template getInternal<T>(field_id);
	const FEEngine & fe_engine = internal_field.getFEEngine();
	UInt nb_data_per_quad = internal_field.getNbComponent();

	ElementTypeMap<UInt> res;
	for (auto ghost_type : ghost_types) {
	for (auto & type : internal_field.elementTypes(ghost_type)) {
	UInt nb_quadrature_points =
	fe_engine.getNbIntegrationPoints(type, ghost_type);
	res(type, ghost_type) = nb_data_per_quad * nb_quadrature_points;
	}
	}

	return res;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Material::flattenInternal(const std::string & field_id,
	ElementTypeMapArray<T> & internal_flat,
	const GhostType ghost_type,
	ElementKind element_kind) const {

	if (!this->template isInternal<T>(field_id, element_kind)) {
	AKANTU_EXCEPTION("Cannot find internal field " << id << " in material "
	<< this->name);
	}

	const InternalField<T> & internal_field =
	this->template getInternal<T>(field_id);

	const FEEngine & fe_engine = internal_field.getFEEngine();
	const Mesh & mesh = fe_engine.getMesh();

	for (auto && type : internal_field.filterTypes(ghost_type)) {
	const Array<Real> & src_vect = internal_field(type, ghost_type);
	const Array<UInt> & filter = internal_field.getFilter(type, ghost_type);

	// total number of elements in the corresponding mesh
	UInt nb_element_dst = mesh.getNbElement(type, ghost_type);
	// number of element in the internal field
	UInt nb_element_src = filter.size();
	// number of quadrature points per elem
	UInt nb_quad_per_elem = fe_engine.getNbIntegrationPoints(type);
	// number of data per quadrature point
	UInt nb_data_per_quad = internal_field.getNbComponent();

	if (!internal_flat.exists(type, ghost_type)) {
	internal_flat.alloc(nb_element_dst * nb_quad_per_elem, nb_data_per_quad,
	type, ghost_type);
	}

	if (nb_element_src == 0) {
	continue;
	}

	// number of data per element
	UInt nb_data = nb_quad_per_elem * nb_data_per_quad;

	Array<Real> & dst_vect = internal_flat(type, ghost_type);
	dst_vect.resize(nb_element_dst * nb_quad_per_elem);

	auto it_dst = make_view(dst_vect, nb_data).begin();

	for (auto && data : zip(filter, make_view(src_vect, nb_data))) {
	it_dst[std::get<0>(data)] = std::get<1>(data);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline const InternalField<T> &
	Material::getInternal([[gnu::unused]] const ID & int_id) const {
	AKANTU_TO_IMPLEMENT();
	return NULL;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline InternalField<T> &
	Material::getInternal([[gnu::unused]] const ID & int_id) {
	AKANTU_TO_IMPLEMENT();
	return NULL;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline const InternalField<Real> &
	Material::getInternal(const ID & int_id) const {
	auto it = internal_vectors_real.find(getID() + ":" + int_id);
	if (it == internal_vectors_real.end()) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain an internal "
	<< int_id << " ("
	<< (getID() + ":" + int_id) << ")");
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline InternalField<Real> & Material::getInternal(const ID & int_id) {
	auto it = internal_vectors_real.find(getID() + ":" + int_id);
	if (it == internal_vectors_real.end()) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain an internal "
	<< int_id << " ("
	<< (getID() + ":" + int_id) << ")");
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline const InternalField<UInt> &
	Material::getInternal(const ID & int_id) const {
	auto it = internal_vectors_uint.find(getID() + ":" + int_id);
	if (it == internal_vectors_uint.end()) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain an internal "
	<< int_id << " ("
	<< (getID() + ":" + int_id) << ")");
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline InternalField<UInt> & Material::getInternal(const ID & int_id) {
	auto it = internal_vectors_uint.find(getID() + ":" + int_id);
	if (it == internal_vectors_uint.end()) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain an internal "
	<< int_id << " ("
	<< (getID() + ":" + int_id) << ")");
	}
	return *it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline const Array<T> & Material::getArray(const ID & vect_id, ElementType type,
	GhostType ghost_type) const {
	try {
	return this->template getInternal<T>(vect_id)(type, ghost_type);
	} catch (debug::Exception & e) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain a vector "
	<< vect_id << " [" << e << "]");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline Array<T> & Material::getArray(const ID & vect_id, ElementType type,
	GhostType ghost_type) {
	try {
	return this->template getInternal<T>(vect_id)(type, ghost_type);
	} catch (debug::Exception & e) {
	AKANTU_SILENT_EXCEPTION("The material " << name << "(" << getID()
	<< ") does not contain a vector "
	<< vect_id << " [" << e << "]");
	}
	}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/material_selector.hh b/src/model/solid_mechanics/material_selector.hh
	index 7c14637ad..5cdc2f3f4 100644
	--- a/src/model/solid_mechanics/material_selector.hh
	+++ b/src/model/solid_mechanics/material_selector.hh
	@@ -1,159 +1,159 @@
	/**
	* @file material_selector.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Apr 09 2021
	*
	* @brief class describing how to choose a material for a given element
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_SELECTOR_HH_
	#define AKANTU_MATERIAL_SELECTOR_HH_

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class SolidMechanicsModel;

	/**
	* main class to assign same or different materials for different
	* elements
	*/
	class MaterialSelector {
	public:
	MaterialSelector() = default;
	virtual ~MaterialSelector() = default;
	virtual inline UInt operator()(const Element & element) {
	if (fallback_selector) {
	return (*fallback_selector)(element);
	}

	return fallback_value;
	}

	inline void setFallback(UInt f) { fallback_value = f; }
	inline void
	setFallback(const std::shared_ptr<MaterialSelector> & fallback_selector) {
	this->fallback_selector = fallback_selector;
	}

	inline std::shared_ptr<MaterialSelector> & getFallbackSelector() {
	return this->fallback_selector;
	}

	inline UInt getFallbackValue() const { return this->fallback_value; }

	protected:
	UInt fallback_value{0};
	std::shared_ptr<MaterialSelector> fallback_selector;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class that assigns the first material to regular elements by default
	*/
	class DefaultMaterialSelector : public MaterialSelector {
	public:
	explicit DefaultMaterialSelector(
	const ElementTypeMapArray<UInt> & material_index)
	: material_index(material_index) {}

	UInt operator()(const Element & element) override {
	if (not material_index.exists(element.type, element.ghost_type)) {
	return MaterialSelector::operator()(element);
	}

	const auto & mat_indexes = material_index(element.type, element.ghost_type);
	if (element.element < mat_indexes.size()) {
	auto && tmp_mat = mat_indexes(element.element);
	if (tmp_mat != UInt(-1)) {
	return tmp_mat;
	}
	}

	return MaterialSelector::operator()(element);
	}

	private:
	const ElementTypeMapArray<UInt> & material_index;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* Use elemental data to assign materials
	*/
	template <typename T>
	class ElementDataMaterialSelector : public MaterialSelector {
	public:
	ElementDataMaterialSelector(const ElementTypeMapArray<T> & element_data,
	const SolidMechanicsModel & model,
	UInt first_index = 1)
	: element_data(element_data), model(model), first_index(first_index) {}

	inline T elementData(const Element & element) {
	DebugLevel dbl = debug::getDebugLevel();
	debug::setDebugLevel(dblError);
	T data = element_data(element.type, element.ghost_type)(element.element);
	debug::setDebugLevel(dbl);
	return data;
	}

	inline UInt operator()(const Element & element) override;

	protected:
	/// list of element with the specified data (i.e. tag value)
	const ElementTypeMapArray<T> & element_data;

	/// the model that the materials belong
	const SolidMechanicsModel & model;

	/// first material index: equal to 1 if none specified
	UInt first_index;
	};

	/* -------------------------------------------------------------------------- */
	/**
	* class to use mesh data information to assign different materials
	* where name is the tag value: tag_0, tag_1
	*/
	template <typename T>
	class MeshDataMaterialSelector : public ElementDataMaterialSelector<T> {
	public:
	MeshDataMaterialSelector(const std::string & name,
	const SolidMechanicsModel & model,
	UInt first_index = 1);
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_SELECTOR_HH_ */
	diff --git a/src/model/solid_mechanics/material_selector_tmpl.hh b/src/model/solid_mechanics/material_selector_tmpl.hh
	index 7ed2c9f28..a770f8c5a 100644
	--- a/src/model/solid_mechanics/material_selector_tmpl.hh
	+++ b/src/model/solid_mechanics/material_selector_tmpl.hh
	@@ -1,82 +1,82 @@
	/**
	* @file material_selector_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of the template MaterialSelector
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_selector.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_SELECTOR_TMPL_HH_
	#define AKANTU_MATERIAL_SELECTOR_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	inline UInt
	ElementDataMaterialSelector<std::string>::operator()(const Element & element) {
	try {
	std::string material_name = this->elementData(element);
	return model.getMaterialIndex(material_name);
	} catch (std::exception & e) {
	return MaterialSelector::operator()(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline UInt
	ElementDataMaterialSelector<UInt>::operator()(const Element & element) {
	try {
	return this->elementData(element) - first_index;
	} catch (...) {
	return MaterialSelector::operator()(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	inline UInt
	ElementDataMaterialSelector<T>::operator()(const Element & element) {
	return MaterialSelector::operator()(element);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	MeshDataMaterialSelector<T>::MeshDataMaterialSelector(
	const std::string & name, const SolidMechanicsModel & model,
	UInt first_index)
	: ElementDataMaterialSelector<T>(model.getMesh().getData<T>(name), model,
	first_index) {}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_SELECTOR_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/internal_field.hh b/src/model/solid_mechanics/materials/internal_field.hh
	index 9b6bd112c..2f0c980db 100644
	--- a/src/model/solid_mechanics/materials/internal_field.hh
	+++ b/src/model/solid_mechanics/materials/internal_field.hh
	@@ -1,286 +1,247 @@
	/**
	* @file internal_field.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Mar 26 2021
	*
	* @brief Material internal properties
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "element_type_map.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTERNAL_FIELD_HH_
	#define AKANTU_INTERNAL_FIELD_HH_

	namespace akantu {

	class Material;
	class FEEngine;

	/**
	* class for the internal fields of materials
	* to store values for each quadrature
	*/
	- template <class Material, typename T> class InternalFieldTmpl : public ElementTypeMapArray<T> {
	+template <class Material, typename T>
	+class InternalFieldTmpl : public ElementTypeMapArray<T> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	InternalFieldTmpl(const ID & id, Material & material);
	~InternalFieldTmpl() override;

	/// This constructor is only here to let cohesive elements compile
	InternalFieldTmpl(const ID & id, Material & material, FEEngine & fem,
	- const ElementTypeMapArray<UInt> & element_filter);
	+ const ElementTypeMapArray<UInt> & element_filter);

	/// More general constructor
	- InternalFieldTmpl(const ID & id, Material & material, UInt dim, FEEngine & fem,
	- const ElementTypeMapArray<UInt> & element_filter);
	-
	- InternalFieldTmpl(const ID & id, const InternalFieldTmpl<Material, T> & other);
	+ InternalFieldTmpl(const ID & id, Material & material, UInt dim,
	+ FEEngine & fem,
	+ const ElementTypeMapArray<UInt> & element_filter);

	+ InternalFieldTmpl(const ID & id,
	+ const InternalFieldTmpl<Material, T> & other);

	-private:
	InternalFieldTmpl operator=(const InternalFieldTmpl &) = delete;

	-
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to reset the FEEngine for the internal field
	virtual void setFEEngine(FEEngine & fe_engine);

	/// function to reset the element kind for the internal
	virtual void setElementKind(ElementKind element_kind);

	/// initialize the field to a given number of component
	virtual void initialize(UInt nb_component);

	/// activate the history of this field
	virtual void initializeHistory();

	/// resize the arrays and set the new element to 0
	virtual void resize();

	/// set the field to a given value v
	virtual void setDefaultValue(const T & v);

	/// reset all the fields to the default value
	virtual void reset();

	/// save the current values in the history
	virtual void saveCurrentValues();

	/// restore the previous values from the history
	virtual void restorePreviousValues();

	/// remove the quadrature points corresponding to suppressed elements
	virtual void
	removeIntegrationPoints(const ElementTypeMapArray<UInt> & new_numbering);

	/// print the content
	void printself(std::ostream & stream, int /indent/ = 0) const override;

	/// get the default value
	inline operator T() const;

	virtual FEEngine & getFEEngine() { return *fem; }

	virtual const FEEngine & getFEEngine() const { return *fem; }

	- /// AKANTU_GET_MACRO(FEEngine, *fem, FEEngine &);
	-
	protected:
	/// initialize the arrays in the ElementTypeMapArray<T>
	void internalInitialize(UInt nb_component);

	/// set the values for new internals
	virtual void setArrayValues(T * begin, T * end);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	- // using type_iterator = typename ElementTypeMapArray<T>::type_iterator;
	- // using filter_type_iterator =
	- // typename ElementTypeMapArray<UInt>::type_iterator;
	-
	- // /// get the type iterator on all types contained in the internal field
	- // type_iterator firstType(GhostType ghost_type = _not_ghost) const {
	- // return ElementTypeMapArray<T>::firstType(this->spatial_dimension,
	- // ghost_type, this->element_kind);
	- // }
	-
	- // /// get the type iterator on the last type contained in the internal field
	- // type_iterator lastType(GhostType ghost_type = _not_ghost) const {
	- // return ElementTypeMapArray<T>::lastType(this->spatial_dimension,
	- // ghost_type,
	- // this->element_kind);
	- // }
	-
	- // /// get the type iterator on all types contained in the internal field
	- // filter_type_iterator
	- // filterFirstType(GhostType ghost_type = _not_ghost) const {
	- // return this->element_filter.firstType(this->spatial_dimension,
	- // ghost_type,
	- // this->element_kind);
	- // }
	-
	- // /// get the type iterator on the last type contained in the internal field
	- // filter_type_iterator
	- // filterLastType(GhostType ghost_type = _not_ghost) const {
	- // return this->element_filter.lastType(this->spatial_dimension, ghost_type,
	- // this->element_kind);
	- // }
	-
	/// get filter types for range loop
	decltype(auto) elementTypes(GhostType ghost_type = _not_ghost) const {
	return ElementTypeMapArray<T>::elementTypes(
	_spatial_dimension = this->spatial_dimension,
	_element_kind = this->element_kind, _ghost_type = ghost_type);
	}

	/// get filter types for range loop
	decltype(auto) filterTypes(GhostType ghost_type = _not_ghost) const {
	return this->element_filter.elementTypes(
	_spatial_dimension = this->spatial_dimension,
	_element_kind = this->element_kind, _ghost_type = ghost_type);
	}

	/// get the array for a given type of the element_filter
	- const Array<UInt> &
	- getFilter(ElementType type,
	- GhostType ghost_type = _not_ghost) const {
	+ const Array<UInt> & getFilter(ElementType type,
	+ GhostType ghost_type = _not_ghost) const {
	return this->element_filter(type, ghost_type);
	}

	/// get the Array corresponding to the type en ghost_type specified
	virtual Array<T> & operator()(ElementType type,
	GhostType ghost_type = _not_ghost) {
	return ElementTypeMapArray<T>::operator()(type, ghost_type);
	}

	- virtual const Array<T> &
	- operator()(ElementType type,
	- GhostType ghost_type = _not_ghost) const {
	+ virtual const Array<T> & operator()(ElementType type,
	+ GhostType ghost_type = _not_ghost) const {
	return ElementTypeMapArray<T>::operator()(type, ghost_type);
	}

	virtual Array<T> & previous(ElementType type,
	GhostType ghost_type = _not_ghost) {
	AKANTU_DEBUG_ASSERT(previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");
	return this->previous_values->operator()(type, ghost_type);
	}

	- virtual const Array<T> &
	- previous(ElementType type,
	- GhostType ghost_type = _not_ghost) const {
	+ virtual const Array<T> & previous(ElementType type,
	+ GhostType ghost_type = _not_ghost) const {
	AKANTU_DEBUG_ASSERT(previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");
	return this->previous_values->operator()(type, ghost_type);
	}

	virtual InternalFieldTmpl<Material, T> & previous() {
	AKANTU_DEBUG_ASSERT(previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");
	return *(this->previous_values);
	}

	- virtual const InternalFieldTmpl<Material, T> & previous() const {
	+ virtual const InternalFieldTmpl<Material, T> & previous() const {
	AKANTU_DEBUG_ASSERT(previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");
	return *(this->previous_values);
	}

	/// check if the history is used or not
	bool hasHistory() const { return (previous_values != nullptr); }

	/// get the kind treated by the internal
	ElementKind getElementKind() const { return element_kind; }

	/// return the number of components
	UInt getNbComponent() const { return nb_component; }

	/// return the spatial dimension corresponding to the internal element type
	/// loop filter
	UInt getSpatialDimension() const { return this->spatial_dimension; }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// the material for which this is an internal parameter
	Material & material;

	/// the fem containing the mesh and the element informations
	FEEngine * fem{nullptr};

	/// Element filter if needed
	const ElementTypeMapArray<UInt> & element_filter;

	/// default value
	T default_value{};

	/// spatial dimension of the element to consider
	UInt spatial_dimension{0};

	/// ElementKind of the element to consider
	ElementKind element_kind{_ek_regular};

	/// Number of component of the internal field
	UInt nb_component{0};

	/// Is the field initialized
	bool is_init{false};

	/// previous values
	std::unique_ptr<InternalFieldTmpl<Material, T>> previous_values;
	};

	-
	/// standard output stream operator
	template <class Material, typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const InternalFieldTmpl<Material, T> & _this) {
	_this.printself(stream);
	return stream;
	}

	-template<typename T>
	-using InternalField = InternalFieldTmpl<Material, T>;
	+template <typename T> using InternalField = InternalFieldTmpl<Material, T>;

	} // namespace akantu

	#endif /* AKANTU_INTERNAL_FIELD_HH_ */
	diff --git a/src/model/solid_mechanics/materials/internal_field_tmpl.hh b/src/model/solid_mechanics/materials/internal_field_tmpl.hh
	index 4d9e2e6da..38eb03344 100644
	--- a/src/model/solid_mechanics/materials/internal_field_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/internal_field_tmpl.hh
	@@ -1,334 +1,335 @@
	/**
	* @file internal_field_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Apr 02 2021
	*
	* @brief Material internal properties
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_INTERNAL_FIELD_TMPL_HH_
	#define AKANTU_INTERNAL_FIELD_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	-InternalFieldTmpl<Material, T>::InternalFieldTmpl(const ID & id, Material & material)
	- : ElementTypeMapArray<T>(id, material.getID()),
	- material(material), fem(&(material.getModel().getFEEngine())),
	- element_filter(material.getElementFilter()),
	- spatial_dimension(material.getModel().getSpatialDimension()) {}
	+InternalFieldTmpl<Material, T>::InternalFieldTmpl(const ID & id,
	+ Material & material)
	+ : ElementTypeMapArray<T>(id, material.getID()), material(material),
	+ fem(&(material.getModel().getFEEngine())),
	+ element_filter(material.getElementFilter()),
	+ spatial_dimension(material.getModel().getSpatialDimension()) {}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	InternalFieldTmpl<Material, T>::InternalFieldTmpl(
	const ID & id, Material & material, FEEngine & fem,
	const ElementTypeMapArray<UInt> & element_filter)
	- : ElementTypeMapArray<T>(id, material.getID()),
	- material(material), fem(&fem), element_filter(element_filter),
	+ : ElementTypeMapArray<T>(id, material.getID()), material(material),
	+ fem(&fem), element_filter(element_filter),
	spatial_dimension(material.getSpatialDimension()) {}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	InternalFieldTmpl<Material, T>::InternalFieldTmpl(
	const ID & id, Material & material, UInt dim, FEEngine & fem,
	const ElementTypeMapArray<UInt> & element_filter)
	- : ElementTypeMapArray<T>(id, material.getID()),
	- material(material), fem(&fem), element_filter(element_filter),
	- spatial_dimension(dim) {}
	+ : ElementTypeMapArray<T>(id, material.getID()), material(material),
	+ fem(&fem), element_filter(element_filter), spatial_dimension(dim) {}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	-InternalFieldTmpl<Material, T>::InternalFieldTmpl(const ID & id,
	- const InternalFieldTmpl<Material, T> & other)
	+InternalFieldTmpl<Material, T>::InternalFieldTmpl(
	+ const ID & id, const InternalFieldTmpl<Material, T> & other)
	: ElementTypeMapArray<T>(id, other.material.getID()),
	material(other.material), fem(other.fem),
	element_filter(other.element_filter), default_value(other.default_value),
	spatial_dimension(other.spatial_dimension),
	element_kind(other.element_kind), nb_component(other.nb_component) {

	AKANTU_DEBUG_ASSERT(other.is_init,
	"Cannot create a copy of a non initialized field");
	this->internalInitialize(this->nb_component);
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	InternalFieldTmpl<Material, T>::~InternalFieldTmpl() {
	if (this->is_init) {
	this->material.unregisterInternal(*this);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::setFEEngine(FEEngine & fe_engine) {
	this->fem = &fe_engine;
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::setElementKind(ElementKind element_kind) {
	this->element_kind = element_kind;
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::initialize(UInt nb_component) {
	internalInitialize(nb_component);
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::initializeHistory() {
	- if (!previous_values)
	- previous_values =
	- std::make_unique<InternalFieldTmpl<Material, T>>("previous_" + this->getID(), *this);
	+ if (!previous_values) {
	+ previous_values = std::make_unique<InternalFieldTmpl<Material, T>>(
	+ "previous_" + this->getID(), *this);
	+ }
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::resize() {
	- if (!this->is_init){
	+ if (!this->is_init) {
	return;
	}

	for (auto ghost : ghost_types) {
	for (const auto & type : this->filterTypes(ghost)) {
	UInt nb_element = this->element_filter(type, ghost).size();

	UInt nb_quadrature_points =
	this->fem->getNbIntegrationPoints(type, ghost);
	UInt new_size = nb_element * nb_quadrature_points;

	UInt old_size = 0;
	Array<T> * vect = nullptr;

	if (this->exists(type, ghost)) {
	vect = &(this->operator()(type, ghost));
	old_size = vect->size();
	vect->resize(new_size);
	} else {
	vect = &(this->alloc(nb_element * nb_quadrature_points, nb_component,
	type, ghost));
	}

	this->setArrayValues(vect->storage() + old_size * vect->getNbComponent(),
	vect->storage() + new_size * vect->getNbComponent());
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::setDefaultValue(const T & value) {
	this->default_value = value;
	this->reset();
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::reset() {
	- for (auto ghost_type : ghost_types){
	+ for (auto ghost_type : ghost_types) {
	for (const auto & type : this->elementTypes(ghost_type)) {
	Array<T> & vect = (*this)(type, ghost_type);
	- //vect.zero();
	+ // vect.zero();
	this->setArrayValues(
	vect.storage(), vect.storage() + vect.size() * vect.getNbComponent());
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::internalInitialize(UInt nb_component) {
	if (!this->is_init) {
	this->nb_component = nb_component;

	for (auto ghost : ghost_types) {
	for (const auto & type : this->filterTypes(ghost)) {
	UInt nb_element = this->element_filter(type, ghost).size();
	UInt nb_quadrature_points =
	this->fem->getNbIntegrationPoints(type, ghost);
	if (this->exists(type, ghost)) {
	this->operator()(type, ghost)
	.resize(nb_element * nb_quadrature_points);
	} else {
	this->alloc(nb_element * nb_quadrature_points, nb_component, type,
	ghost);
	}
	}
	}

	this->material.registerInternal(*this);
	this->is_init = true;
	}
	this->reset();

	if (this->previous_values) {
	this->previous_values->internalInitialize(nb_component);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::setArrayValues(T * begin, T * end) {
	- for (; begin < end; ++begin){
	+ for (; begin < end; ++begin) {
	*begin = this->default_value;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::saveCurrentValues() {
	AKANTU_DEBUG_ASSERT(this->previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");

	if (not this->is_init) {
	return;
	}

	for (auto ghost_type : ghost_types) {
	for (const auto & type : this->elementTypes(ghost_type)) {
	(*this->previous_values)(type, ghost_type)
	.copy((*this)(type, ghost_type));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::restorePreviousValues() {
	AKANTU_DEBUG_ASSERT(this->previous_values != nullptr,
	"The history of the internal "
	<< this->getID() << " has not been activated");

	if (not this->is_init) {
	return;
	}

	for (auto ghost_type : ghost_types) {
	for (const auto & type : this->elementTypes(ghost_type)) {
	(*this)(type, ghost_type)
	.copy((*this->previous_values)(type, ghost_type));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	void InternalFieldTmpl<Material, T>::removeIntegrationPoints(
	const ElementTypeMapArray<UInt> & new_numbering) {
	for (auto ghost_type : ghost_types) {
	for (auto type : new_numbering.elementTypes(_all_dimensions, ghost_type,
	_ek_not_defined)) {
	if (not this->exists(type, ghost_type)) {
	continue;
	}

	Array<T> & vect = (*this)(type, ghost_type);
	if (vect.empty()) {
	continue;
	}

	const Array<UInt> & renumbering = new_numbering(type, ghost_type);

	UInt nb_quad_per_elem = fem->getNbIntegrationPoints(type, ghost_type);
	UInt nb_component = vect.getNbComponent();

	Array<T> tmp(renumbering.size() * nb_quad_per_elem, nb_component);

	AKANTU_DEBUG_ASSERT(
	tmp.size() == vect.size(),
	"Something strange append some mater was created from nowhere!!");

	AKANTU_DEBUG_ASSERT(
	tmp.size() == vect.size(),
	"Something strange append some mater was created or disappeared in "
	<< vect.getID() << "(" << vect.size() << "!=" << tmp.size()
	<< ") "
	"!!");

	UInt new_size = 0;
	for (UInt i = 0; i < renumbering.size(); ++i) {
	UInt new_i = renumbering(i);
	if (new_i != UInt(-1)) {
	memcpy(tmp.storage() + new_i * nb_component * nb_quad_per_elem,
	vect.storage() + i * nb_component * nb_quad_per_elem,
	nb_component * nb_quad_per_elem * sizeof(T));
	++new_size;
	}
	}
	tmp.resize(new_size * nb_quad_per_elem);
	vect.copy(tmp);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	-void InternalFieldTmpl<Material, T>::printself(std::ostream & stream,
	- int indent [[gnu::unused]]) const {
	+void InternalFieldTmpl<Material, T>::printself(std::ostream & stream, int indent
	+ [[gnu::unused]]) const {
	stream << "InternalField [ " << this->getID();
	#if !defined(AKANTU_NDEBUG)
	if (AKANTU_DEBUG_TEST(dblDump)) {
	stream << std::endl;
	ElementTypeMapArray<T>::printself(stream, indent + 3);
	} else {
	#endif
	stream << " {" << this->getData(_not_ghost).size() << " types - "
	<< this->getData(_ghost).size() << " ghost types"
	<< "}";
	#if !defined(AKANTU_NDEBUG)
	}
	#endif
	stream << " ]";
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<InternalField<Real>>::setAuto(const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	Real r = in_param;
	param.setDefaultValue(r);
	}

	/* -------------------------------------------------------------------------- */
	template <class Material, typename T>
	inline InternalFieldTmpl<Material, T>::operator T() const {
	return default_value;
	}

	} // namespace akantu

	#endif /* AKANTU_INTERNAL_FIELD_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_core_includes.hh b/src/model/solid_mechanics/materials/material_core_includes.hh
	index e595aeeba..4351d5783 100644
	--- a/src/model/solid_mechanics/materials/material_core_includes.hh
	+++ b/src/model/solid_mechanics/materials/material_core_includes.hh
	@@ -1,82 +1,81 @@
	/**
	* @file material_core_includes.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Thu Mar 11 2021
	*
	* @brief List of materials for core package
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_CORE_INCLUDES_HH_
	#define AKANTU_MATERIAL_CORE_INCLUDES_HH_

	/* -------------------------------------------------------------------------- */
	/* Material list */
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_CMAKE_LIST_MATERIALS

	// elastic materials
	#include "material_elastic.hh"
	#include "material_elastic_linear_anisotropic.hh"
	#include "material_elastic_orthotropic.hh"
	#include "material_neohookean.hh"

	// visco-elastic materials
	#include "material_standard_linear_solid_deviatoric.hh"

	// damage laws
	#include "material_marigo.hh"
	#include "material_mazars.hh"

	// phasefield laws
	#include "material_phasefield.hh"

	// small-deformation plasticity
	#include "material_linear_isotropic_hardening.hh"

	// Drucker-Prager plasticity
	#include "material_drucker_prager.hh"

	// von-mises plasticity with damage
	#include "material_von_mises_mazars.hh"

	#endif

	-#define AKANTU_CORE_MATERIAL_LIST \
	- ((2, (elastic, MaterialElastic))) \
	- ((2, (neohookean, MaterialNeohookean))) \
	- ((2, (elastic_orthotropic, MaterialElasticOrthotropic))) \
	- ((2, (elastic_anisotropic, MaterialElasticLinearAnisotropic))) \
	- ((2, (sls_deviatoric, MaterialStandardLinearSolidDeviatoric))) \
	- ((2, (marigo, MaterialMarigo)))((2, (mazars, MaterialMazars))) \
	- ((2, (plastic_linear_isotropic_hardening, \
	- MaterialLinearIsotropicHardening))) \
	- ((2, (plastic_drucker_prager, MaterialDruckerPrager))) \
	- ((2, (plastic_mazars, MaterialVonMisesMazars))) \
	- ((2, (phasefield, MaterialPhaseField)))
	+#define AKANTU_CORE_MATERIAL_LIST \
	+ ((2, (elastic, MaterialElastic)))((2, (neohookean, MaterialNeohookean)))( \
	+ (2, (elastic_orthotropic, MaterialElasticOrthotropic)))( \
	+ (2, (elastic_anisotropic, MaterialElasticLinearAnisotropic)))( \
	+ (2, (sls_deviatoric, MaterialStandardLinearSolidDeviatoric)))( \
	+ (2, (marigo, MaterialMarigo)))((2, (mazars, MaterialMazars)))( \
	+ (2, (plastic_linear_isotropic_hardening, \
	+ MaterialLinearIsotropicHardening)))( \
	+ (2, (plastic_drucker_prager, MaterialDruckerPrager)))( \
	+ (2, (plastic_mazars, MaterialVonMisesMazars)))( \
	+ (2, (phasefield, MaterialPhaseField)))

	#endif /* AKANTU_MATERIAL_CORE_INCLUDES_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.cc b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.cc
	index 9e3da3aba..85fb1fc45 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.cc
	@@ -1,84 +1,84 @@
	/**
	* @file material_anisotropic_damage.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jul 03 2019
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Base class for anisotropic damage materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_anisotropic_damage.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */

	namespace {
	template <UInt dim>
	std::unique_ptr<Material>
	materialAnisotropicDamage(std::integral_constant<UInt, dim> /unused/,
	const ID & option, SolidMechanicsModel & model,
	const ID & id) {
	if (option.empty() or option == "mazars") {
	return std::make_unique<MaterialAnisotropicDamage<
	dim, EquivalentStrainMazars, DamageThresholdTan>>(model, id);
	}
	if (option == "mazars-drucker-prager") {
	return std::make_unique<MaterialAnisotropicDamage<
	dim, EquivalentStrainMazarsDruckerPrager, DamageThresholdTan>>(model,
	id);
	}
	AKANTU_EXCEPTION("The option " << option
	<< " is not valid for the material " << id);
	}

	template <class... Args>
	decltype(auto) dimensionDispatch(UInt dim, Args &&... args) {
	switch (dim) {
	case 1:
	return materialAnisotropicDamage(std::integral_constant<UInt, 1>{},
	std::forward<Args>(args)...);
	case 2:
	return materialAnisotropicDamage(std::integral_constant<UInt, 2>{},
	std::forward<Args>(args)...);
	case 3:
	return materialAnisotropicDamage(std::integral_constant<UInt, 3>{},
	std::forward<Args>(args)...);
	default: {
	AKANTU_EXCEPTION("In what dimension are you leaving ?");
	}
	}
	}
	} // namespace
	static bool material_is_alocated_anisotropic_damage [[gnu::unused]] =
	MaterialFactory::getInstance().registerAllocator(
	"anisotropic_damage",
	[](UInt dim, const ID & option, SolidMechanicsModel & model,
	const ID & id) -> std::unique_ptr<Material> {
	return dimensionDispatch(dim, option, model, id);
	});

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.hh b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.hh
	index 54c87919d..18753a634 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage.hh
	@@ -1,91 +1,91 @@
	/**
	* @file material_anisotropic_damage.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Feb 03 2018
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Base class for anisotropic damage materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_HH_
	#define AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_HH_

	namespace akantu {

	template <UInt dim, template <UInt> class EquivalentStrain,
	template <UInt> class DamageThreshold,
	template <UInt> class Parent = MaterialElastic>
	class MaterialAnisotropicDamage : public Parent<dim> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialAnisotropicDamage(SolidMechanicsModel & model, const ID & id = "");
	~MaterialAnisotropicDamage() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void computeStress(ElementType el_type, GhostType ghost_type) override;

	private:
	void damageStress(Matrix<double> & sigma, const Matrix<double> & sigma_el,
	const Matrix<double> & D, Real TrD);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	Real Dc{0.99};

	/// damage internal variable
	InternalField<Real> damage;

	/// elastic stress
	InternalField<Real> elastic_stress;

	/// equivalent strain
	InternalField<Real> equivalent_strain;

	/// trace of the damageThreshold
	InternalField<Real> trace_damage;

	/// damage criteria
	EquivalentStrain<dim> equivalent_strain_function;

	/// damage evolution
	DamageThreshold<dim> damage_threshold_function;
	};

	} // namespace akantu

	#include "material_anisotropic_damage_tmpl.hh"

	#endif /* AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage_tmpl.hh b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage_tmpl.hh
	index 3c8516d07..bd8d91853 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_anisotropic_damage_tmpl.hh
	@@ -1,380 +1,380 @@
	/**
	* @file material_anisotropic_damage_tmpl.hh
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jul 03 2019
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Base class for anisotropic damage materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "material_anisotropic_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_TMPL_HH_
	#define AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_TMPL_HH_

	namespace akantu {
	struct EmptyIteratorContainer {
	struct iterator {
	auto & operator++() { return *this; }
	Real operator*() { return 0; }
	bool operator!=(const iterator & /unused/) const { return true; }
	bool operator==(const iterator & /unused/) const { return false; }
	};

	auto begin() const // NOLINT(readability-convert-member-functions-to-static)
	{
	return iterator();
	}
	-
	+
	auto end() const // NOLINT(readability-convert-member-functions-to-static)
	{
	return iterator();
	}
	};
	} // namespace akantu

	namespace std {
	template <> struct iterator_traits<::akantu::EmptyIteratorContainer::iterator> {
	using iterator_category = forward_iterator_tag;
	using value_type = akantu::Real;
	using difference_type = std::ptrdiff_t;
	using pointer = akantu::Real *;
	using reference = akantu::Real &;
	};
	} // namespace std

	namespace akantu {
	namespace {
	template <UInt dim, class Op>
	void tensorPlus_(const Matrix<Real> & A, Op && oper) {
	Vector<Real> A_eigs(dim);
	A.eig(A_eigs);

	for (auto & ap : A_eigs) {
	oper(ap);
	}
	}

	template <UInt dim> auto tensorPlus2(const Matrix<Real> & A) {
	Real square = 0;
	tensorPlus_<dim>(A, [&](Real eig) {
	eig = std::max(eig, 0.);
	square += eig * eig;
	});

	return square;
	}

	template <UInt dim> auto tensorPlusTrace(const Matrix<Real> & A) {
	Real trace_plus = 0;
	Real trace_minus = 0;
	tensorPlus_<dim>(A, [&](Real eig) {
	trace_plus += std::max(eig, 0.);
	trace_minus += std::min(eig, 0.);
	});

	return std::make_pair(trace_plus, trace_minus);
	}

	template <UInt dim, class Op>
	auto tensorPlusOp(const Matrix<Real> & A, Matrix<Real> & A_directions,
	Op && oper, bool sorted = false) {
	Vector<Real> A_eigs(dim);
	Matrix<Real> A_diag(dim, dim);
	A.eig(A_eigs, A_directions, sorted);

	for (auto && data : enumerate(A_eigs)) {
	auto i = std::get<0>(data);
	A_diag(i, i) = oper(std::max(std::get<1>(data), 0.), i);
	}

	return A_directions * A_diag * A_directions.transpose();
	}

	template <UInt dim, class Op>
	auto tensorPlus(const Matrix<Real> & A, Matrix<Real> & A_directions,
	bool sorted = false) {
	return tensorPlusOp<dim>(
	A, A_directions, [](Real x, Real /unused/) { return x; }, sorted);
	}

	template <UInt dim, class Op>
	auto tensorPlusOp(const Matrix<Real> & A, Op && oper) {
	Matrix<Real> A_directions(dim, dim);
	return tensorPlusOp<dim>(A, A_directions, std::forward<Op>(oper));
	}

	template <UInt dim> auto tensorPlus(const Matrix<Real> & A) {
	return tensorPlusOp<dim>(A, [](Real x, Real /unused/) { return x; });
	}

	template <UInt dim> auto tensorSqrt(const Matrix<Real> & A) {
	return tensorPlusOp<dim>(
	A, [](Real x, UInt /unused/) { return std::sqrt(x); });
	}

	} // namespace

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <UInt dim, template <UInt> class EquivalentStrain,
	template <UInt> class DamageThreshold, template <UInt> class Parent>
	MaterialAnisotropicDamage<dim, EquivalentStrain, DamageThreshold, Parent>::
	MaterialAnisotropicDamage(SolidMechanicsModel & model, const ID & id)
	: Parent<dim>(model, id), damage("damage_tensor", *this),
	elastic_stress("elastic_stress", *this),
	equivalent_strain("equivalent_strain", *this),
	trace_damage("trace_damage", this), equivalent_strain_function(this),
	damage_threshold_function(*this) {
	this->registerParam("Dc", Dc, _pat_parsable, "Critical damage");

	this->damage.initialize(dim * dim);
	this->elastic_stress.initialize(dim * dim);
	this->equivalent_strain.initialize(1);

	this->trace_damage.initialize(1);
	this->trace_damage.initializeHistory();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, template <UInt> class EquivalentStrain,
	template <UInt> class DamageThreshold, template <UInt> class Parent>
	void MaterialAnisotropicDamage<dim, EquivalentStrain, DamageThreshold, Parent>::
	damageStress(Matrix<Real> & sigma, const Matrix<Real> & sigma_el,
	const Matrix<Real> & D, Real TrD) {
	// σ_(n + 1) = (1 − D_(n + 1))^(1/2) σ~_(n + 1) (1 − D_(n + 1))^(1 / 2)
	// - ((1 − D_(n + 1)) : σ~_(n + 1))/ (3 - Tr(D_(n+1))) (1 − D_(n + 1))
	// + 1/3 (1 - Tr(D_(n+1)) <Tr(σ~_(n + 1))>_+ + <Tr(σ~_(n + 1))>_-) I

	auto one_D = Matrix<Real>::eye(dim) - D;
	auto sqrt_one_D = tensorSqrt<dim>(one_D);

	Real Tr_sigma_plus;
	Real Tr_sigma_minus;
	std::tie(Tr_sigma_plus, Tr_sigma_minus) = tensorPlusTrace<dim>(sigma_el);

	auto I = Matrix<Real>::eye(dim);

	sigma = sqrt_one_D * sigma_el * sqrt_one_D -
	(one_D.doubleDot(sigma_el) / (dim - TrD) * one_D) +
	1. / dim * ((1 - TrD) * Tr_sigma_plus - Tr_sigma_minus) * I;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, template <UInt> class EquivalentStrain,
	template <UInt> class DamageThreshold, template <UInt> class Parent>
	void MaterialAnisotropicDamage<dim, EquivalentStrain, DamageThreshold,
	Parent>::computeStress(ElementType type,
	GhostType ghost_type) {

	for (auto && data :
	zip(make_view(this->stress(type, ghost_type), dim, dim),
	make_view(this->gradu(type, ghost_type), dim, dim),
	make_view(this->sigma_th(type, ghost_type)),
	make_view(this->elastic_stress(type, ghost_type), dim, dim),
	make_view(this->equivalent_strain(type, ghost_type)),
	make_view(this->damage(type, ghost_type), dim, dim),
	make_view(this->trace_damage(type, ghost_type)),
	make_view(this->trace_damage.previous(type, ghost_type)),
	equivalent_strain_function, damage_threshold_function)) {
	auto & sigma = std::get<0>(data);
	auto & grad_u = std::get<1>(data);
	auto & sigma_th = std::get<2>(data);
	auto & sigma_el = std::get<3>(data);
	auto & epsilon_hat = std::get<4>(data);
	auto & D = std::get<5>(data);
	auto & TrD_n_1 = std::get<6>(data);
	auto & TrD = std::get<7>(data);
	auto & equivalent_strain_data = std::get<8>(data);
	auto & damage_threshold_data = std::get<9>(data);

	Matrix<Real> Dtmp(dim, dim);
	Real TrD_n_1_tmp;
	Matrix<Real> epsilon(dim, dim);

	// yes you read properly this is a label for a goto
	auto computeDamage = [&]() {
	MaterialElastic<dim>::computeStressOnQuad(grad_u, sigma_el, sigma_th);

	this->template gradUToEpsilon<dim>(grad_u, epsilon);

	// evaluate the damage criteria
	epsilon_hat = equivalent_strain_function(epsilon, equivalent_strain_data);

	// evolve the damage if needed
	auto K_TrD = damage_threshold_function.K(TrD, damage_threshold_data);

	auto f = epsilon_hat - K_TrD;

	// if test function > 0 evolve the damage
	if (f > 0) {
	TrD_n_1_tmp =
	damage_threshold_function.K_inv(epsilon_hat, damage_threshold_data);

	auto epsilon_plus = tensorPlus<dim>(epsilon);
	auto delta_lambda = (TrD_n_1_tmp - TrD) / (epsilon_hat * epsilon_hat);

	Dtmp = D + delta_lambda * epsilon_plus;
	return true;
	}
	return false;
	};

	// compute a temporary version of the new damage
	auto is_damage_updated = computeDamage();

	if (is_damage_updated) {
	/// Check and correct for broken case
	if (Dtmp.trace() > Dc) {
	if (epsilon.trace() > 0) { // tensile loading
	auto kpa = this->kpa;
	auto lambda = this->lambda;

	// change kappa to Kappa_broken = (1-Dc) Kappa
	kpa = (1 - Dc) * kpa;
	this->E = 9 * kpa * (kpa - lambda) / (3 * kpa - lambda);
	this->nu = lambda / (3 * kpa - lambda);
	this->updateInternalParameters();

	computeDamage();
	} else if (std::abs(epsilon.trace()) < 1e-10) { // deviatoric case
	Matrix<Real> n(dim, dim);
	std::vector<UInt> ns;
	tensorPlusOp<dim>(
	Dtmp, n,
	[&](Real x, UInt i) {
	if (x > this->Dc) {
	ns.push_back(i);
	return this->Dc;
	}

	return x;
	},
	true);
	}
	}

	TrD_n_1 = TrD_n_1_tmp;
	D = Dtmp;
	} else {
	TrD_n_1 = TrD;
	}

	// apply the damage to the stress
	damageStress(sigma, sigma_el, D, TrD_n_1);
	}
	}

	/* -------------------------------------------------------------------------- */
	/* EquivalentStrain functions */
	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	class EquivalentStrainMazars : public EmptyIteratorContainer {
	public:
	EquivalentStrainMazars(Material & /mat/) {}

	template <class... Other>
	Real operator()(const Matrix<Real> & epsilon, Other &&... /other/) {
	Real epsilon_hat = 0.;
	std::tie(epsilon_hat, std::ignore) = tensorPlusTrace<dim>(epsilon);
	return std::sqrt(epsilon_hat);
	}
	};

	template <UInt dim>
	class EquivalentStrainMazarsDruckerPrager : public EquivalentStrainMazars<dim> {
	public:
	EquivalentStrainMazarsDruckerPrager(Material & mat)
	: EquivalentStrainMazars<dim>(mat) {
	mat.registerParam("k", k, _pat_parsable, "k");
	}

	template <class... Other>
	Real operator()(const Matrix<Real> & epsilon, Real /unused/) {
	Real epsilon_hat = EquivalentStrainMazars<dim>::operator()(epsilon);
	epsilon_hat += k * epsilon.trace();
	return epsilon_hat;
	}

	protected:
	Real k;
	};

	/* -------------------------------------------------------------------------- */
	/* DamageThreshold functions */
	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	class DamageThresholdLinear : public EmptyIteratorContainer {
	public:
	DamageThresholdLinear(Material & mat) : mat(mat) {
	mat.registerParam("A", A, _pat_parsable, "A");
	mat.registerParam("K0", K0, _pat_parsable, "K0");
	}

	template <class... Other> Real K(Real x, Other &&... /other/) {
	return 1. / A * x + K0;
	}

	template <class... Other> Real K_inv(Real x, Other &&... /other/) {
	return A * (x - K0);
	}

	private:
	Material & mat;
	Real A;
	Real K0;
	};

	template <UInt dim> class DamageThresholdTan : public EmptyIteratorContainer {
	public:
	DamageThresholdTan(Material & mat) : mat(mat) {
	mat.registerParam("a", a, _pat_parsable, "a");
	mat.registerParam("A", A, _pat_parsable, "A");
	mat.registerParam("K0", K0, _pat_parsable, "K0");
	}

	template <class... Other> Real K(Real x, Other &&... /other/) {
	return a * std::tan(std::atan2(x, a) - std::atan2(K0, a));
	}

	template <class... Other> Real K_inv(Real x, Other &&... /other/) {
	return a * A * (std::atan2(x, a) - std::atan2(K0, a));
	}

	private:
	Material & mat;
	Real a{2.93e-4};
	Real A{5e3};
	Real K0{5e-5};
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_ANISOTROPIC_DAMAGE_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_damage.hh b/src/model/solid_mechanics/materials/material_damage/material_damage.hh
	index 9264dc164..809d68bca 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_damage.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_damage.hh
	@@ -1,110 +1,109 @@
	/**
	* @file material_damage.hh
	*
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material isotropic elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_DAMAGE_HH_
	#define AKANTU_MATERIAL_DAMAGE_HH_

	namespace akantu {
	template <UInt spatial_dimension,
	template <UInt> class Parent = MaterialElastic>
	class MaterialDamage : public Parent<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialDamage(SolidMechanicsModel & model, const ID & id = "");
	~MaterialDamage() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	bool hasStiffnessMatrixChanged() override { return true; }

	protected:
	/// update the dissipated energy, must be called after the stress have been
	/// computed
	void updateEnergies(ElementType el_type) override;

	/// compute the tangent stiffness matrix for a given quadrature point
	inline void computeTangentModuliOnQuad(Matrix<Real> & tangent, Real & dam);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// give the dissipated energy for the time step
	Real getDissipatedEnergy() const;

	Real getEnergy(const std::string & type) override;

	AKANTU_GET_MACRO_NOT_CONST(Damage, damage, ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO(Damage, damage, const ElementTypeMapArray<Real> &);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real)

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// damage internal variable
	InternalField<Real> damage;

	/// dissipated energy
	InternalField<Real> dissipated_energy;

	/// contain the current value of @f$ \int_0^{\epsilon}\sigma(\omega)d\omega
	/// @f$ the dissipated energy
	InternalField<Real> int_sigma;
	};

	} // namespace akantu

	#include "material_damage_tmpl.hh"

	#endif /* AKANTU_MATERIAL_DAMAGE_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_damage_non_local.hh b/src/model/solid_mechanics/materials/material_damage/material_damage_non_local.hh
	index e002a0774..d7d60f366 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_damage_non_local.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_damage_non_local.hh
	@@ -1,75 +1,75 @@
	/**
	* @file material_damage_non_local.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Aug 23 2012
	* @date last modification: Fri Apr 09 2021
	*
	* @brief interface for non local damage material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_non_local.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_DAMAGE_NON_LOCAL_HH_
	#define AKANTU_MATERIAL_DAMAGE_NON_LOCAL_HH_

	namespace akantu {

	template <UInt dim, class MaterialDamageLocal>
	class MaterialDamageNonLocal
	: public MaterialNonLocal<dim, MaterialDamageLocal> {
	public:
	using MaterialParent = MaterialNonLocal<dim, MaterialDamageLocal>;

	MaterialDamageNonLocal(SolidMechanicsModel & model, const ID & id)
	: MaterialParent(model, id){};

	protected:
	/* ------------------------------------------------------------------------ */
	virtual void computeNonLocalStress(ElementType type,
	GhostType ghost_type = _not_ghost) = 0;

	/* ------------------------------------------------------------------------ */
	void computeNonLocalStresses(GhostType ghost_type) override {
	AKANTU_DEBUG_IN();

	for (auto type : this->element_filter.elementTypes(dim, ghost_type)) {
	auto & elem_filter = this->element_filter(type, ghost_type);
	if (elem_filter.empty()) {
	continue;
	}

	computeNonLocalStress(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_DAMAGE_NON_LOCAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_damage_tmpl.hh b/src/model/solid_mechanics/materials/material_damage/material_damage_tmpl.hh
	index 635c0307e..5bc63e618 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_damage_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_damage_tmpl.hh
	@@ -1,174 +1,174 @@
	/**
	* @file material_damage_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Marion Estelle Chambart <mchambart@stucky.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Specialization of the material class for the damage material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_damage.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	MaterialDamage<spatial_dimension, Parent>::MaterialDamage(
	SolidMechanicsModel & model, const ID & id)
	: Parent<spatial_dimension>(model, id), damage("damage", *this),
	dissipated_energy("damage dissipated energy", *this),
	int_sigma("integral of sigma", *this) {
	AKANTU_DEBUG_IN();

	this->is_non_local = false;
	this->use_previous_stress = true;
	this->use_previous_gradu = true;

	this->damage.initialize(1);
	this->dissipated_energy.initialize(1);
	this->int_sigma.initialize(1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialDamage<spatial_dimension, Parent>::initMaterial() {
	AKANTU_DEBUG_IN();
	Parent<spatial_dimension>::initMaterial();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Compute the dissipated energy in each element by a trapezoidal approximation
	* of
	* @f$ Ed = \int_0^{\epsilon}\sigma(\omega)d\omega -
	* \frac{1}{2}\sigma:\epsilon@f$
	*/
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialDamage<spatial_dimension, Parent>::updateEnergies(
	ElementType el_type) {
	Parent<spatial_dimension>::updateEnergies(el_type);

	this->computePotentialEnergy(el_type);

	auto epsilon_p =
	this->gradu.previous(el_type).begin(spatial_dimension, spatial_dimension);
	auto sigma_p = this->stress.previous(el_type).begin(spatial_dimension,
	spatial_dimension);

	auto epot = this->potential_energy(el_type).begin();
	auto ints = this->int_sigma(el_type).begin();
	auto ed = this->dissipated_energy(el_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	Matrix<Real> delta_gradu(grad_u);
	delta_gradu -= *epsilon_p;

	Matrix<Real> sigma_h(sigma);
	sigma_h += *sigma_p;

	Real dint = .5 * sigma_h.doubleDot(delta_gradu);

	*ints += dint;
	ed = ints - *epot;

	++epsilon_p;
	++sigma_p;
	++epot;
	++ints;
	++ed;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialDamage<spatial_dimension, Parent>::computeTangentModuli(
	ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Parent<spatial_dimension>::computeTangentModuli(el_type, tangent_matrix,
	ghost_type);

	Real * dam = this->damage(el_type, ghost_type).storage();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	computeTangentModuliOnQuad(tangent, *dam);

	++dam;

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialDamage<spatial_dimension, Parent>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent, Real & dam) {
	tangent *= (1 - dam);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	Real MaterialDamage<spatial_dimension, Parent>::getDissipatedEnergy() const {
	AKANTU_DEBUG_IN();

	Real de = 0.;

	/// integrate the dissipated energy for each type of elements
	for (auto & type :
	this->element_filter.elementTypes(spatial_dimension, _not_ghost)) {
	de +=
	this->fem.integrate(dissipated_energy(type, _not_ghost), type,
	_not_ghost, this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return de;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	Real MaterialDamage<spatial_dimension, Parent>::getEnergy(
	const std::string & type) {
	if (type == "dissipated") {
	return getDissipatedEnergy();
	}
	return Parent<spatial_dimension>::getEnergy(type);
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_marigo.cc b/src/model/solid_mechanics/materials/material_damage/material_marigo.cc
	index 621273af9..256c52a88 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_marigo.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_marigo.cc
	@@ -1,104 +1,104 @@
	/**
	* @file material_marigo.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Specialization of the material class for the marigo material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_marigo.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialMarigo<spatial_dimension>::MaterialMarigo(SolidMechanicsModel & model,
	const ID & id)
	: MaterialDamage<spatial_dimension>(model, id), Yd("Yd", *this),
	damage_in_y(false), yc_limit(false) {
	AKANTU_DEBUG_IN();

	this->registerParam("Sd", Sd, Real(5000.), _pat_parsable \| _pat_modifiable);
	this->registerParam("epsilon_c", epsilon_c, Real(0.), _pat_parsable,
	"Critical strain");
	this->registerParam("Yc limit", yc_limit, false, _pat_internal,
	"As the material a critical Y");
	this->registerParam("damage_in_y", damage_in_y, false, _pat_parsable,
	"Use threshold (1-D)Y");
	this->registerParam("Yd", Yd, _pat_parsable, "Damaging energy threshold");

	this->Yd.initialize(1);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigo<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();
	MaterialDamage<spatial_dimension>::initMaterial();

	updateInternalParameters();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigo<spatial_dimension>::updateInternalParameters() {
	MaterialDamage<spatial_dimension>::updateInternalParameters();
	Yc = .5 * epsilon_c * this->E * epsilon_c;
	yc_limit = (std::abs(epsilon_c) > std::numeric_limits<Real>::epsilon());
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigo<spatial_dimension>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto dam = this->damage(el_type, ghost_type).begin();
	auto Yd_q = this->Yd(el_type, ghost_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Real Y = 0.;
	computeStressOnQuad(grad_u, sigma, dam, Y, Yd_q);

	++dam;
	++Yd_q;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	INSTANTIATE_MATERIAL(marigo, MaterialMarigo);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_marigo.hh b/src/model/solid_mechanics/materials/material_damage/material_marigo.hh
	index 7102ac5f3..01da317dd 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_marigo.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_marigo.hh
	@@ -1,124 +1,124 @@
	/**
	* @file material_marigo.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Marigo damage law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_MARIGO_HH_
	#define AKANTU_MATERIAL_MARIGO_HH_

	namespace akantu {

	/**
	* Material marigo
	*
	* parameters in the material files :
	* - Yd : (default: 50)
	* - Sd : (default: 5000)
	* - Ydrandomness : (default:0)
	*/
	template <UInt spatial_dimension>
	class MaterialMarigo : public MaterialDamage<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialMarigo(SolidMechanicsModel & model, const ID & id = "");
	~MaterialMarigo() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	void updateInternalParameters() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & sigma,
	Real & dam, Real & Y, Real & Ydq);

	inline void computeDamageAndStressOnQuad(Matrix<Real> & sigma, Real & dam,
	Real & Y, Real & Ydq);

	/* ------------------------------------------------------------------------ */
	/* DataAccessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// resistance to damage
	RandomInternalField<Real> Yd;

	/// damage threshold
	Real Sd;

	/// critical epsilon when the material is considered as broken
	Real epsilon_c;

	Real Yc;

	bool damage_in_y;
	bool yc_limit;
	};

	} // namespace akantu

	#include "material_marigo_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_MARIGO_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_marigo_inline_impl.hh b/src/model/solid_mechanics/materials/material_damage/material_marigo_inline_impl.hh
	index 2eaebd93a..c23c7c20b 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_marigo_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_marigo_inline_impl.hh
	@@ -1,135 +1,135 @@
	/**
	* @file material_marigo_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of the inline functions of the material marigo
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_marigo.hh"

	#ifndef AKANTU_MATERIAL_MARIGO_INLINE_IMPL_HH_
	#define AKANTU_MATERIAL_MARIGO_INLINE_IMPL_HH_

	namespace akantu {

	template <UInt spatial_dimension>
	inline void MaterialMarigo<spatial_dimension>::computeStressOnQuad(
	Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam, Real & Y,
	Real & Ydq) {
	MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);

	Y = 0;
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	Y += sigma(i, j) * (grad_u(i, j) + grad_u(j, i)) / 2.;
	}
	}
	Y *= 0.5;

	if (damage_in_y) {
	Y *= (1 - dam);
	}

	if (yc_limit) {
	Y = std::min(Y, Yc);
	}

	if (!this->is_non_local) {
	computeDamageAndStressOnQuad(sigma, dam, Y, Ydq);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialMarigo<spatial_dimension>::computeDamageAndStressOnQuad(
	Matrix<Real> & sigma, Real & dam, Real & Y, Real & Ydq) {
	Real Fd = Y - Ydq - Sd * dam;

	if (Fd > 0) {
	dam = (Y - Ydq) / Sd;
	}
	dam = std::min(dam, Real(1.));

	sigma *= 1 - dam;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline UInt MaterialMarigo<spatial_dimension>::getNbData(
	const Array<Element> & elements, const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	if (tag == SynchronizationTag::_smm_init_mat) {
	size += sizeof(Real) * this->getModel().getNbIntegrationPoints(elements);
	}

	size += MaterialDamage<spatial_dimension>::getNbData(elements, tag);

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialMarigo<spatial_dimension>::packData(
	CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	if (tag == SynchronizationTag::_smm_init_mat) {
	this->packElementDataHelper(Yd, buffer, elements);
	}

	MaterialDamage<spatial_dimension>::packData(buffer, elements, tag);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void
	MaterialMarigo<spatial_dimension>::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	if (tag == SynchronizationTag::_smm_init_mat) {
	this->unpackElementDataHelper(Yd, buffer, elements);
	}

	MaterialDamage<spatial_dimension>::unpackData(buffer, elements, tag);

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_MARIGO_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.cc b/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.cc
	index 557563d85..55bd77f06 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.cc
	@@ -1,107 +1,107 @@
	/**
	* @file material_marigo_non_local.cc
	*
	* @author Marion Estelle Chambart <mchambart@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Marigo non-local inline function implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_marigo_non_local.hh"
	#include "non_local_neighborhood_base.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialMarigoNonLocal<spatial_dimension>::MaterialMarigoNonLocal(
	SolidMechanicsModel & model, const ID & id)
	: MaterialMarigoNonLocalParent(model, id), Y("Y", *this),
	Ynl("Y non local", *this) {
	AKANTU_DEBUG_IN();
	this->is_non_local = true;
	this->Y.initialize(1);
	this->Ynl.initialize(1);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigoNonLocal<spatial_dimension>::registerNonLocalVariables() {
	this->model.getNonLocalManager().registerNonLocalVariable(this->Y.getName(),
	Ynl.getName(), 1);
	this->model.getNonLocalManager()
	.getNeighborhood(this->name)
	.registerNonLocalVariable(Ynl.getName());
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigoNonLocal<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * dam = this->damage(el_type, ghost_type).storage();
	Real * Yt = this->Y(el_type, ghost_type).storage();
	Real * Ydq = this->Yd(el_type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	MaterialMarigo<spatial_dimension>::computeStressOnQuad(grad_u, sigma, *dam,
	Yt, Ydq);
	++dam;
	++Yt;
	++Ydq;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMarigoNonLocal<spatial_dimension>::computeNonLocalStress(
	ElementType type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * dam = this->damage(type, ghost_type).storage();
	Real * Ydq = this->Yd(type, ghost_type).storage();
	Real * Ynlt = this->Ynl(type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(type, ghost_type);
	this->computeDamageAndStressOnQuad(sigma, dam, Ynlt, *Ydq);

	++dam;
	++Ynlt;
	++Ydq;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	INSTANTIATE_MATERIAL(marigo_non_local, MaterialMarigoNonLocal);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.hh b/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.hh
	index 5dddcec10..6eb57196e 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_marigo_non_local.hh
	@@ -1,93 +1,94 @@
	/**
	* @file material_marigo_non_local.hh
	*
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Marigo non-local description
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_damage_non_local.hh"
	#include "material_marigo.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_MARIGO_NON_LOCAL_HH_
	#define AKANTU_MATERIAL_MARIGO_NON_LOCAL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */

	/**
	* Material Marigo
	*
	* parameters in the material files :
	*/
	template <UInt spatial_dimension>
	class MaterialMarigoNonLocal
	: public MaterialDamageNonLocal<spatial_dimension,
	MaterialMarigo<spatial_dimension>> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	- using MaterialMarigoNonLocalParent = MaterialDamageNonLocal<spatial_dimension,
	- MaterialMarigo<spatial_dimension>>;
	+ using MaterialMarigoNonLocalParent =
	+ MaterialDamageNonLocal<spatial_dimension,
	+ MaterialMarigo<spatial_dimension>>;
	MaterialMarigoNonLocal(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	void registerNonLocalVariables() override;

	/// constitutive law
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	void computeNonLocalStress(ElementType type,
	GhostType ghost_type = _not_ghost) override;

	private:
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Y, Y, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	InternalField<Real> Y;
	InternalField<Real> Ynl;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_MARIGO_NON_LOCAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_mazars.cc b/src/model/solid_mechanics/materials/material_damage/material_mazars.cc
	index 26a9d3ed2..7671616fa 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_mazars.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_mazars.cc
	@@ -1,82 +1,82 @@
	/**
	* @file material_mazars.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Specialization of the material class for the damage material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_mazars.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialMazars<spatial_dimension>::MaterialMazars(SolidMechanicsModel & model,
	const ID & id)
	: MaterialDamage<spatial_dimension>(model, id), K0("K0", *this),
	damage_in_compute_stress(true) {
	AKANTU_DEBUG_IN();

	this->registerParam("K0", K0, _pat_parsable, "K0");
	this->registerParam("At", At, Real(0.8), _pat_parsable, "At");
	this->registerParam("Ac", Ac, Real(1.4), _pat_parsable, "Ac");
	this->registerParam("Bc", Bc, Real(1900.), _pat_parsable, "Bc");
	this->registerParam("Bt", Bt, Real(12000.), _pat_parsable, "Bt");
	this->registerParam("beta", beta, Real(1.06), _pat_parsable, "beta");

	this->K0.initialize(1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMazars<spatial_dimension>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * dam = this->damage(el_type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Real Ehat = 0;
	computeStressOnQuad(grad_u, sigma, *dam, Ehat);
	++dam;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(mazars, MaterialMazars);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_mazars.hh b/src/model/solid_mechanics/materials/material_damage/material_mazars.hh
	index 8d22b97af..4ba41edaa 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_mazars.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_mazars.hh
	@@ -1,126 +1,126 @@
	/**
	* @file material_mazars.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Marion Estelle Chambart <mchambart@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Material Following the Mazars law for damage evolution
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_MAZARS_HH_
	#define AKANTU_MATERIAL_MAZARS_HH_

	namespace akantu {

	/**
	* Material Mazars
	*
	* parameters in the material files :
	* - rho : density (default: 0)
	* - E : Young's modulus (default: 0)
	* - nu : Poisson's ratio (default: 1/2)
	* - K0 : Damage threshold
	* - At : Parameter damage traction 1
	* - Bt : Parameter damage traction 2
	* - Ac : Parameter damage compression 1
	* - Bc : Parameter damage compression 2
	* - beta : Parameter for shear
	*/
	template <UInt spatial_dimension>
	class MaterialMazars : public MaterialDamage<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialMazars(SolidMechanicsModel & model, const ID & id = "");
	~MaterialMazars() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & damage,
	Real & Ehat);

	inline void computeDamageAndStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & damage,
	Real & Ehat);

	inline void computeDamageOnQuad(const Real & epsilon_equ,
	const Matrix<Real> & sigma,
	const Vector<Real> & epsilon_princ,
	Real & dam);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// damage threshold
	RandomInternalField<Real> K0;
	/// parameter damage traction 1
	Real At;
	/// parameter damage traction 2
	Real Bt;
	/// parameter damage compression 1
	Real Ac;
	/// parameter damage compression 2
	Real Bc;
	/// parameter for shear
	Real beta;

	/// specify the variable to average false = ehat, true = damage (only valid
	/// for non local version)
	bool damage_in_compute_stress;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "material_mazars_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_MAZARS_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_mazars_inline_impl.hh b/src/model/solid_mechanics/materials/material_damage/material_mazars_inline_impl.hh
	index abd814732..c2e25aa85 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_mazars_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_mazars_inline_impl.hh
	@@ -1,165 +1,165 @@
	/**
	* @file material_mazars_inline_impl.hh
	*
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Marion Estelle Chambart <mchambart@stucky.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Apr 06 2011
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of the material damage
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_mazars.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialMazars<spatial_dimension>::computeStressOnQuad(
	const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
	Real & Ehat) {
	Matrix<Real> epsilon(3, 3);
	epsilon.zero();

	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
	}
	}

	Vector<Real> Fdiag(3);
	Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

	Ehat = 0.;
	for (UInt i = 0; i < 3; ++i) {
	Real epsilon_p = std::max(Real(0.), Fdiag(i));
	Ehat += epsilon_p * epsilon_p;
	}
	Ehat = sqrt(Ehat);

	MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);

	if (damage_in_compute_stress) {
	computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
	}

	if (not this->is_non_local) {
	computeDamageAndStressOnQuad(grad_u, sigma, dam, Ehat);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialMazars<spatial_dimension>::computeDamageAndStressOnQuad(
	const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
	Real & Ehat) {
	if (!damage_in_compute_stress) {
	Vector<Real> Fdiag(3);
	Fdiag.zero();

	Matrix<Real> epsilon(3, 3);
	epsilon.zero();
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
	}
	}

	Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

	computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
	}

	sigma *= 1 - dam;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialMazars<spatial_dimension>::computeDamageOnQuad(
	const Real & epsilon_equ,
	__attribute__((unused)) const Matrix<Real> & sigma,
	const Vector<Real> & epsilon_princ, Real & dam) {
	Real Fs = epsilon_equ - K0;
	if (Fs > 0.) {
	Real dam_t;
	Real dam_c;
	dam_t =
	1 - K0 * (1 - At) / epsilon_equ - At * (exp(-Bt * (epsilon_equ - K0)));
	dam_c =
	1 - K0 * (1 - Ac) / epsilon_equ - Ac * (exp(-Bc * (epsilon_equ - K0)));

	Real Cdiag;
	Cdiag = this->E * (1 - this->nu) / ((1 + this->nu) * (1 - 2 * this->nu));

	Vector<Real> sigma_princ(3);
	sigma_princ(0) = Cdiag * epsilon_princ(0) +
	this->lambda * (epsilon_princ(1) + epsilon_princ(2));
	sigma_princ(1) = Cdiag * epsilon_princ(1) +
	this->lambda * (epsilon_princ(0) + epsilon_princ(2));
	sigma_princ(2) = Cdiag * epsilon_princ(2) +
	this->lambda * (epsilon_princ(1) + epsilon_princ(0));

	Vector<Real> sigma_p(3);
	for (UInt i = 0; i < 3; i++) {
	sigma_p(i) = std::max(Real(0.), sigma_princ(i));
	}
	// sigma_p *= 1. - dam;

	Real trace_p = this->nu / this->E * (sigma_p(0) + sigma_p(1) + sigma_p(2));

	Real alpha_t = 0;
	for (UInt i = 0; i < 3; ++i) {
	Real epsilon_t = (1 + this->nu) / this->E * sigma_p(i) - trace_p;
	Real epsilon_p = std::max(Real(0.), epsilon_princ(i));
	alpha_t += epsilon_t * epsilon_p;
	}

	alpha_t /= epsilon_equ * epsilon_equ;
	alpha_t = std::min(alpha_t, Real(1.));

	Real alpha_c = 1. - alpha_t;

	alpha_t = std::pow(alpha_t, beta);
	alpha_c = std::pow(alpha_c, beta);

	Real damtemp;
	damtemp = alpha_t * dam_t + alpha_c * dam_c;

	dam = std::max(damtemp, dam);
	dam = std::min(dam, Real(1.));
	}
	}

	/* -------------------------------------------------------------------------- */
	// template<UInt spatial_dimension>
	// inline void
	// MaterialMazars<spatial_dimension>::computeTangentModuliOnQuad(Matrix<Real> &
	// tangent) {
	// MaterialElastic<spatial_dimension>::computeTangentModuliOnQuad(tangent);

	// tangent *= (1-dam);
	// }
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.cc b/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.cc
	index a9331b17a..bf378c08e 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.cc
	@@ -1,126 +1,126 @@
	/**
	* @file material_mazars_non_local.cc
	*
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Specialization of the material class for the non-local mazars
	* material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_mazars_non_local.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialMazarsNonLocal<spatial_dimension>::MaterialMazarsNonLocal(
	SolidMechanicsModel & model, const ID & id)
	: MaterialNonLocalParent(model, id), Ehat("epsilon_equ", *this),
	non_local_variable("mazars_non_local", *this) {
	AKANTU_DEBUG_IN();

	this->is_non_local = true;
	this->Ehat.initialize(1);
	this->non_local_variable.initialize(1);

	this->registerParam("average_on_damage", this->damage_in_compute_stress,
	false, _pat_parsable \| _pat_modifiable,
	"Is D the non local variable");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMazarsNonLocal<spatial_dimension>::registerNonLocalVariables() {
	ID local;
	if (this->damage_in_compute_stress) {
	local = this->damage.getName();
	} else {
	local = this->Ehat.getName();
	}

	this->model.getNonLocalManager().registerNonLocalVariable(
	local, non_local_variable.getName(), 1);
	this->model.getNonLocalManager()
	.getNeighborhood(this->name)
	.registerNonLocalVariable(non_local_variable.getName());
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMazarsNonLocal<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * damage = this->damage(el_type, ghost_type).storage();
	Real * epsilon_equ = this->Ehat(el_type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	MaterialMazars<spatial_dimension>::computeStressOnQuad(grad_u, sigma, *damage,
	*epsilon_equ);
	++damage;
	++epsilon_equ;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialMazarsNonLocal<spatial_dimension>::computeNonLocalStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	auto & non_loc_var = non_local_variable(el_type, ghost_type);
	Real * damage;
	Real * epsilon_equ;
	if (this->damage_in_compute_stress) {
	damage = non_loc_var.storage();
	epsilon_equ = this->Ehat(el_type, ghost_type).storage();
	} else {
	damage = this->damage(el_type, ghost_type).storage();
	epsilon_equ = non_loc_var.storage();
	}

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	this->computeDamageAndStressOnQuad(grad_u, sigma, damage, epsilon_equ);

	++damage;
	++epsilon_equ;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	INSTANTIATE_MATERIAL(mazars_non_local, MaterialMazarsNonLocal);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.hh b/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.hh
	index a326996ae..631ef2280 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_mazars_non_local.hh
	@@ -1,92 +1,92 @@
	/**
	* @file material_mazars_non_local.hh
	*
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Mazars non-local description
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_damage_non_local.hh"
	#include "material_mazars.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_MAZARS_NON_LOCAL_HH_
	#define AKANTU_MATERIAL_MAZARS_NON_LOCAL_HH_

	namespace akantu {

	/**
	* Material Mazars Non local
	*
	* parameters in the material files :
	*/
	template <UInt spatial_dimension>
	class MaterialMazarsNonLocal
	: public MaterialDamageNonLocal<spatial_dimension,
	MaterialMazars<spatial_dimension>> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using MaterialNonLocalParent =
	MaterialDamageNonLocal<spatial_dimension,
	MaterialMazars<spatial_dimension>>;

	MaterialMazarsNonLocal(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	void computeNonLocalStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	void registerNonLocalVariables() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// the ehat per quadrature points to perform the averaging
	InternalField<Real> Ehat;

	InternalField<Real> non_local_variable;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_MAZARS_NON_LOCAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_phasefield.cc b/src/model/solid_mechanics/materials/material_damage/material_phasefield.cc
	index c55d48a0a..52b32859a 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_phasefield.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_phasefield.cc
	@@ -1,108 +1,100 @@
	/**
	* @file material_phasefield.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Apr 02 2021
	*
	* @brief Specialization of the material class for the phasefield material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_phasefield.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-template<UInt spatial_dimension>
	-MaterialPhaseField<spatial_dimension>::MaterialPhaseField(SolidMechanicsModel & model,
	- const ID & id)
	- : Parent(model, id) {
	+template <UInt spatial_dimension>
	+MaterialPhaseField<spatial_dimension>::MaterialPhaseField(
	+ SolidMechanicsModel & model, const ID & id)
	+ : Parent(model, id) {

	AKANTU_DEBUG_IN();

	this->registerParam("eta", eta, Real(0.), _pat_parsable, "eta");
	this->damage.initialize(0);

	AKANTU_DEBUG_OUT();
	}

	-
	-
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	-void MaterialPhaseField<spatial_dimension>::computeStress(ElementType el_type,
	- GhostType ghost_type) {
	+void MaterialPhaseField<spatial_dimension>::computeStress(
	+ ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto dam = this->damage(el_type, ghost_type).begin();
	-
	+
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	computeStressOnQuad(grad_u, sigma, *dam);

	++dam;
	-
	+
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialPhaseField<spatial_dimension>::computeTangentModuli(
	- ElementType el_type, Array<Real> & tangent_matrix,
	- GhostType ghost_type) {
	+ ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	- Parent::computeTangentModuli(el_type, tangent_matrix,
	- ghost_type);
	+ Parent::computeTangentModuli(el_type, tangent_matrix, ghost_type);

	Real * dam = this->damage(el_type, ghost_type).storage();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	computeTangentModuliOnQuad(tangent, *dam);

	++dam;

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}
	-
	+
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialPhaseField<spatial_dimension>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent, Real & dam) {
	- tangent = (1 - dam)(1 - dam) + eta;
	+ tangent = (1 - dam) (1 - dam) + eta;
	}

	-
	INSTANTIATE_MATERIAL(phasefield, MaterialPhaseField);
	-
	-
	-} // akantu
	-

	+} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_phasefield.hh b/src/model/solid_mechanics/materials/material_damage/material_phasefield.hh
	index 54ac83922..49bf05ec2 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_phasefield.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_phasefield.hh
	@@ -1,97 +1,92 @@
	/**
	* @file material_phasefield.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 02 2021
	*
	* @brief Phasefield damage law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_damage.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_MATERIAL_PHASEFIELD_HH__
	#define __AKANTU_MATERIAL_PHASEFIELD_HH__

	namespace akantu {

	template <UInt spatial_dimension>
	class MaterialPhaseField : public MaterialDamage<spatial_dimension> {
	using Parent = MaterialDamage<spatial_dimension>;
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialPhaseField(SolidMechanicsModel & model, const ID & id = "");
	~MaterialPhaseField() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	-
	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & sigma,
	Real & dam);

	/// compute the tangent stiffness matrix for a given quadrature point
	inline void computeTangentModuliOnQuad(Matrix<Real> & tangent, Real & dam);

	-
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	-
	Real eta;
	-
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	#include "material_phasefield_inline_impl.cc"

	-} // akantu
	+} // namespace akantu

	#endif /* __AKANTU_MATERIAL_PHASEFIELD_HH__ */
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_phasefield_inline_impl.cc b/src/model/solid_mechanics/materials/material_damage/material_phasefield_inline_impl.cc
	index 1a20942fd..a5f16f0e9 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_phasefield_inline_impl.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_phasefield_inline_impl.cc
	@@ -1,86 +1,86 @@
	/**
	* @file material_phasefield_inline_impl.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Apr 02 2021
	*
	* @brief Implementation of the inline functions of the material phasefield
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	-template<UInt spatial_dimension>
	+template <UInt spatial_dimension>
	inline void MaterialPhaseField<spatial_dimension>::computeStressOnQuad(
	Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam) {

	MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);

	- Matrix<Real> strain( spatial_dimension, spatial_dimension);
	- Matrix<Real> strain_plus( spatial_dimension, spatial_dimension);
	- Matrix<Real> strain_minus( spatial_dimension, spatial_dimension);
	- Matrix<Real> strain_dir( spatial_dimension, spatial_dimension);
	- Matrix<Real> strain_diag_plus( spatial_dimension, spatial_dimension);
	+ Matrix<Real> strain(spatial_dimension, spatial_dimension);
	+ Matrix<Real> strain_plus(spatial_dimension, spatial_dimension);
	+ Matrix<Real> strain_minus(spatial_dimension, spatial_dimension);
	+ Matrix<Real> strain_dir(spatial_dimension, spatial_dimension);
	+ Matrix<Real> strain_diag_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> strain_diag_minus(spatial_dimension, spatial_dimension);

	Vector<Real> strain_values(spatial_dimension);
	-
	+
	Real trace_plus, trace_minus;
	-
	+
	this->template gradUToEpsilon<spatial_dimension>(grad_u, strain);
	-
	+
	strain.eig(strain_values, strain_dir);

	- for (UInt i=0; i < spatial_dimension; i++) {
	- strain_diag_plus(i, i) = std::max(Real(0.), strain_values(i));
	+ for (UInt i = 0; i < spatial_dimension; i++) {
	+ strain_diag_plus(i, i) = std::max(Real(0.), strain_values(i));
	strain_diag_minus(i, i) = std::min(Real(0.), strain_values(i));
	}

	- Matrix<Real> mat_tmp( spatial_dimension, spatial_dimension);
	- Matrix<Real> sigma_plus( spatial_dimension, spatial_dimension);
	+ Matrix<Real> mat_tmp(spatial_dimension, spatial_dimension);
	+ Matrix<Real> sigma_plus(spatial_dimension, spatial_dimension);
	Matrix<Real> sigma_minus(spatial_dimension, spatial_dimension);
	-
	- mat_tmp.mul<false,true>(strain_diag_plus, strain_dir);
	+
	+ mat_tmp.mul<false, true>(strain_diag_plus, strain_dir);
	strain_plus.mul<false, false>(strain_dir, mat_tmp);
	mat_tmp.mul<false, true>(strain_diag_minus, strain_dir);
	strain_minus.mul<false, true>(strain_dir, mat_tmp);
	-
	- trace_plus = std::max(Real(0.), strain.trace());
	+
	+ trace_plus = std::max(Real(0.), strain.trace());
	trace_minus = std::min(Real(0.), strain.trace());

	Real lambda = MaterialElastic<spatial_dimension>::getLambda();
	- Real mu = MaterialElastic<spatial_dimension>::getMu();
	-
	- for (UInt i=0; i < spatial_dimension; i++) {
	- for (UInt j=0; j < spatial_dimension; j++) {
	- sigma_plus(i, j) = (i==j) * lambda * trace_plus
	- + 2 * mu * strain_plus(i, j);
	- sigma_minus(i, j) = (i==j) * lambda * trace_minus
	- + 2 * mu * strain_minus(i, j);
	+ Real mu = MaterialElastic<spatial_dimension>::getMu();
	+
	+ for (UInt i = 0; i < spatial_dimension; i++) {
	+ for (UInt j = 0; j < spatial_dimension; j++) {
	+ sigma_plus(i, j) = static_cast<double>(i == j) * lambda * trace_plus +
	+ 2 * mu * strain_plus(i, j);
	+ sigma_minus(i, j) = static_cast<double>(i == j) * lambda * trace_minus +
	+ 2 * mu * strain_minus(i, j);
	}
	- }
	+ }

	- //sigma = (1 - dam) * sigma_plus + sigma_minus;
	- sigma = (1- dam)(1-dam) + eta;
	+ // sigma = (1 - dam) * sigma_plus + sigma_minus;
	+ sigma = (1 - dam) (1 - dam) + eta;
	}
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.cc b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.cc
	index 8914a034e..2dc753912 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.cc
	@@ -1,186 +1,180 @@
	/**
	* @file material_von_mises_mazars.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Fri Dec 04 2020
	*
	* @brief Mazars damage with Von Misses criteria
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_von_mises_mazars.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	- /* -------------------------------------------------------------------------- */
	+/* -------------------------------------------------------------------------- */
	template <UInt dim, template <UInt> class Parent>
	MaterialVonMisesMazars<dim, Parent>::MaterialVonMisesMazars(
	SolidMechanicsModel & model, const ID & id)
	- : MaterialDamage<dim, Parent>(model, id), K0("K0", *this),
	+ : MaterialDamage<dim, Parent>(model, id), K0("K0", *this),
	damage_in_compute_stress(true) {
	AKANTU_DEBUG_IN();

	-
	this->registerParam("K0", K0, _pat_parsable, "K0");
	this->registerParam("At", At, Real(0.8), _pat_parsable, "At");
	this->registerParam("Ac", Ac, Real(1.4), _pat_parsable, "Ac");
	this->registerParam("Bc", Bc, Real(1900.), _pat_parsable, "Bc");
	this->registerParam("Bt", Bt, Real(12000.), _pat_parsable, "Bt");
	this->registerParam("beta", beta, Real(1.06), _pat_parsable, "beta");

	this->K0.initialize(1);

	-
	AKANTU_DEBUG_OUT();
	}

	-
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	void MaterialVonMisesMazars<spatial_dimension, Parent>::computeStress(
	ElementType el_type, GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	MaterialThermal<spatial_dimension>::computeStress(el_type, ghost_type);
	// infinitesimal and finite deformation
	auto sigma_th_it = this->sigma_th(el_type, ghost_type).begin();

	auto previous_sigma_th_it =
	this->sigma_th.previous(el_type, ghost_type).begin();

	auto previous_gradu_it = this->gradu.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_stress_it = this->stress.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto inelastic_strain_it = this->inelastic_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_inelastic_strain_it =
	this->inelastic_strain.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto iso_hardening_it = this->iso_hardening(el_type, ghost_type).begin();

	auto previous_iso_hardening_it =
	this->iso_hardening.previous(el_type, ghost_type).begin();

	Real * dam = this->damage(el_type, ghost_type).storage();
	-
	+
	//
	// Finite Deformations
	//
	if (this->finite_deformation) {
	auto previous_piola_kirchhoff_2_it =
	this->piola_kirchhoff_2.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto green_strain_it = this->green_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_piola_kirchhoff_2_it;

	auto & green_strain = *green_strain_it;
	this->template gradUToE<spatial_dimension>(grad_u, green_strain);
	Matrix<Real> previous_green_strain(spatial_dimension, spatial_dimension);
	this->template gradUToE<spatial_dimension>(previous_grad_u,
	- previous_green_strain);
	+ previous_green_strain);
	Matrix<Real> F_tensor(spatial_dimension, spatial_dimension);
	this->template gradUToF<spatial_dimension>(grad_u, F_tensor);

	MaterialLinearIsotropicHardening<spatial_dimension>::computeStressOnQuad(
	- green_strain, previous_green_strain, sigma,
	- previous_sigma, inelastic_strain_tensor,
	- previous_inelastic_strain_tensor, *iso_hardening_it,
	- previous_iso_hardening_it, sigma_th_it,
	- *previous_sigma_th_it, F_tensor);
	+ green_strain, previous_green_strain, sigma, previous_sigma,
	+ inelastic_strain_tensor, previous_inelastic_strain_tensor,
	+ iso_hardening_it, previous_iso_hardening_it, *sigma_th_it,
	+ *previous_sigma_th_it, F_tensor);

	++sigma_th_it;
	++inelastic_strain_it;
	++iso_hardening_it;
	++previous_sigma_th_it;
	//++previous_stress_it;
	++previous_gradu_it;
	++green_strain_it;
	++previous_inelastic_strain_it;
	++previous_iso_hardening_it;
	++previous_piola_kirchhoff_2_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	}
	// Infinitesimal deformations
	else {
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Real Ehat = 0;
	-
	+
	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_stress_it;

	MaterialLinearIsotropicHardening<spatial_dimension>::computeStressOnQuad(
	grad_u, previous_grad_u, sigma, previous_sigma, inelastic_strain_tensor,
	previous_inelastic_strain_tensor, *iso_hardening_it,
	- previous_iso_hardening_it, sigma_th_it, *previous_sigma_th_it);
	+ previous_iso_hardening_it, sigma_th_it, *previous_sigma_th_it);

	Matrix<Real> grad_u_elastic(grad_u);
	grad_u_elastic -= inelastic_strain_tensor;
	-
	-
	+
	computeStressOnQuad(grad_u_elastic, sigma, *dam, Ehat);

	++dam;
	-
	+
	++sigma_th_it;
	++inelastic_strain_it;
	++iso_hardening_it;
	++previous_sigma_th_it;
	++previous_stress_it;
	++previous_gradu_it;
	++previous_inelastic_strain_it;
	++previous_iso_hardening_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	AKANTU_DEBUG_OUT();
	-
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(plastic_mazars, MaterialVonMisesMazars);

	-}
	+} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.hh b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.hh
	index 8866a4972..35b19b878 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars.hh
	@@ -1,116 +1,110 @@
	/**
	* @file material_von_mises_mazars.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Dec 04 2020
	*
	* @brief Mazars damage with Von Misses criteria
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	-#include "material_linear_isotropic_hardening.hh"
	#include "material_damage.hh"
	+#include "material_linear_isotropic_hardening.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_MATERIAL_VONMISES_MAZARS_HH__
	#define __AKANTU_MATERIAL_VONMISES_MAZARS_HH__

	namespace akantu {

	template <UInt spatial_dimension,
	- template <UInt> class Parent = MaterialLinearIsotropicHardening>
	+ template <UInt> class Parent = MaterialLinearIsotropicHardening>
	class MaterialVonMisesMazars
	: public MaterialDamage<spatial_dimension, Parent> {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	- MaterialVonMisesMazars(SolidMechanicsModel & model,
	- const ID & id = "");
	+ MaterialVonMisesMazars(SolidMechanicsModel & model, const ID & id = "");
	MaterialVonMisesMazars(SolidMechanicsModel & model, UInt dim,
	- const Mesh & mesh, FEEngine & fe_engine,
	- const ID & id = "");
	+ const Mesh & mesh, FEEngine & fe_engine,
	+ const ID & id = "");
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & damage,
	Real & Ehat);

	inline void computeDamageAndStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & damage,
	Real & Ehat);

	inline void computeDamageOnQuad(const Real & epsilon_equ,
	const Matrix<Real> & sigma,
	const Vector<Real> & epsilon_princ,
	Real & dam);

	-
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// damage threshold
	RandomInternalField<Real> K0;
	/// parameter damage traction 1
	Real At;
	/// parameter damage traction 2
	Real Bt;
	/// parameter damage compression 1
	Real Ac;
	/// parameter damage compression 2
	Real Bc;
	/// parameter for shear
	Real beta;

	/// specify the variable to average false = ehat, true = damage (only valid
	/// for non local version)
	bool damage_in_compute_stress;
	-
	};

	} // namespace akantu

	-
	#include "material_von_mises_mazars_inline_impl.hh"

	-
	#endif /* __AKANTU_MATERIAL_VONMISES_MAZARS_HH__ */
	-
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_inline_impl.hh b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_inline_impl.hh
	index 9b90ca95b..9821fb1f1 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_inline_impl.hh
	@@ -1,156 +1,156 @@
	/**
	* @file material_von_mises_mazars_inline_impl.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Apr 06 2011
	* @date last modification: Wed Dec 23 2020
	*
	* @brief Mazars damage with Von Misses criteria
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_von_mises_mazars.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialVonMisesMazars<spatial_dimension, Parent>::computeStressOnQuad(
	const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
	Real & Ehat) {
	Matrix<Real> epsilon(3, 3);
	epsilon.zero();

	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
	}
	}

	Vector<Real> Fdiag(3);
	Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

	Ehat = 0.;
	for (UInt i = 0; i < 3; ++i) {
	Real epsilon_p = std::max(Real(0.), Fdiag(i));
	Ehat += epsilon_p * epsilon_p;
	}
	Ehat = sqrt(Ehat);

	// MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);

	if (damage_in_compute_stress) {
	computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
	}

	if (not this->is_non_local) {
	computeDamageAndStressOnQuad(grad_u, sigma, dam, Ehat);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialVonMisesMazars<spatial_dimension, Parent>::computeDamageAndStressOnQuad(
	const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & dam,
	Real & Ehat) {
	if (!damage_in_compute_stress) {
	Vector<Real> Fdiag(3);
	Fdiag.zero();

	Matrix<Real> epsilon(3, 3);
	epsilon.zero();
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	epsilon(i, j) = .5 * (grad_u(i, j) + grad_u(j, i));
	}
	}
	Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

	computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
	}

	sigma *= 1 - dam;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension, template <UInt> class Parent>
	inline void
	MaterialVonMisesMazars<spatial_dimension, Parent>::computeDamageOnQuad(
	const Real & epsilon_equ,
	__attribute__((unused)) const Matrix<Real> & sigma,
	const Vector<Real> & epsilon_princ, Real & dam) {
	Real Fs = epsilon_equ - K0;
	if (Fs > 0.) {
	Real dam_t;
	Real dam_c;
	dam_t =
	1 - K0 * (1 - At) / epsilon_equ - At * (exp(-Bt * (epsilon_equ - K0)));
	dam_c =
	1 - K0 * (1 - Ac) / epsilon_equ - Ac * (exp(-Bc * (epsilon_equ - K0)));

	Real Cdiag;
	Cdiag = this->E * (1 - this->nu) / ((1 + this->nu) * (1 - 2 * this->nu));

	Vector<Real> sigma_princ(3);
	sigma_princ(0) = Cdiag * epsilon_princ(0) +
	this->lambda * (epsilon_princ(1) + epsilon_princ(2));
	sigma_princ(1) = Cdiag * epsilon_princ(1) +
	this->lambda * (epsilon_princ(0) + epsilon_princ(2));
	sigma_princ(2) = Cdiag * epsilon_princ(2) +
	this->lambda * (epsilon_princ(1) + epsilon_princ(0));

	Vector<Real> sigma_p(3);
	for (UInt i = 0; i < 3; i++) {
	sigma_p(i) = std::max(Real(0.), sigma_princ(i));
	}
	// sigma_p *= 1. - dam;

	Real trace_p = this->nu / this->E * (sigma_p(0) + sigma_p(1) + sigma_p(2));

	Real alpha_t = 0;
	for (UInt i = 0; i < 3; ++i) {
	Real epsilon_t = (1 + this->nu) / this->E * sigma_p(i) - trace_p;
	Real epsilon_p = std::max(Real(0.), epsilon_princ(i));
	alpha_t += epsilon_t * epsilon_p;
	}

	alpha_t /= epsilon_equ * epsilon_equ;
	alpha_t = std::min(alpha_t, Real(1.));

	Real alpha_c = 1. - alpha_t;

	alpha_t = std::pow(alpha_t, beta);
	alpha_c = std::pow(alpha_c, beta);

	Real damtemp;
	damtemp = alpha_t * dam_t + alpha_c * dam_c;

	dam = std::max(damtemp, dam);
	dam = std::min(dam, Real(1.));
	}
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.cc b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.cc
	index 6b65cec3d..813f889b2 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.cc
	+++ b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.cc
	@@ -1,123 +1,125 @@
	/**
	* @file material_von_mises_mazars_non_local.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Dec 17 2020
	*
	* @brief Mazars damage with Von Misses criteria
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_von_mises_mazars_non_local.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	-MaterialVonMisesMazarsNonLocal<spatial_dimension>::MaterialVonMisesMazarsNonLocal(
	- SolidMechanicsModel & model, const ID & id)
	+MaterialVonMisesMazarsNonLocal<spatial_dimension>::
	+ MaterialVonMisesMazarsNonLocal(SolidMechanicsModel & model, const ID & id)
	: MaterialNonLocalParent(model, id), Ehat("epsilon_equ", *this),
	non_local_variable("mazars_non_local", *this) {
	AKANTU_DEBUG_IN();

	this->is_non_local = true;
	this->Ehat.initialize(1);
	this->non_local_variable.initialize(1);

	this->registerParam("average_on_damage", this->damage_in_compute_stress,
	false, _pat_parsable \| _pat_modifiable,
	"Is D the non local variable");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	-void MaterialVonMisesMazarsNonLocal<spatial_dimension>::registerNonLocalVariables() {
	+void MaterialVonMisesMazarsNonLocal<
	+ spatial_dimension>::registerNonLocalVariables() {
	ID local;
	if (this->damage_in_compute_stress) {
	local = this->damage.getName();
	} else {
	local = this->Ehat.getName();
	}

	this->model.getNonLocalManager().registerNonLocalVariable(
	local, non_local_variable.getName(), 1);
	this->model.getNonLocalManager()
	.getNeighborhood(this->name)
	.registerNonLocalVariable(non_local_variable.getName());
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialVonMisesMazarsNonLocal<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real * damage = this->damage(el_type, ghost_type).storage();
	Real * epsilon_equ = this->Ehat(el_type, ghost_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	- MaterialVonMisesMazars<spatial_dimension>::computeStressOnQuad(grad_u, sigma, *damage,
	- *epsilon_equ);
	+ MaterialVonMisesMazars<spatial_dimension>::computeStressOnQuad(
	+ grad_u, sigma, damage, epsilon_equ);
	++damage;
	++epsilon_equ;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialVonMisesMazarsNonLocal<spatial_dimension>::computeNonLocalStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	auto & non_loc_var = non_local_variable(el_type, ghost_type);
	Real * damage;
	Real * epsilon_equ;
	if (this->damage_in_compute_stress) {
	damage = non_loc_var.storage();
	epsilon_equ = this->Ehat(el_type, ghost_type).storage();
	} else {
	damage = this->damage(el_type, ghost_type).storage();
	epsilon_equ = non_loc_var.storage();
	}

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	this->computeDamageAndStressOnQuad(grad_u, sigma, damage, epsilon_equ);

	++damage;
	++epsilon_equ;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	-INSTANTIATE_MATERIAL(von_mises_mazars_non_local, MaterialVonMisesMazarsNonLocal);
	+INSTANTIATE_MATERIAL(von_mises_mazars_non_local,
	+ MaterialVonMisesMazarsNonLocal);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.hh b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.hh
	index 3275af4c1..958bca1eb 100644
	--- a/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.hh
	+++ b/src/model/solid_mechanics/materials/material_damage/material_von_mises_mazars_non_local.hh
	@@ -1,91 +1,92 @@
	/**
	* @file material_von_mises_mazars_non_local.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Dec 17 2020
	*
	* @brief Mazars damage with Von Misses criteria
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_damage_non_local.hh"
	#include "material_von_mises_mazars.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_VON_MISES_MAZARS_NON_LOCAL_HH_
	#define AKANTU_MATERIAL_VON_MISES_MAZARS_NON_LOCAL_HH_

	namespace akantu {

	/**
	* Material Mazars Non local + Von Mises plasticity
	*
	* parameters in the material files :
	*/
	template <UInt spatial_dimension>
	class MaterialVonMisesMazarsNonLocal
	: public MaterialDamageNonLocal<spatial_dimension,
	MaterialVonMisesMazars<spatial_dimension>> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using MaterialNonLocalParent =
	MaterialDamageNonLocal<spatial_dimension,
	MaterialVonMisesMazars<spatial_dimension>>;

	- MaterialVonMisesMazarsNonLocal(SolidMechanicsModel & model, const ID & id = "");
	+ MaterialVonMisesMazarsNonLocal(SolidMechanicsModel & model,
	+ const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	void computeNonLocalStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	void registerNonLocalVariables() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// the ehat per quadrature points to perform the averaging
	InternalField<Real> Ehat;

	InternalField<Real> non_local_variable;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_VON_MISES_MAZARS_NON_LOCAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_elastic.cc b/src/model/solid_mechanics/materials/material_elastic.cc
	index 5fd3fae00..0d5d6c12b 100644
	--- a/src/model/solid_mechanics/materials/material_elastic.cc
	+++ b/src/model/solid_mechanics/materials/material_elastic.cc
	@@ -1,260 +1,259 @@
	/**
	* @file material_elastic.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Specialization of the material class for the elastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialElastic<dim>::MaterialElastic(SolidMechanicsModel & model,
	const ID & id)
	: Parent(model, id), was_stiffness_assembled(false) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialElastic<dim>::MaterialElastic(SolidMechanicsModel & model,
	- UInt /a_dim/,
	- const Mesh & mesh, FEEngine & fe_engine,
	- const ID & id)
	+ UInt /a_dim/, const Mesh & mesh,
	+ FEEngine & fe_engine, const ID & id)
	: Parent(model, dim, mesh, fe_engine, id), was_stiffness_assembled(false) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialElastic<dim>::initialize() {
	this->registerParam("lambda", lambda, _pat_readable,
	"First Lamé coefficient");
	this->registerParam("mu", mu, _pat_readable, "Second Lamé coefficient");
	this->registerParam("kapa", kpa, _pat_readable, "Bulk coefficient");
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialElastic<dim>::initMaterial() {
	AKANTU_DEBUG_IN();
	Parent::initMaterial();

	if (dim == 1) {
	this->nu = 0.;
	}

	this->updateInternalParameters();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialElastic<dim>::updateInternalParameters() {
	MaterialThermal<dim>::updateInternalParameters();

	this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - 2 * this->nu));
	this->mu = this->E / (2 * (1 + this->nu));

	this->kpa = this->lambda + 2. / 3. * this->mu;

	this->was_stiffness_assembled = false;
	}

	/* -------------------------------------------------------------------------- */
	template <> void MaterialElastic<2>::updateInternalParameters() {
	MaterialThermal<2>::updateInternalParameters();

	this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - 2 * this->nu));
	this->mu = this->E / (2 * (1 + this->nu));

	if (this->plane_stress) {
	this->lambda = this->nu * this->E / ((1 + this->nu) * (1 - this->nu));
	}

	this->kpa = this->lambda + 2. / 3. * this->mu;

	this->was_stiffness_assembled = false;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElastic<dim>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Parent::computeStress(el_type, ghost_type);

	Array<Real>::const_scalar_iterator sigma_th_it =
	this->sigma_th(el_type, ghost_type).begin();

	if (!this->finite_deformation) {
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	const Real & sigma_th = *sigma_th_it;
	this->computeStressOnQuad(grad_u, sigma, sigma_th);
	++sigma_th_it;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	} else {
	/// finite gradus
	Matrix<Real> E(dim, dim);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	/// compute E
	this->template gradUToE<dim>(grad_u, E);

	const Real & sigma_th = *sigma_th_it;

	/// compute second Piola-Kirchhoff stress tensor
	this->computeStressOnQuad(E, sigma, sigma_th);

	++sigma_th_it;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElastic<dim>::computeTangentModuli(ElementType el_type,
	Array<Real> & tangent_matrix,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	this->computeTangentModuliOnQuad(tangent);
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	this->was_stiffness_assembled = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialElastic<dim>::getPushWaveSpeed(const Element & /unused/) const {
	return sqrt((lambda + 2 * mu) / this->rho);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialElastic<dim>::getShearWaveSpeed(const Element & /unused/) const {
	return sqrt(mu / this->rho);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElastic<dim>::computePotentialEnergy(ElementType el_type) {
	AKANTU_DEBUG_IN();

	// MaterialThermal<dim>::computePotentialEnergy(ElementType)
	// needs to be implemented
	// MaterialThermal<dim>::computePotentialEnergy(el_type);

	auto epot = this->potential_energy(el_type, _not_ghost).begin();

	if (!this->finite_deformation) {
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	this->computePotentialEnergyOnQuad(grad_u, sigma, *epot);
	++epot;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	} else {

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);
	auto E = this->template gradUToE<dim>(grad_u);

	this->computePotentialEnergyOnQuad(E, sigma, *epot);
	++epot;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElastic<dim>::computePotentialEnergyByElement(
	ElementType type, UInt index, Vector<Real> & epot_on_quad_points) {
	auto gradu_it = this->gradu(type).begin(dim, dim);
	auto gradu_end = this->gradu(type).begin(dim, dim);
	auto stress_it = this->stress(type).begin(dim, dim);

	if (this->finite_deformation) {
	stress_it = this->piola_kirchhoff_2(type).begin(dim, dim);
	}

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);

	gradu_it += index * nb_quadrature_points;
	gradu_end += (index + 1) * nb_quadrature_points;
	stress_it += index * nb_quadrature_points;

	Real * epot_quad = epot_on_quad_points.storage();

	Matrix<Real> grad_u(dim, dim);

	if (this->finite_deformation) {
	for (; gradu_it != gradu_end; ++gradu_it, ++stress_it, ++epot_quad) {
	auto E = this->template gradUToE<dim>(*gradu_it);
	this->computePotentialEnergyOnQuad(E, stress_it, epot_quad);
	}
	} else {
	for (; gradu_it != gradu_end; ++gradu_it, ++stress_it, ++epot_quad) {
	this->computePotentialEnergyOnQuad(gradu_it, stress_it, *epot_quad);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	Real MaterialElastic<1>::getPushWaveSpeed(const Element & /element/) const {
	return std::sqrt(this->E / this->rho);
	}

	template <>
	Real MaterialElastic<1>::getShearWaveSpeed(const Element & /element/) const {
	AKANTU_EXCEPTION("There is no shear wave speed in 1D");
	}
	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(elastic, MaterialElastic);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_elastic.hh b/src/model/solid_mechanics/materials/material_elastic.hh
	index 1214316dc..c5453132f 100644
	--- a/src/model/solid_mechanics/materials/material_elastic.hh
	+++ b/src/model/solid_mechanics/materials/material_elastic.hh
	@@ -1,160 +1,157 @@
	/**
	* @file material_elastic.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material isotropic elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_thermal.hh"
	#include "plane_stress_toolbox.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ELASTIC_HH_
	#define AKANTU_MATERIAL_ELASTIC_HH_

	namespace akantu {

	/**
	* Material elastic isotropic
	*
	* parameters in the material files :
	* - E : Young's modulus (default: 0)
	* - nu : Poisson's ratio (default: 1/2)
	* - Plane_Stress : if 0: plane strain, else: plane stress (default: 0)
	*/
	template <UInt spatial_dimension>
	class MaterialElastic
	: public PlaneStressToolbox<spatial_dimension,
	MaterialThermal<spatial_dimension>> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	private:
	using Parent =
	PlaneStressToolbox<spatial_dimension, MaterialThermal<spatial_dimension>>;

	public:
	MaterialElastic(SolidMechanicsModel & model, const ID & id = "");
	MaterialElastic(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id = "");

	~MaterialElastic() override = default;

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	/// compute the elastic potential energy
	void computePotentialEnergy(ElementType el_type) override;

	void
	computePotentialEnergyByElement(ElementType type, UInt index,
	Vector<Real> & epot_on_quad_points) override;

	/// compute the p-wave speed in the material
	Real getPushWaveSpeed(const Element & element) const override;

	/// compute the s-wave speed in the material
	Real getShearWaveSpeed(const Element & element) const override;

	protected:
	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma,
	Real sigma_th = 0) const;

	/// compute the tangent stiffness matrix for an element
	inline void computeTangentModuliOnQuad(Matrix<Real> & tangent) const;

	/// recompute the lame coefficient if E or nu changes
	void updateInternalParameters() override;

	static inline void computePotentialEnergyOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & sigma,
	Real & epot);

	bool hasStiffnessMatrixChanged() override {
	return (not was_stiffness_assembled);
	}

	- MatrixType getTangentType() override {
	- return _symmetric;
	- }
	-
	+ MatrixType getTangentType() override { return _symmetric; }
	+
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get first Lame constant
	AKANTU_GET_MACRO(Lambda, lambda, Real);

	/// get second Lame constant
	AKANTU_GET_MACRO(Mu, mu, Real);

	/// get bulk modulus
	AKANTU_GET_MACRO(Kappa, kpa, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// First Lamé coefficient
	Real lambda;

	/// Second Lamé coefficient (shear modulus)
	Real mu;

	/// Bulk modulus
	Real kpa;

	/// defines if the stiffness was computed
	bool was_stiffness_assembled;
	};

	} // namespace akantu

	#include "material_elastic_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_ELASTIC_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_elastic_inline_impl.hh b/src/model/solid_mechanics/materials/material_elastic_inline_impl.hh
	index 7e94d01b1..215d63240 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_elastic_inline_impl.hh
	@@ -1,122 +1,122 @@
	/**
	* @file material_elastic_inline_impl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of the material elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_HH_
	#define AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialElastic<spatial_dimension>::computeStressOnQuad(
	- const Matrix<Real> & grad_u, Matrix<Real> & sigma,
	- Real sigma_th) const {
	+ const Matrix<Real> & grad_u, Matrix<Real> & sigma, Real sigma_th) const {
	Real trace = grad_u.trace(); // trace = (\nabla u)_{kk}

	// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
	// u_{ij} + \nabla u_{ji})
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	sigma(i, j) = Math::kronecker(i, j) * lambda * trace +
	- mu * (grad_u(i, j) + grad_u(j, i)) + Math::kronecker(i, j) * sigma_th;
	+ mu * (grad_u(i, j) + grad_u(j, i)) +
	+ Math::kronecker(i, j) * sigma_th;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void MaterialElastic<1>::computeStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma,
	Real sigma_th) const {
	sigma(0, 0) = this->E * grad_u(0, 0) + sigma_th;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	inline void MaterialElastic<spatial_dimension>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent) const {
	UInt n = tangent.cols();

	// Real Ep = E/((1+nu)(1-2nu));
	Real Miiii = lambda + 2 * mu;
	Real Miijj = lambda;
	Real Mijij = mu;

	if (spatial_dimension == 1) {
	tangent(0, 0) = this->E;
	} else {
	tangent(0, 0) = Miiii;
	}

	// test of dimension should by optimized out by the compiler due to the
	// template
	if (spatial_dimension >= 2) {
	tangent(1, 1) = Miiii;
	tangent(0, 1) = Miijj;
	tangent(1, 0) = Miijj;

	tangent(n - 1, n - 1) = Mijij;
	}

	if (spatial_dimension == 3) {
	tangent(2, 2) = Miiii;
	tangent(0, 2) = Miijj;
	tangent(1, 2) = Miijj;
	tangent(2, 0) = Miijj;
	tangent(2, 1) = Miijj;

	tangent(3, 3) = Mijij;
	tangent(4, 4) = Mijij;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialElastic<dim>::computePotentialEnergyOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & sigma, Real & epot) {
	epot = .5 * sigma.doubleDot(grad_u);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	MaterialElastic<1>::computeTangentModuliOnQuad(Matrix<Real> & tangent) const {
	tangent(0, 0) = E;
	}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.cc b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.cc
	index e065dc3f7..3fa8b9909 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.cc
	+++ b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.cc
	@@ -1,262 +1,262 @@
	/**
	* @file material_elastic_linear_anisotropic.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Till Junge <till.junge@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Sep 25 2013
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Anisotropic elastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "material_elastic_linear_anisotropic.hh"
	#include "solid_mechanics_model.hh"
	#include <algorithm>
	#include <sstream>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialElasticLinearAnisotropic<dim>::MaterialElasticLinearAnisotropic(
	SolidMechanicsModel & model, const ID & id, bool symmetric)
	: Material(model, id), rot_mat(dim, dim), Cprime(dim * dim, dim * dim),
	C(voigt_h::size, voigt_h::size), eigC(voigt_h::size),
	symmetric(symmetric), was_stiffness_assembled(false) {
	AKANTU_DEBUG_IN();

	this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
	(*this->dir_vecs.back())[0] = 1.;
	this->registerParam("n1", *(this->dir_vecs.back()), _pat_parsmod,
	"Direction of main material axis");

	if (dim > 1) {
	this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
	(*this->dir_vecs.back())[1] = 1.;
	this->registerParam("n2", *(this->dir_vecs.back()), _pat_parsmod,
	"Direction of secondary material axis");
	}

	if (dim > 2) {
	this->dir_vecs.push_back(std::make_unique<Vector<Real>>(dim));
	(*this->dir_vecs.back())[2] = 1.;
	this->registerParam("n3", *(this->dir_vecs.back()), _pat_parsmod,
	"Direction of tertiary material axis");
	}

	for (UInt i = 0; i < voigt_h::size; ++i) {
	UInt start = 0;
	if (this->symmetric) {
	start = i;
	}
	for (UInt j = start; j < voigt_h::size; ++j) {
	std::stringstream param("C");
	param << "C" << i + 1 << j + 1;
	this->registerParam(param.str(), this->Cprime(i, j), Real(0.),
	_pat_parsmod, "Coefficient " + param.str());
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void MaterialElasticLinearAnisotropic<dim>::initMaterial() {
	AKANTU_DEBUG_IN();
	Material::initMaterial();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElasticLinearAnisotropic<dim>::updateInternalParameters() {

	Material::updateInternalParameters();
	if (this->symmetric) {
	for (UInt i = 0; i < voigt_h::size; ++i) {
	for (UInt j = i + 1; j < voigt_h::size; ++j) {
	this->Cprime(j, i) = this->Cprime(i, j);
	}
	}
	}
	this->rotateCprime();
	this->C.eig(this->eigC);

	this->was_stiffness_assembled = false;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt Dim> void MaterialElasticLinearAnisotropic<Dim>::rotateCprime() {
	// start by filling the empty parts fo Cprime
	UInt diff = Dim * Dim - voigt_h::size;
	for (UInt i = voigt_h::size; i < Dim * Dim; ++i) {
	for (UInt j = 0; j < Dim * Dim; ++j) {
	this->Cprime(i, j) = this->Cprime(i - diff, j);
	}
	}
	for (UInt i = 0; i < Dim * Dim; ++i) {
	for (UInt j = voigt_h::size; j < Dim * Dim; ++j) {
	this->Cprime(i, j) = this->Cprime(i, j - diff);
	}
	}
	// construction of rotator tensor
	// normalise rotation matrix
	for (UInt j = 0; j < Dim; ++j) {
	Vector<Real> rot_vec = this->rot_mat(j);
	rot_vec = *this->dir_vecs[j];
	rot_vec.normalize();
	}

	// make sure the vectors form a right-handed base
	Vector<Real> test_axis(3);
	Vector<Real> v1(3);
	Vector<Real> v2(3);
	Vector<Real> v3(3, 0.);

	if (Dim == 2) {
	for (UInt i = 0; i < Dim; ++i) {
	v1[i] = this->rot_mat(0, i);
	v2[i] = this->rot_mat(1, i);
	}

	v3.crossProduct(v1, v2);
	if (v3.norm() < 8 * std::numeric_limits<Real>::epsilon()) {
	AKANTU_ERROR("The axis vectors parallel.");
	}

	v3.normalize();
	} else if (Dim == 3) {
	v1 = this->rot_mat(0);
	v2 = this->rot_mat(1);
	v3 = this->rot_mat(2);
	}

	test_axis.crossProduct(v1, v2);
	test_axis -= v3;
	if (test_axis.norm() > 8 * std::numeric_limits<Real>::epsilon()) {
	AKANTU_ERROR("The axis vectors do not form a right-handed coordinate "
	<< "system. I. e., \|\|n1 x n2 - n3\|\| should be zero, but "
	<< "it is " << test_axis.norm() << ".");
	}

	// create the rotator and the reverse rotator
	Matrix<Real> rotator(Dim * Dim, Dim * Dim);
	Matrix<Real> revrotor(Dim * Dim, Dim * Dim);
	for (UInt i = 0; i < Dim; ++i) {
	for (UInt j = 0; j < Dim; ++j) {
	for (UInt k = 0; k < Dim; ++k) {
	for (UInt l = 0; l < Dim; ++l) {
	UInt I = voigt_h::mat[i][j];
	UInt J = voigt_h::mat[k][l];
	rotator(I, J) = this->rot_mat(k, i) * this->rot_mat(l, j);
	revrotor(I, J) = this->rot_mat(i, k) * this->rot_mat(j, l);
	}
	}
	}
	}

	// create the full rotated matrix
	Matrix<Real> Cfull(Dim * Dim, Dim * Dim);
	Cfull = rotator * Cprime * revrotor;

	for (UInt i = 0; i < voigt_h::size; ++i) {
	for (UInt j = 0; j < voigt_h::size; ++j) {
	this->C(i, j) = Cfull(i, j);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElasticLinearAnisotropic<dim>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	// Wikipedia convention:
	// 2*eps_ij (i!=j) = voigt_eps_I
	// http://en.wikipedia.org/wiki/Voigt_notation
	AKANTU_DEBUG_IN();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	this->computeStressOnQuad(grad_u, sigma);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElasticLinearAnisotropic<dim>::computeTangentModuli(
	ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);

	this->computeTangentModuliOnQuad(tangent);

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	this->was_stiffness_assembled = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialElasticLinearAnisotropic<dim>::computePotentialEnergy(
	ElementType el_type) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(!this->finite_deformation,
	"finite deformation not possible in material anisotropic "
	"(TO BE IMPLEMENTED)");

	Array<Real>::scalar_iterator epot =
	this->potential_energy(el_type, _not_ghost).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	computePotentialEnergyOnQuad(grad_u, sigma, *epot);
	++epot;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialElasticLinearAnisotropic<dim>::getCelerity(
	__attribute__((unused)) const Element & element) const {
	return std::sqrt(this->eigC(0) / rho);
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(elastic_anisotropic, MaterialElasticLinearAnisotropic);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.hh b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.hh
	index 1ff23a0dd..309ec4b7d 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.hh
	+++ b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic.hh
	@@ -1,141 +1,138 @@
	/**
	* @file material_elastic_linear_anisotropic.hh
	*
	* @author Till Junge <till.junge@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Orthotropic elastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_HH_
	#define AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_HH_

	namespace akantu {

	/**
	* General linear anisotropic elastic material
	* The only constraint on the elastic tensor is that it can be represented
	* as a symmetric 6x6 matrix (3D) or 3x3 (2D).
	*
	* parameters in the material files :
	* - rho : density (default: 0)
	* - C_ij : entry on the stiffness
	*/
	template <UInt Dim> class MaterialElasticLinearAnisotropic : public Material {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialElasticLinearAnisotropic(SolidMechanicsModel & model,
	const ID & id = "", bool symmetric = true);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	/// compute the elastic potential energy
	void computePotentialEnergy(ElementType el_type) override;

	void updateInternalParameters() override;

	bool hasStiffnessMatrixChanged() override {
	return (not was_stiffness_assembled);
	}

	- MatrixType getTangentType() override {
	- return _symmetric;
	- }
	+ MatrixType getTangentType() override { return _symmetric; }

	protected:
	// compute C from Cprime
	void rotateCprime();

	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(const Matrix<Real> & grad_u,
	Matrix<Real> & sigma) const;

	/// tangent matrix for a given quadrature point
	inline void computeTangentModuliOnQuad(Matrix<Real> & tangent) const;

	inline void computePotentialEnergyOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & sigma,
	Real & epot);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute max wave celerity
	Real getCelerity(const Element & element) const override;

	AKANTU_GET_MACRO(VoigtStiffness, C, Matrix<Real>);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	using voigt_h = VoigtHelper<Dim>;

	/// direction matrix and vectors
	std::vector<std::unique_ptr<Vector<Real>>> dir_vecs;

	Matrix<Real> rot_mat;
	/// Elastic stiffness tensor in material frame and full vectorised notation
	Matrix<Real> Cprime;
	/// Elastic stiffness tensor in voigt notation
	Matrix<Real> C;
	/// eigenvalues of stiffness tensor
	Vector<Real> eigC;

	bool symmetric;

	/// defines if the stiffness was computed
	bool was_stiffness_assembled;
	};
	} // namespace akantu

	#include "material_elastic_linear_anisotropic_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic_inline_impl.hh b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic_inline_impl.hh
	index 9fc848098..8ff964519 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_elastic_linear_anisotropic_inline_impl.hh
	@@ -1,74 +1,74 @@
	/**
	* @file material_elastic_linear_anisotropic_inline_impl.hh
	*
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Feb 16 2018
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of the material elastic linear
	* anisotropic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic_linear_anisotropic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_INLINE_IMPL_HH_
	#define AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialElasticLinearAnisotropic<dim>::computeStressOnQuad(
	const Matrix<Real> & grad_u, Matrix<Real> & sigma) const {
	auto voigt_strain = strainToVoigt<dim>(gradUToEpsilon<dim>(grad_u));
	auto voigt_stress = this->C * voigt_strain;
	voigtToStress<dim>(voigt_stress, sigma);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialElasticLinearAnisotropic<dim>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent) const {

	tangent.copy(this->C);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialElasticLinearAnisotropic<dim>::computePotentialEnergyOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & sigma, Real & epot) {

	AKANTU_DEBUG_ASSERT(this->symmetric,
	"The elastic constants matrix is not symmetric,"
	"energy is not path independent.");

	epot = .5 * sigma.doubleDot(grad_u);
	}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_ELASTIC_LINEAR_ANISOTROPIC_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_elastic_orthotropic.cc b/src/model/solid_mechanics/materials/material_elastic_orthotropic.cc
	index bbddfdd3c..ced8a92d4 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_orthotropic.cc
	+++ b/src/model/solid_mechanics/materials/material_elastic_orthotropic.cc
	@@ -1,177 +1,177 @@
	/**
	* @file material_elastic_orthotropic.cc
	*
	* @author Till Junge <till.junge@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Orthotropic elastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "material_elastic_orthotropic.hh"
	#include "solid_mechanics_model.hh"
	#include <algorithm>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt Dim>
	MaterialElasticOrthotropic<Dim>::MaterialElasticOrthotropic(
	SolidMechanicsModel & model, const ID & id)
	: MaterialElasticLinearAnisotropic<Dim>(model, id) {
	AKANTU_DEBUG_IN();
	this->registerParam("E1", E1, Real(0.), _pat_parsmod, "Young's modulus (n1)");
	this->registerParam("E2", E2, Real(0.), _pat_parsmod, "Young's modulus (n2)");
	this->registerParam("nu12", nu12, Real(0.), _pat_parsmod,
	"Poisson's ratio (12)");
	this->registerParam("G12", G12, Real(0.), _pat_parsmod, "Shear modulus (12)");

	if (Dim > 2) {
	this->registerParam("E3", E3, Real(0.), _pat_parsmod,
	"Young's modulus (n3)");
	this->registerParam("nu13", nu13, Real(0.), _pat_parsmod,
	"Poisson's ratio (13)");
	this->registerParam("nu23", nu23, Real(0.), _pat_parsmod,
	"Poisson's ratio (23)");
	this->registerParam("G13", G13, Real(0.), _pat_parsmod,
	"Shear modulus (13)");
	this->registerParam("G23", G23, Real(0.), _pat_parsmod,
	"Shear modulus (23)");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt Dim> void MaterialElasticOrthotropic<Dim>::initMaterial() {
	AKANTU_DEBUG_IN();
	MaterialElasticLinearAnisotropic<Dim>::initMaterial();

	AKANTU_DEBUG_ASSERT(not this->finite_deformation,
	"finite deformation not possible in material orthotropic "
	"(TO BE IMPLEMENTED)");

	updateInternalParameters();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt Dim>
	void MaterialElasticOrthotropic<Dim>::updateInternalParameters() {

	this->C.zero();
	this->Cprime.zero();

	/* 1) construction of temporary material frame stiffness tensor------------ */
	// http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real nu31 = nu13 * E3 / E1;
	Real nu32 = nu23 * E3 / E2;

	// Full (i.e. dim^2 by dim^2) stiffness tensor in material frame
	if (Dim == 1) {
	AKANTU_ERROR("Dimensions 1 not implemented: makes no sense to have "
	"orthotropy for 1D");
	}

	Real Gamma;

	if (Dim == 3) {
	Gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
	2 * nu21 * nu32 * nu13);
	}

	if (Dim == 2) {
	Gamma = 1 / (1 - nu12 * nu21);
	}

	// Lamé's first parameters
	this->Cprime(0, 0) = E1 * (1 - nu23 * nu32) * Gamma;
	this->Cprime(1, 1) = E2 * (1 - nu13 * nu31) * Gamma;
	if (Dim == 3) {
	this->Cprime(2, 2) = E3 * (1 - nu12 * nu21) * Gamma;
	}

	// normalised poisson's ratio's
	this->Cprime(1, 0) = this->Cprime(0, 1) = E1 * (nu21 + nu31 * nu23) * Gamma;
	if (Dim == 3) {
	this->Cprime(2, 0) = this->Cprime(0, 2) = E1 * (nu31 + nu21 * nu32) * Gamma;
	this->Cprime(2, 1) = this->Cprime(1, 2) = E2 * (nu32 + nu12 * nu31) * Gamma;
	}

	// Lamé's second parameters (shear moduli)
	if (Dim == 3) {
	this->Cprime(3, 3) = G23;
	this->Cprime(4, 4) = G13;
	this->Cprime(5, 5) = G12;
	} else {
	this->Cprime(2, 2) = G12;
	}

	/* 1) rotation of C into the global frame */
	this->rotateCprime();
	this->C.eig(this->eigC);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialElasticOrthotropic<spatial_dimension>::
	computePotentialEnergyByElement(ElementType type, UInt index,
	Vector<Real> & epot_on_quad_points) {

	Array<Real>::matrix_iterator gradu_it =
	this->gradu(type).begin(spatial_dimension, spatial_dimension);
	Array<Real>::matrix_iterator gradu_end =
	this->gradu(type).begin(spatial_dimension, spatial_dimension);
	Array<Real>::matrix_iterator stress_it =
	this->stress(type).begin(spatial_dimension, spatial_dimension);

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);

	gradu_it += index * nb_quadrature_points;
	gradu_end += (index + 1) * nb_quadrature_points;
	stress_it += index * nb_quadrature_points;

	Real * epot_quad = epot_on_quad_points.storage();

	Matrix<Real> grad_u(spatial_dimension, spatial_dimension);

	for (; gradu_it != gradu_end; ++gradu_it, ++stress_it, ++epot_quad) {
	grad_u.copy(*gradu_it);

	this->computePotentialEnergyOnQuad(grad_u, stress_it, epot_quad);
	}
	}

	/* -------------------------------------------------------------------------- */
	INSTANTIATE_MATERIAL(elastic_orthotropic, MaterialElasticOrthotropic);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_elastic_orthotropic.hh b/src/model/solid_mechanics/materials/material_elastic_orthotropic.hh
	index 473dd869b..00ddd8be3 100644
	--- a/src/model/solid_mechanics/materials/material_elastic_orthotropic.hh
	+++ b/src/model/solid_mechanics/materials/material_elastic_orthotropic.hh
	@@ -1,137 +1,137 @@
	/**
	* @file material_elastic_orthotropic.hh
	*
	* @author Till Junge <till.junge@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Orthotropic elastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_elastic_linear_anisotropic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_ELASTIC_ORTHOTROPIC_HH_
	#define AKANTU_MATERIAL_ELASTIC_ORTHOTROPIC_HH_

	namespace akantu {

	/**
	* Orthotropic elastic material
	*
	* parameters in the material files :
	* - n1 : direction of x-axis in material base, normalisation not necessary
	* (default: {1, 0, 0})
	* - n2 : direction of y-axis in material base, normalisation not necessary
	* (default: {0, 1, 0})
	* - n3 : direction of z-axis in material base, normalisation not necessary
	* (default: {0, 0, 1})
	* - rho : density (default: 0)
	* - E1 : Young's modulus along n1 (default: 0)
	* - E2 : Young's modulus along n2 (default: 0)
	* - E3 : Young's modulus along n3 (default: 0)
	* - nu12 : Poisson's ratio along 12 (default: 0)
	* - nu13 : Poisson's ratio along 13 (default: 0)
	* - nu23 : Poisson's ratio along 23 (default: 0)
	* - G12 : Shear modulus along 12 (default: 0)
	* - G13 : Shear modulus along 13 (default: 0)
	* - G23 : Shear modulus along 23 (default: 0)
	*/

	template <UInt Dim>
	class MaterialElasticOrthotropic
	: public MaterialElasticLinearAnisotropic<Dim> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialElasticOrthotropic(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	void updateInternalParameters() override;

	void
	computePotentialEnergyByElement(ElementType type, UInt index,
	Vector<Real> & epot_on_quad_points) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(E1, E1, Real);
	AKANTU_GET_MACRO(E2, E2, Real);
	AKANTU_GET_MACRO(E3, E3, Real);
	AKANTU_GET_MACRO(Nu12, nu12, Real);
	AKANTU_GET_MACRO(Nu13, nu13, Real);
	AKANTU_GET_MACRO(Nu23, nu23, Real);
	AKANTU_GET_MACRO(G12, G12, Real);
	AKANTU_GET_MACRO(G13, G13, Real);
	AKANTU_GET_MACRO(G23, G23, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// the n1 young modulus
	Real E1{0.};

	/// the n2 young modulus
	Real E2{0.};

	/// the n3 young modulus
	Real E3{0.};

	/// 12 Poisson coefficient
	Real nu12{0.};

	/// 13 Poisson coefficient
	Real nu13{0.};

	/// 23 Poisson coefficient
	Real nu23{0.};

	/// 12 shear modulus
	Real G12{0.};

	/// 13 shear modulus
	Real G13{0.};

	/// 23 shear modulus
	Real G23{0.};
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_ELASTIC_ORTHOTROPIC_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_embedded/material_embedded_includes.hh b/src/model/solid_mechanics/materials/material_embedded/material_embedded_includes.hh
	index 2d9466aa5..501bd1461 100644
	--- a/src/model/solid_mechanics/materials/material_embedded/material_embedded_includes.hh
	+++ b/src/model/solid_mechanics/materials/material_embedded/material_embedded_includes.hh
	@@ -1,42 +1,42 @@
	/**
	* @file material_embedded_includes.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jan 04 2013
	* @date last modification: Fri Feb 09 2018
	*
	* @brief List of includes for embedded elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_CMAKE_LIST_MATERIALS
	#include "material_reinforcement.hh"
	#endif

	#define AKANTU_MATERIAL_REINFORCEMENT_LAW_TMPL_LIST \
	((elastic, (MaterialElastic<1>)))( \
	(plastic, (MaterialLinearIsotropicHardening<1>)))

	#define AKANTU_EMBEDDED_MATERIAL_LIST \
	((2, (reinforcement, MaterialReinforcement)))
	diff --git a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
	index 0ec5f9d0f..aa2c13c57 100644
	--- a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
	+++ b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
	@@ -1,210 +1,208 @@
	/**
	* @file material_reinforcement.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Mar 13 2015
	* @date last modification: Fri Feb 09 2018
	*
	* @brief Reinforcement material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_REINFORCEMENT_HH_
	#define AKANTU_MATERIAL_REINFORCEMENT_HH_

	#include "aka_common.hh"

	#include "embedded_interface_model.hh"
	#include "material.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* @brief Material used to represent embedded reinforcements
	*
	* This class is used for computing the reinforcement stiffness matrix
	* along with the reinforcement residual. Room is made for constitutive law,
	* but actual use of contitutive laws is made in MaterialReinforcementTemplate.
	*
	* Be careful with the dimensions in this class :
	* - this->spatial_dimension is always 1
	* - the template parameter dim is the dimension of the problem
	*/

	template <class Mat, UInt dim> class MaterialReinforcement : public Mat {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Constructor
	MaterialReinforcement(EmbeddedInterfaceModel & model, const ID & id = "");

	/// Destructor
	~MaterialReinforcement() override;

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Init the material
	void initMaterial() override;

	/// Init the filters for background elements
	void initFilters();

	/// Init the background shape derivatives
	void initBackgroundShapeDerivatives();

	/// Init the cosine matrices
	void initDirectingCosines();

	/// Assemble stiffness matrix
	void assembleStiffnessMatrix(GhostType ghost_type) override;

	/// Compute all the stresses !
	void computeAllStresses(GhostType ghost_type) override;

	/// Compute energy
	Real getEnergy(const std::string & id) override;

	/// Assemble the residual of one type of element (typically _segment_2)
	void assembleInternalForces(GhostType ghost_type) override;

	/* ------------------------------------------------------------------------ */
	/* Protected methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Allocate the background shape derivatives
	void allocBackgroundShapeDerivatives();

	/// Compute the directing cosines matrix for one element type
	void computeDirectingCosines(ElementType type, GhostType ghost_type);

	/// Compute the directing cosines matrix on quadrature points.
	inline void computeDirectingCosinesOnQuad(const Matrix<Real> & nodes,
	Matrix<Real> & cosines);

	/// Add the prestress to the computed stress
	void addPrestress(ElementType type, GhostType ghost_type);

	/// Compute displacement gradient in reinforcement
	void computeGradU(ElementType interface_type, GhostType ghost_type);

	/// Assemble the stiffness matrix for an element type (typically _segment_2)
	void assembleStiffnessMatrix(ElementType type, GhostType ghost_type);

	/// Assemble the stiffness matrix for background & interface types
	void assembleStiffnessMatrixInterface(ElementType interface_type,
	ElementType background_type,
	GhostType ghost_type);

	/// Compute the background shape derivatives for a type
	void computeBackgroundShapeDerivatives(ElementType type,
	GhostType ghost_type);

	/// Compute the background shape derivatives for a type pair
	void computeBackgroundShapeDerivatives(ElementType interface_type,
	ElementType bg_type,
	GhostType ghost_type,
	const Array<UInt> & filter);

	/// Filter elements crossed by interface of a type
	void filterInterfaceBackgroundElements(Array<UInt> & foreground,
	Array<UInt> & background,
	ElementType type,
	ElementType interface_type,
	GhostType ghost_type);

	/// Assemble the residual of one type of element (typically _segment_2)
	void assembleInternalForces(ElementType type, GhostType ghost_type);

	/// Assemble the residual for a pair of elements
	void assembleInternalForcesInterface(ElementType interface_type,
	ElementType background_type,
	GhostType ghost_type);

	// TODO figure out why voigt size is 4 in 2D
	inline void stressTensorToVoigtVector(const Matrix<Real> & tensor,
	Vector<Real> & vector);
	inline void strainTensorToVoigtVector(const Matrix<Real> & tensor,
	Vector<Real> & vector);

	/// Get background filter
	- Array<UInt> & getBackgroundFilter(ElementType fg_type,
	- ElementType bg_type,
	+ Array<UInt> & getBackgroundFilter(ElementType fg_type, ElementType bg_type,
	GhostType ghost_type) {
	return (*background_filter(fg_type, ghost_type))(bg_type, ghost_type);
	}

	/// Get foreground filter
	- Array<UInt> & getForegroundFilter(ElementType fg_type,
	- ElementType bg_type,
	+ Array<UInt> & getForegroundFilter(ElementType fg_type, ElementType bg_type,
	GhostType ghost_type) {
	return (*foreground_filter(fg_type, ghost_type))(bg_type, ghost_type);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Embedded model
	EmbeddedInterfaceModel & emodel;

	/// Gradu of concrete on reinforcement
	InternalField<Real> gradu_embedded;

	/// C matrix on quad
	InternalField<Real> directing_cosines;

	/// Prestress on quad
	InternalField<Real> pre_stress;

	/// Cross-sectional area
	Real area;

	template <typename T>
	using CrossMap = ElementTypeMap<std::unique_ptr<ElementTypeMapArray<T>>>;

	/// Background mesh shape derivatives
	CrossMap<Real> shape_derivatives;

	/// Foreground mesh filter (contains segment ids)
	CrossMap<UInt> foreground_filter;

	/// Background element filter (contains bg ids)
	CrossMap<UInt> background_filter;
	};

	} // namespace akantu

	#include "material_reinforcement_tmpl.hh"

	#endif // AKANTU_MATERIAL_REINFORCEMENT_HH_
	diff --git a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
	index 973db45b8..cdf84ef1c 100644
	--- a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
	@@ -1,777 +1,777 @@
	/**
	* @file material_reinforcement_tmpl.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Wed Mar 25 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Reinforcement material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	#include "material_reinforcement.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	MaterialReinforcement<Mat, dim>::MaterialReinforcement(
	EmbeddedInterfaceModel & model, const ID & id)
	: Mat(model, 1, model.getInterfaceMesh(),
	model.getFEEngine("EmbeddedInterfaceFEEngine"), id),
	emodel(model),
	gradu_embedded("gradu_embedded", *this, 1,
	model.getFEEngine("EmbeddedInterfaceFEEngine"),
	this->element_filter),
	directing_cosines("directing_cosines", *this, 1,
	model.getFEEngine("EmbeddedInterfaceFEEngine"),
	this->element_filter),
	pre_stress("pre_stress", *this, 1,
	model.getFEEngine("EmbeddedInterfaceFEEngine"),
	this->element_filter),
	area(1.0) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::initialize() {
	AKANTU_DEBUG_IN();

	this->registerParam("area", area, _pat_parsable \| _pat_modifiable,
	"Reinforcement cross-sectional area");
	this->registerParam("pre_stress", pre_stress, _pat_parsable \| _pat_modifiable,
	"Uniform pre-stress");

	// Reallocate the element filter
	this->element_filter.initialize(this->emodel.getInterfaceMesh(),
	_spatial_dimension = 1);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	MaterialReinforcement<Mat, dim>::~MaterialReinforcement() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::initMaterial() {
	Mat::initMaterial();

	gradu_embedded.initialize(dim * dim);
	pre_stress.initialize(1);

	/// We initialise the stuff that is not going to change during the simulation
	this->initFilters();
	this->allocBackgroundShapeDerivatives();
	this->initBackgroundShapeDerivatives();
	this->initDirectingCosines();
	}

	/* -------------------------------------------------------------------------- */
	/// Initialize the filter for background elements
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::initFilters() {
	for (auto gt : ghost_types) {
	for (auto && type : emodel.getInterfaceMesh().elementTypes(1, gt)) {
	std::string shaped_id = "filter";
	if (gt == _ghost) {
	shaped_id += ":ghost";
	}
	auto & background =
	background_filter(std::make_unique<ElementTypeMapArray<UInt>>(
	"bg_" + shaped_id, this->name),
	type, gt);
	auto & foreground = foreground_filter(
	std::make_unique<ElementTypeMapArray<UInt>>(shaped_id, this->name),
	type, gt);
	foreground->initialize(emodel.getMesh(), _nb_component = 1,
	_ghost_type = gt);
	background->initialize(emodel.getMesh(), _nb_component = 1,
	_ghost_type = gt);

	// Computing filters
	for (auto && bg_type : background->elementTypes(dim, gt)) {
	filterInterfaceBackgroundElements(
	(foreground)(bg_type), (background)(bg_type), bg_type, type, gt);
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/// Construct a filter for a (interface_type, background_type) pair
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::filterInterfaceBackgroundElements(
	Array<UInt> & foreground, Array<UInt> & background, ElementType type,
	ElementType interface_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	foreground.resize(0);
	background.resize(0);

	Array<Element> & elements =
	emodel.getInterfaceAssociatedElements(interface_type, ghost_type);
	Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);

	for (auto & elem_id : elem_filter) {
	Element & elem = elements(elem_id);
	if (elem.type == type) {
	background.push_back(elem.element);
	foreground.push_back(elem_id);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	namespace detail {
	class BackgroundShapeDInitializer : public ElementTypeMapArrayInitializer {
	public:
	BackgroundShapeDInitializer(UInt spatial_dimension, FEEngine & engine,
	ElementType foreground_type,
	const ElementTypeMapArray<UInt> & filter,
	GhostType ghost_type)
	: ElementTypeMapArrayInitializer(
	[](ElementType bgtype, GhostType /unused/) {
	return ShapeFunctions::getShapeDerivativesSize(bgtype);
	},
	spatial_dimension, ghost_type, _ek_regular) {
	auto nb_quad = engine.getNbIntegrationPoints(foreground_type);
	// Counting how many background elements are affected by elements of
	// interface_type
	for (auto type : filter.elementTypes(this->spatial_dimension)) {
	// Inserting size
	array_size_per_bg_type(filter(type).size() * nb_quad, type,
	this->ghost_type);
	}
	}

	auto elementTypes() const -> decltype(auto) {
	return array_size_per_bg_type.elementTypes();
	}

	UInt size(ElementType bgtype) const {
	return array_size_per_bg_type(bgtype, this->ghost_type);
	}

	protected:
	ElementTypeMap<UInt> array_size_per_bg_type;
	};
	} // namespace detail

	/**
	* Background shape derivatives need to be stored per background element
	* types but also per embedded element type, which is why they are stored
	* in an ElementTypeMap<ElementTypeMapArray<Real> *>. The outer ElementTypeMap
	* refers to the embedded types, and the inner refers to the background types.
	*/
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::allocBackgroundShapeDerivatives() {
	AKANTU_DEBUG_IN();

	for (auto gt : ghost_types) {
	for (auto && type : emodel.getInterfaceMesh().elementTypes(1, gt)) {
	std::string shaped_id = "embedded_shape_derivatives";
	if (gt == _ghost) {
	shaped_id += ":ghost";
	}

	auto & shaped_etma = shape_derivatives(
	std::make_unique<ElementTypeMapArray<Real>>(shaped_id, this->name),
	type, gt);
	shaped_etma->initialize(
	detail::BackgroundShapeDInitializer(
	emodel.getSpatialDimension(),
	emodel.getFEEngine("EmbeddedInterfaceFEEngine"), type,
	*background_filter(type, gt), gt),
	0, true);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::initBackgroundShapeDerivatives() {
	AKANTU_DEBUG_IN();

	for (auto interface_type :
	this->element_filter.elementTypes(this->spatial_dimension)) {
	for (auto type : background_filter(interface_type)->elementTypes(dim)) {
	computeBackgroundShapeDerivatives(interface_type, type, _not_ghost,
	this->element_filter(interface_type));
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::computeBackgroundShapeDerivatives(
	ElementType interface_type, ElementType bg_type, GhostType ghost_type,
	const Array<UInt> & filter) {
	auto & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");
	auto & engine = emodel.getFEEngine();
	auto & interface_mesh = emodel.getInterfaceMesh();

	const auto nb_nodes_elem_bg = Mesh::getNbNodesPerElement(bg_type);
	// const auto nb_strss = VoigtHelper<dim>::size;
	const auto nb_quads_per_elem =
	interface_engine.getNbIntegrationPoints(interface_type);

	Array<Real> quad_pos(0, dim, "interface_quad_pos");
	interface_engine.interpolateOnIntegrationPoints(interface_mesh.getNodes(),
	quad_pos, dim, interface_type,
	ghost_type, filter);
	auto & background_shapesd =
	(*shape_derivatives(interface_type, ghost_type))(bg_type, ghost_type);
	auto & background_elements =
	(*background_filter(interface_type, ghost_type))(bg_type, ghost_type);
	auto & foreground_elements =
	(*foreground_filter(interface_type, ghost_type))(bg_type, ghost_type);

	auto shapesd_begin =
	background_shapesd.begin(dim, nb_nodes_elem_bg, nb_quads_per_elem);
	auto quad_begin = quad_pos.begin(dim, nb_quads_per_elem);

	for (auto && tuple : zip(background_elements, foreground_elements)) {
	auto bg = std::get<0>(tuple);
	auto fg = std::get<1>(tuple);
	for (UInt i = 0; i < nb_quads_per_elem; ++i) {
	Matrix<Real> shapesd = Tensor3<Real>(shapesd_begin[fg])(i);
	Vector<Real> quads = Matrix<Real>(quad_begin[fg])(i);

	engine.computeShapeDerivatives(quads, bg, bg_type, shapesd, ghost_type);
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::initDirectingCosines() {
	AKANTU_DEBUG_IN();

	Mesh & mesh = emodel.getInterfaceMesh();

	const UInt voigt_size = VoigtHelper<dim>::size;
	directing_cosines.initialize(voigt_size);

	for (auto && type : mesh.elementTypes(1, _not_ghost)) {
	computeDirectingCosines(type, _not_ghost);
	// computeDirectingCosines(*type_it, _ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrix(
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & interface_mesh = emodel.getInterfaceMesh();

	for (auto && type : interface_mesh.elementTypes(1, _not_ghost)) {
	assembleStiffnessMatrix(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleInternalForces(
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & interface_mesh = emodel.getInterfaceMesh();

	for (auto && type : interface_mesh.elementTypes(1, _not_ghost)) {
	this->assembleInternalForces(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::computeAllStresses(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & interface_mesh = emodel.getInterfaceMesh();
	for (auto && type : interface_mesh.elementTypes(_ghost_type = ghost_type)) {
	computeGradU(type, ghost_type);
	this->computeStress(type, ghost_type);
	addPrestress(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::addPrestress(ElementType type,
	GhostType ghost_type) {
	auto & stress = this->stress(type, ghost_type);
	auto & sigma_p = this->pre_stress(type, ghost_type);

	for (auto && tuple : zip(stress, sigma_p)) {
	std::get<0>(tuple) += std::get<1>(tuple);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleInternalForces(
	ElementType type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & mesh = emodel.getMesh();

	for (auto && mesh_type : mesh.elementTypes(dim, ghost_type)) {
	assembleInternalForcesInterface(type, mesh_type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	/**
	* Computes and assemble the residual. Residual in reinforcement is computed as:
	*
	* \f[
	* \vec{r} = A_s \int_S{\mathbf{B}^T\mathbf{C}^T \vec{\sigma_s}\,\mathrm{d}s}
	* \f]
	*/
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleInternalForcesInterface(
	ElementType interface_type, ElementType background_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	UInt voigt_size = VoigtHelper<dim>::size;

	FEEngine & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");

	Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);

	UInt nodes_per_background_e = Mesh::getNbNodesPerElement(background_type);
	UInt nb_quadrature_points =
	interface_engine.getNbIntegrationPoints(interface_type, ghost_type);
	UInt nb_element = elem_filter.size();

	UInt back_dof = dim * nodes_per_background_e;

	Array<Real> & shapesd = (*shape_derivatives(interface_type, ghost_type))(
	background_type, ghost_type);

	Array<Real> integrant(nb_quadrature_points * nb_element, back_dof,
	"integrant");

	auto integrant_it = integrant.begin(back_dof);
	auto integrant_end = integrant.end(back_dof);

	Array<Real>::matrix_iterator B_it =
	shapesd.begin(dim, nodes_per_background_e);
	auto C_it = directing_cosines(interface_type, ghost_type).begin(voigt_size);

	auto sigma_it = this->stress(interface_type, ghost_type).begin();

	Matrix<Real> Bvoigt(voigt_size, back_dof);

	for (; integrant_it != integrant_end;
	++integrant_it, ++B_it, ++C_it, ++sigma_it) {
	VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*B_it, Bvoigt,
	nodes_per_background_e);
	Vector<Real> & C = *C_it;
	Vector<Real> & BtCt_sigma = *integrant_it;

	BtCt_sigma.mul<true>(Bvoigt, C);
	BtCt_sigma = sigma_it * area;
	}

	Array<Real> residual_interface(nb_element, back_dof, "residual_interface");
	interface_engine.integrate(integrant, residual_interface, back_dof,
	interface_type, ghost_type, elem_filter);
	integrant.resize(0);

	Array<UInt> background_filter(nb_element, 1, "background_filter");

	auto & filter =
	getBackgroundFilter(interface_type, background_type, ghost_type);

	emodel.getDOFManager().assembleElementalArrayLocalArray(
	residual_interface, emodel.getInternalForce(), background_type,
	ghost_type, -1., filter);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::computeDirectingCosines(
	ElementType type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & interface_mesh = emodel.getInterfaceMesh();

	const UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const UInt steel_dof = dim * nb_nodes_per_element;
	const UInt voigt_size = VoigtHelper<dim>::size;
	const UInt nb_quad_points = emodel.getFEEngine("EmbeddedInterfaceFEEngine")
	.getNbIntegrationPoints(type, ghost_type);

	Array<Real> node_coordinates(this->element_filter(type, ghost_type).size(),
	steel_dof);

	this->emodel.getFEEngine().template extractNodalToElementField<Real>(
	interface_mesh, interface_mesh.getNodes(), node_coordinates, type,
	ghost_type, this->element_filter(type, ghost_type));

	Array<Real>::matrix_iterator directing_cosines_it =
	directing_cosines(type, ghost_type).begin(1, voigt_size);

	Array<Real>::matrix_iterator node_coordinates_it =
	node_coordinates.begin(dim, nb_nodes_per_element);
	Array<Real>::matrix_iterator node_coordinates_end =
	node_coordinates.end(dim, nb_nodes_per_element);

	for (; node_coordinates_it != node_coordinates_end; ++node_coordinates_it) {
	for (UInt i = 0; i < nb_quad_points; i++, ++directing_cosines_it) {
	Matrix<Real> & nodes = *node_coordinates_it;
	Matrix<Real> & cosines = *directing_cosines_it;

	computeDirectingCosinesOnQuad(nodes, cosines);
	}
	}

	// Mauro: the directing_cosines internal is defined on the quadrature points
	// of each element

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrix(
	ElementType type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh & mesh = emodel.getMesh();

	for (auto && mesh_type : mesh.elementTypes(dim, ghost_type)) {
	assembleStiffnessMatrixInterface(type, mesh_type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Computes the reinforcement stiffness matrix (Gomes & Awruch, 2001)
	* \f[
	* \mathbf{K}_e = \sum_{i=1}^R{A_i\int_{S_i}{\mathbf{B}^T
	* \mathbf{C}_i^T \mathbf{D}_{s, i} \mathbf{C}_i \mathbf{B}\,\mathrm{d}s}}
	* \f]
	*/
	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrixInterface(
	ElementType interface_type, ElementType background_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	UInt voigt_size = VoigtHelper<dim>::size;

	FEEngine & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");

	Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);
	Array<Real> & grad_u = gradu_embedded(interface_type, ghost_type);

	UInt nb_element = elem_filter.size();
	UInt nodes_per_background_e = Mesh::getNbNodesPerElement(background_type);
	UInt nb_quadrature_points =
	interface_engine.getNbIntegrationPoints(interface_type, ghost_type);

	UInt back_dof = dim * nodes_per_background_e;

	UInt integrant_size = back_dof;

	grad_u.resize(nb_quadrature_points * nb_element);

	Array<Real> tangent_moduli(nb_element * nb_quadrature_points, 1,
	"interface_tangent_moduli");
	this->computeTangentModuli(interface_type, tangent_moduli, ghost_type);

	Array<Real> & shapesd = (*shape_derivatives(interface_type, ghost_type))(
	background_type, ghost_type);

	Array<Real> integrant(nb_element * nb_quadrature_points,
	integrant_size * integrant_size, "B^tC^tDCB");

	/// Temporary matrices for integrant product
	Matrix<Real> Bvoigt(voigt_size, back_dof);
	Matrix<Real> DCB(1, back_dof);
	Matrix<Real> CtDCB(voigt_size, back_dof);

	Array<Real>::scalar_iterator D_it = tangent_moduli.begin();
	Array<Real>::scalar_iterator D_end = tangent_moduli.end();

	Array<Real>::matrix_iterator C_it =
	directing_cosines(interface_type, ghost_type).begin(1, voigt_size);
	Array<Real>::matrix_iterator B_it =
	shapesd.begin(dim, nodes_per_background_e);
	Array<Real>::matrix_iterator integrant_it =
	integrant.begin(integrant_size, integrant_size);

	for (; D_it != D_end; ++D_it, ++C_it, ++B_it, ++integrant_it) {
	Real & D = *D_it;
	Matrix<Real> & C = *C_it;
	Matrix<Real> & B = *B_it;
	Matrix<Real> & BtCtDCB = *integrant_it;

	VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(B, Bvoigt,
	nodes_per_background_e);

	DCB.mul<false, false>(C, Bvoigt);
	DCB = D area;
	CtDCB.mul<true, false>(C, DCB);
	BtCtDCB.mul<true, false>(Bvoigt, CtDCB);
	}

	tangent_moduli.resize(0);

	Array<Real> K_interface(nb_element, integrant_size * integrant_size,
	"K_interface");
	interface_engine.integrate(integrant, K_interface,
	integrant_size * integrant_size, interface_type,
	ghost_type, elem_filter);

	integrant.resize(0);

	// Mauro: Here K_interface contains the local stiffness matrices,
	// directing_cosines contains the information about the orientation
	// of the reinforcements, any rotation of the local stiffness matrix
	// can be done here

	auto & filter =
	getBackgroundFilter(interface_type, background_type, ghost_type);

	emodel.getDOFManager().assembleElementalMatricesToMatrix(
	"K", "displacement", K_interface, background_type, ghost_type, _symmetric,
	filter);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Mat, UInt dim>
	Real MaterialReinforcement<Mat, dim>::getEnergy(const std::string & id) {
	AKANTU_DEBUG_IN();
	if (id == "potential") {
	Real epot = 0.;

	this->computePotentialEnergyByElements();

	for (auto && type :
	this->element_filter.elementTypes(this->spatial_dimension)) {
	FEEngine & interface_engine =
	emodel.getFEEngine("EmbeddedInterfaceFEEngine");
	epot += interface_engine.integrate(
	this->potential_energy(type, _not_ghost), type, _not_ghost,
	this->element_filter(type, _not_ghost));
	epot *= area;
	}

	return epot;
	}

	AKANTU_DEBUG_OUT();
	return 0;
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	void MaterialReinforcement<Mat, dim>::computeGradU(ElementType interface_type,
	GhostType ghost_type) {
	// Looping over background types
	for (auto && bg_type :
	background_filter(interface_type, ghost_type)->elementTypes(dim)) {

	const UInt nodes_per_background_e = Mesh::getNbNodesPerElement(bg_type);
	const UInt voigt_size = VoigtHelper<dim>::size;

	auto & bg_shapesd =
	(*shape_derivatives(interface_type, ghost_type))(bg_type, ghost_type);

	auto & filter = getBackgroundFilter(interface_type, bg_type, ghost_type);

	Array<Real> disp_per_element(0, dim * nodes_per_background_e, "disp_elem");

	FEEngine::extractNodalToElementField(
	emodel.getMesh(), emodel.getDisplacement(), disp_per_element, bg_type,
	ghost_type, filter);

	Matrix<Real> concrete_du(dim, dim);
	Matrix<Real> epsilon(dim, dim);
	Vector<Real> evoigt(voigt_size);

	for (auto && tuple :
	zip(make_view(disp_per_element, dim, nodes_per_background_e),
	make_view(bg_shapesd, dim, nodes_per_background_e),
	this->gradu(interface_type, ghost_type),
	make_view(this->directing_cosines(interface_type, ghost_type),
	voigt_size))) {
	auto & u = std::get<0>(tuple);
	auto & B = std::get<1>(tuple);
	auto & du = std::get<2>(tuple);
	auto & C = std::get<3>(tuple);

	concrete_du.mul<false, true>(u, B);
	auto epsilon = 0.5 * (concrete_du + concrete_du.transpose());
	strainTensorToVoigtVector(epsilon, evoigt);
	du = C.dot(evoigt);
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	/**
	* The structure of the directing cosines matrix is :
	* \f{eqnarray*}{
	* C_{1,\cdot} & = & (l^2, m^2, n^2, mn, ln, lm) \\
	* C_{i,j} & = & 0
	* \f}
	*
	* with :
	* \f[
	* (l, m, n) = \frac{1}{\\|\frac{\mathrm{d}\vec{r}(s)}{\mathrm{d}s}\\|} \cdot
	* \frac{\mathrm{d}\vec{r}(s)}{\mathrm{d}s}
	* \f]
	*/
	template <class Mat, UInt dim>
	inline void MaterialReinforcement<Mat, dim>::computeDirectingCosinesOnQuad(
	const Matrix<Real> & nodes, Matrix<Real> & cosines) {
	AKANTU_DEBUG_IN();
	AKANTU_DEBUG_ASSERT(nodes.cols() == 2,
	"Higher order reinforcement elements not implemented");

	const Vector<Real> a = nodes(0);
	const Vector<Real> b = nodes(1);
	Vector<Real> delta = b - a;

	Real sq_length = 0.;
	for (UInt i = 0; i < dim; i++) {
	sq_length += delta(i) * delta(i);
	}

	if (dim == 2) {
	cosines(0, 0) = delta(0) * delta(0); // l^2
	cosines(0, 1) = delta(1) * delta(1); // m^2
	cosines(0, 2) = delta(0) * delta(1); // lm
	} else if (dim == 3) {
	cosines(0, 0) = delta(0) * delta(0); // l^2
	cosines(0, 1) = delta(1) * delta(1); // m^2
	cosines(0, 2) = delta(2) * delta(2); // n^2

	cosines(0, 3) = delta(1) * delta(2); // mn
	cosines(0, 4) = delta(0) * delta(2); // ln
	cosines(0, 5) = delta(0) * delta(1); // lm
	}

	cosines /= sq_length;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	inline void MaterialReinforcement<Mat, dim>::stressTensorToVoigtVector(
	const Matrix<Real> & tensor, Vector<Real> & vector) {
	AKANTU_DEBUG_IN();

	for (UInt i = 0; i < dim; i++) {
	vector(i) = tensor(i, i);
	}

	if (dim == 2) {
	vector(2) = tensor(0, 1);
	} else if (dim == 3) {
	vector(3) = tensor(1, 2);
	vector(4) = tensor(0, 2);
	vector(5) = tensor(0, 1);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	template <class Mat, UInt dim>
	inline void MaterialReinforcement<Mat, dim>::strainTensorToVoigtVector(
	const Matrix<Real> & tensor, Vector<Real> & vector) {
	AKANTU_DEBUG_IN();

	for (UInt i = 0; i < dim; i++) {
	vector(i) = tensor(i, i);
	}

	if (dim == 2) {
	vector(2) = 2 * tensor(0, 1);
	} else if (dim == 3) {
	vector(3) = 2 * tensor(1, 2);
	vector(4) = 2 * tensor(0, 2);
	vector(5) = 2 * tensor(0, 1);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.cc b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.cc
	index d886085a2..1cba8b5f0 100644
	--- a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.cc
	+++ b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.cc
	@@ -1,275 +1,274 @@
	/**
	* @file material_neohookean.cc
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Apr 08 2013
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Specialization of the material class for finite deformation
	* neo-hookean material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_neohookean.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialNeohookean<spatial_dimension>::MaterialNeohookean(
	SolidMechanicsModel & model, const ID & id)
	: PlaneStressToolbox<spatial_dimension>(model, id) {
	AKANTU_DEBUG_IN();

	this->registerParam("E", E, Real(0.), _pat_parsable \| _pat_modifiable,
	"Young's modulus");
	this->registerParam("nu", nu, Real(0.5), _pat_parsable \| _pat_modifiable,
	"Poisson's ratio");
	this->registerParam("lambda", lambda, _pat_readable,
	"First Lamé coefficient");
	this->registerParam("mu", mu, _pat_readable, "Second Lamé coefficient");
	this->registerParam("kapa", kpa, _pat_readable, "Bulk coefficient");

	this->finite_deformation = true;
	this->initialize_third_axis_deformation = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialNeohookean<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();
	PlaneStressToolbox<spatial_dimension>::initMaterial();
	if (spatial_dimension == 1) {
	nu = 0.;
	}
	this->updateInternalParameters();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <> void MaterialNeohookean<2>::initMaterial() {
	AKANTU_DEBUG_IN();
	PlaneStressToolbox<2>::initMaterial();
	this->updateInternalParameters();

	if (this->plane_stress) {
	this->third_axis_deformation.setDefaultValue(1.);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialNeohookean<spatial_dimension>::updateInternalParameters() {
	lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
	mu = E / (2 * (1 + nu));

	kpa = lambda + 2. / 3. * mu;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialNeohookean<dim>::computeCauchyStressPlaneStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	PlaneStressToolbox<dim>::computeCauchyStressPlaneStress(el_type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void MaterialNeohookean<2>::computeCauchyStressPlaneStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto gradu_it = this->gradu(el_type, ghost_type).begin(2, 2);
	auto gradu_end = this->gradu(el_type, ghost_type).end(2, 2);
	auto piola_it = this->piola_kirchhoff_2(el_type, ghost_type).begin(2, 2);
	auto stress_it = this->stress(el_type, ghost_type).begin(2, 2);
	auto c33_it = this->third_axis_deformation(el_type, ghost_type).begin();

	for (; gradu_it != gradu_end; ++gradu_it, ++piola_it, ++stress_it, ++c33_it) {
	Matrix<Real> & grad_u = *gradu_it;
	Matrix<Real> & piola = *piola_it;
	Matrix<Real> & sigma = *stress_it;

	StoCauchy<2>(gradUToF<2>(grad_u), piola, sigma, *c33_it);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialNeohookean<dim>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	computeStressOnQuad(grad_u, sigma);
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void MaterialNeohookean<2>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	if (this->plane_stress) {
	PlaneStressToolbox<2>::computeStress(el_type, ghost_type);

	auto c33_it = this->third_axis_deformation(el_type, ghost_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	computeStressOnQuad(grad_u, sigma, *c33_it);
	++c33_it;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	} else {

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	computeStressOnQuad(grad_u, sigma);
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialNeohookean<dim>::computeThirdAxisDeformation(
	ElementType /el_type/, GhostType /ghost_type/) {}

	/* -------------------------------------------------------------------------- */
	template <>
	void MaterialNeohookean<2>::computeThirdAxisDeformation(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(this->plane_stress, "The third component of the strain "
	"can only be computed for 2D "
	"problems in Plane Stress!!");

	Array<Real>::scalar_iterator c33_it =
	this->third_axis_deformation(el_type, ghost_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);
	computeThirdAxisDeformationOnQuad(grad_u, *c33_it);
	++c33_it;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialNeohookean<spatial_dimension>::computePotentialEnergy(
	ElementType el_type) {
	AKANTU_DEBUG_IN();

	Material::computePotentialEnergy(el_type);

	Array<Real>::scalar_iterator epot = this->potential_energy(el_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	computePotentialEnergyOnQuad(grad_u, *epot);
	++epot;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialNeohookean<spatial_dimension>::computeTangentModuli(
	- __attribute__((unused)) ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ __attribute__((unused)) ElementType el_type, Array<Real> & tangent_matrix,
	__attribute__((unused)) GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	computeTangentModuliOnQuad(tangent, grad_u);
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void MaterialNeohookean<2>::computeTangentModuli(__attribute__((unused))
	ElementType el_type,
	Array<Real> & tangent_matrix,
	__attribute__((unused))
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	if (this->plane_stress) {
	PlaneStressToolbox<2>::computeStress(el_type, ghost_type);

	Array<Real>::const_scalar_iterator c33_it =
	this->third_axis_deformation(el_type, ghost_type).begin();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	computeTangentModuliOnQuad(tangent, grad_u, *c33_it);
	++c33_it;
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	} else {

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	computeTangentModuliOnQuad(tangent, grad_u);
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialNeohookean<spatial_dimension>::getPushWaveSpeed(
	__attribute__((unused)) const Element & element) const {
	return sqrt((this->lambda + 2 * this->mu) / this->rho);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialNeohookean<spatial_dimension>::getShearWaveSpeed(
	__attribute__((unused)) const Element & element) const {
	return sqrt(this->mu / this->rho);
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(neohookean, MaterialNeohookean);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.hh b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.hh
	index 3b9e1480d..de2b5bbf8 100644
	--- a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.hh
	+++ b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean.hh
	@@ -1,171 +1,168 @@
	/**
	* @file material_neohookean.hh
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Material isotropic elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "plane_stress_toolbox.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_NEOHOOKEAN_HH_
	#define AKANTU_MATERIAL_NEOHOOKEAN_HH_

	namespace akantu {

	/**
	* Material elastic isotropic
	*
	* parameters in the material files :
	* - rho : density (default: 0)
	* - E : Young's modulus (default: 0)
	* - nu : Poisson's ratio (default: 1/2)
	* - Plane_Stress : if 0: plane strain, else: plane stress (default: 0)
	*/
	template <UInt spatial_dimension>
	class MaterialNeohookean : public PlaneStressToolbox<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialNeohookean(SolidMechanicsModel & model, const ID & id = "");

	~MaterialNeohookean() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material computed parameter
	void initMaterial() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// Computation of the cauchy stress for plane strain materials
	void
	computeCauchyStressPlaneStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// Non linear computation of the third direction strain in 2D plane stress
	/// case
	void computeThirdAxisDeformation(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the elastic potential energy
	void computePotentialEnergy(ElementType el_type) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	/// compute the p-wave speed in the material
	Real getPushWaveSpeed(const Element & element) const override;

	/// compute the s-wave speed in the material
	Real getShearWaveSpeed(const Element & element) const override;

	- MatrixType getTangentType() override {
	- return _symmetric;
	- }
	+ MatrixType getTangentType() override { return _symmetric; }

	protected:
	/// constitutive law for a given quadrature point
	inline void computePiolaKirchhoffOnQuad(const Matrix<Real> & E,
	Matrix<Real> & S);

	/// constitutive law for a given quadrature point (first piola)
	inline void computeFirstPiolaKirchhoffOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & S,
	Matrix<Real> & P);

	/// constitutive law for a given quadrature point
	inline void computeDeltaStressOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & grad_delta_u,
	Matrix<Real> & delta_S);

	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & S,
	const Real & C33 = 1.0);

	/// constitutive law for a given quadrature point
	inline void computeThirdAxisDeformationOnQuad(Matrix<Real> & grad_u,
	Real & c33_value);

	/// constitutive law for a given quadrature point
	// inline void updateStressOnQuad(const Matrix<Real> & sigma,
	// Matrix<Real> & cauchy_sigma);

	/// compute the potential energy for a quadrature point
	inline void computePotentialEnergyOnQuad(const Matrix<Real> & grad_u,
	Real & epot);

	/// compute the tangent stiffness matrix for an element
	void computeTangentModuliOnQuad(Matrix<Real> & tangent, Matrix<Real> & grad_u,
	const Real & C33 = 1.0);

	/// recompute the lame coefficient if E or nu changes
	void updateInternalParameters() override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// the young modulus
	Real E;

	/// Poisson coefficient
	Real nu;

	/// First Lamé coefficient
	Real lambda;

	/// Second Lamé coefficient (shear modulus)
	Real mu;

	/// Bulk modulus
	Real kpa;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "material_neohookean_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_NEOHOOKEAN_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean_inline_impl.hh b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean_inline_impl.hh
	index 2c2375613..da9909112 100644
	--- a/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_finite_deformation/material_neohookean_inline_impl.hh
	@@ -1,200 +1,201 @@
	/**
	* @file material_neohookean_inline_impl.hh
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	*
	* @date creation: Mon Apr 08 2013
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of the material elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_neohookean.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <iostream>
	#include <utility>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computeDeltaStressOnQuad(
	__attribute__((unused)) const Matrix<Real> & grad_u,
	__attribute__((unused)) const Matrix<Real> & grad_delta_u,
	__attribute__((unused)) Matrix<Real> & delta_S) {}

	//! computes the second piola kirchhoff stress, called S
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computeStressOnQuad(Matrix<Real> & grad_u,
	Matrix<Real> & S,
	const Real & C33) {
	// Neo hookean book
	Matrix<Real> F(dim, dim);
	Matrix<Real> C(dim, dim); // Right green
	Matrix<Real> Cminus(dim, dim); // Right green

	this->template gradUToF<dim>(grad_u, F);
	this->rightCauchy(F, C);
	Real J = F.det() * sqrt(C33); // the term sqrt(C33) corresponds to the off
	// plane strain (2D plane stress)
	// std::cout<<"det(F) -> "<<J<<std::endl;
	Cminus.inverse(C);

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	- S(i, j) = Math::kronecker(i, j) * mu + (lambda * log(J) - mu) * Cminus(i, j);
	+ S(i, j) =
	+ Math::kronecker(i, j) * mu + (lambda * log(J) - mu) * Cminus(i, j);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	class C33_NR : public Math::NewtonRaphsonFunctor {
	public:
	C33_NR(std::string name, const Real & lambda, const Real & mu,
	const Matrix<Real> & C)
	: NewtonRaphsonFunctor(std::move(name)), lambda(lambda), mu(mu), C(C) {}

	inline Real f(Real x) const override {
	return (this->lambda / 2. *
	(std::log(x) + std::log(this->C(0, 0) * this->C(1, 1) -
	Math::pow<2>(this->C(0, 1)))) +
	this->mu * (x - 1.));
	}

	inline Real f_prime(Real x) const override {
	AKANTU_DEBUG_ASSERT(std::abs(x) > Math::getTolerance(),
	"x is zero (x should be the off plane right Cauchy"
	<< " measure in this function so you made a mistake"
	<< " somewhere else that lead to a zero here!!!");
	return (this->lambda / (2. * x) + this->mu);
	}

	private:
	const Real & lambda;
	const Real & mu;
	const Matrix<Real> & C;
	};

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computeThirdAxisDeformationOnQuad(
	Matrix<Real> & grad_u, Real & c33_value) {
	// Neo hookean book
	Matrix<Real> F(dim, dim);
	Matrix<Real> C(dim, dim); // Right green

	this->template gradUToF<dim>(grad_u, F);
	this->rightCauchy(F, C);

	Math::NewtonRaphson nr(1e-5, 100);
	c33_value = nr.solve(
	C33_NR("Neohookean_plan_stress", this->lambda, this->mu, C), c33_value);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void
	MaterialNeohookean<dim>::computePiolaKirchhoffOnQuad(const Matrix<Real> & E,
	Matrix<Real> & S) {

	Real trace = E.trace(); /// \f$ trace = (\nabla u)_{kk} \f$

	/// \f$ \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
	/// u_{ij} + \nabla u_{ji}) \f$
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	S(i, j) = Math::kronecker(i, j) * lambda * trace + 2.0 * mu * E(i, j);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computeFirstPiolaKirchhoffOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & S, Matrix<Real> & P) {

	Matrix<Real> F(dim, dim);
	Matrix<Real> C(dim, dim); // Right green

	this->template gradUToF<dim>(grad_u, F);

	// first Piola-Kirchhoff is computed as the product of the deformation
	// gracient
	// tensor and the second Piola-Kirchhoff stress tensor

	P = F * S;
	}

	/**************************************************************************************/
	/* Computation of the potential energy for a this neo hookean material */
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computePotentialEnergyOnQuad(
	const Matrix<Real> & grad_u, Real & epot) {
	Matrix<Real> F(dim, dim);
	Matrix<Real> C(dim, dim); // Right green

	this->template gradUToF<dim>(grad_u, F);
	this->rightCauchy(F, C);
	Real J = F.det();
	// std::cout<<"det(F) -> "<<J<<std::endl;

	epot =
	0.5 * lambda * pow(log(J), 2.) + mu * (-log(J) + 0.5 * (C.trace() - dim));
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialNeohookean<dim>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent, Matrix<Real> & grad_u, const Real & C33) {

	// Neo hookean book
	UInt cols = tangent.cols();
	UInt rows = tangent.rows();
	Matrix<Real> F(dim, dim);
	Matrix<Real> C(dim, dim);
	Matrix<Real> Cminus(dim, dim);
	this->template gradUToF<dim>(grad_u, F);
	this->rightCauchy(F, C);
	Real J = F.det() * sqrt(C33);
	// std::cout<<"det(F) -> "<<J<<std::endl;
	Cminus.inverse(C);

	for (UInt m = 0; m < rows; m++) {
	UInt i = VoigtHelper<dim>::vec[m][0];
	UInt j = VoigtHelper<dim>::vec[m][1];
	for (UInt n = 0; n < cols; n++) {
	UInt k = VoigtHelper<dim>::vec[n][0];
	UInt l = VoigtHelper<dim>::vec[n][1];

	// book belytchko
	tangent(m, n) = lambda * Cminus(i, j) * Cminus(k, l) +
	(mu - lambda * log(J)) * (Cminus(i, k) * Cminus(j, l) +
	Cminus(i, l) * Cminus(k, j));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_non_local.hh b/src/model/solid_mechanics/materials/material_non_local.hh
	index 60b4d8e23..a5239c9b4 100644
	--- a/src/model/solid_mechanics/materials/material_non_local.hh
	+++ b/src/model/solid_mechanics/materials/material_non_local.hh
	@@ -1,120 +1,119 @@
	/**
	* @file material_non_local.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material class that handle the non locality of a law for example
	* damage.
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_NON_LOCAL_HH_
	#define AKANTU_MATERIAL_NON_LOCAL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class MaterialNonLocalInterface {
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material the non local parts of the material
	void initMaterialNonLocal() {
	this->registerNeighborhood();
	this->registerNonLocalVariables();
	};

	/// insert the quadrature points in the neighborhoods of the non-local manager
	virtual void insertIntegrationPointsInNeighborhoods(
	GhostType ghost_type,
	const ElementTypeMapReal & quadrature_points_coordinates) = 0;

	/// update the values in the non-local internal fields
	virtual void updateNonLocalInternals(ElementTypeMapReal & non_local_flattened,
	const ID & field_id,
	GhostType ghost_type,
	ElementKind kind) = 0;
	/// constitutive law
	virtual void computeNonLocalStresses(GhostType ghost_type = _not_ghost) = 0;

	protected:
	/// get the name of the neighborhood for this material
	virtual ID getNeighborhoodName() = 0;

	/// register the neighborhoods for the material
	virtual void registerNeighborhood() = 0;

	/// register the non local internal variable
	virtual void registerNonLocalVariables() = 0;

	virtual inline void onElementsAdded(const Array<Element> & /unused/,
	const NewElementsEvent & /unused/) {}
	};
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <UInt dim, class LocalParent>
	class MaterialNonLocal : public MaterialNonLocalInterface, public LocalParent {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	explicit MaterialNonLocal(SolidMechanicsModel & model, const ID & id);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// insert the quadrature points in the neighborhoods of the non-local manager
	void insertIntegrationPointsInNeighborhoods(
	GhostType ghost_type,
	const ElementTypeMapReal & quadrature_points_coordinates) override;

	/// update the values in the non-local internal fields
	void updateNonLocalInternals(ElementTypeMapReal & non_local_flattened,
	- const ID & field_id,
	- GhostType ghost_type,
	+ const ID & field_id, GhostType ghost_type,
	ElementKind kind) override;

	/// register the neighborhoods for the material
	void registerNeighborhood() override;

	protected:
	/// get the name of the neighborhood for this material
	ID getNeighborhoodName() override { return this->name; }
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "material_non_local_tmpl.hh"

	#endif /* AKANTU_MATERIAL_NON_LOCAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_non_local_includes.hh b/src/model/solid_mechanics/materials/material_non_local_includes.hh
	index d21efc5b0..f2da04100 100644
	--- a/src/model/solid_mechanics/materials/material_non_local_includes.hh
	+++ b/src/model/solid_mechanics/materials/material_non_local_includes.hh
	@@ -1,42 +1,42 @@
	/**
	* @file material_non_local_includes.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 31 2012
	* @date last modification: Thu Dec 17 2020
	*
	* @brief Non local materials includes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_CMAKE_LIST_MATERIALS
	#include "material_marigo_non_local.hh"
	#include "material_mazars_non_local.hh"
	#include "material_von_mises_mazars_non_local.hh"
	#endif

	#define AKANTU_DAMAGE_NON_LOCAL_MATERIAL_LIST \
	((2, (marigo_non_local, MaterialMarigoNonLocal)))( \
	- (2, (mazars_non_local, MaterialMazarsNonLocal)))( \
	- (2, (von_mises_mazars_non_local, MaterialVonMisesMazarsNonLocal)))
	+ (2, (mazars_non_local, MaterialMazarsNonLocal)))( \
	+ (2, (von_mises_mazars_non_local, MaterialVonMisesMazarsNonLocal)))
	diff --git a/src/model/solid_mechanics/materials/material_non_local_tmpl.hh b/src/model/solid_mechanics/materials/material_non_local_tmpl.hh
	index 67cddbb15..6c033166f 100644
	--- a/src/model/solid_mechanics/materials/material_non_local_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/material_non_local_tmpl.hh
	@@ -1,129 +1,129 @@
	/**
	* @file material_non_local_tmpl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jul 06 2017
	* @date last modification: Fri Mar 26 2021
	*
	* @brief Implementation of material non-local
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	#include "material_non_local.hh"
	#include "non_local_neighborhood.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim, class LocalParent>
	MaterialNonLocal<dim, LocalParent>::MaterialNonLocal(
	SolidMechanicsModel & model, const ID & id)
	: LocalParent(model, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, class LocalParent>
	void MaterialNonLocal<dim, LocalParent>::insertIntegrationPointsInNeighborhoods(
	GhostType ghost_type,
	const ElementTypeMapReal & quadrature_points_coordinates) {

	IntegrationPoint q;
	q.ghost_type = ghost_type;

	auto & neighborhood = this->model.getNonLocalManager().getNeighborhood(
	this->getNeighborhoodName());

	for (auto & type :
	this->element_filter.elementTypes(dim, ghost_type, _ek_regular)) {
	q.type = type;
	const auto & elem_filter = this->element_filter(type, ghost_type);
	UInt nb_element = elem_filter.size();

	if (nb_element != 0U) {
	UInt nb_quad =
	this->getFEEngine().getNbIntegrationPoints(type, ghost_type);

	const auto & quads = quadrature_points_coordinates(type, ghost_type);

	auto nb_total_element =
	this->model.getMesh().getNbElement(type, ghost_type);
	auto quads_it = quads.begin_reinterpret(dim, nb_quad, nb_total_element);
	for (auto & elem : elem_filter) {
	Matrix<Real> quads = quads_it[elem];
	q.element = elem;
	for (UInt nq = 0; nq < nb_quad; ++nq) {
	q.num_point = nq;
	q.global_num = q.element * nb_quad + nq;
	neighborhood.insertIntegrationPoint(q, quads(nq));
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, class LocalParent>
	void MaterialNonLocal<dim, LocalParent>::updateNonLocalInternals(
	ElementTypeMapReal & non_local_flattened, const ID & field_id,
	GhostType ghost_type, ElementKind kind) {

	/// loop over all types in the material
	for (auto & el_type :
	this->element_filter.elementTypes(dim, ghost_type, kind)) {
	Array<Real> & internal =
	this->template getInternal<Real>(field_id)(el_type, ghost_type);

	auto & internal_flat = non_local_flattened(el_type, ghost_type);
	auto nb_component = internal_flat.getNbComponent();

	auto internal_it = internal.begin(nb_component);
	auto internal_flat_it = internal_flat.begin(nb_component);

	/// loop all elements for the given type
	const auto & filter = this->element_filter(el_type, ghost_type);
	UInt nb_quads =
	this->getFEEngine().getNbIntegrationPoints(el_type, ghost_type);
	for (auto & elem : filter) {
	for (UInt q = 0; q < nb_quads; ++q, ++internal_it) {
	UInt global_quad = elem * nb_quads + q;
	*internal_it = internal_flat_it[global_quad];
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim, class LocalParent>
	void MaterialNonLocal<dim, LocalParent>::registerNeighborhood() {
	ID name = this->getNeighborhoodName();
	this->model.getNonLocalManager().registerNeighborhood(name, name);
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.cc b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.cc
	index f0bb0ad1f..e110857cc 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.cc
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.cc
	@@ -1,195 +1,195 @@
	/**
	* @file material_drucker_prager.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Tue Apr 06 2021
	*
	* @brief Implementation of the akantu::MaterialDruckerPrager class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_drucker_prager.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	template <UInt spatial_dimension>
	MaterialDruckerPrager<spatial_dimension>::MaterialDruckerPrager(
	SolidMechanicsModel & model, const ID & id)
	: MaterialPlastic<spatial_dimension>(model, id) {

	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialDruckerPrager<spatial_dimension>::MaterialDruckerPrager(
	SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id)
	: MaterialPlastic<spatial_dimension>(model, dim, mesh, fe_engine, id) {

	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialDruckerPrager<spatial_dimension>::initialize() {
	this->registerParam("phi", phi, Real(0.), _pat_parsable \| _pat_modifiable,
	"Internal friction angle in degrees");
	this->registerParam("fc", fc, Real(1.), _pat_parsable \| _pat_modifiable,
	"Compressive strength");
	this->registerParam("radial_return", radial_return_mapping, bool(true),
	_pat_parsable \| _pat_modifiable, "Radial return mapping");

	this->updateInternalParameters();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialDruckerPrager<spatial_dimension>::updateInternalParameters() {
	MaterialElastic<spatial_dimension>::updateInternalParameters();

	// compute alpha and k parameters for Drucker-Prager
	Real phi_radian = this->phi * M_PI / 180.;
	this->alpha = (6. * sin(phi_radian)) / (3. - sin(phi_radian));
	Real cohesion = this->fc * (1. - sin(phi_radian)) / (2. * cos(phi_radian));
	this->k = (6. * cohesion * cos(phi_radian)) / (3. - sin(phi_radian));
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialDruckerPrager<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	MaterialThermal<spatial_dimension>::computeStress(el_type, ghost_type);
	// infinitesimal and finite deformation
	auto sigma_th_it = this->sigma_th(el_type, ghost_type).begin();

	auto previous_sigma_th_it =
	this->sigma_th.previous(el_type, ghost_type).begin();

	auto previous_gradu_it = this->gradu.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_stress_it = this->stress.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto inelastic_strain_it = this->inelastic_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_inelastic_strain_it =
	this->inelastic_strain.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	//
	// Finite Deformations
	//
	if (this->finite_deformation) {
	auto previous_piola_kirchhoff_2_it =
	this->piola_kirchhoff_2.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto green_strain_it = this->green_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_piola_kirchhoff_2_it;

	auto & green_strain = *green_strain_it;
	this->template gradUToE<spatial_dimension>(grad_u, green_strain);
	Matrix<Real> previous_green_strain(spatial_dimension, spatial_dimension);
	this->template gradUToE<spatial_dimension>(previous_grad_u,
	previous_green_strain);
	Matrix<Real> F_tensor(spatial_dimension, spatial_dimension);
	this->template gradUToF<spatial_dimension>(grad_u, F_tensor);

	computeStressOnQuad(green_strain, previous_green_strain, sigma,
	previous_sigma, inelastic_strain_tensor,
	previous_inelastic_strain_tensor, *sigma_th_it,
	*previous_sigma_th_it, F_tensor);

	++sigma_th_it;
	++inelastic_strain_it;
	++previous_sigma_th_it;
	//++previous_stress_it;
	++previous_gradu_it;
	++green_strain_it;
	++previous_inelastic_strain_it;
	++previous_piola_kirchhoff_2_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	}
	// Infinitesimal deformations
	else {
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_stress_it;

	computeStressOnQuad(
	grad_u, previous_grad_u, sigma, previous_sigma, inelastic_strain_tensor,
	previous_inelastic_strain_tensor, sigma_th_it, previous_sigma_th_it);
	++sigma_th_it;
	++inelastic_strain_it;
	++previous_sigma_th_it;
	++previous_stress_it;
	++previous_gradu_it;
	++previous_inelastic_strain_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	AKANTU_DEBUG_OUT();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialDruckerPrager<spatial_dimension>::computeTangentModuli(
	ElementType /el_type/, Array<Real> & /tangent_matrix/,
	GhostType /ghost_type/) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(plastic_drucker_prager, MaterialDruckerPrager);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.hh b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.hh
	index 0b4f6ed4b..228f4deae 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager.hh
	@@ -1,147 +1,141 @@
	/**
	* @file material_drucker_prager.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Apr 06 2021
	*
	* @brief Specialization of the material class for isotropic
	* plasticity with Drucker-Pruger yield criterion
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	#include "material_plastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_MATERIAL_DRUCKER_PRAGER_HH__
	#define __AKANTU_MATERIAL_DRUCKER_PRAGER_HH__

	namespace akantu {

	/**
	* Material plastic with a Drucker-pruger yield criterion
	*/
	-
	-template<UInt spatial_dimension>
	-class MaterialDruckerPrager
	- : public MaterialPlastic<spatial_dimension> {
	+
	+template <UInt spatial_dimension>
	+class MaterialDruckerPrager : public MaterialPlastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	- MaterialDruckerPrager(SolidMechanicsModel & model,
	- const ID & id = "");
	+ MaterialDruckerPrager(SolidMechanicsModel & model, const ID & id = "");
	MaterialDruckerPrager(SolidMechanicsModel & model, UInt dim,
	- const Mesh & mesh, FEEngine & fe_engine,
	- const ID & id = "");
	+ const Mesh & mesh, FEEngine & fe_engine,
	+ const ID & id = "");

	protected:
	using voigt_h = VoigtHelper<spatial_dimension>;
	-
	+
	void initialize();

	-
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// Infinitesimal deformations
	- inline void computeStressOnQuad(
	- const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	- Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	- Matrix<Real> & inelas_strain, const Matrix<Real> & previous_inelas_strain,
	- const Real & sigma_th, const Real & previous_sigma_th);
	+ inline void
	+ computeStressOnQuad(const Matrix<Real> & grad_u,
	+ const Matrix<Real> & previous_grad_u,
	+ Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	+ Matrix<Real> & inelastic_strain,
	+ const Matrix<Real> & previous_inelastic_strain,
	+ const Real & sigma_th, const Real & previous_sigma_th);

	/// Finite deformations
	inline void computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	- Matrix<Real> & inelas_strain, const Matrix<Real> & previous_inelas_strain,
	- const Real & sigma_th, const Real & previous_sigma_th,
	- const Matrix<Real> & F_tensor);
	+ Matrix<Real> & inelastic_strain,
	+ const Matrix<Real> & previous_inelastic_strain, const Real & sigma_th,
	+ const Real & previous_sigma_th, const Matrix<Real> & F_tensor);

	inline void computeTangentModuliOnQuad(
	Matrix<Real> & tangent, const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u, const Matrix<Real> & sigma_tensor,
	const Matrix<Real> & previous_sigma_tensor) const;

	inline Real computeYieldFunction(const Matrix<Real> & sigma);

	inline Real computeYieldStress(const Matrix<Real> & sigma);

	inline void computeDeviatoricStress(const Matrix<Real> & sigma,
	- Matrix<Real> & sigma_dev);
	+ Matrix<Real> & sigma_dev);

	/// rcompute the alpha and k parameters
	void updateInternalParameters() override;

	-
	public:
	// closet point projection method to compute stress state on the
	// yield surface
	inline void computeGradientAndPlasticMultplier(
	- const Matrix<Real> & sigma_tr, Real & plastic_multiplier_guess,
	+ const Matrix<Real> & sigma_tr, Real & plastic_multiplier_guess,
	Vector<Real> & gradient_f, Vector<Real> & delta_inelastic_strain,
	UInt max_iterations = 100, Real tolerance = 1e-10);

	-
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	// Internal friction angle of the material
	Real phi;

	// Compressive strength of the material
	Real fc;

	// modified friction angle for Drucker-Prager
	Real alpha;

	// modified compressive strength for Drucker-Prager
	Real k;

	// radial return mapping
	bool radial_return_mapping;
	};
	-
	-} // namespace akantu

	+} // namespace akantu

	#include "material_drucker_prager_inline_impl.hh"

	-
	#endif /__AKANTU_MATERIAL_DRUCKER_PRAGER_HH__ /
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager_inline_impl.hh b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager_inline_impl.hh
	index 553af07d5..125c71dbc 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_drucker_prager_inline_impl.hh
	@@ -1,470 +1,471 @@
	/**
	* @file material_drucker_prager_inline_impl.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sat Sep 12 2020
	* @date last modification: Tue Apr 06 2021
	*
	* @brief Implementation of the inline functions of the material
	* Drucker-Prager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "material_drucker_prager.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/// Deviatoric Stress
	-template<UInt dim>
	-inline void MaterialDruckerPrager<dim>::computeDeviatoricStress(const Matrix<Real> & sigma,
	- Matrix<Real> & sigma_dev){
	- for (UInt i = 0; i < dim; ++i)
	- for (UInt j = 0; j < dim; ++j)
	+template <UInt dim>
	+inline void
	+MaterialDruckerPrager<dim>::computeDeviatoricStress(const Matrix<Real> & sigma,
	+ Matrix<Real> & sigma_dev) {
	+ for (UInt i = 0; i < dim; ++i) {
	+ for (UInt j = 0; j < dim; ++j) {
	sigma_dev(i, j) = sigma(i, j);
	+ }
	+ }

	sigma_dev -= Matrix<Real>::eye(dim, sigma.trace() / dim);
	}

	/* -------------------------------------------------------------------------- */
	/// Yield Stress
	-template<UInt dim>
	-inline Real MaterialDruckerPrager<dim>::computeYieldStress(const Matrix<Real> &
	- sigma) {
	+template <UInt dim>
	+inline Real
	+MaterialDruckerPrager<dim>::computeYieldStress(const Matrix<Real> & sigma) {
	return this->alpha * sigma.trace() - this->k;
	}

	-
	-/* -------------------------------------------------------------------------- */
	+/* -------------------------------------------------------------------------- */
	/// Yield function
	-template<UInt dim>
	-inline Real MaterialDruckerPrager<dim>::computeYieldFunction(const Matrix<Real> &
	- sigma) {
	+template <UInt dim>
	+inline Real
	+MaterialDruckerPrager<dim>::computeYieldFunction(const Matrix<Real> & sigma) {
	Matrix<Real> sigma_dev(dim, dim, 0);
	this->computeDeviatoricStress(sigma, sigma_dev);
	-
	+
	// compute deviatoric invariant J2
	- Real j2 = (1./ 2.) * sigma_dev.doubleDot(sigma_dev);
	+ Real j2 = (1. / 2.) * sigma_dev.doubleDot(sigma_dev);
	Real sigma_dev_eff = std::sqrt(3. * j2);

	Real modified_yield_stress = computeYieldStress(sigma);

	return sigma_dev_eff + modified_yield_stress;
	}

	-/* -------------------------------------------------------------------------- */
	-template<UInt dim>
	+/* -------------------------------------------------------------------------- */
	+template <UInt dim>
	inline void MaterialDruckerPrager<dim>::computeGradientAndPlasticMultplier(
	- const Matrix<Real> & sigma_trial, Real & plastic_multiplier_guess,
	- Vector<Real> & gradient_f, Vector<Real> & delta_inelastic_strain,
	- UInt max_iterations,
	- Real tolerance) {
	+ const Matrix<Real> & sigma_trial, Real & plastic_multiplier_guess,
	+ Vector<Real> & gradient_f, Vector<Real> & delta_inelastic_strain,
	+ UInt max_iterations, Real tolerance) {

	UInt size = voigt_h::size;
	-
	+
	// guess stress state at each iteration, initial guess is the trial state
	Matrix<Real> sigma_guess(sigma_trial);

	- // plastic multiplier guess at each iteration, initial guess is zero
	+ // plastic multiplier guess at each iteration, initial guess is zero
	plastic_multiplier_guess = 0.;
	-
	+
	// gradient of yield surface in voigt notation
	gradient_f.zero();
	-
	- // plastic strain increment at each iteration
	+
	+ // plastic strain increment at each iteration
	delta_inelastic_strain.zero();
	-
	+
	// variation in sigma at each iteration
	Vector<Real> delta_sigma(size, 0.);
	-
	+
	// krocker delta vector in voigt notation
	Vector<Real> kronecker_delta(size, 0.);
	- for(auto i : arange(dim))
	+ for (auto i : arange(dim)) {
	kronecker_delta[i] = 1.;
	-
	+ }
	+
	// hessian matrix of yield surface
	Matrix<Real> hessian_f(size, size, 0.);

	// scaling matrix for computing gradient and hessian from voigt notation
	Matrix<Real> scaling_matrix(size, size, 0.);
	scaling_matrix.eye(1.);
	- for(auto i : arange(dim, size))
	- for(auto j : arange(dim, size))
	+ for (auto i : arange(dim, size)) {
	+ for (auto j : arange(dim, size)) {
	scaling_matrix(i, j) *= 2.;
	-
	+ }
	+ }
	+
	// elastic stifnness tensor
	Matrix<Real> De(size, size, 0.);
	MaterialElastic<dim>::computeTangentModuliOnQuad(De);

	// elastic compliance tensor
	Matrix<Real> Ce(size, size, 0.);
	Ce.inverse(De);
	-
	+
	// objective function to be computed
	Vector<Real> f(size, 0.);
	-
	+
	// yield function value at each iteration
	Real yield_function;

	// if sigma is above the threshold value
	auto above_threshold = [&sigma_guess](Real & k, Real & alpha) {
	Real I1 = sigma_guess.trace();

	- return I1 >= k/alpha;
	+ return I1 >= k / alpha;
	};

	-
	// to project stress state at origin of yield function if first
	// invariant is greater than the threshold
	- if(above_threshold(k, alpha) and this->alpha > 0) {
	+ if (above_threshold(k, alpha) and this->alpha > 0) {

	auto update_first_obj = [&sigma_guess]() {
	-
	- //const UInt dimension = sigma_guess.cols();
	+ // const UInt dimension = sigma_guess.cols();

	Matrix<Real> sigma_dev(dim, dim, 0);

	- for (UInt i = 0; i < dim; ++i)
	- for (UInt j = 0; j < dim; ++j)
	- sigma_dev(i, j) = sigma_guess(i, j);
	+ for (UInt i = 0; i < dim; ++i) {
	+ for (UInt j = 0; j < dim; ++j) {
	+ sigma_dev(i, j) = sigma_guess(i, j);
	+ }
	+ }

	sigma_dev -= Matrix<Real>::eye(dim, sigma_guess.trace() / dim);
	-
	- auto error = (1./2) *sigma_dev.doubleDot(sigma_dev);
	+
	+ auto error = (1. / 2) * sigma_dev.doubleDot(sigma_dev);
	return error;
	};

	-
	auto update_sec_obj = [&sigma_guess](Real & k, Real & alpha) {
	- auto error = alpha*sigma_guess.trace() - k;
	+ auto error = alpha * sigma_guess.trace() - k;
	return error;
	};

	-
	-
	auto projection_error = update_first_obj();
	-
	- while(tolerance < projection_error) {
	+
	+ while (tolerance < projection_error) {

	Matrix<Real> delta_sigma(dim, dim);

	Matrix<Real> jacobian(dim, dim);
	Matrix<Real> jacobian_inv(dim, dim);
	-
	+
	Matrix<Real> sigma_dev(dim, dim, 0);
	this->computeDeviatoricStress(sigma_guess, sigma_dev);

	jacobian_inv.inverse(sigma_dev);

	delta_sigma = -projection_error * jacobian_inv;
	sigma_guess += delta_sigma;
	projection_error = update_first_obj();
	}

	projection_error = update_sec_obj(k, alpha);

	- while(tolerance < projection_error) {
	+ while (tolerance < projection_error) {

	Matrix<Real> delta_sigma(dim, dim);
	Matrix<Real> jacobian(dim, dim);
	Matrix<Real> jacobian_inv(dim, dim);

	jacobian = this->alpha * Matrix<Real>::eye(dim, dim);
	jacobian_inv.inverse(jacobian);

	delta_sigma += -projection_error * jacobian_inv;
	sigma_guess += delta_sigma;
	projection_error = update_sec_obj(k, alpha);
	}

	auto delta_sigma_final = sigma_trial - sigma_guess;
	auto delta_sigma_voigt = voigt_h::matrixToVoigt(delta_sigma_final);
	-
	+
	delta_inelastic_strain.mul<false>(Ce, delta_sigma_voigt);

	return;
	}
	-
	+
	// lambda function to compute gradient of yield surface in voigt notation
	auto compute_gradient_f = [&sigma_guess, &scaling_matrix, &kronecker_delta,
	- &gradient_f](Real & alpha){
	+ &gradient_f](Real & alpha) {
	+ // const UInt dimension = sigma_guess.cols();

	- //const UInt dimension = sigma_guess.cols();
	-
	Matrix<Real> sigma_dev(dim, dim, 0);

	- for (UInt i = 0; i < dim; ++i)
	- for (UInt j = 0; j < dim; ++j)
	- sigma_dev(i, j) = sigma_guess(i, j);
	+ for (UInt i = 0; i < dim; ++i) {
	+ for (UInt j = 0; j < dim; ++j) {
	+ sigma_dev(i, j) = sigma_guess(i, j);
	+ }
	+ }

	sigma_dev -= Matrix<Real>::eye(dim, sigma_guess.trace() / dim);

	-
	Vector<Real> sigma_dev_voigt = voigt_h::matrixToVoigt(sigma_dev);

	// compute deviatoric invariant
	- Real j2 = (1./2.) * sigma_dev.doubleDot(sigma_dev);
	-
	- gradient_f.mul<false>(scaling_matrix, sigma_dev_voigt, 3./ (2. * std::sqrt(3. * j2)) );
	+ Real j2 = (1. / 2.) * sigma_dev.doubleDot(sigma_dev);
	+
	+ gradient_f.mul<false>(scaling_matrix, sigma_dev_voigt,
	+ 3. / (2. * std::sqrt(3. * j2)));
	gradient_f += alpha * kronecker_delta;
	};
	-
	+
	// lambda function to compute hessian matrix of yield surface
	- auto compute_hessian_f = [&sigma_guess, &hessian_f, &scaling_matrix,
	- &kronecker_delta](){
	-
	+ auto compute_hessian_f = [&sigma_guess, &hessian_f, &scaling_matrix,
	+ &kronecker_delta]() {
	Matrix<Real> sigma_dev(dim, dim, 0);
	-
	- for (UInt i = 0; i < dim; ++i)
	- for (UInt j = 0; j < dim; ++j)
	- sigma_dev(i, j) = sigma_guess(i, j);
	+
	+ for (UInt i = 0; i < dim; ++i) {
	+ for (UInt j = 0; j < dim; ++j) {
	+ sigma_dev(i, j) = sigma_guess(i, j);
	+ }
	+ }

	sigma_dev -= Matrix<Real>::eye(dim, sigma_guess.trace() / dim);

	auto sigma_dev_voigt = voigt_h::matrixToVoigt(sigma_dev);

	// compute deviatoric invariant J2
	- Real j2 = (1./2.) * sigma_dev.doubleDot(sigma_dev);
	+ Real j2 = (1. / 2.) * sigma_dev.doubleDot(sigma_dev);

	Vector<Real> temp(sigma_dev_voigt.size());
	temp.mul<false>(scaling_matrix, sigma_dev_voigt);

	Matrix<Real> id(kronecker_delta.size(), kronecker_delta.size());
	id.outerProduct(kronecker_delta, kronecker_delta);
	- id *= -1./3.;
	+ id *= -1. / 3.;
	id += Matrix<Real>::eye(kronecker_delta.size(), 1.);

	Matrix<Real> tmp3(kronecker_delta.size(), kronecker_delta.size());
	tmp3.mul<false, false>(scaling_matrix, id);
	hessian_f.outerProduct(temp, temp);
	- hessian_f = -9./(4. pow(3.*j2, 3./2.));
	- hessian_f += (3./(2.* pow(3.j2, 1./2.)))tmp3;
	+ hessian_f = -9. / (4. pow(3. * j2, 3. / 2.));
	+ hessian_f += (3. / (2. * pow(3. * j2, 1. / 2.))) * tmp3;
	};

	/* --------------------------- */
	/* init before iteration loop */
	/* --------------------------- */
	- auto update_f = [&f, &sigma_guess, &sigma_trial, &plastic_multiplier_guess, &Ce, &De,
	- &yield_function, &gradient_f, &delta_inelastic_strain,
	- &compute_gradient_f](Real & k, Real & alpha){
	-
	+ auto update_f = [&f, &sigma_guess, &sigma_trial, &plastic_multiplier_guess,
	+ &Ce, &De, &yield_function, &gradient_f,
	+ &delta_inelastic_strain,
	+ &compute_gradient_f](Real & k, Real & alpha) {
	// compute gradient
	compute_gradient_f(alpha);

	// compute yield function
	Matrix<Real> sigma_dev(dim, dim, 0);

	- for (UInt i = 0; i < dim; ++i)
	- for (UInt j = 0; j < dim; ++j)
	- sigma_dev(i, j) = sigma_guess(i, j);
	+ for (UInt i = 0; i < dim; ++i) {
	+ for (UInt j = 0; j < dim; ++j) {
	+ sigma_dev(i, j) = sigma_guess(i, j);
	+ }
	+ }

	sigma_dev -= Matrix<Real>::eye(dim, sigma_guess.trace() / dim);

	- Real j2 = (1./ 2.) * sigma_dev.doubleDot(sigma_dev);
	+ Real j2 = (1. / 2.) * sigma_dev.doubleDot(sigma_dev);
	Real sigma_dev_eff = std::sqrt(3. * j2);

	Real modified_yield_stress = alpha * sigma_guess.trace() - k;

	- yield_function = sigma_dev_eff + modified_yield_stress;
	-
	+ yield_function = sigma_dev_eff + modified_yield_stress;
	+
	// compute increment strain
	auto sigma_trial_voigt = voigt_h::matrixToVoigt(sigma_trial);
	auto sigma_guess_voigt = voigt_h::matrixToVoigt(sigma_guess);
	auto tmp = sigma_trial_voigt - sigma_guess_voigt;
	delta_inelastic_strain.mul<false>(Ce, tmp);

	- // compute objective function
	+ // compute objective function
	f.mul<false>(De, gradient_f, plastic_multiplier_guess);
	- f = tmp - f;
	-
	+ f = tmp - f;
	+
	// compute error
	auto error = std::max(f.norm<L_2>(), std::abs(yield_function));
	return error;
	};

	Real alpha_tmp{alpha};
	Real k_tmp{k};
	- if(radial_return_mapping){
	+ if (radial_return_mapping) {
	alpha_tmp = 0;
	- k_tmp = std::abs(alpha*sigma_guess.trace() - k);
	+ k_tmp = std::abs(alpha * sigma_guess.trace() - k);
	}
	-
	- auto projection_error = update_f(k_tmp , alpha_tmp);
	-
	+
	+ auto projection_error = update_f(k_tmp, alpha_tmp);
	+
	/* --------------------------- */
	/* iteration loop */
	/* --------------------------- */

	Matrix<Real> xi(size, size);

	Matrix<Real> xi_inv(size, size);

	Vector<Real> tmp(size);

	Vector<Real> tmp1(size);

	Matrix<Real> tmp2(size, size);
	-
	+
	UInt iterations{0};
	- while(tolerance < projection_error and iterations < max_iterations) {
	-
	+ while (tolerance < projection_error and iterations < max_iterations) {
	+
	// compute hessian at previous step
	compute_hessian_f();

	- // compute inverse matrix Xi
	+ // compute inverse matrix Xi
	xi = Ce + plastic_multiplier_guess * hessian_f;

	// compute inverse matrix Xi
	xi_inv.inverse(xi);
	-
	+
	tmp.mul<false>(xi_inv, gradient_f);

	auto denominator = gradient_f.dot(tmp);
	-
	+
	// compute plastic multplier guess
	-
	+
	tmp1.mul<false>(xi_inv, delta_inelastic_strain);
	plastic_multiplier_guess = gradient_f.dot(tmp1);
	plastic_multiplier_guess += yield_function;
	plastic_multiplier_guess /= denominator;

	- // compute delta sigma
	-
	+ // compute delta sigma
	+
	tmp2.outerProduct(tmp, tmp);
	tmp2 /= denominator;

	tmp2 = xi_inv - tmp2;
	delta_sigma.mul<false>(tmp2, delta_inelastic_strain);

	- delta_sigma -= tmp*yield_function/denominator;
	+ delta_sigma -= tmp * yield_function / denominator;

	// compute sigma_guess
	Matrix<Real> delta_sigma_mat(dim, dim);
	voigt_h::voigtToMatrix(delta_sigma, delta_sigma_mat);
	sigma_guess += delta_sigma_mat;

	projection_error = update_f(k_tmp, alpha_tmp);
	iterations++;
	}
	}

	-/* -------------------------------------------------------------------------- */
	+/* -------------------------------------------------------------------------- */
	/// Infinitesimal deformations
	template <UInt dim>
	inline void MaterialDruckerPrager<dim>::computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	- Matrix<Real> & inelastic_strain, const Matrix<Real> & previous_inelastic_strain,
	- const Real & sigma_th, const Real & previous_sigma_th) {
	-
	+ Matrix<Real> & inelastic_strain,
	+ const Matrix<Real> & previous_inelastic_strain, const Real & sigma_th,
	+ const Real & previous_sigma_th) {
	+
	Real delta_sigma_th = sigma_th - previous_sigma_th;

	Matrix<Real> grad_delta_u(grad_u);
	grad_delta_u -= previous_grad_u;

	// Compute trial stress, sigma_tr
	Matrix<Real> sigma_tr(dim, dim);
	MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr,
	delta_sigma_th);
	sigma_tr += previous_sigma;

	// Compute the yielding sress
	/*Real yield_stress = computeYieldStress(sigma_tr);
	-
	+
	Matrix<Real> sigma_tr_dev(dim, dim, 0);
	this->computeDeviatoricStress(sigma_tr, sigma_tr_dev);
	-
	+
	Real j2 = (1./ 2.) * sigma_tr_dev.doubleDot(sigma_tr_dev);
	Real sigma_tr_dev_eff = std::sqrt(3. * j2);
	-
	+
	bool initial_yielding = ((sigma_tr_dev_eff + yield_stress) > 0);*/
	-
	- bool initial_yielding =
	- (this->computeYieldFunction(sigma_tr) > 0);
	+
	+ bool initial_yielding = (this->computeYieldFunction(sigma_tr) > 0);

	// use closet point projection to compute the plastic multiplier and
	- // gradient and inealstic strain at the surface for the given trial stress state
	+ // gradient and inealstic strain at the surface for the given trial stress
	+ // state
	Matrix<Real> delta_inelastic_strain(dim, dim, 0.);

	- if(initial_yielding) {
	+ if (initial_yielding) {

	UInt size = voigt_h::size;

	// plastic multiplier
	Real dp{0.};

	// gradient of yield surface in voigt notation
	Vector<Real> gradient_f(size, 0.);

	// inelastic strain in voigt notation
	Vector<Real> delta_inelastic_strain_voigt(size, 0.);

	// compute using closet-point projection
	this->computeGradientAndPlasticMultplier(sigma_tr, dp, gradient_f,
	- delta_inelastic_strain_voigt);
	+ delta_inelastic_strain_voigt);

	- for(auto i: arange(dim, size))
	+ for (auto i : arange(dim, size)) {
	delta_inelastic_strain_voigt[i] /= 2.;
	-
	+ }
	+
	voigt_h::voigtToMatrix(delta_inelastic_strain_voigt,
	- delta_inelastic_strain);
	+ delta_inelastic_strain);
	}
	-

	// Compute the increment in inelastic strain

	MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
	grad_delta_u, sigma, previous_sigma, inelastic_strain,
	previous_inelastic_strain, delta_inelastic_strain);
	}

	/* -------------------------------------------------------------------------- */
	/// Finite deformations
	template <UInt dim>
	inline void MaterialDruckerPrager<dim>::computeStressOnQuad(
	__attribute__((unused)) const Matrix<Real> & grad_u,
	__attribute__((unused)) const Matrix<Real> & previous_grad_u,
	__attribute__((unused)) Matrix<Real> & sigma,
	__attribute__((unused)) const Matrix<Real> & previous_sigma,
	__attribute__((unused)) Matrix<Real> & inelastic_strain,
	__attribute__((unused)) const Matrix<Real> & previous_inelastic_strain,
	__attribute__((unused)) const Real & sigma_th,
	__attribute__((unused)) const Real & previous_sigma_th,
	- __attribute__((unused)) const Matrix<Real> & F_tensor) {
	-
	-
	-}
	+ __attribute__((unused)) const Matrix<Real> & F_tensor) {}

	/* -------------------------------------------------------------------------- */

	template <UInt dim>
	inline void MaterialDruckerPrager<dim>::computeTangentModuliOnQuad(
	__attribute__((unused)) Matrix<Real> & tangent,
	__attribute__((unused)) const Matrix<Real> & grad_u,
	__attribute__((unused)) const Matrix<Real> & previous_grad_u,
	__attribute__((unused)) const Matrix<Real> & sigma_tensor,
	- __attribute__((unused)) const Matrix<Real> & previous_sigma_tensor) const {
	+ __attribute__((unused)) const Matrix<Real> & previous_sigma_tensor) const {}

	-}
	-
	-}
	+} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.cc b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.cc
	index afeb80be3..610229436 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.cc
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.cc
	@@ -1,205 +1,204 @@
	/**
	* @file material_linear_isotropic_hardening.cc
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Benjamin Paccaud <benjamin.paccaud@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Specialization of the material class for isotropic finite deformation
	* linear hardening plasticity
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_linear_isotropic_hardening.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialLinearIsotropicHardening<dim>::MaterialLinearIsotropicHardening(
	SolidMechanicsModel & model, const ID & id)
	: MaterialPlastic<dim>(model, id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialLinearIsotropicHardening<spatial_dimension>::
	MaterialLinearIsotropicHardening(SolidMechanicsModel & model, UInt dim,
	const Mesh & mesh, FEEngine & fe_engine,
	const ID & id)
	: MaterialPlastic<spatial_dimension>(model, dim, mesh, fe_engine, id) {}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialLinearIsotropicHardening<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// NOLINTNEXTLINE(bugprone-parent-virtual-call)
	MaterialThermal<spatial_dimension>::computeStress(el_type, ghost_type);

	// infinitesimal and finite deformation
	auto sigma_th_it = this->sigma_th(el_type, ghost_type).begin();

	auto previous_sigma_th_it =
	this->sigma_th.previous(el_type, ghost_type).begin();

	auto previous_gradu_it = this->gradu.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_stress_it = this->stress.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto inelastic_strain_it = this->inelastic_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_inelastic_strain_it =
	this->inelastic_strain.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto iso_hardening_it = this->iso_hardening(el_type, ghost_type).begin();

	auto previous_iso_hardening_it =
	this->iso_hardening.previous(el_type, ghost_type).begin();

	//
	// Finite Deformations
	//
	if (this->finite_deformation) {
	auto previous_piola_kirchhoff_2_it =
	this->piola_kirchhoff_2.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto green_strain_it = this->green_strain(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_piola_kirchhoff_2_it;

	auto & green_strain = *green_strain_it;
	this->template gradUToE<spatial_dimension>(grad_u, green_strain);
	Matrix<Real> previous_green_strain(spatial_dimension, spatial_dimension);
	this->template gradUToE<spatial_dimension>(previous_grad_u,
	- previous_green_strain);
	+ previous_green_strain);
	Matrix<Real> F_tensor(spatial_dimension, spatial_dimension);
	this->template gradUToF<spatial_dimension>(grad_u, F_tensor);

	computeStressOnQuad(green_strain, previous_green_strain, sigma,
	previous_sigma, inelastic_strain_tensor,
	previous_inelastic_strain_tensor, *iso_hardening_it,
	previous_iso_hardening_it, sigma_th_it,
	*previous_sigma_th_it, F_tensor);

	++sigma_th_it;
	++inelastic_strain_it;
	++iso_hardening_it;
	++previous_sigma_th_it;
	//++previous_stress_it;
	++previous_gradu_it;
	++green_strain_it;
	++previous_inelastic_strain_it;
	++previous_iso_hardening_it;
	++previous_piola_kirchhoff_2_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	}
	// Infinitesimal deformations
	else {
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	auto & inelastic_strain_tensor = *inelastic_strain_it;
	auto & previous_inelastic_strain_tensor = *previous_inelastic_strain_it;
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_stress_it;

	computeStressOnQuad(
	grad_u, previous_grad_u, sigma, previous_sigma, inelastic_strain_tensor,
	previous_inelastic_strain_tensor, *iso_hardening_it,
	previous_iso_hardening_it, sigma_th_it, *previous_sigma_th_it);
	++sigma_th_it;
	++inelastic_strain_it;
	++iso_hardening_it;
	++previous_sigma_th_it;
	++previous_stress_it;
	++previous_gradu_it;
	++previous_inelastic_strain_it;
	++previous_iso_hardening_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialLinearIsotropicHardening<spatial_dimension>::computeTangentModuli(
	- ElementType el_type, Array<Real> & tangent_matrix,
	- GhostType ghost_type) {
	+ ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto previous_gradu_it = this->gradu.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_stress_it = this->stress.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto iso_hardening = this->iso_hardening(el_type, ghost_type).begin();

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);

	computeTangentModuliOnQuad(tangent, grad_u, *previous_gradu_it, sigma,
	previous_stress_it, iso_hardening);

	++previous_gradu_it;
	++previous_stress_it;
	++iso_hardening;

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	this->was_stiffness_assembled = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(plastic_linear_isotropic_hardening,
	MaterialLinearIsotropicHardening);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.hh b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.hh
	index bd330ea7c..ca0eba853 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening.hh
	@@ -1,116 +1,115 @@
	/**
	* @file material_linear_isotropic_hardening.hh
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Benjamin Paccaud <benjamin.paccaud@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Specialization of the material class for isotropic finite deformation
	* linear hardening plasticity
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	#include "material_plastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_LINEAR_ISOTROPIC_HARDENING_HH_
	#define AKANTU_MATERIAL_LINEAR_ISOTROPIC_HARDENING_HH_

	namespace akantu {

	/**
	* Material plastic with a linear evolution of the yielding stress
	*/
	template <UInt spatial_dimension>
	class MaterialLinearIsotropicHardening
	: public MaterialPlastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialLinearIsotropicHardening(SolidMechanicsModel & model,
	const ID & id = "");
	MaterialLinearIsotropicHardening(SolidMechanicsModel & model, UInt dim,
	const Mesh & mesh, FEEngine & fe_engine,
	const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// Infinitesimal deformations
	inline void
	computeStressOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	Real & iso_hardening, const Real & previous_iso_hardening,
	const Real & sigma_th, const Real & previous_sigma_th);
	/// Finite deformations
	inline void computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain, Real & iso_hardening,
	const Real & previous_iso_hardening, const Real & sigma_th,
	const Real & previous_sigma_th, const Matrix<Real> & F_tensor);

	inline void computeTangentModuliOnQuad(
	Matrix<Real> & tangent, const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u, const Matrix<Real> & sigma_tensor,
	const Matrix<Real> & previous_sigma_tensor,
	const Real & iso_hardening) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};
	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "material_linear_isotropic_hardening_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_LINEAR_ISOTROPIC_HARDENING_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening_inline_impl.hh b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening_inline_impl.hh
	index d5ae4a2a9..ce203ae52 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_linear_isotropic_hardening_inline_impl.hh
	@@ -1,302 +1,302 @@
	/**
	* @file material_linear_isotropic_hardening_inline_impl.hh
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Benjamin Paccaud <benjamin.paccaud@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of the material plasticity
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "material_linear_isotropic_hardening.hh"

	namespace akantu {
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/// Infinitesimal deformations
	template <UInt dim>
	inline void MaterialLinearIsotropicHardening<dim>::computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain, Real & iso_hardening,
	const Real & previous_iso_hardening, const Real & sigma_th,
	const Real & previous_sigma_th) {

	Real delta_sigma_th = sigma_th - previous_sigma_th;

	Matrix<Real> grad_delta_u(grad_u);
	grad_delta_u -= previous_grad_u;

	// Compute trial stress, sigma_tr
	Matrix<Real> sigma_tr(dim, dim);
	MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr,
	delta_sigma_th);
	sigma_tr += previous_sigma;

	// We need a full stress tensor, otherwise the VM stress is messed up
	Matrix<Real> sigma_tr_dev(3, 3, 0);
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	sigma_tr_dev(i, j) = sigma_tr(i, j);
	}
	}

	sigma_tr_dev -= Matrix<Real>::eye(3, sigma_tr.trace() / 3.0);

	// Compute effective deviatoric trial stress
	Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
	Real sigma_tr_dev_eff = std::sqrt(3. / 2. * s);

	bool initial_yielding =
	((sigma_tr_dev_eff - iso_hardening - this->sigma_y) > 0);

	Real dp = (initial_yielding)
	? (sigma_tr_dev_eff - this->sigma_y - previous_iso_hardening) /
	(3 * this->mu + this->h)
	: 0;

	iso_hardening = previous_iso_hardening + this->h * dp;

	// Compute inelastic strain (ignore last components in 1-2D)
	Matrix<Real> delta_inelastic_strain(dim, dim, 0.);
	if (std::abs(sigma_tr_dev_eff) >
	sigma_tr_dev.norm<L_inf>() * Math::getTolerance()) {
	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	delta_inelastic_strain(i, j) = sigma_tr_dev(i, j);
	}
	}
	delta_inelastic_strain = 3. / 2. dp / sigma_tr_dev_eff;
	}

	MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
	grad_delta_u, sigma, previous_sigma, inelastic_strain,
	previous_inelastic_strain, delta_inelastic_strain);
	}

	/* -------------------------------------------------------------------------- */
	/// Finite deformations
	template <UInt dim>
	inline void MaterialLinearIsotropicHardening<dim>::computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain, Real & iso_hardening,
	const Real & previous_iso_hardening, const Real & sigma_th,
	const Real & previous_sigma_th, const Matrix<Real> & F_tensor) {
	// Finite plasticity
	Real dp = 0.0;
	Real d_dp = 0.0;
	UInt n = 0;

	Real delta_sigma_th = sigma_th - previous_sigma_th;

	Matrix<Real> grad_delta_u(grad_u);
	grad_delta_u -= previous_grad_u;

	// Compute trial stress, sigma_tr
	Matrix<Real> sigma_tr(dim, dim);
	MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr,
	delta_sigma_th);
	sigma_tr += previous_sigma;

	// Compute deviatoric trial stress, sigma_tr_dev
	Matrix<Real> sigma_tr_dev(sigma_tr);
	sigma_tr_dev -= Matrix<Real>::eye(dim, sigma_tr.trace() / 3.0);

	// Compute effective deviatoric trial stress
	Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
	Real sigma_tr_dev_eff = std::sqrt(3. / 2. * s);

	// compute the cauchy stress to apply the Von-Mises criterion
	Matrix<Real> cauchy_stress(dim, dim);
	Material::StoCauchy<dim>(F_tensor, sigma_tr, cauchy_stress);
	Matrix<Real> cauchy_stress_dev(cauchy_stress);
	cauchy_stress_dev -= Matrix<Real>::eye(dim, cauchy_stress.trace() / 3.0);
	Real c = cauchy_stress_dev.doubleDot(cauchy_stress_dev);
	Real cauchy_stress_dev_eff = std::sqrt(3. / 2. * c);

	const Real iso_hardening_t = previous_iso_hardening;
	iso_hardening = iso_hardening_t;
	// Loop for correcting stress based on yield function

	// F is written in terms of S
	// bool initial_yielding = ( (sigma_tr_dev_eff - iso_hardening -
	// this->sigma_y) > 0) ;
	// while ( initial_yielding && std::abs(sigma_tr_dev_eff - iso_hardening -
	// this->sigma_y) > Math::getTolerance() ) {

	// d_dp = (sigma_tr_dev_eff - 3. * this->mu *dp - iso_hardening -
	// this->sigma_y)
	// / (3. * this->mu + this->h);

	// //r = r + h * dp;
	// dp = dp + d_dp;
	// iso_hardening = iso_hardening_t + this->h * dp;

	// ++n;

	// /// TODO : explicit this criterion with an error message
	// if ((std::abs(d_dp) < 1e-9) \|\| (n>50)){
	// AKANTU_DEBUG_INFO("convergence of increment of plastic strain. d_dp:"
	// << d_dp << "\tNumber of iteration:"<<n);
	// break;
	// }
	// }

	// F is written in terms of cauchy stress
	bool initial_yielding =
	((cauchy_stress_dev_eff - iso_hardening - this->sigma_y) > 0);
	while (initial_yielding && std::abs(cauchy_stress_dev_eff - iso_hardening -
	this->sigma_y) > Math::getTolerance()) {

	d_dp = (cauchy_stress_dev_eff - 3. * this->mu * dp - iso_hardening -
	this->sigma_y) /
	(3. * this->mu + this->h);

	// r = r + h * dp;
	dp = dp + d_dp;
	iso_hardening = iso_hardening_t + this->h * dp;

	++n;
	/// TODO : explicit this criterion with an error message
	if ((d_dp < 1e-5) \|\| (n > 50)) {
	AKANTU_DEBUG_INFO("convergence of increment of plastic strain. d_dp:"
	<< d_dp << "\tNumber of iteration:" << n);
	break;
	}
	}

	// Update internal variable
	Matrix<Real> delta_inelastic_strain(dim, dim, 0.);
	if (std::abs(sigma_tr_dev_eff) >
	sigma_tr_dev.norm<L_inf>() * Math::getTolerance()) {

	// /// compute the direction of the plastic strain as \frac{\partial
	// F}{\partial S} = \frac{3}{2J\sigma_{effective}}} Ft \sigma_{dev} F
	Matrix<Real> cauchy_dev_F(dim, dim);
	cauchy_dev_F.mul<false, false>(F_tensor, cauchy_stress_dev);
	Real J = F_tensor.det();
	Real constant = not Math::are_float_equal(J, 0.) ? 1. / J : 0;
	constant = 3. dp / (2. * cauchy_stress_dev_eff);
	delta_inelastic_strain.mul<true, false>(F_tensor, cauchy_dev_F, constant);

	// Direction given by the piola kirchhoff deviatoric tensor \frac{\partial
	// F}{\partial S} = \frac{3}{2\sigma_{effective}}}S_{dev}
	// delta_inelastic_strain.copy(sigma_tr_dev);
	// delta_inelastic_strain = 3./2. dp / sigma_tr_dev_eff;
	}

	MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
	grad_delta_u, sigma, previous_sigma, inelastic_strain,
	previous_inelastic_strain, delta_inelastic_strain);
	}

	/* -------------------------------------------------------------------------- */

	template <UInt dim>
	inline void MaterialLinearIsotropicHardening<dim>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent, __attribute__((unused)) const Matrix<Real> & grad_u,
	__attribute__((unused)) const Matrix<Real> & previous_grad_u,
	__attribute__((unused)) const Matrix<Real> & sigma_tensor,
	__attribute__((unused)) const Matrix<Real> & previous_sigma_tensor,
	__attribute__((unused)) const Real & iso_hardening) const {
	// Real r=iso_hardening;

	// Matrix<Real> grad_delta_u(grad_u);
	// grad_delta_u -= previous_grad_u;

	// //Compute trial stress, sigma_tr
	// Matrix<Real> sigma_tr(dim, dim);
	// MaterialElastic<dim>::computeStressOnQuad(grad_delta_u, sigma_tr);
	// sigma_tr += previous_sigma_tensor;

	// // Compute deviatoric trial stress, sigma_tr_dev
	// Matrix<Real> sigma_tr_dev(sigma_tr);
	// sigma_tr_dev -= Matrix<Real>::eye(dim, sigma_tr.trace() / 3.0);

	// // Compute effective deviatoric trial stress
	// Real s = sigma_tr_dev.doubleDot(sigma_tr_dev);
	// Real sigma_tr_dev_eff=std::sqrt(3./2. * s);

	// // Compute deviatoric stress, sigma_dev
	// Matrix<Real> sigma_dev(sigma_tensor);
	// sigma_dev -= Matrix<Real>::eye(dim, sigma_tensor.trace() / 3.0);

	// // Compute effective deviatoric stress
	// s = sigma_dev.doubleDot(sigma_dev);
	// Real sigma_dev_eff = std::sqrt(3./2. * s);

	// Real xr = 0.0;
	// if(sigma_tr_dev_eff > sigma_dev_eff * Math::getTolerance())
	// xr = sigma_dev_eff / sigma_tr_dev_eff;

	// Real __attribute__((unused)) q = 1.5 * (1. / (1. + 3. * this->mu /
	// this->h) - xr);

	/*
	UInt cols = tangent.cols();
	UInt rows = tangent.rows();

	for (UInt m = 0; m < rows; ++m) {
	UInt i = VoigtHelper<dim>::vec[m][0];
	UInt j = VoigtHelper<dim>::vec[m][1];

	for (UInt n = 0; n < cols; ++n) {
	UInt k = VoigtHelper<dim>::vec[n][0];
	UInt l = VoigtHelper<dim>::vec[n][1];
	*/

	// This section of the code is commented
	// There were some problems with the convergence of plastic-coupled
	// simulations with thermal expansion
	// XXX: DO NOT REMOVE
	/*if (((sigma_tr_dev_eff-iso_hardening-sigmay) > 0) && (xr > 0)) {
	tangent(m,n) =
	2. * this->mu * q * (sigma_tr_dev (i,j) / sigma_tr_dev_eff) * (sigma_tr_dev
	(k,l) / sigma_tr_dev_eff) +
	(i==k) * (j==l) * 2. * this->mu * xr +
	(i==j) * (k==l) * (this->kpa - 2./3. * this->mu * xr);
	if ((m == n) && (m>=dim))
	tangent(m, n) = tangent(m, n) - this->mu * xr;
	} else {*/
	/*
	tangent(m,n) = (i==k) * (j==l) * 2. * this->mu +
	(i==j) * (k==l) * this->lambda;
	tangent(m,n) -= (m==n) * (m>=dim) * this->mu;
	*/
	//}
	// correct tangent stiffness for shear component
	//}
	//}
	MaterialElastic<dim>::computeTangentModuliOnQuad(tangent);
	}
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_plastic.cc b/src/model/solid_mechanics/materials/material_plastic/material_plastic.cc
	index 73bf43b23..6148a975f 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_plastic.cc
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_plastic.cc
	@@ -1,202 +1,202 @@
	/**
	* @file material_plastic.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implemantation of the akantu::MaterialPlastic class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_plastic.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialPlastic<spatial_dimension>::MaterialPlastic(SolidMechanicsModel & model,
	const ID & id)
	: MaterialElastic<spatial_dimension>(model, id),
	iso_hardening("iso_hardening", *this),
	inelastic_strain("inelastic_strain", *this),
	plastic_energy("plastic_energy", *this),
	d_plastic_energy("d_plastic_energy", *this) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	template <UInt spatial_dimension>
	MaterialPlastic<spatial_dimension>::MaterialPlastic(SolidMechanicsModel & model,
	UInt dim, const Mesh & mesh,
	FEEngine & fe_engine,
	const ID & id)
	: MaterialElastic<spatial_dimension>(model, dim, mesh, fe_engine, id),
	iso_hardening("iso_hardening", *this, dim, fe_engine,
	this->element_filter),
	inelastic_strain("inelastic_strain", *this, dim, fe_engine,
	this->element_filter),
	plastic_energy("plastic_energy", *this, dim, fe_engine,
	this->element_filter),
	d_plastic_energy("d_plastic_energy", *this, dim, fe_engine,
	this->element_filter) {
	AKANTU_DEBUG_IN();
	this->initialize();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialPlastic<spatial_dimension>::initialize() {
	this->registerParam("h", h, Real(0.), _pat_parsable \| _pat_modifiable,
	"Hardening modulus");
	this->registerParam("sigma_y", sigma_y, Real(0.),
	_pat_parsable \| _pat_modifiable, "Yield stress");

	this->iso_hardening.initialize(1);
	this->iso_hardening.initializeHistory();

	this->plastic_energy.initialize(1);
	this->d_plastic_energy.initialize(1);

	this->use_previous_stress = true;
	this->use_previous_gradu = true;
	this->use_previous_stress_thermal = true;

	this->inelastic_strain.initialize(spatial_dimension * spatial_dimension);
	this->inelastic_strain.initializeHistory();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialPlastic<spatial_dimension>::getEnergy(const std::string & type) {
	if (type == "plastic") {
	return getPlasticEnergy();
	}
	return MaterialElastic<spatial_dimension>::getEnergy(type);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialPlastic<spatial_dimension>::getPlasticEnergy() {
	AKANTU_DEBUG_IN();

	Real penergy = 0.;

	for (auto & type :
	this->element_filter.elementTypes(spatial_dimension, _not_ghost)) {
	penergy +=
	this->fem.integrate(plastic_energy(type, _not_ghost), type, _not_ghost,
	this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return penergy;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialPlastic<spatial_dimension>::computePotentialEnergy(
	ElementType el_type) {
	AKANTU_DEBUG_IN();

	Array<Real>::scalar_iterator epot = this->potential_energy(el_type).begin();

	Array<Real>::const_iterator<Matrix<Real>> inelastic_strain_it =
	this->inelastic_strain(el_type).begin(spatial_dimension,
	spatial_dimension);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	Matrix<Real> elastic_strain(spatial_dimension, spatial_dimension);
	elastic_strain.copy(grad_u);
	elastic_strain -= *inelastic_strain_it;

	MaterialElastic<spatial_dimension>::computePotentialEnergyOnQuad(
	elastic_strain, sigma, *epot);

	++epot;
	++inelastic_strain_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialPlastic<spatial_dimension>::updateEnergies(ElementType el_type) {
	AKANTU_DEBUG_IN();

	MaterialElastic<spatial_dimension>::updateEnergies(el_type);

	Array<Real>::iterator<> pe_it = this->plastic_energy(el_type).begin();

	Array<Real>::iterator<> wp_it = this->d_plastic_energy(el_type).begin();

	Array<Real>::iterator<Matrix<Real>> inelastic_strain_it =
	this->inelastic_strain(el_type).begin(spatial_dimension,
	spatial_dimension);

	Array<Real>::iterator<Matrix<Real>> previous_inelastic_strain_it =
	this->inelastic_strain.previous(el_type).begin(spatial_dimension,
	spatial_dimension);

	Array<Real>::matrix_iterator previous_sigma =
	this->stress.previous(el_type).begin(spatial_dimension,
	spatial_dimension);

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	Matrix<Real> delta_strain_it(*inelastic_strain_it);
	delta_strain_it -= *previous_inelastic_strain_it;

	Matrix<Real> sigma_h(sigma);
	sigma_h += *previous_sigma;

	wp_it = .5 sigma_h.doubleDot(delta_strain_it);

	pe_it += wp_it;

	++pe_it;
	++wp_it;
	++inelastic_strain_it;
	++previous_inelastic_strain_it;
	++previous_sigma;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL_ONLY(MaterialPlastic);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_plastic.hh b/src/model/solid_mechanics/materials/material_plastic/material_plastic.hh
	index 5e908bc97..7fc2c8357 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_plastic.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_plastic.hh
	@@ -1,134 +1,134 @@
	/**
	* @file material_plastic.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Common interface for plastic materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_PLASTIC_HH_
	#define AKANTU_MATERIAL_PLASTIC_HH_

	namespace akantu {

	/**
	* Parent class for the plastic constitutive laws
	* parameters in the material files :
	* - h : Hardening parameter (default: 0)
	* - sigmay : Yield stress
	*/
	template <UInt dim> class MaterialPlastic : public MaterialElastic<dim> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialPlastic(SolidMechanicsModel & model, const ID & id = "");
	MaterialPlastic(SolidMechanicsModel & model, UInt a_dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id = "");

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/**
	* @brief Return potential or plastic energy
	*
	* Plastic dissipated energy is integrated over time.
	*/
	Real getEnergy(const std::string & type) override;

	/// Update the plastic energy for the current timestep
	void updateEnergies(ElementType el_type) override;

	/// Compute the true potential energy (w/ elastic strain)
	void computePotentialEnergy(ElementType el_type) override;

	protected:
	/// compute the stress and inelastic strain for the quadrature point
	inline void computeStressAndInelasticStrainOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	const Matrix<Real> & delta_inelastic_strain) const;

	inline void computeStressAndInelasticStrainOnQuad(
	const Matrix<Real> & delta_grad_u, Matrix<Real> & sigma,
	const Matrix<Real> & previous_sigma, Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	const Matrix<Real> & delta_inelastic_strain) const;

	/// Get the integrated plastic energy for the time step
	Real getPlasticEnergy();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Yield stresss
	Real sigma_y;

	/// hardening modulus
	Real h;

	/// isotropic hardening, r
	InternalField<Real> iso_hardening;

	/// inelastic strain arrays ordered by element types (inelastic deformation)
	InternalField<Real> inelastic_strain;

	/// Plastic energy
	InternalField<Real> plastic_energy;

	/// @todo : add a coefficient beta that will multiply the plastic energy
	/// increment
	/// to compute the energy converted to heat

	/// Plastic energy increment
	InternalField<Real> d_plastic_energy;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "material_plastic_inline_impl.hh"
	#endif /* AKANTU_MATERIAL_PLASTIC_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_plastic/material_plastic_inline_impl.hh b/src/model/solid_mechanics/materials/material_plastic/material_plastic_inline_impl.hh
	index e1361c09b..e73b95db3 100644
	--- a/src/model/solid_mechanics/materials/material_plastic/material_plastic_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/material_plastic/material_plastic_inline_impl.hh
	@@ -1,77 +1,77 @@
	/**
	* @file material_plastic_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Apr 07 2014
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Implementation of the inline functions of akantu::MaterialPlastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef MATERIAL_PLASTIC_INLINE_IMPL_H
	#define MATERIAL_PLASTIC_INLINE_IMPL_H

	#include "material_plastic.hh"

	namespace akantu {

	template <UInt dim>
	inline void MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
	const Matrix<Real> & delta_grad_u, Matrix<Real> & sigma,
	const Matrix<Real> & previous_sigma, Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	const Matrix<Real> & delta_inelastic_strain) const {
	Matrix<Real> grad_u_elastic(dim, dim);
	grad_u_elastic.copy(delta_grad_u);
	grad_u_elastic -= delta_inelastic_strain;
	Matrix<Real> sigma_elastic(dim, dim);
	MaterialElastic<dim>::computeStressOnQuad(grad_u_elastic, sigma_elastic);
	sigma.copy(previous_sigma);
	sigma += sigma_elastic;
	inelastic_strain.copy(previous_inelastic_strain);
	inelastic_strain += delta_inelastic_strain;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialPlastic<dim>::computeStressAndInelasticStrainOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, const Matrix<Real> & previous_sigma,
	Matrix<Real> & inelastic_strain,
	const Matrix<Real> & previous_inelastic_strain,
	const Matrix<Real> & delta_inelastic_strain) const {
	Matrix<Real> delta_grad_u(grad_u);
	delta_grad_u -= previous_grad_u;

	computeStressAndInelasticStrainOnQuad(
	delta_grad_u, sigma, previous_sigma, inelastic_strain,
	previous_inelastic_strain, delta_inelastic_strain);
	}

	} // namespace akantu

	#endif /* MATERIAL_PLASTIC_INLINE_IMPL_H */
	diff --git a/src/model/solid_mechanics/materials/material_thermal.hh b/src/model/solid_mechanics/materials/material_thermal.hh
	index f6a303e42..d29b54b03 100644
	--- a/src/model/solid_mechanics/materials/material_thermal.hh
	+++ b/src/model/solid_mechanics/materials/material_thermal.hh
	@@ -1,110 +1,110 @@
	/**
	* @file material_thermal.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material isotropic thermo-elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_THERMAL_HH_
	#define AKANTU_MATERIAL_THERMAL_HH_

	namespace akantu {
	-template <UInt spatial_dimension> class MaterialThermal : public Material {
	+template <UInt dim> class MaterialThermal : public Material {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialThermal(SolidMechanicsModel & model, const ID & id = "");
	- MaterialThermal(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	- FEEngine & fe_engine, const ID & id = "");
	+ MaterialThermal(SolidMechanicsModel & model, UInt spatial_dimension,
	+ const Mesh & mesh, FEEngine & fe_engine, const ID & id = "");

	~MaterialThermal() override = default;

	protected:
	void initialize();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial() override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type, GhostType ghost_type) override;

	/// local computation of thermal stress
	inline void computeStressOnQuad(Real & sigma, const Real & deltaT);

	/* ------------------------------------------------------------------------ */

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Young modulus
	Real E;

	/// Poisson ratio
	Real nu;

	/// Thermal expansion coefficient
	/// TODO : implement alpha as a matrix
	Real alpha;

	/// Temperature field
	InternalField<Real> delta_T;

	/// Current thermal stress
	InternalField<Real> sigma_th;

	/// Tell if we need to use the previous thermal stress
	bool use_previous_stress_thermal;
	};

	/* ------------------------------------------------------------------------ */
	/* Inline impl */
	/* ------------------------------------------------------------------------ */
	template <UInt dim>
	inline void MaterialThermal<dim>::computeStressOnQuad(Real & sigma,
	const Real & deltaT) {
	sigma = -this->E / (1. - 2. * this->nu) * this->alpha * deltaT;
	}

	template <>
	inline void MaterialThermal<1>::computeStressOnQuad(Real & sigma,
	const Real & deltaT) {
	sigma = -this->E * this->alpha * deltaT;
	}

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_THERMAL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc b/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc
	index a9db37ec7..fec98196a 100644
	--- a/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc
	+++ b/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc
	@@ -1,318 +1,318 @@
	/**
	* @file material_standard_linear_solid_deviatoric.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Vladislav Yastrebov <vladislav.yastrebov@epfl.ch>
	*
	* @date creation: Wed May 04 2011
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material Visco-elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_standard_linear_solid_deviatoric.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	MaterialStandardLinearSolidDeviatoric<
	dim>::MaterialStandardLinearSolidDeviatoric(SolidMechanicsModel & model,
	const ID & id)
	: MaterialElastic<dim>(model, id), stress_dev("stress_dev", *this),
	history_integral("history_integral", *this),
	dissipated_energy("dissipated_energy", *this) {

	AKANTU_DEBUG_IN();

	this->registerParam("Eta", eta, Real(1.), _pat_parsable \| _pat_modifiable,
	"Viscosity");
	this->registerParam("Ev", Ev, Real(1.), _pat_parsable \| _pat_modifiable,
	"Stiffness of the viscous element");
	this->registerParam("Einf", E_inf, Real(1.), _pat_readable,
	"Stiffness of the elastic element");

	UInt stress_size = dim * dim;

	this->stress_dev.initialize(stress_size);
	this->history_integral.initialize(stress_size);
	this->dissipated_energy.initialize(1);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialStandardLinearSolidDeviatoric<dim>::initMaterial() {
	AKANTU_DEBUG_IN();

	updateInternalParameters();
	MaterialElastic<dim>::initMaterial();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialStandardLinearSolidDeviatoric<dim>::updateInternalParameters() {
	MaterialElastic<dim>::updateInternalParameters();
	E_inf = this->E - this->Ev;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialStandardLinearSolidDeviatoric<dim>::setToSteadyState(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
	Array<Real> & history_int_vect = history_integral(el_type, ghost_type);

	Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
	Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);

	/// Loop on all quadrature points
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Matrix<Real> & dev_s = *stress_d;
	Matrix<Real> & h = *history_int;

	/// Compute the first invariant of strain
	Real Theta = grad_u.trace();

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	dev_s(i, j) = 2 * this->mu *
	(.5 * (grad_u(i, j) + grad_u(j, i)) -
	1. / 3. * Theta * Math::kronecker(i, j));
	h(i, j) = 0.;
	}
	}

	/// Save the deviator of stress
	++stress_d;
	++history_int;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialStandardLinearSolidDeviatoric<dim>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real tau = 0.;
	// if(std::abs(Ev) > std::numeric_limits<Real>::epsilon())
	tau = eta / Ev;

	Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
	Array<Real> & history_int_vect = history_integral(el_type, ghost_type);

	Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
	Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);

	Matrix<Real> s(dim, dim);

	Real dt = this->model.getTimeStep();
	Real exp_dt_tau = exp(-dt / tau);
	Real exp_dt_tau_2 = exp(-.5 * dt / tau);

	Matrix<Real> epsilon_v(dim, dim);

	/// Loop on all quadrature points
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Matrix<Real> & dev_s = *stress_d;
	Matrix<Real> & h = *history_int;

	s.zero();
	sigma.zero();

	/// Compute the first invariant of strain
	Real gamma_inf = E_inf / this->E;
	Real gamma_v = Ev / this->E;

	auto epsilon_d = this->template gradUToEpsilon<dim>(grad_u);
	Real Theta = epsilon_d.trace();
	epsilon_v.eye(Theta / Real(3.));
	epsilon_d -= epsilon_v;

	Matrix<Real> U_rond_prim(dim, dim);

	U_rond_prim.eye(gamma_inf * this->kpa * Theta);

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	s(i, j) = 2 * this->mu * epsilon_d(i, j);
	h(i, j) = exp_dt_tau * h(i, j) + exp_dt_tau_2 * (s(i, j) - dev_s(i, j));
	dev_s(i, j) = s(i, j);
	sigma(i, j) = U_rond_prim(i, j) + gamma_inf * s(i, j) + gamma_v * h(i, j);
	}
	}

	/// Save the deviator of stress
	++stress_d;
	++history_int;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	this->updateDissipatedEnergy(el_type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void MaterialStandardLinearSolidDeviatoric<dim>::updateDissipatedEnergy(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// if(ghost_type == _ghost) return 0.;

	Real tau = 0.;
	tau = eta / Ev;
	Real * dis_energy = dissipated_energy(el_type, ghost_type).storage();

	Array<Real> & stress_dev_vect = stress_dev(el_type, ghost_type);
	Array<Real> & history_int_vect = history_integral(el_type, ghost_type);

	Array<Real>::matrix_iterator stress_d = stress_dev_vect.begin(dim, dim);
	Array<Real>::matrix_iterator history_int = history_int_vect.begin(dim, dim);

	Matrix<Real> q(dim, dim);
	Matrix<Real> q_rate(dim, dim);
	Matrix<Real> epsilon_d(dim, dim);
	Matrix<Real> epsilon_v(dim, dim);

	Real dt = this->model.getTimeStep();

	Real gamma_v = Ev / this->E;
	Real alpha = 1. / (2. * this->mu * gamma_v);

	/// Loop on all quadrature points
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	Matrix<Real> & dev_s = *stress_d;
	Matrix<Real> & h = *history_int;

	/// Compute the first invariant of strain
	this->template gradUToEpsilon<dim>(grad_u, epsilon_d);

	Real Theta = epsilon_d.trace();
	epsilon_v.eye(Theta / Real(3.));
	epsilon_d -= epsilon_v;

	q.copy(dev_s);
	q -= h;
	q *= gamma_v;

	q_rate.copy(dev_s);
	q_rate *= gamma_v;
	q_rate -= q;
	q_rate /= tau;

	for (UInt i = 0; i < dim; ++i) {
	for (UInt j = 0; j < dim; ++j) {
	dis_energy += (epsilon_d(i, j) - alpha q(i, j)) * q_rate(i, j) * dt;
	}
	}

	/// Save the deviator of stress
	++stress_d;
	++history_int;
	++dis_energy;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy() const {
	AKANTU_DEBUG_IN();

	Real de = 0.;

	/// integrate the dissipated energy for each type of elements
	for (auto & type : this->element_filter.elementTypes(dim, _not_ghost)) {
	de +=
	this->fem.integrate(dissipated_energy(type, _not_ghost), type,
	_not_ghost, this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return de;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialStandardLinearSolidDeviatoric<dim>::getDissipatedEnergy(
	ElementType type, UInt index) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
	auto it =
	this->dissipated_energy(type, _not_ghost).begin(nb_quadrature_points);
	UInt gindex = (this->element_filter(type, _not_ghost))(index);

	AKANTU_DEBUG_OUT();
	return this->fem.integrate(it[index], type, gindex);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialStandardLinearSolidDeviatoric<dim>::getEnergy(
	const std::string & type) {
	if (type == "dissipated") {
	return getDissipatedEnergy();
	}
	if (type == "dissipated_sls_deviatoric") {
	return getDissipatedEnergy();
	}
	return MaterialElastic<dim>::getEnergy(type);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	Real MaterialStandardLinearSolidDeviatoric<dim>::getEnergy(
	const std::string & energy_id, ElementType type, UInt index) {
	if (energy_id == "dissipated") {
	return getDissipatedEnergy(type, index);
	}
	if (energy_id == "dissipated_sls_deviatoric") {
	return getDissipatedEnergy(type, index);
	}
	return MaterialElastic<dim>::getEnergy(energy_id, type, index);
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(sls_deviatoric, MaterialStandardLinearSolidDeviatoric);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.hh b/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.hh
	index 2a6df1f97..d3799030b 100644
	--- a/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.hh
	+++ b/src/model/solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.hh
	@@ -1,138 +1,138 @@
	/**
	* @file material_standard_linear_solid_deviatoric.hh
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Vladislav Yastrebov <vladislav.yastrebov@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Material Visco-elastic, based on Standard Solid rheological model,
	* see
	* [] J.C. Simo, T.J.R. Hughes, "Computational Inelasticity", Springer (1998),
	* see Sections 10.2 and 10.3
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_STANDARD_LINEAR_SOLID_DEVIATORIC_HH_
	#define AKANTU_MATERIAL_STANDARD_LINEAR_SOLID_DEVIATORIC_HH_

	namespace akantu {

	/**
	* Material standard linear solid deviatoric
	*
	*
	* @verbatim

	E_\inf
	------\|\/\/\\|------
	\| \|
	---\| \|---
	\| \|
	----\|\/\/\\|--[\|----
	E_v \eta

	@endverbatim
	*
	* keyword : sls_deviatoric
	*
	* parameters in the material files :
	* - E : Initial Young's modulus @f$ E = E_i + E_v @f$
	* - eta : viscosity
	* - Ev : stiffness of the viscous element
	*/

	template <UInt spatial_dimension>
	class MaterialStandardLinearSolidDeviatoric
	: public MaterialElastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialStandardLinearSolidDeviatoric(SolidMechanicsModel & model,
	const ID & id = "");
	~MaterialStandardLinearSolidDeviatoric() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material computed parameter
	void initMaterial() override;

	/// update the internal parameters (for modifiable parameters)
	void updateInternalParameters() override;

	/// set material to steady state
	void setToSteadyState(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	protected:
	/// update the dissipated energy, is called after the stress have been
	/// computed
	void updateDissipatedEnergy(ElementType el_type, GhostType ghost_type);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// give the dissipated energy for the time step
	Real getDissipatedEnergy() const;
	Real getDissipatedEnergy(ElementType type, UInt index) const;

	/// get the energy using an energy type string for the time step
	Real getEnergy(const std::string & type) override;
	Real getEnergy(const std::string & energy_id, ElementType type,
	UInt index) override;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// viscosity, viscous elastic modulus
	Real eta, Ev, E_inf;

	Vector<Real> etas;

	/// history of deviatoric stress
	InternalField<Real> stress_dev;

	/// Internal variable: history integral
	InternalField<Real> history_integral;

	/// Dissipated energy
	InternalField<Real> dissipated_energy;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_STANDARD_LINEAR_SOLID_DEVIATORIC_HH_ */
	diff --git a/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc b/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc
	index f0aac9836..76dd3274c 100644
	--- a/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc
	+++ b/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc
	@@ -1,736 +1,736 @@
	/**
	* @file material_viscoelastic_maxwell.cc
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	*
	* @date creation: Mon Jun 04 2018
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material Visco-elastic, based on Maxwell chain,
	* see
	* [] R. de Borst and A.H. van den Boogaard "Finite-element modeling of
	* deformation and cracking in early-age concrete", J.Eng.Mech., 1994
	* as well as
	* [] Manual of DIANA FEA Theory manual v.10.2 Section 37.6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_viscoelastic_maxwell.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialViscoelasticMaxwell<spatial_dimension>::MaterialViscoelasticMaxwell(
	SolidMechanicsModel & model, const ID & id)
	: MaterialElastic<spatial_dimension>(model, id),
	C(voigt_h::size, voigt_h::size), D(voigt_h::size, voigt_h::size),
	sigma_v("sigma_v", this), epsilon_v("epsilon_v", this),
	dissipated_energy("dissipated_energy", *this),
	mechanical_work("mechanical_work", *this) {

	AKANTU_DEBUG_IN();

	this->registerParam("Einf", Einf, Real(1.), _pat_parsable \| _pat_modifiable,
	"Stiffness of the elastic element");
	this->registerParam("previous_dt", previous_dt, Real(0.), _pat_readable,
	"Time step of previous solveStep");
	this->registerParam("Eta", Eta, _pat_parsable \| _pat_modifiable,
	"Viscosity of a Maxwell element");
	this->registerParam("Ev", Ev, _pat_parsable \| _pat_modifiable,
	"Stiffness of a Maxwell element");
	this->update_variable_flag = true;
	this->use_previous_stress = true;
	this->use_previous_gradu = true;
	this->use_previous_stress_thermal = true;

	this->dissipated_energy.initialize(1);
	this->mechanical_work.initialize(1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();

	this->E = Einf + Ev.norm<L_1>();
	// this->E = std::min(this->Einf, this->Ev(0));
	MaterialElastic<spatial_dimension>::initMaterial();
	AKANTU_DEBUG_ASSERT(this->Eta.size() == this->Ev.size(),
	"Eta and Ev have different dimensions! Please correct.");
	AKANTU_DEBUG_ASSERT(
	!this->finite_deformation,
	"Current material works only in infinitesimal deformations.");

	UInt stress_size = spatial_dimension * spatial_dimension;
	this->sigma_v.initialize(stress_size * this->Ev.size());
	this->epsilon_v.initialize(stress_size * this->Ev.size());

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<
	spatial_dimension>::updateInternalParameters() {
	MaterialElastic<spatial_dimension>::updateInternalParameters();

	Real pre_mult = 1 / (1 + this->nu) / (1 - 2 * this->nu);
	UInt n = voigt_h::size;
	Real Miiii = pre_mult * (1 - this->nu);
	Real Miijj = pre_mult * this->nu;
	Real Mijij = pre_mult * 0.5 * (1 - 2 * this->nu);

	Real Diiii = 1;
	Real Diijj = -this->nu;
	Real Dijij = (2 + 2 * this->nu);

	if (spatial_dimension == 1) {
	C(0, 0) = 1;
	D(0, 0) = 1;
	} else {
	C(0, 0) = Miiii;
	D(0, 0) = Diiii;
	}
	if (spatial_dimension >= 2) {
	C(1, 1) = Miiii;
	C(0, 1) = Miijj;
	C(1, 0) = Miijj;
	C(n - 1, n - 1) = Mijij;

	D(1, 1) = Diiii;
	D(0, 1) = Diijj;
	D(1, 0) = Diijj;
	D(n - 1, n - 1) = Dijij;
	}

	if (spatial_dimension == 3) {
	C(2, 2) = Miiii;
	C(0, 2) = Miijj;
	C(1, 2) = Miijj;
	C(2, 0) = Miijj;
	C(2, 1) = Miijj;
	C(3, 3) = Mijij;
	C(4, 4) = Mijij;

	D(2, 2) = Diiii;
	D(0, 2) = Diijj;
	D(1, 2) = Diijj;
	D(2, 0) = Diijj;
	D(2, 1) = Diijj;
	D(3, 3) = Dijij;
	D(4, 4) = Dijij;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <> void MaterialViscoelasticMaxwell<2>::updateInternalParameters() {
	MaterialElastic<2>::updateInternalParameters();

	Real pre_mult = 1 / (1 + this->nu) / (1 - 2 * this->nu);
	UInt n = voigt_h::size;
	Real Miiii = pre_mult * (1 - this->nu);
	Real Miijj = pre_mult * this->nu;
	Real Mijij = pre_mult * 0.5 * (1 - 2 * this->nu);

	Real Diiii = 1;
	Real Diijj = -this->nu;
	Real Dijij = (2 + 2 * this->nu);

	C(0, 0) = Miiii;
	C(1, 1) = Miiii;
	C(0, 1) = Miijj;
	C(1, 0) = Miijj;
	C(n - 1, n - 1) = Mijij;

	D(0, 0) = Diiii;
	D(1, 1) = Diiii;
	D(0, 1) = Diijj;
	D(1, 0) = Diijj;
	D(n - 1, n - 1) = Dijij;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::computeStress(
	ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	// NOLINTNEXTLINE(bugprone-parent-virtual-call)
	MaterialThermal<spatial_dimension>::computeStress(el_type, ghost_type);

	auto sigma_th_it = this->sigma_th(el_type, ghost_type).begin();

	auto previous_gradu_it = this->gradu.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_stress_it = this->stress.previous(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension);

	auto sigma_v_it =
	this->sigma_v(el_type, ghost_type)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	computeStressOnQuad(grad_u, previous_gradu_it, sigma, sigma_v_it,
	*sigma_th_it);
	++sigma_th_it;
	++previous_gradu_it;
	++sigma_v_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::computeStressOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, Tensor3<Real> & sigma_v, const Real & sigma_th) {

	// Wikipedia convention:
	// 2*eps_ij (i!=j) = voigt_eps_I
	// http://en.wikipedia.org/wiki/Voigt_notation
	Vector<Real> voigt_current_strain(voigt_h::size);
	Vector<Real> voigt_previous_strain(voigt_h::size);
	Vector<Real> voigt_stress(voigt_h::size);
	Vector<Real> voigt_sigma_v(voigt_h::size);

	for (UInt I = 0; I < voigt_h::size; ++I) {
	Real voigt_factor = voigt_h::factors[I];
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_current_strain(I) = voigt_factor * (grad_u(i, j) + grad_u(j, i)) / 2.;
	voigt_previous_strain(I) =
	voigt_factor * (previous_grad_u(i, j) + previous_grad_u(j, i)) / 2.;
	}

	voigt_stress = this->Einf * this->C * voigt_current_strain;
	Real dt = this->model.getTimeStep();

	for (UInt k = 0; k < Eta.size(); ++k) {
	Real lambda = this->Eta(k) / this->Ev(k);
	Real exp_dt_lambda = exp(-dt / lambda);
	Real E_additional;

	if (exp_dt_lambda == 1) {
	E_additional = this->Ev(k);
	} else {
	E_additional = (1 - exp_dt_lambda) * this->Ev(k) * lambda / dt;
	}

	for (UInt I = 0; I < voigt_h::size; ++I) {
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_sigma_v(I) = sigma_v(i, j, k);
	}

	voigt_stress += E_additional * this->C *
	(voigt_current_strain - voigt_previous_strain) +
	exp_dt_lambda * voigt_sigma_v;
	}

	for (UInt I = 0; I < voigt_h::size; ++I) {
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	sigma(i, j) = sigma(j, i) =
	voigt_stress(I) + Math::kronecker(i, j) * sigma_th;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::computePotentialEnergy(
	ElementType el_type) {
	AKANTU_DEBUG_IN();

	auto epot = this->potential_energy(el_type).begin();
	auto sigma_v_it = this->sigma_v(el_type).begin(
	spatial_dimension, spatial_dimension, this->Eta.size());
	auto epsilon_v_it = this->epsilon_v(el_type).begin(
	spatial_dimension, spatial_dimension, this->Eta.size());

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	this->computePotentialEnergyOnQuad(grad_u, epot, sigma_v_it, *epsilon_v_it);
	++epot;
	++sigma_v_it;
	++epsilon_v_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::
	computePotentialEnergyOnQuad(const Matrix<Real> & grad_u, Real & epot,
	Tensor3<Real> & sigma_v,
	Tensor3<Real> & epsilon_v) {

	Vector<Real> voigt_strain(voigt_h::size);
	Vector<Real> voigt_stress(voigt_h::size);
	Vector<Real> voigt_sigma_v(voigt_h::size);

	for (UInt I = 0; I < voigt_h::size; ++I) {
	Real voigt_factor = voigt_h::factors[I];
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_strain(I) = voigt_factor * (grad_u(i, j) + grad_u(j, i)) / 2.;
	}

	voigt_stress = this->Einf * this->C * voigt_strain;
	epot = 0.5 * voigt_stress.dot(voigt_strain);

	for (UInt k = 0; k < this->Eta.size(); ++k) {
	Matrix<Real> stress_v = sigma_v(k);
	Matrix<Real> strain_v = epsilon_v(k);
	epot += 0.5 * stress_v.doubleDot(strain_v);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::afterSolveStep(
	bool converged) {

	Material::afterSolveStep(converged);

	if (not converged) {
	return;
	}

	for (auto & el_type : this->element_filter.elementTypes(
	_all_dimensions, _not_ghost, _ek_not_defined)) {
	if (this->update_variable_flag) {
	auto previous_gradu_it = this->gradu.previous(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension);

	auto sigma_v_it =
	this->sigma_v(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	auto epsilon_v_it =
	this->epsilon_v(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	updateIntVarOnQuad(grad_u, previous_gradu_it, sigma_v_it,
	*epsilon_v_it);

	++previous_gradu_it;
	++sigma_v_it;
	++epsilon_v_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}
	this->updateDissipatedEnergy(el_type);
	}
	}
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::updateIntVarOnQuad(
	const Matrix<Real> & grad_u, const Matrix<Real> & previous_grad_u,
	Tensor3<Real> & sigma_v, Tensor3<Real> & epsilon_v) {

	Matrix<Real> grad_delta_u(grad_u);
	grad_delta_u -= previous_grad_u;

	Real dt = this->model.getTimeStep();
	Vector<Real> voigt_delta_strain(voigt_h::size);
	for (UInt I = 0; I < voigt_h::size; ++I) {
	Real voigt_factor = voigt_h::factors[I];
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_delta_strain(I) =
	voigt_factor * (grad_delta_u(i, j) + grad_delta_u(j, i)) / 2.;
	}

	for (UInt k = 0; k < this->Eta.size(); ++k) {
	Real lambda = this->Eta(k) / this->Ev(k);
	Real exp_dt_lambda = exp(-dt / lambda);
	Real E_ef_v;

	if (exp_dt_lambda == 1) {
	E_ef_v = this->Ev(k);
	} else {
	E_ef_v = (1 - exp_dt_lambda) * this->Ev(k) * lambda / dt;
	}

	Vector<Real> voigt_sigma_v(voigt_h::size);
	Vector<Real> voigt_epsilon_v(voigt_h::size);

	for (UInt I = 0; I < voigt_h::size; ++I) {
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	voigt_sigma_v(I) = sigma_v(i, j, k);
	}

	voigt_sigma_v =
	exp_dt_lambda * voigt_sigma_v + E_ef_v * this->C * voigt_delta_strain;
	voigt_epsilon_v = 1 / Ev(k) * this->D * voigt_sigma_v;

	for (UInt I = 0; I < voigt_h::size; ++I) {
	UInt i = voigt_h::vec[I][0];
	UInt j = voigt_h::vec[I][1];

	sigma_v(i, j, k) = sigma_v(j, i, k) = voigt_sigma_v(I);
	epsilon_v(i, j, k) = epsilon_v(j, i, k) = voigt_epsilon_v(I);
	}
	}
	}
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::computeTangentModuli(
	ElementType el_type, Array<Real> & tangent_matrix, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real dt = this->model.getTimeStep();
	Real E_ef = this->Einf;

	for (UInt k = 0; k < Eta.size(); ++k) {
	Real lambda = this->Eta(k) / this->Ev(k);
	Real exp_dt_lambda = exp(-dt / lambda);
	if (exp_dt_lambda == 1) {
	E_ef += this->Ev(k);
	} else {
	E_ef += (1 - exp_dt_lambda) * this->Ev(k) * lambda / dt;
	}
	}

	this->previous_dt = dt;

	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_matrix);
	this->computeTangentModuliOnQuad(tangent);
	MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END;

	tangent_matrix *= E_ef;

	this->was_stiffness_assembled = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::computeTangentModuliOnQuad(
	Matrix<Real> & tangent) {

	tangent.copy(C);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::savePreviousState() {

	for (auto & el_type : this->element_filter.elementTypes(
	_all_dimensions, _not_ghost, _ek_not_defined)) {

	auto sigma_th_it = this->sigma_th(el_type, _not_ghost).begin();

	auto previous_sigma_th_it =
	this->sigma_th.previous(el_type, _not_ghost).begin();

	auto previous_gradu_it = this->gradu.previous(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension);

	auto previous_sigma_it = this->stress.previous(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension);

	auto sigma_v_it =
	this->sigma_v(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);
	auto & previous_grad_u = *previous_gradu_it;
	auto & previous_sigma = *previous_sigma_it;

	previous_grad_u.copy(grad_u);
	previous_sigma.copy(sigma);
	previous_sigma_th_it = sigma_th_it;

	++previous_gradu_it, ++previous_sigma_it, ++previous_sigma_th_it,
	++sigma_v_it, ++sigma_th_it;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::updateIntVariables() {

	for (auto & el_type : this->element_filter.elementTypes(
	_all_dimensions, _not_ghost, _ek_not_defined)) {

	auto previous_gradu_it = this->gradu.previous(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension);
	auto previous_sigma_it = this->stress.previous(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension);

	auto sigma_v_it =
	this->sigma_v(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	auto epsilon_v_it =
	this->epsilon_v(el_type, _not_ghost)
	.begin(spatial_dimension, spatial_dimension, this->Eta.size());

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	updateIntVarOnQuad(grad_u, previous_gradu_it, sigma_v_it, *epsilon_v_it);

	++previous_gradu_it;
	++sigma_v_it;
	++epsilon_v_it;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::updateDissipatedEnergy(
	ElementType el_type) {
	AKANTU_DEBUG_IN();

	this->computePotentialEnergy(el_type);

	auto epot = this->potential_energy(el_type).begin();
	auto dis_energy = this->dissipated_energy(el_type).begin();
	auto mech_work = this->mechanical_work(el_type).begin();
	auto sigma_v_it = this->sigma_v(el_type).begin(
	spatial_dimension, spatial_dimension, this->Eta.size());
	auto epsilon_v_it = this->epsilon_v(el_type).begin(
	spatial_dimension, spatial_dimension, this->Eta.size());
	auto previous_gradu_it =
	this->gradu.previous(el_type).begin(spatial_dimension, spatial_dimension);
	auto previous_sigma_it = this->stress.previous(el_type).begin(
	spatial_dimension, spatial_dimension);

	/// Loop on all quadrature points
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);

	updateDissipatedEnergyOnQuad(grad_u, *previous_gradu_it, sigma,
	previous_sigma_it, dis_energy, *mech_work,
	*epot);
	++previous_gradu_it;
	++previous_sigma_it;
	++dis_energy;
	++mech_work;
	++epot;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::
	updateDissipatedEnergyOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	const Matrix<Real> & sigma,
	const Matrix<Real> & previous_sigma,
	Real & dis_energy, Real & mech_work,
	const Real & pot_energy) {

	Real dt = this->model.getTimeStep();

	Matrix<Real> strain_rate = grad_u;
	strain_rate -= previous_grad_u;
	strain_rate /= dt;

	Matrix<Real> av_stress = sigma;
	av_stress += previous_sigma;
	av_stress /= 2;

	mech_work += av_stress.doubleDot(strain_rate) * dt;

	dis_energy = mech_work - pot_energy;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getDissipatedEnergy()
	const {
	AKANTU_DEBUG_IN();

	Real de = 0.;

	/// integrate the dissipated energy for each type of elements
	for (auto & type :
	this->element_filter.elementTypes(spatial_dimension, _not_ghost)) {
	de +=
	this->fem.integrate(this->dissipated_energy(type, _not_ghost), type,
	_not_ghost, this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return de;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getDissipatedEnergy(
	ElementType type, UInt index) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
	auto it =
	this->dissipated_energy(type, _not_ghost).begin(nb_quadrature_points);
	UInt gindex = (this->element_filter(type, _not_ghost))(index);

	AKANTU_DEBUG_OUT();
	return this->fem.integrate(it[index], type, gindex);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getMechanicalWork() const {
	AKANTU_DEBUG_IN();

	Real mw = 0.;

	/// integrate the dissipated energy for each type of elements
	for (auto & type :
	this->element_filter.elementTypes(spatial_dimension, _not_ghost)) {
	mw +=
	this->fem.integrate(this->mechanical_work(type, _not_ghost), type,
	_not_ghost, this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return mw;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getMechanicalWork(
	ElementType type, UInt index) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
	auto it = this->mechanical_work(type, _not_ghost).begin(nb_quadrature_points);
	UInt gindex = (this->element_filter(type, _not_ghost))(index);

	AKANTU_DEBUG_OUT();
	return this->fem.integrate(it[index], type, gindex);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getPotentialEnergy()
	const {
	AKANTU_DEBUG_IN();

	Real epot = 0.;

	/// integrate the dissipated energy for each type of elements
	for (auto & type :
	this->element_filter.elementTypes(spatial_dimension, _not_ghost)) {
	epot +=
	this->fem.integrate(this->potential_energy(type, _not_ghost), type,
	_not_ghost, this->element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return epot;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getPotentialEnergy(
	ElementType type, UInt index) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->fem.getNbIntegrationPoints(type);
	auto it =
	this->potential_energy(type, _not_ghost).begin(nb_quadrature_points);
	UInt gindex = (this->element_filter(type, _not_ghost))(index);

	AKANTU_DEBUG_OUT();
	return this->fem.integrate(it[index], type, gindex);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getEnergy(
	const std::string & type) {
	if (type == "dissipated") {
	return getDissipatedEnergy();
	}
	if (type == "potential") {
	return getPotentialEnergy();
	}
	if (type == "work") {
	return getMechanicalWork();
	}
	return MaterialElastic<spatial_dimension>::getEnergy(type);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	Real MaterialViscoelasticMaxwell<spatial_dimension>::getEnergy(
	const std::string & energy_id, ElementType type, UInt index) {
	if (energy_id == "dissipated") {
	return getDissipatedEnergy(type, index);
	}
	if (energy_id == "potential") {
	return getPotentialEnergy(type, index);
	}
	if (energy_id == "work") {
	return getMechanicalWork(type, index);
	}
	return MaterialElastic<spatial_dimension>::getEnergy(energy_id, type, index);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::forceUpdateVariable() {
	update_variable_flag = true;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialViscoelasticMaxwell<spatial_dimension>::forceNotUpdateVariable() {
	update_variable_flag = false;
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(viscoelastic_maxwell, MaterialViscoelasticMaxwell);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.hh b/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.hh
	index d8ef5fb17..df2503b0a 100644
	--- a/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.hh
	+++ b/src/model/solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.hh
	@@ -1,231 +1,228 @@
	/**
	* @file material_viscoelastic_maxwell.hh
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	*
	* @date creation: Mon Jun 04 2018
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Material Visco-elastic, based on Maxwell chain,
	* see
	* [] R. de Borst and A.H. van den Boogaard "Finite-element modeling of
	* deformation and cracking in early-age concrete", J.Eng.Mech., 1994
	* as well as
	* [] Manual of DIANA FEA Theory manual v.10.2 Section 37.6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_voigthelper.hh"
	#include "material_elastic.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_
	#define AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_

	namespace akantu {

	/**
	* Material Viscoelastic based on Maxwell chain
	*
	*
	* @verbatim

	E_0
	------\|\/\/\\|-------
	\| \|
	---\| \|---
	\| \|
	----\|\/\/\\|--[\|-----
	\| E_v1 \Eta_1\|
	---\| \|---
	\| \|
	----\|\/\/\\|--[\|-----
	\| E_v2 \Eta_2 \|
	---\| \|---
	\| \|
	----\|\/\/\\|--[\|----
	E_vN \Eta_N

	@endverbatim
	*
	* keyword : viscoelastic_maxwell
	*
	* parameters in the material files :
	* - N : number of Maxwell elements
	* - Einf : one spring element stiffness
	* - Ev1 : stiffness of the 1st viscous element
	* - Eta1: viscosity of the 1st Maxwell element
	* ...
	* - Ev<N> : stiffness of the Nst viscous element
	* - Eta<N>: viscosity of the Nst Maxwell element
	*/

	template <UInt spatial_dimension>
	class MaterialViscoelasticMaxwell : public MaterialElastic<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialViscoelasticMaxwell(SolidMechanicsModel & model, const ID & id = "");
	~MaterialViscoelasticMaxwell() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material computed parameter
	void initMaterial() override;

	/// recompute the lame coefficient and effective tangent moduli
	void updateInternalParameters() override;

	/// update internal variable on a converged Newton
	void afterSolveStep(bool converged) override;

	/// update internal variable based on previous and current strain values
	void updateIntVariables();

	/// update the internal variable sigma_v on quadrature point
	void updateIntVarOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	Tensor3<Real> & sigma_v, Tensor3<Real> & epsilon_v);

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentModuli(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentModuli(ElementType el_type, Array<Real> & tangent_matrix,
	GhostType ghost_type = _not_ghost) override;

	/// save previous stress and strain values into "previous" arrays
	void savePreviousState() override;

	/// change flag of updateIntVar to true
	void forceUpdateVariable();

	/// change flag of updateIntVar to false
	void forceNotUpdateVariable();

	/// compute the elastic potential energy
	void computePotentialEnergy(ElementType el_type) override;

	protected:
	void computePotentialEnergyOnQuad(const Matrix<Real> & grad_u, Real & epot,
	Tensor3<Real> & sigma_v,
	Tensor3<Real> & epsilon_v);

	/// update the dissipated energy, is called after the stress have been
	/// computed
	void updateDissipatedEnergy(ElementType el_type);

	void updateDissipatedEnergyOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	const Matrix<Real> & sigma,
	const Matrix<Real> & previous_sigma,
	Real & dis_energy, Real & mech_work,
	const Real & pot_energy);

	/// compute stresses on a quadrature point
	void computeStressOnQuad(const Matrix<Real> & grad_u,
	const Matrix<Real> & previous_grad_u,
	Matrix<Real> & sigma, Tensor3<Real> & sigma_v,
	const Real & sigma_th);

	/// compute tangent moduli on a quadrature point
	void computeTangentModuliOnQuad(Matrix<Real> & tangent);

	bool hasStiffnessMatrixChanged() override {
	Real dt = this->model.getTimeStep();

	return ((this->previous_dt == dt)
	? (!(this->previous_dt == dt)) * (this->was_stiffness_assembled)
	: (!(this->previous_dt == dt)));
	// return (!(this->previous_dt == dt));
	}

	- MatrixType getTangentType() override {
	- return _symmetric;
	- }
	+ MatrixType getTangentType() override { return _symmetric; }

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// give the dissipated energy
	Real getDissipatedEnergy() const;
	Real getDissipatedEnergy(ElementType type, UInt index) const;

	/// get the potential energy
	Real getPotentialEnergy() const;
	Real getPotentialEnergy(ElementType type, UInt index) const;

	/// get the potential energy
	Real getMechanicalWork() const;
	Real getMechanicalWork(ElementType type, UInt index) const;

	/// get the energy using an energy type string for the time step
	Real getEnergy(const std::string & type) override;
	Real getEnergy(const std::string & energy_id, ElementType type,
	UInt index) override;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	using voigt_h = VoigtHelper<spatial_dimension>;

	/// Vectors of viscosity, viscous elastic modulus, one spring element elastic
	/// modulus
	Vector<Real> Eta;
	Vector<Real> Ev;
	Real Einf;

	/// time step from previous solveStep
	Real previous_dt;

	/// Stiffness matrix template
	Matrix<Real> C;
	/// Compliance matrix template
	Matrix<Real> D;

	/// Internal variable: viscous_stress
	InternalField<Real> sigma_v;

	/// Internal variable: spring strain in Maxwell element
	InternalField<Real> epsilon_v;

	/// Dissipated energy
	InternalField<Real> dissipated_energy;

	/// Mechanical work
	InternalField<Real> mechanical_work;

	/// Update internal variable after solve step or not
	bool update_variable_flag;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/plane_stress_toolbox.hh b/src/model/solid_mechanics/materials/plane_stress_toolbox.hh
	index dc68fdc80..e57e42092 100644
	--- a/src/model/solid_mechanics/materials/plane_stress_toolbox.hh
	+++ b/src/model/solid_mechanics/materials/plane_stress_toolbox.hh
	@@ -1,105 +1,105 @@
	/**
	* @file plane_stress_toolbox.hh
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Sep 16 2014
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Tools to implement the plane stress behavior in a material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PLANE_STRESS_TOOLBOX_HH_
	#define AKANTU_PLANE_STRESS_TOOLBOX_HH_

	namespace akantu {
	class SolidMechanicsModel;
	class FEEngine;
	} // namespace akantu

	namespace akantu {

	/**
	* Empty class in dimensions different from 2
	* This class is only specialized for 2D in the tmpl file
	*/
	template <UInt dim, class ParentMaterial = Material>
	class PlaneStressToolbox : public ParentMaterial {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	PlaneStressToolbox(SolidMechanicsModel & model, const ID & id = "")
	: ParentMaterial(model, id) {}
	PlaneStressToolbox(SolidMechanicsModel & model, UInt spatial_dimension,
	const Mesh & mesh, FEEngine & fe_engine,
	const ID & id = "")
	: ParentMaterial(model, spatial_dimension, mesh, fe_engine, id) {}

	~PlaneStressToolbox() override = default;

	protected:
	void initialize();

	public:
	void computeAllCauchyStresses(GhostType ghost_type = _not_ghost) override {
	ParentMaterial::computeAllCauchyStresses(ghost_type);
	}

	virtual void computeCauchyStressPlaneStress(ElementType /el_type/,
	GhostType /ghost_type/) {
	AKANTU_DEBUG_IN();

	AKANTU_ERROR("The function \"computeCauchyStressPlaneStress\" can "
	"only be used in 2D Plane stress problems, which means "
	"that you made a mistake somewhere!! ");

	AKANTU_DEBUG_OUT();
	}

	virtual void computeThirdAxisDeformation(ElementType /unused/,
	GhostType /unused/) {}

	protected:
	bool initialize_third_axis_deformation{false};
	};

	#define AKANTU_PLANE_STRESS_TOOL_SPEC(dim) \
	template <> \
	inline PlaneStressToolbox<dim, Material>::PlaneStressToolbox( \
	SolidMechanicsModel & model, const ID & id) \
	: Material(model, id) {}

	AKANTU_PLANE_STRESS_TOOL_SPEC(1)
	AKANTU_PLANE_STRESS_TOOL_SPEC(3)

	} // namespace akantu

	#include "plane_stress_toolbox_tmpl.hh"

	#endif /* AKANTU_PLANE_STRESS_TOOLBOX_HH_ */
	diff --git a/src/model/solid_mechanics/materials/plane_stress_toolbox_tmpl.hh b/src/model/solid_mechanics/materials/plane_stress_toolbox_tmpl.hh
	index baf843086..5ba800474 100644
	--- a/src/model/solid_mechanics/materials/plane_stress_toolbox_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/plane_stress_toolbox_tmpl.hh
	@@ -1,167 +1,167 @@
	/**
	* @file plane_stress_toolbox_tmpl.hh
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	*
	* @date creation: Tue Sep 16 2014
	* @date last modification: Fri Apr 09 2021
	*
	* @brief 2D specialization of the akantu::PlaneStressToolbox class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PLANE_STRESS_TOOLBOX_TMPL_HH_
	#define AKANTU_PLANE_STRESS_TOOLBOX_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class ParentMaterial>
	class PlaneStressToolbox<2, ParentMaterial> : public ParentMaterial {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	PlaneStressToolbox(SolidMechanicsModel & model, const ID & id = "");
	PlaneStressToolbox(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id = "");

	~PlaneStressToolbox() override = default;

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ThirdAxisDeformation,
	third_axis_deformation, Real);

	protected:
	void initialize() {
	this->registerParam("Plane_Stress", plane_stress, false, _pat_parsmod,
	"Is plane stress");
	}

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	void initMaterial() override {

	ParentMaterial::initMaterial();
	if (this->plane_stress && this->initialize_third_axis_deformation) {
	this->third_axis_deformation.initialize(1);
	this->third_axis_deformation.resize();
	}
	}

	/* ------------------------------------------------------------------------ */
	void computeStress(ElementType el_type, GhostType ghost_type) override {
	ParentMaterial::computeStress(el_type, ghost_type);
	if (this->plane_stress) {
	computeThirdAxisDeformation(el_type, ghost_type);
	}
	}

	/* ------------------------------------------------------------------------ */
	virtual void computeThirdAxisDeformation(ElementType /unused/,
	GhostType /unused/) {}

	/// Computation of Cauchy stress tensor in the case of finite deformation
	void computeAllCauchyStresses(GhostType ghost_type = _not_ghost) override {
	AKANTU_DEBUG_IN();

	if (this->plane_stress) {
	AKANTU_DEBUG_ASSERT(this->finite_deformation,
	"The Cauchy stress can only be computed if you are "
	"working in finite deformation.");

	for (auto & type : this->fem.getMesh().elementTypes(2, ghost_type)) {
	this->computeCauchyStressPlaneStress(type, ghost_type);
	}
	} else {
	ParentMaterial::computeAllCauchyStresses(ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	virtual void
	computeCauchyStressPlaneStress(__attribute__((unused)) ElementType el_type,
	__attribute__((unused))
	GhostType ghost_type = _not_ghost){};

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// third axis strain measure value
	InternalField<Real> third_axis_deformation;

	/// Plane stress or plane strain
	bool plane_stress;

	/// For non linear materials, the \f[\epsilon_{zz}\f] might be required
	bool initialize_third_axis_deformation;
	};

	template <class ParentMaterial>
	inline PlaneStressToolbox<2, ParentMaterial>::PlaneStressToolbox(
	SolidMechanicsModel & model, const ID & id)
	: ParentMaterial(model, id),
	third_axis_deformation("third_axis_deformation", *this),
	plane_stress(false), initialize_third_axis_deformation(false) {

	/// @todo Plane_Stress should not be possible to be modified after
	/// initMaterial (but before)
	this->initialize();
	}

	template <class ParentMaterial>
	inline PlaneStressToolbox<2, ParentMaterial>::PlaneStressToolbox(
	SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
	FEEngine & fe_engine, const ID & id)
	: ParentMaterial(model, dim, mesh, fe_engine, id),
	third_axis_deformation("third_axis_deformation", *this, dim, fe_engine,
	this->element_filter),
	plane_stress(false), initialize_third_axis_deformation(false) {
	this->initialize();
	}

	template <>
	inline PlaneStressToolbox<2, Material>::PlaneStressToolbox(
	SolidMechanicsModel & model, const ID & id)
	: Material(model, id),
	third_axis_deformation("third_axis_deformation", *this),
	plane_stress(false), initialize_third_axis_deformation(false) {

	/// @todo Plane_Stress should not be possible to be modified after
	/// initMaterial (but before)
	this->registerParam("Plane_Stress", plane_stress, false, _pat_parsmod,
	"Is plane stress");
	}

	} // namespace akantu

	#endif /* AKANTU_PLANE_STRESS_TOOLBOX_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/random_internal_field.hh b/src/model/solid_mechanics/materials/random_internal_field.hh
	index 2696aa03d..58fa09ff6 100644
	--- a/src/model/solid_mechanics/materials/random_internal_field.hh
	+++ b/src/model/solid_mechanics/materials/random_internal_field.hh
	@@ -1,105 +1,106 @@
	/**
	* @file random_internal_field.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Mar 26 2021
	*
	* @brief Random internal material parameter
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_random_generator.hh"
	#include "internal_field.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_RANDOM_INTERNAL_FIELD_HH_
	#define AKANTU_RANDOM_INTERNAL_FIELD_HH_

	namespace akantu {

	/**
	* class for the internal fields of materials with a random
	* distribution
	*/
	template <typename T, template <typename> class BaseField = InternalField,
	template <typename> class Generator = RandomGenerator>
	class RandomInternalField : public BaseField<T> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	RandomInternalField(const ID & id, Material & material);

	~RandomInternalField() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	RandomInternalField operator=(const RandomInternalField &) = delete;

	public:
	- AKANTU_GET_MACRO(RandomParameter, random_parameter, const RandomParameter<T>&);
	+ AKANTU_GET_MACRO(RandomParameter, random_parameter,
	+ const RandomParameter<T> &);

	/// initialize the field to a given number of component
	void initialize(UInt nb_component) override;

	/// set the field to a given value
	void setDefaultValue(const T & value) override;

	/// set the specified random distribution to a given parameter
	void setRandomDistribution(const RandomParameter<T> & param);

	/// print the content
	void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	void setArrayValues(T * begin, T * end) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	inline operator Real() const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// random parameter containing the distribution and base value
	RandomParameter<T> random_parameter;
	};

	/// standard output stream operator
	template <typename T>
	inline std::ostream & operator<<(std::ostream & stream,
	const RandomInternalField<T> & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_RANDOM_INTERNAL_FIELD_HH_ */
	diff --git a/src/model/solid_mechanics/materials/random_internal_field_tmpl.hh b/src/model/solid_mechanics/materials/random_internal_field_tmpl.hh
	index 73487ded8..dc94496a6 100644
	--- a/src/model/solid_mechanics/materials/random_internal_field_tmpl.hh
	+++ b/src/model/solid_mechanics/materials/random_internal_field_tmpl.hh
	@@ -1,126 +1,126 @@
	/**
	* @file random_internal_field_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Mar 26 2021
	*
	* @brief Random internal material parameter implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_random_generator.hh"
	#include "internal_field_tmpl.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_RANDOM_INTERNAL_FIELD_TMPL_HH_
	#define AKANTU_RANDOM_INTERNAL_FIELD_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	RandomInternalField<T, BaseField, Generator>::RandomInternalField(
	const ID & id, Material & material)
	: BaseField<T>(id, material), random_parameter(T()) {}

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	RandomInternalField<T, BaseField, Generator>::~RandomInternalField() = default;

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	void RandomInternalField<T, BaseField, Generator>::initialize(
	UInt nb_component) {
	this->internalInitialize(nb_component);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	void RandomInternalField<T, BaseField, Generator>::setDefaultValue(
	const T & value) {
	random_parameter.setBaseValue(value);
	this->reset();
	}

	/* ------------------------------------------------------------------------ */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	void RandomInternalField<T, BaseField, Generator>::setRandomDistribution(
	const RandomParameter<T> & param) {
	random_parameter = param;
	this->reset();
	}

	/* ------------------------------------------------------------------------ */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	void RandomInternalField<T, BaseField, Generator>::printself(
	std::ostream & stream, int indent [[gnu::unused]]) const {
	stream << "RandomInternalField [ ";
	random_parameter.printself(stream);
	stream << " ]";
	#if !defined(AKANTU_NDEBUG)
	if (AKANTU_DEBUG_TEST(dblDump)) {
	stream << std::endl;
	InternalField<T>::printself(stream, indent);
	}
	#endif
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	void RandomInternalField<T, BaseField, Generator>::setArrayValues(T * begin,
	T * end) {
	random_parameter.template setValues<Generator>(begin, end);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, template <typename> class BaseField,
	template <typename> class Generator>
	inline RandomInternalField<T, BaseField, Generator>::operator Real() const {
	return random_parameter.getBaseValue();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void ParameterTyped<RandomInternalField<Real>>::setAuto(
	const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	RandomParameter<Real> r = in_param;
	param.setRandomDistribution(r);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_RANDOM_INTERNAL_FIELD_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function.hh b/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function.hh
	index e20b1fd12..ee342f289 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function.hh
	@@ -1,81 +1,81 @@
	/**
	* @file damaged_weight_function.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Damaged weight function for non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_DAMAGED_WEIGHT_FUNCTION_HH_
	#define AKANTU_DAMAGED_WEIGHT_FUNCTION_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Damage weight function */
	/* -------------------------------------------------------------------------- */
	class DamagedWeightFunction : public BaseWeightFunction {
	public:
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	DamagedWeightFunction(NonLocalManager & manager)
	: BaseWeightFunction(manager, "damaged"), damage(nullptr) {
	this->init();
	}

	/* --------------------------------------------------------------------------
	*/
	/* Base Weight Function inherited methods */
	/* --------------------------------------------------------------------------
	*/

	/// set the pointers of internals to the right flattend version
	void init() override;

	inline Real operator()(Real r,
	const __attribute__((unused)) IntegrationPoint & q1,
	const IntegrationPoint & q2);

	private:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */

	/// internal pointer to the current damage vector
	ElementTypeMapReal * damage;
	};

	} // namespace akantu

	#include "damaged_weight_function_inline_impl.hh"

	#endif /* AKANTU_DAMAGED_WEIGHT_FUNCTION_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function_inline_impl.hh b/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function_inline_impl.hh
	index 1ac2b9850..3921bad6f 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/damaged_weight_function_inline_impl.hh
	@@ -1,84 +1,84 @@
	/**
	* @file damaged_weight_function_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Fri Jan 15 2016
	*
	* @brief Implementation of inline function of damaged weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "damaged_weight_function.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline Real DamagedWeightFunction::operator()(Real r,
	const __attribute__((unused))
	IntegrationPoint & q1,
	const IntegrationPoint & q2) {
	/// compute the weight
	UInt quad = q2.global_num;
	Array<Real> & dam_array = (*this->damage)(q2.type, q2.ghost_type);
	Real D = dam_array(quad);
	Real Radius_t = 0;
	Real Radius_init = this->R2;

	// if(D <= 0.5)
	// {
	// Radius_t = 2DRadius_init;
	// }
	// else
	// {
	// Radius_t = 2Radius_init(1-D);
	// }
	//

	Radius_t = Radius_init * (1 - D);

	Radius_init *= Radius_init;
	Radius_t *= Radius_t;

	if (Radius_t < Math::getTolerance()) {
	Radius_t = 0.001 * Radius_init;
	}

	Real expb =
	(2 * std::log(0.51)) / (std::log(1.0 - 0.49 * Radius_t / Radius_init));
	Int expb_floor = std::floor(expb);
	Real b = expb_floor + expb_floor % 2;
	Real alpha = std::max(0., 1. - r * r / Radius_init);
	Real w = std::pow(alpha, b);
	return w;
	}

	/* -------------------------------------------------------------------------- */
	inline void DamagedWeightFunction::init() {
	this->damage = &(this->manager.registerWeightFunctionInternal("damage"));
	}
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function.hh b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function.hh
	index 136fa6a97..fc940b2bc 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function.hh
	@@ -1,98 +1,98 @@
	/**
	* @file remove_damaged_weight_function.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Removed damaged weight function for non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_HH_
	#define AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Remove damaged weight function */
	/* -------------------------------------------------------------------------- */
	class RemoveDamagedWeightFunction : public BaseWeightFunction {
	public:
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	RemoveDamagedWeightFunction(NonLocalManager & manager)
	: BaseWeightFunction(manager, "remove_damaged"), damage(nullptr) {
	this->registerParam("damage_limit", this->damage_limit, 1., _pat_parsable,
	"Damage Threshold");
	this->init();
	}

	/* --------------------------------------------------------------------------
	*/
	/* Base Weight Function inherited methods */
	/* --------------------------------------------------------------------------
	*/

	inline void init() override;

	inline Real operator()(Real r, const IntegrationPoint & q1,
	const IntegrationPoint & q2);

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */

	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	private:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	/// limit at which a point is considered as complitely broken
	Real damage_limit;

	/// internal pointer to the current damage vector
	ElementTypeMapReal * damage;
	};

	} // namespace akantu

	#include "remove_damaged_weight_function_inline_impl.hh"

	#endif /* AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function_inline_impl.hh b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function_inline_impl.hh
	index 681fb9e47..b11d2132e 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_weight_function_inline_impl.hh
	@@ -1,108 +1,108 @@
	/**
	* @file remove_damaged_weight_function_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of inline function of remove damaged weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "remove_damaged_weight_function.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_INLINE_IMPL_HH_
	#define AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-inline Real RemoveDamagedWeightFunction::
	-operator()(Real r, const __attribute__((unused)) IntegrationPoint & q1,
	- const IntegrationPoint & q2) {
	+inline Real RemoveDamagedWeightFunction::operator()(
	+ Real r, const __attribute__((unused)) IntegrationPoint & q1,
	+ const IntegrationPoint & q2) {
	/// compute the weight
	UInt quad = q2.global_num;

	if (q1 == q2) {
	return 1.;
	}

	Array<Real> & dam_array = (*this->damage)(q2.type, q2.ghost_type);
	Real D = dam_array(quad);
	Real w = 0.;
	if (D < damage_limit * (1 - Math::getTolerance())) {
	Real alpha = std::max(0., 1. - r * r / this->R2);
	w = alpha * alpha;
	}
	return w;
	}

	/* -------------------------------------------------------------------------- */
	inline void RemoveDamagedWeightFunction::init() {
	this->damage = &(this->manager.registerWeightFunctionInternal("damage"));
	}

	/* -------------------------------------------------------------------------- */
	inline UInt
	RemoveDamagedWeightFunction::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {

	if (tag == SynchronizationTag::_mnl_weight) {
	return this->manager.getModel().getNbIntegrationPoints(elements) *
	sizeof(Real);
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	RemoveDamagedWeightFunction::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	if (tag == SynchronizationTag::_mnl_weight) {
	DataAccessor<Element>::packElementalDataHelper<Real>(
	*damage, buffer, elements, true,
	this->manager.getModel().getFEEngine());
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	RemoveDamagedWeightFunction::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	if (tag == SynchronizationTag::_mnl_weight) {
	DataAccessor<Element>::unpackElementalDataHelper<Real>(
	*damage, buffer, elements, true,
	this->manager.getModel().getFEEngine());
	}
	}

	} // namespace akantu

	#endif /* AKANTU_REMOVE_DAMAGED_WEIGHT_FUNCTION_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function.hh b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function.hh
	index dfe8d7808..b5b88850a 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function.hh
	@@ -1,85 +1,85 @@
	/**
	* @file remove_damaged_with_damage_rate_weight_function.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Removed damaged weight function for non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_REMOVE_DAMAGED_WITH_DAMAGE_RATE_WEIGHT_FUNCTION_HH_
	#define AKANTU_REMOVE_DAMAGED_WITH_DAMAGE_RATE_WEIGHT_FUNCTION_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* Remove damaged with damage rate weight function */
	/* -------------------------------------------------------------------------- */

	class RemoveDamagedWithDamageRateWeightFunction : public BaseWeightFunction {
	public:
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	RemoveDamagedWithDamageRateWeightFunction(NonLocalManager & manager)
	: BaseWeightFunction(manager, "remove_damage_with_damage_rate"),
	damage_with_damage_rate(nullptr) {
	this->registerParam<Real>("damage_limit",
	this->damage_limit_with_damage_rate, 1,
	_pat_parsable, "Damage Threshold");
	this->init();
	}

	/* --------------------------------------------------------------------------
	*/
	/* Base Weight Function inherited methods */
	/* --------------------------------------------------------------------------
	*/
	inline Real operator()(Real r,
	const __attribute__((unused)) IntegrationPoint & q1,
	const IntegrationPoint & q2);

	inline void init() override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// limit at which a point is considered as complitely broken
	Real damage_limit_with_damage_rate;

	/// internal pointer to the current damage vector
	ElementTypeMapReal * damage_with_damage_rate;
	};

	} // namespace akantu

	#include "remove_damaged_with_damage_rate_weight_function_inline_impl.hh"

	#endif /* AKANTU_REMOVE_DAMAGED_WITH_DAMAGE_WEIGHT_FUNCTION_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function_inline_impl.hh b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function_inline_impl.hh
	index 8e282516b..c1ab81375 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/remove_damaged_with_damage_rate_weight_function_inline_impl.hh
	@@ -1,71 +1,71 @@
	/**
	* @file remove_damaged_with_damage_rate_weight_function_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Fri Jan 15 2016
	*
	* @brief Implementation of inline function of remove damaged with
	* damage rate weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "remove_damaged_with_damage_rate_weight_function.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	inline void RemoveDamagedWithDamageRateWeightFunction::init() {
	this->damage_with_damage_rate =
	&(this->manager.registerWeightFunctionInternal("damage-rate"));
	}

	/* -------------------------------------------------------------------------- */
	inline Real RemoveDamagedWithDamageRateWeightFunction::operator()(
	Real r, const __attribute__((unused)) IntegrationPoint & q1,

	const IntegrationPoint & q2) {
	/// compute the weight
	UInt quad = q2.global_num;

	if (q1.global_num == quad) {
	return 1.;
	}

	Array<Real> & dam_array =
	(*this->damage_with_damage_rate)(q2.type, q2.ghost_type);
	Real D = dam_array(quad);
	Real w = 0.;
	Real alphaexp = 1.;
	Real betaexp = 2.;
	if (D < damage_limit_with_damage_rate) {
	Real alpha = std::max(0., 1. - pow((r * r / this->R2), alphaexp));
	w = pow(alpha, betaexp);
	}

	return w;
	}
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.cc b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.cc
	index 536ee7095..f3084b52e 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.cc
	+++ b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.cc
	@@ -1,125 +1,125 @@
	/**
	* @file stress_based_weight_function.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Thu Feb 20 2020
	*
	* @brief implementation of the stres based weight function classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "stress_based_weight_function.hh"
	namespace akantu {
	/* -------------------------------------------------------------------------- */
	StressBasedWeightFunction::StressBasedWeightFunction(NonLocalManager & manager)
	: BaseWeightFunction(manager, "stress_based")
	// stress_diag("stress_diag", material), selected_stress_diag(NULL),
	// stress_base("stress_base", material), selected_stress_base(NULL),
	// characteristic_size("lc", material), selected_characteristic_size(NULL)
	{

	// this->registerParam("ft", this->ft, 0., _pat_parsable, "Tensile strength");
	// stress_diag.initialize(spatial_dimension);
	// stress_base.initialize(spatial_dimension * spatial_dimension);
	// characteristic_size.initialize(1);
	}

	/* -------------------------------------------------------------------------- */
	/// During intialization the characteristic sizes for all quadrature
	/// points are computed
	void StressBasedWeightFunction::init() {
	// const Mesh & mesh = this->material.getModel().getFEEngine().getMesh();
	// for (UInt g = _not_ghost; g <= _ghost; ++g) {
	// GhostType gt = GhostType(g);
	// Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt);
	// Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, gt);
	// for(; it != last_type; ++it) {
	// UInt nb_quadrature_points =
	// this->material.getModel().getFEEngine().getNbQuadraturePoints(*it, gt);
	// const Array<UInt> & element_filter =
	// this->material.getElementFilter(*it, gt);
	// UInt nb_element = element_filter.size();

	// Array<Real> ones(nb_element*nb_quadrature_points, 1, 1.);
	// Array<Real> & lc = characteristic_size(*it, gt);
	// this->material.getModel().getFEEngine().integrateOnQuadraturePoints(ones,
	// lc,
	// 1,
	// *it,
	// gt,
	// element_filter);

	// for (UInt q = 0; q < nb_quadrature_points * nb_element; q++) {
	// lc(q) = pow(lc(q), 1./ Real(spatial_dimension));
	// }
	// }
	// }
	}

	/* -------------------------------------------------------------------------- */
	/// computation of principals stresses and principal directions
	void StressBasedWeightFunction::updatePrincipalStress(__attribute__((unused))
	GhostType ghost_type) {
	// AKANTU_DEBUG_IN();

	// const Mesh & mesh = this->material.getModel().getFEEngine().getMesh();

	// Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
	// Mesh::type_iterator last_type = mesh.lastType(spatial_dimension,
	// ghost_type);
	// for(; it != last_type; ++it) {
	// Array<Real>::const_matrix_iterator sigma =
	// this->material.getStress(*it, ghost_type).begin(spatial_dimension,
	// spatial_dimension);
	// auto eigenvalues =
	// stress_diag(*it, ghost_type).begin(spatial_dimension);
	// auto eigenvalues_end =
	// stress_diag(*it, ghost_type).end(spatial_dimension);
	// Array<Real>::matrix_iterator eigenvector =
	// stress_base(*it, ghost_type).begin(spatial_dimension,
	// spatial_dimension);

	// #ifndef __trick__
	// auto cl = characteristic_size(*it, ghost_type).begin();
	// #endif
	// UInt q = 0;
	// for(;eigenvalues != eigenvalues_end; ++sigma, ++eigenvalues,
	// ++eigenvector, ++cl, ++q) {
	// sigma->eig(eigenvalues, eigenvector);
	// *eigenvalues /= ft;
	// #ifndef __trick__
	// // specify a lower bound for principal stress based on the size of
	// the element
	// for (UInt i = 0; i < spatial_dimension; ++i) {
	// (eigenvalues)(i) = std::max(cl / this->R, (*eigenvalues)(i));
	// }
	// #endif
	// }
	// }
	// AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.hh b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.hh
	index 628bf311c..0a23cb66c 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function.hh
	@@ -1,101 +1,101 @@
	/**
	* @file stress_based_weight_function.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Mon Aug 24 2015
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Removed damaged weight function for non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "base_weight_function.hh"
	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_STRESS_BASED_WEIGHT_FUNCTION_HH_
	#define AKANTU_STRESS_BASED_WEIGHT_FUNCTION_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* Stress Based Weight */
	/* -------------------------------------------------------------------------- */
	/// based on based on Giry et al.: Stress-based nonlocal damage model,
	/// IJSS, 48, 2011
	class StressBasedWeightFunction : public BaseWeightFunction {
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	StressBasedWeightFunction(NonLocalManager & manager);

	/* --------------------------------------------------------------------------
	*/
	/* Base Weight Function inherited methods */
	/* --------------------------------------------------------------------------
	*/
	void init() override;

	inline void updateInternals() override;

	void updatePrincipalStress(GhostType ghost_type);

	inline void updateQuadraturePointsCoordinates(
	ElementTypeMapArray<Real> & quadrature_points_coordinates);

	inline Real operator()(Real r, const IntegrationPoint & q1,
	const IntegrationPoint & q2);

	/// computation of ellipsoid
	inline Real computeRhoSquare(Real r, Vector<Real> & eigs,
	Matrix<Real> & eigenvects, Vector<Real> & x_s);

	protected:
	inline void setInternal();

	private:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	/// tensile strength
	Real ft;

	/// prinicipal stresses
	ElementTypeMapReal * stress_diag;

	/// for preselection of types (optimization)
	ElementTypeMapReal * selected_stress_diag;

	/// principal directions
	ElementTypeMapReal * stress_base;

	/// lenght intrinisic to the material
	ElementTypeMapReal * characteristic_size;
	};

	} // namespace akantu

	#include "stress_based_weight_function_inline_impl.hh"

	#endif /* AKANTU_STRESS_BASED_WEIGHT_FUNCTION_HH_ */
	diff --git a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function_inline_impl.hh b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function_inline_impl.hh
	index 8fe5492c2..df4a5b24a 100644
	--- a/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function_inline_impl.hh
	+++ b/src/model/solid_mechanics/materials/weight_functions/stress_based_weight_function_inline_impl.hh
	@@ -1,198 +1,198 @@
	/**
	* @file stress_based_weight_function_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Fri Apr 13 2012
	* @date last modification: Tue Dec 04 2018
	*
	* @brief Implementation of inline function of remove damaged with
	* damage rate weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "stress_based_weight_function.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	inline void StressBasedWeightFunction::updateInternals() {
	// updatePrincipalStress(_not_ghost);
	// updatePrincipalStress(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	// inline void StressBasedWeightFunction::selectType(ElementType type1,
	// GhostType ghost_type1,
	// ElementType type2,
	// GhostType ghost_type2) {
	// selected_stress_diag = &stress_diag(type2, ghost_type2);
	// selected_stress_base = &stress_base(type2, ghost_type2);

	// selected_characteristic_size = &characteristic_size(type1, ghost_type1);
	// }

	/* -------------------------------------------------------------------------- */
	inline Real StressBasedWeightFunction::
	computeRhoSquare( // NOLINT(readability-convert-member-functions-to-static)
	Real /r/, Vector<Real> & /eigs/, Matrix<Real> & /eigenvects/,
	Vector<Real> & /x_s/) {
	// if (spatial_dimension == 1)
	// return eigs[0];
	// else if (spatial_dimension == 2) {
	// Vector<Real> u1(eigenvects.storage(), 2);
	// Real cos_t = x_s.dot(u1) / (x_s.norm() * u1.norm());

	// Real cos_t_2;
	// Real sin_t_2;

	// Real sigma1_2 = eigs[0]*eigs[0];
	// Real sigma2_2 = eigs[1]*eigs[1];

	// #ifdef __trick__
	// Real zero = std::numeric_limits<Real>::epsilon();
	// if(std::abs(cos_t) < zero) {
	// cos_t_2 = 0;
	// sin_t_2 = 1;
	// } else {
	// cos_t_2 = cos_t * cos_t;
	// sin_t_2 = (1 - cos_t_2);
	// }

	// Real rhop1 = std::max(0., cos_t_2 / sigma1_2);
	// Real rhop2 = std::max(0., sin_t_2 / sigma2_2);
	// #else
	// cos_t_2 = cos_t * cos_t;
	// sin_t_2 = (1 - cos_t_2);

	// Real rhop1 = cos_t_2 / sigma1_2;
	// Real rhop2 = sin_t_2 / sigma2_2;
	// #endif

	// return 1./ (rhop1 + rhop2);
	// } else if (spatial_dimension == 3) {
	// Vector<Real> u1(eigenvects.storage() + 0*3, 3);
	// //Vector<Real> u2(eigenvects.storage() + 1*3, 3);
	// Vector<Real> u3(eigenvects.storage() + 2*3, 3);

	// Real zero = std::numeric_limits<Real>::epsilon();

	// Vector<Real> tmp(3);
	// tmp.crossProduct(x_s, u3);

	// Vector<Real> u3_C_x_s_C_u3(3);
	// u3_C_x_s_C_u3.crossProduct(u3, tmp);

	// Real norm_u3_C_x_s_C_u3 = u3_C_x_s_C_u3.norm();
	// Real cos_t = 0.;
	// if(std::abs(norm_u3_C_x_s_C_u3) > zero) {
	// Real inv_norm_u3_C_x_s_C_u3 = 1. / norm_u3_C_x_s_C_u3;
	// cos_t = u1.dot(u3_C_x_s_C_u3) * inv_norm_u3_C_x_s_C_u3;
	// }

	// Real cos_p = u3.dot(x_s) / r;

	// Real cos_t_2;
	// Real sin_t_2;
	// Real cos_p_2;
	// Real sin_p_2;

	// Real sigma1_2 = eigs[0]*eigs[0];
	// Real sigma2_2 = eigs[1]*eigs[1];
	// Real sigma3_2 = eigs[2]*eigs[2];

	// #ifdef __trick__
	// if(std::abs(cos_t) < zero) {
	// cos_t_2 = 0;
	// sin_t_2 = 1;
	// } else {
	// cos_t_2 = cos_t * cos_t;
	// sin_t_2 = (1 - cos_t_2);
	// }

	// if(std::abs(cos_p) < zero) {
	// cos_p_2 = 0;
	// sin_p_2 = 1;
	// } else {
	// cos_p_2 = cos_p * cos_p;
	// sin_p_2 = (1 - cos_p_2);
	// }

	// Real rhop1 = std::max(0., sin_p_2 * cos_t_2 / sigma1_2);
	// Real rhop2 = std::max(0., sin_p_2 * sin_t_2 / sigma2_2);
	// Real rhop3 = std::max(0., cos_p_2 / sigma3_2);
	// #else
	// cos_t_2 = cos_t * cos_t;
	// sin_t_2 = (1 - cos_t_2);

	// cos_p_2 = cos_p * cos_p;
	// sin_p_2 = (1 - cos_p_2);

	// Real rhop1 = sin_p_2 * cos_t_2 / sigma1_2;
	// Real rhop2 = sin_p_2 * sin_t_2 / sigma2_2;
	// Real rhop3 = cos_p_2 / sigma3_2;
	// #endif

	// return 1./ (rhop1 + rhop2 + rhop3);
	// }
	return 0.;
	}

	/* -------------------------------------------------------------------------- */
	inline Real
	StressBasedWeightFunction::operator()(Real /r/,
	const IntegrationPoint & /q1/,
	const IntegrationPoint & /q2/) {
	// Real zero = std::numeric_limits<Real>::epsilon();

	// if(r < zero) return 1.; // means x and s are the same points

	// const Vector<Real> & x = q1.getPosition();
	// const Vector<Real> & s = q2.getPosition();

	// Vector<Real> eigs =
	// selected_stress_diag->begin(spatial_dimension)[q2.global_num];

	// Matrix<Real> eigenvects =
	// selected_stress_base->begin(spatial_dimension,
	// spatial_dimension)[q2.global_num];

	// Real min_rho_lc = selected_characteristic_size->begin()[q1.global_num];

	// Vector<Real> x_s(spatial_dimension);
	// x_s = x;
	// x_s -= s;

	// Real rho_2 = computeRhoSquare(r, eigs, eigenvects, x_s);

	// Real rho_lc_2 = std::max(this->R2 * rho_2, min_rho_lc*min_rho_lc);

	// // Real w = std::max(0., 1. - r*r / rho_lc_2);
	// // w = w*w;
	// Real w = exp(- 22r*r / rho_lc_2);
	// return w;
	return 0.;
	}
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model.cc b/src/model/solid_mechanics/solid_mechanics_model.cc
	index a2777134a..a36cb1397 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model.cc
	@@ -1,1256 +1,1255 @@
	/**
	* @file solid_mechanics_model.cc
	*
	* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue Jul 27 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Implementation of the SolidMechanicsModel class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	#include "integrator_gauss.hh"
	#include "shape_lagrange.hh"
	#include "solid_mechanics_model_tmpl.hh"

	#include "communicator.hh"
	#include "element_synchronizer.hh"
	#include "sparse_matrix.hh"
	#include "synchronizer_registry.hh"

	#include "dumpable_inline_impl.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_iohelper_paraview.hh"
	#endif

	#include "material_non_local.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/**
	* A solid mechanics model need a mesh and a dimension to be created. the model
	* by it self can not do a lot, the good init functions should be called in
	* order to configure the model depending on what we want to do.
	*
	* @param mesh mesh representing the model we want to simulate
	* @param dim spatial dimension of the problem, if dim = 0 (default value) the
	* dimension of the problem is assumed to be the on of the mesh
	* @param id an id to identify the model
	* @param model_type this is an internal parameter for inheritance purposes
	*/

	SolidMechanicsModel::SolidMechanicsModel(
	Mesh & mesh, UInt dim, const ID & id,
	std::shared_ptr<DOFManager> dof_manager, const ModelType model_type)
	: Model(mesh, model_type, std::move(dof_manager), dim, id),
	material_index("material index", id),
	material_local_numbering("material local numbering", id) {
	AKANTU_DEBUG_IN();

	this->registerFEEngineObject<MyFEEngineType>("SolidMechanicsFEEngine", mesh,
	Model::spatial_dimension);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("solid_mechanics_model", id, true);
	this->mesh.addDumpMesh(mesh, Model::spatial_dimension, _not_ghost,
	_ek_regular);
	#endif

	material_selector = std::make_shared<DefaultMaterialSelector>(material_index);

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, SynchronizationTag::_material_id);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_smm_mass);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_smm_stress);
	this->registerSynchronizer(synchronizer, SynchronizationTag::_for_dump);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SolidMechanicsModel::~SolidMechanicsModel() = default;

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::setTimeStep(Real time_step, const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper().setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	/* Initialization */
	/* -------------------------------------------------------------------------- */
	/**
	* This function groups many of the initialization in on function. For most of
	* basics case the function should be enough. The functions initialize the
	* model, the internal vectors, set them to 0, and depending on the parameters
	* it also initialize the explicit or implicit solver.
	*
	* @param options
	* \parblock
	* contains the different options to initialize the model
	* \li \c analysis_method specify the type of solver to use
	* \endparblock
	*/
	void SolidMechanicsModel::initFullImpl(const ModelOptions & options) {
	material_index.initialize(mesh, _element_kind = _ek_not_defined,
	_default_value = UInt(-1), _with_nb_element = true);
	material_local_numbering.initialize(mesh, _element_kind = _ek_not_defined,
	_with_nb_element = true);

	Model::initFullImpl(options);

	// initialize the materials
	if (not this->parser.getLastParsedFile().empty()) {
	this->instantiateMaterials();
	this->initMaterials();
	}

	this->initBC(this, displacement, displacement_increment, external_force);
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolverType SolidMechanicsModel::getDefaultSolverType() const {
	return TimeStepSolverType::_dynamic_lumped;
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions SolidMechanicsModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["displacement"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	if (this->method == _explicit_consistent_mass) {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_central_difference;
	options.solution_type["displacement"] = IntegrationScheme::_acceleration;
	} else {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_trapezoidal_rule_2;
	options.solution_type["displacement"] = IntegrationScheme::_displacement;
	}
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	SolidMechanicsModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _explicit_consistent_mass: {
	return std::make_tuple("explicit", TimeStepSolverType::_dynamic);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType /unused/) {
	auto & dof_manager = this->getDOFManager();

	/* ------------------------------------------------------------------------ */
	// for alloc type of solvers
	this->allocNodalField(this->displacement, spatial_dimension, "displacement");
	this->allocNodalField(this->previous_displacement, spatial_dimension,
	"previous_displacement");
	this->allocNodalField(this->displacement_increment, spatial_dimension,
	"displacement_increment");
	this->allocNodalField(this->internal_force, spatial_dimension,
	"internal_force");
	this->allocNodalField(this->external_force, spatial_dimension,
	"external_force");
	this->allocNodalField(this->blocked_dofs, spatial_dimension, "blocked_dofs");
	this->allocNodalField(this->current_position, spatial_dimension,
	"current_position");

	// initialize the current positions
	this->current_position->copy(this->mesh.getNodes());

	/* ------------------------------------------------------------------------ */
	if (!dof_manager.hasDOFs("displacement")) {
	dof_manager.registerDOFs("displacement", *this->displacement, _dst_nodal);
	dof_manager.registerBlockedDOFs("displacement", *this->blocked_dofs);
	dof_manager.registerDOFsIncrement("displacement",
	*this->displacement_increment);
	dof_manager.registerDOFsPrevious("displacement",
	*this->previous_displacement);
	}

	/* ------------------------------------------------------------------------ */
	// for dynamic
	if (time_step_solver_type == TimeStepSolverType::_dynamic \|\|
	time_step_solver_type == TimeStepSolverType::_dynamic_lumped) {
	this->allocNodalField(this->velocity, spatial_dimension, "velocity");
	this->allocNodalField(this->acceleration, spatial_dimension,
	"acceleration");

	if (!dof_manager.hasDOFsDerivatives("displacement", 1)) {
	dof_manager.registerDOFsDerivative("displacement", 1, *this->velocity);
	dof_manager.registerDOFsDerivative("displacement", 2,
	*this->acceleration);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the model,basically it pre-compute the shapes, shapes derivatives
	* and jacobian
	*/
	void SolidMechanicsModel::initModel() {
	/// \todo add the current position as a parameter to initShapeFunctions for
	/// large deformation
	getFEEngine().initShapeFunctions(_not_ghost);
	getFEEngine().initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	/* ------------------------------------------------------------------------ */
	// computes the internal forces
	this->assembleInternalForces();

	/* ------------------------------------------------------------------------ */
	this->getDOFManager().assembleToResidual("displacement",
	*this->external_force, 1);
	this->getDOFManager().assembleToResidual("displacement",
	*this->internal_force, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleResidual(const ID & residual_part) {
	AKANTU_DEBUG_IN();

	if ("external" == residual_part) {
	this->getDOFManager().assembleToResidual("displacement",
	*this->external_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	if ("internal" == residual_part) {
	this->assembleInternalForces();
	this->getDOFManager().assembleToResidual("displacement",
	*this->internal_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	AKANTU_CUSTOM_EXCEPTION(
	debug::SolverCallbackResidualPartUnknown(residual_part));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MatrixType SolidMechanicsModel::getMatrixType(const ID & matrix_id) {
	// \TODO check the materials to know what is the correct answer
	if (matrix_id == "C") {
	return _mt_not_defined;
	}

	if (matrix_id == "K") {
	auto matrix_type = _unsymmetric;

	for (auto & material : materials) {
	matrix_type = std::max(matrix_type, material->getMatrixType(matrix_id));
	}
	}
	return _symmetric;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleMatrix(const ID & matrix_id) {
	if (matrix_id == "K") {
	this->assembleStiffnessMatrix();
	} else if (matrix_id == "M") {
	this->assembleMass();
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleLumpedMatrix(const ID & matrix_id) {
	if (matrix_id == "M") {
	this->assembleMassLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::beforeSolveStep() {
	for (auto & material : materials) {
	material->beforeSolveStep();
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::afterSolveStep(bool converged) {
	for (auto & material : materials) {
	material->afterSolveStep(converged);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::predictor() { ++displacement_release; }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::corrector() { ++displacement_release; }

	/* -------------------------------------------------------------------------- */
	/**
	* This function computes the internal forces as \f$F_{int} = \int_{\Omega} N
	* \sigma d\Omega@\f$
	*/
	void SolidMechanicsModel::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the internal forces");

	this->internal_force->zero();

	// compute the stresses of local elements
	AKANTU_DEBUG_INFO("Compute local stresses");
	for (auto & material : materials) {
	material->computeAllStresses(_not_ghost);
	}

	/* ------------------------------------------------------------------------ */
	/* Computation of the non local part */
	if (this->non_local_manager) {
	this->non_local_manager->computeAllNonLocalStresses();
	}

	// communicate the stresses
	AKANTU_DEBUG_INFO("Send data for residual assembly");
	this->asynchronousSynchronize(SynchronizationTag::_smm_stress);

	// assemble the forces due to local stresses
	AKANTU_DEBUG_INFO("Assemble residual for local elements");
	for (auto & material : materials) {
	material->assembleInternalForces(_not_ghost);
	}

	// finalize communications
	AKANTU_DEBUG_INFO("Wait distant stresses");
	this->waitEndSynchronize(SynchronizationTag::_smm_stress);

	// assemble the stresses due to ghost elements
	AKANTU_DEBUG_INFO("Assemble residual for ghost elements");
	for (auto & material : materials) {
	material->assembleInternalForces(_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleStiffnessMatrix(bool need_to_reassemble) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix.");

	// Check if materials need to recompute the matrix
	for (auto & material : materials) {
	need_to_reassemble \|= material->hasMatrixChanged("K");
	}

	if (need_to_reassemble) {
	this->getDOFManager().getMatrix("K").zero();

	// call compute stiffness matrix on each local elements
	for (auto & material : materials) {
	material->assembleStiffnessMatrix(_not_ghost);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateCurrentPosition() {
	if (this->current_position_release == this->displacement_release) {
	return;
	}

	this->current_position->copy(this->mesh.getNodes());

	auto cpos_it = this->current_position->begin(Model::spatial_dimension);
	auto cpos_end = this->current_position->end(Model::spatial_dimension);
	auto disp_it = this->displacement->begin(Model::spatial_dimension);

	for (; cpos_it != cpos_end; ++cpos_it, ++disp_it) {
	cpos_it += disp_it;
	}

	this->current_position_release = this->displacement_release;
	}

	/* -------------------------------------------------------------------------- */
	const Array<Real> & SolidMechanicsModel::getCurrentPosition() {
	this->updateCurrentPosition();
	return *this->current_position;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateDataForNonLocalCriterion(
	ElementTypeMapReal & criterion) {
	const ID field_name = criterion.getName();
	for (auto & material : materials) {
	if (!material->isInternal<Real>(field_name, _ek_regular)) {
	continue;
	}

	for (auto ghost_type : ghost_types) {
	material->flattenInternal(field_name, criterion, ghost_type, _ek_regular);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/* Information */
	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep() {
	AKANTU_DEBUG_IN();

	Real min_dt = getStableTimeStep(_not_ghost);

	/// reduction min over all processors
	mesh.getCommunicator().allReduce(min_dt, SynchronizerOperation::_min);

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Real min_dt = std::numeric_limits<Real>::max();

	this->updateCurrentPosition();

	Element elem;
	elem.ghost_type = ghost_type;

	for (auto type :
	mesh.elementTypes(Model::spatial_dimension, ghost_type, _ek_regular)) {
	elem.type = type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt nb_element = mesh.getNbElement(type);

	auto mat_indexes = material_index(type, ghost_type).begin();
	auto mat_loc_num = material_local_numbering(type, ghost_type).begin();

	Array<Real> X(0, nb_nodes_per_element * Model::spatial_dimension);
	FEEngine::extractNodalToElementField(mesh, *current_position, X, type,
	_not_ghost);

	auto X_el = X.begin(Model::spatial_dimension, nb_nodes_per_element);

	for (UInt el = 0; el < nb_element;
	++el, ++X_el, ++mat_indexes, ++mat_loc_num) {
	elem.element = *mat_loc_num;
	Real el_h = getFEEngine().getElementInradius(*X_el, type);
	Real el_c = this->materials[*mat_indexes]->getCelerity(elem);
	Real el_dt = el_h / el_c;

	min_dt = std::min(min_dt, el_dt);
	}
	}

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy() {
	AKANTU_DEBUG_IN();

	Real ekin = 0.;
	UInt nb_nodes = mesh.getNbNodes();

	if (this->getDOFManager().hasLumpedMatrix("M")) {
	auto m_it = this->mass->begin(Model::spatial_dimension);
	auto m_end = this->mass->end(Model::spatial_dimension);
	auto v_it = this->velocity->begin(Model::spatial_dimension);

	for (UInt n = 0; m_it != m_end; ++n, ++m_it, ++v_it) {
	const auto & v = *v_it;
	const auto & m = *m_it;

	Real mv2 = 0.;
	auto is_local_node = mesh.isLocalOrMasterNode(n);
	// bool is_not_pbc_slave_node = !isPBCSlaveNode(n);
	auto count_node = is_local_node; // && is_not_pbc_slave_node;
	if (count_node) {
	for (UInt i = 0; i < Model::spatial_dimension; ++i) {
	if (m(i) > std::numeric_limits<Real>::epsilon()) {
	mv2 += v(i) * v(i) * m(i);
	}
	}
	}

	ekin += mv2;
	}
	} else if (this->getDOFManager().hasMatrix("M")) {
	Array<Real> Mv(nb_nodes, Model::spatial_dimension);
	this->getDOFManager().assembleMatMulVectToArray("displacement", "M",
	*this->velocity, Mv);

	for (auto && data : zip(arange(nb_nodes), make_view(Mv, spatial_dimension),
	make_view(*this->velocity, spatial_dimension))) {
	ekin += std::get<2>(data).dot(std::get<1>(data)) *
	static_cast<Real>(mesh.isLocalOrMasterNode(std::get<0>(data)));
	}
	} else {
	AKANTU_ERROR("No function called to assemble the mass matrix.");
	}

	mesh.getCommunicator().allReduce(ekin, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return ekin * .5;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy(ElementType type, UInt index) {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);

	Array<Real> vel_on_quad(nb_quadrature_points, Model::spatial_dimension);
	Array<UInt> filter_element(1, 1, index);

	getFEEngine().interpolateOnIntegrationPoints(*velocity, vel_on_quad,
	Model::spatial_dimension, type,
	_not_ghost, filter_element);

	auto vit = vel_on_quad.begin(Model::spatial_dimension);
	auto vend = vel_on_quad.end(Model::spatial_dimension);

	Vector<Real> rho_v2(nb_quadrature_points);

	Real rho = materials[material_index(type)(index)]->getRho();

	for (UInt q = 0; vit != vend; ++vit, ++q) {
	rho_v2(q) = rho * vit->dot(*vit);
	}

	AKANTU_DEBUG_OUT();

	return .5 * getFEEngine().integrate(rho_v2, type, index);
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getExternalWork() {
	AKANTU_DEBUG_IN();

	auto ext_force_it = external_force->begin(Model::spatial_dimension);
	auto int_force_it = internal_force->begin(Model::spatial_dimension);
	auto boun_it = blocked_dofs->begin(Model::spatial_dimension);

	decltype(ext_force_it) incr_or_velo_it;
	if (this->method == _static) {
	incr_or_velo_it =
	this->displacement_increment->begin(Model::spatial_dimension);
	} else {
	incr_or_velo_it = this->velocity->begin(Model::spatial_dimension);
	}

	Real work = 0.;

	UInt nb_nodes = this->mesh.getNbNodes();

	for (UInt n = 0; n < nb_nodes;
	++n, ++ext_force_it, ++int_force_it, ++boun_it, ++incr_or_velo_it) {
	const auto & int_force = *int_force_it;
	const auto & ext_force = *ext_force_it;
	const auto & boun = *boun_it;
	const auto & incr_or_velo = *incr_or_velo_it;

	bool is_local_node = this->mesh.isLocalOrMasterNode(n);
	// bool is_not_pbc_slave_node = !this->isPBCSlaveNode(n);
	bool count_node = is_local_node; // && is_not_pbc_slave_node;

	if (count_node) {
	for (UInt i = 0; i < Model::spatial_dimension; ++i) {
	if (boun(i)) {
	work -= int_force(i) * incr_or_velo(i);
	} else {
	work += ext_force(i) * incr_or_velo(i);
	}
	}
	}
	}

	mesh.getCommunicator().allReduce(work, SynchronizerOperation::_sum);

	if (this->method != _static) {
	work *= this->getTimeStep();
	}

	AKANTU_DEBUG_OUT();
	return work;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy();
	}

	if (energy_id == "external work") {
	return getExternalWork();
	}

	Real energy = 0.;
	for (auto & material : materials) {
	energy += material->getEnergy(energy_id);
	}

	/// reduction sum over all processors
	mesh.getCommunicator().allReduce(energy, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id,
	ElementType type, UInt index) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy(type, index);
	}

	UInt mat_index = this->material_index(type, _not_ghost)(index);
	UInt mat_loc_num = this->material_local_numbering(type, _not_ghost)(index);
	Real energy =
	this->materials[mat_index]->getEnergy(energy_id, type, mat_loc_num);

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	-Real SolidMechanicsModel::getEnergy(const ID & energy_id,
	- const ID & group_id) {
	+Real SolidMechanicsModel::getEnergy(const ID & energy_id, const ID & group_id) {
	auto && group = mesh.getElementGroup(group_id);
	auto energy = 0.;
	- for(auto && type : group.elementTypes()) {
	- for(auto el : group.getElementsIterable(type)) {
	+ for (auto && type : group.elementTypes()) {
	+ for (auto el : group.getElementsIterable(type)) {
	energy += getEnergy(energy_id, el);
	}
	}

	/// reduction sum over all processors
	mesh.getCommunicator().allReduce(energy, SynchronizerOperation::_sum);

	return energy;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	this->material_index.initialize(mesh, _element_kind = _ek_not_defined,
	_with_nb_element = true,
	_default_value = UInt(-1));
	this->material_local_numbering.initialize(
	mesh, _element_kind = _ek_not_defined, _with_nb_element = true,
	_default_value = UInt(-1));

	ElementTypeMapArray<UInt> filter("new_element_filter", this->getID());

	for (const auto & elem : element_list) {
	if (mesh.getSpatialDimension(elem.type) != spatial_dimension) {
	continue;
	}

	if (!filter.exists(elem.type, elem.ghost_type)) {
	filter.alloc(0, 1, elem.type, elem.ghost_type);
	}
	filter(elem.type, elem.ghost_type).push_back(elem.element);
	}

	// this fails in parallel if the event is sent on facet between constructor
	// and initFull \todo: to debug...
	this->assignMaterialToElements(&filter);

	for (auto & material : materials) {
	material->onElementsAdded(element_list, event);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsRemoved(
	const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) {
	for (auto & material : materials) {
	material->onElementsRemoved(element_list, new_numbering, event);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();

	if (displacement) {
	displacement->resize(nb_nodes, 0.);
	++displacement_release;
	}
	if (mass) {
	mass->resize(nb_nodes, 0.);
	}
	if (velocity) {
	velocity->resize(nb_nodes, 0.);
	}
	if (acceleration) {
	acceleration->resize(nb_nodes, 0.);
	}
	if (external_force) {
	external_force->resize(nb_nodes, 0.);
	}
	if (internal_force) {
	internal_force->resize(nb_nodes, 0.);
	}
	if (blocked_dofs) {
	blocked_dofs->resize(nb_nodes, false);
	}
	if (current_position) {
	current_position->resize(nb_nodes, 0.);
	}

	if (previous_displacement) {
	previous_displacement->resize(nb_nodes, 0.);
	}
	if (displacement_increment) {
	displacement_increment->resize(nb_nodes, 0.);
	}

	for (auto & material : materials) {
	material->onNodesAdded(nodes_list, event);
	}

	need_to_reassemble_lumped_mass = true;
	need_to_reassemble_mass = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesRemoved(const Array<UInt> & /element_list/,
	const Array<UInt> & new_numbering,
	const RemovedNodesEvent & /event/) {
	if (displacement) {
	mesh.removeNodesFromArray(*displacement, new_numbering);
	++displacement_release;
	}
	if (mass) {
	mesh.removeNodesFromArray(*mass, new_numbering);
	}
	if (velocity) {
	mesh.removeNodesFromArray(*velocity, new_numbering);
	}
	if (acceleration) {
	mesh.removeNodesFromArray(*acceleration, new_numbering);
	}
	if (internal_force) {
	mesh.removeNodesFromArray(*internal_force, new_numbering);
	}
	if (external_force) {
	mesh.removeNodesFromArray(*external_force, new_numbering);
	}
	if (blocked_dofs) {
	mesh.removeNodesFromArray(*blocked_dofs, new_numbering);
	}

	// if (increment_acceleration)
	// mesh.removeNodesFromArray(*increment_acceleration, new_numbering);
	if (displacement_increment) {
	mesh.removeNodesFromArray(*displacement_increment, new_numbering);
	}

	if (previous_displacement) {
	mesh.removeNodesFromArray(*previous_displacement, new_numbering);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "Solid Mechanics Model [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + spatial dimension : " << Model::spatial_dimension
	<< std::endl;

	stream << space << " + fem [" << std::endl;
	getFEEngine().printself(stream, indent + 2);
	stream << space << " ]" << std::endl;

	stream << space << " + nodals information [" << std::endl;
	displacement->printself(stream, indent + 2);
	if (velocity) {
	velocity->printself(stream, indent + 2);
	}
	if (acceleration) {
	acceleration->printself(stream, indent + 2);
	}
	if (mass) {
	mass->printself(stream, indent + 2);
	}
	external_force->printself(stream, indent + 2);
	internal_force->printself(stream, indent + 2);
	blocked_dofs->printself(stream, indent + 2);
	stream << space << " ]" << std::endl;

	stream << space << " + material information [" << std::endl;
	material_index.printself(stream, indent + 2);
	stream << space << " ]" << std::endl;

	stream << space << " + materials [" << std::endl;
	for (const auto & material : materials) {
	material->printself(stream, indent + 2);
	}
	stream << space << " ]" << std::endl;

	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initializeNonLocal() {
	this->non_local_manager->synchronize(*this, SynchronizationTag::_material_id);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::insertIntegrationPointsInNeighborhoods(
	GhostType ghost_type) {
	for (auto & mat : materials) {
	MaterialNonLocalInterface * mat_non_local;
	if ((mat_non_local =
	dynamic_cast<MaterialNonLocalInterface *>(mat.get())) == nullptr) {
	continue;
	}

	ElementTypeMapArray<Real> quadrature_points_coordinates(
	"quadrature_points_coordinates_tmp_nl", this->id);
	quadrature_points_coordinates.initialize(this->getFEEngine(),
	_nb_component = spatial_dimension,
	_ghost_type = ghost_type);

	for (const auto & type : quadrature_points_coordinates.elementTypes(
	Model::spatial_dimension, ghost_type)) {
	this->getFEEngine().computeIntegrationPointsCoordinates(
	quadrature_points_coordinates(type, ghost_type), type, ghost_type);
	}

	mat_non_local->initMaterialNonLocal();

	mat_non_local->insertIntegrationPointsInNeighborhoods(
	ghost_type, quadrature_points_coordinates);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::computeNonLocalStresses(GhostType ghost_type) {
	for (auto & mat : materials) {
	if (not aka::is_of_type<MaterialNonLocalInterface>(*mat)) {
	continue;
	}

	auto & mat_non_local = dynamic_cast<MaterialNonLocalInterface &>(*mat);
	mat_non_local.computeNonLocalStresses(ghost_type);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateLocalInternal(
	ElementTypeMapReal & internal_flat, GhostType ghost_type,
	ElementKind kind) {
	const ID field_name = internal_flat.getName();
	for (auto & material : materials) {
	if (material->isInternal<Real>(field_name, kind)) {
	material->flattenInternal(field_name, internal_flat, ghost_type, kind);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateNonLocalInternal(
	ElementTypeMapReal & internal_flat, GhostType ghost_type,
	ElementKind kind) {

	const ID field_name = internal_flat.getName();

	for (auto & mat : materials) {
	if (not aka::is_of_type<MaterialNonLocalInterface>(*mat)) {
	continue;
	}

	auto & mat_non_local = dynamic_cast<MaterialNonLocalInterface &>(*mat);
	mat_non_local.updateNonLocalInternals(internal_flat, field_name, ghost_type,
	kind);
	}
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & SolidMechanicsModel::getFEEngineBoundary(const ID & name) {
	return getFEEngineClassBoundary<MyFEEngineType>(name);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::splitElementByMaterial(
	const Array<Element> & elements,
	std::vector<Array<Element>> & elements_per_mat) const {
	for (const auto & el : elements) {
	Element mat_el = el;
	mat_el.element = this->material_local_numbering(el);
	elements_per_mat[this->material_index(el)].push_back(mat_el);
	}
	}

	/* -------------------------------------------------------------------------- */
	UInt SolidMechanicsModel::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes_per_element = 0;

	for (const Element & el : elements) {
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_material_id: {
	size += elements.size() * sizeof(UInt);
	break;
	}
	case SynchronizationTag::_smm_mass: {
	size += nb_nodes_per_element * sizeof(Real) *
	Model::spatial_dimension; // mass vector
	break;
	}
	case SynchronizationTag::_smm_for_gradu: {
	size += nb_nodes_per_element * Model::spatial_dimension *
	sizeof(Real); // displacement
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	// force, displacement, boundary
	size += nb_nodes_per_element * Model::spatial_dimension *
	(2 * sizeof(Real) + sizeof(bool));
	break;
	}
	case SynchronizationTag::_for_dump: {
	// displacement, velocity, acceleration, residual, force
	size += nb_nodes_per_element * Model::spatial_dimension * sizeof(Real) * 5;
	break;
	}
	default: {
	}
	}

	if (tag != SynchronizationTag::_material_id) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	size += mat.getNbData(elements, tag);
	});
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	switch (tag) {
	case SynchronizationTag::_material_id: {
	- packElementalDataHelper(
	- material_index, buffer, elements, false, getFEEngine());
	+ packElementalDataHelper(material_index, buffer, elements, false,
	+ getFEEngine());
	break;
	}
	case SynchronizationTag::_smm_mass: {
	packNodalDataHelper(*mass, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_smm_for_gradu: {
	packNodalDataHelper(*displacement, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_for_dump: {
	packNodalDataHelper(*displacement, buffer, elements, mesh);
	packNodalDataHelper(*velocity, buffer, elements, mesh);
	packNodalDataHelper(*acceleration, buffer, elements, mesh);
	packNodalDataHelper(*internal_force, buffer, elements, mesh);
	packNodalDataHelper(*external_force, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	packNodalDataHelper(*external_force, buffer, elements, mesh);
	packNodalDataHelper(*velocity, buffer, elements, mesh);
	packNodalDataHelper(*blocked_dofs, buffer, elements, mesh);
	break;
	}
	default: {
	}
	}

	if (tag != SynchronizationTag::_material_id) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	mat.packData(buffer, elements, tag);
	});
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	switch (tag) {
	case SynchronizationTag::_material_id: {
	for (auto && element : elements) {
	UInt recv_mat_index;
	buffer >> recv_mat_index;
	UInt & mat_index = material_index(element);
	if (mat_index != UInt(-1)) {
	continue;
	}

	// add ghosts element to the correct material
	mat_index = recv_mat_index;
	UInt index = materials[mat_index]->addElement(element);
	material_local_numbering(element) = index;
	}
	break;
	}
	case SynchronizationTag::_smm_mass: {
	unpackNodalDataHelper(*mass, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_smm_for_gradu: {
	unpackNodalDataHelper(*displacement, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_for_dump: {
	unpackNodalDataHelper(*displacement, buffer, elements, mesh);
	unpackNodalDataHelper(*velocity, buffer, elements, mesh);
	unpackNodalDataHelper(*acceleration, buffer, elements, mesh);
	unpackNodalDataHelper(*internal_force, buffer, elements, mesh);
	unpackNodalDataHelper(*external_force, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	unpackNodalDataHelper(*external_force, buffer, elements, mesh);
	unpackNodalDataHelper(*velocity, buffer, elements, mesh);
	unpackNodalDataHelper(*blocked_dofs, buffer, elements, mesh);
	break;
	}
	default: {
	}
	}

	if (tag != SynchronizationTag::_material_id) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	mat.unpackData(buffer, elements, tag);
	});
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	UInt SolidMechanicsModel::getNbData(const Array<UInt> & dofs,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	// UInt nb_nodes = mesh.getNbNodes();

	switch (tag) {
	case SynchronizationTag::_smm_uv: {
	size += sizeof(Real) * Model::spatial_dimension * 2;
	break;
	}
	case SynchronizationTag::_smm_res: /* FALLTHRU */
	case SynchronizationTag::_smm_mass: {
	size += sizeof(Real) * Model::spatial_dimension;
	break;
	}
	case SynchronizationTag::_for_dump: {
	size += sizeof(Real) * Model::spatial_dimension * 5;
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return size * dofs.size();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::packData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	switch (tag) {
	case SynchronizationTag::_smm_uv: {
	packDOFDataHelper(*displacement, buffer, dofs);
	packDOFDataHelper(*velocity, buffer, dofs);
	break;
	}
	case SynchronizationTag::_smm_res: {
	packDOFDataHelper(*internal_force, buffer, dofs);
	break;
	}
	case SynchronizationTag::_smm_mass: {
	packDOFDataHelper(*mass, buffer, dofs);
	break;
	}
	case SynchronizationTag::_for_dump: {
	packDOFDataHelper(*displacement, buffer, dofs);
	packDOFDataHelper(*velocity, buffer, dofs);
	packDOFDataHelper(*acceleration, buffer, dofs);
	packDOFDataHelper(*internal_force, buffer, dofs);
	packDOFDataHelper(*external_force, buffer, dofs);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	switch (tag) {
	case SynchronizationTag::_smm_uv: {
	unpackDOFDataHelper(*displacement, buffer, dofs);
	unpackDOFDataHelper(*velocity, buffer, dofs);
	break;
	}
	case SynchronizationTag::_smm_res: {
	unpackDOFDataHelper(*internal_force, buffer, dofs);
	break;
	}
	case SynchronizationTag::_smm_mass: {
	unpackDOFDataHelper(*mass, buffer, dofs);
	break;
	}
	case SynchronizationTag::_for_dump: {
	unpackDOFDataHelper(*displacement, buffer, dofs);
	unpackDOFDataHelper(*velocity, buffer, dofs);
	unpackDOFDataHelper(*acceleration, buffer, dofs);
	unpackDOFDataHelper(*internal_force, buffer, dofs);
	unpackDOFDataHelper(*external_force, buffer, dofs);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model.hh b/src/model/solid_mechanics/solid_mechanics_model.hh
	index 7aa62cbed..625f149a4 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model.hh
	@@ -1,594 +1,593 @@
	/**
	* @file solid_mechanics_model.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 27 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Model of Solid Mechanics
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition.hh"
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	#include "model.hh"
	#include "non_local_manager_callback.hh"
	#include "solid_mechanics_model_event_handler.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_HH_

	namespace akantu {
	class Material;
	class MaterialSelector;
	class DumperIOHelper;
	class NonLocalManager;
	template <ElementKind kind, class IntegrationOrderFunctor>
	class IntegratorGauss;
	template <ElementKind kind> class ShapeLagrange;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class SolidMechanicsModel
	: public Model,
	public DataAccessor<Element>,
	public DataAccessor<UInt>,
	public BoundaryCondition<SolidMechanicsModel>,
	public NonLocalManagerCallback,
	public EventHandlerManager<SolidMechanicsModelEventHandler> {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	class NewMaterialElementsEvent : public NewElementsEvent {
	public:
	AKANTU_GET_MACRO_NOT_CONST(MaterialList, material, Array<UInt> &);
	AKANTU_GET_MACRO(MaterialList, material, const Array<UInt> &);

	protected:
	Array<UInt> material;
	};

	using MyFEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	protected:
	using EventManager = EventHandlerManager<SolidMechanicsModelEventHandler>;

	public:
	SolidMechanicsModel(Mesh & mesh, UInt dim = _all_dimensions,
	const ID & id = "solid_mechanics_model",
	std::shared_ptr<DOFManager> dof_manager = nullptr,
	ModelType model_type = ModelType::_solid_mechanics_model);

	~SolidMechanicsModel() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize completely the model
	void initFullImpl(
	const ModelOptions & options = SolidMechanicsModelOptions()) override;

	public:
	/// initialize all internal arrays for materials
	virtual void initMaterials();

	protected:
	/// initialize the model
	void initModel() override;

	/// function to print the containt of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	/// get some default values for derived classes
	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & method) override;

	/* ------------------------------------------------------------------------ */
	/* Solver interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// assembles the stiffness matrix,
	virtual void assembleStiffnessMatrix(bool need_to_reassemble = false);
	/// assembles the internal forces in the array internal_forces
	virtual void assembleInternalForces();

	protected:
	/// callback for the solver, this adds f_{ext} - f_{int} to the residual
	void assembleResidual() override;

	/// callback for the solver, this adds f_{ext} or f_{int} to the residual
	void assembleResidual(const ID & residual_part) override;
	bool canSplitResidual() override { return true; }

	/// get the type of matrix needed
	MatrixType getMatrixType(const ID & matrix_id) override;

	/// callback for the solver, this assembles different matrices
	void assembleMatrix(const ID & matrix_id) override;

	/// callback for the solver, this assembles the stiffness matrix
	void assembleLumpedMatrix(const ID & matrix_id) override;

	/// callback for the solver, this is called at beginning of solve
	void predictor() override;
	/// callback for the solver, this is called at end of solve
	void corrector() override;

	/// callback for the solver, this is called at beginning of solve
	void beforeSolveStep() override;
	/// callback for the solver, this is called at end of solve
	void afterSolveStep(bool converged = true) override;

	/// Callback for the model to instantiate the matricees when needed
	void initSolver(TimeStepSolverType time_step_solver_type,
	NonLinearSolverType non_linear_solver_type) override;

	protected:
	/* ------------------------------------------------------------------------ */
	TimeStepSolverType getDefaultSolverType() const override;
	/* ------------------------------------------------------------------------ */
	ModelSolverOptions
	getDefaultSolverOptions(const TimeStepSolverType & type) const override;

	public:
	bool isDefaultSolverExplicit() {
	return method == _explicit_lumped_mass \|\|
	method == _explicit_consistent_mass;
	}

	protected:
	/// update the current position vector
	void updateCurrentPosition();

	/* ------------------------------------------------------------------------ */
	/* Materials (solid_mechanics_model_material.cc) */
	/* ------------------------------------------------------------------------ */
	public:
	/// register an empty material of a given type
	Material & registerNewMaterial(const ID & mat_name, const ID & mat_type,
	const ID & opt_param);

	/// reassigns materials depending on the material selector
	virtual void reassignMaterial();

	/// apply a constant eigen_grad_u on all quadrature points of a given material
	virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
	const ID & material_name,
	GhostType ghost_type = _not_ghost);

	protected:
	/// register a material in the dynamic database
	Material & registerNewMaterial(const ParserSection & mat_section);

	/// read the material files to instantiate all the materials
	void instantiateMaterials();

	/// set the element_id_by_material and add the elements to the good materials
	virtual void
	assignMaterialToElements(const ElementTypeMapArray<UInt> * filter = nullptr);

	/* ------------------------------------------------------------------------ */
	/* Mass (solid_mechanics_model_mass.cc) */
	/* ------------------------------------------------------------------------ */
	public:
	/// assemble the lumped mass matrix
	void assembleMassLumped();

	/// assemble the mass matrix for consistent mass resolutions
	void assembleMass();

	public:
	/// assemble the lumped mass matrix for local and ghost elements
	void assembleMassLumped(GhostType ghost_type);

	/// assemble the mass matrix for either _ghost or _not_ghost elements
	void assembleMass(GhostType ghost_type);

	-
	protected:
	/// fill a vector of rho
	void computeRho(Array<Real> & rho, ElementType type, GhostType ghost_type);

	/// compute the kinetic energy
	Real getKineticEnergy();
	Real getKineticEnergy(ElementType type, UInt index);

	/// compute the external work (for impose displacement, the velocity should be
	/// given too)
	Real getExternalWork();

	/* ------------------------------------------------------------------------ */
	/* NonLocalManager inherited members */
	/* ------------------------------------------------------------------------ */
	protected:
	void initializeNonLocal() override;

	void updateDataForNonLocalCriterion(ElementTypeMapReal & criterion) override;

	void computeNonLocalStresses(GhostType ghost_type) override;

	void insertIntegrationPointsInNeighborhoods(GhostType ghost_type) override;

	/// update the values of the non local internal
	void updateLocalInternal(ElementTypeMapReal & internal_flat,
	GhostType ghost_type, ElementKind kind) override;

	/// copy the results of the averaging in the materials
	void updateNonLocalInternal(ElementTypeMapReal & internal_flat,
	GhostType ghost_type, ElementKind kind) override;

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	UInt getNbData(const Array<UInt> & dofs,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<UInt> & dofs,
	const SynchronizationTag & tag) override;

	protected:
	void
	splitElementByMaterial(const Array<Element> & elements,
	std::vector<Array<Element>> & elements_per_mat) const;

	template <typename Operation>
	void splitByMaterial(const Array<Element> & elements, Operation && op) const;

	/* ------------------------------------------------------------------------ */
	/* Mesh Event Handler inherited members */
	/* ------------------------------------------------------------------------ */
	protected:
	void onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) override;
	void onNodesRemoved(const Array<UInt> & element_list,
	const Array<UInt> & new_numbering,
	const RemovedNodesEvent & event) override;
	void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) override;
	void onElementsRemoved(const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) override;
	void onElementsChanged(const Array<Element> & /unused/,
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) override{};

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface (kept for convenience) and dumper relative functions */
	/* ------------------------------------------------------------------------ */
	public:
	virtual void onDump();

	//! decide wether a field is a material internal or not
	bool isInternal(const std::string & field_name, ElementKind element_kind);
	//! give the amount of data per element
	virtual ElementTypeMap<UInt>
	getInternalDataPerElem(const std::string & field_name, ElementKind kind);

	//! flatten a given material internal field
	ElementTypeMapArray<Real> &
	flattenInternal(const std::string & field_name, ElementKind kind,
	GhostType ghost_type = _not_ghost);
	//! flatten all the registered material internals
	void flattenAllRegisteredInternals(ElementKind kind);

	std::shared_ptr<dumpers::Field>
	createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) override;

	std::shared_ptr<dumpers::Field>
	createElementalField(const std::string & field_name,
	const std::string & group_name, bool padding_flag,
	UInt spatial_dimension, ElementKind kind) override;

	void dump(const std::string & dumper_name) override;
	void dump(const std::string & dumper_name, UInt step) override;
	void dump(const std::string & dumper_name, Real time, UInt step) override;

	void dump() override;
	void dump(UInt step) override;
	void dump(Real time, UInt step) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// set the value of the time step
	void setTimeStep(Real time_step, const ID & solver_id = "") override;

	/// get the value of the conversion from forces/ mass to acceleration
	AKANTU_GET_MACRO(F_M2A, f_m2a, Real);

	/// set the value of the conversion from forces/ mass to acceleration
	AKANTU_SET_MACRO(F_M2A, f_m2a, Real);

	/// get the SolidMechanicsModel::displacement array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(Displacement, displacement);
	/// get the SolidMechanicsModel::displacement array
	AKANTU_GET_MACRO_DEREF_PTR(Displacement, displacement);

	/// get the SolidMechanicsModel::previous_displacement array
	AKANTU_GET_MACRO_DEREF_PTR(PreviousDisplacement, previous_displacement);

	/// get the SolidMechanicsModel::current_position array
	const Array<Real> & getCurrentPosition();

	/// get the SolidMechanicsModel::displacement_increment array
	AKANTU_GET_MACRO_DEREF_PTR(Increment, displacement_increment);
	/// get the SolidMechanicsModel::displacement_increment array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(Increment, displacement_increment);

	/// get the lumped SolidMechanicsModel::mass array
	AKANTU_GET_MACRO_DEREF_PTR(Mass, mass);

	/// get the SolidMechanicsModel::velocity array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(Velocity, velocity);
	/// get the SolidMechanicsModel::velocity array
	AKANTU_GET_MACRO_DEREF_PTR(Velocity, velocity);

	/// get the SolidMechanicsModel::acceleration array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(Acceleration, acceleration);
	/// get the SolidMechanicsModel::acceleration array
	AKANTU_GET_MACRO_DEREF_PTR(Acceleration, acceleration);

	/// get the SolidMechanicsModel::external_force array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(ExternalForce, external_force);
	/// get the SolidMechanicsModel::external_force array
	AKANTU_GET_MACRO_DEREF_PTR(ExternalForce, external_force);

	/// get the SolidMechanicsModel::force array (external forces)
	[[deprecated("Use getExternalForce instead of this function")]] Array<Real> &
	getForce() {
	return getExternalForce();
	}

	/// get the SolidMechanicsModel::internal_force array (internal forces)
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(InternalForce, internal_force);
	/// get the SolidMechanicsModel::internal_force array (internal forces)
	AKANTU_GET_MACRO_DEREF_PTR(InternalForce, internal_force);

	/// get the SolidMechanicsModel::blocked_dofs array
	AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(BlockedDOFs, blocked_dofs);
	/// get the SolidMechanicsModel::blocked_dofs array
	AKANTU_GET_MACRO_DEREF_PTR(BlockedDOFs, blocked_dofs);

	/// get an iterable on the materials
	inline decltype(auto) getMaterials();

	/// get an iterable on the materials
	inline decltype(auto) getMaterials() const;

	/// get a particular material (by numerical material index)
	inline Material & getMaterial(UInt mat_index);

	/// get a particular material (by numerical material index)
	inline const Material & getMaterial(UInt mat_index) const;

	/// get a particular material (by material name)
	inline Material & getMaterial(const std::string & name);

	/// get a particular material (by material name)
	inline const Material & getMaterial(const std::string & name) const;

	/// get a particular material id from is name
	inline UInt getMaterialIndex(const std::string & name) const;

	/// give the number of materials
	inline UInt getNbMaterials() const { return materials.size(); }

	/// give the material internal index from its id
	Int getInternalIndexFromID(const ID & id) const;

	/// compute the stable time step
	Real getStableTimeStep();

	/**
	* @brief Returns the total energy for a given energy type
	*
	* Energy types of SolidMechanicsModel expected as argument are:
	* - `kinetic`
	* - `external work`
	*
	* Other energy types are passed on to the materials. All materials should
	* define a `potential` energy type. For additional energy types, see material
	* documentation.
	*/
	Real getEnergy(const std::string & energy_id);

	/// Compute energy for an element type and material index
	Real getEnergy(const std::string & energy_id, ElementType type, UInt index);

	/// Compute energy for an individual element
	Real getEnergy(const std::string & energy_id, const Element & element) {
	return getEnergy(energy_id, element.type, element.element);
	}

	/// Compute energy for an element group
	Real getEnergy(const ID & energy_id, const ID & group_id);

	AKANTU_GET_MACRO(MaterialByElement, material_index,
	const ElementTypeMapArray<UInt> &);
	AKANTU_GET_MACRO(MaterialLocalNumbering, material_local_numbering,
	const ElementTypeMapArray<UInt> &);

	/// vectors containing local material element index for each global element
	/// index
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(MaterialByElement, material_index,
	UInt);
	// AKANTU_GET_MACRO_BY_ELEMENT_TYPE(MaterialByElement, material_index, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(MaterialLocalNumbering,
	material_local_numbering, UInt);
	// AKANTU_GET_MACRO_BY_ELEMENT_TYPE(MaterialLocalNumbering,
	// material_local_numbering, UInt);

	AKANTU_GET_MACRO_NOT_CONST(MaterialSelector, material_selector,
	std::shared_ptr<MaterialSelector>);
	void
	setMaterialSelector(std::shared_ptr<MaterialSelector> material_selector) {
	this->material_selector = std::move(material_selector);
	}

	/// Access the non_local_manager interface
	AKANTU_GET_MACRO(NonLocalManager, *non_local_manager, NonLocalManager &);

	/// get the FEEngine object to integrate or interpolate on the boundary
	FEEngine & getFEEngineBoundary(const ID & name = "") override;

	protected:
	/// compute the stable time step
	Real getStableTimeStep(GhostType ghost_type);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// release version of the displacement array
	UInt displacement_release{0};

	/// release version of the current_position array
	UInt current_position_release{0};

	/// Check if materials need to recompute the mass array
	bool need_to_reassemble_lumped_mass{true};
	/// Check if materials need to recompute the mass matrix
	bool need_to_reassemble_mass{true};

	/// mapping between material name and material internal id
	std::map<std::string, UInt> materials_names_to_id;

	protected:
	/// conversion coefficient form force/mass to acceleration
	Real f_m2a{1.0};

	/// displacements array
	std::unique_ptr<Array<Real>> displacement;

	/// displacements array at the previous time step (used in finite deformation)
	std::unique_ptr<Array<Real>> previous_displacement;

	/// increment of displacement
	std::unique_ptr<Array<Real>> displacement_increment;

	/// lumped mass array
	std::unique_ptr<Array<Real>> mass;

	/// velocities array
	std::unique_ptr<Array<Real>> velocity;

	/// accelerations array
	std::unique_ptr<Array<Real>> acceleration;

	/// external forces array
	std::unique_ptr<Array<Real>> external_force;

	/// internal forces array
	std::unique_ptr<Array<Real>> internal_force;

	/// array specifing if a degree of freedom is blocked or not
	std::unique_ptr<Array<bool>> blocked_dofs;

	/// array of current position used during update residual
	std::unique_ptr<Array<Real>> current_position;

	/// Arrays containing the material index for each element
	ElementTypeMapArray<UInt> material_index;

	/// Arrays containing the position in the element filter of the material
	/// (material's local numbering)
	ElementTypeMapArray<UInt> material_local_numbering;

	/// list of used materials
	std::vector<std::unique_ptr<Material>> materials;

	/// class defining of to choose a material
	std::shared_ptr<MaterialSelector> material_selector;

	using flatten_internal_map =
	std::map<std::pair<std::string, ElementKind>,
	std::unique_ptr<ElementTypeMapArray<Real>>>;

	/// tells if the material are instantiated
	flatten_internal_map registered_internals;

	/// non local manager
	std::unique_ptr<NonLocalManager> non_local_manager;

	/// tells if the material are instantiated
	bool are_materials_instantiated{false};

	friend class Material;

	- template <class Model_> friend class CouplerSolidContactTemplate;
	+ template <class Model_> friend class CouplerSolidContactTemplate;
	};

	/* -------------------------------------------------------------------------- */
	namespace BC {
	namespace Neumann {
	using FromStress = FromHigherDim;
	using FromTraction = FromSameDim;
	} // namespace Neumann
	} // namespace BC

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	#include "parser.hh"

	#include "solid_mechanics_model_inline_impl.hh"
	#include "solid_mechanics_model_tmpl.hh"
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.cc
	index 7fcc980c6..79b8e1f3b 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.cc
	@@ -1,547 +1,547 @@
	/**
	* @file fragment_manager.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Thu Jan 23 2014
	* @date last modification: Mon Mar 29 2021
	*
	* @brief Group manager to handle fragments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fragment_manager.hh"
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "element_synchronizer.hh"
	#include "material_cohesive.hh"
	#include "mesh_iterators.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <functional>
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	FragmentManager::FragmentManager(SolidMechanicsModelCohesive & model,
	bool dump_data, const ID & id)
	: GroupManager(model.getMesh(), id), model(model),
	mass_center(0, model.getSpatialDimension(), "mass_center"),
	mass(0, model.getSpatialDimension(), "mass"),
	velocity(0, model.getSpatialDimension(), "velocity"),
	inertia_moments(0, model.getSpatialDimension(), "inertia_moments"),
	principal_directions(
	0, model.getSpatialDimension() * model.getSpatialDimension(),
	"principal_directions"),
	quad_coordinates("quad_coordinates", id),
	mass_density("mass_density", id),
	nb_elements_per_fragment(0, 1, "nb_elements_per_fragment"),
	dump_data(dump_data) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();

	/// compute quadrature points' coordinates
	quad_coordinates.initialize(mesh, _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_ghost_type = _not_ghost);
	// mesh.initElementTypeMapArray(quad_coordinates, spatial_dimension,
	// spatial_dimension, _not_ghost);

	model.getFEEngine().interpolateOnIntegrationPoints(model.getMesh().getNodes(),
	quad_coordinates);

	/// store mass density per quadrature point
	mass_density.initialize(mesh, _spatial_dimension = spatial_dimension,
	_ghost_type = _not_ghost);
	// mesh.initElementTypeMapArray(mass_density, 1, spatial_dimension,
	// _not_ghost);

	storeMassDensityPerIntegrationPoint();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	class CohesiveElementFilter : public GroupManager::ClusteringFilter {
	public:
	CohesiveElementFilter(const SolidMechanicsModelCohesive & model,
	const Real max_damage = 1.)
	: model(model), is_unbroken(max_damage) {}

	bool operator()(const Element & el) const override {
	if (Mesh::getKind(el.type) == _ek_regular) {
	return true;
	}

	const Array<UInt> & mat_indexes =
	model.getMaterialByElement(el.type, el.ghost_type);
	const Array<UInt> & mat_loc_num =
	model.getMaterialLocalNumbering(el.type, el.ghost_type);

	const auto & mat = static_cast<const MaterialCohesive &>(
	model.getMaterial(mat_indexes(el.element)));

	UInt el_index = mat_loc_num(el.element);
	UInt nb_quad_per_element =
	model.getFEEngine("CohesiveFEEngine")
	.getNbIntegrationPoints(el.type, el.ghost_type);

	const Array<Real> & damage_array = mat.getDamage(el.type, el.ghost_type);

	AKANTU_DEBUG_ASSERT(nb_quad_per_element * el_index < damage_array.size(),
	"This quadrature point is out of range");

	const Real * element_damage =
	damage_array.storage() + nb_quad_per_element * el_index;

	UInt unbroken_quads = std::count_if(
	element_damage, element_damage + nb_quad_per_element, is_unbroken);

	return (unbroken_quads > 0);
	}

	private:
	struct IsUnbrokenFunctor {
	IsUnbrokenFunctor(const Real & max_damage) : max_damage(max_damage) {}
	bool operator()(const Real & x) const { return x < max_damage; }
	const Real max_damage;
	};

	const SolidMechanicsModelCohesive & model;
	const IsUnbrokenFunctor is_unbroken;
	};

	/* -------------------------------------------------------------------------- */
	void FragmentManager::buildFragments(Real damage_limit) {
	AKANTU_DEBUG_IN();

	if (mesh.isDistributed()) {
	auto & cohesive_synchronizer = model.getCohesiveSynchronizer();
	cohesive_synchronizer.synchronize(model, SynchronizationTag::_smmc_damage);
	}

	auto & mesh_facets = mesh.getMeshFacets();

	UInt spatial_dimension = model.getSpatialDimension();
	std::string fragment_prefix("fragment");

	/// generate fragments
	global_nb_fragment =
	createClusters(spatial_dimension, mesh_facets, fragment_prefix,
	CohesiveElementFilter(model, damage_limit));

	nb_fragment = getNbElementGroups(spatial_dimension);
	fragment_index.resize(nb_fragment);

	/// loop over fragments
	for (auto && data : zip(iterateElementGroups(), fragment_index)) {
	auto name = std::get<0>(data).getName();
	/// get fragment index
	std::string fragment_index_string = name.substr(fragment_prefix.size() + 1);
	std::get<1>(data) = std::stoul(fragment_index_string);
	}

	/// compute fragments' mass
	computeMass();

	if (dump_data) {
	createDumpDataArray(fragment_index, "fragments", true);
	createDumpDataArray(mass, "fragments mass");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::computeMass() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();

	/// create a unit field per quadrature point, since to compute mass
	/// it's neccessary to integrate only density
	ElementTypeMapArray<Real> unit_field("unit_field", id);
	unit_field.initialize(model.getFEEngine(), _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_ghost_type = _not_ghost, _default_value = 1.);

	integrateFieldOnFragments(unit_field, mass);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::computeCenterOfMass() {
	AKANTU_DEBUG_IN();

	/// integrate position multiplied by density
	integrateFieldOnFragments(quad_coordinates, mass_center);

	/// divide it by the fragments' mass
	Real * mass_storage = mass.storage();
	Real * mass_center_storage = mass_center.storage();

	UInt total_components = mass_center.size() * mass_center.getNbComponent();

	for (UInt i = 0; i < total_components; ++i) {
	mass_center_storage[i] /= mass_storage[i];
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::computeVelocity() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();

	/// compute velocity per quadrature point
	ElementTypeMapArray<Real> velocity_field("velocity_field", id);
	velocity_field.initialize(
	model.getFEEngine(), _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension, _ghost_type = _not_ghost);

	model.getFEEngine().interpolateOnIntegrationPoints(model.getVelocity(),
	velocity_field);

	/// integrate on fragments
	integrateFieldOnFragments(velocity_field, velocity);

	/// divide it by the fragments' mass
	Real * mass_storage = mass.storage();
	Real * velocity_storage = velocity.storage();

	UInt total_components = velocity.size() * velocity.getNbComponent();

	for (UInt i = 0; i < total_components; ++i) {
	velocity_storage[i] /= mass_storage[i];
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Given the distance @f$ \mathbf{r} @f$ between a quadrature point
	* and its center of mass, the moment of inertia is computed as \f[
	* I_\mathrm{CM} = \mathrm{tr}(\mathbf{r}\mathbf{r}^\mathrm{T})
	* \mathbf{I} - \mathbf{r}\mathbf{r}^\mathrm{T} \f] for more
	* information check Wikipedia
	* (http://en.wikipedia.org/wiki/Moment_of_inertia#Identities_for_a_skew-symmetric_matrix)
	*
	*/

	void FragmentManager::computeInertiaMoments() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();

	computeCenterOfMass();

	/// compute local coordinates products with respect to the center of match
	ElementTypeMapArray<Real> moments_coords("moments_coords", id);
	moments_coords.initialize(model.getFEEngine(),
	_nb_component =
	spatial_dimension * spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_ghost_type = _not_ghost, _default_value = 1.);

	/// loop over fragments
	for (auto && data :
	zip(iterateElementGroups(), make_view(mass_center, spatial_dimension))) {
	const auto & el_list = std::get<0>(data).getElements();
	auto & mass_center = std::get<1>(data);

	/// loop over elements of the fragment
	for (auto type :
	el_list.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {
	auto nb_quad_per_element =
	model.getFEEngine().getNbIntegrationPoints(type);

	auto & moments_coords_array = moments_coords(type);
	const auto & quad_coordinates_array = quad_coordinates(type);
	const auto & el_list_array = el_list(type);

	auto moments_begin =
	moments_coords_array.begin(spatial_dimension, spatial_dimension);
	auto quad_coordinates_begin =
	quad_coordinates_array.begin(spatial_dimension);

	Vector<Real> relative_coords(spatial_dimension);

	for (UInt el = 0; el < el_list_array.size(); ++el) {
	UInt global_el = el_list_array(el);

	/// loop over quadrature points
	for (UInt q = 0; q < nb_quad_per_element; ++q) {
	UInt global_q = global_el * nb_quad_per_element + q;
	Matrix<Real> moments_matrix = moments_begin[global_q];
	const Vector<Real> & quad_coord_vector =
	quad_coordinates_begin[global_q];

	/// to understand this read the documentation written just
	/// before this function
	relative_coords = quad_coord_vector;
	relative_coords -= mass_center;

	moments_matrix.outerProduct(relative_coords, relative_coords);
	Real trace = moments_matrix.trace();
	moments_matrix *= -1.;
	moments_matrix += Matrix<Real>::eye(spatial_dimension, trace);
	}
	}
	}
	}

	/// integrate moments
	Array<Real> integrated_moments(global_nb_fragment,
	spatial_dimension * spatial_dimension);

	integrateFieldOnFragments(moments_coords, integrated_moments);

	/// compute and store principal moments
	inertia_moments.resize(global_nb_fragment);
	principal_directions.resize(global_nb_fragment);

	auto integrated_moments_it =
	integrated_moments.begin(spatial_dimension, spatial_dimension);
	auto inertia_moments_it = inertia_moments.begin(spatial_dimension);
	auto principal_directions_it =
	principal_directions.begin(spatial_dimension, spatial_dimension);

	for (UInt frag = 0; frag < global_nb_fragment; ++frag,
	++integrated_moments_it, ++inertia_moments_it,
	++principal_directions_it) {
	integrated_moments_it->eig(inertia_moments_it, principal_directions_it);
	}

	if (dump_data) {
	createDumpDataArray(inertia_moments, "moments of inertia");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::computeAllData(Real damage_limit) {
	AKANTU_DEBUG_IN();

	buildFragments(damage_limit);
	computeVelocity();
	computeInertiaMoments();
	computeNbElementsPerFragment();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::storeMassDensityPerIntegrationPoint() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();

	for (auto type : mesh.elementTypes(_spatial_dimension = spatial_dimension,
	_element_kind = _ek_regular)) {
	Array<Real> & mass_density_array = mass_density(type);

	UInt nb_element = mesh.getNbElement(type);
	UInt nb_quad_per_element = model.getFEEngine().getNbIntegrationPoints(type);
	mass_density_array.resize(nb_element * nb_quad_per_element);

	const Array<UInt> & mat_indexes = model.getMaterialByElement(type);

	Real * mass_density_it = mass_density_array.storage();

	/// store mass_density for each element and quadrature point
	for (UInt el = 0; el < nb_element; ++el) {
	Material & mat = model.getMaterial(mat_indexes(el));

	for (UInt q = 0; q < nb_quad_per_element; ++q, ++mass_density_it) {
	*mass_density_it = mat.getRho();
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::integrateFieldOnFragments(
	ElementTypeMapArray<Real> & field, Array<Real> & output) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();
	UInt nb_component = output.getNbComponent();

	/// integration part
	output.resize(global_nb_fragment);
	output.zero();

	auto output_begin = output.begin(nb_component);

	/// loop over fragments
	for (auto && data : zip(iterateElementGroups(), fragment_index)) {
	const auto & el_list = std::get<0>(data).getElements();
	auto fragment_index = std::get<1>(data);

	/// loop over elements of the fragment
	for (auto type :
	el_list.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {

	UInt nb_quad_per_element =
	model.getFEEngine().getNbIntegrationPoints(type);

	const Array<Real> & density_array = mass_density(type);
	Array<Real> & field_array = field(type);
	const Array<UInt> & elements = el_list(type);

	/// generate array to be integrated by filtering fragment's elements
	Array<Real> integration_array(elements.size() * nb_quad_per_element,
	nb_component);

	auto field_array_begin = field_array.begin_reinterpret(
	nb_quad_per_element, nb_component,
	field_array.size() / nb_quad_per_element);
	auto density_array_begin = density_array.begin_reinterpret(
	nb_quad_per_element, density_array.size() / nb_quad_per_element);

	for (auto && data : enumerate(make_view(
	integration_array, nb_quad_per_element, nb_component))) {
	UInt global_el = elements(std::get<0>(data));
	auto & int_array = std::get<1>(data);
	int_array = field_array_begin[global_el];

	/// multiply field by density
	const Vector<Real> & density_vector = density_array_begin[global_el];

	for (UInt i = 0; i < nb_quad_per_element; ++i) {
	for (UInt j = 0; j < nb_component; ++j) {
	int_array(i, j) *= density_vector(i);
	}
	}
	}

	/// integrate the field over the fragment
	Array<Real> integrated_array(elements.size(), nb_component);
	model.getFEEngine().integrate(integration_array, integrated_array,
	nb_component, type, _not_ghost, elements);

	/// sum over all elements and store the result
	Vector<Real> output_tmp(output_begin[fragment_index]);
	output_tmp += std::accumulate(integrated_array.begin(nb_component),
	integrated_array.end(nb_component),
	Vector<Real>(nb_component));
	}
	}

	/// sum output over all processors
	const Communicator & comm = mesh.getCommunicator();
	comm.allReduce(output, SynchronizerOperation::_sum);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FragmentManager::computeNbElementsPerFragment() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = model.getSpatialDimension();
	nb_elements_per_fragment.resize(global_nb_fragment);
	nb_elements_per_fragment.zero();

	/// loop over fragments
	for (auto && data : zip(iterateElementGroups(), fragment_index)) {
	const auto & el_list = std::get<0>(data).getElements();
	auto fragment_index = std::get<1>(data);

	/// loop over elements of the fragment
	for (auto type :
	el_list.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {
	UInt nb_element = el_list(type).size();

	nb_elements_per_fragment(fragment_index) += nb_element;
	}
	}

	/// sum values over all processors
	const auto & comm = mesh.getCommunicator();
	comm.allReduce(nb_elements_per_fragment, SynchronizerOperation::_sum);

	if (dump_data) {
	createDumpDataArray(nb_elements_per_fragment, "elements per fragment");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void FragmentManager::createDumpDataArray(Array<T> & data, std::string name,
	bool fragment_index_output) {
	AKANTU_DEBUG_IN();

	if (data.empty()) {
	return;
	}

	auto & mesh_not_const = const_cast<Mesh &>(mesh);

	auto && spatial_dimension = mesh.getSpatialDimension();
	auto && nb_component = data.getNbComponent();
	auto && data_begin = data.begin(nb_component);

	/// loop over fragments
	for (auto && data : zip(iterateElementGroups(), fragment_index)) {
	const auto & fragment = std::get<0>(data);
	auto fragment_idx = std::get<1>(data);

	/// loop over cluster types
	for (auto && type : fragment.elementTypes(spatial_dimension)) {
	/// init mesh data
	auto & mesh_data = mesh_not_const.getDataPointer<T>(
	name, type, _not_ghost, nb_component);

	auto mesh_data_begin = mesh_data.begin(nb_component);

	/// fill mesh data
	for (const auto & elem : fragment.getElements(type)) {
	Vector<T> md_tmp = mesh_data_begin[elem];
	if (fragment_index_output) {
	md_tmp(0) = fragment_idx;
	} else {
	md_tmp = data_begin[fragment_idx];
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.hh
	index c702c9522..887924c82 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/fragment_manager.hh
	@@ -1,169 +1,169 @@
	/**
	* @file fragment_manager.hh
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Thu Jan 23 2014
	* @date last modification: Mon Mar 29 2021
	*
	* @brief Group manager to handle fragments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "group_manager.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FRAGMENT_MANAGER_HH_
	#define AKANTU_FRAGMENT_MANAGER_HH_

	namespace akantu {
	class SolidMechanicsModelCohesive;
	}

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class FragmentManager : public GroupManager {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	FragmentManager(SolidMechanicsModelCohesive & model, bool dump_data = true,
	const ID & id = "fragment_manager");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	private:
	/// store mass density per integration point
	void storeMassDensityPerIntegrationPoint();

	/// integrate an elemental field multiplied by density on global
	/// fragments
	void integrateFieldOnFragments(ElementTypeMapArray<Real> & field,
	Array<Real> & output);

	/// compute fragments' mass
	void computeMass();

	/// create dump data for a single array
	template <typename T>
	void createDumpDataArray(Array<T> & data, std::string name,
	bool fragment_index_output = false);

	public:
	/// build fragment list (cohesive elements are considered broken if
	/// damage >= damage_limit)
	void buildFragments(Real damage_limit = 1.);

	/// compute fragments' center of mass
	void computeCenterOfMass();

	/// compute fragments' velocity
	void computeVelocity();

	/// computes principal moments of inertia with respect to the center
	/// of mass of each fragment
	void computeInertiaMoments();

	/// compute all fragments' data
	void computeAllData(Real damage_limit = 1.);

	/// compute number of elements per fragment
	void computeNbElementsPerFragment();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get number of fragments
	AKANTU_GET_MACRO(NbFragment, global_nb_fragment, UInt);

	/// get fragments' mass
	AKANTU_GET_MACRO(Mass, mass, const Array<Real> &);

	/// get fragments' center of mass
	AKANTU_GET_MACRO(CenterOfMass, mass_center, const Array<Real> &);

	/// get fragments' velocity
	AKANTU_GET_MACRO(Velocity, velocity, const Array<Real> &);

	/// get fragments' principal moments of inertia
	AKANTU_GET_MACRO(MomentsOfInertia, inertia_moments, const Array<Real> &);

	/// get fragments' principal directions
	AKANTU_GET_MACRO(PrincipalDirections, principal_directions,
	const Array<Real> &);

	/// get number of elements per fragment
	AKANTU_GET_MACRO(NbElementsPerFragment, nb_elements_per_fragment,
	const Array<UInt> &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// local_fragment index
	Array<UInt> fragment_index;

	/// global number of fragments (parallel simulations)
	UInt global_nb_fragment;

	/// number of fragments
	UInt nb_fragment;

	/// cohesive solid mechanics model associated
	SolidMechanicsModelCohesive & model;

	/// fragments' center of mass
	Array<Real> mass_center;

	/// fragments' mass
	Array<Real> mass;

	/// fragments' velocity
	Array<Real> velocity;

	/// fragments' principal moments of inertia with respect to the
	/// center of mass
	Array<Real> inertia_moments;

	/// fragments' principal directions
	Array<Real> principal_directions;

	/// quadrature points' coordinates
	ElementTypeMapArray<Real> quad_coordinates;

	/// mass density per quadrature point
	ElementTypeMapArray<Real> mass_density;

	/// fragment filter
	Array<UInt> nb_elements_per_fragment;

	/// dump data
	bool dump_data;
	};

	} // namespace akantu

	#endif /* AKANTU_FRAGMENT_MANAGER_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.cc
	index 9da4bd348..74e2a9301 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.cc
	@@ -1,169 +1,169 @@
	/**
	* @file material_selector_cohesive.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Dec 11 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material selector for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_selector_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	DefaultMaterialCohesiveSelector::DefaultMaterialCohesiveSelector(
	const SolidMechanicsModelCohesive & model)
	: facet_material(model.getFacetMaterial()), mesh(model.getMesh()) {
	// backward compatibility v3: to get the former behavior back when the user
	// creates its own selector
	this->fallback_selector =
	std::make_shared<DefaultMaterialSelector>(model.getMaterialByElement());
	}

	/* -------------------------------------------------------------------------- */
	UInt DefaultMaterialCohesiveSelector::operator()(const Element & element) {
	if (Mesh::getKind(element.type) == _ek_cohesive) {
	try {
	const Array<Element> & cohesive_el_to_facet =
	mesh.getMeshFacets().getSubelementToElement(element.type,
	element.ghost_type);
	bool third_dimension = (mesh.getSpatialDimension() == 3);
	const Element & facet =
	cohesive_el_to_facet(element.element, UInt(third_dimension));
	if (facet_material.exists(facet.type, facet.ghost_type)) {
	return facet_material(facet.type, facet.ghost_type)(facet.element);
	}
	return fallback_value;

	} catch (...) {
	return fallback_value;
	}
	} else if (Mesh::getSpatialDimension(element.type) ==
	mesh.getSpatialDimension() - 1) {
	return facet_material(element.type, element.ghost_type)(element.element);
	} else {
	return MaterialSelector::operator()(element);
	}
	}

	/* -------------------------------------------------------------------------- */
	MeshDataMaterialCohesiveSelector::MeshDataMaterialCohesiveSelector(
	const SolidMechanicsModelCohesive & model)
	: model(model), mesh_facets(model.getMeshFacets()),
	material_index(mesh_facets.getData<std::string>("physical_names")) {
	third_dimension = (model.getSpatialDimension() == 3);
	// backward compatibility v3: to get the former behavior back when the user
	// creates its own selector
	this->fallback_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	}

	/* -------------------------------------------------------------------------- */
	UInt MeshDataMaterialCohesiveSelector::operator()(const Element & element) {
	if (Mesh::getKind(element.type) == _ek_cohesive or
	Mesh::getSpatialDimension(element.type) ==
	mesh_facets.getSpatialDimension() - 1) {
	Element facet;
	if (Mesh::getKind(element.type) == _ek_cohesive) {
	facet =
	mesh_facets.getSubelementToElement(element.type, element.ghost_type)(
	element.element, UInt(third_dimension));
	} else {
	facet = element;
	}

	try {
	std::string material_name = this->material_index(facet);
	return this->model.getMaterialIndex(material_name);
	} catch (...) {
	return fallback_value;
	}
	}
	return MaterialSelector::operator()(element);
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	MaterialCohesiveRulesSelector::MaterialCohesiveRulesSelector(
	const SolidMechanicsModelCohesive & model,
	const MaterialCohesiveRules & rules,
	ID mesh_data_id) // what we have here is the name of model and also
	// the name of different materials
	: model(model), mesh_data_id(std::move(mesh_data_id)),
	mesh(model.getMesh()), mesh_facets(model.getMeshFacets()),
	spatial_dimension(model.getSpatialDimension()), rules(rules) {

	// cohesive fallback
	this->fallback_selector =
	std::make_shared<DefaultMaterialCohesiveSelector>(model);

	// non cohesive fallback
	this->fallback_selector->setFallback(
	std::make_shared<MeshDataMaterialSelector<std::string>>(mesh_data_id,
	model));
	}

	/* -------------------------------------------------------------------------- */
	UInt MaterialCohesiveRulesSelector::operator()(const Element & element) {
	if (mesh_facets.getSpatialDimension(element.type) ==
	(spatial_dimension - 1)) {
	const std::vector<Element> & element_to_subelement =
	mesh_facets.getElementToSubelement(element.type,
	element.ghost_type)(element.element);
	// Array<bool> & facets_check = model.getFacetsCheck();

	const Element & el1 = element_to_subelement[0];
	const Element & el2 = element_to_subelement[1];

	ID id1 = mesh.getData<std::string>(mesh_data_id, el1.type,
	el1.ghost_type)(el1.element);

	ID id2 = id1;
	if (el2 != ElementNull) {
	id2 = mesh.getData<std::string>(mesh_data_id, el2.type,
	el2.ghost_type)(el2.element);
	}

	auto rit = rules.find(std::make_pair(id1, id2));
	if (rit == rules.end()) {
	rit = rules.find(std::make_pair(id2, id1));
	}

	if (rit != rules.end()) {
	return model.getMaterialIndex(rit->second);
	}
	}

	return MaterialSelector::operator()(element);
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.hh
	index e4108e199..09e1175a9 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/material_selector_cohesive.hh
	@@ -1,100 +1,100 @@
	/**
	* @file material_selector_cohesive.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Dec 11 2015
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Material selectors for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_selector.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class SolidMechanicsModelCohesive;
	}

	namespace akantu {

	#ifndef AKANTU_MATERIAL_SELECTOR_COHESIVE_HH_
	#define AKANTU_MATERIAL_SELECTOR_COHESIVE_HH_

	/* -------------------------------------------------------------------------- */
	/**
	* class that assigns the first cohesive material by default to the
	* cohesive elements
	*/
	class DefaultMaterialCohesiveSelector : public MaterialSelector {
	public:
	DefaultMaterialCohesiveSelector(const SolidMechanicsModelCohesive & model);
	UInt operator()(const Element & element) override;

	private:
	const ElementTypeMapArray<UInt> & facet_material;
	const Mesh & mesh;
	};

	/* -------------------------------------------------------------------------- */
	/// To be used with intrinsic elements inserted along mesh physical surfaces
	class MeshDataMaterialCohesiveSelector : public MaterialSelector {
	public:
	MeshDataMaterialCohesiveSelector(const SolidMechanicsModelCohesive & model);
	UInt operator()(const Element & element) override;

	protected:
	const SolidMechanicsModelCohesive & model;
	const Mesh & mesh_facets;
	const ElementTypeMapArray<std::string> & material_index;
	bool third_dimension;
	};

	/// bulk1, bulk2 -> cohesive
	using MaterialCohesiveRules = std::map<std::pair<ID, ID>, ID>;

	/* -------------------------------------------------------------------------- */
	class MaterialCohesiveRulesSelector : public MaterialSelector {
	public:
	MaterialCohesiveRulesSelector(const SolidMechanicsModelCohesive & model,
	const MaterialCohesiveRules & rules,
	ID mesh_data_id = "physical_names");
	UInt operator()(const Element & element) override;

	private:
	const SolidMechanicsModelCohesive & model;
	ID mesh_data_id;
	const Mesh & mesh;
	const Mesh & mesh_facets;
	UInt spatial_dimension;
	MaterialCohesiveRules rules;
	};

	#endif /* AKANTU_MATERIAL_SELECTOR_COHESIVE_HH_ */

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field.hh
	index 333afb0e7..e381c16d0 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field.hh
	@@ -1,68 +1,68 @@
	/**
	* @file cohesive_internal_field.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Internal field for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "internal_field.hh"

	#ifndef AKANTU_COHESIVE_INTERNAL_FIELD_HH_
	#define AKANTU_COHESIVE_INTERNAL_FIELD_HH_

	namespace akantu {

	/// internal field class for cohesive materials
	template <typename T> class CohesiveInternalField : public InternalField<T> {
	public:
	CohesiveInternalField(const ID & id, Material & material);
	~CohesiveInternalField() override;

	/// initialize the field to a given number of component
	void initialize(UInt nb_component) override;

	private:
	CohesiveInternalField operator=(__attribute__((unused))
	const CohesiveInternalField & other){};
	};

	/* -------------------------------------------------------------------------- */
	/* Facet Internal Field */
	/* -------------------------------------------------------------------------- */
	template <typename T> class FacetInternalField : public InternalField<T> {
	public:
	FacetInternalField(const ID & id, Material & material);
	~FacetInternalField() override;

	/// initialize the field to a given number of component
	void initialize(UInt nb_component) override;
	};

	} // namespace akantu

	#endif /* AKANTU_COHESIVE_INTERNAL_FIELD_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field_tmpl.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field_tmpl.hh
	index 0104a5d99..08b911828 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field_tmpl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/cohesive_internal_field_tmpl.hh
	@@ -1,96 +1,96 @@
	/**
	* @file cohesive_internal_field_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Nov 13 2013
	* @date last modification: Fri Apr 09 2021
	*
	* @brief implementation of the cohesive internal field
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COHESIVE_INTERNAL_FIELD_TMPL_HH_
	#define AKANTU_COHESIVE_INTERNAL_FIELD_TMPL_HH_

	namespace akantu {

	template <typename T>
	CohesiveInternalField<T>::CohesiveInternalField(const ID & id,
	Material & material)
	: InternalField<T>(
	id, material, material.getModel().getFEEngine("CohesiveFEEngine"),
	aka::as_type<MaterialCohesive>(material).getElementFilter()) {
	this->element_kind = _ek_cohesive;
	}

	template <typename T>
	CohesiveInternalField<T>::~CohesiveInternalField() = default;

	template <typename T>
	void CohesiveInternalField<T>::initialize(UInt nb_component) {
	this->internalInitialize(nb_component);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	FacetInternalField<T>::FacetInternalField(const ID & id, Material & material)
	: InternalField<T>(
	id, material, material.getModel().getFEEngine("FacetsFEEngine"),
	aka::as_type<MaterialCohesive>(material).getFacetFilter()) {
	this->spatial_dimension -= 1;
	this->element_kind = _ek_regular;
	}

	template <typename T> FacetInternalField<T>::~FacetInternalField() = default;

	template <typename T>
	void FacetInternalField<T>::initialize(UInt nb_component) {
	this->internalInitialize(nb_component);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<RandomInternalField<Real, FacetInternalField>>::setAuto(
	const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	RandomParameter<Real> r = in_param;
	param.setRandomDistribution(r);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void
	ParameterTyped<RandomInternalField<Real, CohesiveInternalField>>::setAuto(
	const ParserParameter & in_param) {
	Parameter::setAuto(in_param);
	RandomParameter<Real> r = in_param;
	param.setRandomDistribution(r);
	}

	} // namespace akantu

	#endif /* AKANTU_COHESIVE_INTERNAL_FIELD_TMPL_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc
	index 13f78e652..1853dbb2d 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc
	@@ -1,215 +1,215 @@
	/**
	* @file material_cohesive_bilinear.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Feb 22 2012
	* @date last modification: Sat Dec 19 2020
	*
	* @brief Bilinear cohesive constitutive law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_bilinear.hh"
	//#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveBilinear<spatial_dimension>::MaterialCohesiveBilinear(
	SolidMechanicsModel & model, const ID & id)
	: MaterialCohesiveLinear<spatial_dimension>(model, id) {
	AKANTU_DEBUG_IN();

	this->registerParam("delta_0", delta_0, Real(0.),
	_pat_parsable \| _pat_readable,
	"Elastic limit displacement");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveBilinear<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();

	this->sigma_c_eff.setRandomDistribution(this->sigma_c.getRandomParameter());
	MaterialCohesiveLinear<spatial_dimension>::initMaterial();

	this->delta_max.setDefaultValue(delta_0);
	this->insertion_stress.setDefaultValue(0);

	this->delta_max.reset();
	this->insertion_stress.reset();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveBilinear<spatial_dimension>::onElementsAdded(
	const Array<Element> & element_list, const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	MaterialCohesiveLinear<spatial_dimension>::onElementsAdded(element_list,
	event);

	bool scale_traction = false;

	// don't scale sigma_c if volume_s hasn't been specified by the user
	if (!Math::are_float_equal(this->volume_s, 0.)) {
	scale_traction = true;
	}

	Array<Element>::const_scalar_iterator el_it = element_list.begin();
	Array<Element>::const_scalar_iterator el_end = element_list.end();

	for (; el_it != el_end; ++el_it) {
	// filter not ghost cohesive elements
	if ((el_it->ghost_type != _not_ghost) or
	(Mesh::getKind(el_it->type) != _ek_cohesive)) {
	continue;
	}

	UInt index = el_it->element;
	ElementType type = el_it->type;
	UInt nb_element = this->model->getMesh().getNbElement(type);
	UInt nb_quad_per_element = this->fem_cohesive.getNbIntegrationPoints(type);

	auto sigma_c_begin = this->sigma_c_eff(type).begin_reinterpret(
	nb_quad_per_element, nb_element);
	Vector<Real> sigma_c_vec = sigma_c_begin[index];

	auto delta_c_begin = this->delta_c_eff(type).begin_reinterpret(
	nb_quad_per_element, nb_element);
	Vector<Real> delta_c_vec = delta_c_begin[index];

	if (scale_traction) {
	scaleTraction(*el_it, sigma_c_vec);
	}

	/**
	* Recompute sigma_c as
	* @f$ {\sigma_c}_\textup{new} =
	* \frac{{\sigma_c}_\textup{old} \delta_c} {\delta_c - \delta_0} @f$
	*/

	for (UInt q = 0; q < nb_quad_per_element; ++q) {
	delta_c_vec(q) = 2 * this->G_c / sigma_c_vec(q);

	if (delta_c_vec(q) - delta_0 < Math::getTolerance()) {
	AKANTU_ERROR("delta_0 = " << delta_0 << " must be lower than delta_c = "
	<< delta_c_vec(q)
	<< ", modify your material file");
	}

	sigma_c_vec(q) *= delta_c_vec(q) / (delta_c_vec(q) - delta_0);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveBilinear<spatial_dimension>::scaleTraction(
	const Element & el, Vector<Real> & sigma_c_vec) {
	AKANTU_DEBUG_IN();

	Real base_sigma_c = this->sigma_c_eff;

	const Mesh & mesh_facets = this->model->getMeshFacets();
	const FEEngine & fe_engine = this->model->getFEEngine();

	auto coh_element_to_facet_begin =
	mesh_facets.getSubelementToElement(el.type).begin(2);
	const Vector<Element> & coh_element_to_facet =
	coh_element_to_facet_begin[el.element];

	// compute bounding volume
	Real volume = 0;

	// loop over facets
	for (UInt f = 0; f < 2; ++f) {
	const Element & facet = coh_element_to_facet(f);

	const Array<std::vector<Element>> & facet_to_element =
	mesh_facets.getElementToSubelement(facet.type, facet.ghost_type);

	const std::vector<Element> & element_list = facet_to_element(facet.element);

	auto elem = element_list.begin();
	auto elem_end = element_list.end();

	// loop over elements connected to each facet
	for (; elem != elem_end; ++elem) {
	// skip cohesive elements and dummy elements
	if (*elem == ElementNull \|\| Mesh::getKind(elem->type) == _ek_cohesive) {
	continue;
	}

	// unit vector for integration in order to obtain the volume
	UInt nb_quadrature_points = fe_engine.getNbIntegrationPoints(elem->type);
	Vector<Real> unit_vector(nb_quadrature_points, 1);

	volume += fe_engine.integrate(unit_vector, elem->type, elem->element,
	elem->ghost_type);
	}
	}

	// scale sigma_c
	sigma_c_vec -= base_sigma_c;
	sigma_c_vec *= std::pow(this->volume_s / volume, 1. / this->m_s);
	sigma_c_vec += base_sigma_c;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveBilinear<spatial_dimension>::computeTraction(
	const Array<Real> & normal, ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	MaterialCohesiveLinear<spatial_dimension>::computeTraction(normal, el_type,
	ghost_type);

	// adjust damage
	auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
	auto delta_max_it = this->delta_max(el_type, ghost_type).begin();
	auto damage_it = this->damage(el_type, ghost_type).begin();
	auto damage_end = this->damage(el_type, ghost_type).end();

	for (; damage_it != damage_end; ++damage_it, ++delta_max_it, ++delta_c_it) {
	*damage_it =
	std::max((delta_max_it - delta_0) / (delta_c_it - delta_0), Real(0.));
	damage_it = std::min(damage_it, Real(1.));
	}
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(cohesive_bilinear, MaterialCohesiveBilinear);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.hh
	index dd21d5211..74a2fa5c8 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.hh
	@@ -1,106 +1,106 @@
	/**
	* @file material_cohesive_bilinear.hh
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Bilinear cohesive constitutive law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "material_cohesive_linear.hh"

	#ifndef AKANTU_MATERIAL_COHESIVE_BILINEAR_HH_
	#define AKANTU_MATERIAL_COHESIVE_BILINEAR_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* Cohesive material bilinear
	*
	* parameters in the material files :
	* - delta_0 : elastic limit displacement (default: 0)
	* - sigma_c : critical stress sigma_c (default: 0)
	* - beta : weighting parameter for sliding and normal opening (default:
	* 0)
	* - G_cI : fracture energy for mode I (default: 0)
	* - G_cII : fracture energy for mode II (default: 0)
	* - penalty : stiffness in compression to prevent penetration
	*/
	template <UInt spatial_dimension>
	class MaterialCohesiveBilinear
	: public MaterialCohesiveLinear<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialCohesiveBilinear(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material computed parameter
	void initMaterial() override;

	/// set material parameters for new elements
	void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) override;

	protected:
	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/**
	* Scale traction sigma_c according to the volume of the
	* two elements surrounding an element
	*/
	void scaleTraction(const Element & el, Vector<Real> & sigma_c_vec);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// elastic limit displacement
	Real delta_0;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	//#include "material_cohesive_elastic_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_COHESIVE_BILINEAR_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.cc
	index c8dd09cbf..f9ce8ee20 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.cc
	@@ -1,345 +1,345 @@
	/**
	* @file material_cohesive_exponential.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Mon Jul 09 2012
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Exponential irreversible cohesive law of mixed mode loading
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_exponential.hh"
	#include "dof_synchronizer.hh"
	#include "solid_mechanics_model.hh"
	#include "sparse_matrix.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveExponential<spatial_dimension>::MaterialCohesiveExponential(
	SolidMechanicsModel & model, const ID & id)
	: MaterialCohesive(model, id) {
	AKANTU_DEBUG_IN();

	this->registerParam("beta", beta, Real(0.), _pat_parsable, "Beta parameter");

	this->registerParam("exponential_penalty", exp_penalty, true, _pat_parsable,
	"Is contact penalty following the exponential law?");

	this->registerParam(
	"contact_tangent", contact_tangent, Real(1.0), _pat_parsable,
	"Ratio of contact tangent over the initial exponential tangent");

	// this->initInternalArray(delta_max, 1, _ek_cohesive);

	use_previous_delta_max = true;

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::initMaterial() {

	AKANTU_DEBUG_IN();
	MaterialCohesive::initMaterial();

	if ((exp_penalty) && (contact_tangent != 1)) {

	contact_tangent = 1;
	AKANTU_DEBUG_WARNING("The parsed paramter <contact_tangent> is forced to "
	"1.0 when the contact penalty follows the exponential "
	"law");
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeTraction(
	const Array<Real> & normal, ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto traction_it = tractions(el_type, ghost_type).begin(spatial_dimension);
	auto opening_it = opening(el_type, ghost_type).begin(spatial_dimension);
	auto normal_it = normal.begin(spatial_dimension);
	auto traction_end = tractions(el_type, ghost_type).end(spatial_dimension);
	auto delta_max_it = delta_max(el_type, ghost_type).begin();
	auto delta_max_prev_it = delta_max.previous(el_type, ghost_type).begin();

	/// compute scalars
	Real beta2 = beta * beta;

	/// loop on each quadrature point
	for (; traction_it != traction_end; ++traction_it, ++opening_it, ++normal_it,
	++delta_max_it, ++delta_max_prev_it) {

	/// compute normal and tangential opening vectors
	Real normal_opening_norm = opening_it->dot(*normal_it);
	Vector<Real> normal_opening(spatial_dimension);
	normal_opening = (*normal_it);
	normal_opening *= normal_opening_norm;

	Vector<Real> tangential_opening(spatial_dimension);
	tangential_opening = *opening_it;
	tangential_opening -= normal_opening;

	Real tangential_opening_norm = tangential_opening.norm();

	/**
	* compute effective opening displacement
	* @f$ \delta = \sqrt{
	* \beta^2 \Delta_t^2 + \Delta_n^2 } @f$
	*/
	Real delta = tangential_opening_norm;
	delta = delta beta2;
	delta += normal_opening_norm * normal_opening_norm;

	delta = sqrt(delta);

	if ((normal_opening_norm < 0) &&
	(std::abs(normal_opening_norm) > Math::getTolerance())) {

	Vector<Real> op_n(*normal_it);
	op_n *= normal_opening_norm;
	Vector<Real> delta_s(*opening_it);
	delta_s -= op_n;
	delta = tangential_opening_norm * beta;

	computeCoupledTraction(traction_it, normal_it, delta, delta_s,
	delta_max_it, delta_max_prev_it);

	computeCompressiveTraction(traction_it, normal_it, normal_opening_norm,
	*opening_it);

	} else {
	computeCoupledTraction(traction_it, normal_it, delta, *opening_it,
	delta_max_it, delta_max_prev_it);
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeCoupledTraction(
	Vector<Real> & tract, const Vector<Real> & normal, Real delta,
	const Vector<Real> & opening, Real & delta_max_new, Real delta_max) {
	AKANTU_DEBUG_IN();

	/// full damage case
	if (std::abs(delta) < Math::getTolerance()) {
	/// set traction to zero
	tract.zero();
	} else { /// element not fully damaged
	/**
	* Compute traction loading @f$ \mathbf{T} =
	* e \sigma_c \frac{\delta}{\delta_c} e^{-\delta/ \delta_c}@f$
	*/
	/**
	* Compute traction unloading @f$ \mathbf{T} =
	* \frac{t_{max}}{\delta_{max}} \delta @f$
	*/
	Real beta2 = beta * beta;
	Real normal_open_norm = opening.dot(normal);
	Vector<Real> op_n_n(spatial_dimension);
	op_n_n = normal;
	op_n_n *= (1 - beta2);
	op_n_n *= normal_open_norm;
	tract = beta2 * opening;
	tract += op_n_n;

	delta_max_new = std::max(delta_max, delta);
	tract *=
	std::exp(1.) * sigma_c * std::exp(-delta_max_new / delta_c) / delta_c;
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeCompressiveTraction(
	Vector<Real> & tract, const Vector<Real> & normal, Real delta_n,
	__attribute__((unused)) const Vector<Real> & opening) {
	Vector<Real> temp_tract(normal);

	if (exp_penalty) {
	temp_tract = delta_n std::exp(1) * sigma_c *
	std::exp(-delta_n / delta_c) / delta_c;
	} else {
	Real initial_tg =
	contact_tangent * std::exp(1.) * sigma_c * delta_n / delta_c;
	temp_tract *= initial_tg;
	}

	tract += temp_tract;
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeTangentTraction(
	ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);
	auto tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);
	auto normal_it = normal.begin(spatial_dimension);
	auto opening_it = opening(el_type, ghost_type).begin(spatial_dimension);
	auto delta_max_it = delta_max.previous(el_type, ghost_type).begin();

	Real beta2 = beta * beta;

	/**
	* compute tangent matrix @f$ \frac{\partial \mathbf{t}}
	* {\partial \delta} = \hat{\mathbf{t}} \otimes
	* \frac{\partial (t/\delta)}{\partial \delta}
	* \frac{\hat{\mathbf{t}}}{\delta}+ \frac{t}{\delta} [ \beta^2 \mathbf{I} +
	* (1-\beta^2) (\mathbf{n} \otimes \mathbf{n})] @f$
	**/

	/**
	* In which @f$
	* \frac{\partial(t/ \delta)}{\partial \delta} =
	* \left\{\begin{array} {l l}
	* -e \frac{\sigma_c}{\delta_c^2 }e^{-\delta / \delta_c} & \quad if
	* \delta \geq \delta_{max} \\
	* 0 & \quad if \delta < \delta_{max}, \delta_n > 0
	* \end{array}\right. @f$
	**/

	for (; tangent_it != tangent_end;
	++tangent_it, ++normal_it, ++opening_it, ++delta_max_it) {

	Real normal_opening_norm = opening_it->dot(*normal_it);
	Vector<Real> normal_opening(spatial_dimension);
	normal_opening = (*normal_it);
	normal_opening *= normal_opening_norm;

	Vector<Real> tangential_opening(spatial_dimension);
	tangential_opening = *opening_it;
	tangential_opening -= normal_opening;

	Real tangential_opening_norm = tangential_opening.norm();

	Real delta = tangential_opening_norm;
	delta = delta beta2;
	delta += normal_opening_norm * normal_opening_norm;
	delta = sqrt(delta);

	if ((normal_opening_norm < 0) &&
	(std::abs(normal_opening_norm) > Math::getTolerance())) {

	Vector<Real> op_n(*normal_it);
	op_n *= normal_opening_norm;
	Vector<Real> delta_s(*opening_it);
	delta_s -= op_n;
	delta = tangential_opening_norm * beta;

	computeCoupledTangent(tangent_it, normal_it, delta, delta_s,
	*delta_max_it);

	computeCompressivePenalty(tangent_it, normal_it, normal_opening_norm);

	} else {
	computeCoupledTangent(tangent_it, normal_it, delta, *opening_it,
	*delta_max_it);
	}
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeCoupledTangent(
	Matrix<Real> & tangent, const Vector<Real> & normal, Real delta,
	const Vector<Real> & opening, Real /unused/) {
	AKANTU_DEBUG_IN();

	Real beta2 = beta * beta;
	Matrix<Real> J(spatial_dimension, spatial_dimension);
	J.eye(beta2);

	if (std::abs(delta) < Math::getTolerance()) {
	delta = Math::getTolerance();
	}

	Real opening_normal;
	opening_normal = opening.dot(normal);

	Vector<Real> delta_e(normal);
	delta_e *= opening_normal;
	delta_e *= (1. - beta2);
	delta_e += (beta2 * opening);

	Real exponent = std::exp(1. - delta / delta_c) * sigma_c / delta_c;

	Matrix<Real> first_term(spatial_dimension, spatial_dimension);
	first_term.outerProduct(normal, normal);
	first_term *= (1. - beta2);
	first_term += J;

	Matrix<Real> second_term(spatial_dimension, spatial_dimension);
	second_term.outerProduct(delta_e, delta_e);
	second_term /= delta;
	second_term /= delta_c;

	Matrix<Real> diff(first_term);
	diff -= second_term;

	tangent = diff;
	tangent *= exponent;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveExponential<spatial_dimension>::computeCompressivePenalty(
	Matrix<Real> & tangent, const Vector<Real> & normal, Real delta_n) {

	if (!exp_penalty) {
	delta_n = 0.;
	}

	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	n_outer_n.outerProduct(normal, normal);

	Real normal_tg = contact_tangent * std::exp(1.) * sigma_c *
	std::exp(-delta_n / delta_c) * (1. - delta_n / delta_c) /
	delta_c;

	n_outer_n *= normal_tg;

	tangent += n_outer_n;
	}

	INSTANTIATE_MATERIAL(cohesive_exponential, MaterialCohesiveExponential);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.hh
	index eead5b55e..69c889175 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_exponential.hh
	@@ -1,123 +1,122 @@
	/**
	* @file material_cohesive_exponential.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Exponential irreversible cohesive law of mixed mode loading
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material_cohesive.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_COHESIVE_EXPONENTIAL_HH_
	#define AKANTU_MATERIAL_COHESIVE_EXPONENTIAL_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* Cohesive material Exponential damage
	*
	* parameters in the material files :
	* - sigma_c : critical stress sigma_c (default: 0)
	* - beta : weighting parameter for sliding and normal opening (default:
	* 0)
	* - delta_c : critical opening (default: 0)
	*/
	template <UInt spatial_dimension>
	class MaterialCohesiveExponential : public MaterialCohesive {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialCohesiveExponential(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Initialization
	void initMaterial() override;

	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute the tangent stiffness matrix for an element type
	- void computeTangentTraction(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentTraction(ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal,
	GhostType ghost_type = _not_ghost) override;

	private:
	void computeCoupledTraction(Vector<Real> & tract, const Vector<Real> & normal,
	Real delta, const Vector<Real> & opening,
	Real & delta_max_new, Real delta_max);

	void computeCompressiveTraction(Vector<Real> & tract,
	const Vector<Real> & normal, Real delta_n,
	const Vector<Real> & opening);

	void computeCoupledTangent(Matrix<Real> & tangent,
	const Vector<Real> & normal, Real delta,
	const Vector<Real> & opening, Real delta_max_new);

	void computeCompressivePenalty(Matrix<Real> & tangent,
	const Vector<Real> & normal, Real delta_n);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// beta parameter
	Real beta;

	/// contact penalty = initial slope ?
	bool exp_penalty;

	/// Ratio of contact tangent over the initial exponential tangent
	Real contact_tangent;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	// #include "material_cohesive_exponential_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_COHESIVE_EXPONENTIAL_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.cc
	index 2c73ea05a..7ecd9b191 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.cc
	@@ -1,433 +1,433 @@
	/**
	* @file material_cohesive_linear.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Feb 22 2012
	* @date last modification: Thu Jan 14 2021
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	#include "dof_synchronizer.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <numeric>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveLinear<spatial_dimension>::MaterialCohesiveLinear(
	SolidMechanicsModel & model, const ID & id)
	: MaterialCohesive(model, id), sigma_c_eff("sigma_c_eff", *this),
	delta_c_eff("delta_c_eff", *this),
	insertion_stress("insertion_stress", *this) {
	AKANTU_DEBUG_IN();

	this->registerParam("beta", beta, Real(0.), _pat_parsable \| _pat_readable,
	"Beta parameter");

	this->registerParam("G_c", G_c, Real(0.), _pat_parsable \| _pat_readable,
	"Mode I fracture energy");

	this->registerParam("penalty", penalty, Real(0.),
	_pat_parsable \| _pat_readable, "Penalty coefficient");

	this->registerParam("volume_s", volume_s, Real(0.),
	_pat_parsable \| _pat_readable,
	"Reference volume for sigma_c scaling");

	this->registerParam("m_s", m_s, Real(1.), _pat_parsable \| _pat_readable,
	"Weibull exponent for sigma_c scaling");

	this->registerParam("kappa", kappa, Real(1.), _pat_parsable \| _pat_readable,
	"Kappa parameter");

	this->registerParam(
	"contact_after_breaking", contact_after_breaking, false,
	_pat_parsable \| _pat_readable,
	"Activation of contact when the elements are fully damaged");

	this->registerParam("max_quad_stress_insertion", max_quad_stress_insertion,
	false, _pat_parsable \| _pat_readable,
	"Insertion of cohesive element when stress is high "
	"enough just on one quadrature point");

	this->registerParam("recompute", recompute, false,
	_pat_parsable \| _pat_modifiable, "recompute solution");

	this->use_previous_delta_max = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();

	MaterialCohesive::initMaterial();

	sigma_c_eff.initialize(1);
	delta_c_eff.initialize(1);
	insertion_stress.initialize(spatial_dimension);

	if (not Math::are_float_equal(delta_c, 0.)) {
	delta_c_eff.setDefaultValue(delta_c);
	} else {
	delta_c_eff.setDefaultValue(2 * G_c / sigma_c);
	}

	if (model->getIsExtrinsic()) {
	scaleInsertionTraction();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::updateInternalParameters() {
	/// compute scalars
	beta2_kappa2 = beta * beta / kappa / kappa;
	beta2_kappa = beta * beta / kappa;

	if (Math::are_float_equal(beta, 0)) {
	beta2_inv = 0;
	} else {
	beta2_inv = 1. / beta / beta;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::scaleInsertionTraction() {
	AKANTU_DEBUG_IN();

	// do nothing if volume_s hasn't been specified by the user
	if (Math::are_float_equal(volume_s, 0.)) {
	return;
	}

	const Mesh & mesh_facets = model->getMeshFacets();
	const auto & fe_engine = model->getFEEngine();
	const auto & fe_engine_facet = model->getFEEngine("FacetsFEEngine");

	Real base_sigma_c = sigma_c;

	for (auto && type_facet : mesh_facets.elementTypes(spatial_dimension - 1)) {
	const Array<std::vector<Element>> & facet_to_element =
	mesh_facets.getElementToSubelement(type_facet);

	UInt nb_facet = facet_to_element.size();
	UInt nb_quad_per_facet = fe_engine_facet.getNbIntegrationPoints(type_facet);

	// iterator to modify sigma_c for all the quadrature points of a facet
	auto sigma_c_iterator =
	sigma_c(type_facet).begin_reinterpret(nb_quad_per_facet, nb_facet);

	for (UInt f = 0; f < nb_facet; ++f, ++sigma_c_iterator) {

	const std::vector<Element> & element_list = facet_to_element(f);

	// compute bounding volume
	Real volume = 0;

	auto elem = element_list.begin();
	auto elem_end = element_list.end();

	for (; elem != elem_end; ++elem) {
	if (*elem == ElementNull) {
	continue;
	}

	// unit vector for integration in order to obtain the volume
	UInt nb_quadrature_points =
	fe_engine.getNbIntegrationPoints(elem->type);
	Vector<Real> unit_vector(nb_quadrature_points, 1);

	volume += fe_engine.integrate(unit_vector, elem->type, elem->element,
	elem->ghost_type);
	}

	// scale sigma_c
	*sigma_c_iterator -= base_sigma_c;
	sigma_c_iterator = std::pow(volume_s / volume, 1. / m_s);
	*sigma_c_iterator += base_sigma_c;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::checkInsertion(
	bool check_only) {
	AKANTU_DEBUG_IN();

	const Mesh & mesh_facets = model->getMeshFacets();
	CohesiveElementInserter & inserter = model->getElementInserter();

	for (auto && type_facet : mesh_facets.elementTypes(spatial_dimension - 1)) {
	ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);
	const auto & facets_check = inserter.getCheckFacets(type_facet);
	auto & f_insertion = inserter.getInsertionFacets(type_facet);
	auto & f_filter = facet_filter(type_facet);
	auto & sig_c_eff = sigma_c_eff(type_cohesive);
	auto & del_c = delta_c_eff(type_cohesive);
	auto & ins_stress = insertion_stress(type_cohesive);
	auto & trac_old = tractions.previous(type_cohesive);
	const auto & f_stress = model->getStressOnFacets(type_facet);
	const auto & sigma_lim = sigma_c(type_facet);

	UInt nb_quad_facet =
	model->getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);

	#ifndef AKANTU_NDEBUG
	UInt nb_quad_cohesive = model->getFEEngine("CohesiveFEEngine")
	.getNbIntegrationPoints(type_cohesive);

	AKANTU_DEBUG_ASSERT(nb_quad_cohesive == nb_quad_facet,
	"The cohesive element and the corresponding facet do "
	"not have the same numbers of integration points");
	#endif

	UInt nb_facet = f_filter.size();
	// if (nb_facet == 0) continue;

	auto sigma_lim_it = sigma_lim.begin();

	Matrix<Real> stress_tmp(spatial_dimension, spatial_dimension);
	Matrix<Real> normal_traction(spatial_dimension, nb_quad_facet);
	Vector<Real> stress_check(nb_quad_facet);
	UInt sp2 = spatial_dimension * spatial_dimension;

	const auto & tangents = model->getTangents(type_facet);
	const auto & normals = model->getFEEngine("FacetsFEEngine")
	.getNormalsOnIntegrationPoints(type_facet);
	auto normal_begin = normals.begin(spatial_dimension);
	auto tangent_begin = tangents.begin(tangents.getNbComponent());
	auto facet_stress_begin =
	f_stress.begin(spatial_dimension, spatial_dimension * 2);

	std::vector<Real> new_sigmas;
	std::vector<Vector<Real>> new_normal_traction;
	std::vector<Real> new_delta_c;

	// loop over each facet belonging to this material
	for (UInt f = 0; f < nb_facet; ++f, ++sigma_lim_it) {
	UInt facet = f_filter(f);
	// skip facets where check shouldn't be realized
	if (!facets_check(facet)) {
	continue;
	}

	// compute the effective norm on each quadrature point of the facet
	for (UInt q = 0; q < nb_quad_facet; ++q) {
	UInt current_quad = facet * nb_quad_facet + q;
	const Vector<Real> & normal = normal_begin[current_quad];
	const Vector<Real> & tangent = tangent_begin[current_quad];
	const Matrix<Real> & facet_stress_it = facet_stress_begin[current_quad];

	// compute average stress on the current quadrature point
	Matrix<Real> stress_1(facet_stress_it.storage(), spatial_dimension,
	spatial_dimension);

	Matrix<Real> stress_2(facet_stress_it.storage() + sp2,
	spatial_dimension, spatial_dimension);

	stress_tmp.copy(stress_1);
	stress_tmp += stress_2;
	stress_tmp /= 2.;

	Vector<Real> normal_traction_vec(normal_traction(q));

	// compute normal and effective stress
	stress_check(q) = computeEffectiveNorm(stress_tmp, normal, tangent,
	normal_traction_vec);
	}

	// verify if the effective stress overcomes the threshold
	Real final_stress = stress_check.mean();
	if (max_quad_stress_insertion) {
	final_stress = *std::max_element(
	stress_check.storage(), stress_check.storage() + nb_quad_facet);
	}

	if (final_stress > *sigma_lim_it) {
	f_insertion(facet) = true;

	if (check_only) {
	continue;
	}

	// store the new cohesive material parameters for each quadrature
	// point
	for (UInt q = 0; q < nb_quad_facet; ++q) {
	Real new_sigma = stress_check(q);
	Vector<Real> normal_traction_vec(normal_traction(q));

	if (spatial_dimension != 3) {
	normal_traction_vec *= -1.;
	}

	new_sigmas.push_back(new_sigma);
	new_normal_traction.push_back(normal_traction_vec);

	Real new_delta;

	// set delta_c in function of G_c or a given delta_c value
	if (Math::are_float_equal(delta_c, 0.)) {
	new_delta = 2 * G_c / new_sigma;
	} else {
	new_delta = (sigma_lim_it) / new_sigma delta_c;
	}

	new_delta_c.push_back(new_delta);
	}
	}
	}

	// update material data for the new elements
	UInt old_nb_quad_points = sig_c_eff.size();
	UInt new_nb_quad_points = new_sigmas.size();
	sig_c_eff.resize(old_nb_quad_points + new_nb_quad_points);
	ins_stress.resize(old_nb_quad_points + new_nb_quad_points);
	trac_old.resize(old_nb_quad_points + new_nb_quad_points);
	del_c.resize(old_nb_quad_points + new_nb_quad_points);

	for (UInt q = 0; q < new_nb_quad_points; ++q) {
	sig_c_eff(old_nb_quad_points + q) = new_sigmas[q];
	del_c(old_nb_quad_points + q) = new_delta_c[q];
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	ins_stress(old_nb_quad_points + q, dim) = new_normal_traction[q](dim);
	trac_old(old_nb_quad_points + q, dim) = new_normal_traction[q](dim);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::computeTraction(
	const Array<Real> & normal, ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto traction_it = tractions(el_type, ghost_type).begin(spatial_dimension);
	auto opening_it = opening(el_type, ghost_type).begin(spatial_dimension);
	auto contact_traction_it =
	contact_tractions(el_type, ghost_type).begin(spatial_dimension);
	auto contact_opening_it =
	contact_opening(el_type, ghost_type).begin(spatial_dimension);

	auto normal_it = normal.begin(spatial_dimension);
	auto traction_end = tractions(el_type, ghost_type).end(spatial_dimension);
	auto sigma_c_it = sigma_c_eff(el_type, ghost_type).begin();
	auto delta_max_it = delta_max(el_type, ghost_type).begin();
	auto delta_c_it = delta_c_eff(el_type, ghost_type).begin();
	auto damage_it = damage(el_type, ghost_type).begin();
	auto insertion_stress_it =
	insertion_stress(el_type, ghost_type).begin(spatial_dimension);

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	/// loop on each quadrature point
	for (; traction_it != traction_end;
	++traction_it, ++opening_it, ++normal_it, ++sigma_c_it, ++delta_max_it,
	++delta_c_it, ++damage_it, ++contact_traction_it, ++insertion_stress_it,
	++contact_opening_it) {
	Real normal_opening_norm{0};
	Real tangential_opening_norm{0};
	bool penetration{false};
	this->computeTractionOnQuad(
	traction_it, opening_it, normal_it, delta_max_it, *delta_c_it,
	insertion_stress_it, sigma_c_it, normal_opening, tangential_opening,
	normal_opening_norm, tangential_opening_norm, *damage_it, penetration,
	contact_traction_it, contact_opening_it);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinear<spatial_dimension>::computeTangentTraction(
	ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);

	auto tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);

	auto normal_it = normal.begin(spatial_dimension);

	auto opening_it = opening(el_type, ghost_type).begin(spatial_dimension);

	/// NB: delta_max_it points on delta_max_previous, i.e. the
	/// delta_max related to the solution of the previous incremental
	/// step
	auto delta_max_it = delta_max.previous(el_type, ghost_type).begin();
	auto sigma_c_it = sigma_c_eff(el_type, ghost_type).begin();
	auto delta_c_it = delta_c_eff(el_type, ghost_type).begin();
	auto damage_it = damage(el_type, ghost_type).begin();
	auto contact_opening_it =
	contact_opening(el_type, ghost_type).begin(spatial_dimension);

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	for (; tangent_it != tangent_end; ++tangent_it, ++normal_it, ++opening_it,
	++delta_max_it, ++sigma_c_it, ++delta_c_it,
	++damage_it, ++contact_opening_it) {
	Real normal_opening_norm{0};
	Real tangential_opening_norm{0};
	bool penetration{false};
	this->computeTangentTractionOnQuad(
	tangent_it, delta_max_it, delta_c_it, sigma_c_it, *opening_it,
	*normal_it, normal_opening, tangential_opening, normal_opening_norm,
	tangential_opening_norm, damage_it, penetration, contact_opening_it);
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(cohesive_linear, MaterialCohesiveLinear);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.hh
	index a91c5a986..c590830d2 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear.hh
	@@ -1,189 +1,188 @@
	/**
	* @file material_cohesive_linear.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Mon Sep 14 2020
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_HH_
	#define AKANTU_MATERIAL_COHESIVE_LINEAR_HH_

	namespace akantu {

	/**
	* Cohesive material linear damage for extrinsic case
	*
	* parameters in the material files :
	* - sigma_c : critical stress sigma_c (default: 0)
	* - beta : weighting parameter for sliding and normal opening (default:
	* 0)
	* - G_cI : fracture energy for mode I (default: 0)
	* - G_cII : fracture energy for mode II (default: 0)
	* - penalty : stiffness in compression to prevent penetration
	*/
	template <UInt spatial_dimension>
	class MaterialCohesiveLinear : public MaterialCohesive {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialCohesiveLinear(SolidMechanicsModel & model, const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material parameters
	void initMaterial() override;

	void updateInternalParameters() override;

	/// check stress for cohesive elements' insertion
	void checkInsertion(bool check_only = false) override;

	/// compute effective stress norm for insertion check
	Real computeEffectiveNorm(const Matrix<Real> & stress,
	const Vector<Real> & normal,
	const Vector<Real> & tangent,
	Vector<Real> & normal_traction) const;

	protected:
	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute tangent stiffness matrix
	- void computeTangentTraction(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentTraction(ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal,
	GhostType ghost_type) override;

	/**
	* Scale insertion traction sigma_c according to the volume of the
	* two elements surrounding a facet
	*
	* see the article: F. Zhou and J. F. Molinari "Dynamic crack
	* propagation with cohesive elements: a methodology to address mesh
	* dependency" International Journal for Numerical Methods in
	* Engineering (2004)
	*/
	void scaleInsertionTraction();

	/// compute the traction for a given quadrature point
	inline void computeTractionOnQuad(
	Vector<Real> & traction, Vector<Real> & opening,
	const Vector<Real> & normal, Real & delta_max, const Real & delta_c,
	const Vector<Real> & insertion_stress, const Real & sigma_c,
	Vector<Real> & normal_opening, Vector<Real> & tangential_opening,
	Real & normal_opening_norm, Real & tangential_opening_norm, Real & damage,
	bool & penetration, Vector<Real> & contact_traction,
	Vector<Real> & contact_opening);

	inline void computeTangentTractionOnQuad(
	Matrix<Real> & tangent, Real & delta_max, const Real & delta_c,
	const Real & sigma_c, Vector<Real> & opening, const Vector<Real> & normal,
	Vector<Real> & normal_opening, Vector<Real> & tangential_opening,
	Real & normal_opening_norm, Real & tangential_opening_norm, Real & damage,
	bool & penetration, Vector<Real> & contact_opening);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get sigma_c_eff
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(InsertionTraction, sigma_c_eff, Real);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// beta parameter
	Real beta;

	/// beta square inverse to compute effective norm
	Real beta2_inv;

	/// mode I fracture energy
	Real G_c;

	/// kappa parameter
	Real kappa;

	/// constitutive law scalar to compute delta
	Real beta2_kappa2;

	/// constitutive law scalar to compute traction
	Real beta2_kappa;

	/// penalty coefficient
	Real penalty;

	/// reference volume used to scale sigma_c
	Real volume_s;

	/// weibull exponent used to scale sigma_c
	Real m_s;

	/// variable defining if we are recomputing the last loading step
	/// after load_reduction
	bool recompute;

	/// critical effective stress
	RandomInternalField<Real, CohesiveInternalField> sigma_c_eff;

	/// effective critical displacement (each element can have a
	/// different value)
	CohesiveInternalField<Real> delta_c_eff;

	/// stress at insertion
	CohesiveInternalField<Real> insertion_stress;

	/// variable saying if there should be penalty contact also after
	/// breaking the cohesive elements
	bool contact_after_breaking;

	/// insertion of cohesive element when stress is high enough just on
	/// one quadrature point
	bool max_quad_stress_insertion;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#include "material_cohesive_linear_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_COHESIVE_LINEAR_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.cc
	index df3b83375..69046e2f3 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.cc
	@@ -1,306 +1,306 @@
	/**
	* @file material_cohesive_linear_fatigue.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Feb 20 2015
	* @date last modification: Thu Feb 20 2020
	*
	* @brief See material_cohesive_linear_fatigue.hh for information
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear_fatigue.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveLinearFatigue<spatial_dimension>::MaterialCohesiveLinearFatigue(
	SolidMechanicsModel & model, const ID & id)
	: MaterialCohesiveLinear<spatial_dimension>(model, id),
	delta_prec("delta_prec", this), K_plus("K_plus", this),
	K_minus("K_minus", this), T_1d("T_1d", this),
	switches("switches", this), delta_dot_prec("delta_dot_prec", this),
	normal_regime("normal_regime", *this) {

	this->registerParam("delta_f", delta_f, Real(-1.),
	_pat_parsable \| _pat_readable, "delta_f");

	this->registerParam("progressive_delta_f", progressive_delta_f, false,
	_pat_parsable \| _pat_readable,
	"Whether or not delta_f is equal to delta_max");

	this->registerParam("count_switches", count_switches, false,
	_pat_parsable \| _pat_readable,
	"Count the opening/closing switches per element");

	this->registerParam(
	"fatigue_ratio", fatigue_ratio, Real(1.), _pat_parsable \| _pat_readable,
	"What portion of the cohesive law is subjected to fatigue");
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearFatigue<spatial_dimension>::initMaterial() {
	MaterialCohesiveLinear<spatial_dimension>::initMaterial();

	// check that delta_f has a proper value or assign a defaul value
	if (delta_f < 0) {
	delta_f = this->delta_c_eff;
	} else if (delta_f < this->delta_c_eff) {
	AKANTU_ERROR("Delta_f must be greater or equal to delta_c");
	}

	delta_prec.initialize(1);
	K_plus.initialize(1);
	K_minus.initialize(1);
	T_1d.initialize(1);
	normal_regime.initialize(1);

	if (count_switches) {
	switches.initialize(1);
	delta_dot_prec.initialize(1);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearFatigue<spatial_dimension>::computeTraction(
	const Array<Real> & normal, ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto traction_it =
	this->tractions(el_type, ghost_type).begin(spatial_dimension);

	auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);

	auto contact_traction_it =
	this->contact_tractions(el_type, ghost_type).begin(spatial_dimension);

	auto contact_opening_it =
	this->contact_opening(el_type, ghost_type).begin(spatial_dimension);

	auto normal_it = normal.begin(spatial_dimension);

	auto traction_end =
	this->tractions(el_type, ghost_type).end(spatial_dimension);

	const Array<Real> & sigma_c_array = this->sigma_c_eff(el_type, ghost_type);
	Array<Real> & delta_max_array = this->delta_max(el_type, ghost_type);
	const Array<Real> & delta_c_array = this->delta_c_eff(el_type, ghost_type);
	Array<Real> & damage_array = this->damage(el_type, ghost_type);

	auto insertion_stress_it =
	this->insertion_stress(el_type, ghost_type).begin(spatial_dimension);

	Array<Real> & delta_prec_array = delta_prec(el_type, ghost_type);
	Array<Real> & K_plus_array = K_plus(el_type, ghost_type);
	Array<Real> & K_minus_array = K_minus(el_type, ghost_type);
	Array<Real> & T_1d_array = T_1d(el_type, ghost_type);
	Array<bool> & normal_regime_array = normal_regime(el_type, ghost_type);

	Array<UInt> * switches_array = nullptr;
	Array<Real> * delta_dot_prec_array = nullptr;

	if (count_switches) {
	switches_array = &switches(el_type, ghost_type);
	delta_dot_prec_array = &delta_dot_prec(el_type, ghost_type);
	}

	auto * memory_space = new Real[2 * spatial_dimension];
	Vector<Real> normal_opening(memory_space, spatial_dimension);
	Vector<Real> tangential_opening(memory_space + spatial_dimension,
	spatial_dimension);

	Real tolerance = Math::getTolerance();

	/// loop on each quadrature point
	for (UInt q = 0; traction_it != traction_end; ++traction_it, ++opening_it,
	++normal_it, ++contact_traction_it, ++insertion_stress_it,
	++contact_opening_it, ++q) {

	/// compute normal and tangential opening vectors
	Real normal_opening_norm = opening_it->dot(*normal_it);
	normal_opening = (*normal_it);
	normal_opening *= normal_opening_norm;

	tangential_opening = *opening_it;
	tangential_opening -= normal_opening;

	Real tangential_opening_norm = tangential_opening.norm();

	/**
	* compute effective opening displacement
	* @f$ \delta = \sqrt{
	* \frac{\beta^2}{\kappa^2} \Delta_t^2 + \Delta_n^2 } @f$
	*/
	Real delta =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;

	bool penetration = normal_opening_norm < -tolerance;
	if (not this->contact_after_breaking and
	Math::are_float_equal(damage_array(q), 1.)) {
	penetration = false;
	}

	if (penetration) {
	/// use penalty coefficient in case of penetration
	*contact_traction_it = normal_opening;
	contact_traction_it = this->penalty;
	*contact_opening_it = normal_opening;
	/// don't consider penetration contribution for delta
	*opening_it = tangential_opening;
	normal_opening.zero();
	} else {
	delta += normal_opening_norm * normal_opening_norm;
	contact_traction_it->zero();
	contact_opening_it->zero();
	}

	delta = std::sqrt(delta);

	/**
	* Compute traction @f$ \mathbf{T} = \left(
	* \frac{\beta^2}{\kappa} \Delta_t \mathbf{t} + \Delta_n
	* \mathbf{n} \right) \frac{\sigma_c}{\delta} \left( 1-
	* \frac{\delta}{\delta_c} \right)@f$
	*/

	// update maximum displacement and damage
	delta_max_array(q) = std::max(delta, delta_max_array(q));
	damage_array(q) = std::min(delta_max_array(q) / delta_c_array(q), Real(1.));

	Real delta_dot = delta - delta_prec_array(q);

	// count switches if asked
	if (count_switches) {
	if ((delta_dot > 0. && (*delta_dot_prec_array)(q) <= 0.) \|\|
	(delta_dot < 0. && (*delta_dot_prec_array)(q) >= 0.)) {
	++((*switches_array)(q));
	}

	(*delta_dot_prec_array)(q) = delta_dot;
	}

	// set delta_f equal to delta_max if desired
	if (progressive_delta_f) {
	delta_f = delta_max_array(q);
	}

	// broken element case
	if (Math::are_float_equal(damage_array(q), 1.)) {
	traction_it->zero();
	// just inserted element case
	} else if (Math::are_float_equal(damage_array(q), 0.)) {
	if (penetration) {
	traction_it->zero();
	} else {
	traction_it = insertion_stress_it;
	}
	// initialize the 1d traction to sigma_c
	T_1d_array(q) = sigma_c_array(q);
	}
	// normal case
	else {
	// if element is closed then there are zero tractions
	if (delta <= tolerance) {
	traction_it->zero();
	// otherwise compute new tractions if the new delta is different
	// than the previous one
	} else if (std::abs(delta_dot) > tolerance) {
	// loading case
	if (delta_dot > 0.) {
	if (!normal_regime_array(q)) {
	// equation (4) of the article
	K_plus_array(q) *= 1. - delta_dot / delta_f;
	// equivalent to equation (2) of the article
	T_1d_array(q) += K_plus_array(q) * delta_dot;

	// in case of reloading, traction must not exceed that of the
	// envelop of the cohesive law
	Real max_traction =
	sigma_c_array(q) * (1 - delta / delta_c_array(q));
	bool max_traction_exceeded = T_1d_array(q) > max_traction;
	if (max_traction_exceeded) {
	T_1d_array(q) = max_traction;
	}

	// switch to standard linear cohesive law
	if (delta_max_array(q) > fatigue_ratio * delta_c_array(q)) {
	// reset delta_max to avoid big jumps in the traction
	delta_max_array(q) =
	sigma_c_array(q) /
	(T_1d_array(q) / delta + sigma_c_array(q) / delta_c_array(q));
	damage_array(q) =
	std::min(delta_max_array(q) / delta_c_array(q), Real(1.));
	K_minus_array(q) = sigma_c_array(q) / delta_max_array(q) *
	(1. - damage_array(q));
	normal_regime_array(q) = true;
	} else {
	// equation (3) of the article
	K_minus_array(q) = T_1d_array(q) / delta;

	// if the traction is following the cohesive envelop, then
	// K_plus has to be reset
	if (max_traction_exceeded) {
	K_plus_array(q) = K_minus_array(q);
	}
	}
	} else {
	// compute stiffness according to the standard law
	K_minus_array(q) =
	sigma_c_array(q) / delta_max_array(q) * (1. - damage_array(q));
	}
	}
	// unloading case
	else if (!normal_regime_array(q)) {
	// equation (4) of the article
	K_plus_array(q) +=
	(K_plus_array(q) - K_minus_array(q)) * delta_dot / delta_f;
	// equivalent to equation (2) of the article
	T_1d_array(q) = K_minus_array(q) * delta;
	}

	// applying the actual stiffness
	*traction_it = tangential_opening;
	traction_it = this->beta2_kappa;
	*traction_it += normal_opening;
	traction_it = K_minus_array(q);
	}
	}

	// update precendent delta
	delta_prec_array(q) = delta;
	}

	delete[] memory_space;
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(cohesive_linear_fatigue, MaterialCohesiveLinearFatigue);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.hh
	index da9255785..ec7a93cfd 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.hh
	@@ -1,133 +1,133 @@
	/**
	* @file material_cohesive_linear_fatigue.hh
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Linear irreversible cohesive law with dissipative
	* unloading-reloading cycles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "material_cohesive_linear.hh"

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_FATIGUE_HH_
	#define AKANTU_MATERIAL_COHESIVE_LINEAR_FATIGUE_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* Linear irreversible cohesive law with dissipative
	* unloading-reloading cycles
	*
	* This law uses two different stiffnesses during unloading and
	* reloading. The implementation is based on the article entitled "A
	* cohesive model for fatigue crack growth" by Nguyen, Repetto, Ortiz
	* and Radovitzky (2001). This law is identical to the
	* MaterialCohesiveLinear one except for the unloading-reloading
	* phase.
	*
	* input parameter:
	*
	* - delta_f : it must be greater than delta_c and it is inversely
	* proportional to the dissipation in the unloading-reloading
	* cycles (default: delta_c)
	*/

	template <UInt spatial_dimension>
	class MaterialCohesiveLinearFatigue
	: public MaterialCohesiveLinear<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	MaterialCohesiveLinearFatigue(SolidMechanicsModel & model,
	const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material parameters
	void initMaterial() override;

	protected:
	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the switches
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Switches, switches, UInt);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// delta_f parameter
	Real delta_f;

	/// variable saying if delta_f is equal to delta_max for each
	/// element when the traction is computed
	bool progressive_delta_f;

	/// count the opening/closing switches per element
	bool count_switches;

	/// delta of the previous step
	CohesiveInternalField<Real> delta_prec;

	/// stiffness for reloading
	CohesiveInternalField<Real> K_plus;

	/// stiffness for unloading
	CohesiveInternalField<Real> K_minus;

	/// 1D traction in the cohesive law
	CohesiveInternalField<Real> T_1d;

	/// Number of opening/closing switches
	CohesiveInternalField<UInt> switches;

	/// delta increment of the previous time step
	CohesiveInternalField<Real> delta_dot_prec;

	/// has the element passed to normal regime (not in fatigue anymore)
	CohesiveInternalField<bool> normal_regime;

	/// ratio indicating until what point fatigue is applied in the cohesive law
	Real fatigue_ratio;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_COHESIVE_LINEAR_FATIGUE_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc
	index 857bcddbc..9c5f940be 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc
	@@ -1,283 +1,282 @@
	/**
	* @file material_cohesive_linear_friction.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Tue Jan 12 2016
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear_friction.hh"
	#include "solid_mechanics_model_cohesive.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveLinearFriction<spatial_dimension>::
	MaterialCohesiveLinearFriction(SolidMechanicsModel & model, const ID & id)
	: MaterialParent(model, id), residual_sliding("residual_sliding", *this),
	friction_force("friction_force", *this) {
	AKANTU_DEBUG_IN();

	this->registerParam("mu", mu_max, Real(0.), _pat_parsable \| _pat_readable,
	"Maximum value of the friction coefficient");

	this->registerParam("penalty_for_friction", friction_penalty, Real(0.),
	_pat_parsable \| _pat_readable,
	"Penalty parameter for the friction behavior");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearFriction<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();

	MaterialParent::initMaterial();

	friction_force.initialize(spatial_dimension);
	residual_sliding.initialize(1);
	residual_sliding.initializeHistory();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearFriction<spatial_dimension>::computeTraction(
	__attribute__((unused)) const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	residual_sliding.resize();
	friction_force.resize();

	/// define iterators
	auto traction_it =
	this->tractions(el_type, ghost_type).begin(spatial_dimension);
	auto traction_end =
	this->tractions(el_type, ghost_type).end(spatial_dimension);
	auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);
	auto previous_opening_it =
	this->opening.previous(el_type, ghost_type).begin(spatial_dimension);
	auto contact_traction_it =
	this->contact_tractions(el_type, ghost_type).begin(spatial_dimension);
	auto contact_opening_it =
	this->contact_opening(el_type, ghost_type).begin(spatial_dimension);
	auto normal_it = this->normal.begin(spatial_dimension);
	auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
	auto delta_max_it = this->delta_max(el_type, ghost_type).begin();
	auto delta_max_prev_it =
	this->delta_max.previous(el_type, ghost_type).begin();
	auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
	auto damage_it = this->damage(el_type, ghost_type).begin();
	auto insertion_stress_it =
	this->insertion_stress(el_type, ghost_type).begin(spatial_dimension);
	auto res_sliding_it = this->residual_sliding(el_type, ghost_type).begin();
	auto res_sliding_prev_it =
	this->residual_sliding.previous(el_type, ghost_type).begin();
	auto friction_force_it =
	this->friction_force(el_type, ghost_type).begin(spatial_dimension);

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	if (not this->model->isDefaultSolverExplicit()) {
	this->delta_max(el_type, ghost_type)
	.copy(this->delta_max.previous(el_type, ghost_type));
	}

	/// loop on each quadrature point
	for (; traction_it != traction_end;
	++traction_it, ++opening_it, ++normal_it, ++sigma_c_it, ++delta_max_it,
	++delta_c_it, ++damage_it, ++contact_traction_it, ++insertion_stress_it,
	++contact_opening_it, ++delta_max_prev_it, ++res_sliding_it,
	++res_sliding_prev_it, ++friction_force_it, ++previous_opening_it) {

	Real normal_opening_norm;
	Real tangential_opening_norm;
	bool penetration;
	this->computeTractionOnQuad(
	traction_it, opening_it, normal_it, delta_max_it, *delta_c_it,
	insertion_stress_it, sigma_c_it, normal_opening, tangential_opening,
	normal_opening_norm, tangential_opening_norm, *damage_it, penetration,
	contact_traction_it, contact_opening_it);

	if (penetration) {
	/// the friction coefficient mu increases with the damage. It
	/// equals the maximum value when damage = 1.
	// Real damage = std::min(delta_max_prev_it / delta_c_it,
	// Real(1.));
	Real mu = mu_max; // * damage;

	/// the definition of tau_max refers to the opening
	/// (penetration) of the previous incremental step

	Real tau_max = mu * this->penalty * (std::abs(normal_opening_norm));
	Real delta_sliding_norm =
	std::abs(tangential_opening_norm - *res_sliding_prev_it);

	/// tau is the norm of the friction force, acting tangentially to the
	/// surface
	Real tau = std::min(friction_penalty * delta_sliding_norm, tau_max);

	if ((tangential_opening_norm - *res_sliding_prev_it) < 0.0) {
	tau = -tau;
	}

	/// from tau get the x and y components of friction, to be added in the
	/// force vector
	Vector<Real> tangent_unit_vector(spatial_dimension);
	tangent_unit_vector = tangential_opening / tangential_opening_norm;
	friction_force_it = tau tangent_unit_vector;

	/// update residual_sliding
	if (friction_penalty == 0.) {
	- *res_sliding_it =
	- tangential_opening_norm;
	+ *res_sliding_it = tangential_opening_norm;
	} else {
	*res_sliding_it =
	tangential_opening_norm - (std::abs(tau) / friction_penalty);
	}
	} else {
	friction_force_it->zero();
	}

	traction_it += friction_force_it;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearFriction<spatial_dimension>::computeTangentTraction(
	ElementType el_type, Array<Real> & tangent_matrix,
	__attribute__((unused)) const Array<Real> & normal, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);
	auto tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);

	auto normal_it = this->normal.begin(spatial_dimension);

	auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);
	auto previous_opening_it =
	this->opening.previous(el_type, ghost_type).begin(spatial_dimension);

	/**
	* NB: delta_max_it points on delta_max_previous, i.e. the
	* delta_max related to the solution of the previous incremental
	* step
	*/
	auto delta_max_it = this->delta_max.previous(el_type, ghost_type).begin();
	auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
	auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
	auto damage_it = this->damage(el_type, ghost_type).begin();

	auto contact_opening_it =
	this->contact_opening(el_type, ghost_type).begin(spatial_dimension);

	auto res_sliding_prev_it =
	this->residual_sliding.previous(el_type, ghost_type).begin();

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	for (; tangent_it != tangent_end;
	++tangent_it, ++normal_it, ++opening_it, ++previous_opening_it,
	++delta_max_it, ++sigma_c_it, ++delta_c_it, ++damage_it,
	++contact_opening_it, ++res_sliding_prev_it) {

	Real normal_opening_norm;
	Real tangential_opening_norm;
	bool penetration;
	this->computeTangentTractionOnQuad(
	tangent_it, delta_max_it, delta_c_it, sigma_c_it, *opening_it,
	*normal_it, normal_opening, tangential_opening, normal_opening_norm,
	tangential_opening_norm, damage_it, penetration, contact_opening_it);

	if (penetration) {
	// Real damage = std::min(delta_max_it / delta_c_it, Real(1.));
	Real mu = mu_max; // * damage;

	Real normal_opening_prev_norm =
	std::min(previous_opening_it->dot(*normal_it), Real(0.));
	// Vector<Real> normal_opening_prev = (*normal_it);
	// normal_opening_prev *= normal_opening_prev_norm;

	Real tau_max = mu * this->penalty * (std::abs(normal_opening_prev_norm));
	Real delta_sliding_norm =
	std::abs(tangential_opening_norm - *res_sliding_prev_it);

	// tau is the norm of the friction force, acting tangentially to the
	// surface
	Real tau = std::min(friction_penalty * delta_sliding_norm, tau_max);

	if (tau < tau_max && tau_max > Math::getTolerance()) {
	Matrix<Real> I(spatial_dimension, spatial_dimension);
	I.eye(1.);

	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	n_outer_n.outerProduct(normal_it, normal_it);

	Matrix<Real> nn(n_outer_n);
	I -= nn;
	tangent_it += I friction_penalty;
	}
	}

	// check if the tangential stiffness matrix is symmetric
	// for (UInt h = 0; h < spatial_dimension; ++h){
	// for (UInt l = h; l < spatial_dimension; ++l){
	// if (l > h){
	// Real k_ls = (tangent_it)[spatial_dimensionh+l];
	// Real k_us = (tangent_it)[spatial_dimensionl+h];
	// // std::cout << "k_ls = " << k_ls << std::endl;
	// // std::cout << "k_us = " << k_us << std::endl;
	// if (std::abs(k_ls) > 1e-13 && std::abs(k_us) > 1e-13){
	// Real error = std::abs((k_ls - k_us) / k_us);
	// if (error > 1e-10){
	// std::cout << "non symmetric cohesive matrix" << std::endl;
	// // std::cout << "error " << error << std::endl;
	// }
	// }
	// }
	// }
	// }
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(cohesive_linear_friction, MaterialCohesiveLinearFriction);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.hh
	index fa6de4a8f..d19e561df 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.hh
	@@ -1,106 +1,105 @@
	/**
	* @file material_cohesive_linear_friction.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Tue Apr 28 2020
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "material_cohesive_linear.hh"

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_FRICTION_HH_
	#define AKANTU_MATERIAL_COHESIVE_LINEAR_FRICTION_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* Cohesive material linear with friction force
	*
	* parameters in the material files :
	* - mu : friction coefficient
	* - penalty_for_friction : Penalty parameter for the friction behavior
	*/
	template <UInt spatial_dimension>
	class MaterialCohesiveLinearFriction
	: public MaterialCohesiveLinear<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	using MaterialParent = MaterialCohesiveLinear<spatial_dimension>;

	public:
	MaterialCohesiveLinearFriction(SolidMechanicsModel & model,
	const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material parameters
	void initMaterial() override;

	protected:
	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute tangent stiffness matrix
	- void computeTangentTraction(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentTraction(ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal,
	GhostType ghost_type) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// maximum value of the friction coefficient
	Real mu_max;

	/// penalty parameter for the friction law
	Real friction_penalty;

	/// history parameter for the friction law
	CohesiveInternalField<Real> residual_sliding;

	/// friction force
	CohesiveInternalField<Real> friction_force;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_COHESIVE_LINEAR_FRICTION_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh
	index 9d56e90f7..6e8609fe8 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh
	@@ -1,271 +1,269 @@
	/**
	* @file material_cohesive_linear_inline_impl.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Apr 22 2015
	* @date last modification: Thu Jan 14 2021
	*
	* @brief Inline functions of the MaterialCohesiveLinear
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_
	#define AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline Real MaterialCohesiveLinear<dim>::computeEffectiveNorm(
	const Matrix<Real> & stress, const Vector<Real> & normal,
	const Vector<Real> & tangent, Vector<Real> & normal_traction) const {
	normal_traction.mul<false>(stress, normal);

	Real normal_contrib = normal_traction.dot(normal);

	/// in 3D tangential components must be summed
	Real tangent_contrib = 0;

	if (dim == 2) {
	Real tangent_contrib_tmp = normal_traction.dot(tangent);
	tangent_contrib += tangent_contrib_tmp * tangent_contrib_tmp;
	} else if (dim == 3) {
	for (UInt s = 0; s < dim - 1; ++s) {
	const Vector<Real> tangent_v(tangent.storage() + s * dim, dim);
	Real tangent_contrib_tmp = normal_traction.dot(tangent_v);
	tangent_contrib += tangent_contrib_tmp * tangent_contrib_tmp;
	}
	}

	tangent_contrib = std::sqrt(tangent_contrib);
	normal_contrib = std::max(Real(0.), normal_contrib);

	return std::sqrt(normal_contrib * normal_contrib +
	tangent_contrib * tangent_contrib * beta2_inv);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialCohesiveLinear<dim>::computeTractionOnQuad(
	Vector<Real> & traction, Vector<Real> & opening,
	const Vector<Real> & normal, Real & delta_max, const Real & delta_c,
	const Vector<Real> & insertion_stress, const Real & sigma_c,
	Vector<Real> & normal_opening, Vector<Real> & tangential_opening,
	Real & normal_opening_norm, Real & tangential_opening_norm, Real & damage,
	bool & penetration, Vector<Real> & contact_traction,
	Vector<Real> & contact_opening) {

	/// compute normal and tangential opening vectors
	normal_opening_norm = opening.dot(normal);
	normal_opening = normal;
	normal_opening *= normal_opening_norm;

	tangential_opening = opening;
	tangential_opening -= normal_opening;
	tangential_opening_norm = tangential_opening.norm();

	/**
	* compute effective opening displacement
	* @f$ \delta = \sqrt{
	* \frac{\beta^2}{\kappa^2} \Delta_t^2 + \Delta_n^2 } @f$
	*/
	Real delta =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;

	penetration = normal_opening_norm / delta_c < -Math::getTolerance();
	// penetration = normal_opening_norm < 0.;
	- if (not this->contact_after_breaking and
	- Math::are_float_equal(damage, 1.)) {
	+ if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
	penetration = false;
	}

	if (penetration) {
	/// use penalty coefficient in case of penetration
	contact_traction = normal_opening;
	contact_traction *= this->penalty;
	contact_opening = normal_opening;

	/// don't consider penetration contribution for delta
	opening = tangential_opening;
	normal_opening.zero();
	} else {
	delta += normal_opening_norm * normal_opening_norm;
	contact_traction.zero();
	contact_opening.zero();
	}

	delta = std::sqrt(delta);

	/// update maximum displacement and damage
	delta_max = std::max(delta_max, delta);
	damage = std::min(delta_max / delta_c, Real(1.));

	/**
	* Compute traction @f$ \mathbf{T} = \left(
	* \frac{\beta^2}{\kappa} \Delta_t \mathbf{t} + \Delta_n
	* \mathbf{n} \right) \frac{\sigma_c}{\delta} \left( 1-
	* \frac{\delta}{\delta_c} \right)@f$
	*/

	if (Math::are_float_equal(damage, 1.)) {
	traction.zero();
	} else if (Math::are_float_equal(damage, 0.)) {
	if (penetration) {
	traction.zero();
	} else {
	traction = insertion_stress;
	}
	} else {
	traction = tangential_opening;
	traction *= this->beta2_kappa;
	traction += normal_opening;

	AKANTU_DEBUG_ASSERT(delta_max != 0.,
	"Division by zero, tolerance might be too low");

	traction = sigma_c / delta_max (1. - damage);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	inline void MaterialCohesiveLinear<dim>::computeTangentTractionOnQuad(
	Matrix<Real> & tangent, Real & delta_max, const Real & delta_c,
	const Real & sigma_c, Vector<Real> & opening, const Vector<Real> & normal,
	Vector<Real> & normal_opening, Vector<Real> & tangential_opening,
	Real & normal_opening_norm, Real & tangential_opening_norm, Real & damage,
	bool & penetration, Vector<Real> & contact_opening) {

	/**
	* During the update of the residual the interpenetrations are
	* stored in the array "contact_opening", therefore, in the case
	* of penetration, in the array "opening" there are only the
	* tangential components.
	*/
	opening += contact_opening;

	/// compute normal and tangential opening vectors
	normal_opening_norm = opening.dot(normal);
	normal_opening = normal;
	normal_opening *= normal_opening_norm;

	tangential_opening = opening;
	tangential_opening -= normal_opening;
	tangential_opening_norm = tangential_opening.norm();

	Real delta =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;

	penetration = normal_opening_norm < 0.0;
	- if (not this->contact_after_breaking and
	- Math::are_float_equal(damage, 1.)) {
	+ if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
	penetration = false;
	}

	Real derivative = 0; // derivative = d(t/delta)/ddelta
	Real t = 0;

	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	n_outer_n.outerProduct(normal, normal);

	if (penetration) {
	/// stiffness in compression given by the penalty parameter
	tangent += n_outer_n;
	tangent *= penalty;

	opening = tangential_opening;
	normal_opening_norm = opening.dot(normal);
	normal_opening = normal;
	normal_opening *= normal_opening_norm;
	} else {
	delta += normal_opening_norm * normal_opening_norm;
	}

	delta = std::sqrt(delta);

	/**
	* Delta has to be different from 0 to have finite values of
	* tangential stiffness. At the element insertion, delta =
	* 0. Therefore, a fictictious value is defined, for the
	* evaluation of the first value of K.
	*/
	if (delta < Math::getTolerance()) {
	delta = delta_c / 1000.;
	}

	if (delta >= delta_max) {
	if (delta <= delta_c) {
	derivative = -sigma_c / (delta * delta);
	t = sigma_c * (1 - delta / delta_c);
	} else {
	derivative = 0.;
	t = 0.;
	}
	} else if (delta < delta_max) {
	Real tmax = sigma_c * (1 - delta_max / delta_c);
	t = tmax / delta_max * delta;
	}

	/// computation of the derivative of the constitutive law (dT/ddelta)
	Matrix<Real> I(spatial_dimension, spatial_dimension);
	I.eye(this->beta2_kappa);

	Matrix<Real> nn(n_outer_n);
	nn *= (1. - this->beta2_kappa);
	nn += I;
	nn *= t / delta;

	Vector<Real> t_tilde(normal_opening);
	t_tilde *= (1. - this->beta2_kappa2);

	Vector<Real> mm(opening);
	mm *= this->beta2_kappa2;
	t_tilde += mm;

	Vector<Real> t_hat(normal_opening);
	t_hat += this->beta2_kappa * tangential_opening;

	Matrix<Real> prov(spatial_dimension, spatial_dimension);
	prov.outerProduct(t_hat, t_tilde);
	prov *= derivative / delta;
	prov += nn;

	Matrix<Real> prov_t = prov.transpose();
	tangent += prov_t;
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	-#endif //AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_
	+#endif // AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc
	index 36346d8ea..950eb4e64 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc
	@@ -1,420 +1,420 @@
	/**
	* @file material_cohesive_linear_uncoupled.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Mon Jul 25 2016
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <numeric>

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear_uncoupled.hh"
	#include "solid_mechanics_model_cohesive.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	MaterialCohesiveLinearUncoupled<spatial_dimension>::
	MaterialCohesiveLinearUncoupled(SolidMechanicsModel & model, const ID & id)
	: MaterialCohesiveLinear<spatial_dimension>(model, id),
	delta_n_max("delta_n_max", this), delta_t_max("delta_t_max", this),
	damage_n("damage_n", this), damage_t("damage_t", this) {

	AKANTU_DEBUG_IN();

	this->registerParam(
	"roughness", R, Real(1.), _pat_parsable \| _pat_readable,
	"Roughness to define coupling between mode II and mode I");

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearUncoupled<spatial_dimension>::initMaterial() {
	AKANTU_DEBUG_IN();

	MaterialCohesiveLinear<spatial_dimension>::initMaterial();

	delta_n_max.initialize(1);
	delta_t_max.initialize(1);
	damage_n.initialize(1);
	damage_t.initialize(1);

	delta_n_max.initializeHistory();
	delta_t_max.initializeHistory();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearUncoupled<spatial_dimension>::computeTraction(
	const Array<Real> & /unused/, ElementType el_type, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	delta_n_max.resize();
	delta_t_max.resize();
	damage_n.resize();
	damage_t.resize();

	/// define iterators
	auto traction_it =
	this->tractions(el_type, ghost_type).begin(spatial_dimension);

	auto traction_end =
	this->tractions(el_type, ghost_type).end(spatial_dimension);

	auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);
	auto contact_traction_it =
	this->contact_tractions(el_type, ghost_type).begin(spatial_dimension);
	auto contact_opening_it =
	this->contact_opening(el_type, ghost_type).begin(spatial_dimension);

	auto normal_it = this->normal.begin(spatial_dimension);
	auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
	auto delta_n_max_it = delta_n_max(el_type, ghost_type).begin();
	auto delta_t_max_it = delta_t_max(el_type, ghost_type).begin();
	auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
	auto damage_n_it = damage_n(el_type, ghost_type).begin();
	auto damage_t_it = damage_t(el_type, ghost_type).begin();

	auto insertion_stress_it =
	this->insertion_stress(el_type, ghost_type).begin(spatial_dimension);

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	/// loop on each quadrature point
	for (; traction_it != traction_end;
	++traction_it, ++opening_it, ++contact_traction_it, ++contact_opening_it,
	++normal_it, ++sigma_c_it, ++delta_n_max_it, ++delta_t_max_it,
	++delta_c_it, ++damage_n_it, ++damage_t_it, ++insertion_stress_it) {

	Real normal_opening_norm;
	Real tangential_opening_norm;
	bool penetration;

	Real delta_c2_R2 = delta_c_it (*delta_c_it) / R / R;

	/// compute normal and tangential opening vectors
	normal_opening_norm = opening_it->dot(*normal_it);
	Vector<Real> normal_opening = *normal_it;
	normal_opening *= normal_opening_norm;

	// std::cout<< "normal_opening_norm = " << normal_opening_norm
	// <<std::endl;

	Vector<Real> tangential_opening = *opening_it;
	tangential_opening -= normal_opening;
	tangential_opening_norm = tangential_opening.norm();

	/// compute effective opening displacement
	Real delta_n =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
	Real delta_t =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;

	penetration = normal_opening_norm < 0.0;
	if (not this->contact_after_breaking and
	Math::are_float_equal(*damage_n_it, 1.)) {
	penetration = false;
	}

	if (penetration) {
	/// use penalty coefficient in case of penetration
	*contact_traction_it = normal_opening;
	contact_traction_it = this->penalty;
	*contact_opening_it = normal_opening;

	/// don't consider penetration contribution for delta
	//*opening_it = tangential_opening;
	normal_opening.zero();

	} else {
	delta_n += normal_opening_norm * normal_opening_norm;
	delta_t += normal_opening_norm * normal_opening_norm * delta_c2_R2;
	contact_traction_it->zero();
	contact_opening_it->zero();
	}

	delta_n = std::sqrt(delta_n);
	delta_t = std::sqrt(delta_t);

	/// update maximum displacement and damage
	delta_n_max_it = std::max(delta_n_max_it, delta_n);
	damage_n_it = std::min(delta_n_max_it / *delta_c_it, Real(1.));

	delta_t_max_it = std::max(delta_t_max_it, delta_t);
	damage_t_it = std::min(delta_t_max_it / *delta_c_it, Real(1.));

	Vector<Real> normal_traction(spatial_dimension);
	Vector<Real> shear_traction(spatial_dimension);

	/// NORMAL TRACTIONS
	if (Math::are_float_equal(*damage_n_it, 1.)) {
	normal_traction.zero();
	} else if (Math::are_float_equal(*damage_n_it, 0.)) {
	if (penetration) {
	normal_traction.zero();
	} else {
	normal_traction = *insertion_stress_it;
	}
	} else {
	// the following formulation holds both in loading and in
	// unloading-reloading
	normal_traction = normal_opening;

	AKANTU_DEBUG_ASSERT(*delta_n_max_it != 0.,
	"Division by zero, tolerance might be too low");

	normal_traction = sigma_c_it / (delta_n_max_it) (1. - *damage_n_it);
	}

	/// SHEAR TRACTIONS
	if (Math::are_float_equal(*damage_t_it, 1.) or
	Math::are_float_equal(*damage_t_it, 0.)) {
	shear_traction.zero();
	} else {
	shear_traction = tangential_opening;

	AKANTU_DEBUG_ASSERT(*delta_t_max_it != 0.,
	"Division by zero, tolerance might be too low");

	shear_traction *= this->beta2_kappa;
	shear_traction = sigma_c_it / (delta_t_max_it) (1. - *damage_t_it);
	}

	*traction_it = normal_traction;
	*traction_it += shear_traction;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt spatial_dimension>
	void MaterialCohesiveLinearUncoupled<spatial_dimension>::computeTangentTraction(
	ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & /unused/, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// define iterators
	auto tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);
	auto tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);
	auto normal_it = this->normal.begin(spatial_dimension);
	auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);

	/// NB: delta_max_it points on delta_max_previous, i.e. the
	/// delta_max related to the solution of the previous incremental
	/// step
	auto delta_n_max_it = delta_n_max.previous(el_type, ghost_type).begin();
	auto delta_t_max_it = delta_t_max.previous(el_type, ghost_type).begin();
	auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
	auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
	auto damage_n_it = damage_n(el_type, ghost_type).begin();

	auto contact_opening_it =
	this->contact_opening(el_type, ghost_type).begin(spatial_dimension);

	Vector<Real> normal_opening(spatial_dimension);
	Vector<Real> tangential_opening(spatial_dimension);

	for (; tangent_it != tangent_end; ++tangent_it, ++normal_it, ++opening_it,
	++sigma_c_it, ++delta_c_it,
	++delta_n_max_it, ++delta_t_max_it,
	++damage_n_it, ++contact_opening_it) {

	Real normal_opening_norm;
	Real tangential_opening_norm;
	bool penetration;
	Real delta_c2_R2 = delta_c_it (*delta_c_it) / R / R;

	/**
	* During the update of the residual the interpenetrations are
	* stored in the array "contact_opening", therefore, in the case
	* of penetration, in the array "opening" there are only the
	* tangential components.
	*/
	opening_it += contact_opening_it;

	/// compute normal and tangential opening vectors
	normal_opening_norm = opening_it->dot(*normal_it);
	Vector<Real> normal_opening = *normal_it;
	normal_opening *= normal_opening_norm;

	Vector<Real> tangential_opening = *opening_it;
	tangential_opening -= normal_opening;
	tangential_opening_norm = tangential_opening.norm();

	Real delta_n =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
	Real delta_t =
	tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;

	penetration = normal_opening_norm < 0.0;
	if (not this->contact_after_breaking and
	Math::are_float_equal(*damage_n_it, 1.)) {
	penetration = false;
	}

	Real derivative = 0; // derivative = d(t/delta)/ddelta
	Real T = 0;

	/// TANGENT STIFFNESS FOR NORMAL TRACTIONS
	Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
	n_outer_n.outerProduct(normal_it, normal_it);

	if (penetration) {
	/// stiffness in compression given by the penalty parameter
	*tangent_it = n_outer_n;
	tangent_it = this->penalty;

	//*opening_it = tangential_opening;
	normal_opening.zero();
	} else {
	delta_n += normal_opening_norm * normal_opening_norm;
	delta_n = std::sqrt(delta_n);

	delta_t += normal_opening_norm * normal_opening_norm * delta_c2_R2;

	/**
	* Delta has to be different from 0 to have finite values of
	* tangential stiffness. At the element insertion, delta =
	* 0. Therefore, a fictictious value is defined, for the
	* evaluation of the first value of K.
	*/
	if (delta_n < Math::getTolerance()) {
	delta_n = *delta_c_it / 1000.;
	}

	// loading
	if (delta_n >= *delta_n_max_it) {
	if (delta_n <= *delta_c_it) {
	derivative = -(sigma_c_it) / (delta_n delta_n);
	T = sigma_c_it (1 - delta_n / *delta_c_it);
	} else {
	derivative = 0.;
	T = 0.;
	}
	// unloading-reloading
	} else if (delta_n < *delta_n_max_it) {
	Real T_max = sigma_c_it (1 - delta_n_max_it / delta_c_it);
	derivative = 0.;
	T = T_max / delta_n_max_it delta_n;
	}

	/// computation of the derivative of the constitutive law (dT/ddelta)
	Matrix<Real> nn(n_outer_n);
	nn *= T / delta_n;

	Vector<Real> Delta_tilde(normal_opening);
	Delta_tilde *= (1. - this->beta2_kappa2);
	Vector<Real> mm(*opening_it);
	mm *= this->beta2_kappa2;
	Delta_tilde += mm;

	const Vector<Real> & Delta_hat(normal_opening);
	Matrix<Real> prov(spatial_dimension, spatial_dimension);
	prov.outerProduct(Delta_hat, Delta_tilde);
	prov *= derivative / delta_n;
	prov += nn;

	Matrix<Real> prov_t = prov.transpose();

	*tangent_it = prov_t;
	}

	derivative = 0.;
	T = 0.;

	/// TANGENT STIFFNESS FOR SHEAR TRACTIONS
	delta_t = std::sqrt(delta_t);

	/**
	* Delta has to be different from 0 to have finite values of
	* tangential stiffness. At the element insertion, delta =
	* 0. Therefore, a fictictious value is defined, for the
	* evaluation of the first value of K.
	*/
	if (delta_t < Math::getTolerance()) {
	delta_t = *delta_c_it / 1000.;
	}

	// loading
	if (delta_t >= *delta_t_max_it) {
	if (delta_t <= *delta_c_it) {
	derivative = -(sigma_c_it) / (delta_t delta_t);
	T = sigma_c_it (1 - delta_t / *delta_c_it);
	} else {
	derivative = 0.;
	T = 0.;
	}
	// unloading-reloading
	} else if (delta_t < *delta_t_max_it) {
	Real T_max = sigma_c_it (1 - delta_t_max_it / delta_c_it);
	derivative = 0.;
	T = T_max / delta_t_max_it delta_t;
	}

	/// computation of the derivative of the constitutive law (dT/ddelta)
	Matrix<Real> I(spatial_dimension, spatial_dimension);
	I.eye();
	Matrix<Real> nn(n_outer_n);
	I -= nn;
	I *= T / delta_t;

	Vector<Real> Delta_tilde(normal_opening);
	Delta_tilde *= (delta_c2_R2 - this->beta2_kappa2);
	Vector<Real> mm(*opening_it);
	mm *= this->beta2_kappa2;
	Delta_tilde += mm;

	Vector<Real> Delta_hat(tangential_opening);
	Delta_hat *= this->beta2_kappa;
	Matrix<Real> prov(spatial_dimension, spatial_dimension);
	prov.outerProduct(Delta_hat, Delta_tilde);
	prov *= derivative / delta_t;
	prov += I;

	Matrix<Real> prov_t = prov.transpose();

	*tangent_it += prov_t;
	}

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */

	INSTANTIATE_MATERIAL(cohesive_linear_uncoupled,
	MaterialCohesiveLinearUncoupled);

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.hh
	index c7d19a437..cd5350fbe 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.hh
	@@ -1,103 +1,102 @@
	/**
	* @file material_cohesive_linear_uncoupled.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Feb 20 2020
	*
	* @brief Linear irreversible cohesive law of mixed mode loading with
	* random stress definition for extrinsic type
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "material_cohesive_linear.hh"

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_UNCOUPLED_HH_
	#define AKANTU_MATERIAL_COHESIVE_LINEAR_UNCOUPLED_HH_

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* Cohesive material linear with two different laws for mode I and
	* mode II, for extrinsic case
	*
	* parameters in the material files :
	* - roughness : define the interaction between mode I and mode II (default: 0)
	*/
	template <UInt spatial_dimension>
	class MaterialCohesiveLinearUncoupled
	: public MaterialCohesiveLinear<spatial_dimension> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	// typedef MaterialCohesiveLinear<spatial_dimension> MaterialParent;
	public:
	MaterialCohesiveLinearUncoupled(SolidMechanicsModel & model,
	const ID & id = "");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material parameters
	void initMaterial() override;

	protected:
	/// constitutive law
	void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) override;

	/// compute tangent stiffness matrix
	- void computeTangentTraction(ElementType el_type,
	- Array<Real> & tangent_matrix,
	+ void computeTangentTraction(ElementType el_type, Array<Real> & tangent_matrix,
	const Array<Real> & normal,
	GhostType ghost_type) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// parameter to tune the interaction between mode II and mode I
	Real R;

	/// maximum normal displacement
	CohesiveInternalField<Real> delta_n_max;

	/// maximum tangential displacement
	CohesiveInternalField<Real> delta_t_max;

	/// damage associated to normal tractions
	CohesiveInternalField<Real> damage_n;

	/// damage associated to shear tractions
	CohesiveInternalField<Real> damage_t;
	};

	} // namespace akantu

	#endif /* AKANTU_MATERIAL_COHESIVE_LINEAR_UNCOUPLED_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.cc
	index 8c14d14b0..816c1e240 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.cc
	@@ -1,570 +1,569 @@
	/**
	* @file material_cohesive.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Feb 22 2012
	* @date last modification: Thu Jan 14 2021
	*
	* @brief Specialization of the material class for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive.hh"
	#include "aka_random_generator.hh"
	#include "dof_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "integrator_gauss.hh"
	#include "shape_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MaterialCohesive::MaterialCohesive(SolidMechanicsModel & model, const ID & id)
	- : Material(model, id),
	- facet_filter("facet_filter", id),
	+ : Material(model, id), facet_filter("facet_filter", id),
	fem_cohesive(
	model.getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine")),
	reversible_energy("reversible_energy", *this),
	total_energy("total_energy", this), opening("opening", this),
	tractions("tractions", *this),
	contact_tractions("contact_tractions", *this),
	contact_opening("contact_opening", this), delta_max("delta max", this),
	use_previous_delta_max(false), use_previous_opening(false),
	damage("damage", this), sigma_c("sigma_c", this),
	normal(0, spatial_dimension, "normal") {

	AKANTU_DEBUG_IN();

	this->model = dynamic_cast<SolidMechanicsModelCohesive *>(&model);

	this->registerParam("sigma_c", sigma_c, _pat_parsable \| _pat_readable,
	"Critical stress");
	this->registerParam("delta_c", delta_c, Real(0.),
	_pat_parsable \| _pat_readable, "Critical displacement");

	this->element_filter.initialize(this->model->getMesh(),
	_spatial_dimension = spatial_dimension,
	_element_kind = _ek_cohesive);
	// this->model->getMesh().initElementTypeMapArray(
	// this->element_filter, 1, spatial_dimension, false, _ek_cohesive);

	if (this->model->getIsExtrinsic()) {
	this->facet_filter.initialize(this->model->getMeshFacets(),
	_spatial_dimension = spatial_dimension - 1,
	_element_kind = _ek_regular);
	}
	// this->model->getMeshFacets().initElementTypeMapArray(facet_filter, 1,
	// spatial_dimension -
	// 1);

	this->reversible_energy.initialize(1);
	this->total_energy.initialize(1);

	this->tractions.initialize(spatial_dimension);
	this->tractions.initializeHistory();

	this->contact_tractions.initialize(spatial_dimension);
	this->contact_opening.initialize(spatial_dimension);

	this->opening.initialize(spatial_dimension);
	this->opening.initializeHistory();

	this->delta_max.initialize(1);
	this->damage.initialize(1);

	if (this->model->getIsExtrinsic()) {
	this->sigma_c.initialize(1);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MaterialCohesive::~MaterialCohesive() = default;

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::initMaterial() {
	AKANTU_DEBUG_IN();
	Material::initMaterial();
	if (this->use_previous_delta_max) {
	this->delta_max.initializeHistory();
	}
	if (this->use_previous_opening) {
	this->opening.initializeHistory();
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::assembleInternalForces(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	#if defined(AKANTU_DEBUG_TOOLS)
	debug::element_manager.printData(debug::_dm_material_cohesive,
	"Cohesive Tractions", tractions);
	#endif

	auto & internal_force = const_cast<Array<Real> &>(model->getInternalForce());

	for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type,
	_ek_cohesive)) {
	auto & elem_filter = element_filter(type, ghost_type);
	UInt nb_element = elem_filter.size();
	if (nb_element == 0) {
	continue;
	}

	const auto & shapes = fem_cohesive.getShapes(type, ghost_type);
	auto & traction = tractions(type, ghost_type);
	auto & contact_traction = contact_tractions(type, ghost_type);

	UInt size_of_shapes = shapes.getNbComponent();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points =
	fem_cohesive.getNbIntegrationPoints(type, ghost_type);

	/// compute @f$t_i N_a@f$

	auto * traction_cpy = new Array<Real>(nb_element * nb_quadrature_points,
	spatial_dimension * size_of_shapes);

	auto traction_it = traction.begin(spatial_dimension, 1);
	auto contact_traction_it = contact_traction.begin(spatial_dimension, 1);
	auto shapes_filtered_begin = shapes.begin(1, size_of_shapes);
	auto traction_cpy_it =
	traction_cpy->begin(spatial_dimension, size_of_shapes);

	Matrix<Real> traction_tmp(spatial_dimension, 1);

	for (UInt el = 0; el < nb_element; ++el) {

	UInt current_quad = elem_filter(el) * nb_quadrature_points;

	for (UInt q = 0; q < nb_quadrature_points; ++q, ++traction_it,
	++contact_traction_it, ++current_quad, ++traction_cpy_it) {

	const Matrix<Real> & shapes_filtered =
	shapes_filtered_begin[current_quad];

	traction_tmp.copy(*traction_it);
	traction_tmp += *contact_traction_it;

	traction_cpy_it->mul<false, false>(traction_tmp, shapes_filtered);
	}
	}

	/**
	* compute @f$\int t \cdot N\, dS@f$ by @f$ \sum_q \mathbf{N}^t
	* \mathbf{t}_q \overline w_q J_q@f$
	*/
	auto * partial_int_t_N = new Array<Real>(
	nb_element, spatial_dimension * size_of_shapes, "int_t_N");

	fem_cohesive.integrate(traction_cpy, partial_int_t_N,
	spatial_dimension * size_of_shapes, type, ghost_type,
	elem_filter);

	delete traction_cpy;

	auto * int_t_N = new Array<Real>(
	nb_element, 2 * spatial_dimension * size_of_shapes, "int_t_N");

	Real * int_t_N_val = int_t_N->storage();
	Real * partial_int_t_N_val = partial_int_t_N->storage();
	for (UInt el = 0; el < nb_element; ++el) {
	std::copy_n(partial_int_t_N_val, size_of_shapes * spatial_dimension,
	int_t_N_val);
	std::copy_n(partial_int_t_N_val, size_of_shapes * spatial_dimension,
	int_t_N_val + size_of_shapes * spatial_dimension);

	for (UInt n = 0; n < size_of_shapes * spatial_dimension; ++n) {
	int_t_N_val[n] *= -1.;
	}

	int_t_N_val += nb_nodes_per_element * spatial_dimension;
	partial_int_t_N_val += size_of_shapes * spatial_dimension;
	}

	delete partial_int_t_N;

	/// assemble
	model->getDOFManager().assembleElementalArrayLocalArray(
	*int_t_N, internal_force, type, ghost_type, 1, elem_filter);

	delete int_t_N;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::assembleStiffnessMatrix(GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	for (auto type : element_filter.elementTypes(spatial_dimension, ghost_type,
	_ek_cohesive)) {
	UInt nb_quadrature_points =
	fem_cohesive.getNbIntegrationPoints(type, ghost_type);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	const Array<Real> & shapes = fem_cohesive.getShapes(type, ghost_type);
	Array<UInt> & elem_filter = element_filter(type, ghost_type);

	UInt nb_element = elem_filter.size();

	if (nb_element == 0U) {
	continue;
	}

	UInt size_of_shapes = shapes.getNbComponent();

	auto * shapes_filtered = new Array<Real>(nb_element * nb_quadrature_points,
	size_of_shapes, "filtered shapes");

	Real * shapes_filtered_val = shapes_filtered->storage();
	UInt * elem_filter_val = elem_filter.storage();

	for (UInt el = 0; el < nb_element; ++el) {
	auto * shapes_val = shapes.storage() + elem_filter_val[el] *
	size_of_shapes *
	nb_quadrature_points;
	memcpy(shapes_filtered_val, shapes_val,
	size_of_shapes * nb_quadrature_points * sizeof(Real));
	shapes_filtered_val += size_of_shapes * nb_quadrature_points;
	}

	Matrix<Real> A(spatial_dimension * size_of_shapes,
	spatial_dimension * nb_nodes_per_element);

	for (UInt i = 0; i < spatial_dimension * size_of_shapes; ++i) {
	A(i, i) = 1;
	A(i, i + spatial_dimension * size_of_shapes) = -1;
	}

	/// get the tangent matrix @f$\frac{\partial{(t/\delta)}}{\partial{\delta}}
	/// @f$
	auto * tangent_stiffness_matrix = new Array<Real>(
	nb_element * nb_quadrature_points,
	spatial_dimension * spatial_dimension, "tangent_stiffness_matrix");

	// Array<Real> * normal = new Array<Real>(nb_element *
	// nb_quadrature_points, spatial_dimension, "normal");
	normal.resize(nb_quadrature_points);

	computeNormal(model->getCurrentPosition(), normal, type, ghost_type);

	/// compute openings @f$\mathbf{\delta}@f$
	// computeOpening(model->getDisplacement(), opening(type, ghost_type), type,
	// ghost_type);

	tangent_stiffness_matrix->zero();

	computeTangentTraction(type, *tangent_stiffness_matrix, normal, ghost_type);

	// delete normal;

	UInt size_at_nt_d_n_a = spatial_dimension * nb_nodes_per_element *
	spatial_dimension * nb_nodes_per_element;
	auto * at_nt_d_n_a = new Array<Real>(nb_element * nb_quadrature_points,
	size_at_nt_d_n_a, "A^tN^tDNA");

	Array<Real>::iterator<Vector<Real>> shapes_filt_it =
	shapes_filtered->begin(size_of_shapes);

	Array<Real>::matrix_iterator D_it =
	tangent_stiffness_matrix->begin(spatial_dimension, spatial_dimension);

	Array<Real>::matrix_iterator At_Nt_D_N_A_it =
	at_nt_d_n_a->begin(spatial_dimension * nb_nodes_per_element,
	spatial_dimension * nb_nodes_per_element);

	Array<Real>::matrix_iterator At_Nt_D_N_A_end =
	at_nt_d_n_a->end(spatial_dimension * nb_nodes_per_element,
	spatial_dimension * nb_nodes_per_element);

	Matrix<Real> N(spatial_dimension, spatial_dimension * size_of_shapes);
	Matrix<Real> N_A(spatial_dimension,
	spatial_dimension * nb_nodes_per_element);
	Matrix<Real> D_N_A(spatial_dimension,
	spatial_dimension * nb_nodes_per_element);

	for (; At_Nt_D_N_A_it != At_Nt_D_N_A_end;
	++At_Nt_D_N_A_it, ++D_it, ++shapes_filt_it) {
	N.zero();
	/**
	* store the shapes in voigt notations matrix @f$\mathbf{N} =
	* \begin{array}{cccccc} N_0(\xi) & 0 & N_1(\xi) &0 & N_2(\xi) & 0 \\
	* 0 & * N_0(\xi)& 0 &N_1(\xi)& 0 & N_2(\xi) \end{array} @f$
	**/
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt n = 0; n < size_of_shapes; ++n) {
	N(i, i + spatial_dimension * n) = (*shapes_filt_it)(n);
	}
	}

	/**
	* compute stiffness matrix @f$ \mathbf{K} = \delta \mathbf{U}^T
	* \int_{\Gamma_c} {\mathbf{P}^t \frac{\partial{\mathbf{t}}}
	*{\partial{\delta}}
	* \mathbf{P} d\Gamma \Delta \mathbf{U}} @f$
	**/
	N_A.mul<false, false>(N, A);
	D_N_A.mul<false, false>(*D_it, N_A);
	(*At_Nt_D_N_A_it).mul<true, false>(D_N_A, N_A);
	}

	delete tangent_stiffness_matrix;
	delete shapes_filtered;

	auto * K_e = new Array<Real>(nb_element, size_at_nt_d_n_a, "K_e");

	fem_cohesive.integrate(at_nt_d_n_a, K_e, size_at_nt_d_n_a, type,
	ghost_type, elem_filter);

	delete at_nt_d_n_a;

	model->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "displacement", *K_e, type, ghost_type, _unsymmetric, elem_filter);

	delete K_e;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- *
	* Compute traction from displacements
	*
	* @param[in] ghost_type compute the residual for _ghost or _not_ghost element
	*/
	void MaterialCohesive::computeTraction(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	#if defined(AKANTU_DEBUG_TOOLS)
	debug::element_manager.printData(debug::_dm_material_cohesive,
	"Cohesive Openings", opening);
	#endif

	for (const auto & type : element_filter.elementTypes(
	spatial_dimension, ghost_type, _ek_cohesive)) {
	Array<UInt> & elem_filter = element_filter(type, ghost_type);

	UInt nb_element = elem_filter.size();
	if (nb_element == 0) {
	continue;
	}

	UInt nb_quadrature_points =
	nb_element * fem_cohesive.getNbIntegrationPoints(type, ghost_type);

	normal.resize(nb_quadrature_points);

	/// compute normals @f$\mathbf{n}@f$
	computeNormal(model->getCurrentPosition(), normal, type, ghost_type);

	/// compute openings @f$\mathbf{\delta}@f$
	computeOpening(model->getDisplacement(), opening(type, ghost_type), type,
	ghost_type);

	/// compute traction @f$\mathbf{t}@f$
	computeTraction(normal, type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::computeNormal(const Array<Real> & position,
	Array<Real> & normal, ElementType type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem_cohesive =
	this->model->getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine");

	normal.zero();

	#define COMPUTE_NORMAL(type) \
	fem_cohesive.getShapeFunctions() \
	.computeNormalsOnIntegrationPoints<type, CohesiveReduceFunctionMean>( \
	position, normal, ghost_type, element_filter(type, ghost_type));

	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_NORMAL);
	#undef COMPUTE_NORMAL

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::computeOpening(const Array<Real> & displacement,
	Array<Real> & opening, ElementType type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem_cohesive =
	this->model->getFEEngineClass<MyFEEngineCohesiveType>("CohesiveFEEngine");

	#define COMPUTE_OPENING(type) \
	fem_cohesive.getShapeFunctions() \
	.interpolateOnIntegrationPoints<type, CohesiveReduceFunctionOpening>( \
	displacement, opening, spatial_dimension, ghost_type, \
	element_filter(type, ghost_type));

	AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_OPENING);
	#undef COMPUTE_OPENING

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MaterialCohesive::updateEnergies(ElementType type) {
	AKANTU_DEBUG_IN();

	if (Mesh::getKind(type) != _ek_cohesive) {
	return;
	}

	Vector<Real> b(spatial_dimension);
	Vector<Real> h(spatial_dimension);
	auto erev = reversible_energy(type).begin();
	auto etot = total_energy(type).begin();
	auto traction_it = tractions(type).begin(spatial_dimension);
	auto traction_old_it = tractions.previous(type).begin(spatial_dimension);
	auto opening_it = opening(type).begin(spatial_dimension);
	auto opening_old_it = opening.previous(type).begin(spatial_dimension);

	auto traction_end = tractions(type).end(spatial_dimension);

	/// loop on each quadrature point
	for (; traction_it != traction_end; ++traction_it, ++traction_old_it,
	++opening_it, ++opening_old_it, ++erev,
	++etot) {
	/// trapezoidal integration
	b = *opening_it;
	b -= *opening_old_it;

	h = *traction_old_it;
	h += *traction_it;

	etot += .5 b.dot(h);
	erev = .5 traction_it->dot(*opening_it);
	}

	/// update old values

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real MaterialCohesive::getReversibleEnergy() {
	AKANTU_DEBUG_IN();
	Real erev = 0.;

	/// integrate reversible energy for each type of elements
	for (const auto & type : element_filter.elementTypes(
	spatial_dimension, _not_ghost, _ek_cohesive)) {
	erev +=
	fem_cohesive.integrate(reversible_energy(type, _not_ghost), type,
	_not_ghost, element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return erev;
	}

	/* -------------------------------------------------------------------------- */
	Real MaterialCohesive::getDissipatedEnergy() {
	AKANTU_DEBUG_IN();
	Real edis = 0.;

	/// integrate dissipated energy for each type of elements
	for (const auto & type : element_filter.elementTypes(
	spatial_dimension, _not_ghost, _ek_cohesive)) {
	Array<Real> dissipated_energy(total_energy(type, _not_ghost));
	dissipated_energy -= reversible_energy(type, _not_ghost);
	edis += fem_cohesive.integrate(dissipated_energy, type, _not_ghost,
	element_filter(type, _not_ghost));
	}

	AKANTU_DEBUG_OUT();
	return edis;
	}

	/* -------------------------------------------------------------------------- */
	Real MaterialCohesive::getContactEnergy() {
	AKANTU_DEBUG_IN();
	Real econ = 0.;

	/// integrate contact energy for each type of elements
	for (const auto & type : element_filter.elementTypes(
	spatial_dimension, _not_ghost, _ek_cohesive)) {

	auto & el_filter = element_filter(type, _not_ghost);
	UInt nb_quad_per_el = fem_cohesive.getNbIntegrationPoints(type, _not_ghost);
	UInt nb_quad_points = el_filter.size() * nb_quad_per_el;
	Array<Real> contact_energy(nb_quad_points);

	auto contact_traction_it =
	contact_tractions(type, _not_ghost).begin(spatial_dimension);
	auto contact_opening_it =
	contact_opening(type, _not_ghost).begin(spatial_dimension);

	/// loop on each quadrature point
	for (UInt q = 0; q < nb_quad_points;
	++contact_traction_it, ++contact_opening_it, ++q) {

	contact_energy(q) = .5 * contact_traction_it->dot(*contact_opening_it);
	}

	econ += fem_cohesive.integrate(contact_energy, type, _not_ghost, el_filter);
	}

	AKANTU_DEBUG_OUT();
	return econ;
	}

	/* -------------------------------------------------------------------------- */
	Real MaterialCohesive::getEnergy(const std::string & type) {
	if (type == "reversible") {
	return getReversibleEnergy();
	}
	if (type == "dissipated") {
	return getDissipatedEnergy();
	}
	if (type == "cohesive contact") {
	return getContactEnergy();
	}

	return 0.;
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.hh
	index b584246f2..3a3dd4630 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive.hh
	@@ -1,236 +1,236 @@
	/**
	* @file material_cohesive.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Thu Jan 14 2021
	*
	* @brief Specialization of the material class for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	/* -------------------------------------------------------------------------- */
	#include "cohesive_internal_field.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MATERIAL_COHESIVE_HH_
	#define AKANTU_MATERIAL_COHESIVE_HH_

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class SolidMechanicsModelCohesive;
	}

	namespace akantu {

	class MaterialCohesive : public Material {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	using MyFEEngineCohesiveType =
	FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_cohesive>;

	public:
	MaterialCohesive(SolidMechanicsModel & model, const ID & id = "");
	~MaterialCohesive() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the material computed parameter
	void initMaterial() override;

	/// compute tractions (including normals and openings)
	void computeTraction(GhostType ghost_type = _not_ghost);

	/// assemble residual
	void assembleInternalForces(GhostType ghost_type = _not_ghost) override;

	/// check stress for cohesive elements' insertion, by default it
	/// also updates the cohesive elements' data
	virtual void checkInsertion(bool /check_only/ = false) {
	AKANTU_TO_IMPLEMENT();
	}

	/// interpolate stress on given positions for each element (empty
	/// implemantation to avoid the generic call to be done on cohesive elements)
	virtual void interpolateStress(const ElementType /type/,
	Array<Real> & /result/) {}

	/// compute the stresses
	void computeAllStresses(GhostType /ghost_type/ = _not_ghost) override{};

	// add the facet to be handled by the material
	UInt addFacet(const Element & element);

	protected:
	virtual void computeTangentTraction(ElementType /el_type/,
	Array<Real> & /tangent_matrix/,
	const Array<Real> & /normal/,
	GhostType /ghost_type/ = _not_ghost) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute the normal
	void computeNormal(const Array<Real> & position, Array<Real> & normal,
	ElementType type, GhostType ghost_type);

	/// compute the opening
	void computeOpening(const Array<Real> & displacement, Array<Real> & opening,
	ElementType type, GhostType ghost_type);

	template <ElementType type>
	void computeNormal(const Array<Real> & position, Array<Real> & normal,
	GhostType ghost_type);

	/// assemble stiffness
	void assembleStiffnessMatrix(GhostType ghost_type) override;

	/// constitutive law
	virtual void computeTraction(const Array<Real> & normal, ElementType el_type,
	GhostType ghost_type = _not_ghost) = 0;

	/// parallelism functions
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	protected:
	void updateEnergies(ElementType el_type) override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the opening
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Opening, opening, Real);

	/// get the traction
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Traction, tractions, Real);

	/// get damage
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real);

	/// get facet filter
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(FacetFilter, facet_filter, UInt);
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(FacetFilter, facet_filter, UInt);
	AKANTU_GET_MACRO(FacetFilter, facet_filter,
	const ElementTypeMapArray<UInt> &);
	// AKANTU_GET_MACRO(ElementFilter, element_filter, const
	// ElementTypeMapArray<UInt> &);

	/// compute reversible energy
	Real getReversibleEnergy();

	/// compute dissipated energy
	Real getDissipatedEnergy();

	/// compute contact energy
	Real getContactEnergy();

	/// get energy
	Real getEnergy(const std::string & type) override;

	/// return the energy (identified by id) for the provided element
	Real getEnergy(const std::string & energy_id, ElementType type,
	UInt index) override {
	return Material::getEnergy(energy_id, type, index);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// list of facets assigned to this material
	ElementTypeMapArray<UInt> facet_filter;

	/// Link to the cohesive fem object in the model
	FEEngine & fem_cohesive;

	private:
	/// reversible energy by quadrature point
	CohesiveInternalField<Real> reversible_energy;

	/// total energy by quadrature point
	CohesiveInternalField<Real> total_energy;

	protected:
	/// opening in all elements and quadrature points
	CohesiveInternalField<Real> opening;

	/// traction in all elements and quadrature points
	CohesiveInternalField<Real> tractions;

	/// traction due to contact
	CohesiveInternalField<Real> contact_tractions;

	/// normal openings for contact tractions
	CohesiveInternalField<Real> contact_opening;

	/// maximum displacement
	CohesiveInternalField<Real> delta_max;

	/// tell if the previous delta_max state is needed (in iterative schemes)
	bool use_previous_delta_max;

	/// tell if the previous opening state is needed (in iterative schemes)
	bool use_previous_opening;

	/// damage
	CohesiveInternalField<Real> damage;

	/// pointer to the solid mechanics model for cohesive elements
	SolidMechanicsModelCohesive * model;

	/// critical stress
	RandomInternalField<Real, FacetInternalField> sigma_c;

	/// critical displacement
	Real delta_c;

	/// array to temporarily store the normals
	Array<Real> normal;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	-#include "material_cohesive_inline_impl.hh"
	#include "cohesive_internal_field_tmpl.hh"
	+#include "material_cohesive_inline_impl.hh"

	#endif /* AKANTU_MATERIAL_COHESIVE_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_includes.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_includes.hh
	index 95b80ad2a..408aed805 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_includes.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_includes.hh
	@@ -1,50 +1,50 @@
	/**
	* @file material_cohesive_includes.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Sep 26 2010
	* @date last modification: Fri Apr 02 2021
	*
	* @brief List of includes for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	// /* --------------------------------------------------------------------------
	// */
	// #ifndef AKANTU_CMAKE_LIST_MATERIALS
	// #include "material_cohesive.hh"
	// #include "material_cohesive_bilinear.hh"
	// #include "material_cohesive_exponential.hh"
	// #include "material_cohesive_linear.hh"
	// #include "material_cohesive_linear_fatigue.hh"
	// #include "material_cohesive_linear_friction.hh"
	// #include "material_cohesive_linear_uncoupled.hh"
	// #endif

	#define AKANTU_COHESIVE_MATERIAL_LIST \
	((2, (cohesive_linear, MaterialCohesiveLinear)))( \
	(2, (cohesive_linear_fatigue, MaterialCohesiveLinearFatigue)))( \
	(2, (cohesive_linear_friction, MaterialCohesiveLinearFriction)))( \
	(2, (cohesive_linear_uncoupled, MaterialCohesiveLinearUncoupled)))( \
	(2, (cohesive_bilinear, MaterialCohesiveBilinear)))( \
	(2, (cohesive_exponential, MaterialCohesiveExponential)))
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_inline_impl.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_inline_impl.hh
	index 9234567ca..b7dc0f5b2 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_inline_impl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/materials/material_cohesive_inline_impl.hh
	@@ -1,110 +1,110 @@
	/**
	* @file material_cohesive_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief MaterialCohesive inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt MaterialCohesive::addFacet(const Element & element) {
	Array<UInt> & f_filter = facet_filter(element.type, element.ghost_type);
	f_filter.push_back(element.element);
	return f_filter.size() - 1;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void MaterialCohesive::computeNormal(const Array<Real> & /position/,
	Array<Real> & /normal/,
	GhostType /ghost_type/) {}

	/* -------------------------------------------------------------------------- */
	inline UInt MaterialCohesive::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {

	switch (tag) {
	case SynchronizationTag::_smm_stress: {
	return 2 * spatial_dimension * sizeof(Real) *
	this->getModel().getNbIntegrationPoints(elements,
	"CohesiveFEEngine");
	}
	case SynchronizationTag::_smmc_damage: {
	return sizeof(Real) * this->getModel().getNbIntegrationPoints(
	elements, "CohesiveFEEngine");
	}
	default: {
	}
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */
	inline void MaterialCohesive::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	switch (tag) {
	case SynchronizationTag::_smm_stress: {
	packElementDataHelper(tractions, buffer, elements, "CohesiveFEEngine");
	packElementDataHelper(contact_tractions, buffer, elements,
	"CohesiveFEEngine");
	break;
	}
	case SynchronizationTag::_smmc_damage:
	packElementDataHelper(damage, buffer, elements, "CohesiveFEEngine");
	break;
	default: {
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void MaterialCohesive::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	switch (tag) {
	case SynchronizationTag::_smm_stress: {
	unpackElementDataHelper(tractions, buffer, elements, "CohesiveFEEngine");
	unpackElementDataHelper(contact_tractions, buffer, elements,
	"CohesiveFEEngine");
	break;
	}
	case SynchronizationTag::_smmc_damage:
	unpackElementDataHelper(damage, buffer, elements, "CohesiveFEEngine");
	break;
	default: {
	}
	}
	}
	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.cc
	index bb08d0bf6..28575ae14 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.cc
	@@ -1,696 +1,698 @@
	/**
	* @file solid_mechanics_model_cohesive.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Solid mechanics model for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	#include "aka_iterators.hh"
	#include "cohesive_element_inserter.hh"
	#include "element_synchronizer.hh"
	#include "facet_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "global_ids_updater.hh"
	#include "integrator_gauss.hh"
	#include "material_cohesive.hh"
	#include "mesh_accessor.hh"
	#include "mesh_global_data_updater.hh"
	#include "parser.hh"
	#include "shape_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include "dumpable_inline_impl.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_iohelper_paraview.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class CohesiveMeshGlobalDataUpdater : public MeshGlobalDataUpdater {
	public:
	CohesiveMeshGlobalDataUpdater(SolidMechanicsModelCohesive & model)
	: model(model), mesh(model.getMesh()),
	global_ids_updater(model.getMesh(), *model.cohesive_synchronizer) {}

	/* ------------------------------------------------------------------------ */
	std::tuple<UInt, UInt>
	updateData(NewNodesEvent & nodes_event,
	NewElementsEvent & elements_event) override {
	- auto *cohesive_nodes_event =
	+ auto * cohesive_nodes_event =
	dynamic_cast<CohesiveNewNodesEvent *>(&nodes_event);
	if (cohesive_nodes_event == nullptr) {
	return std::make_tuple(nodes_event.getList().size(),
	elements_event.getList().size());
	}

	/// update nodes type
	auto & new_nodes = cohesive_nodes_event->getList();
	auto & old_nodes = cohesive_nodes_event->getOldNodesList();

	auto local_nb_new_nodes = new_nodes.size();
	auto nb_new_nodes = local_nb_new_nodes;

	if (mesh.isDistributed()) {
	MeshAccessor mesh_accessor(mesh);
	auto & nodes_flags = mesh_accessor.getNodesFlags();
	auto nb_old_nodes = nodes_flags.size();
	nodes_flags.resize(nb_old_nodes + local_nb_new_nodes);

	for (auto && data : zip(old_nodes, new_nodes)) {
	UInt old_node;
	UInt new_node;
	std::tie(old_node, new_node) = data;
	nodes_flags(new_node) = nodes_flags(old_node);
	}

	model.updateCohesiveSynchronizers(elements_event);
	nb_new_nodes = global_ids_updater.updateGlobalIDs(new_nodes.size());
	}

	auto nb_new_elements = elements_event.getList().size();
	const auto & comm = mesh.getCommunicator();
	comm.allReduce(nb_new_elements, SynchronizerOperation::_sum);

	if (nb_new_elements > 0) {
	mesh.sendEvent(elements_event);
	}

	if (nb_new_nodes > 0) {
	mesh.sendEvent(nodes_event);
	}

	return std::make_tuple(nb_new_nodes, nb_new_elements);
	}

	private:
	SolidMechanicsModelCohesive & model;
	Mesh & mesh;
	GlobalIdsUpdater global_ids_updater;
	};

	/* -------------------------------------------------------------------------- */
	SolidMechanicsModelCohesive::SolidMechanicsModelCohesive(
	- Mesh & mesh, UInt dim, const ID & id, std::shared_ptr<DOFManager> dof_manager)
	+ Mesh & mesh, UInt dim, const ID & id,
	+ std::shared_ptr<DOFManager> dof_manager)
	: SolidMechanicsModel(mesh, dim, id, dof_manager,
	ModelType::_solid_mechanics_model_cohesive),
	tangents("tangents", id), facet_stress("facet_stress", id),
	facet_material("facet_material", id) {
	AKANTU_DEBUG_IN();

	registerFEEngineObject<MyFEEngineCohesiveType>("CohesiveFEEngine", mesh,
	Model::spatial_dimension);

	auto && tmp_material_selector =
	std::make_shared<DefaultMaterialCohesiveSelector>(*this);

	tmp_material_selector->setFallback(this->material_selector);
	this->material_selector = tmp_material_selector;

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("cohesive elements", id);
	this->mesh.addDumpMeshToDumper("cohesive elements", mesh,
	Model::spatial_dimension, _not_ghost,
	_ek_cohesive);
	#endif

	if (this->mesh.isDistributed()) {
	/// create the distributed synchronizer for cohesive elements
	this->cohesive_synchronizer = std::make_unique<ElementSynchronizer>(
	mesh, "cohesive_distributed_synchronizer");

	auto & synchronizer = mesh.getElementSynchronizer();
	this->cohesive_synchronizer->split(synchronizer, [](auto && el) {
	return Mesh::getKind(el.type) == _ek_cohesive;
	});

	this->registerSynchronizer(*cohesive_synchronizer,
	SynchronizationTag::_material_id);
	this->registerSynchronizer(*cohesive_synchronizer,
	SynchronizationTag::_smm_stress);
	this->registerSynchronizer(*cohesive_synchronizer,
	SynchronizationTag::_smm_boundary);
	}

	this->inserter = std::make_unique<CohesiveElementInserter>(
	this->mesh, id + ":cohesive_element_inserter");

	registerFEEngineObject<MyFEEngineFacetType>(
	"FacetsFEEngine", mesh.getMeshFacets(), Model::spatial_dimension - 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SolidMechanicsModelCohesive::~SolidMechanicsModelCohesive() = default;

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::setTimeStep(Real time_step,
	const ID & solver_id) {
	SolidMechanicsModel::setTimeStep(time_step, solver_id);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper("cohesive elements").setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::initFullImpl(const ModelOptions & options) {
	AKANTU_DEBUG_IN();

	const auto & smmc_options =
	aka::as_type<SolidMechanicsModelCohesiveOptions>(options);

	this->is_extrinsic = smmc_options.is_extrinsic;

	inserter->setIsExtrinsic(is_extrinsic);

	if (mesh.isDistributed()) {
	auto & mesh_facets = inserter->getMeshFacets();
	auto & synchronizer =
	aka::as_type<FacetSynchronizer>(mesh_facets.getElementSynchronizer());

	// synchronizeGhostFacetsConnectivity();

	/// create the facet synchronizer for extrinsic simulations
	if (is_extrinsic) {
	facet_stress_synchronizer = std::make_unique<ElementSynchronizer>(
	synchronizer, id + ":facet_stress_synchronizer");
	facet_stress_synchronizer->swapSendRecv();
	this->registerSynchronizer(*facet_stress_synchronizer,
	SynchronizationTag::_smmc_facets_stress);
	}
	}

	MeshAccessor mesh_accessor(mesh);
	mesh_accessor.registerGlobalDataUpdater(
	std::make_unique<CohesiveMeshGlobalDataUpdater>(*this));

	ParserSection section;
	bool is_empty;
	std::tie(section, is_empty) = this->getParserSection();

	if (not is_empty) {
	auto inserter_section =
	section.getSubSections(ParserType::_cohesive_inserter);
	if (inserter_section.begin() != inserter_section.end()) {
	inserter->parseSection(*inserter_section.begin());
	}
	}

	SolidMechanicsModel::initFullImpl(options);

	AKANTU_DEBUG_OUT();
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::initMaterials() {
	AKANTU_DEBUG_IN();

	// make sure the material are instantiated
	if (not are_materials_instantiated) {
	instantiateMaterials();
	}

	/// find the first cohesive material
	UInt cohesive_index = UInt(-1);

	for (auto && material : enumerate(materials)) {
	if (dynamic_cast<MaterialCohesive *>(std::get<1>(material).get()) !=
	nullptr) {
	cohesive_index = std::get<0>(material);
	break;
	}
	}

	if (cohesive_index == UInt(-1)) {
	AKANTU_EXCEPTION("No cohesive materials in the material input file");
	}

	material_selector->setFallback(cohesive_index);

	// set the facet information in the material in case of dynamic insertion
	// to know what material to call for stress checks
	const Mesh & mesh_facets = inserter->getMeshFacets();
	facet_material.initialize(
	mesh_facets, _spatial_dimension = spatial_dimension - 1,
	_with_nb_element = true,
	_default_value = material_selector->getFallbackValue());

	for_each_element(
	mesh_facets,
	[&](auto && element) {
	auto mat_index = (*material_selector)(element);
	auto & mat = aka::as_type<MaterialCohesive>(*materials[mat_index]);
	facet_material(element) = mat_index;
	if (is_extrinsic) {
	mat.addFacet(element);
	}
	},
	_spatial_dimension = spatial_dimension - 1, _ghost_type = _not_ghost);

	SolidMechanicsModel::initMaterials();

	if (is_extrinsic) {
	this->initAutomaticInsertion();
	} else {
	this->insertIntrinsicElements();
	}

	AKANTU_DEBUG_OUT();
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the model,basically it pre-compute the shapes, shapes derivatives
	* and jacobian
	*/
	void SolidMechanicsModelCohesive::initModel() {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel::initModel();

	/// add cohesive type connectivity
	ElementType type = _not_defined;
	for (auto && type_ghost : ghost_types) {
	for (const auto & tmp_type :
	mesh.elementTypes(spatial_dimension, type_ghost)) {
	const auto & connectivity = mesh.getConnectivity(tmp_type, type_ghost);
	if (connectivity.empty()) {
	continue;
	}

	type = tmp_type;
	auto type_facet = Mesh::getFacetType(type);
	auto type_cohesive = FEEngine::getCohesiveElementType(type_facet);
	mesh.addConnectivityType(type_cohesive, type_ghost);
	}
	}
	AKANTU_DEBUG_ASSERT(type != _not_defined, "No elements in the mesh");

	getFEEngine("CohesiveFEEngine").initShapeFunctions(_not_ghost);
	getFEEngine("CohesiveFEEngine").initShapeFunctions(_ghost);

	if (is_extrinsic) {
	getFEEngine("FacetsFEEngine").initShapeFunctions(_not_ghost);
	getFEEngine("FacetsFEEngine").initShapeFunctions(_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::insertIntrinsicElements() {
	AKANTU_DEBUG_IN();
	inserter->insertIntrinsicElements();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::initAutomaticInsertion() {
	AKANTU_DEBUG_IN();

	this->inserter->limitCheckFacets();
	this->updateFacetStressSynchronizer();
	this->resizeFacetStress();

	/// compute normals on facets
	this->computeNormals();

	this->initStressInterpolation();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::updateAutomaticInsertion() {
	AKANTU_DEBUG_IN();

	this->inserter->limitCheckFacets();
	this->updateFacetStressSynchronizer();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::initStressInterpolation() {
	Mesh & mesh_facets = inserter->getMeshFacets();

	/// compute quadrature points coordinates on facets
	Array<Real> & position = mesh.getNodes();

	ElementTypeMapArray<Real> quad_facets("quad_facets", id);
	quad_facets.initialize(mesh_facets, _nb_component = Model::spatial_dimension,
	_spatial_dimension = Model::spatial_dimension - 1);
	// mesh_facets.initElementTypeMapArray(quad_facets, Model::spatial_dimension,
	// Model::spatial_dimension - 1);

	getFEEngine("FacetsFEEngine")
	.interpolateOnIntegrationPoints(position, quad_facets);

	/// compute elements quadrature point positions and build
	/// element-facet quadrature points data structure
	ElementTypeMapArray<Real> elements_quad_facets("elements_quad_facets", id);

	elements_quad_facets.initialize(
	mesh, _nb_component = Model::spatial_dimension,
	_spatial_dimension = Model::spatial_dimension);
	// mesh.initElementTypeMapArray(elements_quad_facets,
	// Model::spatial_dimension,
	// Model::spatial_dimension);

	for (auto elem_gt : ghost_types) {
	- for (const auto & type : mesh.elementTypes(Model::spatial_dimension, elem_gt)) {
	+ for (const auto & type :
	+ mesh.elementTypes(Model::spatial_dimension, elem_gt)) {
	UInt nb_element = mesh.getNbElement(type, elem_gt);
	if (nb_element == 0) {
	continue;
	}

	/// compute elements' quadrature points and list of facet
	/// quadrature points positions by element
	const auto & facet_to_element =
	mesh_facets.getSubelementToElement(type, elem_gt);
	auto & el_q_facet = elements_quad_facets(type, elem_gt);

	auto facet_type = Mesh::getFacetType(type);
	auto nb_quad_per_facet =
	getFEEngine("FacetsFEEngine").getNbIntegrationPoints(facet_type);
	auto nb_facet_per_elem = facet_to_element.getNbComponent();

	// small hack in the loop to skip boundary elements, they are silently
	// initialized to NaN to see if this causes problems
	el_q_facet.resize(nb_element * nb_facet_per_elem * nb_quad_per_facet,
	std::numeric_limits<Real>::quiet_NaN());

	for (auto && data :
	zip(make_view(facet_to_element),
	make_view(el_q_facet, spatial_dimension, nb_quad_per_facet))) {
	const auto & global_facet = std::get<0>(data);
	auto & el_q = std::get<1>(data);

	if (global_facet == ElementNull) {
	continue;
	}

	Matrix<Real> quad_f =
	make_view(quad_facets(global_facet.type, global_facet.ghost_type),
	spatial_dimension, nb_quad_per_facet)
	.begin()[global_facet.element];

	el_q = quad_f;
	}
	}
	}

	/// loop over non cohesive materials
	for (auto && material : materials) {
	if (aka::is_of_type<MaterialCohesive>(material)) {
	continue;
	}
	/// initialize the interpolation function
	material->initElementalFieldInterpolation(elements_quad_facets);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::assembleInternalForces() {
	AKANTU_DEBUG_IN();

	// f_int += f_int_cohe
	for (auto & material : this->materials) {
	try {
	auto & mat = aka::as_type<MaterialCohesive>(*material);
	mat.computeTraction(_not_ghost);
	} catch (std::bad_cast & bce) {
	}
	}

	SolidMechanicsModel::assembleInternalForces();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::computeNormals() {
	AKANTU_DEBUG_IN();

	Mesh & mesh_facets = this->inserter->getMeshFacets();
	this->getFEEngine("FacetsFEEngine")
	.computeNormalsOnIntegrationPoints(_not_ghost);

	/**
	* @todo store tangents while computing normals instead of
	* recomputing them as follows:
	*/
	/* ------------------------------------------------------------------------ */
	UInt tangent_components =
	Model::spatial_dimension * (Model::spatial_dimension - 1);

	tangents.initialize(mesh_facets, _nb_component = tangent_components,
	_spatial_dimension = Model::spatial_dimension - 1);
	// mesh_facets.initElementTypeMapArray(tangents, tangent_components,
	// Model::spatial_dimension - 1);

	for (auto facet_type :
	mesh_facets.elementTypes(Model::spatial_dimension - 1)) {
	const Array<Real> & normals =
	this->getFEEngine("FacetsFEEngine")
	.getNormalsOnIntegrationPoints(facet_type);

	Array<Real> & tangents = this->tangents(facet_type);

	Math::compute_tangents(normals, tangents);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::interpolateStress() {
	ElementTypeMapArray<Real> by_elem_result("temporary_stress_by_facets", id);

	for (auto & material : materials) {
	if (not aka::is_of_type<MaterialCohesive>(material)) {
	/// interpolate stress on facet quadrature points positions
	material->interpolateStressOnFacets(facet_stress, by_elem_result);
	}
	}

	this->synchronize(SynchronizationTag::_smmc_facets_stress);
	}

	/* -------------------------------------------------------------------------- */
	UInt SolidMechanicsModelCohesive::checkCohesiveStress() {
	AKANTU_DEBUG_IN();

	if (not is_extrinsic) {
	AKANTU_EXCEPTION(
	"This function can only be used for extrinsic cohesive elements");
	}

	interpolateStress();

	for (auto & mat : materials) {
	if (aka::is_of_type<MaterialCohesive>(mat)) {
	/// check which not ghost cohesive elements are to be created
	auto * mat_cohesive = aka::as_type<MaterialCohesive>(mat.get());
	mat_cohesive->checkInsertion();
	}
	}

	/// communicate data among processors
	// this->synchronize(SynchronizationTag::_smmc_facets);

	/// insert cohesive elements
	UInt nb_new_elements = inserter->insertElements();

	// if (nb_new_elements > 0) {
	// this->reinitializeSolver();
	// }

	AKANTU_DEBUG_OUT();

	return nb_new_elements;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::onElementsAdded(
	const Array<Element> & element_list, const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel::onElementsAdded(element_list, event);

	if (is_extrinsic) {
	resizeFacetStress();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::onNodesAdded(const Array<UInt> & new_nodes,
	const NewNodesEvent & event) {
	AKANTU_DEBUG_IN();

	SolidMechanicsModel::onNodesAdded(new_nodes, event);

	const CohesiveNewNodesEvent * cohesive_event;
	if ((cohesive_event = dynamic_cast<const CohesiveNewNodesEvent *>(&event)) ==
	nullptr) {
	return;
	}

	const auto & old_nodes = cohesive_event->getOldNodesList();

	auto copy = [this, &new_nodes, &old_nodes](auto & arr) {
	UInt new_node;
	UInt old_node;

	auto view = make_view(arr, spatial_dimension);
	auto begin = view.begin();

	for (auto && pair : zip(new_nodes, old_nodes)) {
	std::tie(new_node, old_node) = pair;

	auto old_ = begin + old_node;
	auto new_ = begin + new_node;

	new_ = old_;
	}
	};

	copy(*displacement);
	copy(*blocked_dofs);

	if (velocity) {
	copy(*velocity);
	}

	if (acceleration) {
	copy(*acceleration);
	}

	if (current_position) {
	copy(*current_position);
	}

	if (previous_displacement) {
	copy(*previous_displacement);
	}

	if (displacement_increment) {
	copy(*displacement_increment);
	}

	copy(getDOFManager().getSolution("displacement"));
	// this->assembleMassLumped();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::afterSolveStep(bool converged) {
	AKANTU_DEBUG_IN();

	/*
	* This is required because the Cauchy stress is the stress measure that
	* is used to check the insertion of cohesive elements
	*/
	if (converged) {
	for (auto & mat : materials) {
	if (mat->isFiniteDeformation()) {
	mat->computeAllCauchyStresses(_not_ghost);
	}
	}
	}

	SolidMechanicsModel::afterSolveStep(converged);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::printself(std::ostream & stream,
	int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "SolidMechanicsModelCohesive ["
	<< "\n";
	SolidMechanicsModel::printself(stream, indent + 2);
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::resizeFacetStress() {
	AKANTU_DEBUG_IN();

	this->facet_stress.initialize(getFEEngine("FacetsFEEngine"),
	_nb_component =
	2 * spatial_dimension * spatial_dimension,
	_spatial_dimension = spatial_dimension - 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::addDumpGroupFieldToDumper(
	const std::string & dumper_name, const std::string & field_id,
	const std::string & group_name, ElementKind element_kind,
	bool padding_flag) {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = Model::spatial_dimension;
	ElementKind _element_kind = element_kind;
	if (dumper_name == "cohesive elements") {
	_element_kind = _ek_cohesive;
	} else if (dumper_name == "facets") {
	spatial_dimension = Model::spatial_dimension - 1;
	}

	SolidMechanicsModel::addDumpGroupFieldToDumper(dumper_name, field_id,
	group_name, spatial_dimension,
	_element_kind, padding_flag);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	void SolidMechanicsModelCohesive::onDump() {
	this->flattenAllRegisteredInternals(_ek_cohesive);
	SolidMechanicsModel::onDump();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.hh
	index 85ce58462..6b83bacd6 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive.hh
	@@ -1,310 +1,311 @@
	/**
	* @file solid_mechanics_model_cohesive.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Solid mechanics model for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "cohesive_element_inserter.hh"
	#include "material_selector_cohesive.hh"
	#include "random_internal_field.hh" // included to have the specialization of
	// ParameterTyped::operator Real()
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_HH_

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class FacetSynchronizer;
	class FacetStressSynchronizer;
	class ElementSynchronizer;
	} // namespace akantu

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	struct FacetsCohesiveIntegrationOrderFunctor {
	template <ElementType type, ElementType cohesive_type =
	CohesiveFacetProperty<type>::cohesive_type>
	struct _helper {
	static constexpr int get() {
	return ElementClassProperty<cohesive_type>::polynomial_degree;
	}
	};

	template <ElementType type> struct _helper<type, _not_defined> {
	static constexpr int get() {
	return ElementClassProperty<type>::polynomial_degree;
	}
	};

	template <ElementType type> static inline constexpr int getOrder() {
	return _helper<type>::get();
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Solid Mechanics Model for Cohesive elements */
	/* -------------------------------------------------------------------------- */
	class SolidMechanicsModelCohesive : public SolidMechanicsModel,
	public SolidMechanicsModelEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	class NewCohesiveNodesEvent : public NewNodesEvent {
	public:
	AKANTU_GET_MACRO_NOT_CONST(OldNodesList, old_nodes, Array<UInt> &);
	AKANTU_GET_MACRO(OldNodesList, old_nodes, const Array<UInt> &);

	protected:
	Array<UInt> old_nodes;
	};

	using MyFEEngineCohesiveType =
	FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_cohesive>;
	using MyFEEngineFacetType =
	FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	FacetsCohesiveIntegrationOrderFunctor>;

	- SolidMechanicsModelCohesive(Mesh & mesh, UInt dim = _all_dimensions,
	- const ID & id = "solid_mechanics_model_cohesive",
	- std::shared_ptr<DOFManager> dof_manager = nullptr);
	+ SolidMechanicsModelCohesive(
	+ Mesh & mesh, UInt dim = _all_dimensions,
	+ const ID & id = "solid_mechanics_model_cohesive",
	+ std::shared_ptr<DOFManager> dof_manager = nullptr);

	~SolidMechanicsModelCohesive() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// initialize the cohesive model
	void initFullImpl(const ModelOptions & options) override;

	public:
	/// set the value of the time step
	void setTimeStep(Real time_step, const ID & solver_id = "") override;

	/// assemble the residual for the explicit scheme
	void assembleInternalForces() override;

	/// function to perform a stress check on each facet and insert
	/// cohesive elements if needed (returns the number of new cohesive
	/// elements)
	UInt checkCohesiveStress();

	/// interpolate stress on facets
	void interpolateStress();

	/// update automatic insertion after a change in the element inserter
	void updateAutomaticInsertion();

	/// insert intrinsic cohesive elements
	void insertIntrinsicElements();

	// template <SolveConvergenceMethod cmethod, SolveConvergenceCriteria
	// criteria> bool solveStepCohesive(Real tolerance, Real & error, UInt
	// max_iteration = 100,
	// bool load_reduction = false,
	// Real tol_increase_factor = 1.0,
	// bool do_not_factorize = false);

	protected:
	/// initialize stress interpolation
	void initStressInterpolation();

	/// initialize the model
	void initModel() override;

	/// initialize cohesive material
	void initMaterials() override;

	/// init facet filters for cohesive materials
	void initFacetFilter();

	/// function to print the contain of the class
	void printself(std::ostream & stream, int indent = 0) const override;

	private:
	/// insert cohesive elements along a given physical surface of the mesh
	void insertElementsFromMeshData(const std::string & physical_name);

	/// initialize completely the model for extrinsic elements
	void initAutomaticInsertion();

	/// compute facets' normals
	void computeNormals();

	/// resize facet stress
	void resizeFacetStress();

	/// init facets_check array
	void initFacetsCheck();

	/* ------------------------------------------------------------------------ */
	/* Mesh Event Handler inherited members */
	/* ------------------------------------------------------------------------ */

	protected:
	void onNodesAdded(const Array<UInt> & new_nodes,
	const NewNodesEvent & event) override;
	void onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) override;

	/* ------------------------------------------------------------------------ */
	/* SolidMechanicsModelEventHandler inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	void afterSolveStep(bool converged = true) override;

	/* ------------------------------------------------------------------------ */
	/* Dumpable interface */
	/* ------------------------------------------------------------------------ */
	public:
	void onDump() override;

	void addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind,
	bool padding_flag) override;

	public:
	/// register the tags associated with the parallel synchronizer for
	/// cohesive elements
	// void initParallel(MeshPartition * partition,
	// DataAccessor * data_accessor = NULL,
	// bool extrinsic = false);

	protected:
	- //void synchronizeGhostFacetsConnectivity();
	+ // void synchronizeGhostFacetsConnectivity();

	void updateCohesiveSynchronizers(NewElementsEvent & elements_event);
	void updateFacetStressSynchronizer();

	friend class CohesiveElementInserter;

	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override;

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override;

	protected:
	UInt getNbQuadsForFacetCheck(const Array<Element> & elements) const;

	template <typename T>
	void packFacetStressDataHelper(const ElementTypeMapArray<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements) const;

	template <typename T>
	void unpackFacetStressDataHelper(ElementTypeMapArray<T> & data_to_unpack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements) const;

	template <typename T, bool pack_helper>
	void packUnpackFacetStressDataHelper(ElementTypeMapArray<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<Element> & element) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// get facet mesh
	AKANTU_GET_MACRO(MeshFacets, mesh.getMeshFacets(), const Mesh &);

	/// get stress on facets vector
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(StressOnFacets, facet_stress, Real);

	/// get facet material
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(FacetMaterial, facet_material, UInt);

	/// get facet material
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(FacetMaterial, facet_material, UInt);

	/// get facet material
	AKANTU_GET_MACRO(FacetMaterial, facet_material,
	const ElementTypeMapArray<UInt> &);

	/// @todo THIS HAS TO BE CHANGED
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Tangents, tangents, Real);

	/// get element inserter
	AKANTU_GET_MACRO_NOT_CONST(ElementInserter, *inserter,
	CohesiveElementInserter &);

	/// get is_extrinsic boolean
	AKANTU_GET_MACRO(IsExtrinsic, is_extrinsic, bool);

	/// get cohesive elements synchronizer
	AKANTU_GET_MACRO_NOT_CONST(CohesiveSynchronizer, *cohesive_synchronizer,
	- ElementSynchronizer &);
	+ ElementSynchronizer &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	friend class CohesiveMeshGlobalDataUpdater;

	/// @todo store tangents when normals are computed:
	ElementTypeMapArray<Real> tangents;

	/// stress on facets on the two sides by quadrature point
	ElementTypeMapArray<Real> facet_stress;

	/// material to use if a cohesive element is created on a facet
	ElementTypeMapArray<UInt> facet_material;

	bool is_extrinsic{false};

	/// cohesive element inserter
	std::unique_ptr<CohesiveElementInserter> inserter;

	/// facet stress synchronizer
	std::unique_ptr<ElementSynchronizer> facet_stress_synchronizer;

	/// cohesive elements synchronizer
	std::unique_ptr<ElementSynchronizer> cohesive_synchronizer;
	};

	} // namespace akantu

	#include "solid_mechanics_model_cohesive_inline_impl.hh"

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_inline_impl.hh b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_inline_impl.hh
	index c4dfdbf5a..cea382f2c 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_inline_impl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_inline_impl.hh
	@@ -1,307 +1,307 @@
	/**
	* @file solid_mechanics_model_cohesive_inline_impl.hh
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jan 18 2013
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Implementation of inline functions for the Cohesive element model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_INLINE_IMPL_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	// template <SolveConvergenceMethod cmethod, SolveConvergenceCriteria criteria>
	// bool SolidMechanicsModelCohesive::solveStepCohesive(
	// Real tolerance, Real & error, UInt max_iteration, bool load_reduction,
	// Real tol_increase_factor, bool do_not_factorize) {

	// // EventManager::sendEvent(
	// // SolidMechanicsModelEvent::BeforeSolveStepEvent(method));
	// // this->implicitPred();

	// // bool insertion_new_element = true;
	// // bool converged = false;
	// // Array<Real> * displacement_tmp = NULL;
	// // Array<Real> * velocity_tmp = NULL;
	// // Array<Real> * acceleration_tmp = NULL;
	// // StaticCommunicator & comm = StaticCommunicator::getStaticCommunicator();
	// // Int prank = comm.whoAmI();

	// // /// Loop for the insertion of new cohesive elements
	// // while (insertion_new_element) {

	// // if (is_extrinsic) {
	// // /**
	// // * If in extrinsic the solution of the previous incremental step
	// // * is saved in temporary arrays created for displacements,
	// // * velocities and accelerations. Such arrays are used to find
	// // * the solution with the Newton-Raphson scheme (this is done by
	// // * pointing the pointer "displacement" to displacement_tmp). In
	// // * this way, inside the array "displacement" is kept the
	// // * solution of the previous incremental step, and in
	// // * "displacement_tmp" is saved the current solution.
	// // */

	// // if (!displacement_tmp)
	// // displacement_tmp = new Array<Real>(0, spatial_dimension);

	// // displacement_tmp->copy(*(this->displacement));

	// // if (!velocity_tmp)
	// // velocity_tmp = new Array<Real>(0, spatial_dimension);

	// // velocity_tmp->copy(*(this->velocity));

	// // if (!acceleration_tmp) {
	// // acceleration_tmp = new Array<Real>(0, spatial_dimension);
	// // }

	// // acceleration_tmp->copy(*(this->acceleration));

	// // std::swap(displacement, displacement_tmp);
	// // std::swap(velocity, velocity_tmp);
	// // std::swap(acceleration, acceleration_tmp);
	// // }

	// // this->updateResidual();

	// // AKANTU_DEBUG_ASSERT(stiffness_matrix != NULL,
	// // "You should first initialize the implicit solver and
	// "
	// // "assemble the stiffness matrix");

	// // bool need_factorize = !do_not_factorize;

	// // if (method == _implicit_dynamic) {
	// // AKANTU_DEBUG_ASSERT(mass_matrix != NULL, "You should first initialize
	// "
	// // "the implicit solver and "
	// // "assemble the mass matrix");
	// // }

	// // switch (cmethod) {
	// // case _scm_newton_raphson_tangent:
	// // case _scm_newton_raphson_tangent_not_computed:
	// // break;
	// // case _scm_newton_raphson_tangent_modified:
	// // this->assembleStiffnessMatrix();
	// // break;
	// // default:
	// // AKANTU_ERROR("The resolution method "
	// // << cmethod << " has not been implemented!");
	// // }

	// // UInt iter = 0;
	// // converged = false;
	// // error = 0.;
	// // if (criteria == SolveConvergenceCriteria::_residual) {
	// // converged = this->testConvergence<criteria>(tolerance, error);
	// // if (converged)
	// // return converged;
	// // }

	// // /// Loop to solve the nonlinear system
	// // do {
	// // if (cmethod == _scm_newton_raphson_tangent)
	// // this->assembleStiffnessMatrix();

	// // solve<NewmarkBeta::_displacement_corrector>(*increment, 1.,
	// // need_factorize);

	// // this->implicitCorr();

	// // this->updateResidual();

	// // converged = this->testConvergence<criteria>(tolerance, error);

	// // iter++;
	// // AKANTU_DEBUG_INFO("[" << criteria << "] Convergence iteration "
	// // << std::setw(std::log10(max_iteration)) << iter
	// // << ": error " << error
	// // << (converged ? " < " : " > ") << tolerance);

	// // switch (cmethod) {
	// // case _scm_newton_raphson_tangent:
	// // need_factorize = true;
	// // break;
	// // case _scm_newton_raphson_tangent_not_computed:
	// // case _scm_newton_raphson_tangent_modified:
	// // need_factorize = false;
	// // break;
	// // default:
	// // AKANTU_ERROR("The resolution method "
	// // << cmethod << " has not been implemented!");
	// // }

	// // } while (!converged && iter < max_iteration);

	// // /**
	// // * This is to save the obtained result and proceed with the
	// // * simulation even if the error is higher than the pre-fixed
	// // * tolerance. This is done only after loading reduction
	// // * (load_reduction = true).
	// // */
	// // // if (load_reduction && (error < tolerance * tol_increase_factor))
	// // // converged = true;
	// // if ((error < tolerance * tol_increase_factor))
	// // converged = true;

	// // if (converged) {

	// // } else if (iter == max_iteration) {
	// // if (prank == 0) {
	// // AKANTU_DEBUG_WARNING(
	// // "[" << criteria << "] Convergence not reached after "
	// // << std::setw(std::log10(max_iteration)) << iter << "
	// iteration"
	// // << (iter == 1 ? "" : "s") << "!" << std::endl);
	// // }
	// // }

	// // if (is_extrinsic) {
	// // /**
	// // * If is extrinsic the pointer "displacement" is moved back to
	// // * the array displacement. In this way, the array displacement is
	// // * correctly resized during the checkCohesiveStress function (in
	// // * case new cohesive elements are added). This is possible
	// // * because the procedure called by checkCohesiveStress does not
	// // * use the displacement field (the correct one is now stored in
	// // * displacement_tmp), but directly the stress field that is
	// // * already computed.
	// // */
	// // Array<Real> * tmp_swap;

	// // tmp_swap = displacement_tmp;
	// // displacement_tmp = this->displacement;
	// // this->displacement = tmp_swap;

	// // tmp_swap = velocity_tmp;
	// // velocity_tmp = this->velocity;
	// // this->velocity = tmp_swap;

	// // tmp_swap = acceleration_tmp;
	// // acceleration_tmp = this->acceleration;
	// // this->acceleration = tmp_swap;

	// // /// If convergence is reached, call checkCohesiveStress in order
	// // /// to check if cohesive elements have to be introduced
	// // if (converged) {

	// // UInt new_cohesive_elements = checkCohesiveStress();

	// // if (new_cohesive_elements == 0) {
	// // insertion_new_element = false;
	// // } else {
	// // insertion_new_element = true;
	// // }
	// // }
	// // }

	// // if (!converged && load_reduction)
	// // insertion_new_element = false;

	// // /**
	// // * If convergence is not reached, there is the possibility to
	// // * return back to the main file and reduce the load. Before doing
	// // * this, a pre-fixed value as to be defined for the parameter
	// // * delta_max of the cohesive elements introduced in the current
	// // * incremental step. This is done by calling the function
	// // * checkDeltaMax.
	// // */
	// // if (!converged) {
	// // insertion_new_element = false;

	// // for (UInt m = 0; m < materials.size(); ++m) {
	// // try {
	// // MaterialCohesive & mat =
	// // aka::as_type<MaterialCohesive>(*materials[m]);
	// // mat.checkDeltaMax(_not_ghost);
	// // } catch (std::bad_cast &) {
	// // }
	// // }
	// // }

	// // } // end loop for the insertion of new cohesive elements

	// // /**
	// // * When the solution to the current incremental step is computed (no
	// // * more cohesive elements have to be introduced), call the function
	// // * to compute the energies.
	// // */
	// // if ((is_extrinsic && converged)) {

	// // for (UInt m = 0; m < materials.size(); ++m) {
	// // try {
	// // MaterialCohesive & mat =
	// // aka::as_type<MaterialCohesive>(*materials[m]);
	// // mat.computeEnergies();
	// // } catch (std::bad_cast & bce) {
	// // }
	// // }

	// // EventManager::sendEvent(
	// // SolidMechanicsModelEvent::AfterSolveStepEvent(method));

	// // /**
	// // * The function resetVariables is necessary to correctly set a
	// // * variable that permit to decrease locally the penalty parameter
	// // * for compression.
	// // */
	// // for (UInt m = 0; m < materials.size(); ++m) {
	// // try {
	// // MaterialCohesive & mat =
	// // aka::as_type<MaterialCohesive>(*materials[m]);
	// // mat.resetVariables(_not_ghost);
	// // } catch (std::bad_cast &) {
	// // }
	// // }

	// // /// The correct solution is saved
	// // this->displacement->copy(*displacement_tmp);
	// // this->velocity->copy(*velocity_tmp);
	// // this->acceleration->copy(*acceleration_tmp);
	// // }

	// // delete displacement_tmp;
	// // delete velocity_tmp;
	// // delete acceleration_tmp;

	// // return insertion_new_element;
	//}

	} // namespace akantu

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_COHESIVE_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_parallel.cc b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_parallel.cc
	index bfd5e2ed8..99bf41940 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_parallel.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_cohesive/solid_mechanics_model_cohesive_parallel.cc
	@@ -1,524 +1,527 @@
	/**
	* @file solid_mechanics_model_cohesive_parallel.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Functions for parallel cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "element_synchronizer.hh"
	#include "material_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "solid_mechanics_model_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	// void SolidMechanicsModelCohesive::synchronizeGhostFacetsConnectivity() {
	// AKANTU_DEBUG_IN();

	// const Communicator & comm = mesh.getCommunicator();
	// Int psize = comm.getNbProc();

	// if (psize == 1) {
	// AKANTU_DEBUG_OUT();
	// return;
	// }

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::updateCohesiveSynchronizers(
	NewElementsEvent & elements_event) {
	/// update synchronizers if needed

	if (not mesh.isDistributed()) {
	return;
	}

	ElementTypeMap<Int> nb_new_cohesive_elements;
	for (auto ghost_type : ghost_types) {
	- for(auto cohesive_type : mesh.elementTypes(spatial_dimension, ghost_type, _ek_cohesive)){
	+ for (auto cohesive_type :
	+ mesh.elementTypes(spatial_dimension, ghost_type, _ek_cohesive)) {
	nb_new_cohesive_elements(cohesive_type, ghost_type) = 0;
	}
	}

	- for(auto & el : elements_event.getList()) {
	- if(el.kind() != _ek_cohesive) continue;
	+ for (auto & el : elements_event.getList()) {
	+ if (el.kind() != _ek_cohesive) {
	+ continue;
	+ }
	++nb_new_cohesive_elements(el.type, el.ghost_type);
	}

	auto & mesh_facets = inserter->getMeshFacets();
	auto & facet_synchronizer = mesh_facets.getElementSynchronizer();
	const auto & cfacet_synchronizer = facet_synchronizer;

	// update the cohesive element synchronizer
	- cohesive_synchronizer->updateSchemes([&](auto && scheme, auto && proc,
	- auto && direction) {
	- auto & facet_scheme =
	- cfacet_synchronizer.getCommunications().getScheme(proc, direction);
	-
	- for (auto && facet : facet_scheme) {
	- const auto & cohesive_element = const_cast<const Mesh &>(mesh_facets)
	- .getElementToSubelement(facet)[1];
	-
	- if (cohesive_element == ElementNull or
	- cohesive_element.kind() != _ek_cohesive) {
	- continue;
	- }
	+ cohesive_synchronizer->updateSchemes(
	+ [&](auto && scheme, auto && proc, auto && direction) {
	+ auto & facet_scheme =
	+ cfacet_synchronizer.getCommunications().getScheme(proc, direction);
	+
	+ for (auto && facet : facet_scheme) {
	+ const auto & cohesive_element = const_cast<const Mesh &>(mesh_facets)
	+ .getElementToSubelement(facet)[1];
	+
	+ if (cohesive_element == ElementNull or
	+ cohesive_element.kind() != _ek_cohesive) {
	+ continue;
	+ }

	- auto && cohesive_type = FEEngine::getCohesiveElementType(facet.type);
	- auto old_nb_cohesive_elements =
	- mesh.getNbElement(cohesive_type, facet.ghost_type);
	- old_nb_cohesive_elements -=
	- nb_new_cohesive_elements(cohesive_type, facet.ghost_type);
	+ auto && cohesive_type = FEEngine::getCohesiveElementType(facet.type);
	+ auto old_nb_cohesive_elements =
	+ mesh.getNbElement(cohesive_type, facet.ghost_type);
	+ old_nb_cohesive_elements -=
	+ nb_new_cohesive_elements(cohesive_type, facet.ghost_type);

	- if (cohesive_element.element >= old_nb_cohesive_elements) {
	- scheme.push_back(cohesive_element);
	- }
	- }
	- });
	+ if (cohesive_element.element >= old_nb_cohesive_elements) {
	+ scheme.push_back(cohesive_element);
	+ }
	+ }
	+ });

	if (not facet_stress_synchronizer) {
	return;
	}

	const auto & element_synchronizer = mesh.getElementSynchronizer();
	const auto & comm = mesh.getCommunicator();
	auto && my_rank = comm.whoAmI();

	// update the facet stress synchronizer
	facet_stress_synchronizer->updateSchemes([&](auto && scheme, auto && proc,
	auto && /direction/) {
	auto it_element = scheme.begin();
	for (auto && element : scheme) {
	auto && facet_check = inserter->getCheckFacets(
	element.type, element.ghost_type)(element.element); // slow access
	// here

	if (facet_check) {
	auto && connected_elements = mesh_facets.getElementToSubelement(
	element.type, element.ghost_type)(element.element); // slow access
	// here
	auto && rank_left = element_synchronizer.getRank(connected_elements[0]);
	auto && rank_right =
	element_synchronizer.getRank(connected_elements[1]);

	// keep element if the element is still a boundary element between two
	// processors
	if ((rank_left == Int(proc) and rank_right == my_rank) or
	(rank_left == my_rank and rank_right == Int(proc))) {
	*it_element = element;
	++it_element;
	}
	}
	}
	scheme.resize(it_element - scheme.begin());
	});
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::updateFacetStressSynchronizer() {
	if (facet_stress_synchronizer != nullptr) {
	const auto & rank_to_element =
	mesh.getElementSynchronizer().getElementToRank();
	const auto & facet_checks = inserter->getCheckFacets();
	const auto & mesh_facets = inserter->getMeshFacets();
	const auto & element_to_facet = mesh_facets.getElementToSubelement();
	UInt rank = mesh.getCommunicator().whoAmI();

	facet_stress_synchronizer->updateSchemes(
	[&](auto & scheme, auto & proc, auto & /direction/) {
	UInt el = 0;
	for (auto && element : scheme) {
	if (not facet_checks(element)) {
	continue;
	}

	const auto & next_el = element_to_facet(element);
	UInt rank_left = rank_to_element(next_el[0]);
	UInt rank_right = rank_to_element(next_el[1]);

	if ((rank_left == rank and rank_right == proc) or
	(rank_left == proc and rank_right == rank)) {
	scheme[el] = element;
	++el;
	}
	}
	scheme.resize(el);
	});
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void SolidMechanicsModelCohesive::packFacetStressDataHelper(
	const ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & elements) const {
	packUnpackFacetStressDataHelper<T, true>(
	const_cast<ElementTypeMapArray<T> &>(data_to_pack), buffer, elements);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void SolidMechanicsModelCohesive::unpackFacetStressDataHelper(
	ElementTypeMapArray<T> & data_to_unpack, CommunicationBuffer & buffer,
	const Array<Element> & elements) const {
	packUnpackFacetStressDataHelper<T, false>(data_to_unpack, buffer, elements);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, bool pack_helper>
	void SolidMechanicsModelCohesive::packUnpackFacetStressDataHelper(
	ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & elements) const {
	ElementType current_element_type = _not_defined;
	GhostType current_ghost_type = _casper;
	UInt nb_quad_per_elem = 0;
	UInt sp2 = spatial_dimension * spatial_dimension;
	UInt nb_component = sp2 * 2;
	bool element_rank = false;
	Mesh & mesh_facets = inserter->getMeshFacets();

	Array<T> * vect = nullptr;
	const Array<std::vector<Element>> * element_to_facet = nullptr;

	auto & fe_engine = this->getFEEngine("FacetsFEEngine");
	for (auto && el : elements) {
	if (el.type == _not_defined) {
	AKANTU_EXCEPTION(
	"packUnpackFacetStressDataHelper called with wrong inputs");
	}

	if (el.type != current_element_type \|\|
	el.ghost_type != current_ghost_type) {
	current_element_type = el.type;
	current_ghost_type = el.ghost_type;
	vect = &data_to_pack(el.type, el.ghost_type);

	element_to_facet =
	&(mesh_facets.getElementToSubelement(el.type, el.ghost_type));

	nb_quad_per_elem =
	fe_engine.getNbIntegrationPoints(el.type, el.ghost_type);
	}

	if (pack_helper) {
	element_rank =
	(*element_to_facet)(el.element)[0].ghost_type != _not_ghost;
	} else {
	element_rank =
	(*element_to_facet)(el.element)[0].ghost_type == _not_ghost;
	}

	for (UInt q = 0; q < nb_quad_per_elem; ++q) {
	Vector<T> data(vect->storage() +
	(el.element * nb_quad_per_elem + q) * nb_component +
	element_rank * sp2,
	sp2);

	if (pack_helper) {
	buffer << data;
	} else {
	buffer >> data;
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	UInt SolidMechanicsModelCohesive::getNbQuadsForFacetCheck(
	const Array<Element> & elements) const {
	UInt nb_quads = 0;
	UInt nb_quad_per_facet = 0;

	ElementType current_element_type = _not_defined;
	GhostType current_ghost_type = _casper;
	auto & fe_engine = this->getFEEngine("FacetsFEEngine");
	for (const auto & el : elements) {
	if (el.type != current_element_type \|\|
	el.ghost_type != current_ghost_type) {
	current_element_type = el.type;
	current_ghost_type = el.ghost_type;

	nb_quad_per_facet =
	fe_engine.getNbIntegrationPoints(el.type, el.ghost_type);
	}

	nb_quads += nb_quad_per_facet;
	}

	return nb_quads;
	}

	/* -------------------------------------------------------------------------- */
	UInt SolidMechanicsModelCohesive::getNbData(
	const Array<Element> & elements, const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	if (elements.empty()) {
	return 0;
	}

	/// regular element case
	if (elements(0).kind() == _ek_regular) {
	switch (tag) {
	// case SynchronizationTag::_smmc_facets: {
	// size += elements.size() * sizeof(bool);
	// break;
	// }
	case SynchronizationTag::_smmc_facets_stress: {
	UInt nb_quads = getNbQuadsForFacetCheck(elements);
	size += nb_quads * spatial_dimension * spatial_dimension * sizeof(Real);
	break;
	}
	case SynchronizationTag::_material_id: {
	for (auto && element : elements) {
	if (Mesh::getSpatialDimension(element.type) ==
	(spatial_dimension - 1)) {
	size += sizeof(UInt);
	}
	}

	size += SolidMechanicsModel::getNbData(elements, tag);
	break;
	}

	default: {
	size += SolidMechanicsModel::getNbData(elements, tag);
	}
	}
	}
	/// cohesive element case
	else if (elements(0).kind() == _ek_cohesive) {

	switch (tag) {
	case SynchronizationTag::_material_id: {
	size += elements.size() * sizeof(UInt);
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	UInt nb_nodes_per_element = 0;

	for (auto && el : elements) {
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	// force, displacement, boundary
	size += nb_nodes_per_element * spatial_dimension *
	(2 * sizeof(Real) + sizeof(bool));
	break;
	}
	default:
	break;
	}

	if (tag != SynchronizationTag::_material_id &&
	tag != SynchronizationTag::_smmc_facets) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	size += mat.getNbData(elements, tag);
	});
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::packData(
	CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	if (elements.empty()) {
	return;
	}

	if (elements(0).kind() == _ek_regular) {
	switch (tag) {
	// case SynchronizationTag::_smmc_facets: {
	// packElementalDataHelper(inserter->getInsertionFacetsByElement(),
	// buffer,
	// elements, false, getFEEngine());
	// break;
	// }
	case SynchronizationTag::_smmc_facets_stress: {
	packFacetStressDataHelper(facet_stress, buffer, elements);
	break;
	}
	case SynchronizationTag::_material_id: {
	for (auto && element : elements) {
	if (Mesh::getSpatialDimension(element.type) !=
	(spatial_dimension - 1)) {
	continue;
	}
	buffer << material_index(element);
	}

	SolidMechanicsModel::packData(buffer, elements, tag);
	break;
	}
	default: {
	SolidMechanicsModel::packData(buffer, elements, tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return;
	}

	if (elements(0).kind() == _ek_cohesive) {
	switch (tag) {
	case SynchronizationTag::_material_id: {
	packElementalDataHelper(material_index, buffer, elements, false,
	getFEEngine("CohesiveFEEngine"));
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	packNodalDataHelper(*internal_force, buffer, elements, mesh);
	packNodalDataHelper(*velocity, buffer, elements, mesh);
	packNodalDataHelper(*blocked_dofs, buffer, elements, mesh);
	break;
	}
	default: {
	}
	}

	if (tag != SynchronizationTag::_material_id &&
	tag != SynchronizationTag::_smmc_facets) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	mat.packData(buffer, elements, tag);
	});
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModelCohesive::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	if (elements.empty()) {
	return;
	}

	if (elements(0).kind() == _ek_regular) {
	switch (tag) {
	// case SynchronizationTag::_smmc_facets: {
	// unpackElementalDataHelper(inserter->getInsertionFacetsByElement(),
	// buffer,
	// elements, false, getFEEngine());
	// break;
	// }
	case SynchronizationTag::_smmc_facets_stress: {
	unpackFacetStressDataHelper(facet_stress, buffer, elements);
	break;
	}
	case SynchronizationTag::_material_id: {
	for (auto && element : elements) {
	if (Mesh::getSpatialDimension(element.type) !=
	(spatial_dimension - 1)) {
	continue;
	}

	UInt recv_mat_index;
	buffer >> recv_mat_index;
	UInt & mat_index = material_index(element);
	if (mat_index != UInt(-1)) {
	continue;
	}

	// add ghosts element to the correct material
	mat_index = recv_mat_index;
	auto & mat = aka::as_type<MaterialCohesive>(*materials[mat_index]);
	if (is_extrinsic) {
	mat.addFacet(element);
	}
	facet_material(element) = recv_mat_index;
	}
	SolidMechanicsModel::unpackData(buffer, elements, tag);
	break;
	}
	default: {
	SolidMechanicsModel::unpackData(buffer, elements, tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return;
	}

	if (elements(0).kind() == _ek_cohesive) {
	switch (tag) {
	case SynchronizationTag::_material_id: {
	for (auto && element : elements) {
	UInt recv_mat_index;
	buffer >> recv_mat_index;
	UInt & mat_index = material_index(element);
	if (mat_index != UInt(-1)) {
	continue;
	}

	// add ghosts element to the correct material
	mat_index = recv_mat_index;
	UInt index = materials[mat_index]->addElement(element);
	material_local_numbering(element) = index;
	}
	break;
	}
	case SynchronizationTag::_smm_boundary: {
	unpackNodalDataHelper(*internal_force, buffer, elements, mesh);
	unpackNodalDataHelper(*velocity, buffer, elements, mesh);
	unpackNodalDataHelper(*blocked_dofs, buffer, elements, mesh);
	break;
	}
	default: {
	}
	}

	if (tag != SynchronizationTag::_material_id &&
	tag != SynchronizationTag::_smmc_facets) {
	splitByMaterial(elements, [&](auto && mat, auto && elements) {
	mat.unpackData(buffer, elements, tag);
	});
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc
	index a43eeb1a1..b6aa612e3 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc
	@@ -1,172 +1,172 @@
	/**
	* @file embedded_interface_intersector.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri May 01 2015
	* @date last modification: Tue May 21 2019
	*
	* @brief Class that loads the interface from mesh and computes intersections
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "embedded_interface_intersector.hh"
	#include "mesh_segment_intersector.hh"

	/// Helper macro for types in the mesh. Creates an intersector and computes
	/// intersection queries
	#define INTERFACE_INTERSECTOR_CASE(dim, type) \
	do { \
	MeshSegmentIntersector<dim, type> intersector(this->mesh, interface_mesh); \
	name_to_primitives_it = name_to_primitives_map.begin(); \
	for (; name_to_primitives_it != name_to_primitives_end; \
	++name_to_primitives_it) { \
	intersector.setPhysicalName(name_to_primitives_it->first); \
	intersector.buildResultFromQueryList(name_to_primitives_it->second); \
	} \
	} while (0)

	#define INTERFACE_INTERSECTOR_CASE_2D(type) INTERFACE_INTERSECTOR_CASE(2, type)
	#define INTERFACE_INTERSECTOR_CASE_3D(type) INTERFACE_INTERSECTOR_CASE(3, type)

	namespace akantu {

	EmbeddedInterfaceIntersector::EmbeddedInterfaceIntersector(
	Mesh & mesh, const Mesh & primitive_mesh)
	: MeshGeomAbstract(mesh),
	interface_mesh(mesh.getSpatialDimension(), "interface_mesh"),
	primitive_mesh(primitive_mesh) {
	// Initiating mesh connectivity and data
	interface_mesh.addConnectivityType(_segment_2, _not_ghost);
	interface_mesh.addConnectivityType(_segment_2, _ghost);
	interface_mesh.getElementalData<Element>("associated_element")
	.alloc(0, 1, _segment_2);
	interface_mesh.getElementalData<std::string>("physical_names")
	.alloc(0, 1, _segment_2);
	}

	void EmbeddedInterfaceIntersector::constructData(GhostType /ghost_type/) {
	AKANTU_DEBUG_IN();

	const UInt dim = this->mesh.getSpatialDimension();

	if (dim == 1) {
	AKANTU_ERROR(
	"No embedded model in 1D. Deactivate intersection initialization");
	}

	Array<std::string> * physical_names = nullptr;

	try {
	physical_names = &const_cast<Array<std::string> &>(
	this->primitive_mesh.getData<std::string>("physical_names",
	_segment_2));
	} catch (debug::Exception & e) {
	AKANTU_ERROR("You must define physical names to reinforcements in "
	"order to use the embedded model");
	throw e;
	}

	const UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(_segment_2);
	auto connectivity =
	primitive_mesh.getConnectivity(_segment_2).begin(nb_nodes_per_element);

	auto names_it = physical_names->begin();
	auto names_end = physical_names->end();

	std::map<std::string, std::list<K::Segment_3>> name_to_primitives_map;

	// Loop over the physical names and register segment lists in
	// name_to_primitives_map
	for (; names_it != names_end; ++names_it) {
	UInt element_id = names_it - physical_names->begin();
	const Vector<UInt> el_connectivity = connectivity[element_id];

	K::Segment_3 segment = this->createSegment(el_connectivity);
	name_to_primitives_map[*names_it].push_back(segment);
	}

	// Loop over the background types of the mesh
	auto name_to_primitives_end = name_to_primitives_map.end();
	decltype(name_to_primitives_end) name_to_primitives_it;

	for (auto type : this->mesh.elementTypes(dim, _not_ghost)) {
	// Used in AKANTU_BOOST_ELEMENT_SWITCH
	AKANTU_DEBUG_INFO("Computing intersections with background element type "
	<< type);

	switch (dim) {
	case 1:
	break;

	case 2:
	// Compute intersections for supported 2D elements
	AKANTU_BOOST_ELEMENT_SWITCH(INTERFACE_INTERSECTOR_CASE_2D,
	(_triangle_3)(_triangle_6));
	break;

	case 3:
	// Compute intersections for supported 3D elements
	AKANTU_BOOST_ELEMENT_SWITCH(INTERFACE_INTERSECTOR_CASE_3D,
	(_tetrahedron_4));
	break;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	K::Segment_3
	EmbeddedInterfaceIntersector::createSegment(const Vector<UInt> & connectivity) {
	AKANTU_DEBUG_IN();

	std::unique_ptr<K::Point_3> source;
	std::unique_ptr<K::Point_3> target;
	const Array<Real> & nodes = this->primitive_mesh.getNodes();

	if (this->mesh.getSpatialDimension() == 2) {
	source = std::make_unique<K::Point_3>(nodes(connectivity(0), 0),
	nodes(connectivity(0), 1), 0.);
	target = std::make_unique<K::Point_3>(nodes(connectivity(1), 0),
	nodes(connectivity(1), 1), 0.);
	} else if (this->mesh.getSpatialDimension() == 3) {
	source = std::make_unique<K::Point_3>(nodes(connectivity(0), 0),
	nodes(connectivity(0), 1),
	nodes(connectivity(0), 2));
	target = std::make_unique<K::Point_3>(nodes(connectivity(1), 0),
	nodes(connectivity(1), 1),
	nodes(connectivity(1), 2));
	}

	K::Segment_3 segment(source, target);

	AKANTU_DEBUG_OUT();
	return segment;
	}

	} // namespace akantu

	#undef INTERFACE_INTERSECTOR_CASE
	#undef INTERFACE_INTERSECTOR_CASE_2D
	#undef INTERFACE_INTERSECTOR_CASE_3D
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.hh b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.hh
	index 5f9daae8e..aab5c0789 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.hh
	@@ -1,99 +1,99 @@
	/**
	* @file embedded_interface_intersector.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri May 01 2015
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Class that loads the interface from mesh and computes intersections
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_EMBEDDED_INTERFACE_INTERSECTOR_HH_
	#define AKANTU_EMBEDDED_INTERFACE_INTERSECTOR_HH_

	#include "aka_common.hh"
	#include "mesh_geom_abstract.hh"
	#include "mesh_geom_common.hh"
	#include "mesh_segment_intersector.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	namespace {
	using K = cgal::Cartesian;
	}

	/**
	* @brief Computes the intersections of the reinforcements defined in the
	* primitive mesh
	*
	* The purpose of this class is to look for reinforcements in the primitive
	* mesh, which
	* should be defined by physical groups with the same names as the reinforcement
	* materials
	* in the model.
	*
	* It then constructs the CGAL primitives from the elements of those
	* reinforcements
	* and computes the intersections with the background mesh, to create an
	* `interface_mesh`,
	* which is in turn used by the EmbeddedInterfaceModel.
	*
	* @see MeshSegmentIntersector, MeshGeomAbstract
	* @see EmbeddedInterfaceModel
	*/
	class EmbeddedInterfaceIntersector : public MeshGeomAbstract {

	public:
	/// Construct from mesh and a reinforcement mesh
	explicit EmbeddedInterfaceIntersector(Mesh & mesh,
	const Mesh & primitive_mesh);

	/// Destructor
	~EmbeddedInterfaceIntersector() override = default;

	public:
	/// Generate the interface mesh
	void constructData(GhostType ghost_type = _not_ghost) override;

	/// Create a segment with an element connectivity
	K::Segment_3 createSegment(const Vector<UInt> & connectivity);

	/// Getter for interface mesh
	AKANTU_GET_MACRO_NOT_CONST(InterfaceMesh, interface_mesh, Mesh &);

	protected:
	/// Resulting mesh of intersection
	Mesh interface_mesh;

	/// Mesh used for primitive construction
	const Mesh & primitive_mesh;
	};

	} // namespace akantu

	#endif // AKANTU_EMBEDDED_INTERFACE_INTERSECTOR_HH_
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.cc b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.cc
	index 58a5d0fba..5b1d0202a 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.cc
	@@ -1,174 +1,175 @@
	/**
	* @file embedded_interface_model.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Mar 13 2015
	* @date last modification: Wed Feb 14 2018
	*
	* @brief Model of Solid Mechanics with embedded interfaces
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "embedded_interface_model.hh"
	#include "integrator_gauss.hh"
	#include "material_elastic.hh"
	#include "material_reinforcement.hh"
	#include "mesh_iterators.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumpable_inline_impl.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	EmbeddedInterfaceModel::EmbeddedInterfaceModel(Mesh & mesh,
	Mesh & primitive_mesh,
	UInt spatial_dimension,
	const ID & id)
	: SolidMechanicsModel(mesh, spatial_dimension, id),
	intersector(mesh, primitive_mesh), interface_mesh(nullptr),
	primitive_mesh(primitive_mesh), interface_material_selector(nullptr) {
	this->model_type = ModelType::_embedded_model;

	// This pointer should be deleted by ~SolidMechanicsModel()
	auto mat_sel_pointer =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	*this);

	this->setMaterialSelector(mat_sel_pointer);

	interface_mesh = &(intersector.getInterfaceMesh());

	// Create 1D FEEngine on the interface mesh
	registerFEEngineObject<MyFEEngineType>("EmbeddedInterfaceFEEngine",
	*interface_mesh, 1);

	// Registering allocator for material reinforcement
	MaterialFactory::getInstance().registerAllocator(
	"reinforcement",
	[&](UInt dim, const ID & constitutive, SolidMechanicsModel & /unused/,
	const ID & id) -> std::unique_ptr<Material> {
	if (constitutive == "elastic") {
	using mat = MaterialElastic<1>;
	switch (dim) {
	case 2:
	return std::make_unique<MaterialReinforcement<mat, 2>>(*this, id);
	case 3:
	return std::make_unique<MaterialReinforcement<mat, 3>>(*this, id);
	default:
	AKANTU_EXCEPTION("Dimension 1 is invalid for reinforcements");
	}
	} else {
	AKANTU_EXCEPTION("Reinforcement type" << constitutive
	<< " is not recognized");
	}
	});
	}

	/* -------------------------------------------------------------------------- */
	EmbeddedInterfaceModel::~EmbeddedInterfaceModel() {
	delete interface_material_selector;
	}

	/* -------------------------------------------------------------------------- */
	void EmbeddedInterfaceModel::initFullImpl(const ModelOptions & options) {
	const auto & eim_options =
	aka::as_type<EmbeddedInterfaceModelOptions>(options);

	// Do no initialize interface_mesh if told so
	if (eim_options.has_intersections) {
	intersector.constructData();
	}

	SolidMechanicsModel::initFullImpl(options);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("reinforcement", id);
	this->mesh.addDumpMeshToDumper("reinforcement", *interface_mesh, 1,
	_not_ghost, _ek_regular);
	#endif
	}

	void EmbeddedInterfaceModel::initModel() {
	// Initialize interface FEEngine
	SolidMechanicsModel::initModel();
	FEEngine & engine = getFEEngine("EmbeddedInterfaceFEEngine");
	engine.initShapeFunctions(_not_ghost);
	engine.initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void EmbeddedInterfaceModel::assignMaterialToElements(
	const ElementTypeMapArray<UInt> * filter) {
	delete interface_material_selector;
	interface_material_selector =
	new InterfaceMeshDataMaterialSelector<std::string>("physical_names",
	*this);

	- for_each_element(getInterfaceMesh(),
	- [&](auto && element) {
	- auto mat_index = (*interface_material_selector)(element);
	- // material_index(element) = mat_index;
	- materials[mat_index]->addElement(element);
	- // this->material_local_numbering(element) = index;
	- },
	- _element_filter = filter, _spatial_dimension = 1);
	+ for_each_element(
	+ getInterfaceMesh(),
	+ [&](auto && element) {
	+ auto mat_index = (*interface_material_selector)(element);
	+ // material_index(element) = mat_index;
	+ materials[mat_index]->addElement(element);
	+ // this->material_local_numbering(element) = index;
	+ },
	+ _element_filter = filter, _spatial_dimension = 1);

	SolidMechanicsModel::assignMaterialToElements(filter);
	}

	/* -------------------------------------------------------------------------- */
	void EmbeddedInterfaceModel::addDumpGroupFieldToDumper(
	const std::string & dumper_name, const std::string & field_id,
	const std::string & group_name, ElementKind element_kind,
	bool padding_flag) {
	#ifdef AKANTU_USE_IOHELPER
	std::shared_ptr<dumpers::Field> field;

	// If dumper is reinforcement, create a 1D elemental field
	if (dumper_name == "reinforcement") {
	field = this->createElementalField(field_id, group_name, padding_flag, 1,
	element_kind);
	} else {
	try {
	SolidMechanicsModel::addDumpGroupFieldToDumper(
	dumper_name, field_id, group_name, element_kind, padding_flag);
	} catch (...) {
	}
	}
	if (field) {
	DumperIOHelper & dumper = mesh.getGroupDumper(dumper_name, group_name);
	Model::addDumpGroupFieldToDumper(field_id, field, dumper);
	}

	#endif
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.hh b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.hh
	index 4dc5c4084..0bd97618a 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_model.hh
	@@ -1,155 +1,156 @@
	/**
	* @file embedded_interface_model.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Model of Solid Mechanics with embedded interfaces
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_EMBEDDED_INTERFACE_MODEL_HH_
	#define AKANTU_EMBEDDED_INTERFACE_MODEL_HH_

	#include "aka_common.hh"

	#include "mesh.hh"
	#include "solid_mechanics_model.hh"

	#include "embedded_interface_intersector.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/**
	* @brief Solid mechanics model using the embedded model.
	*
	* This SolidMechanicsModel subclass implements the embedded model,
	* a method used to represent 1D elements in a finite elements model
	* (eg. reinforcements in concrete).
	*
	* In addition to the SolidMechanicsModel properties, this model has
	* a mesh of the 1D elements embedded in the model, and an instance of the
	* EmbeddedInterfaceIntersector class for the computation of the intersections
	* of the
	* 1D elements with the background (bulk) mesh.
	*
	* @see MaterialReinforcement
	*/
	class EmbeddedInterfaceModel : public SolidMechanicsModel {

	using MyFEEngineType = SolidMechanicsModel::MyFEEngineType;

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	/**
	* @brief Constructor
	*
	* @param mesh main mesh (concrete)
	* @param primitive_mesh mesh of the embedded reinforcement
	- * @param spatial_dimension the spatial dimension to be considered by this model
	+ * @param spatial_dimension the spatial dimension to be considered by this
	+ * model
	* @param id the id of the model
	*/
	EmbeddedInterfaceModel(Mesh & mesh, Mesh & primitive_mesh,
	UInt spatial_dimension = _all_dimensions,
	const ID & id = "embedded_interface_model");

	/// Destructor
	~EmbeddedInterfaceModel() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// Initialise the model
	void initFullImpl(
	const ModelOptions & options = EmbeddedInterfaceModelOptions()) override;

	/// Initialise the materials
	void
	assignMaterialToElements(const ElementTypeMapArray<UInt> * filter) override;

	/// Initialize the embedded shape functions
	void initModel() override;

	/// Allows filtering of dump fields which need to be dumpes on interface mesh
	void addDumpGroupFieldToDumper(const std::string & dumper_name,
	const std::string & field_id,
	const std::string & group_name,
	ElementKind element_kind,
	bool padding_flag) override;

	// virtual ElementTypeMap<UInt> getInternalDataPerElem(const std::string &
	// field_name,
	// ElementKind
	// kind);
	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// Get interface mesh
	AKANTU_GET_MACRO(InterfaceMesh, *interface_mesh, Mesh &);

	/// Get associated elements
	AKANTU_GET_MACRO_BY_ELEMENT_TYPE(
	InterfaceAssociatedElements,
	interface_mesh->getData<Element>("associated_element"), Element);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Intersector object to build the interface mesh
	EmbeddedInterfaceIntersector intersector;

	/// Interface mesh (weak reference)
	Mesh * interface_mesh;

	/// Mesh used to create the CGAL primitives for intersections
	Mesh & primitive_mesh;

	/// Material selector for interface
	MaterialSelector * interface_material_selector;
	};

	/// Material selector based on mesh data for interface elements
	template <typename T>
	class InterfaceMeshDataMaterialSelector
	: public ElementDataMaterialSelector<T> {
	public:
	InterfaceMeshDataMaterialSelector(const std::string & name,
	const EmbeddedInterfaceModel & model,
	UInt first_index = 1)
	: ElementDataMaterialSelector<T>(
	model.getInterfaceMesh().getData<T>(name), model, first_index) {}
	};

	} // namespace akantu

	#endif // AKANTU_EMBEDDED_INTERFACE_MODEL_HH_
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_event_handler.hh b/src/model/solid_mechanics/solid_mechanics_model_event_handler.hh
	index eba37f94b..ab4481fc8 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_event_handler.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_event_handler.hh
	@@ -1,127 +1,127 @@
	/**
	* @file solid_mechanics_model_event_handler.hh
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 08 2017
	*
	* @brief EventHandler implementation for SolidMechanicsEvents
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_EVENT_HANDLER_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_EVENT_HANDLER_HH_

	namespace akantu {

	/// akantu::SolidMechanicsModelEvent is the base event for model
	namespace SolidMechanicsModelEvent {
	struct BeforeSolveStepEvent {
	BeforeSolveStepEvent(AnalysisMethod & method) : method(method) {}
	AnalysisMethod method;
	};
	struct AfterSolveStepEvent {
	AfterSolveStepEvent(AnalysisMethod & method) : method(method) {}
	AnalysisMethod method;
	};
	struct BeforeDumpEvent {
	BeforeDumpEvent() = default;
	};
	struct BeginningOfDamageIterationEvent {
	BeginningOfDamageIterationEvent() = default;
	};
	struct AfterDamageEvent {
	AfterDamageEvent() = default;
	};
	} // namespace SolidMechanicsModelEvent

	/// akantu::SolidMechanicsModelEvent
	class SolidMechanicsModelEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	virtual ~SolidMechanicsModelEventHandler() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	/// Send what is before the solve step to the beginning of solve step through
	/// EventManager
	inline void
	sendEvent(const SolidMechanicsModelEvent::BeforeSolveStepEvent & event) {
	onBeginningSolveStep(event.method);
	}
	/// Send what is after the solve step to the end of solve step through
	/// EventManager
	inline void
	sendEvent(const SolidMechanicsModelEvent::AfterSolveStepEvent & event) {
	onEndSolveStep(event.method);
	}
	/// Send what is before dump to current dump through EventManager
	inline void
	sendEvent(__attribute__((unused))
	const SolidMechanicsModelEvent::BeforeDumpEvent & event) {
	onDump();
	}
	/// Send what is at the beginning of damage iteration to Damage iteration
	/// through EventManager
	inline void sendEvent(
	__attribute__((unused))
	const SolidMechanicsModelEvent::BeginningOfDamageIterationEvent & event) {
	onDamageIteration();
	}
	/// Send what is after damage for the damage update through EventManager
	inline void
	sendEvent(__attribute__((unused))
	const SolidMechanicsModelEvent::AfterDamageEvent & event) {
	onDamageUpdate();
	}

	template <class EventHandler> friend class EventHandlerManager;

	/* ------------------------------------------------------------------------ */
	/* Interface */
	/* ------------------------------------------------------------------------ */
	public:
	/// function to implement to react on akantu::BeforeSolveStepEvent
	virtual void onBeginningSolveStep(__attribute__((unused))
	const AnalysisMethod & method) {}
	/// function to implement to react on akantu::AfterSolveStepEvent
	virtual void onEndSolveStep(__attribute__((unused))
	const AnalysisMethod & method) {}
	/// function to implement to react on akantu::BeforeDumpEvent
	virtual void onDump() {}
	/// function to implement to react on akantu::BeginningOfDamageIterationEvent
	virtual void onDamageIteration() {}
	/// function to implement to react on akantu::AfterDamageEvent
	virtual void onDamageUpdate() {}
	};

	} // namespace akantu

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_EVENT_HANDLER_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_inline_impl.hh b/src/model/solid_mechanics/solid_mechanics_model_inline_impl.hh
	index 5a62684d9..ec19b7bff 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_inline_impl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_inline_impl.hh
	@@ -1,108 +1,111 @@
	/**
	* @file solid_mechanics_model_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Fri Mar 26 2021
	*
	* @brief Implementation of the inline functions of the SolidMechanicsModel
	* class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_named_argument.hh"
	#include "material_selector.hh"
	#include "material_selector_tmpl.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_INLINE_IMPL_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline decltype(auto) SolidMechanicsModel::getMaterials() {
	return make_dereference_adaptor(materials);
	}

	/* -------------------------------------------------------------------------- */
	inline decltype(auto) SolidMechanicsModel::getMaterials() const {
	return make_dereference_adaptor(materials);
	}

	/* -------------------------------------------------------------------------- */
	inline Material & SolidMechanicsModel::getMaterial(UInt mat_index) {
	AKANTU_DEBUG_ASSERT(mat_index < materials.size(),
	"The model " << id << " has no material no "
	<< mat_index);
	return *materials.at(mat_index);
	}

	/* -------------------------------------------------------------------------- */
	inline const Material & SolidMechanicsModel::getMaterial(UInt mat_index) const {
	AKANTU_DEBUG_ASSERT(mat_index < materials.size(),
	"The model " << id << " has no material no "
	<< mat_index);
	return *materials.at(mat_index);
	}

	/* -------------------------------------------------------------------------- */
	inline Material & SolidMechanicsModel::getMaterial(const std::string & name) {
	std::map<std::string, UInt>::const_iterator it =
	materials_names_to_id.find(name);
	- if(it == materials_names_to_id.end()) {
	- AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named " << name);
	+ if (it == materials_names_to_id.end()) {
	+ AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named "
	+ << name);
	}

	return *materials[it->second];
	}

	/* -------------------------------------------------------------------------- */
	inline UInt
	SolidMechanicsModel::getMaterialIndex(const std::string & name) const {
	auto it = materials_names_to_id.find(name);
	if (it == materials_names_to_id.end()) {
	- AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named " << name);
	+ AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named "
	+ << name);
	}
	-
	+
	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	inline const Material &
	SolidMechanicsModel::getMaterial(const std::string & name) const {
	auto it = materials_names_to_id.find(name);
	- if(it == materials_names_to_id.end()) {
	- AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named " << name);
	+ if (it == materials_names_to_id.end()) {
	+ AKANTU_SILENT_EXCEPTION("The model " << id << " has no material named "
	+ << name);
	}
	return *materials[it->second];
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_INLINE_IMPL_HH_ */
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_io.cc b/src/model/solid_mechanics/solid_mechanics_model_io.cc
	index d4797c909..a77cbf731 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_io.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_io.cc
	@@ -1,335 +1,335 @@
	/**
	* @file solid_mechanics_model_io.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jul 09 2017
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Dumpable part of the SolidMechnicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"

	#include "group_manager_inline_impl.hh"

	#include "dumpable_inline_impl.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_element_partition.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_field.hh"
	#include "dumper_homogenizing_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper.hh"
	#include "dumper_material_padders.hh"
	#include "dumper_paraview.hh"
	#endif

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::isInternal(const std::string & field_name,
	ElementKind element_kind) {
	/// check if at least one material contains field_id as an internal
	for (auto & material : materials) {
	bool is_internal = material->isInternal<Real>(field_name, element_kind);
	if (is_internal) {
	return true;
	}
	}

	return false;
	}

	/* -------------------------------------------------------------------------- */
	ElementTypeMap<UInt>
	SolidMechanicsModel::getInternalDataPerElem(const std::string & field_name,
	ElementKind element_kind) {
	if (!(this->isInternal(field_name, element_kind))) {
	AKANTU_EXCEPTION("unknown internal " << field_name);
	}

	for (auto & material : materials) {
	if (material->isInternal<Real>(field_name, element_kind)) {
	return material->getInternalDataPerElem<Real>(field_name, element_kind);
	}
	}

	return ElementTypeMap<UInt>();
	}

	/* -------------------------------------------------------------------------- */
	ElementTypeMapArray<Real> &
	SolidMechanicsModel::flattenInternal(const std::string & field_name,
	ElementKind kind,
	const GhostType ghost_type) {
	auto key = std::make_pair(field_name, kind);

	ElementTypeMapArray<Real> * internal_flat;

	auto it = this->registered_internals.find(key);
	if (it == this->registered_internals.end()) {
	auto internal =
	std::make_unique<ElementTypeMapArray<Real>>(field_name, this->id);

	internal_flat = internal.get();
	this->registered_internals[key] = std::move(internal);
	} else {
	internal_flat = it->second.get();
	}

	for (auto type :
	mesh.elementTypes(Model::spatial_dimension, ghost_type, kind)) {
	if (internal_flat->exists(type, ghost_type)) {
	auto & internal = (*internal_flat)(type, ghost_type);
	internal.resize(0);
	}
	}

	for (auto & material : materials) {
	if (material->isInternal<Real>(field_name, kind)) {
	material->flattenInternal(field_name, *internal_flat, ghost_type, kind);
	}
	}

	return *internal_flat;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::flattenAllRegisteredInternals(ElementKind kind) {
	ElementKind _kind;
	ID _id;

	for (auto & internal : this->registered_internals) {
	std::tie(_id, _kind) = internal.first;
	if (kind == _kind) {
	this->flattenInternal(_id, kind);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onDump() {
	this->flattenAllRegisteredInternals(_ek_regular);
	}

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	std::shared_ptr<dumpers::Field> SolidMechanicsModel::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool padding_flag, UInt spatial_dimension, ElementKind kind) {

	std::shared_ptr<dumpers::Field> field;

	if (field_name == "partitions") {
	field = mesh.createElementalField<UInt, dumpers::ElementPartitionField>(
	mesh.getConnectivities(), group_name, spatial_dimension, kind);
	} else if (field_name == "material_index") {
	field = mesh.createElementalField<UInt, Vector, dumpers::ElementalField>(
	material_index, group_name, spatial_dimension, kind);
	} else {
	// this copy of field_name is used to compute derivated data such as
	// strain and von mises stress that are based on grad_u and stress
	std::string field_name_copy(field_name);

	if (field_name == "strain" \|\| field_name == "Green strain" \|\|
	field_name == "principal strain" \|\|
	field_name == "principal Green strain") {
	field_name_copy = "grad_u";
	} else if (field_name == "Von Mises stress") {
	field_name_copy = "stress";
	}

	bool is_internal = this->isInternal(field_name_copy, kind);

	if (is_internal) {
	auto nb_data_per_elem =
	this->getInternalDataPerElem(field_name_copy, kind);
	auto & internal_flat = this->flattenInternal(field_name_copy, kind);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	internal_flat, group_name, spatial_dimension, kind, nb_data_per_elem);

	std::unique_ptr<dumpers::ComputeFunctorInterface> func;
	if (field_name == "strain") {
	func = std::make_unique<dumpers::ComputeStrain<false>>(*this);
	} else if (field_name == "Von Mises stress") {
	func = std::make_unique<dumpers::ComputeVonMisesStress>(*this);
	} else if (field_name == "Green strain") {
	func = std::make_unique<dumpers::ComputeStrain<true>>(*this);
	} else if (field_name == "principal strain") {
	func = std::make_unique<dumpers::ComputePrincipalStrain<false>>(*this);
	} else if (field_name == "principal Green strain") {
	func = std::make_unique<dumpers::ComputePrincipalStrain<true>>(*this);
	}

	if (func) {
	field = dumpers::FieldComputeProxy::createFieldCompute(field,
	std::move(func));
	}
	// treat the paddings
	if (padding_flag) {
	if (field_name == "stress") {
	if (spatial_dimension == 2) {
	auto foo = std::make_unique<dumpers::StressPadder<2>>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(
	field, std::move(foo));
	}
	} else if (field_name == "strain" \|\| field_name == "Green strain") {
	if (spatial_dimension == 2) {
	auto foo = std::make_unique<dumpers::StrainPadder<2>>(*this);
	field = dumpers::FieldComputeProxy::createFieldCompute(
	field, std::move(foo));
	}
	}
	}

	// homogenize the field
	auto foo = dumpers::HomogenizerProxy::createHomogenizer(*field);

	field =
	dumpers::FieldComputeProxy::createFieldCompute(field, std::move(foo));
	}
	}
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	SolidMechanicsModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["displacement"] = this->displacement.get();
	real_nodal_fields["mass"] = this->mass.get();
	real_nodal_fields["velocity"] = this->velocity.get();
	real_nodal_fields["acceleration"] = this->acceleration.get();
	real_nodal_fields["external_force"] = this->external_force.get();
	real_nodal_fields["internal_force"] = this->internal_force.get();
	real_nodal_fields["increment"] = this->displacement_increment.get();

	if (field_name == "force") {
	AKANTU_EXCEPTION("The 'force' field has been renamed in 'external_force'");
	} else if (field_name == "residual") {
	AKANTU_EXCEPTION(
	"The 'residual' field has been replaced by 'internal_force'");
	}

	std::shared_ptr<dumpers::Field> field;
	if (padding_flag) {
	field = this->mesh.createNodalField(real_nodal_fields[field_name],
	group_name, 3);
	} else {
	field =
	this->mesh.createNodalField(real_nodal_fields[field_name], group_name);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> SolidMechanicsModel::createNodalFieldBool(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs.get();

	std::shared_ptr<dumpers::Field> field;
	field = mesh.createNodalField(uint_nodal_fields[field_name], group_name);
	return field;
	}
	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> SolidMechanicsModel::createElementalField(
	const std::string &, const std::string &, bool, const UInt &, ElementKind) {
	return nullptr;
	}
	/* --------------------------------------------------------------------------
	*/
	std::shaed_ptr<dumpers::Field>
	SolidMechanicsModel::createNodalFieldReal(const std::string &,
	const std::string &, bool) {
	return nullptr;
	}

	/* --------------------------------------------------------------------------
	*/
	std::shared_ptr<dumpers::Field>
	SolidMechanicsModel::createNodalFieldBool(const std::string &,
	const std::string &, bool) {
	return nullptr;
	}

	#endif
	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(const std::string & dumper_name) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(const std::string & dumper_name, UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name, step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(const std::string & dumper_name, Real time,
	UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump() {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(Real time, UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(time, step);
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_mass.cc b/src/model/solid_mechanics/solid_mechanics_model_mass.cc
	index 23ad3716b..c17adc8cd 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_mass.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_mass.cc
	@@ -1,156 +1,156 @@
	/**
	* @file solid_mechanics_model_mass.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Oct 05 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief function handling mass computation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss.hh"
	#include "material.hh"
	#include "model_solver.hh"
	#include "shape_lagrange.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class ComputeRhoFunctor {
	public:
	explicit ComputeRhoFunctor(const SolidMechanicsModel & model)
	: model(model){};

	void operator()(Matrix<Real> & rho, const Element & element) {
	const Array<UInt> & mat_indexes =
	model.getMaterialByElement(element.type, element.ghost_type);
	Real mat_rho =
	model.getMaterial(mat_indexes(element.element)).getParam("rho");
	rho.set(mat_rho);
	}

	private:
	const SolidMechanicsModel & model;
	};

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleMassLumped() {
	AKANTU_DEBUG_IN();

	if (not need_to_reassemble_lumped_mass) {
	return;
	}

	this->allocNodalField(this->mass, spatial_dimension, "mass");
	mass->zero();

	if (!this->getDOFManager().hasLumpedMatrix("M")) {
	this->getDOFManager().getNewLumpedMatrix("M");
	}

	this->getDOFManager().zeroLumpedMatrix("M");

	assembleMassLumped(_not_ghost);
	assembleMassLumped(_ghost);

	this->getDOFManager().getLumpedMatrixPerDOFs("displacement", "M",
	*(this->mass));

	/// for not connected nodes put mass to one in order to avoid
	#if !defined(AKANTU_NDEBUG)
	bool has_unconnected_nodes = false;
	auto mass_it = mass->begin_reinterpret(mass->size() * mass->getNbComponent());
	auto mass_end = mass->end_reinterpret(mass->size() * mass->getNbComponent());
	for (; mass_it != mass_end; ++mass_it) {
	if (std::abs(*mass_it) < std::numeric_limits<Real>::epsilon() \|\|
	Math::isnan(*mass_it)) {
	has_unconnected_nodes = true;
	break;
	}
	}

	if (has_unconnected_nodes) {
	AKANTU_DEBUG_WARNING("There are nodes that seem to not be connected to any "
	"elements, beware that they have lumped mass of 0.");
	}
	#endif

	this->synchronize(SynchronizationTag::_smm_mass);

	need_to_reassemble_lumped_mass = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleMass() {
	AKANTU_DEBUG_IN();

	if (not need_to_reassemble_mass) {
	return;
	}

	this->getDOFManager().zeroMatrix("M");
	assembleMass(_not_ghost);

	need_to_reassemble_mass = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleMassLumped(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem = getFEEngineClass<MyFEEngineType>();
	ComputeRhoFunctor compute_rho(*this);

	for (auto type :
	mesh.elementTypes(Model::spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldLumped(compute_rho, "M", "displacement",
	this->getDOFManager(), type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleMass(GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem = getFEEngineClass<MyFEEngineType>();
	ComputeRhoFunctor compute_rho(*this);

	for (auto type :
	mesh.elementTypes(Model::spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldMatrix(compute_rho, "M", "displacement",
	this->getDOFManager(), type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_material.cc b/src/model/solid_mechanics/solid_mechanics_model_material.cc
	index 0e3ee0422..84984baac 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_material.cc
	+++ b/src/model/solid_mechanics/solid_mechanics_model_material.cc
	@@ -1,246 +1,246 @@
	/**
	* @file solid_mechanics_model_material.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Nov 26 2010
	* @date last modification: Fri Mar 26 2021
	*
	* @brief instatiation of materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_factory.hh"
	#include "aka_math.hh"
	#include "material_non_local.hh"
	#include "mesh_iterators.hh"
	#include "non_local_manager.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Material &
	SolidMechanicsModel::registerNewMaterial(const ParserSection & section) {
	std::string mat_name;
	std::string mat_type = section.getName();
	std::string opt_param = section.getOption();

	try {
	std::string tmp = section.getParameter("name");
	mat_name = tmp; /** this can seam weird, but there is an ambiguous operator
	* overload that i couldn't solve. @todo remove the
	* weirdness of this code
	*/
	} catch (debug::Exception &) {
	AKANTU_ERROR("A material of type \'"
	<< mat_type
	<< "\' in the input file has been defined without a name!");
	}
	Material & mat = this->registerNewMaterial(mat_name, mat_type, opt_param);

	mat.parseSection(section);

	return mat;
	}

	/* -------------------------------------------------------------------------- */
	Material & SolidMechanicsModel::registerNewMaterial(const ID & mat_name,
	const ID & mat_type,
	const ID & opt_param) {
	AKANTU_DEBUG_ASSERT(materials_names_to_id.find(mat_name) ==
	materials_names_to_id.end(),
	"A material with this name '"
	<< mat_name << "' has already been registered. "
	<< "Please use unique names for materials");

	UInt mat_count = materials.size();
	materials_names_to_id[mat_name] = mat_count;

	std::stringstream sstr_mat;
	sstr_mat << this->id << ":" << mat_count << ":" << mat_type;
	ID mat_id = sstr_mat.str();

	std::unique_ptr<Material> material = MaterialFactory::getInstance().allocate(
	mat_type, spatial_dimension, opt_param, *this, mat_id);

	materials.push_back(std::move(material));

	return *(materials.back());
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::instantiateMaterials() {
	ParserSection model_section;
	bool is_empty;
	std::tie(model_section, is_empty) = this->getParserSection();

	if (not is_empty) {
	auto model_materials = model_section.getSubSections(ParserType::_material);
	for (const auto & section : model_materials) {
	this->registerNewMaterial(section);
	}
	}

	auto sub_sections = this->parser.getSubSections(ParserType::_material);
	for (const auto & section : sub_sections) {
	this->registerNewMaterial(section);
	}

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	for (auto & material : materials) {
	if (dynamic_cast<MaterialNonLocalInterface *>(material.get()) == nullptr) {
	continue;
	}

	this->non_local_manager = std::make_unique<NonLocalManager>(
	this, this, id + ":non_local_manager");
	break;
	}
	#endif

	if (materials.empty()) {
	AKANTU_EXCEPTION("No materials where instantiated for the model"
	<< getID());
	}
	are_materials_instantiated = true;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assignMaterialToElements(
	const ElementTypeMapArray<UInt> * filter) {

	for_each_element(
	mesh,
	[&](auto && element) {
	UInt mat_index = (*material_selector)(element);
	AKANTU_DEBUG_ASSERT(
	mat_index < materials.size(),
	"The material selector returned an index that does not exists");
	material_index(element) = mat_index;
	},
	_element_filter = filter, _ghost_type = _not_ghost);

	if (non_local_manager) {
	non_local_manager->synchronize(*this, SynchronizationTag::_material_id);
	}

	for_each_element(
	mesh,
	[&](auto && element) {
	auto mat_index = material_index(element);
	auto index = materials[mat_index]->addElement(element);
	material_local_numbering(element) = index;
	},
	_element_filter = filter, _ghost_type = _not_ghost);

	// synchronize the element material arrays
	this->synchronize(SynchronizationTag::_material_id);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initMaterials() {
	AKANTU_DEBUG_ASSERT(not materials.empty(), "No material to initialize !");

	// if (!are_materials_instantiated)
	// instantiateMaterials();

	this->assignMaterialToElements();

	for (auto & material : materials) {
	/// init internals properties
	material->initMaterial();
	}

	this->synchronize(SynchronizationTag::_smm_init_mat);

	if (this->non_local_manager) {
	this->non_local_manager->initialize();
	}
	}

	/* -------------------------------------------------------------------------- */
	Int SolidMechanicsModel::getInternalIndexFromID(const ID & id) const {
	AKANTU_DEBUG_IN();

	auto it = materials.begin();
	auto end = materials.end();

	for (; it != end; ++it) {
	if ((*it)->getID() == id) {
	AKANTU_DEBUG_OUT();
	return (it - materials.begin());
	}
	}

	AKANTU_DEBUG_OUT();
	return -1;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::reassignMaterial() {
	AKANTU_DEBUG_IN();

	std::vector<Array<Element>> element_to_add(materials.size());
	std::vector<Array<Element>> element_to_remove(materials.size());

	for_each_element(mesh, [&](auto && element) {
	auto old_material = material_index(element);
	auto new_material = (*material_selector)(element);
	if (old_material != new_material) {
	element_to_add[new_material].push_back(element);
	element_to_remove[old_material].push_back(element);
	}
	});

	for (auto && data : enumerate(materials)) {
	auto mat_index = std::get<0>(data);
	auto & mat = *std::get<1>(data);

	mat.removeElements(element_to_remove[mat_index]);
	mat.addElements(element_to_add[mat_index]);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::applyEigenGradU(
	const Matrix<Real> & prescribed_eigen_grad_u, const ID & material_name,
	const GhostType ghost_type) {
	AKANTU_DEBUG_ASSERT(prescribed_eigen_grad_u.size() ==
	spatial_dimension * spatial_dimension,
	"The prescribed grad_u is not of the good size");
	for (auto & material : materials) {
	if (material->getName() == material_name) {
	material->applyEigenGradU(prescribed_eigen_grad_u, ghost_type);
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/solid_mechanics/solid_mechanics_model_tmpl.hh b/src/model/solid_mechanics/solid_mechanics_model_tmpl.hh
	index 5d1a3a50d..441ed43fd 100644
	--- a/src/model/solid_mechanics/solid_mechanics_model_tmpl.hh
	+++ b/src/model/solid_mechanics/solid_mechanics_model_tmpl.hh
	@@ -1,63 +1,63 @@
	/**
	* @file solid_mechanics_model_tmpl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Mar 26 2021
	*
	* @brief template part of solid mechanics model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLID_MECHANICS_MODEL_TMPL_HH_
	#define AKANTU_SOLID_MECHANICS_MODEL_TMPL_HH_

	namespace akantu {

	#define FWD(...) ::std::forward<decltype(__VA_ARGS__)>(__VA_ARGS__)

	/* -------------------------------------------------------------------------- */
	template <typename Operation>
	void SolidMechanicsModel::splitByMaterial(const Array<Element> & elements,
	Operation && op) const {
	std::vector<Array<Element>> elements_per_mat(materials.size());
	this->splitElementByMaterial(elements, elements_per_mat);

	for (auto && mat : zip(materials, elements_per_mat)) {
	FWD(op)(FWD(*std::get<0>(mat)), FWD(std::get<1>(mat)));
	}
	}

	#undef FWD
	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_SOLID_MECHANICS_MODEL_TMPL_HH_ */
	diff --git a/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_2.hh b/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_2.hh
	index 637619027..d468a43f0 100644
	--- a/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_2.hh
	+++ b/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_2.hh
	@@ -1,72 +1,72 @@
	/**
	* @file structural_element_bernoulli_beam_2.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 11 2017
	* @date last modification: Fri Feb 05 2021
	*
	* @brief Specific functions for bernoulli beam 2d
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_2_HH_
	#define AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_2_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	void StructuralMechanicsModel::computeTangentModuli<_bernoulli_beam_2>(
	Array<Real> & tangent_moduli) {
	// auto nb_element = getFEEngine().getMesh().getNbElement(_bernoulli_beam_2);
	auto nb_quadrature_points =
	getFEEngine().getNbIntegrationPoints(_bernoulli_beam_2);
	auto tangent_size = 2;

	tangent_moduli.zero();
	auto D_it = tangent_moduli.begin(tangent_size, tangent_size);
	auto el_mat = element_material(_bernoulli_beam_2, _not_ghost).begin();

	for (auto & mat : element_material(_bernoulli_beam_2, _not_ghost)) {
	auto E = materials[mat].E;
	auto A = materials[mat].A;
	auto I = materials[mat].I;
	for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_it) {
	auto & D = *D_it;
	D(0, 0) = E * A;
	D(1, 1) = E * I;
	}
	}
	}

	} // namespace akantu

	#endif /* AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_2_HH_ */
	diff --git a/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_3.hh b/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_3.hh
	index 70f543ad5..913a81752 100644
	--- a/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_3.hh
	+++ b/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_3.hh
	@@ -1,76 +1,76 @@
	/**
	* @file structural_element_bernoulli_beam_3.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Wed Oct 11 2017
	* @date last modification: Fri Feb 05 2021
	*
	* @brief Specific functions for bernoulli beam 3d
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH_
	#define AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH_

	#include "structural_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	void StructuralMechanicsModel::computeTangentModuli<_bernoulli_beam_3>(
	Array<Real> & tangent_moduli) {
	UInt nb_element = getFEEngine().getMesh().getNbElement(_bernoulli_beam_3);
	UInt nb_quadrature_points =
	getFEEngine().getNbIntegrationPoints(_bernoulli_beam_3);
	UInt tangent_size = 4;

	tangent_moduli.zero();
	Array<Real>::matrix_iterator D_it =
	tangent_moduli.begin(tangent_size, tangent_size);

	for (UInt e = 0; e < nb_element; ++e) {
	UInt mat = element_material(_bernoulli_beam_3, _not_ghost)(e);
	Real E = materials[mat].E;
	Real A = materials[mat].A;
	Real Iz = materials[mat].Iz;
	Real Iy = materials[mat].Iy;
	Real GJ = materials[mat].GJ;
	for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_it) {
	Matrix<Real> & D = *D_it;
	D(0, 0) = E * A;
	D(1, 1) = E * Iz;
	D(2, 2) = E * Iy;
	D(3, 3) = GJ;
	}
	}
	}

	} // namespace akantu

	#endif /* AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH_ */
	diff --git a/src/model/structural_mechanics/structural_elements/structural_element_kirchhoff_shell.hh b/src/model/structural_mechanics/structural_elements/structural_element_kirchhoff_shell.hh
	index 8e9f2ffef..aa9cfb8a4 100644
	--- a/src/model/structural_mechanics/structural_elements/structural_element_kirchhoff_shell.hh
	+++ b/src/model/structural_mechanics/structural_elements/structural_element_kirchhoff_shell.hh
	@@ -1,74 +1,74 @@
	/**
	* @file structural_element_kirchhoff_shell.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Wed Oct 11 2017
	* @date last modification: Fri Feb 05 2021
	*
	* @brief Specific functions for bernoulli kirchhoff shell
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_KIRCHHOFF_SHELL_HH_
	#define AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_KIRCHHOFF_SHELL_HH_

	#include "structural_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <>
	void StructuralMechanicsModel::computeTangentModuli<
	_discrete_kirchhoff_triangle_18>(Array<Real> & tangent_moduli) {

	auto tangent_size =
	ElementClass<_discrete_kirchhoff_triangle_18>::getNbStressComponents();
	auto nb_quad =
	getFEEngine().getNbIntegrationPoints(_discrete_kirchhoff_triangle_18);

	auto H_it = tangent_moduli.begin(tangent_size, tangent_size);

	for (UInt mat :
	element_material(_discrete_kirchhoff_triangle_18, _not_ghost)) {
	auto & m = materials[mat];

	for (UInt q = 0; q < nb_quad; ++q, ++H_it) {
	auto & H = *H_it;
	H.zero();
	Matrix<Real> D = {{1, m.nu, 0}, {m.nu, 1, 0}, {0, 0, (1 - m.nu) / 2}};
	D = m.E m.t / (1 - m.nu * m.nu);
	H.block(D, 0, 0); // in plane membrane behavior
	H.block(D * Math::pow<3>(m.t) / 12., 3, 3); // bending behavior
	}
	}
	}

	} // namespace akantu

	#endif /* AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_DISCRETE_KIRCHHOFF_TRIANGLE_18_HH_ \
	*/
	diff --git a/src/model/structural_mechanics/structural_mechanics_model.cc b/src/model/structural_mechanics/structural_mechanics_model.cc
	index 57c7b6e89..69da5e251 100644
	--- a/src/model/structural_mechanics/structural_mechanics_model.cc
	+++ b/src/model/structural_mechanics/structural_mechanics_model.cc
	@@ -1,627 +1,627 @@
	/**
	* @file structural_mechanics_model.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Fri Jul 15 2011
	* @date last modification: Mon Mar 15 2021
	*
	* @brief Model implementation for Structural Mechanics elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "structural_mechanics_model.hh"
	#include "dof_manager.hh"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "shape_structural.hh"
	#include "sparse_matrix.hh"
	#include "time_step_solver.hh"
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "dumpable_inline_impl.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#include "group_manager_inline_impl.hh"
	#endif
	/* -------------------------------------------------------------------------- */
	#include "structural_element_bernoulli_beam_2.hh"
	#include "structural_element_bernoulli_beam_3.hh"
	#include "structural_element_kirchhoff_shell.hh"
	/* -------------------------------------------------------------------------- */
	//#include "structural_mechanics_model_inline_impl.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt StructuralMechanicsModel::getNbDegreeOfFreedom(ElementType type) {
	UInt ndof = 0;
	#define GET_(type) ndof = ElementClass<type>::getNbDegreeOfFreedom()
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_, _ek_structural);
	#undef GET_

	return ndof;
	}

	/* -------------------------------------------------------------------------- */
	StructuralMechanicsModel::StructuralMechanicsModel(Mesh & mesh, UInt dim,
	const ID & id)
	: Model(mesh, ModelType::_structural_mechanics_model, dim, id), f_m2a(1.0),
	stress("stress", id), element_material("element_material", id),
	set_ID("beam sets", id) {
	AKANTU_DEBUG_IN();

	registerFEEngineObject<MyFEEngineType>("StructuralMechanicsFEEngine", mesh,
	spatial_dimension);

	if (spatial_dimension == 2) {
	nb_degree_of_freedom = 3;
	} else if (spatial_dimension == 3) {
	nb_degree_of_freedom = 6;
	} else {
	AKANTU_TO_IMPLEMENT();
	}

	#ifdef AKANTU_USE_IOHELPER
	this->mesh.registerDumper<DumperParaview>("structural_mechanics_model", id,
	true);
	#endif
	this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_structural);

	this->initDOFManager();

	this->dumper_default_element_kind = _ek_structural;

	mesh.getElementalData<Real>("extra_normal")
	.initialize(mesh, _element_kind = _ek_structural,
	_nb_component = spatial_dimension, _with_nb_element = true,
	_default_value = 0.);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	StructuralMechanicsModel::~StructuralMechanicsModel() = default;

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::initFullImpl(const ModelOptions & options) {
	Model::initFullImpl(options);

	// Initializing stresses
	ElementTypeMap<UInt> stress_components;

	/// TODO this is ugly af, maybe add a function to FEEngine
	for (auto && type : mesh.elementTypes(_spatial_dimension = _all_dimensions,
	_element_kind = _ek_structural)) {
	UInt nb_components = 0;

	// Getting number of components for each element type
	#define GET_(type) nb_components = ElementClass<type>::getNbStressComponents()
	AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(GET_);
	#undef GET_

	stress_components(nb_components, type);
	}

	stress.initialize(
	getFEEngine(), _spatial_dimension = _all_dimensions,
	_element_kind = _ek_structural,
	_nb_component = [&stress_components](ElementType type,
	GhostType /unused/) -> UInt {
	return stress_components(type);
	});
	}

	/* -------------------------------------------------------------------------- */

	void StructuralMechanicsModel::initFEEngineBoundary() {
	/// TODO: this function should not be reimplemented
	/// we're just avoiding a call to Model::initFEEngineBoundary()
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::setTimeStep(Real time_step,
	const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);
	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper().setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	/* Initialisation */
	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::initSolver(
	TimeStepSolverType time_step_solver_type, NonLinearSolverType /unused/) {
	AKANTU_DEBUG_IN();

	this->allocNodalField(displacement_rotation, nb_degree_of_freedom,
	"displacement");
	this->allocNodalField(external_force, nb_degree_of_freedom, "external_force");
	this->allocNodalField(internal_force, nb_degree_of_freedom, "internal_force");
	this->allocNodalField(blocked_dofs, nb_degree_of_freedom, "blocked_dofs");

	auto & dof_manager = this->getDOFManager();

	if (not dof_manager.hasDOFs("displacement")) {
	dof_manager.registerDOFs("displacement", *displacement_rotation,
	_dst_nodal);
	dof_manager.registerBlockedDOFs("displacement", *this->blocked_dofs);
	}

	if (time_step_solver_type == TimeStepSolverType::_dynamic \|\|
	time_step_solver_type == TimeStepSolverType::_dynamic_lumped) {
	this->allocNodalField(velocity, nb_degree_of_freedom, "velocity");
	this->allocNodalField(acceleration, nb_degree_of_freedom, "acceleration");

	if (!dof_manager.hasDOFsDerivatives("displacement", 1)) {
	dof_manager.registerDOFsDerivative("displacement", 1, *this->velocity);
	dof_manager.registerDOFsDerivative("displacement", 2,
	*this->acceleration);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::initModel() {
	element_material.initialize(mesh, _element_kind = _ek_structural,
	_default_value = 0, _with_nb_element = true);

	getFEEngine().initShapeFunctions(_not_ghost);
	getFEEngine().initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	if (not need_to_reassemble_stiffness) {
	return;
	}

	if (not getDOFManager().hasMatrix("K")) {
	getDOFManager().getNewMatrix("K", getMatrixType("K"));
	}

	this->getDOFManager().zeroMatrix("K");

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_structural)) {
	#define ASSEMBLE_STIFFNESS_MATRIX(type) assembleStiffnessMatrix<type>();

	AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(ASSEMBLE_STIFFNESS_MATRIX);
	#undef ASSEMBLE_STIFFNESS_MATRIX
	}

	need_to_reassemble_stiffness = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::computeStresses() {
	AKANTU_DEBUG_IN();

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_structural)) {
	#define COMPUTE_STRESS_ON_QUAD(type) computeStressOnQuad<type>();

	AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(COMPUTE_STRESS_ON_QUAD);
	#undef COMPUTE_STRESS_ON_QUAD
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> StructuralMechanicsModel::createNodalFieldBool(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs.get();

	return mesh.createNodalField(uint_nodal_fields[field_name], group_name);
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field>
	StructuralMechanicsModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	UInt n;
	if (spatial_dimension == 2) {
	n = 2;
	} else {
	n = 3;
	}

	UInt padding_size = 0;
	if (padding_flag) {
	padding_size = 3;
	}

	if (field_name == "displacement") {
	return mesh.createStridedNodalField(displacement_rotation.get(), group_name,
	n, 0, padding_size);
	}

	if (field_name == "velocity") {
	return mesh.createStridedNodalField(velocity.get(), group_name, n, 0,
	padding_size);
	}

	if (field_name == "acceleration") {
	return mesh.createStridedNodalField(acceleration.get(), group_name, n, 0,
	padding_size);
	}

	if (field_name == "rotation") {
	return mesh.createStridedNodalField(displacement_rotation.get(), group_name,
	nb_degree_of_freedom - n, n,
	padding_size);
	}

	if (field_name == "force") {
	return mesh.createStridedNodalField(external_force.get(), group_name, n, 0,
	padding_size);
	}
	if (field_name == "external_force") {
	return mesh.createStridedNodalField(external_force.get(), group_name, n, 0,
	padding_size);
	}

	if (field_name == "momentum") {
	return mesh.createStridedNodalField(external_force.get(), group_name,
	nb_degree_of_freedom - n, n,
	padding_size);
	}

	if (field_name == "internal_force") {
	return mesh.createStridedNodalField(internal_force.get(), group_name, n, 0,
	padding_size);
	}

	if (field_name == "internal_momentum") {
	return mesh.createStridedNodalField(internal_force.get(), group_name,
	nb_degree_of_freedom - n, n,
	padding_size);
	}

	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> StructuralMechanicsModel::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool /unused/, UInt spatial_dimension, ElementKind kind) {

	std::shared_ptr<dumpers::Field> field;

	if (field_name == "element_index_by_material") {
	field = mesh.createElementalField<UInt, Vector, dumpers::ElementalField>(
	field_name, group_name, spatial_dimension, kind);
	}
	if (field_name == "stress") {
	ElementTypeMap<UInt> nb_data_per_elem = this->mesh.getNbDataPerElem(stress);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	stress, group_name, this->spatial_dimension, kind, nb_data_per_elem);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	/* Virtual methods from SolverCallback */
	/* -------------------------------------------------------------------------- */
	/// get the type of matrix needed
	MatrixType StructuralMechanicsModel::getMatrixType(const ID & /id/) {
	return _symmetric;
	}

	/// callback to assemble a Matrix
	void StructuralMechanicsModel::assembleMatrix(const ID & id) {
	if (id == "K") {
	assembleStiffnessMatrix();
	} else if (id == "M") {
	assembleMassMatrix();
	}
	}

	/// callback to assemble a lumped Matrix
	void StructuralMechanicsModel::assembleLumpedMatrix(const ID & /id/) {}

	/// callback to assemble the residual StructuralMechanicsModel::(rhs)
	void StructuralMechanicsModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	auto & dof_manager = getDOFManager();

	assembleInternalForce();

	dof_manager.assembleToResidual("displacement", *external_force, 1);
	dof_manager.assembleToResidual("displacement", *internal_force, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleResidual(const ID & residual_part) {
	AKANTU_DEBUG_IN();

	if ("external" == residual_part) {
	this->getDOFManager().assembleToResidual("displacement",
	*this->external_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	if ("internal" == residual_part) {
	this->assembleInternalForce();
	this->getDOFManager().assembleToResidual("displacement",
	*this->internal_force, 1);
	AKANTU_DEBUG_OUT();
	return;
	}

	AKANTU_CUSTOM_EXCEPTION(
	debug::SolverCallbackResidualPartUnknown(residual_part));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/* Virtual methods from Model */
	/* -------------------------------------------------------------------------- */
	/// get some default values for derived classes
	std::tuple<ID, TimeStepSolverType>
	StructuralMechanicsModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* ------------------------------------------------------------------------ */
	ModelSolverOptions StructuralMechanicsModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["displacement"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["displacement"] =
	IntegrationSchemeType::_trapezoidal_rule_2;
	options.solution_type["displacement"] = IntegrationScheme::_displacement;
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleInternalForce() {
	internal_force->zero();
	computeStresses();

	for (auto type : mesh.elementTypes(_spatial_dimension = _all_dimensions,
	_element_kind = _ek_structural)) {
	assembleInternalForce(type, _not_ghost);
	// assembleInternalForce(type, _ghost);
	}
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleInternalForce(ElementType type,
	GhostType gt) {
	auto & fem = getFEEngine();
	auto & sigma = stress(type, gt);
	auto ndof = getNbDegreeOfFreedom(type);
	auto nb_nodes = mesh.getNbNodesPerElement(type);
	auto ndof_per_elem = ndof * nb_nodes;

	Array<Real> BtSigma(fem.getNbIntegrationPoints(type) *
	mesh.getNbElement(type),
	ndof_per_elem, "BtSigma");
	fem.computeBtD(sigma, BtSigma, type, gt);

	Array<Real> intBtSigma(0, ndof_per_elem, "intBtSigma");
	fem.integrate(BtSigma, intBtSigma, ndof_per_elem, type, gt);

	getDOFManager().assembleElementalArrayLocalArray(intBtSigma, *internal_force,
	type, gt, -1.);
	}

	/* -------------------------------------------------------------------------- */
	Real StructuralMechanicsModel::getKineticEnergy() {
	if (not this->getDOFManager().hasMatrix("M")) {
	return 0.;
	}

	Real ekin = 0.;
	UInt nb_nodes = mesh.getNbNodes();

	Array<Real> Mv(nb_nodes, nb_degree_of_freedom);
	this->getDOFManager().assembleMatMulVectToArray("displacement", "M",
	*this->velocity, Mv);

	for (auto && data : zip(arange(nb_nodes), make_view(Mv, nb_degree_of_freedom),
	make_view(*this->velocity, nb_degree_of_freedom))) {
	ekin += std::get<2>(data).dot(std::get<1>(data)) *
	static_cast<Real>(mesh.isLocalOrMasterNode(std::get<0>(data)));
	}

	mesh.getCommunicator().allReduce(ekin, SynchronizerOperation::_sum);

	return ekin / 2.;
	}

	/* -------------------------------------------------------------------------- */
	Real StructuralMechanicsModel::getPotentialEnergy() {
	Real epot = 0.;
	UInt nb_nodes = mesh.getNbNodes();

	Array<Real> Ku(nb_nodes, nb_degree_of_freedom);
	this->getDOFManager().assembleMatMulVectToArray(
	"displacement", "K", *this->displacement_rotation, Ku);

	for (auto && data :
	zip(arange(nb_nodes), make_view(Ku, nb_degree_of_freedom),
	make_view(*this->displacement_rotation, nb_degree_of_freedom))) {
	epot += std::get<2>(data).dot(std::get<1>(data)) *
	static_cast<Real>(mesh.isLocalOrMasterNode(std::get<0>(data)));
	}

	mesh.getCommunicator().allReduce(epot, SynchronizerOperation::_sum);

	return epot / 2.;
	}

	/* -------------------------------------------------------------------------- */
	Real StructuralMechanicsModel::getEnergy(const ID & energy) {
	if (energy == "kinetic") {
	return getKineticEnergy();
	}

	if (energy == "potential") {
	return getPotentialEnergy();
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::computeForcesByLocalTractionArray(
	const Array<Real> & tractions, ElementType type) {
	AKANTU_DEBUG_IN();

	auto nb_element = getFEEngine().getMesh().getNbElement(type);
	auto nb_nodes_per_element =
	getFEEngine().getMesh().getNbNodesPerElement(type);
	auto nb_quad = getFEEngine().getNbIntegrationPoints(type);

	// check dimension match
	AKANTU_DEBUG_ASSERT(
	Mesh::getSpatialDimension(type) == getFEEngine().getElementDimension(),
	"element type dimension does not match the dimension of boundaries : "
	<< getFEEngine().getElementDimension()
	<< " != " << Mesh::getSpatialDimension(type));

	// check size of the vector
	AKANTU_DEBUG_ASSERT(
	tractions.size() == nb_quad * nb_element,
	"the size of the vector should be the total number of quadrature points");

	// check number of components
	AKANTU_DEBUG_ASSERT(tractions.getNbComponent() == nb_degree_of_freedom,
	"the number of components should be the spatial "
	"dimension of the problem");

	Array<Real> Ntbs(nb_element * nb_quad,
	nb_degree_of_freedom * nb_nodes_per_element);

	auto & fem = getFEEngine();
	fem.computeNtb(tractions, Ntbs, type);

	// allocate the vector that will contain the integrated values
	auto name = id + std::to_string(type) + ":integral_boundary";
	Array<Real> int_funct(nb_element, nb_degree_of_freedom * nb_nodes_per_element,
	name);

	// do the integration
	getFEEngine().integrate(Ntbs, int_funct,
	nb_degree_of_freedom * nb_nodes_per_element, type);

	// assemble the result into force vector
	getDOFManager().assembleElementalArrayLocalArray(int_funct, *external_force,
	type, _not_ghost, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::computeForcesByGlobalTractionArray(
	const Array<Real> & traction_global, ElementType type) {
	AKANTU_DEBUG_IN();

	UInt nb_element = mesh.getNbElement(type);
	UInt nb_quad = getFEEngine().getNbIntegrationPoints(type);

	Array<Real> traction_local(nb_element * nb_quad, nb_degree_of_freedom,
	id + ":structuralmechanics:imposed_linear_load");

	auto R_it = getFEEngineClass<MyFEEngineType>()
	.getShapeFunctions()
	.getRotations(type)
	.begin(nb_degree_of_freedom, nb_degree_of_freedom);

	auto Te_it = traction_global.begin(nb_degree_of_freedom);
	auto te_it = traction_local.begin(nb_degree_of_freedom);

	for (UInt e = 0; e < nb_element; ++e, ++R_it) {
	for (UInt q = 0; q < nb_quad; ++q, ++Te_it, ++te_it) {
	// turn the traction in the local referential
	te_it->template mul<false>(R_it, Te_it);
	}
	}

	computeForcesByLocalTractionArray(traction_local, type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::afterSolveStep(bool converged) {
	if (converged) {
	assembleInternalForce();
	}
	}

	} // namespace akantu
	diff --git a/src/model/structural_mechanics/structural_mechanics_model_boundary.cc b/src/model/structural_mechanics/structural_mechanics_model_boundary.cc
	index 6a7e7c1fa..b80dd2491 100644
	--- a/src/model/structural_mechanics/structural_mechanics_model_boundary.cc
	+++ b/src/model/structural_mechanics/structural_mechanics_model_boundary.cc
	@@ -1,47 +1,47 @@
	/**
	* @file structural_mechanics_model_boundary.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Fri Jul 15 2011
	* @date last modification: Fri Oct 13 2017
	*
	* @brief Implementation of the boundary conditions for
	* StructuralMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss.hh"
	#include "model.hh"
	#include "shape_structural.hh"
	#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/model/structural_mechanics/structural_mechanics_model_inline_impl.hh b/src/model/structural_mechanics/structural_mechanics_model_inline_impl.hh
	index fd638f708..77ae249b7 100644
	--- a/src/model/structural_mechanics/structural_mechanics_model_inline_impl.hh
	+++ b/src/model/structural_mechanics/structural_mechanics_model_inline_impl.hh
	@@ -1,282 +1,282 @@
	/**
	* @file structural_mechanics_model_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Fri Jul 15 2011
	* @date last modification: Mon Mar 15 2021
	*
	* @brief Implementation of inline functions of StructuralMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_
	#define AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt StructuralMechanicsModel::addMaterial(StructuralMaterial & material,
	const ID & name) {

	const auto material_index = materials.size();

	auto material_name = name;
	if (name.empty()) {
	material_name = "material_" + std::to_string(material_index);
	}

	if (materials_names_to_id.find(material_name) !=
	materials_names_to_id.end()) {
	AKANTU_EXCEPTION("The material " << material_name
	<< " already exists in the model " << id);
	}

	AKANTU_DEBUG_ASSERT(material_index <=
	(::std::size_t)::std::numeric_limits<UInt>::max(),
	"Can not represent the material ID");

	materials_names_to_id[material_name] = material_index;
	materials.push_back(material); // add the material, might cause
	// reallocation.

	return UInt(material_index);
	}

	/* -------------------------------------------------------------------------- */
	inline const StructuralMaterial &
	StructuralMechanicsModel::getMaterialByElement(const Element & element) const {
	return materials[element_material(element)];
	}

	/* -------------------------------------------------------------------------- */
	inline const StructuralMaterial &
	StructuralMechanicsModel::getMaterial(UInt material_index) const {
	return materials.at(material_index);
	}

	/* -------------------------------------------------------------------------- */
	inline const StructuralMaterial &
	StructuralMechanicsModel::getMaterial(const ID & name) const {
	auto it = materials_names_to_id.find(name);
	if (it == materials_names_to_id.end()) {
	AKANTU_EXCEPTION("The material " << name << " was not found in the model "
	<< id);
	}

	return materials.at(it->second);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void StructuralMechanicsModel::computeTangentModuli(
	Array<Real> & /tangent_moduli/) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void StructuralMechanicsModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	auto nb_element = getFEEngine().getMesh().getNbElement(type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
	auto tangent_size = ElementClass<type>::getNbStressComponents();

	auto tangent_moduli = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points, tangent_size * tangent_size,
	"tangent_stiffness_matrix");
	computeTangentModuli<type>(*tangent_moduli);

	/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
	UInt bt_d_b_size = nb_degree_of_freedom * nb_nodes_per_element;

	auto bt_d_b = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points, bt_d_b_size * bt_d_b_size, "B^tDB");

	const auto & b = getFEEngine().getShapesDerivatives(type);

	Matrix<Real> BtD(bt_d_b_size, tangent_size);

	for (auto && tuple :
	zip(make_view(b, tangent_size, bt_d_b_size),
	make_view(*tangent_moduli, tangent_size, tangent_size),
	make_view(*bt_d_b, bt_d_b_size, bt_d_b_size))) {
	auto & B = std::get<0>(tuple);
	auto & D = std::get<1>(tuple);
	auto & BtDB = std::get<2>(tuple);
	BtD.mul<true, false>(B, D);
	BtDB.template mul<false, false>(BtD, B);
	}

	/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
	auto int_bt_d_b = std::make_unique<Array<Real>>(
	nb_element, bt_d_b_size * bt_d_b_size, "int_B^tDB");

	getFEEngine().integrate(bt_d_b, int_bt_d_b, bt_d_b_size * bt_d_b_size,
	type);

	getDOFManager().assembleElementalMatricesToMatrix(
	"K", "displacement", *int_bt_d_b, type, _not_ghost, _symmetric);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void StructuralMechanicsModel::computeStressOnQuad() {
	AKANTU_DEBUG_IN();

	auto & sigma = stress(type, _not_ghost);

	auto nb_element = mesh.getNbElement(type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
	auto tangent_size = ElementClass<type>::getNbStressComponents();

	auto tangent_moduli = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points, tangent_size * tangent_size,
	"tangent_stiffness_matrix");

	computeTangentModuli<type>(*tangent_moduli);

	/// compute DB
	auto d_b_size = nb_degree_of_freedom * nb_nodes_per_element;

	auto d_b = std::make_unique<Array<Real>>(nb_element * nb_quadrature_points,
	d_b_size * tangent_size, "D*B");

	const auto & b = getFEEngine().getShapesDerivatives(type);

	auto B = b.begin(tangent_size, d_b_size);
	auto D = tangent_moduli->begin(tangent_size, tangent_size);
	auto D_B = d_b->begin(tangent_size, d_b_size);

	for (UInt e = 0; e < nb_element; ++e) {
	for (UInt q = 0; q < nb_quadrature_points; ++q, ++B, ++D, ++D_B) {
	D_B->template mul<false, false>(D, B);
	}
	}

	/// compute DBu
	D_B = d_b->begin(tangent_size, d_b_size);
	auto DBu = sigma.begin(tangent_size);

	Array<Real> u_el(0, d_b_size);
	FEEngine::extractNodalToElementField(mesh, *displacement_rotation, u_el,
	type);

	auto ug = u_el.begin(d_b_size);

	// No need to rotate because B is post-multiplied
	for (UInt e = 0; e < nb_element; ++e, ++ug) {
	for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_B, ++DBu) {
	DBu->template mul<false>(D_B, ug);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @param myf pointer to a function that fills a vector/tensor with respect to
	* passed coordinates
	*/
	#if 0
	template <ElementType type>
	inline void StructuralMechanicsModel::computeForcesFromFunction(
	BoundaryFunction myf, BoundaryFunctionType function_type) {
	/** function type is
	** _bft_forces : linear load is given
	** _bft_stress : stress function is given -> Not already done for this kind
	*of model
	*/

	std::stringstream name;
	name << id << ":structuralmechanics:imposed_linear_load";
	Array<Real> lin_load(0, nb_degree_of_freedom, name.str());
	name.zero();

	UInt offset = nb_degree_of_freedom;

	// prepare the loop over element types
	UInt nb_quad = getFEEngine().getNbIntegrationPoints(type);
	UInt nb_element = getFEEngine().getMesh().getNbElement(type);

	name.zero();
	name << id << ":structuralmechanics:quad_coords";
	Array<Real> quad_coords(nb_element * nb_quad, spatial_dimension,
	"quad_coords");

	getFEEngineClass<MyFEEngineType>()
	.getShapeFunctions()
	.interpolateOnIntegrationPoints<type>(getFEEngine().getMesh().getNodes(),
	quad_coords, spatial_dimension);
	getFEEngineClass<MyFEEngineType>()
	.getShapeFunctions()
	.interpolateOnIntegrationPoints<type>(
	getFEEngine().getMesh().getNodes(), quad_coords, spatial_dimension,
	_not_ghost, empty_filter, true, 0, 1, 1);
	if (spatial_dimension == 3)
	getFEEngineClass<MyFEEngineType>()
	.getShapeFunctions()
	.interpolateOnIntegrationPoints<type>(
	getFEEngine().getMesh().getNodes(), quad_coords, spatial_dimension,
	_not_ghost, empty_filter, true, 0, 2, 2);
	lin_load.resize(nb_element * nb_quad);
	Real * imposed_val = lin_load.storage();

	/// sigma/load on each quadrature points
	Real * qcoord = quad_coords.storage();
	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt q = 0; q < nb_quad; ++q) {
	myf(qcoord, imposed_val, NULL, 0);
	imposed_val += offset;
	qcoord += spatial_dimension;
	}
	}

	switch (function_type) {
	case _bft_traction_local:
	computeForcesByLocalTractionArray<type>(lin_load);
	break;
	case _bft_traction:
	computeForcesByGlobalTractionArray<type>(lin_load);
	break;
	default:
	break;
	}
	}
	#endif
	} // namespace akantu

	#endif /* AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_ */
	diff --git a/src/model/structural_mechanics/structural_mechanics_model_mass.cc b/src/model/structural_mechanics/structural_mechanics_model_mass.cc
	index 768322ab0..d444e27e5 100644
	--- a/src/model/structural_mechanics/structural_mechanics_model_mass.cc
	+++ b/src/model/structural_mechanics/structural_mechanics_model_mass.cc
	@@ -1,91 +1,91 @@
	/**
	* @file structural_mechanics_model_mass.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jul 07 2014
	* @date last modification: Thu Mar 04 2021
	*
	* @brief function handling mass computation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss.hh"
	#include "material.hh"
	#include "shape_structural.hh"
	#include "structural_mechanics_model.hh"

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class ComputeRhoFunctorStruct {
	public:
	explicit ComputeRhoFunctorStruct(const StructuralMechanicsModel & model)
	: model(model){};

	void operator()(Matrix<Real> & rho, const Element & element) const {
	Real mat_rho = model.getMaterialByElement(element).rho;
	rho.set(mat_rho);
	}

	private:
	const StructuralMechanicsModel & model;
	};

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleMassMatrix() {
	AKANTU_DEBUG_IN();

	if (not need_to_reassemble_mass) {
	return;
	}

	if (not getDOFManager().hasMatrix("M")) {
	getDOFManager().getNewMatrix("M", getMatrixType("M"));
	}

	this->getDOFManager().zeroMatrix("M");
	assembleMassMatrix(_not_ghost);

	need_to_reassemble_mass = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void StructuralMechanicsModel::assembleMassMatrix(GhostType ghost_type) {
	AKANTU_DEBUG_IN();
	auto & fem = getFEEngineClass<MyFEEngineType>();
	ComputeRhoFunctorStruct compute_rho(*this);

	for (auto type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_structural)) {
	fem.assembleFieldMatrix(compute_rho, "M", "displacement",
	this->getDOFManager(), type, ghost_type);
	}
	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/solver/petsc_wrapper.hh b/src/solver/petsc_wrapper.hh
	index 247032eb5..09603ba3d 100644
	--- a/src/solver/petsc_wrapper.hh
	+++ b/src/solver/petsc_wrapper.hh
	@@ -1,80 +1,80 @@
	/**
	* @file petsc_wrapper.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Sat May 23 2020
	*
	* @brief Wrapper of PETSc structures
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PETSC_WRAPPER_HH_
	#define AKANTU_PETSC_WRAPPER_HH_

	/* -------------------------------------------------------------------------- */
	#include <mpi.h>
	#include <petscao.h>
	#include <petscis.h>
	#include <petscksp.h>
	#include <petscmat.h>
	#include <petscvec.h>

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	struct PETScMatrixWrapper {
	Mat mat;
	AO ao;
	ISLocalToGlobalMapping mapping;
	/// MPI communicator for PETSc commands
	MPI_Comm communicator;
	};

	/* -------------------------------------------------------------------------- */
	struct PETScSolverWrapper {
	KSP ksp;
	Vec solution;
	Vec rhs;
	// MPI communicator for PETSc commands
	MPI_Comm communicator;
	};

	#if not defined(PETSC_CLANGUAGE_CXX)
	extern int aka_PETScError(int ierr);

	#define CHKERRXX(x) \
	do { \
	int error = aka_PETScError(x); \
	if (error != 0) { \
	AKANTU_EXCEPTION("Error in PETSC"); \
	} \
	} while (0)
	#endif

	} // namespace akantu

	#endif /* AKANTU_PETSC_WRAPPER_HH_ */
	diff --git a/src/solver/solver_petsc.cc b/src/solver/solver_petsc.cc
	index 72352ebb7..696c75c24 100644
	--- a/src/solver/solver_petsc.cc
	+++ b/src/solver/solver_petsc.cc
	@@ -1,93 +1,93 @@
	/**
	* @file solver_petsc.cc
	*
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 13 2014
	* @date last modification: Tue May 26 2020
	*
	* @brief Solver class implementation for the petsc solver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_petsc.hh"
	#include "dof_manager_petsc.hh"
	#include "mpi_communicator_data.hh"
	#include "solver_vector_petsc.hh"
	#include "sparse_matrix_petsc.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscksp.h>
	//#include <petscsys.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SolverPETSc::SolverPETSc(DOFManagerPETSc & dof_manager, const ID & matrix_id,
	const ID & id)
	- : SparseSolver(dof_manager, matrix_id, id),
	- dof_manager(dof_manager), matrix(dof_manager.getMatrix(matrix_id)) {
	+ : SparseSolver(dof_manager, matrix_id, id), dof_manager(dof_manager),
	+ matrix(dof_manager.getMatrix(matrix_id)) {
	auto && mpi_comm = dof_manager.getMPIComm();

	/// create a solver context
	PETSc_call(KSPCreate, mpi_comm, &this->ksp);
	}

	/* -------------------------------------------------------------------------- */
	SolverPETSc::~SolverPETSc() {
	if (ksp != nullptr) {
	PETSc_call(KSPDestroy, &ksp);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::setOperators() {
	// set the matrix that defines the linear system and the matrix for
	// preconditioning (here they are the same)
	#if PETSC_VERSION_MAJOR >= 3 && PETSC_VERSION_MINOR >= 5
	PETSc_call(KSPSetOperators, ksp, this->matrix.getMat(),
	this->matrix.getMat());
	#else
	PETSc_call(KSPSetOperators, ksp, this->matrix.getMat(), this->matrix.getMat(),
	SAME_NONZERO_PATTERN);
	#endif

	// If this is not called the solution vector is zeroed in the call to
	// KSPSolve().
	PETSc_call(KSPSetInitialGuessNonzero, ksp, PETSC_TRUE);
	PETSc_call(KSPSetFromOptions, ksp);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::solve() {
	Vec & rhs(this->dof_manager.getResidual());
	Vec & solution(this->dof_manager.getSolution());

	PETSc_call(KSPSolve, ksp, rhs, solution);
	}

	} // namespace akantu
	diff --git a/src/solver/solver_petsc.hh b/src/solver/solver_petsc.hh
	index 8bf5d32b4..e0b573f35 100644
	--- a/src/solver/solver_petsc.hh
	+++ b/src/solver/solver_petsc.hh
	@@ -1,83 +1,82 @@
	/**
	* @file solver_petsc.hh
	*
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 13 2014
	* @date last modification: Tue May 26 2020
	*
	* @brief Solver class interface for the petsc solver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscksp.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_PETSC_HH_
	#define AKANTU_SOLVER_PETSC_HH_

	namespace akantu {
	class SparseMatrixPETSc;
	class DOFManagerPETSc;
	} // namespace akantu

	namespace akantu {

	class SolverPETSc : public SparseSolver {

	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SolverPETSc(DOFManagerPETSc & dof_manager, const ID & matrix_id,
	const ID & id = "solver_petsc");

	~SolverPETSc() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// create the solver context and set the matrices
	virtual void setOperators();
	void solve() override;

	private:
	/// DOFManager correctly typed
	DOFManagerPETSc & dof_manager;

	/// PETSc linear solver
	KSP ksp;

	/// Matrix defining the system of equations
	SparseMatrixPETSc & matrix;
	};

	-
	} // namespace akantu

	#endif /* AKANTU_SOLVER_PETSC_HH_ */
	diff --git a/src/solver/solver_vector.hh b/src/solver/solver_vector.hh
	index c3a02d5fe..85fff5ccc 100644
	--- a/src/solver/solver_vector.hh
	+++ b/src/solver/solver_vector.hh
	@@ -1,91 +1,91 @@
	/**
	* @file solver_vector.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue May 26 2020
	*
	* @brief Solver vector interface base class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_VECTOR_HH_
	#define AKANTU_SOLVER_VECTOR_HH_

	namespace akantu {
	class DOFManager;
	}

	namespace akantu {

	class SolverVector {
	public:
	SolverVector(DOFManager & dof_manager, const ID & id = "solver_vector")
	: id(id), _dof_manager(dof_manager) {}

	SolverVector(const SolverVector & vector, const ID & id = "solver_vector")
	: id(id), _dof_manager(vector._dof_manager) {}

	virtual ~SolverVector() = default;

	// resize the vector to the size of the problem
	virtual void resize() = 0;

	// clear the vector
	virtual void set(Real val) = 0;
	void zero() { this->set({}); }

	virtual operator const Array<Real> &() const = 0;

	virtual Int size() const = 0;
	virtual Int localSize() const = 0;

	virtual SolverVector & operator+(const SolverVector & y) = 0;
	virtual SolverVector & operator=(const SolverVector & y) = 0;

	UInt & release() { return release_; }
	UInt release() const { return release_; }

	virtual void printself(std::ostream & stream, int indent = 0) const = 0;

	protected:
	ID id;

	/// Underlying dof manager
	DOFManager & _dof_manager;

	UInt release_{0};
	};

	inline std::ostream & operator<<(std::ostream & stream, SolverVector & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#endif /* AKANTU_SOLVER_VECTOR_HH_ */
	diff --git a/src/solver/solver_vector_default.hh b/src/solver/solver_vector_default.hh
	index 19b167d76..060c95668 100644
	--- a/src/solver/solver_vector_default.hh
	+++ b/src/solver/solver_vector_default.hh
	@@ -1,144 +1,144 @@
	/**
	* @file solver_vector_default.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 01 2019
	* @date last modification: Sat May 23 2020
	*
	* @brief Solver vector interface to Array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_vector.hh"
	/* -------------------------------------------------------------------------- */
	#include <utility>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_VECTOR_DEFAULT_HH_
	#define AKANTU_SOLVER_VECTOR_DEFAULT_HH_

	namespace akantu {
	class DOFManagerDefault;
	} // namespace akantu

	namespace akantu {

	class SolverVectorArray : public SolverVector {
	public:
	SolverVectorArray(DOFManagerDefault & dof_manager, const ID & id);
	SolverVectorArray(const SolverVectorArray & vector, const ID & id);

	~SolverVectorArray() override = default;

	virtual Array<Real> & getVector() = 0;
	virtual const Array<Real> & getVector() const = 0;

	void printself(std::ostream & stream, int indent = 0) const override {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "SolverVectorArray [" << std::endl;
	stream << space << " + id: " << id << std::endl;
	this->getVector().printself(stream, indent + 1);
	stream << space << "]" << std::endl;
	}
	};

	/* -------------------------------------------------------------------------- */
	template <class Array_> class SolverVectorArrayTmpl : public SolverVectorArray {
	public:
	SolverVectorArrayTmpl(DOFManagerDefault & dof_manager, Array_ & vector,
	const ID & id = "solver_vector_default")
	: SolverVectorArray(dof_manager, id), dof_manager(dof_manager),
	vector(vector) {}

	template <class A = Array_,
	std::enable_if_t<not std::is_reference<A>::value> * = nullptr>
	SolverVectorArrayTmpl(DOFManagerDefault & dof_manager,
	const ID & id = "solver_vector_default")
	: SolverVectorArray(dof_manager, id), dof_manager(dof_manager),
	vector(0, 1, id + ":vector") {}

	SolverVectorArrayTmpl(const SolverVectorArrayTmpl & vector,
	const ID & id = "solver_vector_default")
	: SolverVectorArray(vector, id), dof_manager(vector.dof_manager),
	vector(vector.vector) {}

	operator const Array<Real> &() const override { return getVector(); };
	virtual operator Array<Real> &() { return getVector(); };

	SolverVector & operator+(const SolverVector & y) override;
	SolverVector & operator=(const SolverVector & y) override;

	void resize() override {
	static_assert(not std::is_const<std::remove_reference_t<Array_>>::value,
	"Cannot resize a const Array");
	this->vector.resize(this->localSize(), 0.);
	++this->release_;
	}

	void set(Real val) override {
	- static_assert(not std::is_const<std::remove_reference_t<Array_>>::value,
	+ static_assert(not std::is_const<std::remove_reference_t<Array_>>::value,
	"Cannot clear a const Array");
	this->vector.set(val);
	++this->release_;
	}

	public:
	Array<Real> & getVector() override { return vector; }
	const Array<Real> & getVector() const override { return vector; }

	Int size() const override;
	Int localSize() const override;

	virtual Array<Real> & getGlobalVector() { return this->vector; }
	virtual void setGlobalVector(const Array<Real> & solution) {
	this->vector.copy(solution);
	}

	protected:
	DOFManagerDefault & dof_manager;
	Array_ vector;

	template <class A> friend class SolverVectorArrayTmpl;
	};

	/* -------------------------------------------------------------------------- */
	using SolverVectorDefault = SolverVectorArrayTmpl<Array<Real>>;

	/* -------------------------------------------------------------------------- */
	template <class Array>
	using SolverVectorDefaultWrap = SolverVectorArrayTmpl<Array &>;

	template <class Array>
	decltype(auto) make_solver_vector_default_wrap(DOFManagerDefault & dof_manager,
	Array & vector) {
	return SolverVectorDefaultWrap<Array>(dof_manager, vector);
	}

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "solver_vector_default_tmpl.hh"
	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_SOLVER_VECTOR_DEFAULT_HH_ */
	diff --git a/src/solver/solver_vector_default_tmpl.hh b/src/solver/solver_vector_default_tmpl.hh
	index 9e0683669..100ad11d8 100644
	--- a/src/solver/solver_vector_default_tmpl.hh
	+++ b/src/solver/solver_vector_default_tmpl.hh
	@@ -1,87 +1,87 @@
	/**
	* @file solver_vector_default_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 01 2019
	* @date last modification: Sat May 23 2020
	*
	* @brief Solver vector interface to Array
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_default.hh"
	#include "solver_vector_default.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_VECTOR_DEFAULT_TMPL_HH_
	#define AKANTU_SOLVER_VECTOR_DEFAULT_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline SolverVectorArray::SolverVectorArray(DOFManagerDefault & dof_manager,
	const ID & id)
	: SolverVector(dof_manager, id) {}

	/* -------------------------------------------------------------------------- */
	inline SolverVectorArray::SolverVectorArray(const SolverVectorArray & vector,
	const ID & id)
	: SolverVector(vector, id) {}

	/* -------------------------------------------------------------------------- */
	template <class Array_>
	-SolverVector & SolverVectorArrayTmpl<Array_>::
	-operator+(const SolverVector & y) {
	+SolverVector &
	+SolverVectorArrayTmpl<Array_>::operator+(const SolverVector & y) {
	const auto & y_ = aka::as_type<SolverVectorArray>(y);
	this->vector += y_.getVector();

	++this->release_;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <class Array_>
	-SolverVector & SolverVectorArrayTmpl<Array_>::
	-operator=(const SolverVector & y) {
	+SolverVector &
	+SolverVectorArrayTmpl<Array_>::operator=(const SolverVector & y) {
	const auto & y_ = aka::as_type<SolverVectorArray>(y);
	this->vector.copy(y_.getVector());

	this->release_ = y.release();
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <class Array_> inline Int SolverVectorArrayTmpl<Array_>::size() const {
	return this->dof_manager.getSystemSize();
	}

	/* -------------------------------------------------------------------------- */
	template <class Array_>
	inline Int SolverVectorArrayTmpl<Array_>::localSize() const {
	return dof_manager.getLocalSystemSize();
	}

	} // namespace akantu

	#endif /* AKANTU_SOLVER_VECTOR_DEFAULT_TMPL_HH_ */
	diff --git a/src/solver/solver_vector_distributed.cc b/src/solver/solver_vector_distributed.cc
	index 90e1aa108..4eacf65a1 100644
	--- a/src/solver/solver_vector_distributed.cc
	+++ b/src/solver/solver_vector_distributed.cc
	@@ -1,81 +1,81 @@
	/**
	* @file solver_vector_distributed.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 01 2019
	* @date last modification: Sat May 23 2020
	*
	* @brief Solver vector interface for distributed arrays
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_vector_distributed.hh"
	#include "dof_manager_default.hh"
	#include "dof_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SolverVectorDistributed::SolverVectorDistributed(
	DOFManagerDefault & dof_manager, const ID & id)
	: SolverVectorDefault(dof_manager, id) {}

	/* -------------------------------------------------------------------------- */
	SolverVectorDistributed::SolverVectorDistributed(
	const SolverVectorDefault & vector, const ID & id)
	: SolverVectorDefault(vector, id) {}

	/* -------------------------------------------------------------------------- */
	Array<Real> & SolverVectorDistributed::getGlobalVector() {
	auto & synchronizer = dof_manager.getSynchronizer();

	if (not this->global_vector) {
	this->global_vector =
	std::make_unique<Array<Real>>(0, 1, "global_residual");
	}

	if (synchronizer.getCommunicator().whoAmI() == 0) {
	this->global_vector->resize(dof_manager.getSystemSize());
	synchronizer.gather(this->vector, *this->global_vector);
	} else {
	synchronizer.gather(this->vector);
	}

	return *this->global_vector;
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorDistributed::setGlobalVector(const Array<Real> & solution) {
	auto & synchronizer = dof_manager.getSynchronizer();
	if (synchronizer.getCommunicator().whoAmI() == 0) {
	synchronizer.scatter(this->vector, solution);
	} else {
	synchronizer.scatter(this->vector);
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/solver/solver_vector_distributed.hh b/src/solver/solver_vector_distributed.hh
	index 65e8127ec..26df926f4 100644
	--- a/src/solver/solver_vector_distributed.hh
	+++ b/src/solver/solver_vector_distributed.hh
	@@ -1,59 +1,59 @@
	/**
	* @file solver_vector_distributed.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Tue Jan 01 2019
	*
	* @brief Solver vector interface for distributed arrays
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_vector_default.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_VECTOR_DISTRIBUTED_HH_
	#define AKANTU_SOLVER_VECTOR_DISTRIBUTED_HH_

	namespace akantu {

	class SolverVectorDistributed : public SolverVectorDefault {
	public:
	SolverVectorDistributed(DOFManagerDefault & dof_manager,
	const ID & id = "solver_vector_mumps");

	SolverVectorDistributed(const SolverVectorDefault & vector,
	const ID & id = "solver_vector_mumps");

	Array<Real> & getGlobalVector() override;
	void setGlobalVector(const Array<Real> & solution) override;

	protected:
	// full vector in case it needs to be centralized on master
	std::unique_ptr<Array<Real>> global_vector;
	};

	} // namespace akantu

	#endif /* AKANTU_SOLVER_VECTOR_DISTRIBUTED_HH_ */
	diff --git a/src/solver/solver_vector_petsc.cc b/src/solver/solver_vector_petsc.cc
	index ac9f76af4..e9019ed7b 100644
	--- a/src/solver/solver_vector_petsc.cc
	+++ b/src/solver/solver_vector_petsc.cc
	@@ -1,293 +1,293 @@
	/**
	* @file solver_vector_petsc.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 01 2019
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Solver vector interface for PETSc
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solver_vector_petsc.hh"
	#include "dof_manager_petsc.hh"
	#include "mpi_communicator_data.hh"
	/* -------------------------------------------------------------------------- */
	#include <numeric>
	#include <petscvec.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc::SolverVectorPETSc(DOFManagerPETSc & dof_manager,
	const ID & id)
	: SolverVector(dof_manager, id), dof_manager(dof_manager) {
	auto && mpi_comm = dof_manager.getMPIComm();
	PETSc_call(VecCreate, mpi_comm, &x);
	detail::PETScSetName(x, id);

	PETSc_call(VecSetFromOptions, x);

	auto local_system_size = dof_manager.getLocalSystemSize();
	auto nb_local_dofs = dof_manager.getPureLocalSystemSize();
	PETSc_call(VecSetSizes, x, nb_local_dofs, PETSC_DECIDE);

	VecType vec_type;
	PETSc_call(VecGetType, x, &vec_type);
	if (std::string(vec_type) == std::string(VECMPI)) {
	PetscInt lowest_gidx;
	PetscInt highest_gidx;
	PETSc_call(VecGetOwnershipRange, x, &lowest_gidx, &highest_gidx);

	std::vector<PetscInt> ghost_idx;
	for (auto && d : arange(local_system_size)) {
	int gidx = dof_manager.localToGlobalEquationNumber(d);
	if (gidx != -1) {
	if ((gidx < lowest_gidx) or (gidx >= highest_gidx)) {
	ghost_idx.push_back(gidx);
	}
	}
	}

	PETSc_call(VecMPISetGhost, x, ghost_idx.size(), ghost_idx.data());
	} else {
	std::vector<int> idx(nb_local_dofs);
	std::iota(idx.begin(), idx.end(), 0);
	ISLocalToGlobalMapping is;
	PETSc_call(ISLocalToGlobalMappingCreate, PETSC_COMM_SELF, 1, idx.size(),
	idx.data(), PETSC_COPY_VALUES, &is);
	PETSc_call(VecSetLocalToGlobalMapping, x, is);
	PETSc_call(ISLocalToGlobalMappingDestroy, &is);
	}
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc::SolverVectorPETSc( // NOLINT(bugprone-copy-constructor-init)
	const SolverVectorPETSc & vector, const ID & id)
	: SolverVector(vector, id), dof_manager(vector.dof_manager) {
	if (vector.x != nullptr) {
	PETSc_call(VecDuplicate, vector.x, &x);
	PETSc_call(VecCopy, vector.x, x);
	detail::PETScSetName(x, id);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "SolverVectorPETSc [" << std::endl;
	stream << space << " + id: " << id << std::endl;
	PETSc_call(PetscViewerPushFormat, PETSC_VIEWER_STDOUT_WORLD,
	PETSC_VIEWER_ASCII_INDEX);
	PETSc_call(VecView, x, PETSC_VIEWER_STDOUT_WORLD);
	PETSc_call(PetscViewerPopFormat, PETSC_VIEWER_STDOUT_WORLD);
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc::SolverVectorPETSc(Vec x, DOFManagerPETSc & dof_manager,
	const ID & id)
	: SolverVector(dof_manager, id), dof_manager(dof_manager) {
	PETSc_call(VecDuplicate, x, &this->x);

	PETSc_call(VecCopy, x, this->x);
	detail::PETScSetName(x, id);
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc::~SolverVectorPETSc() {
	if (x != nullptr) {
	PETSc_call(VecDestroy, &x);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::resize() {
	// the arrays are destroyed and recreated in the dof manager
	// resize is so not implemented
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::set(Real val) {
	PETSc_call(VecSet, x, val);
	applyModifications();
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::applyModifications() {
	PETSc_call(VecAssemblyBegin, x);
	PETSc_call(VecAssemblyEnd, x);
	updateGhost();
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::updateGhost() {
	Vec x_ghosted{nullptr};
	PETSc_call(VecGhostGetLocalForm, x, &x_ghosted);
	if (x_ghosted != nullptr) {
	PETSc_call(VecGhostUpdateBegin, x, INSERT_VALUES, SCATTER_FORWARD);
	PETSc_call(VecGhostUpdateEnd, x, INSERT_VALUES, SCATTER_FORWARD);
	}
	PETSc_call(VecGhostRestoreLocalForm, x, &x_ghosted);
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::getValues(const Array<Int> & idx,
	Array<Real> & values) const {
	if (idx.empty()) {
	return;
	}

	ISLocalToGlobalMapping is_ltog_map;
	PETSc_call(VecGetLocalToGlobalMapping, x, &is_ltog_map);

	PetscInt n;
	Array<PetscInt> lidx(idx.size());
	PETSc_call(ISGlobalToLocalMappingApply, is_ltog_map, IS_GTOLM_MASK,
	idx.size(), idx.storage(), &n, lidx.storage());

	getValuesLocal(lidx, values);
	}
	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::getValuesLocal(const Array<Int> & idx,
	Array<Real> & values) const {
	if (idx.empty()) {
	return;
	}

	Vec x_ghosted{nullptr};
	PETSc_call(VecGhostGetLocalForm, x, &x_ghosted);
	// VecScatterBegin(scatter, x, x_local, INSERT_VALUES, SCATTER_FORWARD);
	// VecScatterEnd(scatter, x, x_local, INSERT_VALUES, SCATTER_FORWARD);

	if (x_ghosted == nullptr) {
	const PetscScalar * array;
	PETSc_call(VecGetArrayRead, x, &array);

	for (auto && data : zip(idx, make_view(values))) {
	auto i = std::get<0>(data);
	if (i != -1) {
	std::get<1>(data) = array[i];
	}
	}

	PETSc_call(VecRestoreArrayRead, x, &array);
	return;
	}

	PETSc_call(VecSetOption, x_ghosted, VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE);
	PETSc_call(VecGetValues, x_ghosted, idx.size(), idx.storage(),
	values.storage());
	PETSc_call(VecGhostRestoreLocalForm, x, &x_ghosted);
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::addValues(const Array<Int> & gidx,
	const Array<Real> & values,
	Real scale_factor) {
	Real * to_add = values.storage();
	Array<Real> scaled_array;
	if (scale_factor != 1.) {
	scaled_array.copy(values, false);
	scaled_array *= scale_factor;
	to_add = scaled_array.storage();
	}

	PETSc_call(VecSetOption, x, VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE);
	PETSc_call(VecSetValues, x, gidx.size(), gidx.storage(), to_add, ADD_VALUES);

	applyModifications();
	}

	/* -------------------------------------------------------------------------- */
	void SolverVectorPETSc::addValuesLocal(const Array<Int> & lidx,
	const Array<Real> & values,
	Real scale_factor) {
	Vec x_ghosted{nullptr};
	PETSc_call(VecGhostGetLocalForm, x, &x_ghosted);

	if (x_ghosted == nullptr) {
	Real * to_add = values.storage();
	Array<Real> scaled_array;
	if (scale_factor != 1.) {
	scaled_array.copy(values, false);
	scaled_array *= scale_factor;
	to_add = scaled_array.storage();
	}

	PETSc_call(VecSetOption, x, VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE);
	PETSc_call(VecSetValuesLocal, x, lidx.size(), lidx.storage(), to_add,
	ADD_VALUES);
	return;
	}

	PETSc_call(VecGhostRestoreLocalForm, x, &x_ghosted);

	ISLocalToGlobalMapping is_ltog_map;
	PETSc_call(VecGetLocalToGlobalMapping, x, &is_ltog_map);

	Array<Int> gidx(lidx.size());
	PETSc_call(ISLocalToGlobalMappingApply, is_ltog_map, lidx.size(),
	lidx.storage(), gidx.storage());
	addValues(gidx, values, scale_factor);
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc::operator const Array<Real> &() const {
	const_cast<Array<Real> &>(cache).resize(local_size());

	auto xl = internal::make_petsc_local_vector(x);
	auto cachep = internal::make_petsc_wraped_vector(this->cache);

	PETSc_call(VecCopy, cachep, xl);
	return cache;
	}

	/* -------------------------------------------------------------------------- */
	SolverVectorPETSc & SolverVectorPETSc::operator=(const SolverVectorPETSc & y) {
	if (size() != y.size()) {
	PETSc_call(VecDuplicate, y, &x);
	}

	PETSc_call(VecCopy, y.x, x);
	release_ = y.release_;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	SolverVector & SolverVectorPETSc::operator=(const SolverVector & y) {
	const auto & y_ = aka::as_type<SolverVectorPETSc>(y);
	return operator=(y_);
	}

	/* -------------------------------------------------------------------------- */
	SolverVector & SolverVectorPETSc::operator+(const SolverVector & y) {
	const auto & y_ = aka::as_type<SolverVectorPETSc>(y);
	PETSc_call(VecAXPY, x, 1., y_.x);
	release_ = y_.release_;
	return *this;
	}

	} // namespace akantu
	diff --git a/src/solver/solver_vector_petsc.hh b/src/solver/solver_vector_petsc.hh
	index 0155667c2..223d59a98 100644
	--- a/src/solver/solver_vector_petsc.hh
	+++ b/src/solver/solver_vector_petsc.hh
	@@ -1,208 +1,208 @@
	/**
	* @file solver_vector_petsc.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 01 2019
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Solver vector interface for PETSc
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_petsc.hh"
	#include "solver_vector.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscvec.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_VECTOR_PETSC_HH_
	#define AKANTU_SOLVER_VECTOR_PETSC_HH_

	namespace akantu {
	class DOFManagerPETSc;
	} // namespace akantu

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	namespace internal {
	/* ------------------------------------------------------------------------ */
	class PETScVector {
	public:
	virtual ~PETScVector() = default;

	operator Vec &() { return x; }
	operator const Vec &() const { return x; }

	Int size() const {
	PetscInt n;
	PETSc_call(VecGetSize, x, &n);
	return n;
	}
	Int local_size() const {
	PetscInt n;
	PETSc_call(VecGetLocalSize, x, &n);
	return n;
	}

	AKANTU_GET_MACRO_NOT_CONST(Vec, x, auto &);
	AKANTU_GET_MACRO(Vec, x, const auto &);

	protected:
	Vec x{nullptr};
	};

	} // namespace internal

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	class SolverVectorPETSc : public SolverVector, public internal::PETScVector {
	public:
	SolverVectorPETSc(DOFManagerPETSc & dof_manager,
	const ID & id = "solver_vector_petsc");

	SolverVectorPETSc(const SolverVectorPETSc & vector,
	const ID & id = "solver_vector_petsc");

	SolverVectorPETSc(Vec x, DOFManagerPETSc & dof_manager,
	const ID & id = "solver_vector_petsc");

	~SolverVectorPETSc() override;

	// resize the vector to the size of the problem
	void resize() override;
	void set(Real val) override;

	operator const Array<Real> &() const override;

	SolverVector & operator+(const SolverVector & y) override;
	SolverVector & operator=(const SolverVector & y) override;
	SolverVectorPETSc & operator=(const SolverVectorPETSc & y);

	/// get values using processors global indexes
	void getValues(const Array<Int> & idx, Array<Real> & values) const;

	/// get values using processors local indexes
	void getValuesLocal(const Array<Int> & idx, Array<Real> & values) const;

	/// adding values to the vector using the global indices
	void addValues(const Array<Int> & gidx, const Array<Real> & values,
	Real scale_factor = 1.);

	/// adding values to the vector using the local indices
	void addValuesLocal(const Array<Int> & lidx, const Array<Real> & values,
	Real scale_factor = 1.);

	Int size() const override { return internal::PETScVector::size(); }
	Int localSize() const override { return internal::PETScVector::local_size(); }

	void printself(std::ostream & stream, int indent = 0) const override;

	protected:
	void applyModifications();
	void updateGhost();

	protected:
	DOFManagerPETSc & dof_manager;

	// used for the conversion operator
	Array<Real> cache;
	};

	/* -------------------------------------------------------------------------- */
	namespace internal {
	/* ------------------------------------------------------------------------ */
	template <class Array> class PETScWrapedVector : public PETScVector {
	public:
	PETScWrapedVector(Array && array) : array(array) {
	PETSc_call(VecCreateSeqWithArray, PETSC_COMM_SELF, 1, array.size(),
	array.storage(), &x);
	}

	~PETScWrapedVector() override { PETSc_call(VecDestroy, &x); }

	private:
	Array array;
	};

	/* ------------------------------------------------------------------------ */
	template <bool read_only> class PETScLocalVector : public PETScVector {
	public:
	PETScLocalVector(const Vec & g) : g(g) {
	PETSc_call(VecGetLocalVectorRead, g, x);
	}
	PETScLocalVector(const SolverVectorPETSc & g)
	: PETScLocalVector(g.getVec()) {}
	~PETScLocalVector() override {
	PETSc_call(VecRestoreLocalVectorRead, g, x);
	PETSc_call(VecDestroy, &x);
	}

	private:
	const Vec & g;
	};

	template <> class PETScLocalVector<false> : public PETScVector {
	public:
	PETScLocalVector(Vec & g) : g(g) {
	PETSc_call(VecGetLocalVectorRead, g, x);
	}
	PETScLocalVector(SolverVectorPETSc & g) : PETScLocalVector(g.getVec()) {}
	~PETScLocalVector() override {
	PETSc_call(VecRestoreLocalVectorRead, g, x);
	PETSc_call(VecDestroy, &x);
	}

	private:
	Vec & g;
	};

	/* ------------------------------------------------------------------------ */
	template <class Array>
	decltype(auto) make_petsc_wraped_vector(Array && array) {
	return PETScWrapedVector<Array>(std::forward<Array>(array));
	}

	template <
	typename V,
	std::enable_if_t<std::is_same<Vec, std::decay_t<V>>::value> * = nullptr>
	decltype(auto) make_petsc_local_vector(V && vec) {
	constexpr auto read_only = std::is_const<std::remove_reference_t<V>>::value;
	return PETScLocalVector<read_only>(vec);
	}

	template <typename V, std::enable_if_t<std::is_base_of<
	SolverVector, std::decay_t<V>>::value> * = nullptr>
	decltype(auto) make_petsc_local_vector(V && vec) {
	constexpr auto read_only = std::is_const<std::remove_reference_t<V>>::value;
	return PETScLocalVector<read_only>(
	dynamic_cast<std::conditional_t<read_only, const SolverVectorPETSc,
	SolverVectorPETSc> &>(vec));
	}

	} // namespace internal

	} // namespace akantu

	#endif /* AKANTU_SOLVER_VECTOR_PETSC_HH_ */
	diff --git a/src/solver/sparse_matrix.cc b/src/solver/sparse_matrix.cc
	index 2706faedd..f8728faf9 100644
	--- a/src/solver/sparse_matrix.cc
	+++ b/src/solver/sparse_matrix.cc
	@@ -1,82 +1,82 @@
	/**
	* @file sparse_matrix.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Tue May 26 2020
	*
	* @brief implementation of the SparseMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "dof_manager.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SparseMatrix::SparseMatrix(DOFManager & dof_manager,
	const MatrixType & matrix_type, const ID & id)
	: id(id), _dof_manager(dof_manager), matrix_type(matrix_type),
	size_(dof_manager.getSystemSize()), nb_non_zero(0) {
	AKANTU_DEBUG_IN();

	const auto & comm = _dof_manager.getCommunicator();
	this->nb_proc = comm.getNbProc();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix::SparseMatrix(const SparseMatrix & matrix, const ID & id)
	: SparseMatrix(matrix._dof_manager, matrix.matrix_type, id) {
	nb_non_zero = matrix.nb_non_zero;
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix::~SparseMatrix() = default;

	// /* --------------------------------------------------------------------------
	// / Array<Real> & operator=(SolverVector & vect, const SparseMatrix & mat) {
	// Array<Real> tmp(vect.size(), vect.getNbComponent(), 0.);
	// mat.matVecMul(vect, tmp);

	// vect.copy(tmp);
	// return vect;
	// }

	/* -------------------------------------------------------------------------- */
	void SparseMatrix::add(const SparseMatrix & B, Real alpha) {
	B.addMeTo(*this, alpha);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/solver/sparse_matrix.hh b/src/solver/sparse_matrix.hh
	index 4720a2ac8..3c27783fc 100644
	--- a/src/solver/sparse_matrix.hh
	+++ b/src/solver/sparse_matrix.hh
	@@ -1,170 +1,168 @@
	/**
	* @file sparse_matrix.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Wed Sep 16 2020
	*
	* @brief sparse matrix storage class (distributed assembled matrix)
	* This is a COO format (Coordinate List)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SPARSE_MATRIX_HH_
	#define AKANTU_SPARSE_MATRIX_HH_

	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class DOFManager;
	class TermsToAssemble;
	class SolverVector;
	} // namespace akantu

	namespace akantu {

	class SparseMatrix {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SparseMatrix(DOFManager & dof_manager, const MatrixType & matrix_type,
	const ID & id = "sparse_matrix");

	SparseMatrix(const SparseMatrix & matrix, const ID & id = "sparse_matrix");

	virtual ~SparseMatrix();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// remove the existing profile
	virtual void clearProfile();

	/// set the matrix to 0
	virtual void set(Real val) = 0;

	virtual void zero() { this->set(0); }

	/// add a non-zero element to the profile
	virtual UInt add(UInt i, UInt j) = 0;

	/// assemble a local matrix in the sparse one
	virtual void add(UInt i, UInt j, Real value) = 0;

	/// save the profil in a file using the MatrixMarket file format
	virtual void saveProfile(const std::string & /* filename */) const {
	AKANTU_TO_IMPLEMENT();
	}

	/// save the matrix in a file using the MatrixMarket file format
	virtual void saveMatrix(const std::string & /* filename */) const {
	AKANTU_TO_IMPLEMENT();
	};

	/// multiply the matrix by a coefficient
	virtual void mul(Real alpha) = 0;

	/// add matrices
	virtual void add(const SparseMatrix & B, Real alpha = 1.);

	/// Equivalent of *gemv in blas
	virtual void matVecMul(const SolverVector & x, SolverVector & y,
	Real alpha = 1., Real beta = 0.) const = 0;

	/// modify the matrix to "remove" the blocked dof
	virtual void applyBoundary(Real block_val = 1.) = 0;

	/// copy the profile of another matrix
	virtual void copyProfile(const SparseMatrix & other) = 0;

	/// operator *=
	SparseMatrix & operator*=(Real alpha) {
	this->mul(alpha);
	return *this;
	}

	protected:
	/// This is the revert of add \f[B += \alpha * *this\f];
	virtual void addMeTo(SparseMatrix & B, Real alpha) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// return the values at potition i, j
	virtual inline Real operator()(UInt /i/, UInt /j/) const {
	AKANTU_TO_IMPLEMENT();
	}
	/// return the values at potition i, j
	virtual inline Real & operator()(UInt /i/, UInt /j/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// return the minimum value
	- virtual inline Real min() {
	- AKANTU_TO_IMPLEMENT();
	- }
	+ virtual inline Real min() { AKANTU_TO_IMPLEMENT(); }

	AKANTU_GET_MACRO(NbNonZero, nb_non_zero, UInt);
	UInt size() const { return size_; }
	AKANTU_GET_MACRO(MatrixType, matrix_type, const MatrixType &);

	virtual UInt getRelease() const = 0;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	ID id;

	/// Underlying dof manager
	DOFManager & _dof_manager;

	/// sparce matrix type
	MatrixType matrix_type;

	/// Size of the matrix
	UInt size_;

	/// number of processors
	UInt nb_proc;

	/// number of non zero element
	UInt nb_non_zero;
	};

	// Array<Real> & operator*=(Array<Real> & vect, const SparseMatrix & mat);

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix_inline_impl.hh"

	#endif /* AKANTU_SPARSE_MATRIX_HH_ */
	diff --git a/src/solver/sparse_matrix_aij.cc b/src/solver/sparse_matrix_aij.cc
	index 317045647..cb4db6eb2 100644
	--- a/src/solver/sparse_matrix_aij.cc
	+++ b/src/solver/sparse_matrix_aij.cc
	@@ -1,302 +1,301 @@
	/**
	* @file sparse_matrix_aij.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Aug 21 2015
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of the AIJ sparse matrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix_aij.hh"
	#include "aka_iterators.hh"
	#include "dof_manager_default.hh"
	#include "dof_synchronizer.hh"
	#include "solver_vector_default.hh"
	#include "terms_to_assemble.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SparseMatrixAIJ::SparseMatrixAIJ(DOFManagerDefault & dof_manager,
	const MatrixType & matrix_type, const ID & id)
	: SparseMatrix(dof_manager, matrix_type, id), dof_manager(dof_manager),
	irn(0, 1, id + ":irn"), jcn(0, 1, id + ":jcn"), a(0, 1, id + ":a") {}

	/* -------------------------------------------------------------------------- */
	SparseMatrixAIJ::SparseMatrixAIJ(const SparseMatrixAIJ & matrix, const ID & id)
	: SparseMatrix(matrix, id), dof_manager(matrix.dof_manager),
	irn(matrix.irn, id + ":irn"), jcn(matrix.jcn, id + ":jcn"),
	a(matrix.a, id + ":a") {}

	/* -------------------------------------------------------------------------- */
	SparseMatrixAIJ::~SparseMatrixAIJ() = default;

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::applyBoundary(Real block_val) {
	AKANTU_DEBUG_IN();

	const auto & blocked_dofs = this->dof_manager.getGlobalBlockedDOFs();
	auto begin = blocked_dofs.begin();
	auto end = blocked_dofs.end();

	auto is_blocked = [&](auto && i) -> bool {
	auto il = this->dof_manager.globalToLocalEquationNumber(i);
	return std::binary_search(begin, end, il);
	};

	for (auto && ij_a : zip(irn, jcn, a)) {
	UInt ni = std::get<0>(ij_a) - 1;
	UInt nj = std::get<1>(ij_a) - 1;

	if (is_blocked(ni) or is_blocked(nj)) {

	std::get<2>(ij_a) =
	- std::get<0>(ij_a) != std::get<1>(ij_a)
	- ? 0.
	- : this->dof_manager.isLocalOrMasterDOF(
	- this->dof_manager.globalToLocalEquationNumber(ni))
	- ? block_val
	- : 0.;
	+ std::get<0>(ij_a) != std::get<1>(ij_a) ? 0.
	+ : this->dof_manager.isLocalOrMasterDOF(
	+ this->dof_manager.globalToLocalEquationNumber(ni))
	+ ? block_val
	+ : 0.;
	}
	}

	this->value_release++;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::saveProfile(const std::string & filename) const {
	AKANTU_DEBUG_IN();

	std::ofstream outfile;
	outfile.open(filename.c_str());

	UInt m = this->size_;

	auto & comm = dof_manager.getCommunicator();

	// write header
	if (comm.whoAmI() == 0) {

	outfile << "%%MatrixMarket matrix coordinate pattern";
	if (this->matrix_type == _symmetric) {
	outfile << " symmetric";
	} else {
	outfile << " general";
	}
	outfile << std::endl;
	outfile << m << " " << m << " " << this->nb_non_zero << std::endl;
	}

	for (auto p : arange(comm.getNbProc())) {
	// write content
	if (comm.whoAmI() == p) {
	for (UInt i = 0; i < this->nb_non_zero; ++i) {
	outfile << this->irn.storage()[i] << " " << this->jcn.storage()[i]
	<< " 1" << std::endl;
	}
	}
	comm.barrier();
	}

	outfile.close();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::saveMatrix(const std::string & filename) const {
	AKANTU_DEBUG_IN();
	auto & comm = dof_manager.getCommunicator();

	// open and set the properties of the stream
	std::ofstream outfile;

	if (0 == comm.whoAmI()) {
	outfile.open(filename.c_str());
	} else {
	outfile.open(filename.c_str(), std::ios_base::app);
	}

	outfile.precision(std::numeric_limits<Real>::digits10);
	// write header
	decltype(nb_non_zero) nnz = this->nb_non_zero;
	comm.allReduce(nnz);

	if (comm.whoAmI() == 0) {
	outfile << "%%MatrixMarket matrix coordinate real";
	if (this->matrix_type == _symmetric) {
	outfile << " symmetric";
	} else {
	outfile << " general";
	}
	outfile << std::endl;
	outfile << this->size_ << " " << this->size_ << " " << nnz << std::endl;
	}

	for (auto p : arange(comm.getNbProc())) {
	// write content
	if (comm.whoAmI() == p) {
	for (UInt i = 0; i < this->nb_non_zero; ++i) {
	outfile << this->irn(i) << " " << this->jcn(i) << " " << this->a(i)
	<< std::endl;
	}
	}
	comm.barrier();
	}
	// time to end
	outfile.close();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::matVecMul(const Array<Real> & x, Array<Real> & y,
	Real alpha, Real beta) const {
	AKANTU_DEBUG_IN();

	y *= beta;

	auto i_it = this->irn.begin();
	auto j_it = this->jcn.begin();
	auto a_it = this->a.begin();
	auto a_end = this->a.end();
	auto x_it = x.begin_reinterpret(x.size() * x.getNbComponent());
	auto y_it = y.begin_reinterpret(x.size() * x.getNbComponent());

	for (; a_it != a_end; ++i_it, ++j_it, ++a_it) {
	Int i = this->dof_manager.globalToLocalEquationNumber(*i_it - 1);
	Int j = this->dof_manager.globalToLocalEquationNumber(*j_it - 1);
	const Real & A = *a_it;

	y_it[i] += alpha * A * x_it[j];

	if ((this->matrix_type == _symmetric) && (i != j)) {
	y_it[j] += alpha * A * x_it[i];
	}
	}

	if (this->dof_manager.hasSynchronizer()) {
	this->dof_manager.getSynchronizer().reduceSynchronizeArray<AddOperation>(y);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::matVecMul(const SolverVector & _x, SolverVector & _y,
	Real alpha, Real beta) const {
	AKANTU_DEBUG_IN();

	auto && x = aka::as_type<SolverVectorArray>(_x).getVector();
	auto && y = aka::as_type<SolverVectorArray>(_y).getVector();
	this->matVecMul(x, y, alpha, beta);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::copyContent(const SparseMatrix & matrix) {
	AKANTU_DEBUG_IN();
	const auto & mat = aka::as_type<SparseMatrixAIJ>(matrix);
	AKANTU_DEBUG_ASSERT(nb_non_zero == mat.getNbNonZero(),
	"The to matrix don't have the same profiles");
	memcpy(a.storage(), mat.getA().storage(), nb_non_zero * sizeof(Real));

	this->value_release++;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::copyProfile(const SparseMatrix & other) {
	const auto & A = aka::as_type<SparseMatrixAIJ>(other);

	SparseMatrix::clearProfile();

	this->irn.copy(A.irn);
	this->jcn.copy(A.jcn);

	this->irn_jcn_k.clear();

	UInt i;
	UInt j;
	UInt k;
	for (auto && data : enumerate(irn, jcn)) {
	std::tie(k, i, j) = data;

	this->irn_jcn_k[this->key(i - 1, j - 1)] = k;
	}

	this->nb_non_zero = this->irn.size();
	this->a.resize(this->nb_non_zero);

	this->a.set(0.);
	this->size_ = A.size_;

	this->profile_release = A.profile_release;
	this->value_release++;
	}

	/* -------------------------------------------------------------------------- */
	template <class MatrixType>
	void SparseMatrixAIJ::addMeToTemplated(MatrixType & B, Real alpha) const {
	UInt i;
	UInt j;
	Real A_ij;
	for (auto && tuple : zip(irn, jcn, a)) {
	std::tie(i, j, A_ij) = tuple;
	B.add(i - 1, j - 1, alpha * A_ij);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::addMeTo(SparseMatrix & B, Real alpha) const {

	if (aka::is_of_type<SparseMatrixAIJ>(B)) {
	this->addMeToTemplated<SparseMatrixAIJ>(aka::as_type<SparseMatrixAIJ>(B),
	alpha);
	} else {
	// this->addMeToTemplated<SparseMatrix>(*this, alpha);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::mul(Real alpha) {
	this->a *= alpha;
	this->value_release++;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixAIJ::set(Real val) {
	a.set(val);

	this->value_release++;
	}

	} // namespace akantu
	diff --git a/src/solver/sparse_matrix_aij.hh b/src/solver/sparse_matrix_aij.hh
	index 3a7e143ff..ebcbd1dee 100644
	--- a/src/solver/sparse_matrix_aij.hh
	+++ b/src/solver/sparse_matrix_aij.hh
	@@ -1,204 +1,203 @@
	/**
	* @file sparse_matrix_aij.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Wed Sep 16 2020
	*
	* @brief AIJ implementation of the SparseMatrix (this the format used by
	* Mumps)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SPARSE_MATRIX_AIJ_HH_
	#define AKANTU_SPARSE_MATRIX_AIJ_HH_

	namespace akantu {
	class DOFManagerDefault;
	class TermsToAssemble;
	} // namespace akantu

	namespace akantu {

	class SparseMatrixAIJ : public SparseMatrix {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SparseMatrixAIJ(DOFManagerDefault & dof_manager,
	const MatrixType & matrix_type,
	const ID & id = "sparse_matrix_aij");

	SparseMatrixAIJ(const SparseMatrixAIJ & matrix,
	const ID & id = "sparse_matrix_aij");

	~SparseMatrixAIJ() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// remove the existing profile
	inline void clearProfile() override;

	/// add a non-zero element
	inline UInt add(UInt i, UInt j) override;

	/// set the matrix to 0
	void set(Real val) override;

	/// assemble a local matrix in the sparse one
	inline void add(UInt i, UInt j, Real value) override;

	/// add a block of values
	inline void addValues(const Vector<Int> & is, const Vector<Int> & js,
	const Matrix<Real> & values, MatrixType values_type);

	/// set the size of the matrix
	void resize(UInt size) { this->size_ = size; }

	/// modify the matrix to "remove" the blocked dof
	void applyBoundary(Real block_val = 1.) override;

	/// save the profil in a file using the MatrixMarket file format
	void saveProfile(const std::string & filename) const override;

	/// save the matrix in a file using the MatrixMarket file format
	void saveMatrix(const std::string & filename) const override;

	/// copy assuming the profile are the same
	virtual void copyContent(const SparseMatrix & matrix);

	/// multiply the matrix by a scalar
	void mul(Real alpha) override;

	/// Equivalent of *gemv in blas
	void matVecMul(const SolverVector & x, SolverVector & y, Real alpha = 1.,
	Real beta = 0.) const override;

	void matVecMul(const Array<Real> & x, Array<Real> & y, Real alpha = 1.,
	Real beta = 0.) const;

	/// copy the profile of another matrix
	void copyProfile(const SparseMatrix & other) override;

	/* ------------------------------------------------------------------------ */
	/// accessor to A_{ij} - if (i, j) not present it returns 0
	inline Real operator()(UInt i, UInt j) const override;

	/// accessor to A_{ij} - if (i, j) not present it fails, (i, j) should be
	/// first added to the profile
	inline Real & operator()(UInt i, UInt j) override;

	/// accessor to get the minimum value of A_{ij}
	inline Real min() override;

	-
	protected:
	void addMeTo(SparseMatrix & B, Real alpha) const override;

	inline void addSymmetricValuesToSymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values);
	inline void addUnsymmetricValuesToSymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values);
	inline void addValuesToUnsymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values);

	private:
	/// This is just to inline the addToMatrix function
	template <class MatrixType>
	void addMeToTemplated(MatrixType & B, Real alpha) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(IRN, irn, const Array<Int> &);

	AKANTU_GET_MACRO(JCN, jcn, const Array<Int> &);

	AKANTU_GET_MACRO(A, a, const Array<Real> &);

	/// The release changes at each call of a function that changes the profile,
	/// it in increasing but could overflow so it should be checked as
	/// (my_release != release) and not as (my_release < release)
	AKANTU_GET_MACRO(ProfileRelease, profile_release, UInt);
	AKANTU_GET_MACRO(ValueRelease, value_release, UInt);
	UInt getRelease() const override { return value_release; }
	-
	+
	protected:
	using KeyCOO = std::pair<UInt, UInt>;
	using coordinate_list_map = std::unordered_map<KeyCOO, UInt>;

	/// get the pair corresponding to (i, j)
	inline KeyCOO key(UInt i, UInt j) const {
	if (this->matrix_type == _symmetric && (i > j)) {
	return std::make_pair(j, i);
	}
	return std::make_pair(i, j);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	DOFManagerDefault & dof_manager;

	/// row indexes
	Array<Int> irn;

	/// column indexes
	Array<Int> jcn;

	/// values : A[k] = Matrix[irn[k]][jcn[k]]
	Array<Real> a;

	/// Profile release
	UInt profile_release{1};

	/// Value release
	UInt value_release{1};

	/// map for (i, j) -> k correspondence
	coordinate_list_map irn_jcn_k;
	};

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix_aij_inline_impl.hh"

	#endif /* AKANTU_SPARSE_MATRIX_AIJ_HH_ */
	diff --git a/src/solver/sparse_matrix_aij_inline_impl.hh b/src/solver/sparse_matrix_aij_inline_impl.hh
	index e381871fb..95a3e7a81 100644
	--- a/src/solver/sparse_matrix_aij_inline_impl.hh
	+++ b/src/solver/sparse_matrix_aij_inline_impl.hh
	@@ -1,203 +1,201 @@
	/**
	* @file sparse_matrix_aij_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Aug 21 2015
	* @date last modification: Tue Mar 31 2020
	*
	* @brief Implementation of inline functions of SparseMatrixAIJ
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix_aij.hh"

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_SPARSE_MATRIX_AIJ_INLINE_IMPL_HH_
	#define AKANTU_SPARSE_MATRIX_AIJ_INLINE_IMPL_HH_

	namespace akantu {

	inline UInt SparseMatrixAIJ::add(UInt i, UInt j) {
	KeyCOO jcn_irn = this->key(i, j);

	auto it = this->irn_jcn_k.find(jcn_irn);

	if (!(it == this->irn_jcn_k.end())) {
	return it->second;
	}

	if (i + 1 > this->size_) {
	this->size_ = i + 1;
	}
	if (j + 1 > this->size_) {
	this->size_ = j + 1;
	}

	this->irn.push_back(i + 1);
	this->jcn.push_back(j + 1);
	this->a.push_back(0.);

	this->irn_jcn_k[jcn_irn] = this->nb_non_zero;

	(this->nb_non_zero)++;

	this->profile_release++;
	this->value_release++;

	return (this->nb_non_zero - 1);
	}

	/* -------------------------------------------------------------------------- */
	inline void SparseMatrixAIJ::clearProfile() {
	SparseMatrix::clearProfile();

	this->irn_jcn_k.clear();

	this->irn.clear();
	this->jcn.clear();
	this->a.clear();

	this->size_ = 0;
	this->nb_non_zero = 0;

	this->profile_release++;
	this->value_release++;
	}

	/* -------------------------------------------------------------------------- */
	inline void SparseMatrixAIJ::add(UInt i, UInt j, Real value) {
	UInt idx = this->add(i, j);

	this->a(idx) += value;

	this->value_release++;
	}

	/* -------------------------------------------------------------------------- */
	inline Real SparseMatrixAIJ::operator()(UInt i, UInt j) const {
	KeyCOO jcn_irn = this->key(i, j);
	auto irn_jcn_k_it = this->irn_jcn_k.find(jcn_irn);

	if (irn_jcn_k_it == this->irn_jcn_k.end()) {
	return 0.;
	}
	return this->a(irn_jcn_k_it->second);
	}

	/* -------------------------------------------------------------------------- */
	inline Real & SparseMatrixAIJ::operator()(UInt i, UInt j) {
	KeyCOO jcn_irn = this->key(i, j);
	auto irn_jcn_k_it = this->irn_jcn_k.find(jcn_irn);
	AKANTU_DEBUG_ASSERT(irn_jcn_k_it != this->irn_jcn_k.end(),
	"Couple (i,j) = (" << i << "," << j
	<< ") does not exist in the profile");

	// it may change the profile so it is considered as a change
	this->value_release++;

	return this->a(irn_jcn_k_it->second);
	}

	/* -------------------------------------------------------------------------- */
	inline void
	SparseMatrixAIJ::addSymmetricValuesToSymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values) {
	for (UInt i = 0; i < values.rows(); ++i) {
	UInt c_irn = is(i);
	if (c_irn < size_) {
	for (UInt j = i; j < values.cols(); ++j) {
	UInt c_jcn = js(j);
	if (c_jcn < size_) {
	operator()(c_irn, c_jcn) += values(i, j);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	SparseMatrixAIJ::addUnsymmetricValuesToSymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values) {
	for (UInt i = 0; i < values.rows(); ++i) {
	UInt c_irn = is(i);
	if (c_irn < size_) {
	for (UInt j = 0; j < values.cols(); ++j) {
	UInt c_jcn = js(j);
	if (c_jcn < size_) {
	if (c_jcn >= c_irn) {
	operator()(c_irn, c_jcn) += values(i, j);
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void
	SparseMatrixAIJ::addValuesToUnsymmetric(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values) {
	for (UInt i = 0; i < values.rows(); ++i) {
	UInt c_irn = is(i);
	if (c_irn < size_) {
	for (UInt j = 0; j < values.cols(); ++j) {
	UInt c_jcn = js(j);
	if (c_jcn < size_) {
	operator()(c_irn, c_jcn) += values(i, j);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void SparseMatrixAIJ::addValues(const Vector<Int> & is,
	const Vector<Int> & js,
	const Matrix<Real> & values,
	MatrixType values_type) {
	if (getMatrixType() == _symmetric) {
	if (values_type == _symmetric) {
	this->addSymmetricValuesToSymmetric(is, js, values);
	} else {
	this->addUnsymmetricValuesToSymmetric(is, js, values);
	}
	} else {
	this->addValuesToUnsymmetric(is, js, values);
	}
	}

	-
	/* -------------------------------------------------------------------------- */
	inline Real SparseMatrixAIJ::min() {
	return *std::min(this->a.begin(), this->a.end());
	}

	-
	} // namespace akantu

	#endif /* AKANTU_SPARSE_MATRIX_AIJ_INLINE_IMPL_HH_ */
	diff --git a/src/solver/sparse_matrix_inline_impl.hh b/src/solver/sparse_matrix_inline_impl.hh
	index fbdc8fc75..536f5a10d 100644
	--- a/src/solver/sparse_matrix_inline_impl.hh
	+++ b/src/solver/sparse_matrix_inline_impl.hh
	@@ -1,37 +1,37 @@
	/**
	* @file sparse_matrix_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Jan 15 2016
	*
	* @brief implementation of inline methods of the SparseMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	inline void SparseMatrix::clearProfile() { this->nb_non_zero = 0; }

	} // namespace akantu
	diff --git a/src/solver/sparse_matrix_petsc.cc b/src/solver/sparse_matrix_petsc.cc
	index 4170d01c4..a6ccc79cc 100644
	--- a/src/solver/sparse_matrix_petsc.cc
	+++ b/src/solver/sparse_matrix_petsc.cc
	@@ -1,289 +1,290 @@
	/**
	* @file sparse_matrix_petsc.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of PETSc matrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix_petsc.hh"
	#include "dof_manager_petsc.hh"
	#include "mpi_communicator_data.hh"
	#include "solver_vector_petsc.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SparseMatrixPETSc::SparseMatrixPETSc(DOFManagerPETSc & dof_manager,
	const MatrixType & matrix_type,
	const ID & id)
	: SparseMatrix(dof_manager, matrix_type, id), dof_manager(dof_manager) {
	AKANTU_DEBUG_IN();

	auto && mpi_comm = dof_manager.getMPIComm();

	PETSc_call(MatCreate, mpi_comm, &mat);
	detail::PETScSetName(mat, id);

	resize();

	PETSc_call(MatSetFromOptions, mat);

	PETSc_call(MatSetUp, mat);

	PETSc_call(MatSetOption, mat, MAT_ROW_ORIENTED, PETSC_TRUE);
	PETSc_call(MatSetOption, mat, MAT_NEW_NONZERO_LOCATIONS, PETSC_TRUE);

	if (matrix_type == _symmetric) {
	PETSc_call(MatSetOption, mat, MAT_SYMMETRIC, PETSC_TRUE);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrixPETSc::SparseMatrixPETSc(const SparseMatrixPETSc & matrix,
	const ID & id)
	: SparseMatrix(matrix, id), dof_manager(matrix.dof_manager) {
	PETSc_call(MatDuplicate, matrix.mat, MAT_COPY_VALUES, &mat);
	detail::PETScSetName(mat, id);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrixPETSc::~SparseMatrixPETSc() {
	AKANTU_DEBUG_IN();

	if (mat != nullptr) {
	PETSc_call(MatDestroy, &mat);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::resize() {
	auto local_size = dof_manager.getPureLocalSystemSize();
	PETSc_call(MatSetSizes, mat, local_size, local_size, size_, size_);

	auto & is_ltog_mapping = dof_manager.getISLocalToGlobalMapping();
	PETSc_call(MatSetLocalToGlobalMapping, mat, is_ltog_mapping, is_ltog_mapping);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Method to save the nonzero pattern and the values stored at each position
	* @param filename name of the file in which the information will be stored
	*/
	void SparseMatrixPETSc::saveMatrix(const std::string & filename) const {
	AKANTU_DEBUG_IN();

	auto && mpi_comm = dof_manager.getMPIComm();

	/// create Petsc viewer
	PetscViewer viewer;
	PETSc_call(PetscViewerASCIIOpen, mpi_comm, filename.c_str(), &viewer);
	PETSc_call(PetscViewerPushFormat, viewer, PETSC_VIEWER_ASCII_MATRIXMARKET);
	PETSc_call(MatView, mat, viewer);
	PETSc_call(PetscViewerPopFormat, viewer);
	PETSc_call(PetscViewerDestroy, &viewer);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/// Equivalent of *gemv in blas
	void SparseMatrixPETSc::matVecMul(const SolverVector & _x, SolverVector & _y,
	Real alpha, Real beta) const {
	const auto & x = aka::as_type<SolverVectorPETSc>(_x);
	auto & y = aka::as_type<SolverVectorPETSc>(_y);

	// y = alpha A x + beta y
	SolverVectorPETSc w(x, this->id + ":tmp");

	// w = A x
	if (release == 0) {
	PETSc_call(VecZeroEntries, w);
	} else {
	PETSc_call(MatMult, mat, x, w);
	}

	if (alpha != 1.) {
	// w = alpha w
	PETSc_call(VecScale, w, alpha);
	}

	// y = w + beta y
	PETSc_call(VecAYPX, y, beta, w);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addMeToImpl(SparseMatrixPETSc & B, Real alpha) const {
	PETSc_call(MatAXPY, B.mat, alpha, mat, SAME_NONZERO_PATTERN);

	B.release++;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addMeTo(SparseMatrix & B, Real alpha) const {
	if (aka::is_of_type<SparseMatrixPETSc>(B)) {
	auto & B_petsc = aka::as_type<SparseMatrixPETSc>(B);
	this->addMeToImpl(B_petsc, alpha);
	} else {
	AKANTU_TO_IMPLEMENT();
	// this->addMeToTemplated<SparseMatrix>(*this, alpha);
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* MatSetValues() generally caches the values. The matrix is ready to
	* use only after MatAssemblyBegin() and MatAssemblyEnd() have been
	* called. (http://www.mcs.anl.gov/petsc/)
	*/
	void SparseMatrixPETSc::applyModifications() {
	this->beginAssembly();
	this->endAssembly();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::beginAssembly() {
	PETSc_call(MatAssemblyBegin, mat, MAT_FINAL_ASSEMBLY);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::endAssembly() {
	PETSc_call(MatAssemblyEnd, mat, MAT_FINAL_ASSEMBLY);
	PETSc_call(MatSetOption, mat, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);

	this->release++;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::copyProfile(const SparseMatrix & other) {
	const auto & A = aka::as_type<SparseMatrixPETSc>(other);

	MatDestroy(&mat);
	MatDuplicate(A.mat, MAT_DO_NOT_COPY_VALUES, &mat);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::applyBoundary(Real block_val) {
	AKANTU_DEBUG_IN();

	const auto & blocked_dofs = this->dof_manager.getGlobalBlockedDOFs();
	// std::vector<PetscInt> rows;
	// for (auto && data : enumerate(blocked)) {
	// if (std::get<1>(data)) {
	// rows.push_back(std::get<0>(data));
	// }
	// }
	// applyModifications();

	static int c = 0;

	saveMatrix("before_blocked_" + std::to_string(c) + ".mtx");

	PETSc_call(MatZeroRowsColumnsLocal, mat, blocked_dofs.size(),
	blocked_dofs.storage(), block_val, nullptr, nullptr);

	saveMatrix("after_blocked_" + std::to_string(c) + ".mtx");
	++c;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::mul(Real alpha) {
	PETSc_call(MatScale, mat, alpha);
	this->release++;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::zero() {
	PETSc_call(MatZeroEntries, mat);
	this->release++;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::clearProfile() {
	SparseMatrix::clearProfile();
	PETSc_call(MatResetPreallocation, mat);
	PETSc_call(MatSetOption, mat, MAT_NEW_NONZERO_LOCATIONS, PETSC_TRUE);
	// PETSc_call(MatSetOption, MAT_KEEP_NONZERO_PATTERN, PETSC_TRUE);
	// PETSc_call(MatSetOption, MAT_NEW_NONZERO_ALLOCATIONS, PETSC_TRUE);
	// PETSc_call(MatSetOption, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE);

	this->zero();
	}

	/* -------------------------------------------------------------------------- */
	UInt SparseMatrixPETSc::add(UInt i, UInt j) {
	PETSc_call(MatSetValue, mat, i, j, 0, ADD_VALUES);
	return 0;
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::add(UInt i, UInt j, Real val) {
	PETSc_call(MatSetValue, mat, i, j, val, ADD_VALUES);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addLocal(UInt i, UInt j) {
	PETSc_call(MatSetValueLocal, mat, i, j, 0, ADD_VALUES);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addLocal(UInt i, UInt j, Real val) {
	PETSc_call(MatSetValueLocal, mat, i, j, val, ADD_VALUES);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addLocal(const Vector<Int> & rows,
	const Vector<Int> & cols,
	const Matrix<Real> & values) {
	PETSc_call(MatSetValuesLocal, mat, rows.size(), rows.storage(), cols.size(),
	cols.storage(), values.storage(), ADD_VALUES);
	}

	/* -------------------------------------------------------------------------- */
	void SparseMatrixPETSc::addValues(const Vector<Int> & rows,
	const Vector<Int> & cols,
	- const Matrix<Real> & values, MatrixType values_type) {
	+ const Matrix<Real> & values,
	+ MatrixType values_type) {
	if (values_type == _unsymmetric and matrix_type == _symmetric) {
	PETSc_call(MatSetOption, mat, MAT_SYMMETRIC, PETSC_FALSE);
	PETSc_call(MatSetOption, mat, MAT_STRUCTURALLY_SYMMETRIC, PETSC_FALSE);
	}

	PETSc_call(MatSetValues, mat, rows.size(), rows.storage(), cols.size(),
	cols.storage(), values.storage(), ADD_VALUES);
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/solver/sparse_matrix_petsc.hh b/src/solver/sparse_matrix_petsc.hh
	index e7ff7b21d..2d20d85eb 100644
	--- a/src/solver/sparse_matrix_petsc.hh
	+++ b/src/solver/sparse_matrix_petsc.hh
	@@ -1,162 +1,160 @@
	/**
	* @file sparse_matrix_petsc.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Interface for PETSc matrices
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PETSC_MATRIX_HH_
	#define AKANTU_PETSC_MATRIX_HH_

	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */
	#include <petscmat.h>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class DOFManagerPETSc;
	}

	namespace akantu {

	class SparseMatrixPETSc : public SparseMatrix {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SparseMatrixPETSc(DOFManagerPETSc & dof_manager,
	const MatrixType & matrix_type,
	const ID & id = "sparse_matrix_petsc");

	SparseMatrixPETSc(const SparseMatrixPETSc & matrix,
	const ID & id = "sparse_matrix_petsc");

	~SparseMatrixPETSc() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// set the matrix to 0
	void zero() override;
	- void set(Real /val/) override {
	- AKANTU_TO_IMPLEMENT();
	- }
	+ void set(Real /val/) override { AKANTU_TO_IMPLEMENT(); }
	void clearProfile() override;

	/// add a non-zero element to the profile
	UInt add(UInt i, UInt j) override;

	/// assemble a local matrix in the sparse one
	void add(UInt i, UInt j, Real value) override;

	void addLocal(UInt i, UInt j);
	void addLocal(UInt i, UInt j, Real val);

	void addLocal(const Vector<Int> & rows, const Vector<Int> & cols,
	const Matrix<Real> & values);

	/// add a block of values
	void addValues(const Vector<Int> & rows, const Vector<Int> & cols,
	const Matrix<Real> & values, MatrixType values_type);

	/// save the profil in a file using the MatrixMarket file format
	// void saveProfile(__attribute__((unused)) const std::string &) const
	// override {
	// AKANTU_DEBUG_TO_IMPLEMENT();
	// }

	/// save the matrix in a file using the MatrixMarket file format
	void saveMatrix(const std::string & filename) const override;

	/// multiply the matrix by a coefficient
	void mul(Real alpha) override;

	/// Equivalent of *gemv in blas
	void matVecMul(const SolverVector & x, SolverVector & y, Real alpha = 1.,
	Real beta = 0.) const override;

	/// modify the matrix to "remove" the blocked dof
	void applyBoundary(Real block_val = 1.) override;

	/// copy the profile of a matrix
	void copyProfile(const SparseMatrix & other) override;

	void applyModifications();

	void resize();

	protected:
	void addMeTo(SparseMatrix & B, Real alpha) const override;

	/// This is the specific implementation
	void addMeToImpl(SparseMatrixPETSc & B, Real alpha) const;

	void beginAssembly();
	void endAssembly();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// return the values at potition i, j
	inline Real operator()(UInt /i/, UInt /j/) const override {
	AKANTU_TO_IMPLEMENT();
	}
	/// return the values at potition i, j
	inline Real & operator()(UInt /i/, UInt /j/) override {
	AKANTU_TO_IMPLEMENT();
	}

	UInt getRelease() const override { return release; };

	operator Mat &() { return mat; }
	operator const Mat &() const { return mat; }
	AKANTU_GET_MACRO(Mat, mat, const Mat &);
	AKANTU_GET_MACRO_NOT_CONST(Mat, mat, Mat &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	// DOFManagerPETSc that contains the numbering for petsc
	DOFManagerPETSc & dof_manager;

	/// store the PETSc matrix
	Mat mat;

	/// matrix release
	UInt release{0};
	};

	} // namespace akantu

	#endif /* AKANTU_PETSC_MATRIX_HH_ */
	diff --git a/src/solver/sparse_solver.cc b/src/solver/sparse_solver.cc
	index fb3de0afb..cf22ccb2f 100644
	--- a/src/solver/sparse_solver.cc
	+++ b/src/solver/sparse_solver.cc
	@@ -1,85 +1,84 @@
	/**
	* @file sparse_solver.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Tue Feb 02 2016
	*
	* @brief Solver interface class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_solver.hh"
	#include "communicator.hh"
	#include "dof_manager.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SparseSolver::SparseSolver(DOFManager & dof_manager, const ID & matrix_id,
	const ID & id)
	- : Parsable(ParserType::_solver, id),
	- _dof_manager(dof_manager), matrix_id(matrix_id),
	- communicator(dof_manager.getCommunicator()) {
	+ : Parsable(ParserType::_solver, id), _dof_manager(dof_manager),
	+ matrix_id(matrix_id), communicator(dof_manager.getCommunicator()) {
	AKANTU_DEBUG_IN();

	// OK this is fishy...
	this->communicator.registerEventHandler(*this);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SparseSolver::~SparseSolver() {
	AKANTU_DEBUG_IN();

	// this->destroyInternalData();
	this->communicator.unregisterEventHandler(*this);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolver::beforeStaticSolverDestroy() {
	AKANTU_DEBUG_IN();

	try {
	this->destroyInternalData();
	} catch (...) {
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolver::createSynchronizerRegistry() {
	// this->synch_registry = new SynchronizerRegistry(this);
	}

	void SparseSolver::onCommunicatorFinalize() { this->destroyInternalData(); }

	} // namespace akantu
	diff --git a/src/solver/sparse_solver.hh b/src/solver/sparse_solver.hh
	index 7e43ef63a..14547daf4 100644
	--- a/src/solver/sparse_solver.hh
	+++ b/src/solver/sparse_solver.hh
	@@ -1,128 +1,128 @@
	/**
	* @file sparse_solver.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jan 24 2018
	*
	* @brief interface for solvers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator_event_handler.hh"
	#include "parsable.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_HH_
	#define AKANTU_SOLVER_HH_

	namespace akantu {
	enum SolverParallelMethod {
	_not_parallel,
	_fully_distributed,
	_master_slave_distributed
	};

	class DOFManager;
	} // namespace akantu

	namespace akantu {

	class SparseSolver : public Parsable, public CommunicatorEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SparseSolver(DOFManager & dof_manager, const ID & matrix_id,
	const ID & id = "solver");

	~SparseSolver() override;
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// initialize the solver
	virtual void initialize() = 0;

	virtual void analysis(){};

	virtual void factorize(){};

	virtual void solve(){};

	protected:
	virtual void destroyInternalData(){};

	public:
	virtual void beforeStaticSolverDestroy();

	void createSynchronizerRegistry();
	/* ------------------------------------------------------------------------ */
	/* Data Accessor inherited members */
	/* ------------------------------------------------------------------------ */
	public:
	void onCommunicatorFinalize() override;

	// inline virtual UInt getNbDataForDOFs(const Array<UInt> & dofs,
	// SynchronizationTag tag) const;

	// inline virtual void packDOFData(CommunicationBuffer & buffer,
	// const Array<UInt> & dofs,
	// SynchronizationTag tag) const;

	// inline virtual void unpackDOFData(CommunicationBuffer & buffer,
	// const Array<UInt> & dofs,
	// SynchronizationTag tag);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// manager handling the dofs for this SparseMatrix solver
	DOFManager & _dof_manager;

	/// The id of the associated matrix
	ID matrix_id;

	/// How to parallelize the solve
	SolverParallelMethod parallel_method;

	/// Communicator used by the solver
	Communicator & communicator;
	};

	namespace debug {
	class SingularMatrixException : public Exception {
	public:
	SingularMatrixException(const SparseMatrix & matrix)
	: Exception("Solver encountered singular matrix"), matrix(matrix) {}
	const SparseMatrix & matrix;
	};
	} // namespace debug

	} // namespace akantu

	#endif /* AKANTU_SOLVER_HH_ */
	diff --git a/src/solver/sparse_solver_inline_impl.hh b/src/solver/sparse_solver_inline_impl.hh
	index 6ee1343ca..f71d17fa9 100644
	--- a/src/solver/sparse_solver_inline_impl.hh
	+++ b/src/solver/sparse_solver_inline_impl.hh
	@@ -1,88 +1,88 @@
	/**
	* @file sparse_solver_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Sun Dec 30 2018
	*
	* @brief implementation of solver inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	// inline UInt Solver::getNbDataForDOFs(const Array<UInt> & dofs,
	// SynchronizationTag tag) const {
	// AKANTU_DEBUG_IN();

	// UInt size = 0;

	// switch(tag) {
	// case SynchronizationTag::_solver_solution: {
	// size += dofs.size() * sizeof(Real);
	// break;
	// }
	// default: { }
	// }

	// AKANTU_DEBUG_OUT();
	// return size;
	// }

	// /* --------------------------------------------------------------------------
	// */
	// inline void Solver::packDOFData(CommunicationBuffer & buffer,
	// const Array<UInt> & dofs,
	// SynchronizationTag tag) const {
	// AKANTU_DEBUG_IN();

	// switch(tag) {
	// case SynchronizationTag::_solver_solution: {
	// packDOFDataHelper(*solution, buffer, dofs);
	// break;
	// }
	// default: {
	// }
	// }

	// AKANTU_DEBUG_OUT();
	// }

	// /* --------------------------------------------------------------------------
	// */
	// inline void Solver::unpackDOFData(CommunicationBuffer & buffer,
	// const Array<UInt> & dofs,
	// SynchronizationTag tag) {
	// AKANTU_DEBUG_IN();

	// switch(tag) {
	// case SynchronizationTag::_solver_solution: {
	// unpackDOFDataHelper(*solution, buffer, dofs);
	// break;
	// }
	// default: {
	// }
	// }

	// AKANTU_DEBUG_OUT();
	// }
	diff --git a/src/solver/sparse_solver_mumps.cc b/src/solver/sparse_solver_mumps.cc
	index 2e38531bd..45a4632e1 100644
	--- a/src/solver/sparse_solver_mumps.cc
	+++ b/src/solver/sparse_solver_mumps.cc
	@@ -1,398 +1,398 @@
	/**
	* @file sparse_solver_mumps.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Dec 13 2010
	* @date last modification: Wed Sep 02 2020
	*
	* @brief implem of SparseSolverMumps class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dof_manager_default.hh"
	#include "dof_synchronizer.hh"
	#include "solver_vector_default.hh"
	#include "sparse_matrix_aij.hh"
	#if defined(AKANTU_USE_MPI)
	#include "mpi_communicator_data.hh"
	#endif
	#include "sparse_solver_mumps.hh"
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	// static std::ostream & operator <<(std::ostream & stream, const DMUMPS_STRUC_C
	// & _this) {
	// stream << "DMUMPS Data [" << std::endl;
	// stream << " + job : " << _this.job << std::endl;
	// stream << " + par : " << _this.par << std::endl;
	// stream << " + sym : " << _this.sym << std::endl;
	// stream << " + comm_fortran : " << _this.comm_fortran << std::endl;
	// stream << " + nz : " << _this.nz << std::endl;
	// stream << " + irn : " << _this.irn << std::endl;
	// stream << " + jcn : " << _this.jcn << std::endl;
	// stream << " + nz_loc : " << _this.nz_loc << std::endl;
	// stream << " + irn_loc : " << _this.irn_loc << std::endl;
	// stream << " + jcn_loc : " << _this.jcn_loc << std::endl;
	// stream << "]";
	// return stream;
	// }

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SparseSolverMumps::SparseSolverMumps(DOFManagerDefault & dof_manager,
	const ID & matrix_id, const ID & id)
	- : SparseSolver(dof_manager, matrix_id, id),
	- dof_manager(dof_manager), master_rhs_solution(0, 1) {
	+ : SparseSolver(dof_manager, matrix_id, id), dof_manager(dof_manager),
	+ master_rhs_solution(0, 1) {
	AKANTU_DEBUG_IN();

	this->prank = communicator.whoAmI();

	#ifdef AKANTU_USE_MPI
	this->parallel_method = _fully_distributed;
	#else // AKANTU_USE_MPI
	this->parallel_method = _not_parallel;
	#endif // AKANTU_USE_MPI

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SparseSolverMumps::~SparseSolverMumps() {
	AKANTU_DEBUG_IN();

	mumpsDataDestroy();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::mumpsDataDestroy() {
	#ifdef AKANTU_USE_MPI
	int finalized = 0;
	MPI_Finalized(&finalized);
	if (finalized != 0) { // Da fuck !?
	return;
	}
	#endif

	if (this->is_initialized) {
	this->mumps_data.job = _smj_destroy; // destroy
	dmumps_c(&this->mumps_data);
	this->is_initialized = false;
	}
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::destroyInternalData() { mumpsDataDestroy(); }

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::checkInitialized() {
	if (this->is_initialized) {
	return;
	}

	this->initialize();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::setOutputLevel() {
	// Output setup
	icntl(1) = 0; // error output
	icntl(2) = 0; // diagnostics output
	icntl(3) = 0; // information
	icntl(4) = 0;

	#if !defined(AKANTU_NDEBUG)
	DebugLevel dbg_lvl = debug::debugger.getDebugLevel();

	if (AKANTU_DEBUG_TEST(dblDump)) {
	strcpy(this->mumps_data.write_problem, "mumps_matrix.mtx");
	}

	// clang-format off
	icntl(1) = (dbg_lvl >= dblWarning) ? 6 : 0;
	icntl(3) = (dbg_lvl >= dblInfo) ? 6 : 0;
	icntl(2) = (dbg_lvl >= dblTrace) ? 6 : 0;

	icntl(4) =
	dbg_lvl >= dblDump ? 4 :
	dbg_lvl >= dblTrace ? 3 :
	dbg_lvl >= dblInfo ? 2 :
	dbg_lvl >= dblWarning ? 1 :
	0;

	// clang-format on
	#endif
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::initMumpsData() {
	auto & A = dof_manager.getMatrix(matrix_id);

	// Default Scaling
	icntl(8) = 77;

	// Assembled matrix
	icntl(5) = 0;

	/// Default centralized dense second member
	icntl(20) = 0;
	icntl(21) = 0;

	// automatic choice for analysis
	icntl(28) = 0;

	UInt size = A.size();

	if (prank == 0) {
	this->master_rhs_solution.resize(size);
	}

	this->mumps_data.nz_alloc = 0;
	this->mumps_data.n = size;

	switch (this->parallel_method) {
	case _fully_distributed:
	icntl(18) = 3; // fully distributed

	this->mumps_data.nz_loc = A.getNbNonZero();
	this->mumps_data.irn_loc = A.getIRN().storage();
	this->mumps_data.jcn_loc = A.getJCN().storage();

	break;
	case _not_parallel:
	case _master_slave_distributed:
	icntl(18) = 0; // centralized

	if (prank == 0) {
	this->mumps_data.nz = A.getNbNonZero();
	this->mumps_data.irn = A.getIRN().storage();
	this->mumps_data.jcn = A.getJCN().storage();
	} else {
	this->mumps_data.nz = 0;
	this->mumps_data.irn = nullptr;
	this->mumps_data.jcn = nullptr;
	}
	break;
	default:
	AKANTU_ERROR("This case should not happen!!");
	}
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::initialize() {
	AKANTU_DEBUG_IN();

	this->mumps_data.par = 1; // The host is part of computations

	switch (this->parallel_method) {
	case _not_parallel:
	break;
	case _master_slave_distributed:
	this->mumps_data.par = 0; // The host is not part of the computations
	/* FALLTHRU */
	/* [[fallthrough]]; un-comment when compiler will get it */
	case _fully_distributed:
	#ifdef AKANTU_USE_MPI
	const auto & mpi_data =
	aka::as_type<MPICommunicatorData>(communicator.getCommunicatorData());
	MPI_Comm mpi_comm = mpi_data.getMPICommunicator();
	this->mumps_data.comm_fortran = MPI_Comm_c2f(mpi_comm);
	#else
	AKANTU_ERROR(
	"You cannot use parallel method to solve without activating MPI");
	#endif
	break;
	}

	const auto & A = dof_manager.getMatrix(matrix_id);

	this->mumps_data.sym = 2 * static_cast<int>(A.getMatrixType() == _symmetric);
	this->prank = communicator.whoAmI();

	this->setOutputLevel();

	this->mumps_data.job = _smj_initialize; // initialize
	dmumps_c(&this->mumps_data);

	this->setOutputLevel();

	this->is_initialized = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::analysis() {
	AKANTU_DEBUG_IN();

	initMumpsData();

	this->mumps_data.job = _smj_analyze; // analyze
	dmumps_c(&this->mumps_data);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::factorize() {
	AKANTU_DEBUG_IN();

	auto & A = dof_manager.getMatrix(matrix_id);

	if (parallel_method == _fully_distributed) {
	this->mumps_data.a_loc = A.getA().storage();
	} else {
	if (prank == 0) {
	this->mumps_data.a = A.getA().storage();
	}
	}

	this->mumps_data.job = _smj_factorize; // factorize
	dmumps_c(&this->mumps_data);

	this->printError();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::solve(Array<Real> & x, const Array<Real> & b) {
	auto & synch = this->dof_manager.getSynchronizer();

	if (this->prank == 0) {
	this->master_rhs_solution.resize(this->dof_manager.getSystemSize());
	synch.gather(b, this->master_rhs_solution);
	} else {
	synch.gather(b);
	}

	this->solveInternal();

	if (this->prank == 0) {
	synch.scatter(x, this->master_rhs_solution);
	} else {
	synch.scatter(x);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::solve() {
	this->master_rhs_solution.copy(
	aka::as_type<SolverVectorDefault>(this->dof_manager.getResidual())
	.getGlobalVector());

	this->solveInternal();

	aka::as_type<SolverVectorDefault>(this->dof_manager.getSolution())
	.setGlobalVector(this->master_rhs_solution);

	this->dof_manager.splitSolutionPerDOFs();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::solveInternal() {
	AKANTU_DEBUG_IN();

	this->checkInitialized();

	const auto & A = dof_manager.getMatrix(matrix_id);

	this->setOutputLevel();

	if (this->last_profile_release != A.getProfileRelease()) {
	this->analysis();
	this->last_profile_release = A.getProfileRelease();
	}

	if (AKANTU_DEBUG_TEST(dblDump)) {
	A.saveMatrix("solver_mumps" + std::to_string(prank) + ".mtx");
	}

	if (this->last_value_release != A.getValueRelease()) {
	this->factorize();
	this->last_value_release = A.getValueRelease();
	}

	if (prank == 0) {
	this->mumps_data.rhs = this->master_rhs_solution.storage();
	}

	this->mumps_data.job = _smj_solve; // solve
	dmumps_c(&this->mumps_data);

	this->printError();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SparseSolverMumps::printError() {
	Vector<Int> _info_v(2);
	_info_v[0] = info(1); // to get errors
	_info_v[1] = -info(1); // to get warnings
	dof_manager.getCommunicator().allReduce(_info_v, SynchronizerOperation::_min);
	_info_v[1] = -_info_v[1];

	if (_info_v[0] < 0) { // < 0 is an error
	switch (_info_v[0]) {
	case -10: {
	AKANTU_CUSTOM_EXCEPTION(
	debug::SingularMatrixException(dof_manager.getMatrix(matrix_id)));
	break;
	}
	case -9: {
	icntl(14) += 10;
	if (icntl(14) != 90) {
	// std::cout << "Dynamic memory increase of 10%" << std::endl;
	AKANTU_DEBUG_WARNING("MUMPS dynamic memory is insufficient it will be "
	"increased allowed to use 10% more");

	// change releases to force a recompute
	this->last_value_release--;
	this->last_profile_release--;

	this->solve();
	} else {
	AKANTU_ERROR("The MUMPS workarray is too small INFO(2)="
	<< info(2) << "No further increase possible");
	}
	break;
	}
	default:
	AKANTU_ERROR("Error in mumps during solve process, check mumps "
	"user guide INFO(1) = "
	<< _info_v[1]);
	}
	} else if (_info_v[1] > 0) {
	AKANTU_DEBUG_WARNING("Warning in mumps during solve process, check mumps "
	"user guide INFO(1) = "
	<< _info_v[1]);
	}
	}

	} // namespace akantu
	diff --git a/src/solver/sparse_solver_mumps.hh b/src/solver/sparse_solver_mumps.hh
	index 63e78b8e3..3517b3934 100644
	--- a/src/solver/sparse_solver_mumps.hh
	+++ b/src/solver/sparse_solver_mumps.hh
	@@ -1,158 +1,158 @@
	/**
	* @file sparse_solver_mumps.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri May 19 2017
	*
	* @brief Solver class implementation for the mumps solver
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <dmumps_c.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SOLVER_MUMPS_HH_
	#define AKANTU_SOLVER_MUMPS_HH_

	namespace akantu {
	class DOFManagerDefault;
	class SparseMatrixAIJ;
	} // namespace akantu

	namespace akantu {

	class SparseSolverMumps : public SparseSolver {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SparseSolverMumps(DOFManagerDefault & dof_manager, const ID & matrix_id,
	const ID & id = "sparse_solver_mumps");

	~SparseSolverMumps() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// build the profile and do the analysis part
	void initialize() override;

	/// analysis (symbolic facto + permutations)
	void analysis() override;

	/// factorize the matrix
	void factorize() override;

	/// solve the system
	virtual void solve(Array<Real> & x, const Array<Real> & b);

	/// solve using residual and solution from the dof_manager
	void solve() override;

	private:
	/// print the error if any happened in mumps
	void printError();

	/// solve the system with master_rhs_solution as b and x
	void solveInternal();

	/// set internal values;
	void initMumpsData();

	/// set the level of verbosity of mumps based on the debug level of akantu
	void setOutputLevel();

	protected:
	/// de-initialize the internal data
	void destroyInternalData() override;

	/// check if initialized and except if it is not the case
	void checkInitialized();

	private:
	void mumpsDataDestroy();

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	private:
	/// access the control variable
	inline Int & icntl(UInt i) { return mumps_data.icntl[i - 1]; }

	/// access the results info
	inline Int & info(UInt i) { return mumps_data.info[i - 1]; }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// DOFManager used by the Mumps implementation of the SparseSolver
	DOFManagerDefault & dof_manager;

	/// Full right hand side on the master processors and solution after solve
	Array<Real> master_rhs_solution;

	/// mumps data
	DMUMPS_STRUC_C mumps_data;

	/// Rank of the current process
	UInt prank;

	/// matrix release at last solve
	UInt last_profile_release{UInt(-1)};

	/// matrix release at last solve
	UInt last_value_release{UInt(-1)};

	/// check if the solver data are initialized
	bool is_initialized{false};

	/* ------------------------------------------------------------------------ */
	/* Local types */
	/* ------------------------------------------------------------------------ */
	private:
	SolverParallelMethod parallel_method;

	// bool rhs_is_local;

	enum SolverMumpsJob {
	_smj_initialize = -1,
	_smj_analyze = 1,
	_smj_factorize = 2,
	_smj_solve = 3,
	_smj_analyze_factorize = 4,
	_smj_factorize_solve = 5,
	_smj_complete = 6, // analyze, factorize, solve
	_smj_destroy = -2
	};
	};

	} // namespace akantu

	#endif /* AKANTU_SOLVER_MUMPS_HH_ */
	diff --git a/src/solver/terms_to_assemble.hh b/src/solver/terms_to_assemble.hh
	index 5964a9c41..26e29db38 100644
	--- a/src/solver/terms_to_assemble.hh
	+++ b/src/solver/terms_to_assemble.hh
	@@ -1,101 +1,101 @@
	/**
	* @file terms_to_assemble.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Oct 11 2017
	*
	* @brief List of terms to assemble to a matrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TERMS_TO_ASSEMBLE_HH_
	#define AKANTU_TERMS_TO_ASSEMBLE_HH_

	namespace akantu {

	class TermsToAssemble {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	TermsToAssemble() = default;
	virtual ~TermsToAssemble() = default;

	class TermToAssemble {
	public:
	TermToAssemble(UInt i, UInt j) : _i(i), _j(j), val(0.) {}
	inline TermToAssemble & operator=(Real val) {
	this->val = val;
	return *this;
	}
	inline TermToAssemble operator+=(Real val) {
	this->val += val;
	return *this;
	}
	inline operator Real() const { return val; }
	inline UInt i() const { return _i; }
	inline UInt j() const { return _j; }

	private:
	UInt _i, _j;
	Real val;
	};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	inline TermToAssemble & operator()(UInt i, UInt j) {
	terms.emplace_back(i, j);
	return terms.back();
	}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	private:
	using TermsContainer = std::vector<TermToAssemble>;

	public:
	using const_terms_iterator = TermsContainer::const_iterator;

	const_terms_iterator begin() const { return terms.begin(); }
	const_terms_iterator end() const { return terms.end(); }

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	TermsContainer terms;
	};

	} // namespace akantu

	#endif /* AKANTU_TERMS_TO_ASSEMBLE_HH_ */
	diff --git a/src/synchronizer/communication_buffer.hh b/src/synchronizer/communication_buffer.hh
	index 48dd9193c..9181fa943 100644
	--- a/src/synchronizer/communication_buffer.hh
	+++ b/src/synchronizer/communication_buffer.hh
	@@ -1,183 +1,183 @@
	/**
	* @file communication_buffer.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Dec 11 2019
	*
	* @brief Buffer for packing and unpacking data
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "element.hh"
	/* -------------------------------------------------------------------------- */
	#include <array>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATION_BUFFER_HH_
	#define AKANTU_COMMUNICATION_BUFFER_HH_

	namespace akantu {

	template <bool is_static = true> class CommunicationBufferTemplated {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	explicit CommunicationBufferTemplated(UInt size) : buffer(size, 1, char()) {
	ptr_pack = buffer.storage();
	ptr_unpack = buffer.storage();
	};

	CommunicationBufferTemplated() : CommunicationBufferTemplated(0) {}

	CommunicationBufferTemplated(const CommunicationBufferTemplated & other) =
	delete;
	CommunicationBufferTemplated &
	operator=(const CommunicationBufferTemplated & other) = delete;

	CommunicationBufferTemplated(CommunicationBufferTemplated && other) noexcept =
	default;

	virtual ~CommunicationBufferTemplated() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// reset to "empty"
	inline void reset();

	/// resize the internal buffer do not allocate on dynamic buffers
	inline void resize(UInt size);

	/// resize the internal buffer allocate always
	inline void reserve(UInt size);

	/// clear buffer context
	inline void zero();

	private:
	inline void packResize(UInt size);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	inline char * storage() { return buffer.storage(); };
	inline const char * storage() const { return buffer.storage(); };
	/* ------------------------------------------------------------------------ */
	/* Operators */
	/* ------------------------------------------------------------------------ */
	public:
	/// printing tool
	template <typename T> inline std::string extractStream(UInt block_size);

	/// packing data
	template <typename T>
	inline CommunicationBufferTemplated & operator<<(const T & to_pack);

	template <typename T>
	inline CommunicationBufferTemplated & operator<<(const Vector<T> & to_pack);

	template <typename T>
	inline CommunicationBufferTemplated & operator<<(const Matrix<T> & to_pack);

	template <typename T>
	inline CommunicationBufferTemplated &
	operator<<(const std::vector<T> & to_pack);

	/// unpacking data
	template <typename T>
	inline CommunicationBufferTemplated & operator>>(T & to_unpack);

	template <typename T>
	inline CommunicationBufferTemplated & operator>>(Vector<T> & to_unpack);

	template <typename T>
	inline CommunicationBufferTemplated & operator>>(Matrix<T> & to_unpack);

	template <typename T>
	inline CommunicationBufferTemplated & operator>>(std::vector<T> & to_unpack);

	inline CommunicationBufferTemplated & operator<<(const std::string & to_pack);
	inline CommunicationBufferTemplated & operator>>(std::string & to_unpack);

	private:
	template <typename T> inline void packIterable(T & to_pack);
	template <typename T> inline void unpackIterable(T & to_unpack);

	/* ------------------------------------------------------------------------ */
	/* Accessor */
	/* ------------------------------------------------------------------------ */
	public:
	template <typename T> static inline UInt sizeInBuffer(const T & data);
	template <typename T> static inline UInt sizeInBuffer(const Vector<T> & data);
	template <typename T> static inline UInt sizeInBuffer(const Matrix<T> & data);
	template <typename T>
	static inline UInt sizeInBuffer(const std::vector<T> & data);
	static inline UInt sizeInBuffer(const std::string & data);

	/// return the size in bytes of the stored values
	inline UInt getPackedSize() const { return ptr_pack - buffer.storage(); };
	/// return the size in bytes of data left to be unpacked
	inline UInt getLeftToUnpack() const {
	return buffer.size() - (ptr_unpack - buffer.storage());
	};
	/// return the global size allocated
	inline UInt size() const { return buffer.size(); };

	/// is the buffer empty
	inline bool empty() const {
	return (getPackedSize() == 0) and (getLeftToUnpack() == 0);
	}

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	/// current position for packing
	char * ptr_pack;

	/// current position for unpacking
	char * ptr_unpack;

	/// storing buffer
	Array<char> buffer;
	};

	using CommunicationBuffer = CommunicationBufferTemplated<true>;
	using DynamicCommunicationBuffer = CommunicationBufferTemplated<false>;

	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "communication_buffer_inline_impl.hh"

	#endif /* AKANTU_COMMUNICATION_BUFFER_HH_ */
	diff --git a/src/synchronizer/communication_buffer_inline_impl.hh b/src/synchronizer/communication_buffer_inline_impl.hh
	index 93bf84d4a..e2d3764ea 100644
	--- a/src/synchronizer/communication_buffer_inline_impl.hh
	+++ b/src/synchronizer/communication_buffer_inline_impl.hh
	@@ -1,331 +1,331 @@
	/**
	* @file communication_buffer_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Apr 14 2011
	* @date last modification: Tue Dec 04 2018
	*
	* @brief CommunicationBuffer inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_buffer.hh"
	#include <cstring>
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline UInt
	CommunicationBufferTemplated<is_static>::sizeInBuffer(const T & /unused/) {
	return sizeof(T);
	}

	template <bool is_static>
	template <typename T>
	inline UInt
	CommunicationBufferTemplated<is_static>::sizeInBuffer(const Vector<T> & data) {
	UInt size = data.size() * sizeof(T);
	return size;
	}

	template <bool is_static>
	template <typename T>
	inline UInt
	CommunicationBufferTemplated<is_static>::sizeInBuffer(const Matrix<T> & data) {
	UInt size = data.size() * sizeof(T);
	return size;
	}

	template <bool is_static>
	template <typename T>
	inline UInt CommunicationBufferTemplated<is_static>::sizeInBuffer(
	const std::vector<T> & data) {
	UInt size = data.size() * sizeof(T) + sizeof(size_t);
	return size;
	}

	template <bool is_static>
	inline UInt CommunicationBufferTemplated<is_static>::sizeInBuffer(
	const std::string & data) {
	UInt size = data.size() * sizeof(std::string::value_type) + sizeof(size_t);
	return size;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline void CommunicationBufferTemplated<is_static>::packResize(UInt size) {
	if (not is_static) {
	char * values = buffer.storage();
	auto nb_packed = ptr_pack - values;

	if (buffer.size() > nb_packed + size) {
	return;
	}

	buffer.resize(nb_packed + size);
	ptr_pack = buffer.storage() + nb_packed;
	ptr_unpack = buffer.storage() + (ptr_unpack - values);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator<<(const T & to_pack) {
	UInt size = sizeInBuffer(to_pack);
	packResize(size);
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_pack + size),
	"Packing too much data in the CommunicationBufferTemplated");
	std::memcpy(ptr_pack, reinterpret_cast<const char *>(&to_pack), size);
	ptr_pack += size;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator>>(T & to_unpack) {
	UInt size = sizeInBuffer(to_unpack);

	alignas(alignof(T)) std::array<char, sizeof(T)> aligned_ptr;
	memcpy(aligned_ptr.data(), ptr_unpack, size);

	auto * tmp = reinterpret_cast<T *>(aligned_ptr.data());
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_unpack + size),
	"Unpacking too much data in the CommunicationBufferTemplated");
	to_unpack = *tmp;
	// memcpy(reinterpret_cast<char *>(&to_unpack), ptr_unpack, size);
	ptr_unpack += size;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	/* Specialization */
	/* -------------------------------------------------------------------------- */

	/**
	* Vector
	*/

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator<<(const Vector<T> & to_pack) {
	UInt size = sizeInBuffer(to_pack);
	packResize(size);
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_pack + size),
	"Packing too much data in the CommunicationBufferTemplated");
	memcpy(ptr_pack, to_pack.storage(), size);
	ptr_pack += size;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator>>(Vector<T> & to_unpack) {
	UInt size = sizeInBuffer(to_unpack);
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_unpack + size),
	"Unpacking too much data in the CommunicationBufferTemplated");
	memcpy(to_unpack.storage(), ptr_unpack, size);
	ptr_unpack += size;
	return *this;
	}

	/**
	* Matrix
	*/

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator<<(const Matrix<T> & to_pack) {
	UInt size = sizeInBuffer(to_pack);
	packResize(size);
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_pack + size),
	"Packing too much data in the CommunicationBufferTemplated");
	memcpy(ptr_pack, to_pack.storage(), size);
	ptr_pack += size;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator>>(Matrix<T> & to_unpack) {
	UInt size = sizeInBuffer(to_unpack);
	AKANTU_DEBUG_ASSERT(
	(buffer.storage() + buffer.size()) >= (ptr_unpack + size),
	"Unpacking too much data in the CommunicationBufferTemplated");
	memcpy(to_unpack.storage(), ptr_unpack, size);
	ptr_unpack += size;
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline void CommunicationBufferTemplated<is_static>::packIterable(T & to_pack) {
	operator<<(size_t(to_pack.size()));
	auto it = to_pack.begin();
	auto end = to_pack.end();
	for (; it != end; ++it) {
	operator<<(*it);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline void
	CommunicationBufferTemplated<is_static>::unpackIterable(T & to_unpack) {
	size_t size;
	operator>>(size);
	to_unpack.resize(size);
	auto it = to_unpack.begin();
	auto end = to_unpack.end();
	for (; it != end; ++it) {
	operator>>(*it);
	}
	}

	/**
	* std::vector<T>
	*/
	/* -------------------------------------------------------------------------- */

	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator<<(
	const std::vector<T> & to_pack) {
	packIterable(to_pack);
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator>>(
	std::vector<T> & to_unpack) {
	unpackIterable(to_unpack);
	return *this;
	}

	/**
	* std::string
	*/
	/* -------------------------------------------------------------------------- */

	template <bool is_static>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator<<(
	const std::string & to_pack) {
	packIterable(to_pack);
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline CommunicationBufferTemplated<is_static> &
	CommunicationBufferTemplated<is_static>::operator>>(std::string & to_unpack) {
	unpackIterable(to_unpack);
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	template <typename T>
	inline std::string
	CommunicationBufferTemplated<is_static>::extractStream(UInt block_size) {
	std::stringstream str;
	auto * ptr = reinterpret_cast<T *>(buffer.storage());
	UInt sz = buffer.size() / sizeof(T);
	UInt sz_block = block_size / sizeof(T);

	UInt n_block = 0;
	for (UInt i = 0; i < sz; ++i) {
	if (i % sz_block == 0) {
	str << std::endl << n_block << " ";
	++n_block;
	}
	str << *ptr << " ";
	++ptr;
	}
	return str.str();
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline void CommunicationBufferTemplated<is_static>::resize(UInt size) {
	if (!is_static) {
	buffer.resize(0, 0);
	} else {
	buffer.resize(size, 0);
	}
	reset();
	#ifndef AKANTU_NDEBUG
	zero();
	#endif
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline void CommunicationBufferTemplated<is_static>::reserve(UInt size) {
	char * values = buffer.storage();
	auto nb_packed = ptr_pack - values;

	buffer.resize(size);
	ptr_pack = buffer.storage() + nb_packed;
	ptr_unpack = buffer.storage() + (ptr_unpack - values);
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline void CommunicationBufferTemplated<is_static>::zero() {
	buffer.zero();
	}

	/* -------------------------------------------------------------------------- */
	template <bool is_static>
	inline void CommunicationBufferTemplated<is_static>::reset() {
	ptr_pack = buffer.storage();
	ptr_unpack = buffer.storage();
	}

	} // namespace akantu
	diff --git a/src/synchronizer/communication_descriptor.hh b/src/synchronizer/communication_descriptor.hh
	index 2d6b293d2..71a2af303 100644
	--- a/src/synchronizer/communication_descriptor.hh
	+++ b/src/synchronizer/communication_descriptor.hh
	@@ -1,155 +1,155 @@
	/**
	* @file communication_descriptor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Thu Jan 25 2018
	*
	* @brief Implementation of the helper classes for the synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "communication_request.hh"
	#include "communication_tag.hh"
	#include "data_accessor.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATION_DESCRIPTOR_HH_
	#define AKANTU_COMMUNICATION_DESCRIPTOR_HH_

	namespace akantu {

	/* ------------------------------------------------------------------------ */
	enum CommunicationSendRecv { _send, _recv, _csr_not_defined };

	/* -------------------------------------------------------------------------- */
	struct CommunicationSRType {
	using type = CommunicationSendRecv;
	static const type _begin_ = _send;
	static const type _end_ = _csr_not_defined;
	};

	using send_recv_t = safe_enum<CommunicationSRType>;

	namespace {
	send_recv_t iterate_send_recv{};
	}

	/* ------------------------------------------------------------------------ */
	class Communication {
	public:
	explicit Communication(const CommunicationSendRecv & type = _csr_not_defined)
	: _type(type) {}

	Communication(const Communication &) = delete;
	Communication & operator=(const Communication &) = delete;

	void resize(UInt size) {
	this->_size = size;
	this->_buffer.resize(size);
	}

	inline const CommunicationSendRecv & type() const { return this->_type; }
	inline const UInt & size() const { return this->_size; }

	inline const CommunicationRequest & request() const { return this->_request; }
	inline CommunicationRequest & request() { return this->_request; }

	inline const CommunicationBuffer & buffer() const { return this->_buffer; }
	inline CommunicationBuffer & buffer() { return this->_buffer; }

	private:
	UInt _size{0};
	CommunicationBuffer _buffer;
	CommunicationRequest _request;
	CommunicationSendRecv _type;
	};

	template <class Entity> class Communications;

	/* ------------------------------------------------------------------------ */
	template <class Entity> class CommunicationDescriptor {
	public:
	CommunicationDescriptor(Communication & communication, Array<Entity> & scheme,
	Communications<Entity> & communications,
	const SynchronizationTag & tag, UInt proc);

	CommunicationDescriptor(const CommunicationDescriptor &) = default;

	CommunicationDescriptor &
	operator=(const CommunicationDescriptor &) = default;

	/// get the quantity of data in the buffer
	UInt getNbData() { return communication.size(); }
	/// set the quantity of data in the buffer
	void setNbData(UInt size) { communication.resize(size); }

	/// get the corresponding tag
	const SynchronizationTag & getTag() const { return tag; }
	/// get the data buffer
	CommunicationBuffer & getBuffer();

	/// get the corresponding request
	CommunicationRequest & getRequest();

	/// get the communication scheme
	const Array<Entity> & getScheme();

	/// reset the buffer before pack or after unpack
	void resetBuffer();

	/// pack data for entities in the buffer
	void packData(const DataAccessor<Entity> & accessor);

	/// unpack data for entities from the buffer
	void unpackData(DataAccessor<Entity> & accessor);

	/// posts asynchronous send requests
	void postSend(int hash_id);

	/// posts asynchronous receive requests
	void postRecv(int hash_id);

	/// free the request
	void freeRequest();

	UInt getProc() { return proc; }

	protected:
	Communication & communication;
	const Array<Entity> & scheme;
	Communications<Entity> & communications;
	const SynchronizationTag & tag;
	UInt proc;
	UInt rank;
	UInt counter;
	};

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#include "communication_descriptor_tmpl.hh"

	#endif /* AKANTU_COMMUNICATION_DESCRIPTOR_HH_ */
	diff --git a/src/synchronizer/communication_descriptor_tmpl.hh b/src/synchronizer/communication_descriptor_tmpl.hh
	index 262cc4d87..f4c85e242 100644
	--- a/src/synchronizer/communication_descriptor_tmpl.hh
	+++ b/src/synchronizer/communication_descriptor_tmpl.hh
	@@ -1,153 +1,153 @@
	/**
	* @file communication_descriptor_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Thu Jan 25 2018
	*
	* @brief implementation of CommunicationDescriptor
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_descriptor.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATION_DESCRIPTOR_TMPL_HH_
	#define AKANTU_COMMUNICATION_DESCRIPTOR_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Implementations */
	/* -------------------------------------------------------------------------- */
	template <class Entity>
	CommunicationDescriptor<Entity>::CommunicationDescriptor(
	Communication & communication, Array<Entity> & scheme,
	Communications<Entity> & communications, const SynchronizationTag & tag,
	UInt proc)
	: communication(communication), scheme(scheme),
	communications(communications), tag(tag), proc(proc),
	rank(communications.getCommunicator().whoAmI()) {
	counter = communications.getCounter(tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	CommunicationBuffer & CommunicationDescriptor<Entity>::getBuffer() {
	return communication.buffer();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	CommunicationRequest & CommunicationDescriptor<Entity>::getRequest() {
	return communication.request();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> void CommunicationDescriptor<Entity>::freeRequest() {
	const auto & comm = communications.getCommunicator();

	// comm.test(communication.request());
	comm.freeCommunicationRequest(communication.request());

	communications.decrementPending(tag, communication.type());
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	const Array<Entity> & CommunicationDescriptor<Entity>::getScheme() {
	return scheme;
	}

	template <class Entity> void CommunicationDescriptor<Entity>::resetBuffer() {
	this->communication.buffer().reset();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void CommunicationDescriptor<Entity>::packData(
	const DataAccessor<Entity> & accessor) {
	AKANTU_DEBUG_ASSERT(
	communication.type() == _send,
	"Cannot pack data on communication that is not of type _send");
	accessor.packData(communication.buffer(), scheme, tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void CommunicationDescriptor<Entity>::unpackData(
	DataAccessor<Entity> & accessor) {
	AKANTU_DEBUG_ASSERT(
	communication.type() == _recv,
	"Cannot unpack data from communication that is not of type _recv");
	accessor.unpackData(communication.buffer(), scheme, tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void CommunicationDescriptor<Entity>::postSend(int hash_id) {
	AKANTU_DEBUG_ASSERT(communication.type() == _send,
	"Cannot send a communication that is not of type _send");
	Tag comm_tag = Tag::genTag(rank, counter, tag, hash_id);
	AKANTU_DEBUG_ASSERT(communication.buffer().getPackedSize() ==
	communication.size(),
	"a problem have been introduced with "
	<< "false sent sizes declaration "
	<< communication.buffer().getPackedSize()
	<< " != " << communication.size());

	AKANTU_DEBUG_INFO("Posting send to proc " << proc << " (tag: " << tag << " - "
	<< communication.size()
	<< " data to send) "
	<< " [ " << comm_tag << " ]");

	CommunicationRequest & request = communication.request();
	request = communications.getCommunicator().asyncSend(communication.buffer(),
	proc, comm_tag);
	communications.incrementPending(tag, communication.type());
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void CommunicationDescriptor<Entity>::postRecv(int hash_id) {
	AKANTU_DEBUG_ASSERT(communication.type() == _recv,
	"Cannot receive data for communication ("
	<< communication.type()
	<< ")that is not of type _recv");

	Tag comm_tag = Tag::genTag(proc, counter, tag, hash_id);
	AKANTU_DEBUG_INFO("Posting receive from proc "
	<< proc << " (tag: " << tag << " - " << communication.size()
	<< " data to receive) "
	<< " [ " << comm_tag << " ]");

	CommunicationRequest & request = communication.request();
	request = communications.getCommunicator().asyncReceive(
	communication.buffer(), proc, comm_tag);
	communications.incrementPending(tag, communication.type());
	}

	} // namespace akantu

	#endif /* AKANTU_COMMUNICATION_DESCRIPTOR_TMPL_HH_ */
	diff --git a/src/synchronizer/communication_request.hh b/src/synchronizer/communication_request.hh
	index dc571e6e5..f593c5e11 100644
	--- a/src/synchronizer/communication_request.hh
	+++ b/src/synchronizer/communication_request.hh
	@@ -1,113 +1,113 @@
	/**
	* @file communication_request.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Tue Nov 07 2017
	*
	* @brief empty class just for inheritance
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_REAL_STATIC_COMMUNICATOR_HH_
	#define AKANTU_REAL_STATIC_COMMUNICATOR_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	class InternalCommunicationRequest {
	public:
	InternalCommunicationRequest(UInt source, UInt dest);
	virtual ~InternalCommunicationRequest();

	virtual void printself(std::ostream & stream, int indent = 0) const;

	AKANTU_GET_MACRO(Source, source, UInt);
	AKANTU_GET_MACRO(Destination, destination, UInt);

	private:
	UInt source;
	UInt destination;
	UInt id;
	static UInt counter;
	};

	/* -------------------------------------------------------------------------- */
	class CommunicationRequest {
	public:
	CommunicationRequest(
	std::shared_ptr<InternalCommunicationRequest> request = nullptr)
	: request(std::move(request)) {}

	virtual ~CommunicationRequest() = default;

	virtual void free() { request.reset(); }

	void printself(std::ostream & stream, int indent = 0) const {
	request->printself(stream, indent);
	};

	UInt getSource() const { return request->getSource(); }
	UInt getDestination() const { return request->getDestination(); }

	bool isFreed() const { return request == nullptr; }

	InternalCommunicationRequest & getInternal() { return *request; }

	private:
	std::shared_ptr<InternalCommunicationRequest> request;
	};

	/* -------------------------------------------------------------------------- */
	class CommunicationStatus {
	public:
	AKANTU_GET_MACRO(Source, source, Int);
	UInt size() const { return size_; }
	AKANTU_GET_MACRO(Tag, tag, Int);

	AKANTU_SET_MACRO(Source, source, Int);
	AKANTU_SET_MACRO(Size, size_, UInt);
	AKANTU_SET_MACRO(Tag, tag, Int);

	private:
	Int source{0};
	UInt size_{0};
	Int tag{0};
	};

	/* -------------------------------------------------------------------------- */
	/// Datatype to pack pairs for MPI_{MIN,MAX}LOC
	template <typename T1, typename T2> struct SCMinMaxLoc {
	T1 min_max;
	T2 loc;
	};

	} // namespace akantu

	#endif /* AKANTU_REAL_STATIC_COMMUNICATOR_HH_ */
	diff --git a/src/synchronizer/communication_tag.hh b/src/synchronizer/communication_tag.hh
	index 3716a5b0d..cb7974912 100644
	--- a/src/synchronizer/communication_tag.hh
	+++ b/src/synchronizer/communication_tag.hh
	@@ -1,129 +1,129 @@
	/**
	* @file communication_tag.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Mon Feb 10 2020
	*
	* @brief Description of the communication tags
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATION_TAG_HH_
	#define AKANTU_COMMUNICATION_TAG_HH_

	namespace akantu {
	/**
	* tag = \|__________20_________\|___8____\|_4_\|
	* \| proc \| num mes\| ct\|
	*/
	class Tag {
	public:
	Tag() = default;
	Tag(int val) : tag(val) {}
	Tag(int val, int hash) : tag(val), hash(hash) {}

	operator int() const {
	return int(max_tag == 0 ? tag : (uint32_t(tag) % max_tag));
	}

	/// generates a tag
	template <typename CommTag>
	static inline Tag genTag(int proc, UInt msg_count, CommTag tag) {
	int _tag = ((((proc & 0xFFFFF) << 12) + ((msg_count & 0xFF) << 4) +
	((int)tag & 0xF)));
	Tag t(_tag);
	return t;
	}

	/// generates a tag and hashes it
	template <typename CommTag>
	static inline Tag genTag(int proc, UInt msg_count, CommTag tag, int hash) {
	Tag t = genTag(proc, msg_count, tag);
	t.tag = t.tag ^ hash;
	t.hash = hash;
	return t;
	}

	virtual void printself(std::ostream & stream, int /unused/) const {
	int t = tag;
	stream << "TAG(";
	if (hash != 0) {
	t = t ^ hash;
	}
	stream << (t >> 12) << ":" << (t >> 4 & 0xFF) << ":" << (t & 0xF) << " -> "
	<< std::hex << "0x" << int(*this);
	if (hash != 0) {
	stream << " {hash: 0x" << hash << "}";
	}
	stream << " [0x" << max_tag << "]";
	stream << ")" << std::dec;
	}

	enum CommTags : int {
	_sizes = 1,
	_connectivity = 2,
	_data = 3,
	_partitions = 4,
	_nb_nodes = 5,
	_nodes = 6,
	_coordinates = 7,
	_nodes_type = 8,
	_mesh_data = 9,
	_element_group = 10,
	_node_group = 11,
	_modify_scheme = 12,
	_gather_initialization = 1,
	_gather = 2,
	_scatter = 3,
	_synchronize = 15,
	_reduce,
	_periodic_slaves,
	_periodic_nodes,
	};

	private:
	static void setMaxTag(int _max_tag) { max_tag = _max_tag; }
	friend void initialize(const std::string & /input_file/, int & /argc/,
	char *& /argv*/);

	private:
	int tag{0};
	int hash{0};
	static int max_tag;
	};

	/* -------------------------------------------------------------------------- */
	inline std::ostream & operator<<(std::ostream & stream, const Tag & _this) {
	_this.printself(stream, 0);
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* AKANTU_COMMUNICATION_TAG_HH_ */
	diff --git a/src/synchronizer/communications.hh b/src/synchronizer/communications.hh
	index e4c945cb7..915d18935 100644
	--- a/src/synchronizer/communications.hh
	+++ b/src/synchronizer/communications.hh
	@@ -1,277 +1,277 @@
	/**
	* @file communications.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Class handling the pending communications and the communications
	* schemes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_descriptor.hh"
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATIONS_HH_
	#define AKANTU_COMMUNICATIONS_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Entity> class Communications {
	public:
	using Scheme = Array<Entity>;

	protected:
	using CommunicationPerProcs = std::map<UInt, Communication>;
	using CommunicationsPerTags =
	std::map<SynchronizationTag, CommunicationPerProcs>;
	using CommunicationSchemes = std::map<UInt, Scheme>;
	using Request = std::map<UInt, std::vector<CommunicationRequest>>;

	friend class CommunicationDescriptor<Entity>;

	public:
	using scheme_iterator = typename CommunicationSchemes::iterator;
	using const_scheme_iterator = typename CommunicationSchemes::const_iterator;

	/* ------------------------------------------------------------------------ */
	class iterator;
	class tag_iterator;
	/* ------------------------------------------------------------------------ */

	public:
	CommunicationPerProcs & getCommunications(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);

	/* ------------------------------------------------------------------------ */
	bool hasPending(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) const;
	UInt getPending(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) const;

	/* ------------------------------------------------------------------------ */
	iterator begin(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);
	iterator end(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);

	/* ------------------------------------------------------------------------ */
	iterator waitAny(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);

	/* ------------------------------------------------------------------------ */
	void waitAll(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);
	void incrementPending(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);
	void decrementPending(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);
	void freeRequests(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr);

	/* ------------------------------------------------------------------------ */
	Scheme & createScheme(UInt proc, const CommunicationSendRecv & sr);
	void resetSchemes(const CommunicationSendRecv & sr);

	/* ------------------------------------------------------------------------ */
	void setCommunicationSize(const SynchronizationTag & tag, UInt proc,
	UInt size, const CommunicationSendRecv & sr);

	public:
	explicit Communications(const Communicator & communicator);
	explicit Communications(const Communications & other);

	/* ------------------------------------------------------------------------ */
	void swapSendRecv();

	/* ------------------------------------------------------------------------ */
	class IterableCommunicationDesc {
	public:
	IterableCommunicationDesc(Communications & communications,
	SynchronizationTag tag, CommunicationSendRecv sr)
	: communications(communications), tag(tag), sr(sr) {}
	auto begin() { return communications.begin(tag, sr); }
	auto end() { return communications.end(tag, sr); }

	private:
	Communications & communications;
	SynchronizationTag tag;
	CommunicationSendRecv sr;
	};

	auto iterateRecv(const SynchronizationTag & tag) {
	return IterableCommunicationDesc(*this, tag, _recv);
	}
	auto iterateSend(const SynchronizationTag & tag) {
	return IterableCommunicationDesc(*this, tag, _send);
	}

	/* ------------------------------------------------------------------------ */
	// iterator begin_send(const SynchronizationTag & tag);
	// iterator end_send(const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	// iterator begin_recv(const SynchronizationTag & tag);
	// iterator end_recv(const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	class IterableTags {
	public:
	explicit IterableTags(Communications & communications)
	: communications(communications) {}
	decltype(auto) begin() { return communications.begin_tag(); }
	decltype(auto) end() { return communications.end_tag(); }

	private:
	Communications & communications;
	};

	decltype(auto) iterateTags() { return IterableTags(*this); }

	tag_iterator begin_tag();
	tag_iterator end_tag();

	/* ------------------------------------------------------------------------ */
	bool hasCommunication(const SynchronizationTag & tag) const;
	void incrementCounter(const SynchronizationTag & tag);
	UInt getCounter(const SynchronizationTag & tag) const;
	bool hasCommunicationSize(const SynchronizationTag & tag) const;
	void invalidateSizes();

	/* ------------------------------------------------------------------------ */
	bool hasPendingRecv(const SynchronizationTag & tag) const;
	bool hasPendingSend(const SynchronizationTag & tag) const;

	const auto & getCommunicator() const;

	/* ------------------------------------------------------------------------ */
	iterator waitAnyRecv(const SynchronizationTag & tag);
	iterator waitAnySend(const SynchronizationTag & tag);

	void waitAllRecv(const SynchronizationTag & tag);
	void waitAllSend(const SynchronizationTag & tag);

	void freeSendRequests(const SynchronizationTag & tag);
	void freeRecvRequests(const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	/* ------------------------------------------------------------------------ */
	class IterableSchemes {
	public:
	IterableSchemes(Communications & communications, CommunicationSendRecv sr)
	: communications(communications), sr(sr) {}
	decltype(auto) begin() { return communications.begin_scheme(sr); }
	decltype(auto) end() { return communications.end_scheme(sr); }

	private:
	Communications & communications;
	CommunicationSendRecv sr;
	};

	class ConstIterableSchemes {
	public:
	ConstIterableSchemes(const Communications & communications,
	CommunicationSendRecv sr)
	: communications(communications), sr(sr) {}
	decltype(auto) begin() const { return communications.begin_scheme(sr); }
	decltype(auto) end() const { return communications.end_scheme(sr); }

	private:
	const Communications & communications;
	CommunicationSendRecv sr;
	};

	decltype(auto) iterateSchemes(const CommunicationSendRecv & sr) {
	return IterableSchemes(*this, sr);
	}
	decltype(auto) iterateSchemes(const CommunicationSendRecv & sr) const {
	return ConstIterableSchemes(*this, sr);
	}

	decltype(auto) iterateSendSchemes() { return IterableSchemes(*this, _send); }
	decltype(auto) iterateSendSchemes() const {
	return ConstIterableSchemes(*this, _send);
	}

	decltype(auto) iterateRecvSchemes() { return IterableSchemes(*this, _recv); }
	decltype(auto) iterateRecvSchemes() const {
	return ConstIterableSchemes(*this, _recv);
	}

	scheme_iterator begin_scheme(const CommunicationSendRecv & sr);
	scheme_iterator end_scheme(const CommunicationSendRecv & sr);
	const_scheme_iterator begin_scheme(const CommunicationSendRecv & sr) const;
	const_scheme_iterator end_scheme(const CommunicationSendRecv & sr) const;

	/* ------------------------------------------------------------------------ */
	scheme_iterator begin_send_scheme();
	scheme_iterator end_send_scheme();
	const_scheme_iterator begin_send_scheme() const;
	const_scheme_iterator end_send_scheme() const;

	/* ------------------------------------------------------------------------ */
	scheme_iterator begin_recv_scheme();
	scheme_iterator end_recv_scheme();
	const_scheme_iterator begin_recv_scheme() const;
	const_scheme_iterator end_recv_scheme() const;

	/* ------------------------------------------------------------------------ */
	Scheme & createSendScheme(UInt proc);
	Scheme & createRecvScheme(UInt proc);

	/* ------------------------------------------------------------------------ */
	Scheme & getScheme(UInt proc, const CommunicationSendRecv & sr);
	const Scheme & getScheme(UInt proc, const CommunicationSendRecv & sr) const;

	/* ------------------------------------------------------------------------ */
	void resetSchemes();
	/* ------------------------------------------------------------------------ */
	void setSendCommunicationSize(const SynchronizationTag & tag, UInt proc,
	UInt size);
	void setRecvCommunicationSize(const SynchronizationTag & tag, UInt proc,
	UInt size);

	void initializeCommunications(const SynchronizationTag & tag);

	protected:
	CommunicationSchemes schemes[2];
	CommunicationsPerTags communications[2];

	std::map<SynchronizationTag, UInt> comm_counter;
	std::map<SynchronizationTag, UInt> pending_communications[2];
	std::map<SynchronizationTag, bool> comm_size_computed;

	const Communicator & communicator;
	};

	} // namespace akantu

	#include "communications_tmpl.hh"

	#endif /* AKANTU_COMMUNICATIONS_HH_ */
	diff --git a/src/synchronizer/communications_tmpl.hh b/src/synchronizer/communications_tmpl.hh
	index 623f28cbe..b80769b93 100644
	--- a/src/synchronizer/communications_tmpl.hh
	+++ b/src/synchronizer/communications_tmpl.hh
	@@ -1,554 +1,554 @@
	/**
	* @file communications_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of Communications
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communications.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATIONS_TMPL_HH_
	#define AKANTU_COMMUNICATIONS_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	Communications<Entity>::Communications(const Communicator & communicator)
	: communicator(communicator) {}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	Communications<Entity>::Communications(const Communications & other)
	: communicator(other.communicator) {
	for (auto sr : iterate_send_recv) {
	for (const auto & scheme_pair : other.iterateSchemes(sr)) {
	auto proc = scheme_pair.first;
	auto & other_scheme = scheme_pair.second;
	auto & scheme = this->createScheme(proc, sr);
	scheme.copy(other_scheme);
	}
	}

	this->invalidateSizes();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> void Communications<Entity>::swapSendRecv() {
	std::swap(schemes[_send], schemes[_recv]);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> class Communications<Entity>::iterator {
	using communication_iterator =
	typename std::map<UInt, Communication>::iterator;

	public:
	iterator() : communications(nullptr) {}
	iterator(scheme_iterator scheme_it, communication_iterator comm_it,
	Communications<Entity> & communications,
	const SynchronizationTag & tag)
	: scheme_it(scheme_it), comm_it(comm_it), communications(&communications),
	tag(tag) {}

	iterator(const iterator & other) = default;
	iterator(iterator && other) noexcept = default;
	iterator & operator=(const iterator & other) = default;
	iterator & operator=(iterator && other) noexcept = default;

	iterator & operator++() {
	++scheme_it;
	++comm_it;
	return *this;
	}

	CommunicationDescriptor<Entity> operator*() {
	AKANTU_DEBUG_ASSERT(
	scheme_it->first == comm_it->first,
	"The two iterators are not in phase, something wrong"
	<< " happened, time to take out your favorite debugger ("
	<< scheme_it->first << " != " << comm_it->first << ")");
	return CommunicationDescriptor<Entity>(comm_it->second, scheme_it->second,
	*communications, tag,
	scheme_it->first);
	}

	bool operator==(const iterator & other) const {
	return scheme_it == other.scheme_it && comm_it == other.comm_it;
	}

	bool operator!=(const iterator & other) const {
	return scheme_it != other.scheme_it \|\| comm_it != other.comm_it;
	}

	private:
	scheme_iterator scheme_it;
	communication_iterator comm_it;
	Communications<Entity> * communications;
	SynchronizationTag tag;
	};

	/* -------------------------------------------------------------------------- */
	template <class Entity> class Communications<Entity>::tag_iterator {
	using internal_iterator = std::map<SynchronizationTag, UInt>::const_iterator;

	public:
	tag_iterator(const internal_iterator & it) : it(it) {}
	tag_iterator & operator++() {
	++it;
	return *this;
	}
	SynchronizationTag operator*() { return it->first; }
	bool operator==(const tag_iterator & other) const { return it == other.it; }
	bool operator!=(const tag_iterator & other) const { return it != other.it; }

	private:
	internal_iterator it;
	};

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::CommunicationPerProcs &
	Communications<Entity>::getCommunications(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	auto comm_it = this->communications[sr].find(tag);
	if (comm_it == this->communications[sr].end()) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::CommunicationException(),
	"No known communications for the tag: " << tag);
	}
	return comm_it->second;
	}

	/* ---------------------------------------------------------------------- */
	template <class Entity>
	UInt Communications<Entity>::getPending(
	const SynchronizationTag & tag, const CommunicationSendRecv & sr) const {
	const std::map<SynchronizationTag, UInt> & pending =
	pending_communications[sr];
	auto it = pending.find(tag);

	if (it == pending.end()) {
	return 0;
	}
	return it->second;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	bool Communications<Entity>::hasPending(
	const SynchronizationTag & tag, const CommunicationSendRecv & sr) const {
	return this->hasCommunication(tag) && (this->getPending(tag, sr) != 0);
	}

	/* ---------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::iterator
	Communications<Entity>::begin(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	auto & comms = this->getCommunications(tag, sr);
	return iterator(this->schemes[sr].begin(), comms.begin(), *this, tag);
	}

	template <class Entity>
	typename Communications<Entity>::iterator
	Communications<Entity>::end(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	auto & comms = this->getCommunications(tag, sr);
	return iterator(this->schemes[sr].end(), comms.end(), *this, tag);
	}

	/* ---------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::iterator
	Communications<Entity>::waitAny(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	auto & comms = this->getCommunications(tag, sr);
	auto it = comms.begin();
	auto end = comms.end();

	std::vector<CommunicationRequest> requests;

	for (; it != end; ++it) {
	auto & request = it->second.request();
	if (!request.isFreed()) {
	requests.push_back(request);
	}
	}

	UInt req_id = Communicator::waitAny(requests);
	if (req_id != UInt(-1)) {
	auto & request = requests[req_id];
	UInt proc = sr == _recv ? request.getSource() : request.getDestination();

	return iterator(this->schemes[sr].find(proc), comms.find(proc), *this, tag);
	}
	return this->end(tag, sr);
	}

	/* ---------------------------------------------------------------------- */
	template <class Entity>
	void Communications<Entity>::waitAll(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	auto & comms = this->getCommunications(tag, sr);
	auto it = comms.begin();
	auto end = comms.end();

	std::vector<CommunicationRequest> requests;

	for (; it != end; ++it) {
	requests.push_back(it->second.request());
	}

	Communicator::waitAll(requests);
	}

	template <class Entity>
	void Communications<Entity>::incrementPending(
	const SynchronizationTag & tag, const CommunicationSendRecv & sr) {
	++(pending_communications[sr][tag]);
	}

	template <class Entity>
	void Communications<Entity>::decrementPending(
	const SynchronizationTag & tag, const CommunicationSendRecv & sr) {
	--(pending_communications[sr][tag]);
	}

	template <class Entity>
	void Communications<Entity>::freeRequests(const SynchronizationTag & tag,
	const CommunicationSendRecv & sr) {
	iterator it = this->begin(tag, sr);
	iterator end = this->end(tag, sr);

	for (; it != end; ++it) {
	(*it).freeRequest();
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::Scheme &
	Communications<Entity>::createScheme(UInt proc,
	const CommunicationSendRecv & sr) {
	// scheme_iterator it = schemes[sr].find(proc);
	// if (it != schemes[sr].end()) {
	// AKANTU_CUSTOM_EXCEPTION_INFO(debug::CommunicationException(),
	// "Communication scheme("
	// << sr
	// << ") already created for proc: " <<
	// proc);
	// }
	return schemes[sr][proc];
	}

	template <class Entity>
	void Communications<Entity>::resetSchemes(const CommunicationSendRecv & sr) {
	auto it = this->schemes[sr].begin();
	auto end = this->schemes[sr].end();
	for (; it != end; ++it) {
	it->second.resize(0);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void Communications<Entity>::setCommunicationSize(
	const SynchronizationTag & tag, UInt proc, UInt size,
	const CommunicationSendRecv & sr) {
	// accessor that fails if it does not exists
	comm_size_computed[tag] = true; // TODO: need perhaps to be split based on sr
	auto & comms = this->communications[sr];
	auto & comms_per_tag = comms.at(tag);

	comms_per_tag.at(proc).resize(size);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void Communications<Entity>::initializeCommunications(
	const SynchronizationTag & tag) {

	for (auto t : send_recv_t{}) {
	pending_communications[t].insert(std::make_pair(tag, 0));

	auto & comms = this->communications[t];
	auto & comms_per_tag =
	comms.insert(std::make_pair(tag, CommunicationPerProcs()))
	.first->second;

	for (const auto & pair : this->schemes[t]) {
	comms_per_tag.emplace(std::piecewise_construct,
	std::forward_as_tuple(pair.first),
	std::forward_as_tuple(t));
	}
	}

	comm_counter.insert(std::make_pair(tag, 0));
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::tag_iterator
	Communications<Entity>::begin_tag() {
	return tag_iterator(comm_counter.begin());
	}

	template <class Entity>
	typename Communications<Entity>::tag_iterator
	Communications<Entity>::end_tag() {
	return tag_iterator(comm_counter.end());
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::begin_scheme(const CommunicationSendRecv & sr) {
	return this->schemes[sr].begin();
	}

	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::end_scheme(const CommunicationSendRecv & sr) {
	return this->schemes[sr].end();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::begin_scheme(const CommunicationSendRecv & sr) const {
	return this->schemes[sr].begin();
	}

	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::end_scheme(const CommunicationSendRecv & sr) const {
	return this->schemes[sr].end();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::begin_send_scheme() {
	return this->begin_scheme(_send);
	}

	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::end_send_scheme() {
	return this->end_scheme(_send);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::begin_send_scheme() const {
	return this->begin_scheme(_send);
	}

	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::end_send_scheme() const {
	return this->end_scheme(_send);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::begin_recv_scheme() {
	return this->begin_scheme(_recv);
	}

	template <class Entity>
	typename Communications<Entity>::scheme_iterator
	Communications<Entity>::end_recv_scheme() {
	return this->end_scheme(_recv);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::begin_recv_scheme() const {
	return this->begin_scheme(_recv);
	}

	template <class Entity>
	typename Communications<Entity>::const_scheme_iterator
	Communications<Entity>::end_recv_scheme() const {
	return this->end_scheme(_recv);
	}

	/* ------------------------------------------------------------------------ */
	template <class Entity>
	bool Communications<Entity>::hasCommunication(
	const SynchronizationTag & tag) const {
	return (communications[_send].find(tag) != communications[_send].end());
	}

	template <class Entity>
	void Communications<Entity>::incrementCounter(const SynchronizationTag & tag) {
	auto it = comm_counter.find(tag);
	if (it == comm_counter.end()) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::CommunicationException(),
	"No counter initialized in communications for the tags: " << tag);
	}

	++(it->second);
	}

	template <class Entity>
	UInt Communications<Entity>::getCounter(const SynchronizationTag & tag) const {
	auto it = comm_counter.find(tag);
	if (it == comm_counter.end()) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::CommunicationException(),
	"No counter initialized in communications for the tags: " << tag);
	}

	return it->second;
	}

	template <class Entity>
	bool Communications<Entity>::hasCommunicationSize(
	const SynchronizationTag & tag) const {
	auto it = comm_size_computed.find(tag);
	if (it == comm_size_computed.end()) {
	return false;
	}

	return it->second;
	}

	template <class Entity> void Communications<Entity>::invalidateSizes() {
	for (auto && pair : comm_size_computed) {
	pair.second = false;
	}
	}

	template <class Entity>
	bool Communications<Entity>::hasPendingRecv(
	const SynchronizationTag & tag) const {
	return this->hasPending(tag, _recv);
	}

	template <class Entity>
	bool Communications<Entity>::hasPendingSend(
	const SynchronizationTag & tag) const {
	return this->hasPending(tag, _send);
	}

	template <class Entity>
	const auto & Communications<Entity>::getCommunicator() const {
	return communicator;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::iterator
	Communications<Entity>::waitAnyRecv(const SynchronizationTag & tag) {
	return this->waitAny(tag, _recv);
	}

	template <class Entity>
	typename Communications<Entity>::iterator
	Communications<Entity>::waitAnySend(const SynchronizationTag & tag) {
	return this->waitAny(tag, _send);
	}

	template <class Entity>
	void Communications<Entity>::waitAllRecv(const SynchronizationTag & tag) {
	this->waitAll(tag, _recv);
	}

	template <class Entity>
	void Communications<Entity>::waitAllSend(const SynchronizationTag & tag) {
	this->waitAll(tag, _send);
	}

	template <class Entity>
	void Communications<Entity>::freeSendRequests(const SynchronizationTag & tag) {
	this->freeRequests(tag, _send);
	}

	template <class Entity>
	void Communications<Entity>::freeRecvRequests(const SynchronizationTag & tag) {
	this->freeRequests(tag, _recv);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::Scheme &
	Communications<Entity>::createSendScheme(UInt proc) {
	return createScheme(proc, _send);
	}

	template <class Entity>
	typename Communications<Entity>::Scheme &
	Communications<Entity>::createRecvScheme(UInt proc) {
	return createScheme(proc, _recv);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> void Communications<Entity>::resetSchemes() {
	resetSchemes(_send);
	resetSchemes(_recv);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	typename Communications<Entity>::Scheme &
	Communications<Entity>::getScheme(UInt proc, const CommunicationSendRecv & sr) {
	return this->schemes[sr].find(proc)->second;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	const typename Communications<Entity>::Scheme &
	Communications<Entity>::getScheme(UInt proc,
	const CommunicationSendRecv & sr) const {
	return this->schemes[sr].find(proc)->second;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void Communications<Entity>::setSendCommunicationSize(
	const SynchronizationTag & tag, UInt proc, UInt size) {
	this->setCommunicationSize(tag, proc, size, _send);
	}

	template <class Entity>
	void Communications<Entity>::setRecvCommunicationSize(
	const SynchronizationTag & tag, UInt proc, UInt size) {
	this->setCommunicationSize(tag, proc, size, _recv);
	}

	} // namespace akantu

	#endif /* AKANTU_COMMUNICATIONS_TMPL_HH_ */
	diff --git a/src/synchronizer/communicator.cc b/src/synchronizer/communicator.cc
	index 43c7e2474..35465e618 100644
	--- a/src/synchronizer/communicator.cc
	+++ b/src/synchronizer/communicator.cc
	@@ -1,192 +1,192 @@
	/**
	* @file communicator.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Jun 05 2019
	*
	* @brief implementation of the common part of the static communicator
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#if defined(AKANTU_USE_MPI)
	#include "mpi_communicator_data.hh"
	#endif
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	#if defined(AKANTU_USE_MPI)
	int MPICommunicatorData::is_externaly_initialized = 0;
	#endif

	UInt InternalCommunicationRequest::counter = 0;

	/* -------------------------------------------------------------------------- */
	InternalCommunicationRequest::InternalCommunicationRequest(UInt source,
	UInt dest)
	: source(source), destination(dest) {
	this->id = counter++;
	}

	/* -------------------------------------------------------------------------- */
	InternalCommunicationRequest::~InternalCommunicationRequest() = default;

	/* -------------------------------------------------------------------------- */
	void InternalCommunicationRequest::printself(std::ostream & stream,
	int indent) const {
	std::string space(indent, AKANTU_INDENT);

	stream << space << "CommunicationRequest [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + source : " << source << std::endl;
	stream << space << " + destination : " << destination << std::endl;
	stream << space << "]" << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	Communicator::~Communicator() {
	auto * event = new FinalizeCommunicatorEvent(*this);
	this->sendEvent(*event);
	delete event;
	}

	/* -------------------------------------------------------------------------- */
	Communicator & Communicator::getStaticCommunicator() {
	AKANTU_DEBUG_IN();

	if (!static_communicator) {
	int nb_args = 0;
	char ** null = nullptr;
	static_communicator =
	std::make_unique<Communicator>(nb_args, null, private_member{});
	}

	AKANTU_DEBUG_OUT();
	return *static_communicator;
	}

	/* -------------------------------------------------------------------------- */
	Communicator & Communicator::getStaticCommunicator(int & argc, char **& argv) {
	if (!static_communicator) {
	static_communicator =
	std::make_unique<Communicator>(argc, argv, private_member{});
	}
	return getStaticCommunicator();
	}

	} // namespace akantu

	#ifdef AKANTU_USE_MPI
	#include "communicator_mpi_inline_impl.hh"
	#else
	#include "communicator_dummy_inline_impl.hh"
	#endif

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* Template instantiation */
	/* -------------------------------------------------------------------------- */
	#define AKANTU_COMM_INSTANTIATE(T) \
	template void Communicator::probe<T>(Int sender, Int tag, \
	CommunicationStatus & status) const; \
	template bool Communicator::asyncProbe<T>( \
	Int sender, Int tag, CommunicationStatus & status) const; \
	template void Communicator::sendImpl<T>( \
	const T * buffer /NOLINT/, Int size, Int receiver, Int tag, \
	const CommunicationMode & mode) const; \
	template void Communicator::receiveImpl<T>(T * buffer /NOLINT/, Int size, \
	Int sender, Int tag) const; \
	template CommunicationRequest Communicator::asyncSendImpl<T>( \
	const T * buffer /NOLINT/, Int size, Int receiver, Int tag, \
	const CommunicationMode & mode) const; \
	template CommunicationRequest Communicator::asyncReceiveImpl<T>( \
	T * buffer /* NOLINT */, Int size, Int sender, Int tag) const; \
	template void Communicator::allGatherImpl<T>(T * values /NOLINT/, \
	int nb_values) const; \
	template void Communicator::allGatherVImpl<T>(T * values /NOLINT/, \
	int * nb_values) const; \
	template void Communicator::gatherImpl<T>(T * values /NOLINT/, \
	int nb_values, int root) const; \
	template void Communicator::gatherImpl<T>( \
	T * values /NOLINT/, int nb_values, T * gathered /NOLINT/, \
	int nb_gathered) const; \
	template void Communicator::gatherVImpl<T>(T * values /NOLINT/, \
	int * nb_values, int root) const; \
	template void Communicator::broadcastImpl<T>(T * values /NOLINT/, \
	int nb_values, int root) const; \
	template void Communicator::allReduceImpl<T>( \
	T * values /NOLINT/, int nb_values, SynchronizerOperation op) const; \
	template void Communicator::scanImpl<T>(T * values /NOLINT/, \
	T * /NOLINT/, int nb_values, \
	SynchronizerOperation op) const; \
	template void Communicator::exclusiveScanImpl<T>( \
	T * values /NOLINT/, T * /NOLINT/, int nb_values, \
	SynchronizerOperation op) const

	#define MIN_MAX_REAL SCMinMaxLoc<Real, int>

	#if !defined(DOXYGEN)

	AKANTU_COMM_INSTANTIATE(bool);
	AKANTU_COMM_INSTANTIATE(Real);
	AKANTU_COMM_INSTANTIATE(UInt);
	AKANTU_COMM_INSTANTIATE(Int);
	AKANTU_COMM_INSTANTIATE(char);
	AKANTU_COMM_INSTANTIATE(NodeFlag);
	AKANTU_COMM_INSTANTIATE(MIN_MAX_REAL);

	#if AKANTU_INTEGER_SIZE > 4
	AKANTU_COMM_INSTANTIATE(int);
	#endif

	#endif

	// template void Communicator::send<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * buffer, Int size, Int receiver, Int tag);
	// template void Communicator::receive<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * buffer, Int size, Int sender, Int tag);
	// template CommunicationRequest
	// Communicator::asyncSend<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * buffer, Int size, Int receiver, Int tag);
	// template CommunicationRequest
	// Communicator::asyncReceive<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * buffer, Int size, Int sender, Int tag);
	// template void Communicator::probe<SCMinMaxLoc<Real, int>>(
	// Int sender, Int tag, CommunicationStatus & status);
	// template void Communicator::allGather<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int nb_values);
	// template void Communicator::allGatherV<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int * nb_values);
	// template void Communicator::gather<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int nb_values, int root);
	// template void Communicator::gatherV<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int * nb_values, int root);
	// template void Communicator::broadcast<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int nb_values, int root);
	// template void Communicator::allReduce<SCMinMaxLoc<Real, int>>(
	// SCMinMaxLoc<Real, int> * values, int nb_values,
	// const SynchronizerOperation & op);
	} // namespace akantu
	diff --git a/src/synchronizer/communicator.hh b/src/synchronizer/communicator.hh
	index 3c30f7bf1..be9e40c47 100644
	--- a/src/synchronizer/communicator.hh
	+++ b/src/synchronizer/communicator.hh
	@@ -1,561 +1,560 @@
	/**
	* @file communicator.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Class handling the parallel communications
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "aka_event_handler_manager.hh"
	#include "communication_buffer.hh"
	#include "communication_request.hh"
	#include "communicator_event_handler.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_STATIC_COMMUNICATOR_HH_
	#define AKANTU_STATIC_COMMUNICATOR_HH_

	namespace akantu {

	namespace debug {
	class CommunicationException : public Exception {
	public:
	CommunicationException()
	: Exception("An exception happen during a communication process.") {}
	};
	} // namespace debug

	/// @enum SynchronizerOperation reduce operation that the synchronizer can
	/// perform
	enum class SynchronizerOperation {
	_sum,
	_min,
	_max,
	_prod,
	_land,
	_band,
	_lor,
	_bor,
	_lxor,
	_bxor,
	_min_loc,
	_max_loc,
	_null
	};

	enum class CommunicationMode { _auto, _synchronous, _ready };

	namespace {
	int _any_source = -1;
	}
	} // namespace akantu

	namespace akantu {

	struct CommunicatorInternalData {
	virtual ~CommunicatorInternalData() = default;
	};

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	class Communicator : public EventHandlerManager<CommunicatorEventHandler> {
	struct private_member {};
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Communicator(int & argc, char *& argv, const private_member & /m*/);
	Communicator(const private_member & /unused/ = private_member{});
	~Communicator() override;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Point to Point */
	/* ------------------------------------------------------------------------ */
	template <typename T>
	void probe(Int sender, Int tag, CommunicationStatus & status) const;

	template <typename T>
	bool asyncProbe(Int sender, Int tag, CommunicationStatus & status) const;

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void receive(Array<T> & values, Int sender, Int tag) const {
	return this->receiveImpl(
	values.storage(), values.size() * values.getNbComponent(), sender, tag);
	}

	template <typename T>
	inline void receive(std::vector<T> & values, Int sender, Int tag) const {
	return this->receiveImpl(values.data(), values.size(), sender, tag);
	}

	template <typename Tensor>
	inline void
	receive(Tensor & values, Int sender, Int tag,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	return this->receiveImpl(values.storage(), values.size(), sender, tag);
	}

	inline void receive(CommunicationBufferTemplated<true> & values, Int sender,
	Int tag) const {
	return this->receiveImpl(values.storage(), values.size(), sender, tag);
	}

	inline void receive(CommunicationBufferTemplated<false> & values, Int sender,
	Int tag) const {
	CommunicationStatus status;
	this->probe<char>(sender, tag, status);
	values.reserve(status.size());
	return this->receiveImpl(values.storage(), values.size(), sender, tag);
	}

	template <typename T>
	inline void
	receive(T & values, Int sender, Int tag,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	return this->receiveImpl(&values, 1, sender, tag);
	}
	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void
	send(const Array<T> & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->sendImpl(values.storage(),
	values.size() * values.getNbComponent(), receiver,
	tag, mode);
	}

	template <typename T>
	inline void
	send(const std::vector<T> & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->sendImpl(values.data(), values.size(), receiver, tag, mode);
	}

	template <typename Tensor>
	inline void
	send(const Tensor & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	return this->sendImpl(values.storage(), values.size(), receiver, tag, mode);
	}

	template <bool is_static>
	inline void
	send(const CommunicationBufferTemplated<is_static> & values, Int receiver,
	Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->sendImpl(values.storage(), values.size(), receiver, tag, mode);
	}
	template <typename T>
	inline void send(const T & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	return this->sendImpl(&values, 1, receiver, tag, mode);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline CommunicationRequest
	asyncSend(const Array<T> & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->asyncSendImpl(values.storage(),
	values.size() * values.getNbComponent(),
	receiver, tag, mode);
	}
	template <typename T>
	inline CommunicationRequest
	asyncSend(const std::vector<T> & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->asyncSendImpl(values.data(), values.size(), receiver, tag,
	mode);
	}

	template <typename Tensor>
	inline CommunicationRequest
	asyncSend(const Tensor & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	return this->asyncSendImpl(values.storage(), values.size(), receiver, tag,
	mode);
	}
	template <bool is_static>
	inline CommunicationRequest
	asyncSend(const CommunicationBufferTemplated<is_static> & values,
	Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const {
	return this->asyncSendImpl(values.storage(), values.size(), receiver, tag,
	mode);
	}
	template <typename T>
	inline CommunicationRequest
	asyncSend(const T & values, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	return this->asyncSendImpl(&values, 1, receiver, tag, mode);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline CommunicationRequest asyncReceive(Array<T> & values, Int sender,
	Int tag) const {
	return this->asyncReceiveImpl(
	values.storage(), values.size() * values.getNbComponent(), sender, tag);
	}
	template <typename T>
	inline CommunicationRequest asyncReceive(std::vector<T> & values, Int sender,
	Int tag) const {
	return this->asyncReceiveImpl(values.data(), values.size(), sender, tag);
	}

	template <typename Tensor,
	typename = std::enable_if_t<aka::is_tensor<Tensor>::value>>
	inline CommunicationRequest asyncReceive(Tensor & values, Int sender,
	Int tag) const {
	return this->asyncReceiveImpl(values.storage(), values.size(), sender, tag);
	}
	template <bool is_static>
	inline CommunicationRequest
	asyncReceive(CommunicationBufferTemplated<is_static> & values, Int sender,
	Int tag) const {
	return this->asyncReceiveImpl(values.storage(), values.size(), sender, tag);
	}

	/* ------------------------------------------------------------------------ */
	/* Collectives */
	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void
	allReduce(Array<T> & values,
	SynchronizerOperation op = SynchronizerOperation::_sum) const {
	this->allReduceImpl(values.storage(),
	values.size() * values.getNbComponent(), op);
	}

	template <typename Tensor>
	inline void
	allReduce(Tensor & values,
	SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	this->allReduceImpl(values.storage(), values.size(), op);
	}

	template <typename T>
	inline void
	allReduce(T & values, SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->allReduceImpl(&values, 1, op);
	}

	template <typename T>
	inline void
	scan(Array<T> & values,
	SynchronizerOperation op = SynchronizerOperation::_sum) const {
	this->scanImpl(values.storage(), values.storage(),
	values.size() * values.getNbComponent(), op);
	}

	template <typename Tensor>
	inline void
	scan(Tensor & values, SynchronizerOperation op,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	this->scanImpl(values.storage(), values.storage(), values.size(), op);
	}

	template <typename T>
	inline void scan(T & values,
	SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->scanImpl(&values, &values, 1, op);
	}

	template <typename T>
	inline void
	exclusiveScan(Array<T> & values,
	SynchronizerOperation op = SynchronizerOperation::_sum) const {
	this->exclusiveScanImpl(values.storage(), values.storage(),
	values.size() * values.getNbComponent(), op);
	}

	template <typename Tensor>
	inline void
	exclusiveScan(Tensor & values,
	SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	this->exclusiveScanImpl(values.storage(), values.storage(), values.size(),
	op);
	}

	template <typename T>
	inline void
	exclusiveScan(T & values,
	SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->exclusiveScanImpl(&values, &values, 1, op);
	}

	template <typename T>
	inline void
	exclusiveScan(T & values, T & result,
	SynchronizerOperation op = SynchronizerOperation::_sum,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->exclusiveScanImpl(&values, &result, 1, op);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T> inline void allGather(Array<T> & values) const {
	AKANTU_DEBUG_ASSERT(UInt(getNbProc()) == values.size(),
	"The array size is not correct");
	this->allGatherImpl(values.storage(), values.getNbComponent());
	}

	template <typename Tensor,
	typename = std::enable_if_t<aka::is_tensor<Tensor>::value>>
	inline void allGather(Tensor & values) const {
	AKANTU_DEBUG_ASSERT(values.size() / getNbProc() > 0,
	"The vector size is not correct");
	this->allGatherImpl(values.storage(), values.size() / getNbProc());
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void allGatherV(Array<T> & values, const Array<Int> & sizes) const {
	this->allGatherVImpl(values.storage(), sizes.storage());
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void reduce(Array<T> & values, SynchronizerOperation op,
	int root = 0) const {
	this->reduceImpl(values.storage(), values.size() * values.getNbComponent(),
	op, root);
	}

	/* ------------------------------------------------------------------------ */
	template <typename Tensor>
	inline void
	gather(Tensor & values, int root = 0,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	this->gatherImpl(values.storage(), values.getNbComponent(), root);
	}
	template <typename T>
	inline void
	gather(T values, int root = 0,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->gatherImpl(&values, 1, root);
	}
	/* ------------------------------------------------------------------------ */
	template <typename Tensor, typename T>
	inline void
	gather(Tensor & values, Array<T> & gathered,
	std::enable_if_t<aka::is_tensor<Tensor>::value> * /unused/ =
	nullptr) const {
	AKANTU_DEBUG_ASSERT(values.size() == gathered.getNbComponent(),
	"The array size is not correct");
	gathered.resize(getNbProc());
	this->gatherImpl(values.data(), values.size(), gathered.storage(),
	gathered.getNbComponent());
	}

	template <typename T>
	inline void
	gather(T values, Array<T> & gathered,
	std::enable_if_t<std::is_arithmetic<T>::value> * /unused/ =
	nullptr) const {
	this->gatherImpl(&values, 1, gathered.storage(), 1);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void gatherV(Array<T> & values, const Array<Int> & sizes,
	int root = 0) const {
	this->gatherVImpl(values.storage(), sizes.storage(), root);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	inline void broadcast(Array<T> & values, int root = 0) const {
	this->broadcastImpl(values.storage(),
	values.size() * values.getNbComponent(), root);
	}

	template <typename T>
	inline void broadcast(std::vector<T> & values, int root = 0) const {
	this->broadcastImpl(values.data(), values.size(), root);
	}

	inline void broadcast(CommunicationBufferTemplated<true> & buffer,
	int root = 0) const {
	this->broadcastImpl(buffer.storage(), buffer.size(), root);
	}

	inline void broadcast(CommunicationBufferTemplated<false> & buffer,
	int root = 0) const {
	UInt buffer_size = buffer.size();
	this->broadcastImpl(&buffer_size, 1, root);
	if (whoAmI() != root) {
	buffer.reserve(buffer_size);
	}

	if (buffer_size == 0) {
	return;
	}
	this->broadcastImpl(buffer.storage(), buffer.size(), root);
	}

	template <typename T> inline void broadcast(T & values, int root = 0) const {
	this->broadcastImpl(&values, 1, root);
	}

	/* ------------------------------------------------------------------------ */
	void barrier() const;
	CommunicationRequest asyncBarrier() const;

	/* ------------------------------------------------------------------------ */
	/* Request handling */
	/* ------------------------------------------------------------------------ */
	static bool test(CommunicationRequest & request);
	static bool testAll(std::vector<CommunicationRequest> & request);
	static void wait(CommunicationRequest & request);
	static void waitAll(std::vector<CommunicationRequest> & requests);
	static UInt waitAny(std::vector<CommunicationRequest> & requests);
	static inline void freeCommunicationRequest(CommunicationRequest & request);
	static inline void
	freeCommunicationRequest(std::vector<CommunicationRequest> & requests);

	template <typename T, typename MsgProcessor>
	inline void
	receiveAnyNumber(std::vector<CommunicationRequest> & send_requests,
	MsgProcessor && processor, Int tag) const;

	protected:
	template <typename T>
	void
	sendImpl(const T * buffer, Int size, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const;

	template <typename T>
	void receiveImpl(T * buffer, Int size, Int sender, Int tag) const;

	template <typename T>
	CommunicationRequest asyncSendImpl(
	const T * buffer, Int size, Int receiver, Int tag,
	const CommunicationMode & mode = CommunicationMode::_auto) const;

	template <typename T>
	CommunicationRequest asyncReceiveImpl(T * buffer, Int size, Int sender,
	Int tag) const;

	template <typename T>
	void allReduceImpl(T * values, int nb_values, SynchronizerOperation op) const;

	template <typename T>
	void scanImpl(T * values, T * results, int nb_values,
	SynchronizerOperation op) const;

	template <typename T>
	void exclusiveScanImpl(T * values, T * results, int nb_values,
	SynchronizerOperation op) const;

	template <typename T> void allGatherImpl(T * values, int nb_values) const;
	template <typename T> void allGatherVImpl(T * values, int * nb_values) const;

	template <typename T>
	void reduceImpl(T * values, int nb_values, SynchronizerOperation op,
	int root = 0) const;
	template <typename T>
	void gatherImpl(T * values, int nb_values, int root = 0) const;

	template <typename T>
	void gatherImpl(T * values, int nb_values, T * gathered,
	int nb_gathered = 0) const;

	template <typename T>
	void gatherVImpl(T * values, int * nb_values, int root = 0) const;

	template <typename T>
	void broadcastImpl(T * values, int nb_values, int root = 0) const;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	-
	Int getNbProc() const;
	Int whoAmI() const;

	static Communicator & getStaticCommunicator();
	static Communicator & getStaticCommunicator(int & argc, char **& argv);

	int getMaxTag() const;
	int getMinTag() const;

	AKANTU_GET_MACRO(CommunicatorData, (*communicator_data), decltype(auto));

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	static std::unique_ptr<Communicator> static_communicator;

	protected:
	std::unique_ptr<CommunicatorInternalData> communicator_data;
	};

	inline std::ostream & operator<<(std::ostream & stream,
	const CommunicationRequest & _this) {
	_this.printself(stream);
	return stream;
	}

	} // namespace akantu

	#include "communicator_inline_impl.hh"

	#endif /* AKANTU_STATIC_COMMUNICATOR_HH_ */
	diff --git a/src/synchronizer/communicator_dummy_inline_impl.hh b/src/synchronizer/communicator_dummy_inline_impl.hh
	index 632742b9f..8eec30acc 100644
	--- a/src/synchronizer/communicator_dummy_inline_impl.hh
	+++ b/src/synchronizer/communicator_dummy_inline_impl.hh
	@@ -1,152 +1,152 @@
	/**
	* @file communicator_dummy_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 07 2017
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Dummy communicator to make everything work im sequential
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstring>
	#include <type_traits>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	Communicator::Communicator(int & /argc/, char *& /argv*/,
	const private_member & /unused/) {}

	Communicator::Communicator(const private_member & /unused/) {}

	template <typename T>
	void Communicator::sendImpl(const T * /unused/, Int /unused/,
	Int /unused/, Int /unused/,
	const CommunicationMode & /unused/) const {}
	template <typename T>
	void Communicator::receiveImpl(T * /unused/, Int /unused/, Int /unused/,
	Int /unused/) const {}

	template <typename T>
	CommunicationRequest
	Communicator::asyncSendImpl(const T * /unused/, Int /unused/,
	Int /unused/, Int /unused/,
	const CommunicationMode & /unused/) const {
	return std::shared_ptr<InternalCommunicationRequest>(
	new InternalCommunicationRequest(0, 0));
	}

	template <typename T>
	CommunicationRequest
	Communicator::asyncReceiveImpl(T * /unused/, Int /unused/, Int /unused/,
	Int /unused/) const {
	return std::shared_ptr<InternalCommunicationRequest>(
	new InternalCommunicationRequest(0, 0));
	}

	template <typename T>
	void Communicator::probe(Int /unused/, Int /unused/,
	CommunicationStatus & /unused/) const {}
	template <typename T>
	bool Communicator::asyncProbe(Int /unused/, Int /unused/,
	CommunicationStatus & /unused/) const {
	return true;
	}

	bool Communicator::test(CommunicationRequest & /unused/) { return true; }
	bool Communicator::testAll(std::vector<CommunicationRequest> & /unused/) {
	return true;
	}
	void Communicator::wait(CommunicationRequest & /unused/) {}
	void Communicator::waitAll(std::vector<CommunicationRequest> & /unused/) {}
	UInt Communicator::waitAny(std::vector<CommunicationRequest> & /unused/) {
	return UInt(-1);
	}

	void Communicator::barrier() const {}
	CommunicationRequest Communicator::asyncBarrier() const {
	return std::shared_ptr<InternalCommunicationRequest>(
	new InternalCommunicationRequest(0, 0));
	}

	template <typename T>
	void Communicator::reduceImpl(T * /unused/, int /unused/,
	SynchronizerOperation /unused/,
	int /unused/) const {}

	template <typename T>
	void Communicator::allReduceImpl(T * /unused/, int /unused/,
	SynchronizerOperation /unused/) const {}

	template <typename T>
	void Communicator::scanImpl(T * values, T * result, int n,
	SynchronizerOperation /unused/) const {
	if (values == result) {
	return;
	}

	std::copy_n(values, n, result);
	}

	template <typename T>
	void Communicator::exclusiveScanImpl(T * /values/, T * result, int n,
	SynchronizerOperation /unused/) const {
	std::fill_n(result, n, T());
	}

	template <typename T>
	inline void Communicator::allGatherImpl(T * /unused/, int /unused/) const {}
	template <typename T>
	inline void Communicator::allGatherVImpl(T * /unused/,
	int * /unused/) const {}

	template <typename T>
	inline void Communicator::gatherImpl(T * /unused/, int /unused/,
	int /unused/) const {}
	template <typename T>
	void Communicator::gatherImpl(T * values, int nb_values, T * gathered,
	int /unused/) const {
	static_assert(std::is_trivially_copyable<T>{},
	"Cannot send this type of data");
	std::memcpy(gathered, values, nb_values);
	}

	template <typename T>
	inline void Communicator::gatherVImpl(T * /unused/, int * /unused/,
	int /unused/) const {}
	template <typename T>
	inline void Communicator::broadcastImpl(T * /unused/, int /unused/,
	int /unused/) const {}

	int Communicator::getMaxTag() const { return std::numeric_limits<int>::max(); }
	int Communicator::getMinTag() const { return 0; }

	Int Communicator::getNbProc() const { return 1; }
	Int Communicator::whoAmI() const { return 0; }

	} // namespace akantu
	diff --git a/src/synchronizer/communicator_event_handler.hh b/src/synchronizer/communicator_event_handler.hh
	index ab8fcb8e1..cdd0a6d23 100644
	--- a/src/synchronizer/communicator_event_handler.hh
	+++ b/src/synchronizer/communicator_event_handler.hh
	@@ -1,62 +1,62 @@
	/**
	* @file communicator_event_handler.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 15 2017
	*
	* @brief Event handler of the communicator
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_COMMUNICATOR_EVENT_HANDLER_HH_
	#define AKANTU_COMMUNICATOR_EVENT_HANDLER_HH_

	namespace akantu {

	class Communicator;

	struct FinalizeCommunicatorEvent {
	explicit FinalizeCommunicatorEvent(const Communicator & comm)
	: communicator(comm) {}
	const Communicator & communicator;
	};

	class CommunicatorEventHandler {
	public:
	virtual ~CommunicatorEventHandler() = default;
	virtual void onCommunicatorFinalize() = 0;

	private:
	inline void sendEvent(const FinalizeCommunicatorEvent & /unused/) {
	this->onCommunicatorFinalize();
	}

	template <class EventHandler> friend class EventHandlerManager;
	};

	} // namespace akantu

	#endif /* AKANTU_COMMUNICATOR_EVENT_HANDLER_HH_ */
	diff --git a/src/synchronizer/communicator_inline_impl.hh b/src/synchronizer/communicator_inline_impl.hh
	index 74dc26591..de27c353d 100644
	--- a/src/synchronizer/communicator_inline_impl.hh
	+++ b/src/synchronizer/communicator_inline_impl.hh
	@@ -1,101 +1,101 @@
	/**
	* @file communicator_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 02 2016
	* @date last modification: Thu Mar 11 2021
	*
	* @brief implementation of inline functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_STATIC_COMMUNICATOR_INLINE_IMPL_HH_
	#define AKANTU_STATIC_COMMUNICATOR_INLINE_IMPL_HH_

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	- inline void
	+inline void
	Communicator::freeCommunicationRequest(CommunicationRequest & request) {
	request.free();
	}

	/* -------------------------------------------------------------------------- */
	- inline void Communicator::freeCommunicationRequest(
	+inline void Communicator::freeCommunicationRequest(
	std::vector<CommunicationRequest> & requests) {
	std::vector<CommunicationRequest>::iterator it;
	for (it = requests.begin(); it != requests.end(); ++it) {
	it->free();
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, typename MsgProcessor>
	inline void Communicator::receiveAnyNumber(
	std::vector<CommunicationRequest> & send_requests,
	MsgProcessor && processor, Int tag) const {
	CommunicationRequest barrier_request;
	bool got_all{false};
	bool are_send_finished{false};
	if (getNbProc() == 1) {
	return;
	}
	-
	+
	AKANTU_DEBUG_INFO("Sending " << send_requests.size()
	<< " messages and checking for receives TAG["
	<< tag << "]");

	while (not got_all) {
	bool are_receives_ready = true;
	while (are_receives_ready) {
	CommunicationStatus status;
	are_receives_ready = asyncProbe<T>(_any_source, tag, status);
	if (are_receives_ready) {
	AKANTU_DEBUG_INFO("Receiving message from " << status.getSource());
	Array<T> receive_buffer(status.size(), 1);
	receive(receive_buffer, status.getSource(), tag);
	std::forward<MsgProcessor>(processor)(status.getSource(),
	receive_buffer);
	}
	}

	if (not are_send_finished) {
	are_send_finished = testAll(send_requests);
	if (are_send_finished) {
	AKANTU_DEBUG_INFO("All messages send, checking for more receives");
	barrier_request = asyncBarrier();
	}
	}

	if (are_send_finished) {
	got_all = test(barrier_request);
	}
	}
	AKANTU_DEBUG_INFO("Finished receiving");
	}
	} // namespace akantu

	#endif /* AKANTU_STATIC_COMMUNICATOR_INLINE_IMPL_HH_ */
	diff --git a/src/synchronizer/communicator_mpi_inline_impl.hh b/src/synchronizer/communicator_mpi_inline_impl.hh
	index b3ff61814..15b6194ff 100644
	--- a/src/synchronizer/communicator_mpi_inline_impl.hh
	+++ b/src/synchronizer/communicator_mpi_inline_impl.hh
	@@ -1,511 +1,510 @@
	/**
	* @file communicator_mpi_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 07 2017
	* @date last modification: Wed Dec 09 2020
	*
	* @brief StaticCommunicatorMPI implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "mpi_communicator_data.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	#include <type_traits>
	#include <unordered_map>
	#include <vector>
	/* -------------------------------------------------------------------------- */
	#include <mpi.h>
	/* -------------------------------------------------------------------------- */

	#if (defined(__GNUC__) \|\| defined(__GNUG__))
	#if AKA_GCC_VERSION < 60000
	namespace std {
	template <> struct hash<akantu::SynchronizerOperation> {
	using argument_type = akantu::SynchronizerOperation;
	size_t operator()(const argument_type & e) const noexcept {
	auto ue = underlying_type_t<argument_type>(e);
	return uh(ue);
	}

	private:
	const hash<underlying_type_t<argument_type>> uh{};
	};
	} // namespace std
	#endif
	#endif

	namespace akantu {

	class CommunicationRequestMPI : public InternalCommunicationRequest {
	public:
	CommunicationRequestMPI(UInt source, UInt dest)
	: InternalCommunicationRequest(source, dest),
	request(std::make_unique<MPI_Request>()) {}
	MPI_Request & getMPIRequest() { return *request; };

	private:
	std::unique_ptr<MPI_Request> request;
	};

	namespace {
	template <typename T> inline MPI_Datatype getMPIDatatype();
	MPI_Op getMPISynchronizerOperation(SynchronizerOperation op) {
	std::unordered_map<SynchronizerOperation, MPI_Op> _operations{
	{SynchronizerOperation::_sum, MPI_SUM},
	{SynchronizerOperation::_min, MPI_MIN},
	{SynchronizerOperation::_max, MPI_MAX},
	{SynchronizerOperation::_prod, MPI_PROD},
	{SynchronizerOperation::_land, MPI_LAND},
	{SynchronizerOperation::_band, MPI_BAND},
	{SynchronizerOperation::_lor, MPI_LOR},
	{SynchronizerOperation::_bor, MPI_BOR},
	{SynchronizerOperation::_lxor, MPI_LXOR},
	{SynchronizerOperation::_bxor, MPI_BXOR},
	{SynchronizerOperation::_min_loc, MPI_MINLOC},
	{SynchronizerOperation::_max_loc, MPI_MAXLOC},
	{SynchronizerOperation::_null, MPI_OP_NULL}};
	return _operations[op];
	}

	template <typename T> MPI_Datatype inline getMPIDatatype() {
	return MPI_DATATYPE_NULL;
	}

	#define SPECIALIZE_MPI_DATATYPE(type, mpi_type) \
	template <> MPI_Datatype inline getMPIDatatype<type>() { return mpi_type; }

	#define COMMA ,
	SPECIALIZE_MPI_DATATYPE(char, MPI_CHAR)
	SPECIALIZE_MPI_DATATYPE(std::uint8_t, MPI_UINT8_T)
	SPECIALIZE_MPI_DATATYPE(float, MPI_FLOAT)
	SPECIALIZE_MPI_DATATYPE(double, MPI_DOUBLE)
	SPECIALIZE_MPI_DATATYPE(long double, MPI_LONG_DOUBLE)
	SPECIALIZE_MPI_DATATYPE(signed int, MPI_INT)
	SPECIALIZE_MPI_DATATYPE(unsigned int, MPI_UNSIGNED)
	SPECIALIZE_MPI_DATATYPE(signed long int, MPI_LONG)
	SPECIALIZE_MPI_DATATYPE(unsigned long int, MPI_UNSIGNED_LONG)
	SPECIALIZE_MPI_DATATYPE(signed long long int, MPI_LONG_LONG)
	SPECIALIZE_MPI_DATATYPE(unsigned long long int, MPI_UNSIGNED_LONG_LONG)
	SPECIALIZE_MPI_DATATYPE(SCMinMaxLoc<double COMMA int>, MPI_DOUBLE_INT)
	SPECIALIZE_MPI_DATATYPE(SCMinMaxLoc<float COMMA int>, MPI_FLOAT_INT)
	SPECIALIZE_MPI_DATATYPE(bool, MPI_CXX_BOOL)

	template <> MPI_Datatype inline getMPIDatatype<NodeFlag>() {
	return getMPIDatatype<std::underlying_type_t<NodeFlag>>();
	}

	inline int getMPISource(int src) {
	if (src == _any_source) {
	return MPI_ANY_SOURCE;
	}
	return src;
	}

	decltype(auto) convertRequests(std::vector<CommunicationRequest> & requests) {
	std::vector<MPI_Request> mpi_requests(requests.size());

	for (auto && request_pair : zip(requests, mpi_requests)) {
	auto && req = std::get<0>(request_pair);
	auto && mpi_req = std::get<1>(request_pair);
	mpi_req = aka::as_type<CommunicationRequestMPI>(req.getInternal())
	.getMPIRequest();
	}
	return mpi_requests;
	}

	} // namespace

	// this is ugly but shorten the code a lot
	#define MPIDATA \
	(reinterpret_cast<MPICommunicatorData >(communicator_data.get()))

	/* -------------------------------------------------------------------------- */
	/* Implementation */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	Communicator::Communicator(int & /argc/, char *& /argv*/,
	const private_member & m)
	: Communicator(m) {}

	/* -------------------------------------------------------------------------- */
	Communicator::Communicator(const private_member & /unused/)
	- : communicator_data(std::make_unique<MPICommunicatorData>()) {
	-}
	+ : communicator_data(std::make_unique<MPICommunicatorData>()) {}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::sendImpl(const T * buffer, Int size, Int receiver, Int tag,
	const CommunicationMode & mode) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	switch (mode) {
	case CommunicationMode::_auto:
	MPI_Send(buffer, size, type, receiver, tag, communicator);
	break;
	case CommunicationMode::_synchronous:
	MPI_Ssend(buffer, size, type, receiver, tag, communicator);
	break;
	case CommunicationMode::_ready:
	MPI_Rsend(buffer, size, type, receiver, tag, communicator);
	break;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::receiveImpl(T * buffer, Int size, Int sender,
	Int tag) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Status status;
	MPI_Datatype type = getMPIDatatype<T>();
	MPI_Recv(buffer, size, type, getMPISource(sender), tag, communicator,
	&status);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	CommunicationRequest
	Communicator::asyncSendImpl(const T * buffer, Int size, Int receiver, Int tag,
	const CommunicationMode & mode) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	auto * request = new CommunicationRequestMPI(whoAmI(), receiver);
	MPI_Request & req = request->getMPIRequest();

	MPI_Datatype type = getMPIDatatype<T>();

	switch (mode) {
	case CommunicationMode::_auto:
	MPI_Isend(buffer, size, type, receiver, tag, communicator, &req);
	break;
	case CommunicationMode::_synchronous:
	MPI_Issend(buffer, size, type, receiver, tag, communicator, &req);
	break;
	case CommunicationMode::_ready:
	MPI_Irsend(buffer, size, type, receiver, tag, communicator, &req);
	break;
	}
	return std::shared_ptr<InternalCommunicationRequest>(request);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	CommunicationRequest Communicator::asyncReceiveImpl(T * buffer, Int size,
	Int sender, Int tag) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	auto * request = new CommunicationRequestMPI(sender, whoAmI());
	MPI_Datatype type = getMPIDatatype<T>();

	MPI_Request & req = request->getMPIRequest();
	MPI_Irecv(buffer, size, type, getMPISource(sender), tag, communicator, &req);
	return std::shared_ptr<InternalCommunicationRequest>(request);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::probe(Int sender, Int tag,
	CommunicationStatus & status) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Status mpi_status;
	MPI_Probe(getMPISource(sender), tag, communicator, &mpi_status);

	MPI_Datatype type = getMPIDatatype<T>();
	int count;
	MPI_Get_count(&mpi_status, type, &count);

	status.setSource(mpi_status.MPI_SOURCE);
	status.setTag(mpi_status.MPI_TAG);
	status.setSize(count);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	bool Communicator::asyncProbe(Int sender, Int tag,
	CommunicationStatus & status) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Status mpi_status;
	int test;
	MPI_Iprobe(getMPISource(sender), tag, communicator, &test, &mpi_status);

	if (not test) {
	return false;
	}

	MPI_Datatype type = getMPIDatatype<T>();
	int count;
	MPI_Get_count(&mpi_status, type, &count);

	status.setSource(mpi_status.MPI_SOURCE);
	status.setTag(mpi_status.MPI_TAG);
	status.setSize(count);
	return true;
	}

	/* -------------------------------------------------------------------------- */
	bool Communicator::test(CommunicationRequest & request) {
	MPI_Status status;
	int flag;
	auto & req_mpi = aka::as_type<CommunicationRequestMPI>(request.getInternal());

	MPI_Request & req = req_mpi.getMPIRequest();
	MPI_Test(&req, &flag, &status);

	return flag != 0;
	}

	/* -------------------------------------------------------------------------- */
	bool Communicator::testAll(std::vector<CommunicationRequest> & requests) {
	// int are_finished;
	// auto && mpi_requests = convertRequests(requests);
	// MPI_Testall(mpi_requests.size(), mpi_requests.data(), &are_finished,
	// MPI_STATUSES_IGNORE);
	// return are_finished;
	for (auto & request : requests) {
	if (not test(request)) {
	return false;
	}
	}
	return true;
	}

	/* -------------------------------------------------------------------------- */
	void Communicator::wait(CommunicationRequest & request) {
	MPI_Status status;
	auto & req_mpi = aka::as_type<CommunicationRequestMPI>(request.getInternal());
	MPI_Request & req = req_mpi.getMPIRequest();
	MPI_Wait(&req, &status);
	}

	/* -------------------------------------------------------------------------- */
	void Communicator::waitAll(std::vector<CommunicationRequest> & requests) {
	auto && mpi_requests = convertRequests(requests);
	MPI_Waitall(mpi_requests.size(), mpi_requests.data(), MPI_STATUSES_IGNORE);
	}

	/* -------------------------------------------------------------------------- */
	UInt Communicator::waitAny(std::vector<CommunicationRequest> & requests) {
	auto && mpi_requests = convertRequests(requests);

	int pos;
	MPI_Waitany(mpi_requests.size(), mpi_requests.data(), &pos,
	MPI_STATUSES_IGNORE);

	if (pos != MPI_UNDEFINED) {
	return pos;
	}
	return UInt(-1);
	}

	/* -------------------------------------------------------------------------- */
	void Communicator::barrier() const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Barrier(communicator);
	}

	/* -------------------------------------------------------------------------- */
	CommunicationRequest Communicator::asyncBarrier() const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	auto * request = new CommunicationRequestMPI(0, 0);

	MPI_Request & req = request->getMPIRequest();
	MPI_Ibarrier(communicator, &req);

	return std::shared_ptr<InternalCommunicationRequest>(request);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::reduceImpl(T * values, int nb_values,
	SynchronizerOperation op, int root) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	MPI_Reduce(MPI_IN_PLACE, values, nb_values, type,
	getMPISynchronizerOperation(op), root, communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::allReduceImpl(T * values, int nb_values,
	SynchronizerOperation op) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	MPI_Allreduce(MPI_IN_PLACE, values, nb_values, type,
	getMPISynchronizerOperation(op), communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::scanImpl(T * values, T * result, int nb_values,
	SynchronizerOperation op) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	if (values == result) {
	values = reinterpret_cast<T *>(MPI_IN_PLACE);
	}

	MPI_Scan(values, result, nb_values, type, getMPISynchronizerOperation(op),
	communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::exclusiveScanImpl(T * values, T * result, int nb_values,
	SynchronizerOperation op) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	if (values == result) {
	values = reinterpret_cast<T *>(MPI_IN_PLACE);
	}

	MPI_Exscan(values, result, nb_values, type, getMPISynchronizerOperation(op),
	communicator);

	if (whoAmI() == 0) {
	result[0] = T();
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::allGatherImpl(T * values, int nb_values) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();

	MPI_Allgather(MPI_IN_PLACE, nb_values, type, values, nb_values, type,
	communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::allGatherVImpl(T * values, int * nb_values) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	std::vector<int> displs(getNbProc());
	displs[0] = 0;
	for (int i = 1; i < getNbProc(); ++i) {
	displs[i] = displs[i - 1] + nb_values[i - 1];
	}

	MPI_Datatype type = getMPIDatatype<T>();
	MPI_Allgatherv(MPI_IN_PLACE, *nb_values, type, values, nb_values,
	displs.data(), type, communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::gatherImpl(T * values, int nb_values, int root) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	T * send_buf = nullptr;
	T * recv_buf = nullptr;
	if (whoAmI() == root) {
	send_buf = (T *)MPI_IN_PLACE;
	recv_buf = values;
	} else {
	send_buf = values;
	}

	MPI_Datatype type = getMPIDatatype<T>();
	MPI_Gather(send_buf, nb_values, type, recv_buf, nb_values, type, root,
	communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::gatherImpl(T * values, int nb_values, T * gathered,
	int nb_gathered) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	T * send_buf = values;
	T * recv_buf = gathered;

	if (nb_gathered == 0) {
	nb_gathered = nb_values;
	}

	MPI_Datatype type = getMPIDatatype<T>();
	- MPI_Gather(send_buf, nb_values, type, recv_buf, nb_gathered, type,
	- whoAmI(), communicator);
	+ MPI_Gather(send_buf, nb_values, type, recv_buf, nb_gathered, type, whoAmI(),
	+ communicator);
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::gatherVImpl(T * values, int * nb_values, int root) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	int * displs = nullptr;
	auto psize = getNbProc();
	- auto prank = whoAmI();
	+ auto prank = whoAmI();
	if (prank == root) {
	displs = new int[psize];
	displs[0] = 0;
	for (int i = 1; i < psize; ++i) {
	displs[i] = displs[i - 1] + nb_values[i - 1];
	}
	}

	T * send_buf = nullptr;
	T * recv_buf = nullptr;
	if (prank == root) {
	send_buf = (T *)MPI_IN_PLACE;
	recv_buf = values;
	} else {
	send_buf = values;
	}

	MPI_Datatype type = getMPIDatatype<T>();

	MPI_Gatherv(send_buf, *nb_values, type, recv_buf, nb_values, displs, type,
	root, communicator);

	if (prank == root) {
	delete[] displs;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void Communicator::broadcastImpl(T * values, int nb_values, int root) const {
	MPI_Comm communicator = MPIDATA.getMPICommunicator();
	MPI_Datatype type = getMPIDatatype<T>();
	MPI_Bcast(values, nb_values, type, root, communicator);
	}

	/* -------------------------------------------------------------------------- */
	int Communicator::getMaxTag() const { return MPIDATA.getMaxTag(); }
	int Communicator::
	getMinTag() // NOLINT(readability-convert-member-functions-to-static)
	const {
	return 0;
	}
	/* -------------------------------------------------------------------------- */
	Int Communicator::getNbProc() const { return MPIDATA.size(); }
	Int Communicator::whoAmI() const { return MPIDATA.rank(); }

	} // namespace akantu
	diff --git a/src/synchronizer/data_accessor.cc b/src/synchronizer/data_accessor.cc
	index 4e13401f1..2d41ddc73 100644
	--- a/src/synchronizer/data_accessor.cc
	+++ b/src/synchronizer/data_accessor.cc
	@@ -1,158 +1,158 @@
	/**
	* @file data_accessor.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief data accessors constructor functions
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "fe_engine.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T, bool pack_helper>
	void DataAccessor<Element>::packUnpackNodalDataHelper(
	Array<T> & data, CommunicationBuffer & buffer,
	const Array<Element> & elements, const Mesh & mesh) {
	UInt nb_component = data.getNbComponent();
	UInt nb_nodes_per_element = 0;

	ElementType current_element_type = _not_defined;
	GhostType current_ghost_type = _casper;
	UInt * conn = nullptr;

	for (const auto & el : elements) {
	if (el.type != current_element_type \|\|
	el.ghost_type != current_ghost_type) {
	current_element_type = el.type;
	current_ghost_type = el.ghost_type;
	conn = mesh.getConnectivity(el.type, el.ghost_type).storage();
	nb_nodes_per_element = Mesh::getNbNodesPerElement(el.type);
	}

	UInt el_offset = el.element * nb_nodes_per_element;
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt offset_conn = conn[el_offset + n];
	Vector<T> data_vect(data.storage() + offset_conn * nb_component,
	nb_component);

	if (pack_helper) {
	buffer << data_vect;
	} else {
	buffer >> data_vect;
	}
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	template <typename T, bool pack_helper>
	void DataAccessor<Element>::packUnpackElementalDataHelper(
	ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & element, bool per_quadrature_point_data,
	const FEEngine & fem) {
	ElementType current_element_type = _not_defined;
	GhostType current_ghost_type = _casper;
	UInt nb_quad_per_elem = 0;
	UInt nb_component = 0;

	Array<T> * vect = nullptr;

	for (const auto & el : element) {
	if (el.type != current_element_type \|\|
	el.ghost_type != current_ghost_type) {
	current_element_type = el.type;
	current_ghost_type = el.ghost_type;
	vect = &data_to_pack(el.type, el.ghost_type);

	nb_quad_per_elem =
	per_quadrature_point_data
	? fem.getNbIntegrationPoints(el.type, el.ghost_type)
	: 1;
	nb_component = vect->getNbComponent();
	}

	Vector<T> data(vect->storage() +
	el.element * nb_component * nb_quad_per_elem,
	nb_component * nb_quad_per_elem);
	if (pack_helper) {
	buffer << data;
	} else {
	buffer >> data;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, bool pack_helper>
	void DataAccessor<UInt>::packUnpackDOFDataHelper(Array<T> & data,
	CommunicationBuffer & buffer,
	const Array<UInt> & dofs) {
	T * data_ptr = data.storage();
	for (const auto & dof : dofs) {
	if (pack_helper) {
	buffer << data_ptr[dof];
	} else {
	buffer >> data_ptr[dof];
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	#define DECLARE_HELPERS(T) \
	template void DataAccessor<Element>::packUnpackNodalDataHelper<T, false>( \
	Array<T> & data, CommunicationBuffer & buffer, \
	const Array<Element> & elements, const Mesh & mesh); \
	template void DataAccessor<Element>::packUnpackNodalDataHelper<T, true>( \
	Array<T> & data, CommunicationBuffer & buffer, \
	const Array<Element> & elements, const Mesh & mesh); \
	template void \
	DataAccessor<Element>::packUnpackElementalDataHelper<T, false>( \
	ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer, \
	const Array<Element> & element, bool per_quadrature_point_data, \
	const FEEngine & fem); \
	template void DataAccessor<Element>::packUnpackElementalDataHelper<T, true>( \
	ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer, \
	const Array<Element> & element, bool per_quadrature_point_data, \
	const FEEngine & fem); \
	template void DataAccessor<UInt>::packUnpackDOFDataHelper<T, true>( \
	Array<T> & data, CommunicationBuffer & buffer, \
	const Array<UInt> & dofs); \
	template void DataAccessor<UInt>::packUnpackDOFDataHelper<T, false>( \
	Array<T> & data, CommunicationBuffer & buffer, const Array<UInt> & dofs)

	/* -------------------------------------------------------------------------- */
	DECLARE_HELPERS(Real);
	DECLARE_HELPERS(UInt);
	DECLARE_HELPERS(bool);
	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/synchronizer/data_accessor.hh b/src/synchronizer/data_accessor.hh
	index df3370722..e706856d6 100644
	--- a/src/synchronizer/data_accessor.hh
	+++ b/src/synchronizer/data_accessor.hh
	@@ -1,354 +1,355 @@
	/**
	* @file data_accessor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Sep 01 2010
	* @date last modification: Fri Apr 09 2021
	*
	* @brief Interface of accessors for pack_unpack system
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "communication_buffer.hh"
	#include "element.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DATA_ACCESSOR_HH_
	#define AKANTU_DATA_ACCESSOR_HH_

	namespace akantu {
	class FEEngine;
	} // namespace akantu

	namespace akantu {

	class DataAccessorBase {
	public:
	DataAccessorBase() = default;
	virtual ~DataAccessorBase() = default;
	};

	template <class T> class DataAccessor : public virtual DataAccessorBase {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DataAccessor() = default;
	~DataAccessor() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/**
	* @brief get the number of data to exchange for a given array of T
	* (elements or dofs) and a given akantu::SynchronizationTag
	*/
	virtual UInt getNbData(const Array<T> & elements,
	const SynchronizationTag & tag) const = 0;

	/**
	* @brief pack the data for a given array of T (elements or dofs) and a given
	* akantu::SynchronizationTag
	*/
	virtual void packData(CommunicationBuffer & buffer, const Array<T> & element,
	const SynchronizationTag & tag) const = 0;

	/**
	* @brief unpack the data for a given array of T (elements or dofs) and a
	* given akantu::SynchronizationTag
	*/
	virtual void unpackData(CommunicationBuffer & buffer,
	const Array<T> & element,
	const SynchronizationTag & tag) = 0;
	};

	/* -------------------------------------------------------------------------- */
	/* Specialization */
	/* -------------------------------------------------------------------------- */
	template <> class DataAccessor<Element> : public virtual DataAccessorBase {
	public:
	DataAccessor() = default;
	~DataAccessor() override = default;

	virtual UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const = 0;
	virtual void packData(CommunicationBuffer & buffer,
	const Array<Element> & element,
	const SynchronizationTag & tag) const = 0;
	virtual void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & element,
	const SynchronizationTag & tag) = 0;

	/* ------------------------------------------------------------------------ */
	public:
	template <typename T, bool pack_helper>
	static void
	packUnpackNodalDataHelper(Array<T> & data, CommunicationBuffer & buffer,
	const Array<Element> & elements, const Mesh & mesh);

	/* ------------------------------------------------------------------------ */
	template <typename T, bool pack_helper>
	static void packUnpackElementalDataHelper(
	ElementTypeMapArray<T> & data_to_pack, CommunicationBuffer & buffer,
	const Array<Element> & element, bool per_quadrature_point_data,
	const FEEngine & fem);

	/* ------------------------------------------------------------------------ */
	template <typename T>
	static void
	packNodalDataHelper(const Array<T> & data, CommunicationBuffer & buffer,
	const Array<Element> & elements, const Mesh & mesh) {
	packUnpackNodalDataHelper<T, true>(const_cast<Array<T> &>(data), buffer,
	elements, mesh);
	}

	template <typename T>
	static inline void
	unpackNodalDataHelper(Array<T> & data, CommunicationBuffer & buffer,
	const Array<Element> & elements, const Mesh & mesh) {
	packUnpackNodalDataHelper<T, false>(data, buffer, elements, mesh);
	}

	/* ------------------------------------------------------------------------ */
	template <typename T>
	static inline void
	packElementalDataHelper(const ElementTypeMapArray<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	bool per_quadrature_point, const FEEngine & fem) {
	packUnpackElementalDataHelper<T, true>(
	const_cast<ElementTypeMapArray<T> &>(data_to_pack), buffer, elements,
	per_quadrature_point, fem);
	}

	template <typename T>
	static inline void
	unpackElementalDataHelper(ElementTypeMapArray<T> & data_to_unpack,
	CommunicationBuffer & buffer,
	const Array<Element> & elements,
	bool per_quadrature_point, const FEEngine & fem) {
	packUnpackElementalDataHelper<T, false>(data_to_unpack, buffer, elements,
	per_quadrature_point, fem);
	}
	};

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <> class DataAccessor<UInt> : public virtual DataAccessorBase {
	public:
	DataAccessor() = default;
	~DataAccessor() override = default;

	virtual UInt getNbData(const Array<UInt> & elements,
	const SynchronizationTag & tag) const = 0;
	virtual void packData(CommunicationBuffer & buffer,
	const Array<UInt> & element,
	const SynchronizationTag & tag) const = 0;
	virtual void unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & element,
	const SynchronizationTag & tag) = 0;
	/* ------------------------------------------------------------------------ */
	public:
	template <typename T, bool pack_helper>
	static void packUnpackDOFDataHelper(Array<T> & data,
	CommunicationBuffer & buffer,
	const Array<UInt> & dofs);

	template <typename T>
	static inline void packDOFDataHelper(const Array<T> & data_to_pack,
	CommunicationBuffer & buffer,
	const Array<UInt> & dofs) {
	packUnpackDOFDataHelper<T, true>(const_cast<Array<T> &>(data_to_pack),
	buffer, dofs);
	}

	template <typename T>
	static inline void unpackDOFDataHelper(Array<T> & data_to_unpack,
	CommunicationBuffer & buffer,
	const Array<UInt> & dofs) {
	packUnpackDOFDataHelper<T, false>(data_to_unpack, buffer, dofs);
	}
	};

	/* -------------------------------------------------------------------------- */
	template <typename T> class AddOperation {
	public:
	inline T operator()(T & a, T & b) { return a + b; };
	};

	template <typename T> class IdentityOperation {
	public:
	inline T & operator()(T & /unused/, T & b) { return b; };
	};
	/* -------------------------------------------------------------------------- */

	-
	/* -------------------------------------------------------------------------- */
	template <class Entity, template <class> class Op, class T>
	class ReduceDataAccessor : public virtual DataAccessor<Entity> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ReduceDataAccessor(Array<T> & data, const SynchronizationTag & tag)
	: data(data), tag(tag) {}

	~ReduceDataAccessor() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	UInt getNbData(const Array<Entity> & entities,
	const SynchronizationTag & tag) const override {
	if (tag != this->tag) {
	return 0;
	}

	Vector<T> tmp(data.getNbComponent());
	return entities.size() * CommunicationBuffer::sizeInBuffer(tmp);
	}

	/* ------------------------------------------------------------------------ */
	void packData(CommunicationBuffer & buffer, const Array<Entity> & entities,
	const SynchronizationTag & tag) const override {
	if (tag != this->tag) {
	return;
	}

	auto data_it = data.begin(data.getNbComponent());
	for (auto el : entities) {
	buffer << Vector<T>(data_it[el]);
	}
	}

	/* ------------------------------------------------------------------------ */
	void unpackData(CommunicationBuffer & buffer, const Array<Entity> & entities,
	const SynchronizationTag & tag) override {
	if (tag != this->tag) {
	return;
	}

	auto data_it = data.begin(data.getNbComponent());
	for (auto el : entities) {
	Vector<T> unpacked(data.getNbComponent());
	Vector<T> vect(data_it[el]);
	buffer >> unpacked;
	vect = oper(vect, unpacked);
	}
	}

	protected:
	/// data to (un)pack
	Array<T> & data;

	/// Tag to consider
	SynchronizationTag tag;

	/// reduction operator
	Op<Vector<T>> oper;
	};

	-
	/* -------------------------------------------------------------------------- */
	template <class T>
	using SimpleUIntDataAccessor = ReduceDataAccessor<UInt, IdentityOperation, T>;

	/* -------------------------------------------------------------------------- */
	template <class T>
	class SimpleElementDataAccessor : public virtual DataAccessor<Element> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SimpleElementDataAccessor(ElementTypeMapArray<T> & data,
	- const SynchronizationTag & tag)
	+ const SynchronizationTag & tag)
	: data(data), tag(tag) {}

	~SimpleElementDataAccessor() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	- if (tag != this->tag)
	+ if (tag != this->tag) {
	return 0;
	+ }

	Int size = 0;

	- for (auto & el : elements) {
	+ for (const auto & el : elements) {
	auto && data_type = data(el.type, el.ghost_type);
	size += sizeof(T) * data_type.getNbComponent();
	}

	return size;
	}

	/* ------------------------------------------------------------------------ */
	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	- if (tag != this->tag)
	+ if (tag != this->tag) {
	return;
	+ }

	- for (auto & el : elements) {
	+ for (const auto & el : elements) {
	auto && data_type = data(el.type, el.ghost_type);
	for (auto c : arange(data_type.getNbComponent())) {
	const auto & data_per_element = data_type(el.element, c);
	buffer << data_per_element;
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override {
	- if (tag != this->tag)
	+ if (tag != this->tag) {
	return;
	+ }

	- for (auto & el : elements) {
	+ for (const auto & el : elements) {
	auto && data_type = data(el.type, el.ghost_type);
	for (auto c : arange(data_type.getNbComponent())) {
	auto & data_per_element = data_type(el.element, c);
	buffer >> data_per_element;
	}
	}
	}

	protected:
	/// data to (un)pack
	ElementTypeMapArray<T> & data;

	/// Tag to consider
	SynchronizationTag tag;
	};

	} // namespace akantu

	#endif /* AKANTU_DATA_ACCESSOR_HH_ */
	diff --git a/src/synchronizer/dof_synchronizer.cc b/src/synchronizer/dof_synchronizer.cc
	index 93a63872a..f414619c2 100644
	--- a/src/synchronizer/dof_synchronizer.cc
	+++ b/src/synchronizer/dof_synchronizer.cc
	@@ -1,231 +1,231 @@
	/**
	* @file dof_synchronizer.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 17 2011
	* @date last modification: Fri Jul 24 2020
	*
	* @brief DOF synchronizing object implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_synchronizer.hh"
	#include "aka_iterators.hh"
	#include "dof_manager_default.hh"
	#include "mesh.hh"
	#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/**
	* A DOFSynchronizer needs a mesh and the number of degrees of freedom
	* per node to be created. In the constructor computes the local and global dof
	* number for each dof. The member
	* proc_informations (std vector) is resized with the number of mpi
	* processes. Each entry in the vector is a PerProcInformations object
	* that contains the interactions of the current mpi process (prank) with the
	* mpi process corresponding to the position of that entry. Every
	* ProcInformations object contains one array with the dofs that have
	* to be sent to prank and a second one with dofs that willl be received form
	* prank.
	* This information is needed for the asychronous communications. The
	* constructor sets up this information.
	*/
	DOFSynchronizer::DOFSynchronizer(DOFManagerDefault & dof_manager, const ID & id)
	: SynchronizerImpl<UInt>(dof_manager.getCommunicator(), id),
	dof_manager(dof_manager) {
	std::vector<ID> dof_ids = dof_manager.getDOFIDs();

	// Transfers nodes to global equation numbers in new schemes
	for (const ID & dof_id : dof_ids) {
	registerDOFs(dof_id);
	}
	}

	/* -------------------------------------------------------------------------- */
	DOFSynchronizer::~DOFSynchronizer() = default;

	/* -------------------------------------------------------------------------- */
	void DOFSynchronizer::registerDOFs(const ID & dof_id) {
	if (this->nb_proc == 1) {
	return;
	}

	if (dof_manager.getSupportType(dof_id) != _dst_nodal) {
	return;
	}

	const auto & equation_numbers = dof_manager.getLocalEquationsNumbers(dof_id);

	const auto & associated_nodes = dof_manager.getDOFsAssociatedNodes(dof_id);
	const auto & node_synchronizer = dof_manager.getMesh().getNodeSynchronizer();
	const auto & node_communications = node_synchronizer.getCommunications();

	auto transcode_node_to_global_dof_scheme =
	[this, &associated_nodes, &equation_numbers](
	auto && it, auto && end, const CommunicationSendRecv & sr) -> void {
	for (; it != end; ++it) {
	auto & scheme = communications.createScheme(it->first, sr);

	const auto & node_scheme = it->second;
	for (auto & node : node_scheme) {
	auto an_begin = associated_nodes.begin();
	auto an_it = an_begin;
	auto an_end = associated_nodes.end();

	std::vector<UInt> global_dofs_per_node;
	while ((an_it = std::find(an_it, an_end, node)) != an_end) {
	UInt pos = an_it - an_begin;
	UInt local_eq_num = equation_numbers(pos);
	UInt global_eq_num =
	dof_manager.localToGlobalEquationNumber(local_eq_num);
	global_dofs_per_node.push_back(global_eq_num);
	++an_it;
	}

	std::sort(global_dofs_per_node.begin(), global_dofs_per_node.end());
	std::transform(global_dofs_per_node.begin(), global_dofs_per_node.end(),
	global_dofs_per_node.begin(), [this](UInt g) -> UInt {
	UInt l = dof_manager.globalToLocalEquationNumber(g);
	return l;
	});
	for (auto & leqnum : global_dofs_per_node) {
	scheme.push_back(leqnum);
	}
	}
	}
	};

	for (auto sr : send_recv_t{}) {
	auto ncs_it = node_communications.begin_scheme(sr);
	auto ncs_end = node_communications.end_scheme(sr);

	transcode_node_to_global_dof_scheme(ncs_it, ncs_end, sr);
	}

	entities_changed = true;
	}

	/* -------------------------------------------------------------------------- */
	void DOFSynchronizer::fillEntityToSend(Array<UInt> & dofs_to_send) {
	UInt nb_dofs = dof_manager.getLocalSystemSize();

	this->entities_from_root.zero();
	dofs_to_send.resize(0);

	for (UInt d : arange(nb_dofs)) {
	if (not dof_manager.isLocalOrMasterDOF(d)) {
	continue;
	}

	entities_from_root.push_back(d);
	}

	for (auto d : entities_from_root) {
	UInt global_dof = dof_manager.localToGlobalEquationNumber(d);
	dofs_to_send.push_back(global_dof);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFSynchronizer::onNodesAdded(const Array<UInt> & /nodes_list/) {
	auto dof_ids = dof_manager.getDOFIDs();

	for (auto sr : iterate_send_recv) {
	for (auto && data : communications.iterateSchemes(sr)) {
	auto & scheme = data.second;
	scheme.resize(0);
	}
	}

	for (auto & dof_id : dof_ids) {
	registerDOFs(dof_id);
	}

	// const auto & node_synchronizer =
	// dof_manager.getMesh().getNodeSynchronizer(); const auto &
	// node_communications = node_synchronizer.getCommunications();

	// std::map<UInt, std::vector<UInt>> nodes_per_proc[2];

	// for (auto sr : iterate_send_recv) {
	// for (auto && data : node_communications.iterateSchemes(sr)) {
	// auto proc = data.first;
	// const auto & scheme = data.second;
	// for (auto node : scheme) {
	// nodes_per_proc[sr][proc].push_back(node);
	// }
	// }
	// }

	// std::map<UInt, std::vector<UInt>> dofs_per_proc[2];
	// for (auto & dof_id : dof_ids) {
	// const auto & associated_nodes =
	// dof_manager.getDOFsAssociatedNodes(dof_id); const auto &
	// local_equation_numbers =
	// dof_manager.getEquationsNumbers(dof_id);

	// for (auto tuple : zip(associated_nodes, local_equation_numbers)) {
	// UInt assoc_node;
	// UInt local_eq_num;
	// std::tie(assoc_node, local_eq_num) = tuple;

	// for (auto sr_it = send_recv_t::begin(); sr_it != send_recv_t::end();
	// ++sr_it) {
	// for (auto & pair : nodes_per_proc[*sr_it]) {
	// if (std::find(pair.second.end(), pair.second.end(), assoc_node) !=
	// pair.second.end()) {
	// dofs_per_proc[*sr_it][pair.first].push_back(local_eq_num);
	// }
	// }
	// }
	// }
	// }

	// for (auto sr_it = send_recv_t::begin(); sr_it != send_recv_t::end();
	// ++sr_it) {
	// for (auto & pair : dofs_per_proc[*sr_it]) {
	// std::sort(pair.second.begin(), pair.second.end(),
	// [this](UInt la, UInt lb) -> bool {
	// UInt ga = dof_manager.localToGlobalEquationNumber(la);
	// UInt gb = dof_manager.localToGlobalEquationNumber(lb);
	// return ga < gb;
	// });

	// auto & scheme = communications.getScheme(pair.first, *sr_it);
	// scheme.resize(0);
	// for (auto leq : pair.second) {
	// scheme.push_back(leq);
	// }
	// }
	// }
	this->entities_changed = true;
	}

	} // namespace akantu
	diff --git a/src/synchronizer/dof_synchronizer.hh b/src/synchronizer/dof_synchronizer.hh
	index 169bca2b1..606295588 100644
	--- a/src/synchronizer/dof_synchronizer.hh
	+++ b/src/synchronizer/dof_synchronizer.hh
	@@ -1,85 +1,85 @@
	/**
	* @file dof_synchronizer.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 17 2011
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Synchronize Array of DOFs
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "synchronizer_impl.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	class Mesh;
	class DOFManagerDefault;
	} // namespace akantu

	#ifndef AKANTU_DOF_SYNCHRONIZER_HH_
	#define AKANTU_DOF_SYNCHRONIZER_HH_

	namespace akantu {

	class DOFSynchronizer : public SynchronizerImpl<UInt> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DOFSynchronizer(DOFManagerDefault & dof_manager,
	const ID & id = "dof_synchronizer");
	~DOFSynchronizer() override;

	virtual void registerDOFs(const ID & dof_id);
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void onNodesAdded(const Array<UInt> & nodes);

	protected:
	Int getRank(const UInt & /node/) const final { AKANTU_TO_IMPLEMENT(); }

	/// list the entities to send to root process
	void fillEntityToSend(Array<UInt> & dofs_to_send) override;

	inline UInt canScatterSize() override;
	inline UInt gatheredSize() override;

	inline UInt localToGlobalEntity(const UInt & local) override;

	private:
	/// information on the dofs
	DOFManagerDefault & dof_manager;
	};

	} // namespace akantu

	#include "dof_synchronizer_inline_impl.hh"

	#endif /* AKANTU_DOF_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/dof_synchronizer_inline_impl.hh b/src/synchronizer/dof_synchronizer_inline_impl.hh
	index ac3b3d6d5..1fddfa545 100644
	--- a/src/synchronizer/dof_synchronizer_inline_impl.hh
	+++ b/src/synchronizer/dof_synchronizer_inline_impl.hh
	@@ -1,62 +1,62 @@
	/**
	* @file dof_synchronizer_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 17 2011
	* @date last modification: Wed Mar 04 2020
	*
	* @brief DOFSynchronizer inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_buffer.hh"
	#include "data_accessor.hh"
	#include "dof_manager_default.hh"
	#include "dof_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_DOF_SYNCHRONIZER_INLINE_IMPL_HH_
	#define AKANTU_DOF_SYNCHRONIZER_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline UInt DOFSynchronizer::canScatterSize() {
	return dof_manager.getLocalSystemSize();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt DOFSynchronizer::gatheredSize() {
	return dof_manager.getSystemSize();
	}

	inline UInt DOFSynchronizer::localToGlobalEntity(const UInt & local) {
	return dof_manager.localToGlobalEquationNumber(local);
	}
	} // namespace akantu

	#endif /* AKANTU_DOF_SYNCHRONIZER_INLINE_IMPL_HH_ */
	diff --git a/src/synchronizer/element_info_per_processor.cc b/src/synchronizer/element_info_per_processor.cc
	index 044e56b75..1539dd643 100644
	--- a/src/synchronizer/element_info_per_processor.cc
	+++ b/src/synchronizer/element_info_per_processor.cc
	@@ -1,127 +1,127 @@
	/**
	* @file element_info_per_processor.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Helper class to distribute a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_info_per_processor.hh"
	#include "communicator.hh"
	#include "element_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <iostream>
	#include <map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	ElementInfoPerProc::ElementInfoPerProc(ElementSynchronizer & synchronizer,
	UInt message_cnt, UInt root,
	ElementType type)
	: MeshAccessor(synchronizer.getMesh()), synchronizer(synchronizer),
	rank(synchronizer.getCommunicator().whoAmI()),
	nb_proc(synchronizer.getCommunicator().getNbProc()), root(root),
	type(type), message_count(message_cnt), mesh(synchronizer.getMesh()),
	comm(synchronizer.getCommunicator()) {}

	/* -------------------------------------------------------------------------- */
	bool ElementInfoPerProc::synchronize() {
	auto need_synchronize = needSynchronize();

	if (need_synchronize) {
	synchronizeConnectivities();
	synchronizePartitions();
	synchronizeTags();
	synchronizeGroups();
	}

	return need_synchronize;
	}

	/* -------------------------------------------------------------------------- */
	void ElementInfoPerProc::fillCommunicationScheme(
	const Array<UInt> & partition) {
	AKANTU_DEBUG_IN();

	Element element;
	element.type = this->type;

	auto & communications = this->synchronizer.getCommunications();
	auto part = partition.begin();

	std::map<UInt, Array<Element>> send_array_per_proc;
	for (UInt lel = 0; lel < nb_local_element; ++lel) {
	UInt nb_send = *part;
	++part;

	element.element = lel;
	element.ghost_type = _not_ghost;
	for (UInt p = 0; p < nb_send; ++p, ++part) {
	UInt proc = *part;

	AKANTU_DEBUG(dblAccessory,
	"Must send : " << element << " to proc " << proc);
	send_array_per_proc[proc].push_back(element);
	}
	}

	for (auto & send_schemes : send_array_per_proc) {
	if (send_schemes.second.empty()) {
	continue;
	}
	auto & scheme = communications.createSendScheme(send_schemes.first);
	scheme.append(send_schemes.second);
	}

	std::map<UInt, Array<Element>> recv_array_per_proc;

	for (UInt gel = 0; gel < nb_ghost_element; ++gel, ++part) {
	UInt proc = *part;
	element.element = gel;
	element.ghost_type = _ghost;
	AKANTU_DEBUG(dblAccessory,
	"Must recv : " << element << " from proc " << proc);
	recv_array_per_proc[proc].push_back(element);
	}

	for (auto & recv_schemes : recv_array_per_proc) {
	if (recv_schemes.second.empty()) {
	continue;
	}
	auto & scheme = communications.createRecvScheme(recv_schemes.first);
	scheme.append(recv_schemes.second);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/synchronizer/element_info_per_processor.hh b/src/synchronizer/element_info_per_processor.hh
	index 7503a598f..46cd1e225 100644
	--- a/src/synchronizer/element_info_per_processor.hh
	+++ b/src/synchronizer/element_info_per_processor.hh
	@@ -1,152 +1,152 @@
	/**
	* @file element_info_per_processor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Helper classes to create the distributed synchronizer and distribute
	* a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "communication_buffer.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_INFO_PER_PROCESSOR_HH_
	#define AKANTU_ELEMENT_INFO_PER_PROCESSOR_HH_

	namespace akantu {
	class ElementSynchronizer;
	class Communicator;
	class MeshPartition;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class ElementInfoPerProc : protected MeshAccessor {
	public:
	ElementInfoPerProc(ElementSynchronizer & synchronizer, UInt message_cnt,
	UInt root, ElementType type);
	bool synchronize();

	protected:
	virtual void synchronizeConnectivities() = 0;
	virtual void synchronizePartitions() = 0;
	virtual void synchronizeTags() = 0;
	virtual void synchronizeGroups() = 0;
	virtual bool needSynchronize() = 0;

	protected:
	void fillCommunicationScheme(const Array<UInt> & partition);

	template <class CommunicationBuffer>
	void fillElementGroupsFromBuffer(CommunicationBuffer & buffer);

	template <typename T, typename BufferType>
	void fillMeshDataTemplated(BufferType & buffer, const std::string & tag_name,
	UInt nb_component);

	template <typename BufferType>
	void fillMeshData(BufferType & buffer, const std::string & tag_name,
	const MeshDataTypeCode & type_code, UInt nb_component);

	protected:
	ElementSynchronizer & synchronizer;

	UInt rank{0};
	UInt nb_proc{1};

	UInt root{0};

	ElementType type{_not_defined};

	UInt nb_tags{0};
	UInt nb_nodes_per_element{0};
	UInt nb_element{0};

	UInt nb_local_element{0};
	UInt nb_ghost_element{0};

	UInt message_count{0};
	Mesh & mesh;
	const Communicator & comm;
	};

	/* -------------------------------------------------------------------------- */
	class MasterElementInfoPerProc : public ElementInfoPerProc {
	public:
	MasterElementInfoPerProc(ElementSynchronizer & synchronizer, UInt message_cnt,
	UInt root, ElementType type,
	const MeshPartition & partition);

	protected:
	void synchronizeConnectivities() override;
	void synchronizePartitions() override;
	void synchronizeTags() override;
	void synchronizeGroups() override;
	bool needSynchronize() override { return type != _not_defined; }

	protected:
	template <typename T>
	void fillTagBufferTemplated(std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name);
	void fillTagBuffer(std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name);

	private:
	const MeshPartition & partition;

	Vector<UInt> all_nb_local_element;
	Vector<UInt> all_nb_ghost_element;
	Vector<UInt> all_nb_element_to_send;
	};

	/* -------------------------------------------------------------------------- */
	class SlaveElementInfoPerProc : public ElementInfoPerProc {
	public:
	SlaveElementInfoPerProc(ElementSynchronizer & synchronizer, UInt message_cnt,
	UInt root);

	protected:
	void synchronizeConnectivities() override;
	void synchronizePartitions() override;
	void synchronizeTags() override;
	void synchronizeGroups() override;

	bool needSynchronize() override;

	private:
	UInt nb_element_to_receive{0};
	};

	} // namespace akantu

	#include "element_info_per_processor_tmpl.hh"

	#endif /* AKANTU_ELEMENT_INFO_PER_PROCESSOR_HH_ */
	diff --git a/src/synchronizer/element_info_per_processor_tmpl.hh b/src/synchronizer/element_info_per_processor_tmpl.hh
	index 2ab1e7bce..135bf9b9b 100644
	--- a/src/synchronizer/element_info_per_processor_tmpl.hh
	+++ b/src/synchronizer/element_info_per_processor_tmpl.hh
	@@ -1,148 +1,148 @@
	/**
	* @file element_info_per_processor_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Thu Nov 12 2020
	*
	* @brief Helper classes to create the distributed synchronizer and distribute
	* a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "element_info_per_processor.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_INFO_PER_PROCESSOR_TMPL_HH_
	#define AKANTU_ELEMENT_INFO_PER_PROCESSOR_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename T, typename BufferType>
	void ElementInfoPerProc::fillMeshDataTemplated(BufferType & buffer,
	const std::string & tag_name,
	UInt nb_component) {

	AKANTU_DEBUG_ASSERT(this->mesh.getNbElement(this->type) == nb_local_element,
	"Did not got enought informations for the tag "
	<< tag_name << " and the element type " << this->type
	<< ":"
	<< "_not_ghost."
	<< " Got " << nb_local_element << " values, expected "
	<< mesh.getNbElement(this->type));

	mesh.getElementalData<T>(tag_name);
	Array<T> & data = mesh.getElementalDataArrayAlloc<T>(
	tag_name, this->type, _not_ghost, nb_component);

	data.resize(nb_local_element);
	/// unpacking the data, element by element
	for (UInt i(0); i < nb_local_element; ++i) {
	for (UInt j(0); j < nb_component; ++j) {
	buffer >> data(i, j);
	}
	}

	AKANTU_DEBUG_ASSERT(mesh.getNbElement(this->type, _ghost) == nb_ghost_element,
	"Did not got enought informations for the tag "
	<< tag_name << " and the element type " << this->type
	<< ":"
	<< "_ghost."
	<< " Got " << nb_ghost_element << " values, expected "
	<< mesh.getNbElement(this->type, _ghost));

	Array<T> & data_ghost = mesh.getElementalDataArrayAlloc<T>(
	tag_name, this->type, _ghost, nb_component);
	data_ghost.resize(nb_ghost_element);

	/// unpacking the ghost data, element by element
	for (UInt j(0); j < nb_ghost_element; ++j) {
	for (UInt k(0); k < nb_component; ++k) {
	buffer >> data_ghost(j, k);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <typename BufferType>
	void ElementInfoPerProc::fillMeshData(BufferType & buffer,
	const std::string & tag_name,
	const MeshDataTypeCode & type_code,
	UInt nb_component) {
	#define AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA(r, extra_param, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	fillMeshDataTemplated<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(buffer, tag_name, \
	nb_component); \
	break; \
	}

	switch (type_code) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA, ,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Could not determine the type of tag" << tag_name << "!");
	break;
	}
	#undef AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA
	}

	/* -------------------------------------------------------------------------- */
	template <class CommunicationBuffer>
	void ElementInfoPerProc::fillElementGroupsFromBuffer(
	CommunicationBuffer & buffer) {
	AKANTU_DEBUG_IN();

	Element el;
	el.type = type;

	for (auto ghost_type : ghost_types) {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	el.ghost_type = ghost_type;

	for (UInt e = 0; e < nb_element; ++e) {
	el.element = e;

	std::vector<std::string> element_to_group;
	buffer >> element_to_group;

	AKANTU_DEBUG_ASSERT(e < mesh.getNbElement(type, ghost_type),
	"The mesh does not have the element " << e);

	for (auto && group : element_to_group) {
	mesh.getElementGroup(group).add(el, false, false);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

	#endif /* AKANTU_ELEMENT_INFO_PER_PROCESSOR_TMPL_HH_ */
	diff --git a/src/synchronizer/element_synchronizer.cc b/src/synchronizer/element_synchronizer.cc
	index c2d65a1ad..2fcf74b46 100644
	--- a/src/synchronizer/element_synchronizer.cc
	+++ b/src/synchronizer/element_synchronizer.cc
	@@ -1,295 +1,295 @@
	/**
	* @file element_synchronizer.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of a communicator using a static_communicator for
	* real
	* send/receive
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_synchronizer.hh"
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <iostream>
	#include <map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	#if defined(AKANTU_MODULE)
	#define AKANTU_MODULE_SAVE_ AKANTU_MODULE
	#undef AKANTU_MODULE
	#endif

	#define AKANTU_MODULE element_synchronizer

	/* -------------------------------------------------------------------------- */
	ElementSynchronizer::ElementSynchronizer(Mesh & mesh, const ID & id,
	bool register_to_event_manager,
	EventHandlerPriority event_priority)
	- : SynchronizerImpl<Element>(mesh.getCommunicator(), id),
	- mesh(mesh), element_to_prank("element_to_prank", id) {
	+ : SynchronizerImpl<Element>(mesh.getCommunicator(), id), mesh(mesh),
	+ element_to_prank("element_to_prank", id) {
	AKANTU_DEBUG_IN();

	if (register_to_event_manager) {
	this->mesh.registerEventHandler(*this, event_priority);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ElementSynchronizer::ElementSynchronizer(const ElementSynchronizer & other,
	const ID & id,
	bool register_to_event_manager,
	EventHandlerPriority event_priority)
	: SynchronizerImpl<Element>(other, id), mesh(other.mesh),
	element_to_prank("element_to_prank", id) {
	AKANTU_DEBUG_IN();

	element_to_prank.copy(other.element_to_prank);

	if (register_to_event_manager) {
	this->mesh.registerEventHandler(*this, event_priority);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	ElementSynchronizer::~ElementSynchronizer() = default;

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::substituteElements(
	const std::map<Element, Element> & old_to_new_elements) {
	auto found_element_end = old_to_new_elements.end();

	// substitute old elements with new ones
	for (auto && sr : iterate_send_recv) {
	for (auto && scheme_pair : communications.iterateSchemes(sr)) {
	auto & list = scheme_pair.second;
	for (auto & el : list) {
	auto found_element_it = old_to_new_elements.find(el);
	if (found_element_it != found_element_end) {
	el = found_element_it->second;
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::onElementsChanged(
	const Array<Element> & old_elements_list,
	const Array<Element> & new_elements_list,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) {
	// create a map to link old elements to new ones
	std::map<Element, Element> old_to_new_elements;

	for (UInt el = 0; el < old_elements_list.size(); ++el) {
	AKANTU_DEBUG_ASSERT(old_to_new_elements.find(old_elements_list(el)) ==
	old_to_new_elements.end(),
	"The same element cannot appear twice in the list");

	old_to_new_elements[old_elements_list(el)] = new_elements_list(el);
	}

	substituteElements(old_to_new_elements);

	communications.invalidateSizes();
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::onElementsRemoved(
	const Array<Element> & element_to_remove,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & /unused/) {
	AKANTU_DEBUG_IN();

	this->filterScheme([&](auto && element) {
	return std::find(element_to_remove.begin(), element_to_remove.end(),
	element) == element_to_remove.end();
	});

	this->renumberElements(new_numbering);

	communications.invalidateSizes();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::buildElementToPrank() {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	element_to_prank.initialize(mesh, _spatial_dimension = spatial_dimension,
	_element_kind = _ek_not_defined,
	_with_nb_element = true, _default_value = rank);

	/// assign prank to all ghost elements
	for (auto && scheme : communications.iterateSchemes(_recv)) {
	auto & recv = scheme.second;
	auto proc = scheme.first;

	for (auto & element : recv) {
	element_to_prank(element) = proc;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Int ElementSynchronizer::getRank(const Element & element) const {
	if (not element_to_prank.exists(element.type, element.ghost_type)) {
	// Nicolas: Ok This is nasty I know....
	const_cast<ElementSynchronizer *>(this)->buildElementToPrank();
	}

	return element_to_prank(element);
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::renumberElements(
	const ElementTypeMapArray<UInt> & new_numbering) {
	for (auto && sr : iterate_send_recv) {
	for (auto && scheme_pair : communications.iterateSchemes(sr)) {
	auto & list = scheme_pair.second;
	for (auto && el : list) {
	if (new_numbering.exists(el.type, el.ghost_type)) {
	el.element = new_numbering(el);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	UInt ElementSynchronizer::sanityCheckDataSize(const Array<Element> & elements,
	const SynchronizationTag & tag,
	bool from_comm_desc) const {
	UInt size = SynchronizerImpl<Element>::sanityCheckDataSize(elements, tag,
	from_comm_desc);

	// global connectivities;
	size += mesh.getNbNodesPerElementList(elements) * sizeof(UInt);

	// barycenters
	size += (elements.size() * mesh.getSpatialDimension() * sizeof(Real));
	return size;
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::packSanityCheckData(
	CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & /tag/) const {
	for (auto && element : elements) {
	Vector<Real> barycenter(mesh.getSpatialDimension());
	mesh.getBarycenter(element, barycenter);
	buffer << barycenter;

	const auto & conns = mesh.getConnectivity(element.type, element.ghost_type);
	for (auto n : arange(conns.getNbComponent())) {
	buffer << mesh.getNodeGlobalId(conns(element.element, n));
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void ElementSynchronizer::unpackSanityCheckData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag,
	UInt proc, UInt rank) const {
	auto spatial_dimension = mesh.getSpatialDimension();

	std::set<SynchronizationTag> skip_conn_tags{
	SynchronizationTag::_smmc_facets_conn,
	SynchronizationTag::_giu_global_conn};

	bool is_skip_tag_conn = skip_conn_tags.find(tag) != skip_conn_tags.end();

	for (auto && element : elements) {
	Vector<Real> barycenter_loc(spatial_dimension);
	mesh.getBarycenter(element, barycenter_loc);

	Vector<Real> barycenter(spatial_dimension);
	buffer >> barycenter;

	auto dist = barycenter_loc.distance(barycenter);
	if (not Math::are_float_equal(dist, 0.)) {
	AKANTU_EXCEPTION("Unpacking an unknown value for the element "
	<< element << "(barycenter " << barycenter_loc
	<< " != buffer " << barycenter << ") [" << dist
	<< "] - tag: " << tag << " comm from " << proc << " to "
	<< rank);
	}

	const auto & conns = mesh.getConnectivity(element.type, element.ghost_type);
	Vector<UInt> global_conn(conns.getNbComponent());
	Vector<UInt> local_global_conn(conns.getNbComponent());

	auto is_same = true;
	for (auto n : arange(global_conn.size())) {
	buffer >> global_conn(n);

	auto node = conns(element.element, n);
	local_global_conn(n) = mesh.getNodeGlobalId(node);

	is_same &= is_skip_tag_conn or mesh.isPureGhostNode(node) or
	(local_global_conn(n) == global_conn(n));
	}

	if (not is_same) {
	AKANTU_DEBUG_WARNING(
	"The connectivity of the element "
	<< element << " " << local_global_conn
	<< " does not match the connectivity of the equivalent "
	"element on proc "
	<< proc << " " << global_conn << " in communication with tag "
	<< tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#if defined(AKANTU_MODULE_SAVE_)
	#undef AKANTU_MODULE
	#define AKANTU_MODULE AKANTU_MODULE_SAVE_
	#undef AKANTU_MODULE_SAVE_
	#endif
	diff --git a/src/synchronizer/element_synchronizer.hh b/src/synchronizer/element_synchronizer.hh
	index 34f6e9de1..c1dd946c4 100644
	--- a/src/synchronizer/element_synchronizer.hh
	+++ b/src/synchronizer/element_synchronizer.hh
	@@ -1,202 +1,198 @@
	/**
	* @file element_synchronizer.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Main element synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_ELEMENT_SYNCHRONIZER_HH_
	#define AKANTU_ELEMENT_SYNCHRONIZER_HH_

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_common.hh"
	#include "mesh_partition.hh"
	#include "synchronizer_impl.hh"

	namespace akantu {
	class Mesh;
	}

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	class ElementSynchronizer : public SynchronizerImpl<Element>,
	public MeshEventHandler {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	ElementSynchronizer(Mesh & mesh, const ID & id = "element_synchronizer",
	bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	ElementSynchronizer(const ElementSynchronizer & other,
	const ID & id = "element_synchronizer_copy",
	bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	public:
	~ElementSynchronizer() override;

	friend class ElementInfoPerProc;
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/// mesh event handler onElementsChanged
	void onElementsChanged(const Array<Element> & old_elements_list,
	const Array<Element> & new_elements_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const ChangedElementsEvent & event) override;

	/// mesh event handler onRemovedElement
	void onElementsRemoved(const Array<Element> & element_to_remove,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) override;

	protected:
	/// remove elements from the synchronizer without renumbering them
	void removeElements(const Array<Element> & element_to_remove);

	/// renumber the elements in the synchronizer
	void renumberElements(const ElementTypeMapArray<UInt> & new_numbering);

	/// build processor to element correspondence
	void buildElementToPrank();

	protected:
	/// fill the nodes type vector
	void fillNodesType(const MeshData & mesh_data,
	DynamicCommunicationBuffer * buffers,
	const std::string & tag_name, ElementType el_type,
	const Array<UInt> & partition_num);

	template <typename T>
	void fillTagBufferTemplated(const MeshData & mesh_data,
	DynamicCommunicationBuffer * buffers,
	- const std::string & tag_name,
	- ElementType el_type,
	+ const std::string & tag_name, ElementType el_type,
	const Array<UInt> & partition_num,
	const CSR<UInt> & ghost_partition);

	void fillTagBuffer(const MeshData & mesh_data,
	DynamicCommunicationBuffer * buffers,
	const std::string & tag_name, ElementType el_type,
	const Array<UInt> & partition_num,
	const CSR<UInt> & ghost_partition);

	/// function that handels the MeshData to be split (root side)
	static void synchronizeTagsSend(ElementSynchronizer & communicator, UInt root,
	- Mesh & mesh, UInt nb_tags,
	- ElementType type,
	+ Mesh & mesh, UInt nb_tags, ElementType type,
	const Array<UInt> & partition_num,
	const CSR<UInt> & ghost_partition,
	UInt nb_local_element, UInt nb_ghost_element);

	/// function that handles the MeshData to be split (other nodes)
	static void synchronizeTagsRecv(ElementSynchronizer & communicator, UInt root,
	- Mesh & mesh, UInt nb_tags,
	- ElementType type,
	+ Mesh & mesh, UInt nb_tags, ElementType type,
	UInt nb_local_element, UInt nb_ghost_element);

	/// function that handles the preexisting groups in the mesh
	static void synchronizeElementGroups(ElementSynchronizer & communicator,
	- UInt root, Mesh & mesh,
	- ElementType type,
	+ UInt root, Mesh & mesh, ElementType type,
	const Array<UInt> & partition_num,
	const CSR<UInt> & ghost_partition,
	UInt nb_element);

	/// function that handles the preexisting groups in the mesh
	static void synchronizeElementGroups(ElementSynchronizer & communicator,
	UInt root, Mesh & mesh,
	ElementType type);

	/// function that handles the preexisting groups in the mesh
	static void synchronizeNodeGroupsMaster(ElementSynchronizer & communicator,
	UInt root, Mesh & mesh);

	/// function that handles the preexisting groups in the mesh
	static void synchronizeNodeGroupsSlaves(ElementSynchronizer & communicator,
	UInt root, Mesh & mesh);

	template <class CommunicationBuffer>
	static void fillNodeGroupsFromBuffer(ElementSynchronizer & communicator,
	Mesh & mesh,
	CommunicationBuffer & buffer);

	/// substitute elements in the send and recv arrays
	void
	substituteElements(const std::map<Element, Element> & old_to_new_elements);

	/* ------------------------------------------------------------------------ */
	/* Sanity checks */
	/* ------------------------------------------------------------------------ */
	UInt sanityCheckDataSize(const Array<Element> & elements,
	const SynchronizationTag & tag,
	bool from_comm_desc = true) const override;
	void packSanityCheckData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/) const override;
	void unpackSanityCheckData(CommunicationBuffer & /buffer/,
	const Array<Element> & /elements/,
	const SynchronizationTag & /tag/, UInt /proc/,
	UInt /rank/) const override;

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Mesh, mesh, Mesh &);
	AKANTU_GET_MACRO(ElementToRank, element_to_prank,
	const ElementTypeMapArray<Int> &);

	Int getRank(const Element & element) const final;
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// reference to the underlying mesh
	Mesh & mesh;

	friend class FacetSynchronizer;

	ElementTypeMapArray<Int> element_to_prank;
	};

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	#endif /* AKANTU_ELEMENT_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/facet_synchronizer.cc b/src/synchronizer/facet_synchronizer.cc
	index e3c13d589..c0f5492c2 100644
	--- a/src/synchronizer/facet_synchronizer.cc
	+++ b/src/synchronizer/facet_synchronizer.cc
	@@ -1,228 +1,227 @@
	/**
	* @file facet_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Facet synchronizer for parallel simulations with cohesive elments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "facet_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	#if defined(AKANTU_MODULE)
	#define AKANTU_MODULE_SAVE_ AKANTU_MODULE
	#undef AKANTU_MODULE
	#endif

	#define AKANTU_MODULE facet_synchronizer

	-
	namespace akantu {

	/* -------------------------------------------------------------------------- */
	FacetSynchronizer::FacetSynchronizer(
	Mesh & mesh, const ElementSynchronizer & element_synchronizer,
	const ID & id)
	: ElementSynchronizer(mesh, id) {

	auto spatial_dimension = mesh.getSpatialDimension();

	element_to_prank.initialize(mesh, _spatial_dimension = spatial_dimension - 1,
	_ghost_type = _ghost, _with_nb_element = true,
	_default_value = rank);

	// Build element to prank
	for (auto && scheme_pair :
	element_synchronizer.communications.iterateSchemes(_recv)) {
	auto proc = std::get<0>(scheme_pair);
	const auto & scheme = std::get<1>(scheme_pair);

	for (auto && elem : scheme) {
	const auto & facet_to_element =
	mesh.getSubelementToElement(elem.type, elem.ghost_type);
	Vector<Element> facets = facet_to_element.begin(
	facet_to_element.getNbComponent())[elem.element];

	for (UInt f = 0; f < facets.size(); ++f) {
	const auto & facet = facets(f);
	if (facet == ElementNull) {
	continue;
	}

	if (facet.ghost_type == _not_ghost) {
	continue;
	}

	auto & facet_rank = element_to_prank(facet);
	if ((proc < UInt(facet_rank)) \|\| (UInt(facet_rank) == rank)) {
	facet_rank = proc;
	}
	}
	}
	}

	ElementTypeMapArray<UInt> facet_global_connectivities(
	"facet_global_connectivities", id);
	facet_global_connectivities.initialize(
	mesh, _spatial_dimension = spatial_dimension - 1, _with_nb_element = true,
	_with_nb_nodes_per_element = true);
	mesh.getGlobalConnectivity(facet_global_connectivities);

	// \TODO perhaps a global element numbering might be useful here...
	for (auto type : facet_global_connectivities.elementTypes(_spatial_dimension =
	_all_dimensions,
	_element_kind = _ek_not_defined, _ghost_type = _not_ghost)) {
	auto & conn = facet_global_connectivities(type, _not_ghost);
	auto conn_view = make_view(conn, conn.getNbComponent());
	std::for_each(conn_view.begin(), conn_view.end(), [&](auto & conn) {
	std::sort(conn.storage(), conn.storage() + conn.size());
	});
	}

	/// init facet check tracking
	ElementTypeMapArray<bool> facet_checked("facet_checked", id);
	std::map<UInt, ElementTypeMapArray<UInt>> recv_connectivities;

	/// Generate the recv scheme and connnectivities to send to the other
	/// processors
	for (auto && scheme_pair :
	element_synchronizer.communications.iterateSchemes(_recv)) {
	facet_checked.initialize(mesh, _spatial_dimension = spatial_dimension - 1,
	_ghost_type = _ghost, _with_nb_element = true,
	_default_value = false);

	auto proc = scheme_pair.first;
	const auto & elements = scheme_pair.second;
	auto & facet_scheme = communications.createScheme(proc, _recv);

	// this creates empty arrays...
	auto & connectivities_for_proc = recv_connectivities[proc];

	connectivities_for_proc.setID(
	id + ":connectivities_for_proc:" + std::to_string(proc));
	connectivities_for_proc.initialize(
	mesh, _spatial_dimension = spatial_dimension - 1,
	_with_nb_nodes_per_element = true, _ghost_type = _ghost);

	// for every element in the element synchronizer communication scheme,
	// check the facets to see if they should be communicated and create a
	// connectivity array to match with the one other processors might send
	for (auto && element : elements) {
	const auto & facet_to_element =
	mesh.getSubelementToElement(element.type, element.ghost_type);
	Vector<Element> facets = facet_to_element.begin(
	facet_to_element.getNbComponent())[element.element];

	for (UInt f = 0; f < facets.size(); ++f) {
	auto & facet = facets(f);

	// exclude no valid facets
	if (facet == ElementNull) {
	continue;
	}

	// exclude _ghost facet from send scheme and _not_ghost from receive
	if (facet.ghost_type != _ghost) {
	continue;
	}

	// exclude facet from other processors then the one of current
	// interest in case of receive scheme
	if (UInt(element_to_prank(facet)) != proc) {
	continue;
	}

	auto & checked = facet_checked(facet);
	// skip already checked facets
	if (checked) {
	continue;
	}

	checked = true;

	facet_scheme.push_back(facet);

	auto & global_conn =
	facet_global_connectivities(facet.type, facet.ghost_type);
	Vector<UInt> conn =
	global_conn.begin(global_conn.getNbComponent())[facet.element];
	std::sort(conn.storage(), conn.storage() + conn.size());

	connectivities_for_proc(facet.type, facet.ghost_type).push_back(conn);
	}
	}
	}

	std::vector<CommunicationRequest> send_requests;
	/// do every communication by element type
	for (auto && type : mesh.elementTypes(spatial_dimension - 1)) {
	for (auto && pair : recv_connectivities) {
	auto proc = std::get<0>(pair);
	const auto & connectivities_for_proc = std::get<1>(pair);
	auto && tag = Tag::genTag(proc, type, 1337);
	send_requests.push_back(
	communicator.asyncSend(connectivities_for_proc(type, _ghost), proc,
	tag, CommunicationMode::_synchronous));
	}

	auto nb_nodes_per_facet = Mesh::getNbNodesPerElement(type);

	communicator.receiveAnyNumber<UInt>(
	send_requests,
	[&](auto && proc, auto && message) {
	auto & local_connectivities =
	facet_global_connectivities(type, _not_ghost);
	auto & send_scheme = communications.createScheme(proc, _send);

	auto conn_view = make_view(local_connectivities, nb_nodes_per_facet);
	auto conn_begin = conn_view.begin();
	auto conn_end = conn_view.end();
	for (const auto & c_to_match :
	make_view(message, nb_nodes_per_facet)) {
	auto it = std::find(conn_begin, conn_end, c_to_match);

	if (it != conn_end) {
	auto facet = Element{type, UInt(it - conn_begin), _not_ghost};
	send_scheme.push_back(facet);
	} else {
	AKANTU_EXCEPTION("No local facet found to send to proc "
	<< proc << " corresponding to " << c_to_match);
	}
	}
	},
	Tag::genTag(rank, type, 1337));
	}
	}

	} // namespace akantu

	#if defined(AKANTU_MODULE_SAVE_)
	#undef AKANTU_MODULE
	#define AKANTU_MODULE AKANTU_MODULE_SAVE_
	#undef AKANTU_MODULE_SAVE_
	#endif
	diff --git a/src/synchronizer/facet_synchronizer.hh b/src/synchronizer/facet_synchronizer.hh
	index 19a42c195..98b6176b7 100644
	--- a/src/synchronizer/facet_synchronizer.hh
	+++ b/src/synchronizer/facet_synchronizer.hh
	@@ -1,113 +1,113 @@
	/**
	* @file facet_synchronizer.hh
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Facet synchronizer for parallel simulations with cohesive elments
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_FACET_SYNCHRONIZER_HH_
	#define AKANTU_FACET_SYNCHRONIZER_HH_

	namespace akantu {

	class FacetSynchronizer : public ElementSynchronizer {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	FacetSynchronizer(Mesh & mesh,
	const ElementSynchronizer & element_synchronizer,
	const ID & id = "facet_synchronizer");

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// update distributed synchronizer after elements' insertion
	void
	updateDistributedSynchronizer(ElementSynchronizer & distributed_synchronizer,
	DataAccessor<Element> & data_accessor,
	const Mesh & mesh_cohesive);

	protected:
	/// update elements list based on facets list
	void updateElementList(Array<Element> * elements,
	const Array<Element> * facets,
	const Mesh & mesh_cohesive);

	/// setup facet synchronization
	void
	setupFacetSynchronization(ElementSynchronizer & distributed_synchronizer);

	/// build send facet arrays
	void buildSendElementList(
	const Array<ElementTypeMapArray<UInt> *> & send_connectivity,
	const Array<ElementTypeMapArray<UInt> *> & recv_connectivity,
	const Array<ElementTypeMapArray<UInt> *> & temp_send_element);

	/// build recv facet arrays
	void buildRecvElementList(
	const Array<ElementTypeMapArray<UInt> *> & temp_recv_element);

	/// get facets' global connectivity for a list of elements
	template <GhostType ghost_facets>
	inline void getFacetGlobalConnectivity(
	const ElementSynchronizer & distributed_synchronizer,
	const ElementTypeMapArray<UInt> & rank_to_facet,
	const Array<Element> * elements,
	Array<ElementTypeMapArray<UInt> *> & connectivity,
	Array<ElementTypeMapArray<UInt> *> & facets);

	/// initialize ElementTypeMap containing correspondance between
	/// facets and processors
	void initRankToFacet(ElementTypeMapArray<UInt> & rank_to_facet);

	/// find which processor a facet is assigned to
	void buildRankToFacet(ElementTypeMapArray<UInt> & rank_to_facet,
	const Array<Element> * elements);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	ElementTypeMapArray<UInt> facet_to_rank;
	};

	} // namespace akantu

	#include "facet_synchronizer_inline_impl.hh"

	#endif /* AKANTU_FACET_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/facet_synchronizer_inline_impl.hh b/src/synchronizer/facet_synchronizer_inline_impl.hh
	index 0d1e221b5..b0074ee31 100644
	--- a/src/synchronizer/facet_synchronizer_inline_impl.hh
	+++ b/src/synchronizer/facet_synchronizer_inline_impl.hh
	@@ -1,32 +1,31 @@
	/**
	* @file facet_synchronizer_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Tue Dec 04 2018
	*
	* @brief facet synchronizer inline implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/
	-
	diff --git a/src/synchronizer/grid_synchronizer.cc b/src/synchronizer/grid_synchronizer.cc
	index 55316802b..5b45622b9 100644
	--- a/src/synchronizer/grid_synchronizer.cc
	+++ b/src/synchronizer/grid_synchronizer.cc
	@@ -1,487 +1,487 @@
	/**
	* @file grid_synchronizer.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Oct 03 2011
	* @date last modification: Fri Jul 24 2020
	*
	* @brief implementation of the grid synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "grid_synchronizer.hh"
	#include "aka_grid_dynamic.hh"
	#include "communicator.hh"
	#include "fe_engine.hh"
	#include "integration_point.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include <iostream>

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class E>
	void GridSynchronizer::createGridSynchronizer(const SpatialGrid<E> & grid) {
	AKANTU_DEBUG_IN();

	const Communicator & comm = this->mesh.getCommunicator();
	UInt nb_proc = comm.getNbProc();
	UInt my_rank = comm.whoAmI();

	if (nb_proc == 1) {
	return;
	}

	UInt spatial_dimension = this->mesh.getSpatialDimension();

	BBox my_bounding_box(spatial_dimension);

	const auto & lower = grid.getLowerBounds();
	const auto & upper = grid.getUpperBounds();
	const auto & spacing = grid.getSpacing();

	my_bounding_box.getLowerBounds() = lower - spacing;
	my_bounding_box.getUpperBounds() = upper + spacing;

	AKANTU_DEBUG_INFO(
	"Exchange of bounding box to detect the overlapping regions.");

	auto && bboxes = my_bounding_box.allGather(comm);

	std::vector<bool> intersects_proc(nb_proc);
	std::fill(intersects_proc.begin(), intersects_proc.end(), true);

	Matrix<Int> first_cells(spatial_dimension, nb_proc);
	Matrix<Int> last_cells(spatial_dimension, nb_proc);

	std::map<UInt, ElementTypeMapArray<UInt>> element_per_proc;

	// check the overlapping between my box and the one from other processors
	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == my_rank) {
	continue;
	}

	const auto & proc_bounding_box = bboxes[p];
	auto intersection = my_bounding_box.intersection(proc_bounding_box);

	Vector<Int> first_cell_p = first_cells(p);
	Vector<Int> last_cell_p = last_cells(p);

	intersects_proc[p] = intersection;

	if (intersects_proc[p]) {
	for (UInt s = 0; s < spatial_dimension; ++s) {
	first_cell_p(s) = grid.getCellID(intersection.getLowerBounds()(s), s);
	last_cell_p(s) = grid.getCellID(intersection.getUpperBounds()(s), s);
	}
	}

	// create the list of cells in the overlapping
	using CellID = typename SpatialGrid<E>::CellID;

	std::vector<CellID> cell_ids;

	if (intersects_proc[p]) {
	AKANTU_DEBUG_INFO("I intersects with processor " << p);

	CellID cell_id(spatial_dimension);

	// for (UInt i = 0; i < spatial_dimension; ++i) {
	// if(first_cell_p[i] != 0) --first_cell_p[i];
	// if(last_cell_p[i] != 0) ++last_cell_p[i];
	// }

	for (Int fd = first_cell_p(0); fd <= last_cell_p(0); ++fd) {
	cell_id.setID(0, fd);
	if (spatial_dimension == 1) {
	cell_ids.push_back(cell_id);
	} else {
	for (Int sd = first_cell_p(1); sd <= last_cell_p(1); ++sd) {
	cell_id.setID(1, sd);
	if (spatial_dimension == 2) {
	cell_ids.push_back(cell_id);
	} else {
	for (Int ld = first_cell_p(2); ld <= last_cell_p(2); ++ld) {
	cell_id.setID(2, ld);
	cell_ids.push_back(cell_id);
	}
	}
	}
	}
	}

	// get the list of elements in the cells of the overlapping
	std::set<Element> to_send;
	for (auto & cur_cell_id : cell_ids) {
	auto & cell = grid.getCell(cur_cell_id);
	for (auto & element : cell) {
	to_send.insert(element);
	}
	}

	AKANTU_DEBUG_INFO("I have prepared " << to_send.size()
	<< " elements to send to processor "
	<< p);
	auto & scheme = this->getCommunications().createSendScheme(p);
	std::stringstream sstr;
	sstr << "element_per_proc_" << p;
	- element_per_proc.emplace(
	- std::piecewise_construct, std::forward_as_tuple(p),
	- std::forward_as_tuple(sstr.str(), id));
	+ element_per_proc.emplace(std::piecewise_construct,
	+ std::forward_as_tuple(p),
	+ std::forward_as_tuple(sstr.str(), id));

	ElementTypeMapArray<UInt> & elempproc = element_per_proc[p];

	for (auto elem : to_send) {
	ElementType type = elem.type;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	// /!\ this part must be slow due to the access in the
	// ElementTypeMapArray<UInt>
	if (!elempproc.exists(type, _not_ghost)) {
	elempproc.alloc(0, nb_nodes_per_element, type, _not_ghost);
	}

	Vector<UInt> global_connect(nb_nodes_per_element);
	Vector<UInt> local_connect = mesh.getConnectivity(type).begin(
	nb_nodes_per_element)[elem.element];

	for (UInt i = 0; i < nb_nodes_per_element; ++i) {
	global_connect(i) = mesh.getNodeGlobalId(local_connect(i));
	AKANTU_DEBUG_ASSERT(
	global_connect(i) < mesh.getNbGlobalNodes(),
	"This global node send in the connectivity does not seem correct "
	<< global_connect(i) << " corresponding to "
	<< local_connect(i) << " from element " << elem.element);
	}

	elempproc(type).push_back(global_connect);
	scheme.push_back(elem);
	}
	}
	}

	AKANTU_DEBUG_INFO("I have finished to compute intersection,"
	<< " no it's time to communicate with my neighbors");

	/**
	* Sending loop, sends the connectivity asynchronously to all concerned proc
	*/
	std::vector<CommunicationRequest> isend_requests;
	Tensor3<UInt> space(2, _max_element_type, nb_proc);

	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == my_rank) {
	continue;
	}

	if (not intersects_proc[p]) {
	continue;
	}

	Matrix<UInt> info_proc = space(p);
	auto & elempproc = element_per_proc[p];
	UInt count = 0;

	for (auto type : elempproc.elementTypes(_all_dimensions, _not_ghost)) {
	Array<UInt> & conn = elempproc(type, _not_ghost);

	Vector<UInt> info = info_proc((UInt)type);
	info[0] = (UInt)type;
	info[1] = conn.size() * conn.getNbComponent();

	AKANTU_DEBUG_INFO(
	"I have " << conn.size() << " elements of type " << type
	<< " to send to processor " << p << " (communication tag : "
	<< Tag::genTag(my_rank, count, DATA_TAG) << ")");

	isend_requests.push_back(
	comm.asyncSend(info, p, Tag::genTag(my_rank, count, SIZE_TAG)));

	if (info[1] != 0) {
	isend_requests.push_back(comm.asyncSend<UInt>(
	conn, p, Tag::genTag(my_rank, count, DATA_TAG)));
	}

	++count;
	}

	Vector<UInt> info = info_proc((UInt)_not_defined);
	info[0] = (UInt)_not_defined;
	info[1] = 0;
	isend_requests.push_back(
	comm.asyncSend(info, p, Tag::genTag(my_rank, count, SIZE_TAG)));
	}

	/**
	* Receives the connectivity and store them in the ghosts elements
	*/
	MeshAccessor mesh_accessor(mesh);
	auto & global_nodes_ids = mesh_accessor.getNodesGlobalIds();
	auto & nodes_type = mesh_accessor.getNodesFlags();

	std::vector<CommunicationRequest> isend_nodes_requests;
	Vector<UInt> nb_nodes_to_recv(nb_proc);

	UInt nb_total_nodes_to_recv = 0;
	UInt nb_current_nodes = global_nodes_ids.size();

	NewNodesEvent new_nodes;
	NewElementsEvent new_elements;

	std::map<UInt, std::vector<UInt>> ask_nodes_per_proc;

	for (UInt p = 0; p < nb_proc; ++p) {
	nb_nodes_to_recv(p) = 0;
	if (p == my_rank) {
	continue;
	}

	if (!intersects_proc[p]) {
	continue;
	}

	auto & scheme = this->getCommunications().createRecvScheme(p);

	ask_nodes_per_proc.emplace(std::piecewise_construct,
	std::forward_as_tuple(p),
	std::forward_as_tuple(0));

	auto & ask_nodes = ask_nodes_per_proc[p];
	UInt count = 0;

	ElementType type = _not_defined;
	do {
	Vector<UInt> info(2);
	comm.receive(info, p, Tag::genTag(p, count, SIZE_TAG));

	type = (ElementType)info[0];

	if (type == _not_defined) {
	break;
	}

	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	UInt nb_element = info[1] / nb_nodes_per_element;

	Array<UInt> tmp_conn(nb_element, nb_nodes_per_element);
	tmp_conn.zero();
	if (info[1] != 0) {
	comm.receive<UInt>(tmp_conn, p, Tag::genTag(p, count, DATA_TAG));
	}

	AKANTU_DEBUG_INFO("I will receive "
	<< nb_element << " elements of type "
	<< ElementType(info[0]) << " from processor " << p
	<< " (communication tag : "
	<< Tag::genTag(p, count, DATA_TAG) << ")");

	auto & ghost_connectivity = mesh_accessor.getConnectivity(type, _ghost);
	auto & ghost_counter = mesh_accessor.getGhostsCounters(type, _ghost);

	UInt nb_ghost_element = ghost_connectivity.size();
	Element element{type, 0, _ghost};

	Vector<UInt> conn(nb_nodes_per_element);
	for (UInt el = 0; el < nb_element; ++el) {
	UInt nb_node_to_ask_for_elem = 0;

	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt gn = tmp_conn(el, n);
	UInt ln = global_nodes_ids.find(gn);

	AKANTU_DEBUG_ASSERT(gn < mesh.getNbGlobalNodes(),
	"This global node seems not correct "
	<< gn << " from element " << el << " node "
	<< n);

	if (ln == UInt(-1)) {
	global_nodes_ids.push_back(gn);
	nodes_type.push_back(NodeFlag::_pure_ghost); // pure ghost node
	ln = nb_current_nodes;

	new_nodes.getList().push_back(ln);
	++nb_current_nodes;
	ask_nodes.push_back(gn);
	++nb_node_to_ask_for_elem;
	}
	conn[n] = ln;
	}

	// all the nodes are already known locally, the element should
	// already exists
	auto c = UInt(-1);
	if (nb_node_to_ask_for_elem == 0) {
	c = ghost_connectivity.find(conn);
	element.element = c;
	}

	if (c == UInt(-1)) {
	element.element = nb_ghost_element;
	++nb_ghost_element;
	ghost_connectivity.push_back(conn);
	ghost_counter.push_back(1);
	new_elements.getList().push_back(element);
	} else {
	++ghost_counter(c);
	}

	scheme.push_back(element);
	}

	count++;
	} while (type != _not_defined);

	AKANTU_DEBUG_INFO("I have "
	<< ask_nodes.size()
	<< " missing nodes for elements coming from processor "
	<< p << " (communication tag : "
	<< Tag::genTag(my_rank, 0, ASK_NODES_TAG) << ")");

	ask_nodes.push_back(UInt(-1));

	isend_nodes_requests.push_back(
	comm.asyncSend(ask_nodes, p, Tag::genTag(my_rank, 0, ASK_NODES_TAG)));
	nb_nodes_to_recv(p) = ask_nodes.size() - 1;
	nb_total_nodes_to_recv += nb_nodes_to_recv(p);
	}

	Communicator::waitAll(isend_requests);
	Communicator::freeCommunicationRequest(isend_requests);

	/**
	* Sends requested nodes to proc
	*/
	auto & nodes = const_cast<Array<Real> &>(mesh.getNodes());
	UInt nb_nodes = nodes.size();

	std::vector<CommunicationRequest> isend_coordinates_requests;
	std::map<UInt, Array<Real>> nodes_to_send_per_proc;
	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == my_rank \|\| !intersects_proc[p]) {
	continue;
	}

	Array<UInt> asked_nodes;
	CommunicationStatus status;
	AKANTU_DEBUG_INFO("Waiting list of nodes to send to processor "
	<< p << "(communication tag : "
	<< Tag::genTag(p, 0, ASK_NODES_TAG) << ")");

	comm.probe<UInt>(p, Tag::genTag(p, 0, ASK_NODES_TAG), status);
	UInt nb_nodes_to_send = status.size();
	asked_nodes.resize(nb_nodes_to_send);

	AKANTU_DEBUG_INFO("I have " << nb_nodes_to_send - 1
	<< " nodes to send to processor " << p
	<< " (communication tag : "
	<< Tag::genTag(p, 0, ASK_NODES_TAG) << ")");

	AKANTU_DEBUG_INFO("Getting list of nodes to send to processor "
	<< p << " (communication tag : "
	<< Tag::genTag(p, 0, ASK_NODES_TAG) << ")");

	comm.receive(asked_nodes, p, Tag::genTag(p, 0, ASK_NODES_TAG));

	nb_nodes_to_send--;
	asked_nodes.resize(nb_nodes_to_send);

	nodes_to_send_per_proc.emplace(std::piecewise_construct,
	std::forward_as_tuple(p),
	std::forward_as_tuple(0, spatial_dimension));

	auto & nodes_to_send = nodes_to_send_per_proc[p];
	auto node_it = nodes.begin(spatial_dimension);

	for (UInt n = 0; n < nb_nodes_to_send; ++n) {
	UInt ln = global_nodes_ids.find(asked_nodes(n));
	AKANTU_DEBUG_ASSERT(ln != UInt(-1), "The node ["
	<< asked_nodes(n)
	<< "] requested by proc " << p
	<< " was not found locally!");
	nodes_to_send.push_back(node_it + ln);
	}

	if (nb_nodes_to_send != 0) {
	AKANTU_DEBUG_INFO("Sending the "
	<< nb_nodes_to_send << " nodes to processor " << p
	<< " (communication tag : "
	<< Tag::genTag(p, 0, SEND_NODES_TAG) << ")");

	isend_coordinates_requests.push_back(comm.asyncSend(
	nodes_to_send, p, Tag::genTag(my_rank, 0, SEND_NODES_TAG)));
	}
	#if not defined(AKANTU_NDEBUG)
	else {
	AKANTU_DEBUG_INFO("No nodes to send to processor " << p);
	}
	#endif
	}

	Communicator::waitAll(isend_nodes_requests);
	Communicator::freeCommunicationRequest(isend_nodes_requests);

	nodes.resize(nb_total_nodes_to_recv + nb_nodes);
	for (UInt p = 0; p < nb_proc; ++p) {
	if ((p != my_rank) && (nb_nodes_to_recv(p) > 0)) {
	AKANTU_DEBUG_INFO("Receiving the "
	<< nb_nodes_to_recv(p) << " nodes from processor " << p
	<< " (communication tag : "
	<< Tag::genTag(p, 0, SEND_NODES_TAG) << ")");

	Vector<Real> nodes_to_recv(nodes.storage() + nb_nodes * spatial_dimension,
	nb_nodes_to_recv(p) * spatial_dimension);
	comm.receive(nodes_to_recv, p, Tag::genTag(p, 0, SEND_NODES_TAG));
	nb_nodes += nb_nodes_to_recv(p);
	}
	#if not defined(AKANTU_NDEBUG)
	else {
	if (p != my_rank) {
	AKANTU_DEBUG_INFO("No nodes to receive from processor " << p);
	}
	}
	#endif
	}

	Communicator::waitAll(isend_coordinates_requests);
	Communicator::freeCommunicationRequest(isend_coordinates_requests);

	mesh.sendEvent(new_nodes);
	mesh.sendEvent(new_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template void GridSynchronizer::createGridSynchronizer<IntegrationPoint>(
	const SpatialGrid<IntegrationPoint> & grid);

	template void GridSynchronizer::createGridSynchronizer<Element>(
	const SpatialGrid<Element> & grid);
	-
	+
	} // namespace akantu
	diff --git a/src/synchronizer/grid_synchronizer.hh b/src/synchronizer/grid_synchronizer.hh
	index 1be656981..20908693f 100644
	--- a/src/synchronizer/grid_synchronizer.hh
	+++ b/src/synchronizer/grid_synchronizer.hh
	@@ -1,103 +1,103 @@
	/**
	* @file grid_synchronizer.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Synchronizer based on spatial grid
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "element_synchronizer.hh"
	#include "synchronizer_registry.hh"

	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_GRID_SYNCHRONIZER_HH_
	#define AKANTU_GRID_SYNCHRONIZER_HH_

	namespace akantu {

	class Mesh;
	template <class T> class SpatialGrid;

	class GridSynchronizer : public ElementSynchronizer {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	template <typename E>
	GridSynchronizer(Mesh & mesh, const SpatialGrid<E> & grid,
	const ID & id = "grid_synchronizer",
	bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	template <typename E>
	GridSynchronizer(Mesh & mesh, const SpatialGrid<E> & grid,
	SynchronizerRegistry & synchronizer_registry,
	const std::set<SynchronizationTag> & tags_to_register,
	const ID & id = "grid_synchronizer",
	bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	~GridSynchronizer() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	private:
	/**
	*Create the Grid Synchronizer:
	*Compute intersection and send info to neighbours that will be stored in
	*ghosts elements
	*/
	template <typename E>
	void createGridSynchronizer(const SpatialGrid<E> & grid);

	protected:
	/// Define the tags that will be used in the send and receive instructions
	enum CommTags {
	SIZE_TAG = 0,
	DATA_TAG = 1,
	ASK_NODES_TAG = 2,
	SEND_NODES_TAG = 3
	};

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	};

	} // namespace akantu

	#include "grid_synchronizer_tmpl.hh"

	#endif /* AKANTU_GRID_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/grid_synchronizer_tmpl.hh b/src/synchronizer/grid_synchronizer_tmpl.hh
	index 58b17773c..dc08c5e08 100644
	--- a/src/synchronizer/grid_synchronizer_tmpl.hh
	+++ b/src/synchronizer/grid_synchronizer_tmpl.hh
	@@ -1,76 +1,74 @@
	/**
	* @file grid_synchronizer_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jul 06 2017
	* @date last modification: Wed Aug 09 2017
	*
	* @brief implementation of the templated part of the grid syncrhonizers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "grid_synchronizer.hh"

	#ifndef AKANTU_GRID_SYNCHRONIZER_TMPL_HH_
	#define AKANTU_GRID_SYNCHRONIZER_TMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <typename E>
	GridSynchronizer::GridSynchronizer(Mesh & mesh, const SpatialGrid<E> & grid,
	const ID & id,
	const bool register_to_event_manager,
	EventHandlerPriority event_priority)
	- : ElementSynchronizer(mesh, id, register_to_event_manager,
	- event_priority) {
	+ : ElementSynchronizer(mesh, id, register_to_event_manager, event_priority) {
	AKANTU_DEBUG_IN();

	this->createGridSynchronizer(grid);

	AKANTU_DEBUG_OUT();
	}

	template <typename E>
	GridSynchronizer::GridSynchronizer(
	Mesh & mesh, const SpatialGrid<E> & grid,
	SynchronizerRegistry & synchronizer_registry,
	const std::set<SynchronizationTag> & tags_to_register, const ID & id,
	- const bool register_to_event_manager,
	- EventHandlerPriority event_priority)
	+ const bool register_to_event_manager, EventHandlerPriority event_priority)
	: GridSynchronizer(mesh, grid, id, register_to_event_manager,
	event_priority) {
	AKANTU_DEBUG_IN();

	// Register the tags if any
	for (const auto & tag : tags_to_register) {
	synchronizer_registry.registerSynchronizer(*this, tag);
	}

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu

	#endif /* AKANTU_GRID_SYNCHRONIZER_TMPL_HH_ */
	diff --git a/src/synchronizer/master_element_info_per_processor.cc b/src/synchronizer/master_element_info_per_processor.cc
	index 871728443..fa088465b 100644
	--- a/src/synchronizer/master_element_info_per_processor.cc
	+++ b/src/synchronizer/master_element_info_per_processor.cc
	@@ -1,455 +1,455 @@
	/**
	* @file master_element_info_per_processor.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Thu Nov 12 2020
	*
	* @brief Helper class to distribute a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "element_group.hh"
	#include "element_info_per_processor.hh"
	#include "element_synchronizer.hh"
	#include "mesh_iterators.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <iostream>
	#include <map>
	#include <tuple>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MasterElementInfoPerProc::MasterElementInfoPerProc(
	ElementSynchronizer & synchronizer, UInt message_cnt, UInt root,
	ElementType type, const MeshPartition & partition)
	: ElementInfoPerProc(synchronizer, message_cnt, root, type),
	partition(partition), all_nb_local_element(nb_proc, 0),
	all_nb_ghost_element(nb_proc, 0), all_nb_element_to_send(nb_proc, 0) {
	Vector<UInt> size(5);
	size(0) = (UInt)type;

	if (type != _not_defined) {
	nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	nb_element = mesh.getNbElement(type);
	const auto & partition_num =
	this->partition.getPartition(this->type, _not_ghost);
	const auto & ghost_partition =
	this->partition.getGhostPartitionCSR()(this->type, _not_ghost);

	for (UInt el = 0; el < nb_element; ++el) {
	this->all_nb_local_element[partition_num(el)]++;
	for (auto part = ghost_partition.begin(el);
	part != ghost_partition.end(el); ++part) {
	this->all_nb_ghost_element[*part]++;
	}
	this->all_nb_element_to_send[partition_num(el)] +=
	ghost_partition.getNbCols(el) + 1;
	}

	/// tag info
	auto && tag_names = this->mesh.getTagNames(type);
	this->nb_tags = tag_names.size();

	size(4) = nb_tags;

	for (UInt p = 0; p < nb_proc; ++p) {
	if (p != root) {
	size(1) = this->all_nb_local_element[p];
	size(2) = this->all_nb_ghost_element[p];
	size(3) = this->all_nb_element_to_send[p];
	AKANTU_DEBUG_INFO(
	"Sending connectivities informations to proc "
	<< p << " TAG("
	<< Tag::genTag(this->rank, this->message_count, Tag::_sizes)
	<< ")");
	comm.send(size, p,
	Tag::genTag(this->rank, this->message_count, Tag::_sizes));
	} else {
	this->nb_local_element = this->all_nb_local_element[p];
	this->nb_ghost_element = this->all_nb_ghost_element[p];
	}
	}
	} else {
	for (UInt p = 0; p < this->nb_proc; ++p) {
	if (p != this->root) {
	AKANTU_DEBUG_INFO(
	"Sending empty connectivities informations to proc "
	<< p << " TAG("
	<< Tag::genTag(this->rank, this->message_count, Tag::_sizes)
	<< ")");
	comm.send(size, p,
	Tag::genTag(this->rank, this->message_count, Tag::_sizes));
	}
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	void MasterElementInfoPerProc::synchronizeConnectivities() {
	const auto & partition_num =
	this->partition.getPartition(this->type, _not_ghost);
	const auto & ghost_partition =
	this->partition.getGhostPartitionCSR()(this->type, _not_ghost);

	std::vector<Array<UInt>> buffers(this->nb_proc);

	const auto & connectivities =
	this->mesh.getConnectivity(this->type, _not_ghost);

	/// copying the local connectivity
	for (auto && part_conn :
	zip(partition_num,
	make_view(connectivities, this->nb_nodes_per_element))) {
	auto && part = std::get<0>(part_conn);
	auto && conn = std::get<1>(part_conn);
	for (UInt i = 0; i < conn.size(); ++i) {
	buffers[part].push_back(conn[i]);
	}
	}

	/// copying the connectivity of ghost element
	for (auto && tuple :
	enumerate(make_view(connectivities, this->nb_nodes_per_element))) {
	auto && el = std::get<0>(tuple);
	auto && conn = std::get<1>(tuple);
	for (auto part = ghost_partition.begin(el); part != ghost_partition.end(el);
	++part) {
	UInt proc = *part;
	for (UInt i = 0; i < conn.size(); ++i) {
	buffers[proc].push_back(conn[i]);
	}
	}
	}

	#ifndef AKANTU_NDEBUG
	for (auto p : arange(this->nb_proc)) {
	UInt size = this->nb_nodes_per_element *
	(this->all_nb_local_element[p] + this->all_nb_ghost_element[p]);
	AKANTU_DEBUG_ASSERT(
	buffers[p].size() == size,
	"The connectivity data packed in the buffer are not correct");
	}
	#endif

	/// send all connectivity and ghost information to all processors
	std::vector<CommunicationRequest> requests;
	for (auto p : arange(this->nb_proc)) {
	if (p == this->root) {
	continue;
	}
	auto && tag =
	Tag::genTag(this->rank, this->message_count, Tag::_connectivity);
	AKANTU_DEBUG_INFO("Sending connectivities to proc " << p << " TAG(" << tag
	<< ")");
	requests.push_back(comm.asyncSend(buffers[p], p, tag));
	}

	Array<UInt> & old_nodes = this->getNodesGlobalIds();

	/// create the renumbered connectivity
	AKANTU_DEBUG_INFO("Renumbering local connectivities");
	MeshUtils::renumberMeshNodes(mesh, buffers[root], all_nb_local_element[root],
	all_nb_ghost_element[root], type, old_nodes);

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	}

	/* ------------------------------------------------------------------------ */
	void MasterElementInfoPerProc::synchronizePartitions() {
	const auto & partition_num =
	this->partition.getPartition(this->type, _not_ghost);
	const auto & ghost_partition =
	this->partition.getGhostPartitionCSR()(this->type, _not_ghost);

	std::vector<Array<UInt>> buffers(this->partition.getNbPartition());

	/// splitting the partition information to send them to processors
	Vector<UInt> count_by_proc(nb_proc, 0);
	for (UInt el = 0; el < nb_element; ++el) {
	UInt proc = partition_num(el);
	buffers[proc].push_back(ghost_partition.getNbCols(el));

	UInt i(0);
	for (auto part = ghost_partition.begin(el); part != ghost_partition.end(el);
	++part, ++i) {
	buffers[proc].push_back(*part);
	}
	}

	for (UInt el = 0; el < nb_element; ++el) {
	UInt i(0);
	for (auto part = ghost_partition.begin(el); part != ghost_partition.end(el);
	++part, ++i) {
	buffers[*part].push_back(partition_num(el));
	}
	}

	#ifndef AKANTU_NDEBUG
	for (UInt p = 0; p < this->nb_proc; ++p) {
	AKANTU_DEBUG_ASSERT(buffers[p].size() == (this->all_nb_ghost_element[p] +
	this->all_nb_element_to_send[p]),
	"Data stored in the buffer are most probably wrong");
	}
	#endif

	std::vector<CommunicationRequest> requests;
	/// last data to compute the communication scheme
	for (UInt p = 0; p < this->nb_proc; ++p) {
	if (p == this->root) {
	continue;
	}

	auto && tag =
	Tag::genTag(this->rank, this->message_count, Tag::_partitions);
	AKANTU_DEBUG_INFO("Sending partition informations to proc " << p << " TAG("
	<< tag << ")");
	requests.push_back(comm.asyncSend(buffers[p], p, tag));
	}

	if (Mesh::getSpatialDimension(this->type) ==
	this->mesh.getSpatialDimension()) {
	AKANTU_DEBUG_INFO("Creating communications scheme");
	this->fillCommunicationScheme(buffers[this->rank]);
	}

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	}

	/* -------------------------------------------------------------------------- */
	void MasterElementInfoPerProc::synchronizeTags() {
	AKANTU_DEBUG_IN();

	if (this->nb_tags == 0) {
	AKANTU_DEBUG_OUT();
	return;
	}

	/// tag info
	auto tag_names = mesh.getTagNames(type);

	// Make sure the tags are sorted (or at least not in random order),
	// because they come from a map !!
	std::sort(tag_names.begin(), tag_names.end());

	// Sending information about the tags in mesh_data: name, data type and
	// number of components of the underlying array associated to the current
	// type
	DynamicCommunicationBuffer mesh_data_sizes_buffer;
	for (auto && tag_name : tag_names) {
	mesh_data_sizes_buffer << tag_name;
	mesh_data_sizes_buffer << mesh.getTypeCode(tag_name);
	mesh_data_sizes_buffer << mesh.getNbComponent(tag_name, type);
	}

	AKANTU_DEBUG_INFO(
	"Broadcasting the size of the information about the mesh data tags: ("
	<< mesh_data_sizes_buffer.size() << ").");
	AKANTU_DEBUG_INFO(
	"Broadcasting the information about the mesh data tags, addr "
	<< (void *)mesh_data_sizes_buffer.storage());

	comm.broadcast(mesh_data_sizes_buffer, root);

	if (mesh_data_sizes_buffer.empty()) {
	return;
	}

	// Sending the actual data to each processor
	std::vector<DynamicCommunicationBuffer> buffers(nb_proc);
	// Loop over each tag for the current type
	for (auto && tag_name : tag_names) {
	// Type code of the current tag (i.e. the tag named *names_it)
	this->fillTagBuffer(buffers, tag_name);
	}

	std::vector<CommunicationRequest> requests;
	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == root) {
	continue;
	}

	auto && tag = Tag::genTag(this->rank, this->message_count, Tag::_mesh_data);
	AKANTU_DEBUG_INFO("Sending " << buffers[p].size()
	<< " bytes of mesh data to proc " << p
	<< " TAG(" << tag << ")");

	requests.push_back(comm.asyncSend(buffers[p], p, tag));
	}

	// Loop over each tag for the current type
	for (auto && tag_name : tag_names) {
	// Reinitializing the mesh data on the master
	this->fillMeshData(buffers[root], tag_name, mesh.getTypeCode(tag_name),
	mesh.getNbComponent(tag_name, type));
	}

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	requests.clear();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void MasterElementInfoPerProc::fillTagBufferTemplated(
	std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name) {
	const auto & data = mesh.getElementalDataArray<T>(tag_name, type);
	const auto & partition_num =
	this->partition.getPartition(this->type, _not_ghost);
	const auto & ghost_partition =
	this->partition.getGhostPartitionCSR()(this->type, _not_ghost);

	// Not possible to use the iterator because it potentially triggers the
	// creation of complex
	// type templates (such as akantu::Vector< std::vector<Element> > which don't
	// implement the right interface
	// (e.g. operator<< in that case).
	// typename Array<T>::template const_iterator< Vector<T> > data_it =
	// data.begin(data.getNbComponent());
	// typename Array<T>::template const_iterator< Vector<T> > data_end =
	// data.end(data.getNbComponent());

	const T * data_it = data.storage();
	const T * data_end = data.storage() + data.size() * data.getNbComponent();
	const UInt * part = partition_num.storage();

	/// copying the data, element by element
	for (; data_it != data_end; ++part) {
	for (UInt j(0); j < data.getNbComponent(); ++j, ++data_it) {
	buffers[part] << data_it;
	}
	}

	data_it = data.storage();
	/// copying the data for the ghost element
	for (UInt el(0); data_it != data_end;
	data_it += data.getNbComponent(), ++el) {
	auto it = ghost_partition.begin(el);
	auto end = ghost_partition.end(el);
	for (; it != end; ++it) {
	UInt proc = *it;
	for (UInt j(0); j < data.getNbComponent(); ++j) {
	buffers[proc] << data_it[j];
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void MasterElementInfoPerProc::fillTagBuffer(
	std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name) {
	#define AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA(r, extra_param, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	this->fillTagBufferTemplated<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(buffers, \
	tag_name); \
	break; \
	}

	MeshDataTypeCode data_type_code = mesh.getTypeCode(tag_name);
	switch (data_type_code) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA, ,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Could not obtain the type of tag" << tag_name << "!");
	break;
	}
	#undef AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA
	}

	/* -------------------------------------------------------------------------- */
	void MasterElementInfoPerProc::synchronizeGroups() {
	AKANTU_DEBUG_IN();

	std::vector<DynamicCommunicationBuffer> buffers(nb_proc);

	using ElementToGroup = std::vector<std::vector<std::string>>;
	ElementToGroup element_to_group(nb_element);

	for (auto & eg : mesh.iterateElementGroups()) {
	const auto & name = eg.getName();

	for (const auto & element : eg.getElements(type, _not_ghost)) {
	element_to_group[element].push_back(name);
	}

	eg.clear(type, _not_ghost);
	}

	const auto & partition_num =
	this->partition.getPartition(this->type, _not_ghost);
	const auto & ghost_partition =
	this->partition.getGhostPartitionCSR()(this->type, _not_ghost);

	/// copying the data, element by element
	for (auto && pair : zip(partition_num, element_to_group)) {
	buffers[std::get<0>(pair)] << std::get<1>(pair);
	}

	/// copying the data for the ghost element
	for (auto && pair : enumerate(element_to_group)) {
	auto && el = std::get<0>(pair);
	auto it = ghost_partition.begin(el);
	auto end = ghost_partition.end(el);
	for (; it != end; ++it) {
	UInt proc = *it;
	buffers[proc] << std::get<1>(pair);
	}
	}

	std::vector<CommunicationRequest> requests;
	for (UInt p = 0; p < this->nb_proc; ++p) {
	if (p == this->rank) {
	continue;
	}

	auto && tag = Tag::genTag(this->rank, p, Tag::_element_group);
	AKANTU_DEBUG_INFO("Sending element groups to proc " << p << " TAG(" << tag
	<< ")");
	requests.push_back(comm.asyncSend(buffers[p], p, tag));
	}

	this->fillElementGroupsFromBuffer(buffers[this->rank]);

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	requests.clear();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/synchronizer/mpi_communicator_data.hh b/src/synchronizer/mpi_communicator_data.hh
	index 756ce87d8..45d51b8dd 100644
	--- a/src/synchronizer/mpi_communicator_data.hh
	+++ b/src/synchronizer/mpi_communicator_data.hh
	@@ -1,142 +1,142 @@
	/**
	* @file mpi_communicator_data.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Jun 14 2010
	* @date last modification: Tue Jun 16 2020
	*
	* @brief Wrapper on MPI types to have a better separation between libraries
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#if __cplusplus > 199711L
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wliteral-suffix"
	#endif
	#endif

	#include <mpi.h>

	#if defined(__INTEL_COMPILER)
	//#pragma warning ( disable : 383 )
	#elif defined(__clang__) // test clang to be sure that when we test for gnu it
	// is only gnu
	#elif (defined(__GNUC__) \|\| defined(__GNUG__))
	#if __cplusplus > 199711L
	#pragma GCC diagnostic pop
	#endif
	#endif

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_MPI_TYPE_WRAPPER_HH_
	#define AKANTU_MPI_TYPE_WRAPPER_HH_

	namespace akantu {

	class MPICommunicatorData : public CommunicatorInternalData {
	public:
	MPICommunicatorData() {
	MPI_Initialized(&is_externaly_initialized);
	if (is_externaly_initialized == 0) {
	MPI_Init(nullptr, nullptr); // valid according to the spec
	}

	MPI_Comm_create_errhandler(MPICommunicatorData::errorHandler,
	&error_handler);
	MPI_Comm_set_errhandler(MPI_COMM_WORLD, error_handler);
	setMPICommunicator(MPI_COMM_WORLD);
	}

	~MPICommunicatorData() override {
	if (is_externaly_initialized == 0) {
	MPI_Comm_set_errhandler(communicator, save_error_handler);
	MPI_Errhandler_free(&error_handler);
	MPI_Finalize();
	}
	}

	inline void setMPICommunicator(MPI_Comm comm) {
	MPI_Comm_set_errhandler(communicator, save_error_handler);
	communicator = comm;
	MPI_Comm_get_errhandler(comm, &save_error_handler);
	MPI_Comm_set_errhandler(comm, error_handler);
	}

	inline int rank() const {
	int prank;
	MPI_Comm_rank(communicator, &prank);
	return prank;
	}

	inline int size() const {
	int psize;
	MPI_Comm_size(communicator, &psize);
	return psize;
	}

	inline MPI_Comm getMPICommunicator() const { return communicator; }
	static int getMaxTag() {
	int flag;
	int * value;
	// not defined on derived intra-communicator
	MPI_Comm_get_attr(MPI_COMM_WORLD, MPI_TAG_UB, &value, &flag);
	AKANTU_DEBUG_ASSERT(flag, "No attribute MPI_TAG_UB.");
	return *value;
	}

	private:
	MPI_Comm communicator{MPI_COMM_WORLD};
	MPI_Errhandler save_error_handler{MPI_ERRORS_ARE_FATAL};
	static int is_externaly_initialized;
	/* ------------------------------------------------------------------------ */
	MPI_Errhandler error_handler;

	static void
	errorHandler(MPI_Comm * /comm/,
	int * error_code, // NOLINT(readability-non-const-parameter)
	...) {
	char error_string[MPI_MAX_ERROR_STRING];
	int str_len;
	MPI_Error_string(*error_code, error_string, &str_len);
	AKANTU_CUSTOM_EXCEPTION_INFO(debug::CommunicationException(),
	"MPI failed with the error code "
	<< *error_code << ": \"" << error_string
	<< "\"");
	}
	};

	} // namespace akantu

	#endif /* AKANTU_MPI_TYPE_WRAPPER_HH_ */
	diff --git a/src/synchronizer/node_info_per_processor.cc b/src/synchronizer/node_info_per_processor.cc
	index cd4f62d73..05cfe1f3a 100644
	--- a/src/synchronizer/node_info_per_processor.cc
	+++ b/src/synchronizer/node_info_per_processor.cc
	@@ -1,848 +1,848 @@
	/**
	* @file node_info_per_processor.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Please type the brief for file: Helper classes to create the
	* distributed synchronizer and distribute a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "node_info_per_processor.hh"
	#include "communicator.hh"
	#include "node_group.hh"
	#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NodeInfoPerProc::NodeInfoPerProc(NodeSynchronizer & synchronizer,
	UInt message_cnt, UInt root)
	: MeshAccessor(synchronizer.getMesh()), synchronizer(synchronizer),
	comm(synchronizer.getCommunicator()), rank(comm.whoAmI()),
	nb_proc(comm.getNbProc()), root(root), mesh(synchronizer.getMesh()),
	spatial_dimension(synchronizer.getMesh().getSpatialDimension()),
	message_count(message_cnt) {}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::synchronize() {
	synchronizeNodes();
	synchronizeTypes();
	synchronizeGroups();
	synchronizePeriodicity();
	synchronizeTags();
	}

	/* -------------------------------------------------------------------------- */
	template <class CommunicationBuffer>
	void NodeInfoPerProc::fillNodeGroupsFromBuffer(CommunicationBuffer & buffer) {
	AKANTU_DEBUG_IN();

	std::vector<std::vector<std::string>> node_to_group;

	buffer >> node_to_group;

	AKANTU_DEBUG_ASSERT(node_to_group.size() == mesh.getNbGlobalNodes(),
	"Not the good amount of nodes where transmitted");

	const auto & global_nodes = mesh.getGlobalNodesIds();

	for (auto && data : enumerate(global_nodes)) {
	for (const auto & node : node_to_group[std::get<1>(data)]) {
	mesh.getNodeGroup(node).add(std::get<0>(data), false);
	}
	}

	for (auto && ng_data : mesh.iterateNodeGroups()) {
	ng_data.optimize();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::fillNodesType() {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = mesh.getNbNodes();
	auto & nodes_flags = this->getNodesFlags();

	Array<UInt> nodes_set(nb_nodes);
	nodes_set.set(0);

	enum NodeSet {
	NORMAL_SET = 1,
	GHOST_SET = 2,
	};

	Array<bool> already_seen(nb_nodes, 1, false);

	for (auto gt : ghost_types) {
	UInt set = NORMAL_SET;
	if (gt == _ghost) {
	set = GHOST_SET;
	}

	already_seen.set(false);
	for (auto && type :
	mesh.elementTypes(_all_dimensions, gt, _ek_not_defined)) {
	const auto & connectivity = mesh.getConnectivity(type, gt);

	for (const auto & conn :
	make_view(connectivity, connectivity.getNbComponent())) {
	for (UInt n = 0; n < conn.size(); ++n) {
	AKANTU_DEBUG_ASSERT(conn(n) < nb_nodes,
	"Node " << conn(n)
	<< " bigger than number of nodes "
	<< nb_nodes);
	if (!already_seen(conn(n))) {
	nodes_set(conn(n)) += set;
	already_seen(conn(n)) = true;
	}
	}
	}
	}
	}

	nodes_flags.resize(nb_nodes);
	for (UInt i = 0; i < nb_nodes; ++i) {
	if (nodes_set(i) == NORMAL_SET) {
	nodes_flags(i) = NodeFlag::_normal;
	} else if (nodes_set(i) == GHOST_SET) {
	nodes_flags(i) = NodeFlag::_pure_ghost;
	} else if (nodes_set(i) == (GHOST_SET + NORMAL_SET)) {
	nodes_flags(i) = NodeFlag::_master;
	} else {
	AKANTU_EXCEPTION("Gni ?");
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::fillCommunicationScheme(const Array<UInt> & master_info) {
	AKANTU_DEBUG_IN();

	Communications<UInt> & communications =
	this->synchronizer.getCommunications();

	{ // send schemes
	std::map<UInt, Array<UInt>> send_array_per_proc;

	for (const auto & send_info : make_view(master_info, 2)) {
	send_array_per_proc[send_info(0)].push_back(send_info(1));
	}

	for (auto & send_schemes : send_array_per_proc) {
	auto & scheme = communications.createSendScheme(send_schemes.first);

	auto & sends = send_schemes.second;
	std::sort(sends.begin(), sends.end());
	std::transform(sends.begin(), sends.end(), sends.begin(),
	[this](UInt g) -> UInt { return mesh.getNodeLocalId(g); });
	scheme.copy(sends);
	AKANTU_DEBUG_INFO("Proc " << rank << " has " << sends.size()
	<< " nodes to send to to proc "
	<< send_schemes.first);
	}
	}

	{ // receive schemes
	std::map<UInt, Array<UInt>> recv_array_per_proc;

	for (auto node : arange(mesh.getNbNodes())) {
	if (mesh.isSlaveNode(node)) {
	recv_array_per_proc[mesh.getNodePrank(node)].push_back(
	mesh.getNodeGlobalId(node));
	}
	}

	for (auto & recv_schemes : recv_array_per_proc) {
	auto & scheme = communications.createRecvScheme(recv_schemes.first);

	auto & recvs = recv_schemes.second;
	std::sort(recvs.begin(), recvs.end());
	std::transform(recvs.begin(), recvs.end(), recvs.begin(),
	[this](UInt g) -> UInt { return mesh.getNodeLocalId(g); });

	scheme.copy(recvs);
	AKANTU_DEBUG_INFO("Proc " << rank << " will receive " << recvs.size()
	<< " nodes from proc " << recv_schemes.first);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::fillPeriodicPairs(const Array<UInt> & global_pairs,
	std::vector<UInt> & missing_nodes) {
	this->wipePeriodicInfo();
	auto & nodes_flags = this->getNodesFlags();

	auto checkIsLocal = [&](auto && global_node) {
	auto && node = mesh.getNodeLocalId(global_node);
	if (node == UInt(-1)) {
	auto & global_nodes = this->getNodesGlobalIds();
	node = global_nodes.size();

	global_nodes.push_back(global_node);
	nodes_flags.push_back(NodeFlag::_pure_ghost);
	missing_nodes.push_back(global_node);
	std::cout << "Missing node " << node << std::endl;
	}
	return node;
	};

	for (auto && pairs : make_view(global_pairs, 2)) {
	UInt slave = checkIsLocal(pairs(0));
	UInt master = checkIsLocal(pairs(1));

	this->addPeriodicSlave(slave, master);
	}

	this->markMeshPeriodic();
	}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::receiveMissingPeriodic(
	DynamicCommunicationBuffer & buffer) {
	auto & nodes = this->getNodes();
	Communications<UInt> & communications =
	this->synchronizer.getCommunications();

	std::size_t nb_nodes;
	buffer >> nb_nodes;

	for (auto _ [[gnu::unused]] : arange(nb_nodes)) {
	Vector<Real> pos(spatial_dimension);
	Int prank;
	buffer >> pos;
	buffer >> prank;

	UInt node = nodes.size();

	this->setNodePrank(node, prank);
	nodes.push_back(pos);

	auto & scheme = communications.createRecvScheme(prank);
	scheme.push_back(node);
	}

	while (buffer.getLeftToUnpack() != 0) {
	Int prank;
	UInt gnode;

	buffer >> gnode;
	buffer >> prank;
	auto node = mesh.getNodeLocalId(gnode);

	AKANTU_DEBUG_ASSERT(node != UInt(-1),
	"I cannot send the node "
	<< gnode << " to proc " << prank
	<< " because it is note a local node");

	auto & scheme = communications.createSendScheme(prank);
	scheme.push_back(node);
	}
	}

	/* -------------------------------------------------------------------------- */
	void NodeInfoPerProc::fillNodalData(DynamicCommunicationBuffer & buffer,
	const std::string & tag_name) {

	#define AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA(r, _, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	auto & nodal_data = \
	mesh.getNodalData<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(tag_name); \
	nodal_data.resize(mesh.getNbNodes()); \
	for (auto && data : make_view(nodal_data)) { \
	buffer >> data; \
	} \
	break; \
	}

	MeshDataTypeCode data_type_code =
	mesh.getTypeCode(tag_name, MeshDataType::_nodal);
	switch (data_type_code) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA, ,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Could not obtain the type of tag" << tag_name << "!");
	break;
	}
	#undef AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	MasterNodeInfoPerProc::MasterNodeInfoPerProc(NodeSynchronizer & synchronizer,
	UInt message_cnt, UInt root)
	: NodeInfoPerProc(synchronizer, message_cnt, root),
	all_nodes(0, synchronizer.getMesh().getSpatialDimension()) {
	UInt nb_global_nodes = this->mesh.getNbGlobalNodes();
	this->comm.broadcast(nb_global_nodes, this->root);
	}

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::synchronizeNodes() {
	this->nodes_per_proc.resize(nb_proc);
	this->nb_nodes_per_proc.resize(nb_proc);

	Array<Real> local_nodes(0, spatial_dimension);
	Array<Real> & nodes = this->getNodes();

	all_nodes.copy(nodes);
	nodes_pranks.resize(nodes.size(), UInt(-1));

	for (UInt p = 0; p < nb_proc; ++p) {
	UInt nb_nodes = 0;
	// UInt * buffer;
	Array<Real> * nodes_to_send{nullptr};

	Array<UInt> & nodespp = nodes_per_proc[p];
	if (p != root) {
	nodes_to_send = new Array<Real>(0, spatial_dimension);
	AKANTU_DEBUG_INFO("Receiving number of nodes from proc "
	<< p << " " << Tag::genTag(p, 0, Tag::_nb_nodes));
	comm.receive(nb_nodes, p, Tag::genTag(p, 0, Tag::_nb_nodes));
	nodespp.resize(nb_nodes);
	this->nb_nodes_per_proc(p) = nb_nodes;

	AKANTU_DEBUG_INFO("Receiving list of nodes from proc "
	<< p << " " << Tag::genTag(p, 0, Tag::_nodes));
	comm.receive(nodespp, p, Tag::genTag(p, 0, Tag::_nodes));
	} else {
	Array<UInt> & local_ids = this->getNodesGlobalIds();
	this->nb_nodes_per_proc(p) = local_ids.size();
	nodespp.copy(local_ids);
	nodes_to_send = &local_nodes;
	}

	/// get the coordinates for the selected nodes
	for (const auto & node : nodespp) {
	Vector<Real> coord(nodes.storage() + spatial_dimension * node,
	spatial_dimension);
	nodes_to_send->push_back(coord);
	}

	if (p != root) { /// send them for distant processors
	AKANTU_DEBUG_INFO("Sending coordinates to proc "
	<< p << " "
	<< Tag::genTag(this->rank, 0, Tag::_coordinates));
	comm.send(*nodes_to_send, p,
	Tag::genTag(this->rank, 0, Tag::_coordinates));

	delete nodes_to_send;
	}
	}

	/// construct the local nodes coordinates
	nodes.copy(local_nodes);
	}

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::synchronizeTypes() {
	// <global_id, <proc, local_id> >
	std::multimap<UInt, std::pair<UInt, UInt>> nodes_to_proc;
	std::vector<Array<NodeFlag>> nodes_flags_per_proc(nb_proc);
	std::vector<Array<Int>> nodes_prank_per_proc(nb_proc);

	if (mesh.isPeriodic()) {
	all_periodic_flags.copy(this->getNodesFlags());
	}

	// arrays containing pairs of (proc, node)
	std::vector<Array<UInt>> nodes_to_send_per_proc(nb_proc);
	for (UInt p = 0; p < nb_proc; ++p) {
	nodes_flags_per_proc[p].resize(nb_nodes_per_proc(p), NodeFlag(0xFF));
	nodes_prank_per_proc[p].resize(nb_nodes_per_proc(p), -1);
	}

	this->fillNodesType();

	auto is_master = [](auto && flag) {
	return (flag & NodeFlag::_shared_mask) == NodeFlag::_master;
	};

	auto is_local = [](auto && flag) {
	return (flag & NodeFlag::_shared_mask) == NodeFlag::_normal;
	};

	for (auto p : arange(nb_proc)) {
	auto & nodes_flags = nodes_flags_per_proc[p];

	if (p != root) {
	AKANTU_DEBUG_INFO(
	"Receiving first nodes types from proc "
	<< p << " "
	<< Tag::genTag(this->rank, this->message_count, Tag::_nodes_type));
	comm.receive(nodes_flags, p, Tag::genTag(p, 0, Tag::_nodes_type));
	} else {
	nodes_flags.copy(this->getNodesFlags());
	}

	// stack all processors claiming to be master for a node
	for (auto local_node : arange(nb_nodes_per_proc(p))) {
	auto global_node = nodes_per_proc[p](local_node);

	if (is_master(nodes_flags(local_node))) {
	nodes_to_proc.insert(
	std::make_pair(global_node, std::make_pair(p, local_node)));

	} else if (is_local(nodes_flags(local_node))) {
	nodes_pranks[global_node] = p;
	}
	}
	}

	for (auto i : arange(mesh.getNbGlobalNodes())) {
	auto it_range = nodes_to_proc.equal_range(i);
	if (it_range.first == nodes_to_proc.end() \|\| it_range.first->first != i) {
	continue;
	}

	// pick the first processor out of the multi-map as the actual master
	UInt master_proc = (it_range.first)->second.first;
	nodes_pranks[i] = master_proc;

	for (auto && data : range(it_range.first, it_range.second)) {
	auto proc = data.second.first;
	auto node = data.second.second;

	if (proc != master_proc) {
	// store the info on all the slaves for a given master
	nodes_flags_per_proc[proc](node) = NodeFlag::_slave;
	nodes_to_send_per_proc[master_proc].push_back(proc);
	nodes_to_send_per_proc[master_proc].push_back(i);
	}
	}
	}

	/// Fills the nodes prank per proc
	for (auto && data : zip(arange(nb_proc), nodes_per_proc, nodes_prank_per_proc,
	nodes_flags_per_proc)) {
	for (auto && node_data :
	zip(std::get<1>(data), std::get<2>(data), std::get<3>(data))) {
	if (std::get<2>(node_data) == NodeFlag::_normal) {
	std::get<1>(node_data) = std::get<0>(data);
	} else {
	std::get<1>(node_data) = nodes_pranks(std::get<0>(node_data));
	}
	}
	}

	std::vector<CommunicationRequest> requests_send_type;
	std::vector<CommunicationRequest> requests_send_master_info;
	for (UInt p = 0; p < nb_proc; ++p) {
	if (p != root) {
	auto tag0 = Tag::genTag(this->rank, 0, Tag::_nodes_type);
	AKANTU_DEBUG_INFO("Sending nodes types to proc " << p << " " << tag0);
	requests_send_type.push_back(
	comm.asyncSend(nodes_flags_per_proc[p], p, tag0));

	auto tag2 = Tag::genTag(this->rank, 2, Tag::_nodes_type);
	AKANTU_DEBUG_INFO("Sending nodes pranks to proc " << p << " " << tag2);
	requests_send_type.push_back(
	comm.asyncSend(nodes_prank_per_proc[p], p, tag2));

	auto & nodes_to_send = nodes_to_send_per_proc[p];

	auto tag1 = Tag::genTag(this->rank, 1, Tag::_nodes_type);
	AKANTU_DEBUG_INFO("Sending nodes master info to proc " << p << " "
	<< tag1);
	requests_send_master_info.push_back(
	comm.asyncSend(nodes_to_send, p, tag1));
	} else {
	this->getNodesFlags().copy(nodes_flags_per_proc[p]);
	for (auto && data : enumerate(nodes_prank_per_proc[p])) {
	auto node = std::get<0>(data);
	if (not(mesh.isMasterNode(node) or mesh.isLocalNode(node))) {
	this->setNodePrank(node, std::get<1>(data));
	}
	}

	this->fillCommunicationScheme(nodes_to_send_per_proc[root]);
	}
	}

	Communicator::waitAll(requests_send_type);
	Communicator::freeCommunicationRequest(requests_send_type);

	Communicator::waitAll(requests_send_master_info);
	Communicator::freeCommunicationRequest(requests_send_master_info);
	}

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::synchronizeGroups() {
	AKANTU_DEBUG_IN();

	UInt nb_total_nodes = mesh.getNbGlobalNodes();

	DynamicCommunicationBuffer buffer;

	using NodeToGroup = std::vector<std::vector<std::string>>;
	NodeToGroup node_to_group;
	node_to_group.resize(nb_total_nodes);

	for (auto & ng : mesh.iterateNodeGroups()) {
	std::string name = ng.getName();

	for (auto && node : ng.getNodes()) {
	node_to_group[node].push_back(name);
	}

	ng.clear();
	}

	buffer << node_to_group;

	std::vector<CommunicationRequest> requests;
	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == this->rank) {
	continue;
	}
	AKANTU_DEBUG_INFO("Sending node groups to proc "
	<< p << " "
	<< Tag::genTag(this->rank, p, Tag::_node_group));
	requests.push_back(comm.asyncSend(
	buffer, p, Tag::genTag(this->rank, p, Tag::_node_group)));
	}

	this->fillNodeGroupsFromBuffer(buffer);

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	requests.clear();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::synchronizePeriodicity() {
	bool is_periodic = mesh.isPeriodic();
	comm.broadcast(is_periodic, root);

	if (not is_periodic) {
	return;
	}

	std::vector<CommunicationRequest> requests;
	std::vector<Array<UInt>> periodic_info_to_send_per_proc;
	for (auto p : arange(nb_proc)) {
	periodic_info_to_send_per_proc.emplace_back(0, 2);
	auto && periodic_info = periodic_info_to_send_per_proc.back();

	for (UInt proc_local_node : arange(nb_nodes_per_proc(p))) {
	UInt global_node = nodes_per_proc[p](proc_local_node);
	if ((all_periodic_flags[global_node] & NodeFlag::_periodic_mask) ==
	NodeFlag::_periodic_slave) {
	periodic_info.push_back(
	Vector<UInt>{global_node, mesh.getPeriodicMaster(global_node)});
	}
	}

	if (p == root) {
	continue;
	}

	auto && tag = Tag::genTag(this->rank, p, Tag::_periodic_slaves);
	AKANTU_DEBUG_INFO("Sending periodic info to proc " << p << " " << tag);
	requests.push_back(comm.asyncSend(periodic_info, p, tag));
	}

	CommunicationStatus status;
	std::vector<DynamicCommunicationBuffer> buffers(nb_proc);
	std::vector<std::vector<UInt>> proc_missings(nb_proc);
	auto nodes_it = all_nodes.begin(spatial_dimension);

	for (UInt p = 0; p < nb_proc; ++p) {
	auto & proc_missing = proc_missings[p];
	if (p != root) {
	auto && tag = Tag::genTag(p, 0, Tag::_periodic_nodes);
	comm.probe<UInt>(p, tag, status);

	proc_missing.resize(status.size());
	comm.receive(proc_missing, p, tag);
	} else {
	fillPeriodicPairs(periodic_info_to_send_per_proc[root], proc_missing);
	}

	auto & buffer = buffers[p];
	buffer.reserve((spatial_dimension * sizeof(Real) + sizeof(Int)) *
	proc_missing.size());
	buffer << proc_missing.size();
	for (auto && node : proc_missing) {
	buffer << *(nodes_it + node);
	buffer << nodes_pranks(node);
	}
	}

	for (UInt p = 0; p < nb_proc; ++p) {
	for (auto && node : proc_missings[p]) {
	auto & buffer = buffers[nodes_pranks(node)];
	buffer << node;
	buffer << p;
	}
	}

	for (UInt p = 0; p < nb_proc; ++p) {
	if (p != root) {
	auto && tag_send = Tag::genTag(p, 1, Tag::_periodic_nodes);
	requests.push_back(comm.asyncSend(buffers[p], p, tag_send));
	} else {
	receiveMissingPeriodic(buffers[p]);
	}
	}

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	}

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::fillTagBuffers(
	std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name) {
	#define AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA(r, _, elem) \
	case MeshDataTypeCode::BOOST_PP_TUPLE_ELEM(2, 0, elem): { \
	auto & nodal_data = \
	mesh.getNodalData<BOOST_PP_TUPLE_ELEM(2, 1, elem)>(tag_name); \
	for (auto && data : enumerate(nodes_per_proc)) { \
	auto proc = std::get<0>(data); \
	auto & nodes = std::get<1>(data); \
	auto & buffer = buffers[proc]; \
	for (auto & node : nodes) { \
	for (auto i : arange(nodal_data.getNbComponent())) { \
	buffer << nodal_data(node, i); \
	} \
	} \
	} \
	break; \
	}

	MeshDataTypeCode data_type_code =
	mesh.getTypeCode(tag_name, MeshDataType::_nodal);
	switch (data_type_code) {
	BOOST_PP_SEQ_FOR_EACH(AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA, ,
	AKANTU_MESH_DATA_TYPES)
	default:
	AKANTU_ERROR("Could not obtain the type of tag" << tag_name << "!");
	break;
	}
	#undef AKANTU_DISTRIBUTED_SYNHRONIZER_TAG_DATA
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	void MasterNodeInfoPerProc::synchronizeTags() {
	/// tag info
	auto tag_names = mesh.getTagNames();

	DynamicCommunicationBuffer tags_buffer;
	for (auto && tag_name : tag_names) {
	tags_buffer << tag_name;
	tags_buffer << mesh.getTypeCode(tag_name, MeshDataType::_nodal);
	tags_buffer << mesh.getNbComponent(tag_name);
	}

	AKANTU_DEBUG_INFO(
	"Broadcasting the information about the nodes mesh data tags: ("
	<< tags_buffer.size() << ").");
	comm.broadcast(tags_buffer, root);

	for (auto && tag_data : enumerate(tag_names)) {
	auto tag_count = std::get<0>(tag_data);
	auto & tag_name = std::get<1>(tag_data);
	std::vector<DynamicCommunicationBuffer> buffers;
	std::vector<CommunicationRequest> requests;
	buffers.resize(nb_proc);
	fillTagBuffers(buffers, tag_name);
	for (auto && data : enumerate(buffers)) {
	auto && proc = std::get<0>(data);
	auto & buffer = std::get<1>(data);
	if (proc == root) {
	fillNodalData(buffer, tag_name);
	} else {
	auto && tag = Tag::genTag(this->rank, tag_count, Tag::_mesh_data);
	requests.push_back(comm.asyncSend(buffer, proc, tag));
	}
	}

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	}
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	SlaveNodeInfoPerProc::SlaveNodeInfoPerProc(NodeSynchronizer & synchronizer,
	UInt message_cnt, UInt root)
	: NodeInfoPerProc(synchronizer, message_cnt, root) {
	UInt nb_global_nodes = 0;
	comm.broadcast(nb_global_nodes, root);
	this->setNbGlobalNodes(nb_global_nodes);
	}

	/* -------------------------------------------------------------------------- */
	void SlaveNodeInfoPerProc::synchronizeNodes() {
	AKANTU_DEBUG_INFO("Sending list of nodes to proc "
	<< root << " " << Tag::genTag(this->rank, 0, Tag::_nb_nodes)
	<< " " << Tag::genTag(this->rank, 0, Tag::_nodes));
	Array<UInt> & local_ids = this->getNodesGlobalIds();
	Array<Real> & nodes = this->getNodes();

	UInt nb_nodes = local_ids.size();
	comm.send(nb_nodes, root, Tag::genTag(this->rank, 0, Tag::_nb_nodes));
	comm.send(local_ids, root, Tag::genTag(this->rank, 0, Tag::_nodes));

	/* --------<<<<-COORDINATES---------------------------------------------- */
	nodes.resize(nb_nodes);
	AKANTU_DEBUG_INFO("Receiving coordinates from proc "
	<< root << " " << Tag::genTag(root, 0, Tag::_coordinates));
	comm.receive(nodes, root, Tag::genTag(root, 0, Tag::_coordinates));
	}

	/* -------------------------------------------------------------------------- */
	void SlaveNodeInfoPerProc::synchronizeTypes() {
	this->fillNodesType();

	auto & nodes_flags = this->getNodesFlags();

	AKANTU_DEBUG_INFO("Sending first nodes types to proc "
	<< root << ""
	<< Tag::genTag(this->rank, 0, Tag::_nodes_type));
	comm.send(nodes_flags, root, Tag::genTag(this->rank, 0, Tag::_nodes_type));

	AKANTU_DEBUG_INFO("Receiving nodes types from proc "
	<< root << " " << Tag::genTag(root, 0, Tag::_nodes_type));
	comm.receive(nodes_flags, root, Tag::genTag(root, 0, Tag::_nodes_type));

	Array<Int> nodes_prank(nodes_flags.size());

	AKANTU_DEBUG_INFO("Receiving nodes pranks from proc "
	<< root << " " << Tag::genTag(root, 2, Tag::_nodes_type));
	comm.receive(nodes_prank, root, Tag::genTag(root, 2, Tag::_nodes_type));
	for (auto && data : enumerate(nodes_prank)) {
	auto node = std::get<0>(data);
	if (not(mesh.isMasterNode(node) or mesh.isLocalNode(node))) {
	this->setNodePrank(node, std::get<1>(data));
	}
	}

	AKANTU_DEBUG_INFO("Receiving nodes master info from proc "
	<< root << " " << Tag::genTag(root, 1, Tag::_nodes_type));
	CommunicationStatus status;
	comm.probe<UInt>(root, Tag::genTag(root, 1, Tag::_nodes_type), status);

	Array<UInt> nodes_master_info(status.size());
	comm.receive(nodes_master_info, root, Tag::genTag(root, 1, Tag::_nodes_type));

	this->fillCommunicationScheme(nodes_master_info);
	}

	/* -------------------------------------------------------------------------- */
	void SlaveNodeInfoPerProc::synchronizeGroups() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Receiving node groups from proc "
	<< root << " "
	<< Tag::genTag(root, this->rank, Tag::_node_group));

	DynamicCommunicationBuffer buffer;
	comm.receive(buffer, root, Tag::genTag(root, this->rank, Tag::_node_group));

	this->fillNodeGroupsFromBuffer(buffer);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SlaveNodeInfoPerProc::synchronizePeriodicity() {
	bool is_periodic;
	comm.broadcast(is_periodic, root);

	if (not is_periodic) {
	return;
	}

	CommunicationStatus status;
	auto && tag = Tag::genTag(root, this->rank, Tag::_periodic_slaves);
	comm.probe<UInt>(root, tag, status);

	Array<UInt> periodic_info(status.size() / 2, 2);
	comm.receive(periodic_info, root, tag);

	std::vector<UInt> proc_missing;
	fillPeriodicPairs(periodic_info, proc_missing);

	auto && tag_missing_request =
	Tag::genTag(this->rank, 0, Tag::_periodic_nodes);
	comm.send(proc_missing, root, tag_missing_request);

	DynamicCommunicationBuffer buffer;
	auto && tag_missing = Tag::genTag(this->rank, 1, Tag::_periodic_nodes);
	comm.receive(buffer, root, tag_missing);

	receiveMissingPeriodic(buffer);
	}

	/* -------------------------------------------------------------------------- */
	void SlaveNodeInfoPerProc::synchronizeTags() {
	DynamicCommunicationBuffer tags_buffer;
	comm.broadcast(tags_buffer, root);

	std::vector<std::string> tag_names;
	while (tags_buffer.getLeftToUnpack() > 0) {
	std::string name;
	MeshDataTypeCode code;
	UInt nb_components;
	tags_buffer >> name;
	tags_buffer >> code;
	tags_buffer >> nb_components;

	mesh.registerNodalData(name, nb_components, code);
	tag_names.push_back(name);
	}

	for (auto && tag_data : enumerate(tag_names)) {
	auto tag_count = std::get<0>(tag_data);
	auto & tag_name = std::get<1>(tag_data);
	DynamicCommunicationBuffer buffer;
	auto && tag = Tag::genTag(this->root, tag_count, Tag::_mesh_data);
	comm.receive(buffer, this->root, tag);

	fillNodalData(buffer, tag_name);
	}
	}

	} // namespace akantu
	diff --git a/src/synchronizer/node_info_per_processor.hh b/src/synchronizer/node_info_per_processor.hh
	index 1b51003ef..9ed2b2181 100644
	--- a/src/synchronizer/node_info_per_processor.hh
	+++ b/src/synchronizer/node_info_per_processor.hh
	@@ -1,130 +1,130 @@
	/**
	* @file node_info_per_processor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Helper classes to create the distributed synchronizer and distribute
	* a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communication_buffer.hh"
	#include "mesh_accessor.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NODE_INFO_PER_PROCESSOR_HH_
	#define AKANTU_NODE_INFO_PER_PROCESSOR_HH_

	namespace akantu {
	class NodeSynchronizer;
	class Communicator;
	} // namespace akantu

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class NodeInfoPerProc : protected MeshAccessor {
	public:
	NodeInfoPerProc(NodeSynchronizer & synchronizer, UInt message_cnt, UInt root);

	void synchronize();

	protected:
	virtual void synchronizeNodes() = 0;
	virtual void synchronizeTypes() = 0;
	virtual void synchronizeGroups() = 0;
	virtual void synchronizePeriodicity() = 0;
	virtual void synchronizeTags() = 0;

	protected:
	template <class CommunicationBuffer>
	void fillNodeGroupsFromBuffer(CommunicationBuffer & buffer);
	void fillNodesType();

	void fillCommunicationScheme(const Array<UInt> & /master_info/);
	void fillNodalData(DynamicCommunicationBuffer & buffer,
	const std::string & tag_name);

	void fillPeriodicPairs(const Array<UInt> & /global_pairs/,
	std::vector<UInt> & /missing_nodes/);
	void receiveMissingPeriodic(DynamicCommunicationBuffer & /buffer/);

	protected:
	NodeSynchronizer & synchronizer;
	const Communicator & comm;
	UInt rank;
	UInt nb_proc;
	UInt root;

	Mesh & mesh;

	UInt spatial_dimension;
	UInt message_count;
	};

	/* -------------------------------------------------------------------------- */
	class MasterNodeInfoPerProc : public NodeInfoPerProc {
	public:
	MasterNodeInfoPerProc(NodeSynchronizer & synchronizer, UInt message_cnt,
	UInt root);

	void synchronizeNodes() override;
	void synchronizeTypes() override;
	void synchronizeGroups() override;
	void synchronizePeriodicity() override;
	void synchronizeTags() override;

	private:
	void fillTagBuffers(std::vector<DynamicCommunicationBuffer> & buffers,
	const std::string & tag_name);

	/// get the list of nodes to send and send them
	std::vector<Array<UInt>> nodes_per_proc;
	Array<UInt> nb_nodes_per_proc;
	Array<Real> all_nodes;
	Array<NodeFlag> all_periodic_flags;
	Array<Int> nodes_pranks;
	};

	/* -------------------------------------------------------------------------- */
	class SlaveNodeInfoPerProc : public NodeInfoPerProc {
	public:
	SlaveNodeInfoPerProc(NodeSynchronizer & synchronizer, UInt message_cnt,
	UInt root);

	void synchronizeNodes() override;
	void synchronizeTypes() override;
	void synchronizeGroups() override;
	void synchronizePeriodicity() override;
	void synchronizeTags() override;

	private:
	};

	} // namespace akantu

	#endif /* AKANTU_NODE_INFO_PER_PROCESSOR_HH_ */
	diff --git a/src/synchronizer/node_synchronizer.cc b/src/synchronizer/node_synchronizer.cc
	index 874c54d55..a64cd2f07 100644
	--- a/src/synchronizer/node_synchronizer.cc
	+++ b/src/synchronizer/node_synchronizer.cc
	@@ -1,248 +1,247 @@
	/**
	* @file node_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Implementation of the node synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "node_synchronizer.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	NodeSynchronizer::NodeSynchronizer(Mesh & mesh, const ID & id,
	const bool register_to_event_manager,
	EventHandlerPriority event_priority)
	- : SynchronizerImpl<UInt>(mesh.getCommunicator(), id),
	- mesh(mesh) {
	+ : SynchronizerImpl<UInt>(mesh.getCommunicator(), id), mesh(mesh) {
	AKANTU_DEBUG_IN();

	if (register_to_event_manager) {
	this->mesh.registerEventHandler(*this, event_priority);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	NodeSynchronizer::~NodeSynchronizer() = default;

	/* -------------------------------------------------------------------------- */
	Int NodeSynchronizer::getRank(const UInt & node) const {
	return this->mesh.getNodePrank(node);
	}

	/* -------------------------------------------------------------------------- */
	void NodeSynchronizer::onNodesAdded(const Array<UInt> & /nodes_list/,
	const NewNodesEvent & /unused/) {
	std::map<UInt, std::vector<UInt>> nodes_per_proc;

	// recreates fully the schemes due to changes of global ids
	// \TODO add an event to handle global id changes
	for (auto && data : communications.iterateSchemes(_recv)) {
	auto & scheme = data.second;
	scheme.resize(0);
	}

	for (auto && local_id : arange(mesh.getNbNodes())) {
	if (not mesh.isSlaveNode(local_id)) {
	continue; // local, master or pure ghost
	}

	auto global_id = mesh.getNodeGlobalId(local_id);
	auto proc = mesh.getNodePrank(local_id);
	AKANTU_DEBUG_ASSERT(
	proc != -1,
	"The node " << local_id << " does not have a valid associated prank");
	nodes_per_proc[proc].push_back(global_id);

	auto & scheme = communications.createScheme(proc, _recv);
	scheme.push_back(local_id);
	}

	std::vector<CommunicationRequest> send_requests;
	for (auto && pair : communications.iterateSchemes(_recv)) {
	auto proc = pair.first;
	AKANTU_DEBUG_ASSERT(proc != UInt(-1),
	"For real I should send something to proc -1");

	// if proc not in nodes_per_proc this should insert an empty array to send
	send_requests.push_back(communicator.asyncSend(
	nodes_per_proc[proc], proc, Tag::genTag(rank, proc, 0xcafe)));
	}

	for (auto && data : communications.iterateSchemes(_send)) {
	auto proc = data.first;
	auto & scheme = data.second;
	CommunicationStatus status;

	auto tag = Tag::genTag(proc, rank, 0xcafe);
	communicator.probe<UInt>(proc, tag, status);

	scheme.resize(status.size());
	communicator.receive(scheme, proc, tag);
	std::transform(scheme.begin(), scheme.end(), scheme.begin(),
	[&](auto & gnode) { return mesh.getNodeLocalId(gnode); });
	}

	// communicator.receiveAnyNumber<UInt>(
	// send_requests,
	// [&](auto && proc, auto && nodes) {
	// auto & scheme = communications.createScheme(proc, _send);
	// scheme.resize(nodes.size());
	// for (auto && data : enumerate(nodes)) {
	// auto global_id = std::get<1>(data);
	// auto local_id = mesh.getNodeLocalId(global_id);
	// AKANTU_DEBUG_ASSERT(local_id != UInt(-1),
	// "The global node " << global_id
	// << "is not known on rank "
	// << rank);
	// scheme[std::get<0>(data)] = local_id;
	// }
	// },
	// Tag::genTag(rank, count, 0xcafe));
	// ++count;

	Communicator::waitAll(send_requests);
	Communicator::freeCommunicationRequest(send_requests);

	this->entities_changed = true;
	}

	/* -------------------------------------------------------------------------- */
	UInt NodeSynchronizer::sanityCheckDataSize(const Array<UInt> & nodes,
	const SynchronizationTag & tag,
	bool from_comm_desc) const {
	UInt size =
	SynchronizerImpl<UInt>::sanityCheckDataSize(nodes, tag, from_comm_desc);

	// global id
	if (tag != SynchronizationTag::_giu_global_conn) {
	size += sizeof(UInt) * nodes.size();
	}

	// flag
	size += sizeof(NodeFlag) * nodes.size();

	// positions
	size += mesh.getSpatialDimension() * sizeof(Real) * nodes.size();

	return size;
	}

	/* -------------------------------------------------------------------------- */
	void NodeSynchronizer::packSanityCheckData(
	CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag & tag) const {
	auto dim = mesh.getSpatialDimension();
	for (auto && node : nodes) {
	if (tag != SynchronizationTag::_giu_global_conn) {
	buffer << mesh.getNodeGlobalId(node);
	}
	buffer << mesh.getNodeFlag(node);
	buffer << Vector<Real>(mesh.getNodes().begin(dim)[node]);
	}
	}

	/* -------------------------------------------------------------------------- */
	void NodeSynchronizer::unpackSanityCheckData(CommunicationBuffer & buffer,
	const Array<UInt> & nodes,
	const SynchronizationTag & tag,
	UInt proc, UInt rank) const {
	auto dim = mesh.getSpatialDimension();

	#ifndef AKANTU_NDEBUG
	auto periodic = [&](auto && flag) { return flag & NodeFlag::_periodic_mask; };
	auto distrib = [&](auto && flag) { return flag & NodeFlag::_shared_mask; };
	#endif

	for (auto && node : nodes) {
	if (tag != SynchronizationTag::_giu_global_conn) {
	UInt global_id;
	buffer >> global_id;
	AKANTU_DEBUG_ASSERT(global_id == mesh.getNodeGlobalId(node),
	"The nodes global ids do not match: "
	<< global_id
	<< " != " << mesh.getNodeGlobalId(node));
	}

	NodeFlag flag;
	buffer >> flag;
	AKANTU_DEBUG_ASSERT(
	(periodic(flag) == periodic(mesh.getNodeFlag(node))) and
	(((distrib(flag) == NodeFlag::_master) and
	(distrib(mesh.getNodeFlag(node)) ==
	NodeFlag::_slave)) or // master to slave
	((distrib(flag) == NodeFlag::_slave) and
	(distrib(mesh.getNodeFlag(node)) ==
	NodeFlag::_master)) or // reverse comm slave to master
	(distrib(mesh.getNodeFlag(node)) ==
	NodeFlag::_pure_ghost or // pure ghost nodes
	distrib(flag) == NodeFlag::_pure_ghost)),
	"The node flags: " << flag << " and " << mesh.getNodeFlag(node));

	Vector<Real> pos_remote(dim);
	buffer >> pos_remote;
	Vector<Real> pos(mesh.getNodes().begin(dim)[node]);

	auto dist = pos_remote.distance(pos);
	if (not Math::are_float_equal(dist, 0.)) {
	AKANTU_EXCEPTION("Unpacking an unknown value for the node "
	<< node << "(position " << pos << " != buffer "
	<< pos_remote << ") [" << dist << "] - tag: " << tag
	<< " comm from " << proc << " to " << rank);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void NodeSynchronizer::fillEntityToSend(Array<UInt> & nodes_to_send) {
	UInt nb_nodes = mesh.getNbNodes();

	this->entities_from_root.clear();
	nodes_to_send.resize(0);

	for (UInt n : arange(nb_nodes)) {
	if (not mesh.isLocalOrMasterNode(n)) {
	continue;
	}

	entities_from_root.push_back(n);
	}

	for (auto n : entities_from_root) {
	UInt global_node = mesh.getNodeGlobalId(n);
	nodes_to_send.push_back(global_node);
	}
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/synchronizer/node_synchronizer.hh b/src/synchronizer/node_synchronizer.hh
	index b85d1d246..d13c2f628 100644
	--- a/src/synchronizer/node_synchronizer.hh
	+++ b/src/synchronizer/node_synchronizer.hh
	@@ -1,114 +1,115 @@
	/**
	* @file node_synchronizer.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Synchronizer for nodal information
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_events.hh"
	#include "synchronizer_impl.hh"
	/* -------------------------------------------------------------------------- */
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NODE_SYNCHRONIZER_HH_
	#define AKANTU_NODE_SYNCHRONIZER_HH_

	namespace akantu {

	class NodeSynchronizer : public MeshEventHandler,
	public SynchronizerImpl<UInt> {
	public:
	NodeSynchronizer(Mesh & mesh, const ID & id = "element_synchronizer",
	bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	~NodeSynchronizer() override;

	UInt sanityCheckDataSize(const Array<UInt> & nodes,
	const SynchronizationTag & tag,
	bool from_comm_desc) const override;
	void packSanityCheckData(CommunicationBuffer & buffer,
	const Array<UInt> & nodes,
	const SynchronizationTag & /tag/) const override;
	void unpackSanityCheckData(CommunicationBuffer & buffer,
	const Array<UInt> & nodes,
	const SynchronizationTag & tag, UInt proc,
	UInt rank) const override;

	/// function to implement to react on akantu::NewNodesEvent
	void onNodesAdded(const Array<UInt> & /unused/,
	const NewNodesEvent & /unused/) override;

	/// function to implement to react on akantu::RemovedNodesEvent
	void onNodesRemoved(const Array<UInt> & /unused/,
	const Array<UInt> & /unused/,
	const RemovedNodesEvent & /unused/) override {}
	/// function to implement to react on akantu::NewElementsEvent
	void onElementsAdded(const Array<Element> & /unused/,
	const NewElementsEvent & /unused/) override {}
	/// function to implement to react on akantu::RemovedElementsEvent
	void onElementsRemoved(const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const RemovedElementsEvent & /unused/) override {}
	/// function to implement to react on akantu::ChangedElementsEvent
	void onElementsChanged(const Array<Element> & /unused/,
	const Array<Element> & /unused/,
	const ElementTypeMapArray<UInt> & /unused/,
	const ChangedElementsEvent & /unused/) override {}

	/* ------------------------------------------------------------------------ */
	NodeSynchronizer & operator=(const NodeSynchronizer & other) {
	copySchemes(other);
	return *this;
	}

	friend class NodeInfoPerProc;
	+
	protected:
	void fillEntityToSend(Array<UInt> & nodes_to_send) override;

	public:
	AKANTU_GET_MACRO(Mesh, mesh, Mesh &);

	inline UInt canScatterSize() override;
	inline UInt gatheredSize() override;

	inline UInt localToGlobalEntity(const UInt & local) override;
	-
	+
	protected:
	Int getRank(const UInt & node) const final;

	protected:
	Mesh & mesh;
	};

	} // namespace akantu

	#include "node_synchronizer_inline_impl.hh"

	#endif /* AKANTU_NODE_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/node_synchronizer_inline_impl.hh b/src/synchronizer/node_synchronizer_inline_impl.hh
	index 6eb13ce6d..828eb6a20 100644
	--- a/src/synchronizer/node_synchronizer_inline_impl.hh
	+++ b/src/synchronizer/node_synchronizer_inline_impl.hh
	@@ -1,59 +1,55 @@
	/**
	* @file node_synchronizer_inline_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Synchronizer for nodal information
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	-#include "node_synchronizer.hh"
	#include "mesh.hh"
	+#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_NODE_SYNCHRONIZER_INLINE_IMPL_HH_
	#define AKANTU_NODE_SYNCHRONIZER_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	-inline UInt NodeSynchronizer::canScatterSize() {
	- return mesh.getNbNodes();
	-}
	+inline UInt NodeSynchronizer::canScatterSize() { return mesh.getNbNodes(); }

	/* -------------------------------------------------------------------------- */
	-inline UInt NodeSynchronizer::gatheredSize() {
	- return mesh.getNbGlobalNodes();
	-}
	+inline UInt NodeSynchronizer::gatheredSize() { return mesh.getNbGlobalNodes(); }

	/* -------------------------------------------------------------------------- */
	inline UInt NodeSynchronizer::localToGlobalEntity(const UInt & local) {
	return mesh.getNodeGlobalId(local);
	}

	-} // akantu
	+} // namespace akantu

	#endif // AKANTU_NODE_SYNCHRONIZER_INLINE_IMPL_HH_
	diff --git a/src/synchronizer/periodic_node_synchronizer.cc b/src/synchronizer/periodic_node_synchronizer.cc
	index 9ba529d05..a74feda8c 100644
	--- a/src/synchronizer/periodic_node_synchronizer.cc
	+++ b/src/synchronizer/periodic_node_synchronizer.cc
	@@ -1,135 +1,135 @@
	/**
	* @file periodic_node_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 30 2018
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Implementation of the periodic node synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "periodic_node_synchronizer.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	PeriodicNodeSynchronizer::PeriodicNodeSynchronizer(
	- Mesh & mesh, const ID & id,
	- const bool register_to_event_manager, EventHandlerPriority event_priority)
	- : NodeSynchronizer(mesh, id + ":masters",
	- register_to_event_manager, event_priority) {}
	+ Mesh & mesh, const ID & id, const bool register_to_event_manager,
	+ EventHandlerPriority event_priority)
	+ : NodeSynchronizer(mesh, id + ":masters", register_to_event_manager,
	+ event_priority) {}

	/* -------------------------------------------------------------------------- */
	void PeriodicNodeSynchronizer::update() {
	static int count = 0;
	const auto & masters_to_slaves = this->mesh.getPeriodicMasterSlaves();
	masters_list.resize(0);
	masters_list.reserve(masters_to_slaves.size());

	slaves_list.resize(0);
	slaves_list.reserve(masters_to_slaves.size());

	reset();

	std::set<UInt> masters_to_receive;
	for (auto && data : masters_to_slaves) {
	auto master = std::get<0>(data);
	auto slave = std::get<1>(data);

	masters_list.push_back(master);
	slaves_list.push_back(slave);

	if (not(mesh.isMasterNode(master) or mesh.isLocalNode(master))) {
	masters_to_receive.insert(master);
	}
	}

	if (not mesh.isDistributed() or nb_proc == 1) {
	return;
	}

	std::map<Int, Array<UInt>> buffers;
	for (auto node : masters_to_receive) {
	auto && proc = mesh.getNodePrank(node);
	auto && scheme = this->communications.createRecvScheme(proc);
	scheme.push_back(node);

	buffers[proc].push_back(mesh.getNodeGlobalId(node));
	}

	auto tag = Tag::genTag(0, count, Tag::_modify_scheme);
	std::vector<CommunicationRequest> requests;
	for (auto && data : buffers) {
	auto proc = std::get<0>(data);
	auto & buffer = std::get<1>(data);

	requests.push_back(communicator.asyncSend(buffer, proc, tag,
	CommunicationMode::_synchronous));
	std::cout << "Recv from proc : " << proc << " -> "
	<< this->communications.getScheme(proc, _recv).size()
	<< std::endl;
	}

	communicator.receiveAnyNumber<UInt>(
	requests,
	[&](auto && proc, auto && msg) {
	auto && scheme = this->communications.createSendScheme(proc);
	for (auto node : msg) {
	scheme.push_back(mesh.getNodeLocalId(node));
	}
	std::cout << "Send to proc : " << proc << " -> " << scheme.size()
	<< " [" << tag << "]" << std::endl;
	},
	tag);
	++count;
	}

	/* -------------------------------------------------------------------------- */
	void PeriodicNodeSynchronizer::synchronizeOnceImpl(
	DataAccessor<UInt> & data_accessor, const SynchronizationTag & tag) const {
	NodeSynchronizer::synchronizeOnceImpl(data_accessor, tag);

	auto size = data_accessor.getNbData(masters_list, tag);
	CommunicationBuffer buffer(size);

	data_accessor.packData(buffer, masters_list, tag);
	data_accessor.unpackData(buffer, slaves_list, tag);
	}

	/* -------------------------------------------------------------------------- */
	void PeriodicNodeSynchronizer::waitEndSynchronizeImpl(
	DataAccessor<UInt> & data_accessor, const SynchronizationTag & tag) {
	NodeSynchronizer::waitEndSynchronizeImpl(data_accessor, tag);

	auto size = data_accessor.getNbData(masters_list, tag);
	CommunicationBuffer buffer(size);

	data_accessor.packData(buffer, masters_list, tag);
	data_accessor.unpackData(buffer, slaves_list, tag);
	}

	} // namespace akantu
	diff --git a/src/synchronizer/periodic_node_synchronizer.hh b/src/synchronizer/periodic_node_synchronizer.hh
	index b928bd82e..5af1d010c 100644
	--- a/src/synchronizer/periodic_node_synchronizer.hh
	+++ b/src/synchronizer/periodic_node_synchronizer.hh
	@@ -1,96 +1,97 @@
	/**
	* @file periodic_node_synchronizer.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed May 30 2018
	* @date last modification: Fri Jul 24 2020
	*
	* @brief PeriodicNodeSynchronizer definition
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PERIODIC_NODE_SYNCHRONIZER_HH_
	#define AKANTU_PERIODIC_NODE_SYNCHRONIZER_HH_

	namespace akantu {

	class PeriodicNodeSynchronizer : public NodeSynchronizer {
	public:
	PeriodicNodeSynchronizer(
	- Mesh & mesh, const ID & id = "periodic_node_synchronizer", bool register_to_event_manager = true,
	+ Mesh & mesh, const ID & id = "periodic_node_synchronizer",
	+ bool register_to_event_manager = true,
	EventHandlerPriority event_priority = _ehp_synchronizer);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void update();

	/// Uses the synchronizer to perform a reduction on the vector
	template <template <class> class Op, typename T>
	void reduceSynchronizeWithPBCSlaves(Array<T> & array) const;

	/// synchronize ghosts without state
	void synchronizeOnceImpl(DataAccessor<UInt> & data_accessor,
	const SynchronizationTag & tag) const override;

	// /// asynchronous synchronization of ghosts
	// void asynchronousSynchronizeImpl(const DataAccessor<UInt> & data_accessor,
	// const SynchronizationTag & tag) override;

	/// wait end of asynchronous synchronization of ghosts
	void waitEndSynchronizeImpl(DataAccessor<UInt> & data_accessor,
	const SynchronizationTag & tag) override;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	// NodeSynchronizer master_to_slaves_synchronizer;
	Array<UInt> masters_list;
	Array<UInt> slaves_list;
	};

	/* -------------------------------------------------------------------------- */
	template <template <class> class Op, typename T>
	void PeriodicNodeSynchronizer::reduceSynchronizeWithPBCSlaves(
	Array<T> & array) const {
	ReduceDataAccessor<UInt, Op, T> data_accessor(array,
	SynchronizationTag::_whatever);
	auto size =
	data_accessor.getNbData(slaves_list, SynchronizationTag::_whatever);
	CommunicationBuffer buffer(size);

	data_accessor.packData(buffer, slaves_list, SynchronizationTag::_whatever);
	data_accessor.unpackData(buffer, masters_list, SynchronizationTag::_whatever);

	this->reduceSynchronizeArray<Op>(array);
	}

	} // namespace akantu

	#endif /* AKANTU_PERIODIC_NODE_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/slave_element_info_per_processor.cc b/src/synchronizer/slave_element_info_per_processor.cc
	index 0e3b22467..67ab41230 100644
	--- a/src/synchronizer/slave_element_info_per_processor.cc
	+++ b/src/synchronizer/slave_element_info_per_processor.cc
	@@ -1,195 +1,195 @@
	/**
	* @file slave_element_info_per_processor.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Mar 16 2016
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Helper class to distribute a mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "element_info_per_processor.hh"
	#include "element_synchronizer.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <iostream>
	#include <map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SlaveElementInfoPerProc::SlaveElementInfoPerProc(
	ElementSynchronizer & synchronizer, UInt message_cnt, UInt root)
	: ElementInfoPerProc(synchronizer, message_cnt, root, _not_defined) {

	Vector<UInt> size(5);
	comm.receive(size, this->root,
	Tag::genTag(this->root, this->message_count, Tag::_sizes));

	this->type = (ElementType)size[0];
	this->nb_local_element = size[1];
	this->nb_ghost_element = size[2];
	this->nb_element_to_receive = size[3];
	this->nb_tags = size[4];

	if (this->type != _not_defined) {
	this->nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	}
	}

	/* -------------------------------------------------------------------------- */

	bool SlaveElementInfoPerProc::needSynchronize() {
	return this->type != _not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void SlaveElementInfoPerProc::synchronizeConnectivities() {
	Array<UInt> local_connectivity(
	(this->nb_local_element + this->nb_ghost_element) *
	this->nb_nodes_per_element);

	AKANTU_DEBUG_INFO("Receiving connectivities from proc " << root);
	comm.receive(
	local_connectivity, this->root,
	Tag::genTag(this->root, this->message_count, Tag::_connectivity));

	auto & old_nodes = this->getNodesGlobalIds();
	AKANTU_DEBUG_INFO("Renumbering local connectivities");
	MeshUtils::renumberMeshNodes(this->mesh, local_connectivity,
	this->nb_local_element, this->nb_ghost_element,
	this->type, old_nodes);
	}

	/* -------------------------------------------------------------------------- */
	void SlaveElementInfoPerProc::synchronizePartitions() {
	Array<UInt> local_partitions(this->nb_element_to_receive +
	this->nb_ghost_element * 2);
	AKANTU_DEBUG_INFO("Receiving partition informations from proc " << root);
	this->comm.receive(local_partitions, this->root,
	Tag::genTag(root, this->message_count, Tag::_partitions));

	if (Mesh::getSpatialDimension(this->type) ==
	this->mesh.getSpatialDimension()) {
	AKANTU_DEBUG_INFO("Creating communications scheme");
	this->fillCommunicationScheme(local_partitions);
	}
	}

	/* -------------------------------------------------------------------------- */
	void SlaveElementInfoPerProc::synchronizeTags() {
	AKANTU_DEBUG_IN();

	if (this->nb_tags == 0) {
	AKANTU_DEBUG_OUT();
	return;
	}

	/* --------<<<<-TAGS------------------------------------------------- */
	DynamicCommunicationBuffer mesh_data_sizes_buffer;
	comm.broadcast(mesh_data_sizes_buffer, root);
	AKANTU_DEBUG_INFO("Size of the information about the mesh data: "
	<< mesh_data_sizes_buffer.size());

	if (mesh_data_sizes_buffer.empty()) {
	return;
	}

	AKANTU_DEBUG_INFO("Receiving the information about the mesh data tags, addr "
	<< (void *)mesh_data_sizes_buffer.storage());

	std::vector<std::string> tag_names;
	std::vector<MeshDataTypeCode> tag_type_codes;
	std::vector<UInt> tag_nb_component;
	tag_names.resize(nb_tags);
	tag_type_codes.resize(nb_tags);
	tag_nb_component.resize(nb_tags);
	CommunicationBuffer mesh_data_buffer;
	UInt type_code_int;
	for (UInt i(0); i < nb_tags; ++i) {
	mesh_data_sizes_buffer >> tag_names[i];
	mesh_data_sizes_buffer >> type_code_int;
	tag_type_codes[i] = static_cast<MeshDataTypeCode>(type_code_int);
	mesh_data_sizes_buffer >> tag_nb_component[i];
	}

	std::vector<std::string>::const_iterator names_it = tag_names.begin();
	std::vector<std::string>::const_iterator names_end = tag_names.end();

	CommunicationStatus mesh_data_comm_status;
	AKANTU_DEBUG_INFO("Checking size of data to receive for mesh data TAG("
	<< Tag::genTag(root, this->message_count, Tag::_mesh_data)
	<< ")");
	comm.probe<char>(root,
	Tag::genTag(root, this->message_count, Tag::_mesh_data),
	mesh_data_comm_status);
	UInt mesh_data_buffer_size(mesh_data_comm_status.size());
	AKANTU_DEBUG_INFO("Receiving "
	<< mesh_data_buffer_size << " bytes of mesh data TAG("
	<< Tag::genTag(root, this->message_count, Tag::_mesh_data)
	<< ")");
	mesh_data_buffer.resize(mesh_data_buffer_size);
	comm.receive(mesh_data_buffer, root,
	Tag::genTag(root, this->message_count, Tag::_mesh_data));

	// Loop over each tag for the current type
	UInt k(0);
	for (; names_it != names_end; ++names_it, ++k) {
	this->fillMeshData(mesh_data_buffer, *names_it, tag_type_codes[k],
	tag_nb_component[k]);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SlaveElementInfoPerProc::synchronizeGroups() {
	AKANTU_DEBUG_IN();

	const Communicator & comm = mesh.getCommunicator();
	UInt my_rank = comm.whoAmI();

	AKANTU_DEBUG_INFO("Receiving element groups from proc "
	<< root << " TAG("
	<< Tag::genTag(root, my_rank, Tag::_element_group) << ")");

	CommunicationStatus status;
	comm.probe<char>(root, Tag::genTag(root, my_rank, Tag::_element_group),
	status);

	CommunicationBuffer buffer(status.size());
	comm.receive(buffer, root, Tag::genTag(root, my_rank, Tag::_element_group));

	this->fillElementGroupsFromBuffer(buffer);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/src/synchronizer/synchronizer.cc b/src/synchronizer/synchronizer.cc
	index 5bf27d221..24f2df280 100644
	--- a/src/synchronizer/synchronizer.cc
	+++ b/src/synchronizer/synchronizer.cc
	@@ -1,56 +1,56 @@
	/**
	* @file synchronizer.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Sep 01 2010
	* @date last modification: Wed Nov 15 2017
	*
	* @brief implementation of the common part
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "synchronizer.hh"
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <functional>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	Synchronizer::Synchronizer(const Communicator & comm, const ID & id)
	: communicator(comm) {
	int max_tag = comm.getMaxTag();

	this->hash_id = std::hash<std::string>()(id);
	if (max_tag != 0) {
	this->hash_id = this->hash_id % max_tag;
	}

	this->nb_proc = communicator.getNbProc();
	this->rank = communicator.whoAmI();
	}

	} // namespace akantu
	diff --git a/src/synchronizer/synchronizer.hh b/src/synchronizer/synchronizer.hh
	index 84cf96eab..27c3a9f0f 100644
	--- a/src/synchronizer/synchronizer.hh
	+++ b/src/synchronizer/synchronizer.hh
	@@ -1,130 +1,130 @@
	/**
	* @file synchronizer.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Common interface for synchronizers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SYNCHRONIZER_HH_
	#define AKANTU_SYNCHRONIZER_HH_

	namespace akantu {
	class Communicator;
	}

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Base class for synchronizers */
	/* -------------------------------------------------------------------------- */
	class Synchronizer {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	Synchronizer(const Communicator & comm, const ID & id = "synchronizer");

	Synchronizer(const Synchronizer & other) = default;

	- virtual ~Synchronizer() = default;
	+ virtual ~Synchronizer() = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// synchronous communications form slaves to master
	template <class DataAccessor>
	void slaveReductionOnce(DataAccessor & data_accessor,
	const SynchronizationTag & tag) const;

	/// synchronize ghosts without state
	template <class DataAccessor>
	void synchronizeOnce(DataAccessor & data_accessor,
	const SynchronizationTag & tag) const;

	/// synchronize ghosts
	template <class DataAccessor>
	void synchronize(DataAccessor & data_accessor,
	const SynchronizationTag & tag);

	/// asynchronous synchronization of ghosts
	template <class DataAccessor>
	void asynchronousSynchronize(const DataAccessor & data_accessor,
	const SynchronizationTag & tag);

	/// wait end of asynchronous synchronization of ghosts
	template <class DataAccessor>
	void waitEndSynchronize(DataAccessor & data_accessor,
	const SynchronizationTag & tag);

	/// compute buffer size for a given tag and data accessor
	template <class DataAccessor>
	void computeBufferSize(const DataAccessor & data_accessor,
	const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	AKANTU_GET_MACRO(Communicator, communicator, const Communicator &);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// id of the synchronizer
	ID id;

	/// hashed version of the id
	int hash_id;

	/// message counter per tag
	std::map<SynchronizationTag, UInt> tag_counter;

	/// the static memory instance
	const Communicator & communicator;

	/// nb processors in the communicator
	UInt nb_proc;

	/// rank in the communicator
	UInt rank;
	};

	} // namespace akantu

	#include "synchronizer_tmpl.hh"

	#endif /* AKANTU_SYNCHRONIZER_HH_ */
	diff --git a/src/synchronizer/synchronizer_impl.hh b/src/synchronizer/synchronizer_impl.hh
	index 16b0d04ff..10ac7ef7e 100644
	--- a/src/synchronizer/synchronizer_impl.hh
	+++ b/src/synchronizer/synchronizer_impl.hh
	@@ -1,218 +1,213 @@
	/**
	* @file synchronizer_impl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Wed Mar 04 2020
	*
	* @brief Implementation of the generic part of synchronizers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communications.hh"
	#include "synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SYNCHRONIZER_IMPL_HH_
	#define AKANTU_SYNCHRONIZER_IMPL_HH_

	namespace akantu {

	template <class Entity> class SynchronizerImpl : public Synchronizer {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SynchronizerImpl(const Communicator & communicator,
	const ID & id = "synchronizer");

	SynchronizerImpl(const SynchronizerImpl & other, const ID & id);

	~SynchronizerImpl() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	protected:
	void communicateOnce(
	const std::tuple<CommunicationSendRecv, CommunicationSendRecv> &
	send_recv_schemes,
	const Tag::CommTags & comm_tag, DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const;

	public:
	/// synchronous synchronization without state
	virtual void slaveReductionOnceImpl(DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const;

	/// synchronous synchronization without state
	virtual void synchronizeOnceImpl(DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const;

	/// asynchronous synchronization of ghosts
	virtual void
	asynchronousSynchronizeImpl(const DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag);

	/// wait end of asynchronous synchronization of ghosts
	virtual void waitEndSynchronizeImpl(DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag);

	/// compute all buffer sizes
	virtual void
	computeAllBufferSizes(const DataAccessor<Entity> & data_accessor);

	/// compute buffer size for a given tag and data accessor
	virtual void computeBufferSizeImpl(const DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	virtual void synchronizeImpl(DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) {
	this->asynchronousSynchronizeImpl(data_accessor, tag);
	this->waitEndSynchronizeImpl(data_accessor, tag);
	}

	/* ------------------------------------------------------------------------ */
	/// reset send and recv element lists
	void reset();

	/// extract the elements that have a true predicate from in_synchronizer and
	/// store them in the current synchronizer
	template <typename Pred>
	void split(SynchronizerImpl & in_synchronizer, Pred && pred);

	/// update schemes in a synchronizer
	template <typename Updater> void updateSchemes(Updater && scheme_updater);

	/// filter the send scheme and let the other processor now about iterate
	template <typename Pred> void filterScheme(Pred && pred);

	/// flip send and receive schemes
	void swapSendRecv();

	/// copy the schemes of an other communicator.
	SynchronizerImpl & operator=(const SynchronizerImpl & other);

	/// gather data on the predefined root process (master version)
	template <typename T>
	void gather(const Array<T> & to_gather, Array<T> & gathered);

	/// gather data on the predefined root process (slave version)
	template <typename T> void gather(const Array<T> & to_gather);

	/// scatter data from the predefined root process (master version)
	template <typename T>
	void scatter(Array<T> & scattered, const Array<T> & to_scatter);

	/// scatter data from the predefined root process (slave version)
	template <typename T> void scatter(Array<T> & scattered);

	- template <typename T>
	- void synchronizeArray(Array<T> & array) const;
	+ template <typename T> void synchronizeArray(Array<T> & array) const;

	- /// Uses the synchronizer to perform a reduction on the vector
	+ /// Uses the synchronizer to perform a reduction on the vector
	template <template <class> class Op, typename T>
	void reduceSynchronizeArray(Array<T> & array) const;

	protected:
	/// copy schemes
	void copySchemes(const SynchronizerImpl & other);

	/// check if dof changed set on at least one processor
	inline bool hasChanged();

	/// init the scheme for scatter and gather operation, need extra memory
	inline void initScatterGatherCommunicationScheme();

	/// list the entities to send to root process
	virtual void fillEntityToSend(Array<Entity> & /entities_to_send/) {
	AKANTU_TO_IMPLEMENT();
	}

	virtual Entity localToGlobalEntity(const Entity & /local/) {
	AKANTU_TO_IMPLEMENT();
	}

	- virtual UInt canScatterSize() {
	- AKANTU_TO_IMPLEMENT();
	- }
	- virtual UInt gatheredSize() {
	- AKANTU_TO_IMPLEMENT();
	- }
	+ virtual UInt canScatterSize() { AKANTU_TO_IMPLEMENT(); }
	+ virtual UInt gatheredSize() { AKANTU_TO_IMPLEMENT(); }

	public:
	/* ------------------------------------------------------------------------ */
	virtual UInt sanityCheckDataSize(const Array<Entity> & elements,
	const SynchronizationTag & tag,
	bool is_comm_desc = true) const;
	virtual void
	packSanityCheckData(CommunicationDescriptor<Entity> & comm_desc) const;
	virtual void
	unpackSanityCheckData(CommunicationDescriptor<Entity> & comm_desc) const;

	virtual void packSanityCheckData(CommunicationBuffer & /buffer/,
	const Array<Entity> & /elements/,
	const SynchronizationTag & /tag/) const {}
	virtual void unpackSanityCheckData(CommunicationBuffer & /buffer/,
	const Array<Entity> & /elements/,
	const SynchronizationTag & /tag/,
	UInt /proc/, UInt /rank/) const {}

	public:
	AKANTU_GET_MACRO(Communications, communications,
	const Communications<Entity> &);

	protected:
	AKANTU_GET_MACRO_NOT_CONST(Communications, communications,
	Communications<Entity> &);

	virtual Int getRank(const Entity & entity) const = 0;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	/// information on the communications
	Communications<Entity> communications;

	/// did the scheme change, this is to recreate the scatter/gather data if
	/// needed
	bool entities_changed{true};

	/// Root processor for scatter/gather operations
	Int root{0};

	/// entities coming/going from/to root
	Array<Entity> entities_from_root;

	/// entities received from slaves proc (only on master)
	std::map<UInt, Array<Entity>> master_receive_entities;
	};

	} // namespace akantu

	#include "synchronizer_impl_tmpl.hh"

	#endif /* AKANTU_SYNCHRONIZER_IMPL_HH_ */
	diff --git a/src/synchronizer/synchronizer_impl_tmpl.hh b/src/synchronizer/synchronizer_impl_tmpl.hh
	index 7bfe86d43..93bce3446 100644
	--- a/src/synchronizer/synchronizer_impl_tmpl.hh
	+++ b/src/synchronizer/synchronizer_impl_tmpl.hh
	@@ -1,869 +1,869 @@
	/**
	* @file synchronizer_impl_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Wed Dec 09 2020
	*
	* @brief Implementation of the SynchronizerImpl
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "synchronizer_impl.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	SynchronizerImpl<Entity>::SynchronizerImpl(const Communicator & comm,
	const ID & id)

	: Synchronizer(comm, id), communications(comm) {}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	SynchronizerImpl<Entity>::SynchronizerImpl(const SynchronizerImpl & other,
	const ID & id)
	: Synchronizer(other), communications(other.communications) {
	this->id = id;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::communicateOnce(
	const std::tuple<CommunicationSendRecv, CommunicationSendRecv> &
	send_recv_schemes,
	const Tag::CommTags & comm_tag, DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const {
	// no need to synchronize
	if (this->nb_proc == 1) {
	return;
	}

	CommunicationSendRecv send_dir;
	CommunicationSendRecv recv_dir;
	std::tie(send_dir, recv_dir) = send_recv_schemes;

	using CommunicationRequests = std::vector<CommunicationRequest>;
	using CommunicationBuffers = std::map<UInt, CommunicationBuffer>;

	CommunicationRequests send_requests;
	CommunicationRequests recv_requests;
	CommunicationBuffers send_buffers;
	CommunicationBuffers recv_buffers;

	auto postComm = [&](const auto & sr, auto & buffers,
	auto & requests) -> void {
	for (auto && pair : communications.iterateSchemes(sr)) {
	auto & proc = pair.first;
	const auto & scheme = pair.second;

	if (scheme.empty()) {
	continue;
	}

	auto & buffer = buffers[proc];

	auto buffer_size = data_accessor.getNbData(scheme, tag);
	if (buffer_size == 0) {
	continue;
	}

	#ifndef AKANTU_NDEBUG
	buffer_size += this->sanityCheckDataSize(scheme, tag, false);
	#endif

	buffer.resize(buffer_size);

	if (sr == recv_dir) {
	requests.push_back(communicator.asyncReceive(
	buffer, proc,
	Tag::genTag(this->rank, UInt(tag), comm_tag, this->hash_id)));
	} else {
	#ifndef AKANTU_NDEBUG
	this->packSanityCheckData(buffer, scheme, tag);
	#endif
	data_accessor.packData(buffer, scheme, tag);

	AKANTU_DEBUG_ASSERT(
	buffer.getPackedSize() == buffer.size(),
	"The data accessor did not pack all the data it "
	"promised in communication with tag "
	<< tag << " (Promised: " << buffer.size()
	<< "bytes, packed: " << buffer.getPackedSize() << "bytes [avg: "
	<< Real(buffer.size() - buffer.getPackedSize()) / scheme.size()
	<< "bytes per entity missing])");

	send_requests.push_back(communicator.asyncSend(
	buffer, proc,
	Tag::genTag(proc, UInt(tag), comm_tag, this->hash_id)));
	}
	}
	};

	// post the receive requests
	postComm(recv_dir, recv_buffers, recv_requests);

	// post the send data requests
	postComm(send_dir, send_buffers, send_requests);

	// treat the receive requests
	UInt request_ready;
	while ((request_ready = Communicator::waitAny(recv_requests)) != UInt(-1)) {
	auto & req = recv_requests[request_ready];
	auto proc = req.getSource();

	auto & buffer = recv_buffers[proc];
	const auto & scheme = this->communications.getScheme(proc, recv_dir);

	#ifndef AKANTU_NDEBUG
	this->unpackSanityCheckData(buffer, scheme, tag, proc, this->rank);
	#endif

	data_accessor.unpackData(buffer, scheme, tag);

	AKANTU_DEBUG_ASSERT(
	buffer.getLeftToUnpack() == 0,
	"The data accessor ignored some data in communication with tag "
	<< tag);

	req.free();
	recv_requests.erase(recv_requests.begin() + request_ready);
	}

	Communicator::waitAll(send_requests);
	Communicator::freeCommunicationRequest(send_requests);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::slaveReductionOnceImpl(
	DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const {
	communicateOnce(std::make_tuple(_recv, _send), Tag::_reduce, data_accessor,
	tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::synchronizeOnceImpl(
	DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) const {
	communicateOnce(std::make_tuple(_send, _recv), Tag::_synchronize,
	data_accessor, tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::asynchronousSynchronizeImpl(
	const DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	if (not this->communications.hasCommunicationSize(tag)) {
	this->computeBufferSize(data_accessor, tag);
	}

	this->communications.incrementCounter(tag);

	// Posting the receive -------------------------------------------------------
	if (this->communications.hasPendingRecv(tag)) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::CommunicationException(),
	"There must still be some pending receive communications."
	<< " Tag is " << tag << " Cannot start new ones");
	}

	for (auto && comm_desc : this->communications.iterateRecv(tag)) {
	comm_desc.postRecv(this->hash_id);
	}

	// Posting the sends -------------------------------------------------------
	if (communications.hasPendingSend(tag)) {
	AKANTU_CUSTOM_EXCEPTION_INFO(
	debug::CommunicationException(),
	"There must be some pending sending communications."
	<< " Tag is " << tag);
	}

	for (auto && comm_desc : this->communications.iterateSend(tag)) {
	comm_desc.resetBuffer();

	#ifndef AKANTU_NDEBUG
	this->packSanityCheckData(comm_desc);
	#endif

	comm_desc.packData(data_accessor);
	comm_desc.postSend(this->hash_id);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::waitEndSynchronizeImpl(
	DataAccessor<Entity> & data_accessor, const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	#ifndef AKANTU_NDEBUG
	if (this->communications.begin(tag, _recv) !=
	this->communications.end(tag, _recv) &&
	!this->communications.hasPendingRecv(tag)) {
	AKANTU_CUSTOM_EXCEPTION_INFO(debug::CommunicationException(),
	"No pending communication with the tag \""
	<< tag);
	}
	#endif

	auto recv_end = this->communications.end(tag, _recv);
	decltype(recv_end) recv_it;

	while ((recv_it = this->communications.waitAnyRecv(tag)) != recv_end) {
	auto && comm_desc = *recv_it;
	#ifndef AKANTU_NDEBUG
	this->unpackSanityCheckData(comm_desc);
	#endif

	comm_desc.unpackData(data_accessor);
	comm_desc.resetBuffer();
	comm_desc.freeRequest();
	}

	this->communications.waitAllSend(tag);
	this->communications.freeSendRequests(tag);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::computeAllBufferSizes(
	const DataAccessor<Entity> & data_accessor) {
	for (auto && tag : this->communications.iterateTags()) {
	this->computeBufferSize(data_accessor, tag);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::computeBufferSizeImpl(
	const DataAccessor<Entity> & data_accessor,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	if (not this->communications.hasCommunication(tag)) {
	this->communications.initializeCommunications(tag);
	AKANTU_DEBUG_ASSERT(communications.hasCommunication(tag) == true,
	"Communications where not properly initialized");
	}

	for (auto sr : iterate_send_recv) {
	for (auto && pair : this->communications.iterateSchemes(sr)) {
	auto proc = pair.first;
	const auto & scheme = pair.second;
	UInt size = 0;
	#ifndef AKANTU_NDEBUG
	size += this->sanityCheckDataSize(scheme, tag);
	#endif
	size += data_accessor.getNbData(scheme, tag);
	AKANTU_DEBUG_INFO("I have "
	<< size << "(" << printMemorySize<char>(size) << " - "
	<< scheme.size() << " element(s)) data to "
	<< std::string(sr == _recv ? "receive from" : "send to")
	<< proc << " for tag " << tag);

	this->communications.setCommunicationSize(tag, proc, size, sr);
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename Entity> void SynchronizerImpl<Entity>::reset() {
	AKANTU_DEBUG_IN();
	communications.resetSchemes();
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename Entity>
	template <typename Pred>
	void SynchronizerImpl<Entity>::split(SynchronizerImpl<Entity> & in_synchronizer,
	Pred && pred) {
	AKANTU_DEBUG_IN();

	auto filter_list = [&](auto & list, auto & new_list) {
	auto copy = list;
	list.resize(0);
	new_list.resize(0);

	for (auto && entity : copy) {
	if (std::forward<Pred>(pred)(entity)) {
	new_list.push_back(entity);
	} else {
	list.push_back(entity);
	}
	}
	};

	for (auto sr : iterate_send_recv) {
	for (auto & scheme_pair :
	in_synchronizer.communications.iterateSchemes(sr)) {
	auto proc = scheme_pair.first;
	auto & scheme = scheme_pair.second;
	auto & new_scheme = communications.createScheme(proc, sr);
	filter_list(scheme, new_scheme);
	}
	}

	in_synchronizer.communications.invalidateSizes();
	communications.invalidateSizes();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <typename Entity>
	template <typename Updater>
	void SynchronizerImpl<Entity>::updateSchemes(Updater && scheme_updater) {
	for (auto sr : iterate_send_recv) {
	for (auto & scheme_pair : communications.iterateSchemes(sr)) {
	auto proc = scheme_pair.first;
	auto & scheme = scheme_pair.second;
	std::forward<Updater>(scheme_updater)(scheme, proc, sr);
	}
	}

	communications.invalidateSizes();
	}

	/* -------------------------------------------------------------------------- */
	template <typename Entity>
	template <typename Pred>
	void SynchronizerImpl<Entity>::filterScheme(Pred && pred) {
	std::vector<CommunicationRequest> requests;
	std::unordered_map<UInt, Array<UInt>> keep_entities;

	auto filter_list = [](const auto & keep, auto & list) {
	Array<Entity> new_list;
	for (const auto & keep_entity : keep) {
	const Entity & entity = list(keep_entity);
	new_list.push_back(entity);
	}
	list.copy(new_list);
	};

	// loop over send_schemes
	for (auto & scheme_pair : communications.iterateSchemes(_recv)) {
	auto proc = scheme_pair.first;
	auto & scheme = scheme_pair.second;

	auto & keep_entity = keep_entities[proc];
	for (auto && entity : enumerate(scheme)) {
	if (pred(std::get<1>(entity))) {
	keep_entity.push_back(std::get<0>(entity));
	}
	}

	auto tag = Tag::genTag(this->rank, 0, Tag::_modify_scheme);
	AKANTU_DEBUG_INFO("I have " << keep_entity.size()
	<< " elements to still receive from processor "
	<< proc << " (communication tag : " << tag
	<< ")");

	filter_list(keep_entity, scheme);
	requests.push_back(communicator.asyncSend(keep_entity, proc, tag));
	}

	// clean the receive scheme
	for (auto & scheme_pair : communications.iterateSchemes(_send)) {
	auto proc = scheme_pair.first;
	auto & scheme = scheme_pair.second;

	auto tag = Tag::genTag(proc, 0, Tag::_modify_scheme);
	AKANTU_DEBUG_INFO("Waiting list of elements to keep from processor "
	<< proc << " (communication tag : " << tag << ")");

	CommunicationStatus status;
	communicator.probe<UInt>(proc, tag, status);

	Array<UInt> keep_entity(status.size(), 1, "keep_element");
	AKANTU_DEBUG_INFO("I have "
	<< keep_entity.size()
	<< " elements to keep in my send list to processor "
	<< proc << " (communication tag : " << tag << ")");

	communicator.receive(keep_entity, proc, tag);

	filter_list(keep_entity, scheme);
	}

	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);
	communications.invalidateSizes();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> void SynchronizerImpl<Entity>::swapSendRecv() {
	communications.swapSendRecv();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::copySchemes(const SynchronizerImpl & other) {
	reset();

	for (auto sr : iterate_send_recv) {
	for (auto & scheme_pair : other.communications.iterateSchemes(sr)) {
	auto proc = scheme_pair.first;
	auto & other_scheme = scheme_pair.second;
	auto & scheme = communications.createScheme(proc, sr);
	scheme.copy(other_scheme);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	SynchronizerImpl<Entity> &
	SynchronizerImpl<Entity>::operator=(const SynchronizerImpl & other) {
	copySchemes(other);
	return *this;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	UInt SynchronizerImpl<Entity>::sanityCheckDataSize(
	const Array<Entity> & /unused/, const SynchronizationTag & /unused/,
	bool is_comm_desc) const {
	if (not is_comm_desc) {
	return 0;
	}

	UInt size = 0;
	size += sizeof(SynchronizationTag); // tag
	size += sizeof(UInt); // comm_desc.getNbData();
	size += sizeof(UInt); // comm_desc.getProc();
	size += sizeof(this->rank); // mesh.getCommunicator().whoAmI();

	return size;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::packSanityCheckData(
	CommunicationDescriptor<Entity> & comm_desc) const {
	auto & buffer = comm_desc.getBuffer();
	buffer << comm_desc.getTag();
	buffer << comm_desc.getNbData();
	buffer << comm_desc.getProc();
	buffer << this->rank;

	const auto & tag = comm_desc.getTag();
	const auto & send_element = comm_desc.getScheme();

	this->packSanityCheckData(buffer, send_element, tag);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::unpackSanityCheckData(
	CommunicationDescriptor<Entity> & comm_desc) const {
	auto & buffer = comm_desc.getBuffer();
	const auto & tag = comm_desc.getTag();

	auto nb_data = comm_desc.getNbData();
	auto proc = comm_desc.getProc();
	auto rank = this->rank;

	decltype(nb_data) recv_nb_data;
	decltype(proc) recv_proc;
	decltype(rank) recv_rank;

	SynchronizationTag t;
	buffer >> t;
	buffer >> recv_nb_data;
	buffer >> recv_proc;
	buffer >> recv_rank;

	AKANTU_DEBUG_ASSERT(
	t == tag, "The tag received does not correspond to the tag expected");

	AKANTU_DEBUG_ASSERT(
	nb_data == recv_nb_data,
	"The nb_data received does not correspond to the nb_data expected");

	AKANTU_DEBUG_ASSERT(UInt(recv_rank) == proc,
	"The rank received does not correspond to the proc");

	AKANTU_DEBUG_ASSERT(recv_proc == UInt(rank),
	"The proc received does not correspond to the rank");

	auto & recv_element = comm_desc.getScheme();
	this->unpackSanityCheckData(buffer, recv_element, tag, proc, rank);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity> bool SynchronizerImpl<Entity>::hasChanged() {
	communicator.allReduce(entities_changed, SynchronizerOperation::_lor);
	return entities_changed;
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	void SynchronizerImpl<Entity>::initScatterGatherCommunicationScheme() {
	if (this->nb_proc == 1) {
	entities_changed = false;
	AKANTU_DEBUG_OUT();
	return;
	}

	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <>
	inline void SynchronizerImpl<UInt>::initScatterGatherCommunicationScheme() {
	AKANTU_DEBUG_IN();

	if (this->nb_proc == 1) {
	entities_changed = false;
	AKANTU_DEBUG_OUT();
	return;
	}

	this->entities_from_root.clear();
	this->master_receive_entities.clear();

	Array<UInt> entities_to_send;
	fillEntityToSend(entities_to_send);

	std::vector<CommunicationRequest> requests;

	if (this->rank == UInt(this->root)) {
	master_receive_entities[this->root].copy(entities_to_send);

	Array<UInt> nb_entities_per_proc(this->nb_proc);
	communicator.gather(entities_to_send.size(), nb_entities_per_proc);

	for (UInt p = 0; p < nb_proc; ++p) {
	if (p == UInt(this->root)) {
	continue;
	}

	auto & receive_per_proc = master_receive_entities[p];
	receive_per_proc.resize(nb_entities_per_proc(p));
	if (nb_entities_per_proc(p) == 0) {
	continue;
	}

	requests.push_back(communicator.asyncReceive(
	receive_per_proc, p,
	Tag::genTag(p, 0, Tag::_gather_initialization, this->hash_id)));
	}
	} else {
	communicator.gather(entities_to_send.size(), this->root);
	AKANTU_DEBUG(dblDebug, "I have " << entities_to_send.size()
	<< " entities to send to master proc");

	if (not entities_to_send.empty()) {
	requests.push_back(communicator.asyncSend(
	entities_to_send, this->root,
	Tag::genTag(this->rank, 0, Tag::_gather_initialization,
	this->hash_id)));
	}
	}

	entities_changed = false;
	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <typename T>
	void SynchronizerImpl<Entity>::gather(const Array<T> & to_gather,
	Array<T> & gathered) {
	if (this->hasChanged()) {
	initScatterGatherCommunicationScheme();
	}

	AKANTU_DEBUG_ASSERT(this->rank == UInt(this->root),
	"This function cannot be called on a slave processor");
	AKANTU_DEBUG_ASSERT(to_gather.size() == this->canScatterSize(),
	"The array to gather does not have the correct size");
	AKANTU_DEBUG_ASSERT(gathered.size() == this->gatheredSize(),
	"The gathered array does not have the correct size");

	if (this->nb_proc == 1) {
	gathered.copy(to_gather, true);

	AKANTU_DEBUG_OUT();
	return;
	}

	std::map<UInt, CommunicationBuffer> buffers;
	std::vector<CommunicationRequest> requests;
	for (UInt p = 0; p < this->nb_proc; ++p) {
	if (p == UInt(this->root)) {
	continue;
	}

	auto receive_it = this->master_receive_entities.find(p);
	AKANTU_DEBUG_ASSERT(receive_it != this->master_receive_entities.end(),
	"Could not find the receive list for dofs of proc "
	<< p);
	const auto & receive_entities = receive_it->second;
	if (receive_entities.empty()) {
	continue;
	}

	CommunicationBuffer & buffer = buffers[p];

	buffer.resize(receive_entities.size() * to_gather.getNbComponent() *
	sizeof(T));

	AKANTU_DEBUG_INFO(
	"Preparing to receive data for "
	<< receive_entities.size() << " entities from processor " << p << " "
	<< Tag::genTag(p, this->root, Tag::_gather, this->hash_id));

	requests.push_back(communicator.asyncReceive(
	buffer, p, Tag::genTag(p, this->root, Tag::_gather, this->hash_id)));
	}

	auto data_gathered_it = gathered.begin(to_gather.getNbComponent());

	{ // copy master data
	auto data_to_gather_it = to_gather.begin(to_gather.getNbComponent());
	for (auto local_entity : entities_from_root) {
	UInt global_entity = localToGlobalEntity(local_entity);

	Vector<T> entity_data_gathered = data_gathered_it[global_entity];
	Vector<T> entity_data_to_gather = data_to_gather_it[local_entity];
	entity_data_gathered = entity_data_to_gather;
	}
	}

	auto rr = UInt(-1);
	while ((rr = Communicator::waitAny(requests)) != UInt(-1)) {
	auto & request = requests[rr];
	auto sender = request.getSource();

	AKANTU_DEBUG_ASSERT(this->master_receive_entities.find(sender) !=
	this->master_receive_entities.end() &&
	buffers.find(sender) != buffers.end(),
	"Missing infos concerning proc " << sender);

	const auto & receive_entities =
	this->master_receive_entities.find(sender)->second;
	auto & buffer = buffers[sender];

	for (auto global_entity : receive_entities) {
	Vector<T> entity_data = data_gathered_it[global_entity];
	buffer >> entity_data;
	}

	requests.erase(requests.begin() + rr);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <typename T>
	void SynchronizerImpl<Entity>::gather(const Array<T> & to_gather) {
	AKANTU_DEBUG_IN();

	if (this->hasChanged()) {
	initScatterGatherCommunicationScheme();
	}

	AKANTU_DEBUG_ASSERT(this->rank != UInt(this->root),
	"This function cannot be called on the root processor");
	AKANTU_DEBUG_ASSERT(to_gather.size() == this->canScatterSize(),
	"The array to gather does not have the correct size");

	if (this->entities_from_root.empty()) {
	AKANTU_DEBUG_OUT();
	return;
	}
	CommunicationBuffer buffer(this->entities_from_root.size() *
	to_gather.getNbComponent() * sizeof(T));

	auto data_it = to_gather.begin(to_gather.getNbComponent());
	for (auto entity : this->entities_from_root) {
	Vector<T> data = data_it[entity];
	buffer << data;
	}

	AKANTU_DEBUG_INFO("Gathering data for "
	<< to_gather.size() << " dofs on processor " << this->root
	<< " "
	<< Tag::genTag(this->rank, 0, Tag::_gather, this->hash_id));

	communicator.send(buffer, this->root,
	Tag::genTag(this->rank, 0, Tag::_gather, this->hash_id));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <typename T>
	void SynchronizerImpl<Entity>::scatter(Array<T> & scattered,
	const Array<T> & to_scatter) {
	AKANTU_DEBUG_IN();

	if (this->hasChanged()) {
	initScatterGatherCommunicationScheme();
	}

	AKANTU_DEBUG_ASSERT(this->rank == UInt(this->root),
	"This function cannot be called on a slave processor");
	AKANTU_DEBUG_ASSERT(scattered.size() == this->canScatterSize(),
	"The scattered array does not have the correct size");
	AKANTU_DEBUG_ASSERT(to_scatter.size() == this->gatheredSize(),
	"The array to scatter does not have the correct size");

	if (this->nb_proc == 1) {
	scattered.copy(to_scatter, true);
	AKANTU_DEBUG_OUT();
	return;
	}

	std::map<UInt, CommunicationBuffer> buffers;
	std::vector<CommunicationRequest> requests;

	for (UInt p = 0; p < nb_proc; ++p) {
	auto data_to_scatter_it = to_scatter.begin(to_scatter.getNbComponent());

	if (p == this->rank) {
	auto data_scattered_it = scattered.begin(to_scatter.getNbComponent());

	// copy the data for the local processor
	for (auto local_entity : entities_from_root) {
	auto global_entity = localToGlobalEntity(local_entity);

	Vector<T> entity_data_to_scatter = data_to_scatter_it[global_entity];
	Vector<T> entity_data_scattered = data_scattered_it[local_entity];
	entity_data_scattered = entity_data_to_scatter;
	}

	continue;
	}

	const auto & receive_entities =
	this->master_receive_entities.find(p)->second;

	// prepare the send buffer
	CommunicationBuffer & buffer = buffers[p];
	buffer.resize(receive_entities.size() * scattered.getNbComponent() *
	sizeof(T));

	// pack the data
	for (auto global_entity : receive_entities) {
	Vector<T> entity_data_to_scatter = data_to_scatter_it[global_entity];
	buffer << entity_data_to_scatter;
	}

	// send the data
	requests.push_back(communicator.asyncSend(
	buffer, p, Tag::genTag(p, 0, Tag::_scatter, this->hash_id)));
	}

	// wait a clean communications
	Communicator::waitAll(requests);
	Communicator::freeCommunicationRequest(requests);

	// synchronize slave and ghost nodes
	synchronizeArray(scattered);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <typename T>
	void SynchronizerImpl<Entity>::scatter(Array<T> & scattered) {
	AKANTU_DEBUG_IN();

	if (this->hasChanged()) {
	this->initScatterGatherCommunicationScheme();
	}

	AKANTU_DEBUG_ASSERT(this->rank != UInt(this->root),
	"This function cannot be called on the root processor");
	AKANTU_DEBUG_ASSERT(scattered.size() == this->canScatterSize(),
	"The scattered array does not have the correct size");

	// prepare the data
	auto data_scattered_it = scattered.begin(scattered.getNbComponent());
	CommunicationBuffer buffer(this->entities_from_root.size() *
	scattered.getNbComponent() * sizeof(T));

	// receive the data
	communicator.receive(
	buffer, this->root,
	Tag::genTag(this->rank, 0, Tag::_scatter, this->hash_id));

	// unpack the data
	for (auto local_entity : entities_from_root) {
	Vector<T> data_scattered(data_scattered_it[local_entity]);
	buffer >> data_scattered;
	}

	// synchronize the ghosts
	synchronizeArray(scattered);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <typename T>
	void SynchronizerImpl<Entity>::synchronizeArray(Array<T> & array) const {
	static_assert(std::is_same<Entity, UInt>::value,
	"Not implemented for other type than UInt");
	SimpleUIntDataAccessor<T> data_accessor(array, SynchronizationTag::_whatever);
	this->synchronizeOnce(data_accessor, SynchronizationTag::_whatever);
	}

	/* -------------------------------------------------------------------------- */
	template <class Entity>
	template <template <class> class Op, typename T>
	void SynchronizerImpl<Entity>::reduceSynchronizeArray(Array<T> & array) const {
	static_assert(std::is_same<Entity, UInt>::value,
	"Not implemented for other type than UInt");
	ReduceDataAccessor<UInt, Op, T> data_accessor(array,
	SynchronizationTag::_whatever);
	this->slaveReductionOnceImpl(data_accessor, SynchronizationTag::_whatever);
	this->synchronizeArray(array);
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/src/synchronizer/synchronizer_registry.cc b/src/synchronizer/synchronizer_registry.cc
	index d04579393..9ceacd539 100644
	--- a/src/synchronizer/synchronizer_registry.cc
	+++ b/src/synchronizer/synchronizer_registry.cc
	@@ -1,121 +1,121 @@
	/**
	* @file synchronizer_registry.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jun 16 2011
	* @date last modification: Wed Nov 15 2017
	*
	* @brief Registry of synchronizers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "synchronizer_registry.hh"
	#include "synchronizer.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	SynchronizerRegistry::SynchronizerRegistry() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SynchronizerRegistry::~SynchronizerRegistry() {
	AKANTU_DEBUG_IN();

	synchronizers.clear();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SynchronizerRegistry::registerDataAccessor(
	DataAccessorBase & data_accessor) {
	this->data_accessor = &data_accessor;
	}

	/* -------------------------------------------------------------------------- */
	void SynchronizerRegistry::synchronize(SynchronizationTag tag) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(data_accessor != nullptr, "No data accessor set.");

	std::pair<Tag2Sync::iterator, Tag2Sync::iterator> range =
	synchronizers.equal_range(tag);

	for (auto it = range.first; it != range.second; ++it) {
	it->second->synchronize(*data_accessor, tag);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SynchronizerRegistry::asynchronousSynchronize(SynchronizationTag tag) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(data_accessor != nullptr, "No data accessor set.");

	std::pair<Tag2Sync::iterator, Tag2Sync::iterator> range =
	synchronizers.equal_range(tag);

	for (auto it = range.first; it != range.second; ++it) {
	(it).second->asynchronousSynchronize(data_accessor, tag);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SynchronizerRegistry::waitEndSynchronize(SynchronizationTag tag) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(data_accessor != nullptr, "No data accessor set.");

	std::pair<Tag2Sync::iterator, Tag2Sync::iterator> range =
	synchronizers.equal_range(tag);

	for (auto it = range.first; it != range.second; ++it) {
	(it).second->waitEndSynchronize(data_accessor, tag);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SynchronizerRegistry::registerSynchronizer(Synchronizer & synchronizer,
	SynchronizationTag tag) {
	AKANTU_DEBUG_IN();

	synchronizers.insert(
	std::pair<SynchronizationTag, Synchronizer *>(tag, &synchronizer));

	AKANTU_DEBUG_OUT();
	}

	} // namespace akantu
	diff --git a/src/synchronizer/synchronizer_registry.hh b/src/synchronizer/synchronizer_registry.hh
	index f38030471..c93e3638f 100644
	--- a/src/synchronizer/synchronizer_registry.hh
	+++ b/src/synchronizer/synchronizer_registry.hh
	@@ -1,91 +1,91 @@
	/**
	* @file synchronizer_registry.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jun 18 2010
	* @date last modification: Wed Nov 15 2017
	*
	* @brief Registry of synchronizers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SYNCHRONIZER_REGISTRY_HH_
	#define AKANTU_SYNCHRONIZER_REGISTRY_HH_

	namespace akantu {
	class DataAccessorBase;
	class Synchronizer;
	} // namespace akantu

	namespace akantu {

	class SynchronizerRegistry {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	SynchronizerRegistry();
	virtual ~SynchronizerRegistry();

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	/// synchronize operation
	void synchronize(SynchronizationTag tag);

	/// asynchronous synchronization
	void asynchronousSynchronize(SynchronizationTag tag);

	/// wait end of asynchronous synchronization
	void waitEndSynchronize(SynchronizationTag tag);

	/// register a new synchronization
	void registerSynchronizer(Synchronizer & synchronizer,
	SynchronizationTag tag);

	/// Register a different data accessor.
	void registerDataAccessor(DataAccessorBase & data_accessor);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	using Tag2Sync = std::multimap<SynchronizationTag, Synchronizer *>;
	/// list of registered synchronization
	Tag2Sync synchronizers;

	/// data accessor that will permit to do the pack/unpack things
	DataAccessorBase * data_accessor{nullptr};
	};

	} // namespace akantu

	#endif /* AKANTU_SYNCHRONIZER_REGISTRY_HH_ */
	diff --git a/src/synchronizer/synchronizer_tmpl.hh b/src/synchronizer/synchronizer_tmpl.hh
	index 3311e7bb5..de3fa71ea 100644
	--- a/src/synchronizer/synchronizer_tmpl.hh
	+++ b/src/synchronizer/synchronizer_tmpl.hh
	@@ -1,138 +1,138 @@
	/**
	* @file synchronizer_tmpl.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Dec 02 2016
	* @date last modification: Mon Feb 26 2018
	*
	* @brief Implementation of the helper classes for the synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "data_accessor.hh"
	#include "synchronizer.hh"
	#include "synchronizer_impl.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_SYNCHRONIZER_TMPL_HH_
	#define AKANTU_SYNCHRONIZER_TMPL_HH_

	namespace akantu {

	template <class DataAccessorT>
	void Synchronizer::slaveReductionOnce(DataAccessorT & data_accessor,
	const SynchronizationTag & tag) const {
	if (const auto * synch_el =
	dynamic_cast<const SynchronizerImpl<Element> *>(this)) {
	synch_el->slaveReductionOnceImpl(
	dynamic_cast<DataAccessor<Element> &>(data_accessor), tag);
	} else if (const auto * synch_dof =
	dynamic_cast<const SynchronizerImpl<UInt> *>(this)) {
	synch_dof->slaveReductionOnceImpl(
	dynamic_cast<DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	template <class DataAccessorT>
	void Synchronizer::synchronizeOnce(DataAccessorT & data_accessor,
	const SynchronizationTag & tag) const {
	if (const auto * synch_el =
	dynamic_cast<const SynchronizerImpl<Element> *>(this)) {
	synch_el->synchronizeOnceImpl(
	dynamic_cast<DataAccessor<Element> &>(data_accessor), tag);
	} else if (const auto * synch_dof =
	dynamic_cast<const SynchronizerImpl<UInt> *>(this)) {
	synch_dof->synchronizeOnceImpl(
	dynamic_cast<DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	/// synchronize ghosts
	template <class DataAccessorT>
	void Synchronizer::synchronize(DataAccessorT & data_accessor,
	const SynchronizationTag & tag) {
	if (auto * synch_el = dynamic_cast<SynchronizerImpl<Element> *>(this)) {
	synch_el->synchronizeImpl(
	dynamic_cast<DataAccessor<Element> &>(data_accessor), tag);
	} else if (auto * synch_dof = dynamic_cast<SynchronizerImpl<UInt> *>(this)) {
	synch_dof->synchronizeImpl(
	dynamic_cast<DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class DataAccessorT>
	void Synchronizer::asynchronousSynchronize(const DataAccessorT & data_accessor,
	const SynchronizationTag & tag) {
	if (auto * synch_el = dynamic_cast<SynchronizerImpl<Element> *>(this)) {
	synch_el->asynchronousSynchronizeImpl(
	dynamic_cast<const DataAccessor<Element> &>(data_accessor), tag);
	} else if (auto * synch_dof = dynamic_cast<SynchronizerImpl<UInt> *>(this)) {
	synch_dof->asynchronousSynchronizeImpl(
	dynamic_cast<const DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	/* -------------------------------------------------------------------------- */
	template <class DataAccessorT>
	void Synchronizer::waitEndSynchronize(DataAccessorT & data_accessor,
	const SynchronizationTag & tag) {
	if (auto * synch_el = dynamic_cast<SynchronizerImpl<Element> *>(this)) {
	synch_el->waitEndSynchronizeImpl(
	dynamic_cast<DataAccessor<Element> &>(data_accessor), tag);
	} else if (auto * synch_dof = dynamic_cast<SynchronizerImpl<UInt> *>(this)) {
	synch_dof->waitEndSynchronizeImpl(
	dynamic_cast<DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	/// compute buffer size for a given tag and data accessor
	template <class DataAccessorT>
	void Synchronizer::computeBufferSize(const DataAccessorT & data_accessor,
	const SynchronizationTag & tag) {
	if (auto * synch_el = dynamic_cast<SynchronizerImpl<Element> *>(this)) {
	synch_el->computeBufferSizeImpl(
	dynamic_cast<const DataAccessor<Element> &>(data_accessor), tag);
	} else if (auto * synch_dof = dynamic_cast<SynchronizerImpl<UInt> *>(this)) {
	synch_dof->computeBufferSizeImpl(
	dynamic_cast<const DataAccessor<UInt> &>(data_accessor), tag);
	} else {
	AKANTU_EXCEPTION("You synchronizer is not of a known type");
	}
	}

	} // namespace akantu

	#endif /* AKANTU_SYNCHRONIZER_TMPL_HH_ */
	diff --git a/test/ci/debian:testing/Dockerfile b/test/ci/debian:testing/Dockerfile
	index 53faf4015..13e3e7116 100644
	--- a/test/ci/debian:testing/Dockerfile
	+++ b/test/ci/debian:testing/Dockerfile
	@@ -1,35 +1,37 @@
	FROM debian:testing
	MAINTAINER Nicolas Richart <nicolas.richart@epfl.ch>

	# library dependencies
	RUN apt-get -qq update && apt-get -qq -y install \
	g++ gfortran clang cmake \
	openmpi-bin libmumps-dev libscotch-dev \
	libboost-dev libopenblas-dev \
	python3 python3-dev python3-numpy python3-scipy python3-mpi4py \
	&& rm -rf /var/lib/apt/lists/*

	# for documentation
	RUN apt-get -qq update && apt-get -qq -y install \
	python3-sphinx \
	python3-sphinxcontrib.bibtex \
	python3-sphinx-rtd-theme \
	python3-breathe \
	python3-git python3-jinja2 \
	doxygen graphviz \
	&& rm -rf /var/lib/apt/lists/*

	# for ci
	RUN apt-get -qq update && apt-get -qq -y install \
	- gmsh python3-pytest \
	- ccache clang-format python3-flake8 clang-tidy \
	+ gmsh python3-pytest python3-click python3-termcolor \
	+ ccache clang-format python3-flake8 python3-pip clang-tidy \
	curl git xsltproc jq \
	gcovr llvm binutils \
	&& rm -rf /var/lib/apt/lists/*

	+RUN pip3 install warning_parser
	+
	COPY .openmpi /root/.openmpi

	# for debug
	RUN apt-get -qq update && apt-get -qq -y install \
	gdb valgrind \
	&& rm -rf /var/lib/apt/lists/*
	diff --git a/test/ci/includes_for_ci/aka_config.hh b/test/ci/includes_for_ci/aka_config.hh
	index 3b02f7015..a734453da 100644
	--- a/test/ci/includes_for_ci/aka_config.hh
	+++ b/test/ci/includes_for_ci/aka_config.hh
	@@ -1,100 +1,99 @@
	/**
	* @file aka_config.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Feb 08 2021
	* @date last modification: Mon Feb 08 2021
	*
	* @brief Compilation time configuration of Akantu
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_AKA_CONFIG_HH_
	#define AKANTU_AKA_CONFIG_HH_

	#define AKANTU_VERSION_MAJOR 4
	#define AKANTU_VERSION_MINOR 0
	#define AKANTU_VERSION_PATCH 0
	-#define AKANTU_VERSION (AKANTU_VERSION_MAJOR * 10000 \
	- + AKANTU_VERSION_MINOR * 100 \
	- + AKANTU_VERSION_PATCH)
	-
	+#define AKANTU_VERSION \
	+ (AKANTU_VERSION_MAJOR * 10000 + AKANTU_VERSION_MINOR * 100 + \
	+ AKANTU_VERSION_PATCH)

	namespace akantu {
	using Real = double;
	using Int = int;
	using UInt = unsigned int;
	-} // akantu
	+} // namespace akantu

	#define AKANTU_INTEGER_SIZE 4
	#define AKANTU_FLOAT_SIZE 8

	/* #undef AKANTU_HAS_STRDUP */

	/* #undef AKANTU_USE_BLAS */
	#define AKANTU_USE_LAPACK

	#define AKANTU_PARALLEL
	#define AKANTU_USE_MPI

	#define AKANTU_USE_SCOTCH
	/* #undef AKANTU_USE_PTSCOTCH */
	/* #undef AKANTU_SCOTCH_NO_EXTERN */

	#define AKANTU_IMPLICIT
	#define AKANTU_USE_MUMPS
	/* #undef AKANTU_USE_PETSC */

	#define AKANTU_USE_IOHELPER
	/* #undef AKANTU_USE_QVIEW */
	/* #undef AKANTU_USE_BLACKDYNAMITE */

	#define AKANTU_USE_PYBIND11

	/* #undef AKANTU_USE_OBSOLETE_GETTIMEOFDAY */

	/* #undef AKANTU_EXTRA_MATERIALS */
	/* #undef AKANTU_STUDENTS_EXTRA_PACKAGE */
	#define AKANTU_DAMAGE_NON_LOCAL

	#define AKANTU_SOLID_MECHANICS
	#define AKANTU_STRUCTURAL_MECHANICS
	#define AKANTU_HEAT_TRANSFER
	#define AKANTU_PYTHON_INTERFACE

	#define AKANTU_COHESIVE_ELEMENT
	/* #undef AKANTU_PARALLEL_COHESIVE_ELEMENT */

	/* #undef AKANTU_IGFEM */

	/* #undef AKANTU_USE_CGAL */
	/* #undef AKANTU_EMBEDDED */

	// Debug tools
	/* #undef AKANTU_NDEBUG */
	/* #undef AKANTU_DEBUG_TOOLS */
	-#define READLINK_COMMAND /bin/readlink
	-#define ADDR2LINE_COMMAND /usr/bin/addr2line
	+#define READLINK_COMMAND / bin / readlink
	+#define ADDR2LINE_COMMAND / usr / bin / addr2line

	#endif /* AKANTU_AKA_CONFIG_HH_ */
	diff --git a/test/ci/includes_for_ci/aka_element_classes_info.hh b/test/ci/includes_for_ci/aka_element_classes_info.hh
	index c00436f70..1b59dc9bc 100644
	--- a/test/ci/includes_for_ci/aka_element_classes_info.hh
	+++ b/test/ci/includes_for_ci/aka_element_classes_info.hh
	@@ -1,376 +1,316 @@
	/**
	* @file aka_element_classes_info.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jul 19 2015
	* @date last modification: Mon Feb 08 2021
	*
	* @brief Declaration of the enums for the element classes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_safe_enum.hh"
	/* -------------------------------------------------------------------------- */
	#include <boost/preprocessor.hpp>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_AKA_ELEMENT_CLASSES_INFO_HH_
	#define AKANTU_AKA_ELEMENT_CLASSES_INFO_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	/* Element Types */
	/* -------------------------------------------------------------------------- */

	/// @enum ElementType type of elements
	enum ElementType {
	_not_defined,
	_cohesive_1d_2,
	_cohesive_2d_4,
	_cohesive_2d_6,
	_cohesive_3d_12,
	_cohesive_3d_16,
	_cohesive_3d_6,
	_cohesive_3d_8,
	_point_1,
	_segment_2,
	_segment_3,
	_triangle_3,
	_triangle_6,
	_quadrangle_4,
	_quadrangle_8,
	_tetrahedron_4,
	_tetrahedron_10,
	_pentahedron_6,
	_pentahedron_15,
	_hexahedron_8,
	_hexahedron_20,
	_bernoulli_beam_2,
	_bernoulli_beam_3,
	_discrete_kirchhoff_triangle_18,
	_max_element_type
	};

	+#define AKANTU_ek_cohesive_ELEMENT_TYPE \
	+ (_cohesive_1d_2)(_cohesive_2d_4)(_cohesive_2d_6)(_cohesive_3d_12)( \
	+ _cohesive_3d_16)(_cohesive_3d_6)(_cohesive_3d_8)
	+
	+#define AKANTU_ek_regular_ELEMENT_TYPE \
	+ (_point_1)(_segment_2)(_segment_3)(_triangle_3)(_triangle_6)(_quadrangle_4)( \
	+ _quadrangle_8)(_tetrahedron_4)(_tetrahedron_10)(_pentahedron_6)( \
	+ _pentahedron_15)(_hexahedron_8)(_hexahedron_20)

	-#define AKANTU_ek_cohesive_ELEMENT_TYPE \
	- (_cohesive_1d_2) \
	- (_cohesive_2d_4) \
	- (_cohesive_2d_6) \
	- (_cohesive_3d_12) \
	- (_cohesive_3d_16) \
	- (_cohesive_3d_6) \
	- (_cohesive_3d_8)
	-
	-#define AKANTU_ek_regular_ELEMENT_TYPE \
	- (_point_1) \
	- (_segment_2) \
	- (_segment_3) \
	- (_triangle_3) \
	- (_triangle_6) \
	- (_quadrangle_4) \
	- (_quadrangle_8) \
	- (_tetrahedron_4) \
	- (_tetrahedron_10) \
	- (_pentahedron_6) \
	- (_pentahedron_15) \
	- (_hexahedron_8) \
	- (_hexahedron_20)
	-
	-#define AKANTU_ek_structural_ELEMENT_TYPE \
	- (_bernoulli_beam_2) \
	- (_bernoulli_beam_3) \
	- (_discrete_kirchhoff_triangle_18)
	-
	-
	-#define AKANTU_ALL_ELEMENT_TYPE \
	- AKANTU_ek_cohesive_ELEMENT_TYPE \
	- AKANTU_ek_regular_ELEMENT_TYPE \
	- AKANTU_ek_structural_ELEMENT_TYPE
	+#define AKANTU_ek_structural_ELEMENT_TYPE \
	+ (_bernoulli_beam_2)(_bernoulli_beam_3)(_discrete_kirchhoff_triangle_18)
	+
	+#define AKANTU_ALL_ELEMENT_TYPE \
	+ AKANTU_ek_cohesive_ELEMENT_TYPE AKANTU_ek_regular_ELEMENT_TYPE \
	+ AKANTU_ek_structural_ELEMENT_TYPE

	/* -------------------------------------------------------------------------- */
	/* Element Kinds */
	/* -------------------------------------------------------------------------- */

	-#define AKANTU_COHESIVE_KIND (_ek_cohesive)
	-#define AKANTU_REGULAR_KIND (_ek_regular)
	-#define AKANTU_STRUCTURAL_KIND (_ek_structural)
	+#define AKANTU_COHESIVE_KIND (_ek_cohesive)
	+#define AKANTU_REGULAR_KIND (_ek_regular)
	+#define AKANTU_STRUCTURAL_KIND (_ek_structural)

	-#define AKANTU_ELEMENT_KIND \
	- AKANTU_COHESIVE_KIND \
	- AKANTU_REGULAR_KIND \
	+#define AKANTU_ELEMENT_KIND \
	+ AKANTU_COHESIVE_KIND \
	+ AKANTU_REGULAR_KIND \
	AKANTU_STRUCTURAL_KIND

	-enum ElementKind {
	- BOOST_PP_SEQ_ENUM(AKANTU_ELEMENT_KIND),
	- _ek_not_defined
	-};
	-
	+enum ElementKind { BOOST_PP_SEQ_ENUM(AKANTU_ELEMENT_KIND), _ek_not_defined };

	/* -------------------------------------------------------------------------- */
	struct ElementKind_def {
	using type = ElementKind;
	static const type _begin_ = BOOST_PP_SEQ_HEAD(AKANTU_ELEMENT_KIND);
	- static const type _end_ = _ek_not_defined;
	+ static const type _end_ = _ek_not_defined;
	};

	-using element_kind_t = safe_enum<ElementKind_def> ;
	+using element_kind_t = safe_enum<ElementKind_def>;

	/* -------------------------------------------------------------------------- */
	/// @enum GeometricalType type of element potentially contained in a Mesh
	enum GeometricalType {
	_gt_cohesive_1d_2,
	_gt_cohesive_2d_4,
	_gt_cohesive_2d_6,
	_gt_cohesive_3d_12,
	_gt_cohesive_3d_16,
	_gt_cohesive_3d_6,
	_gt_cohesive_3d_8,
	_gt_point,
	_gt_segment_2,
	_gt_segment_3,
	_gt_triangle_3,
	_gt_triangle_6,
	_gt_quadrangle_4,
	_gt_quadrangle_8,
	_gt_tetrahedron_4,
	_gt_tetrahedron_10,
	_gt_hexahedron_8,
	_gt_hexahedron_20,
	_gt_pentahedron_6,
	_gt_pentahedron_15,
	_gt_not_defined
	};

	/* -------------------------------------------------------------------------- */
	/* Interpolation Types */
	/* -------------------------------------------------------------------------- */
	-#define AKANTU_INTERPOLATION_TYPES \
	- (_itp_lagrange_point_1) \
	- (_itp_lagrange_segment_2) \
	- (_itp_lagrange_segment_3) \
	- (_itp_lagrange_triangle_3) \
	- (_itp_lagrange_triangle_6) \
	- (_itp_lagrange_quadrangle_4) \
	- (_itp_serendip_quadrangle_8) \
	- (_itp_lagrange_tetrahedron_4) \
	- (_itp_lagrange_tetrahedron_10) \
	- (_itp_lagrange_hexahedron_8) \
	- (_itp_serendip_hexahedron_20) \
	- (_itp_lagrange_pentahedron_6) \
	- (_itp_lagrange_pentahedron_15)\
	- (_itp_hermite_2) \
	- (_itp_bernoulli_beam_2) \
	- (_itp_bernoulli_beam_3) \
	- (_itp_discrete_kirchhoff_triangle_6) \
	- (_itp_discrete_kirchhoff_triangle_18)
	+#define AKANTU_INTERPOLATION_TYPES \
	+ (_itp_lagrange_point_1)(_itp_lagrange_segment_2)(_itp_lagrange_segment_3)( \
	+ _itp_lagrange_triangle_3)(_itp_lagrange_triangle_6)( \
	+ _itp_lagrange_quadrangle_4)(_itp_serendip_quadrangle_8)( \
	+ _itp_lagrange_tetrahedron_4)(_itp_lagrange_tetrahedron_10)( \
	+ _itp_lagrange_hexahedron_8)(_itp_serendip_hexahedron_20)( \
	+ _itp_lagrange_pentahedron_6)(_itp_lagrange_pentahedron_15)( \
	+ _itp_hermite_2)(_itp_bernoulli_beam_2)(_itp_bernoulli_beam_3)( \
	+ _itp_discrete_kirchhoff_triangle_6)(_itp_discrete_kirchhoff_triangle_18)

	/// @enum InterpolationType type of elements
	enum InterpolationType {
	BOOST_PP_SEQ_ENUM(AKANTU_INTERPOLATION_TYPES),
	_itp_not_defined
	};

	/* -------------------------------------------------------------------------- */
	/* Some sub types less probable to change */
	/* -------------------------------------------------------------------------- */
	/// @enum GeometricalShapeType types of shapes to define the contains
	/// function in the element classes
	enum GeometricalShapeType {
	_gst_point,
	_gst_triangle,
	_gst_square,
	_gst_prism,
	_gst_not_defined
	};

	/* -------------------------------------------------------------------------- */
	/// @enum GaussIntegrationType classes of types using common
	/// description of the gauss point position and weights
	enum GaussIntegrationType {
	_git_point,
	_git_segment,
	_git_triangle,
	_git_tetrahedron,
	_git_pentahedron,
	_git_not_defined
	};

	/* -------------------------------------------------------------------------- */
	/// @enum InterpolationKind the family of interpolation types
	-enum InterpolationKind {
	- _itk_lagrangian,
	- _itk_structural,
	- _itk_not_defined
	-};
	+enum InterpolationKind { _itk_lagrangian, _itk_structural, _itk_not_defined };

	/* -------------------------------------------------------------------------- */
	// BOOST PART: TOUCH ONLY IF YOU KNOW WHAT YOU ARE DOING
	#define AKANTU_BOOST_CASE_MACRO(r, macro, _type) \
	case _type: { \
	macro(_type); \
	break; \
	}

	#define AKANTU_BOOST_LIST_SWITCH(macro1, list1, var) \
	do { \
	switch (var) { \
	BOOST_PP_SEQ_FOR_EACH(AKANTU_BOOST_CASE_MACRO, macro1, list1) \
	default: { \
	AKANTU_ERROR("Type (" \
	<< var /* NOLINT */ << ") not handled by this function"); \
	} \
	} \
	} while (0)

	#define AKANTU_BOOST_LIST_SWITCH_NO_DEFAULT(macro1, list1, var) \
	do { \
	switch (var) { \
	BOOST_PP_SEQ_FOR_EACH(AKANTU_BOOST_CASE_MACRO, macro1, list1) \
	case _not_defined: /* FALLTHRU */ \
	case _max_element_type: \
	break; \
	} \
	} while (0)

	#define AKANTU_BOOST_ELEMENT_SWITCH(macro1, list1) \
	AKANTU_BOOST_LIST_SWITCH(macro1, list1, type)

	#define AKANTU_BOOST_ELEMENT_SWITCH_NO_DEFAULT(macro1, list1) \
	AKANTU_BOOST_LIST_SWITCH_NO_DEFAULT(macro1, list1, type)

	#define AKANTU_BOOST_ALL_ELEMENT_SWITCH(macro) \
	AKANTU_BOOST_ELEMENT_SWITCH(macro, AKANTU_ALL_ELEMENT_TYPE)

	#define AKANTU_BOOST_ALL_ELEMENT_SWITCH_NO_DEFAULT(macro) \
	AKANTU_BOOST_ELEMENT_SWITCH_NO_DEFAULT(macro, AKANTU_ALL_ELEMENT_TYPE)

	#define AKANTU_BOOST_LIST_MACRO(r, macro, type) macro(type)

	#define AKANTU_BOOST_APPLY_ON_LIST(macro, list) \
	BOOST_PP_SEQ_FOR_EACH(AKANTU_BOOST_LIST_MACRO, macro, list)

	#define AKANTU_BOOST_ALL_ELEMENT_LIST(macro) \
	AKANTU_BOOST_APPLY_ON_LIST(macro, AKANTU_ALL_ELEMENT_TYPE)

	#define AKANTU_GET_ELEMENT_LIST(kind) AKANTU##kind##_ELEMENT_TYPE

	#define AKANTU_BOOST_KIND_ELEMENT_SWITCH(macro, kind) \
	AKANTU_BOOST_ELEMENT_SWITCH(macro, AKANTU_GET_ELEMENT_LIST(kind))

	// BOOST_PP_SEQ_TO_LIST does not exists in Boost < 1.49
	#define AKANTU_GENERATE_KIND_LIST(seq) \
	BOOST_PP_TUPLE_TO_LIST(BOOST_PP_SEQ_SIZE(seq), BOOST_PP_SEQ_TO_TUPLE(seq))

	#define AKANTU_ELEMENT_KIND_BOOST_LIST \
	AKANTU_GENERATE_KIND_LIST(AKANTU_ELEMENT_KIND)

	#define AKANTU_BOOST_ALL_KIND_LIST(macro, list) \
	BOOST_PP_LIST_FOR_EACH(AKANTU_BOOST_LIST_MACRO, macro, list)

	#define AKANTU_BOOST_ALL_KIND(macro) \
	AKANTU_BOOST_ALL_KIND_LIST(macro, AKANTU_ELEMENT_KIND_BOOST_LIST)

	#define AKANTU_BOOST_ALL_KIND_SWITCH(macro) \
	AKANTU_BOOST_LIST_SWITCH(macro, AKANTU_ELEMENT_KIND, kind)

	+#define AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(macro) \
	+ AKANTU_BOOST_ELEMENT_SWITCH(macro, AKANTU_ek_cohesive_ELEMENT_TYPE)

	-#define AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(macro) \
	- AKANTU_BOOST_ELEMENT_SWITCH(macro, \
	- AKANTU_ek_cohesive_ELEMENT_TYPE)
	-
	-#define AKANTU_BOOST_COHESIVE_ELEMENT_LIST(macro) \
	- AKANTU_BOOST_APPLY_ON_LIST(macro, \
	- AKANTU_ek_cohesive_ELEMENT_TYPE)
	-
	-#define AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(macro) \
	- AKANTU_BOOST_ELEMENT_SWITCH(macro, \
	- AKANTU_ek_regular_ELEMENT_TYPE)
	+#define AKANTU_BOOST_COHESIVE_ELEMENT_LIST(macro) \
	+ AKANTU_BOOST_APPLY_ON_LIST(macro, AKANTU_ek_cohesive_ELEMENT_TYPE)

	-#define AKANTU_BOOST_REGULAR_ELEMENT_LIST(macro) \
	- AKANTU_BOOST_APPLY_ON_LIST(macro, \
	- AKANTU_ek_regular_ELEMENT_TYPE)
	+#define AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(macro) \
	+ AKANTU_BOOST_ELEMENT_SWITCH(macro, AKANTU_ek_regular_ELEMENT_TYPE)

	-#define AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(macro) \
	- AKANTU_BOOST_ELEMENT_SWITCH(macro, \
	- AKANTU_ek_structural_ELEMENT_TYPE)
	+#define AKANTU_BOOST_REGULAR_ELEMENT_LIST(macro) \
	+ AKANTU_BOOST_APPLY_ON_LIST(macro, AKANTU_ek_regular_ELEMENT_TYPE)

	-#define AKANTU_BOOST_STRUCTURAL_ELEMENT_LIST(macro) \
	- AKANTU_BOOST_APPLY_ON_LIST(macro, \
	- AKANTU_ek_structural_ELEMENT_TYPE)
	+#define AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(macro) \
	+ AKANTU_BOOST_ELEMENT_SWITCH(macro, AKANTU_ek_structural_ELEMENT_TYPE)

	+#define AKANTU_BOOST_STRUCTURAL_ELEMENT_LIST(macro) \
	+ AKANTU_BOOST_APPLY_ON_LIST(macro, AKANTU_ek_structural_ELEMENT_TYPE)

	// /// define kept for compatibility reasons (they are most probably not needed
	// /// anymore) \todo check if they can be removed
	// #define AKANTU_REGULAR_ELEMENT_TYPE AKANTU_ek_regular_ELEMENT_TYPE
	// #define AKANTU_COHESIVE_ELEMENT_TYPE AKANTU_ek_cohesive_ELEMENT_TYPE
	// #define AKANTU_STRUCTURAL_ELEMENT_TYPE AKANTU_ek_structural_ELEMENT_TYPE
	// #define AKANTU_IGFEM_ELEMENT_TYPE AKANTU_ek_igfem_ELEMENT_TYPE

	/* -------------------------------------------------------------------------- */
	/* Lists of interests for FEEngineTemplate functions */
	/* -------------------------------------------------------------------------- */
	-#define AKANTU_FE_ENGINE_LIST_ASSEMBLE_FIELDS \
	- AKANTU_GENERATE_KIND_LIST((_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES_DERIVATIVES \
	- AKANTU_GENERATE_KIND_LIST((_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES \
	- AKANTU_GENERATE_KIND_LIST((_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_INTERPOLATE \
	+#define AKANTU_FE_ENGINE_LIST_ASSEMBLE_FIELDS \
	+ AKANTU_GENERATE_KIND_LIST((_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES_DERIVATIVES \
	+ AKANTU_GENERATE_KIND_LIST((_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES \
	+ AKANTU_GENERATE_KIND_LIST((_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_INTERPOLATE \
	AKANTU_GENERATE_KIND_LIST((_ek_regular))
	-#define AKANTU_FE_ENGINE_LIST_LAGRANGE_BASE \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular))
	-#define AKANTU_FE_ENGINE_LIST_INVERSE_MAP \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular))
	-#define AKANTU_FE_ENGINE_LIST_INTERPOLATE_ON_INTEGRATION_POINTS \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_GRADIENT_ON_INTEGRATION_POINTS \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_GET_SHAPES_DERIVATIVES \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular) \
	- (_ek_structural))
	-#define AKANTU_FE_ENGINE_LIST_CONTAINS \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular))
	-#define AKANTU_FE_ENGINE_LIST_COMPUTE_NORMALS_ON_INTEGRATION_POINTS \
	- AKANTU_GENERATE_KIND_LIST((_ek_cohesive) \
	- (_ek_regular))
	-
	-
	-} // akantu
	+#define AKANTU_FE_ENGINE_LIST_LAGRANGE_BASE \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular))
	+#define AKANTU_FE_ENGINE_LIST_INVERSE_MAP \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular))
	+#define AKANTU_FE_ENGINE_LIST_INTERPOLATE_ON_INTEGRATION_POINTS \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_GRADIENT_ON_INTEGRATION_POINTS \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_GET_SHAPES_DERIVATIVES \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular)(_ek_structural))
	+#define AKANTU_FE_ENGINE_LIST_CONTAINS \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular))
	+#define AKANTU_FE_ENGINE_LIST_COMPUTE_NORMALS_ON_INTEGRATION_POINTS \
	+ AKANTU_GENERATE_KIND_LIST((_ek_cohesive)(_ek_regular))
	+
	+} // namespace akantu

	#endif /* AKANTU_AKA_ELEMENT_CLASSES_INFO_HH_ */

	#include "aka_element_classes_info_inline_impl.hh"
	diff --git a/test/ci/includes_for_ci/aka_fortran_mangling.hh b/test/ci/includes_for_ci/aka_fortran_mangling.hh
	index e6da111ec..9550658e9 100644
	--- a/test/ci/includes_for_ci/aka_fortran_mangling.hh
	+++ b/test/ci/includes_for_ci/aka_fortran_mangling.hh
	@@ -1,47 +1,47 @@
	/**
	* @file aka_fortran_mangling.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Feb 08 2021
	* @date last modification: Mon Feb 08 2021
	*
	* @brief Copy of the auto generated aka_fortran_mangling.hh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#ifndef AKA_FC_HEADER_INCLUDED
	#define AKA_FC_HEADER_INCLUDED

	/* Mangling for Fortran global symbols without underscores. */
	-#define AKA_FC_GLOBAL(name,NAME) name##_
	+#define AKA_FC_GLOBAL(name, NAME) name##_

	/* Mangling for Fortran global symbols with underscores. */
	-#define AKA_FC_GLOBAL_(name,NAME) name##_
	+#define AKA_FC_GLOBAL_(name, NAME) name##_

	/* Mangling for Fortran module symbols without underscores. */
	-#define AKA_FC_MODULE(mod_name,name, mod_NAME,NAME) __##mod_name##_MOD_##name
	+#define AKA_FC_MODULE(mod_name, name, mod_NAME, NAME) __##mod_name##_MOD_##name

	/* Mangling for Fortran module symbols with underscores. */
	-#define AKA_FC_MODULE_(mod_name,name, mod_NAME,NAME) __##mod_name##_MOD_##name
	+#define AKA_FC_MODULE_(mod_name, name, mod_NAME, NAME) __##mod_name##_MOD_##name

	#endif
	diff --git a/test/ci/includes_for_ci/material_list.hh b/test/ci/includes_for_ci/material_list.hh
	index 52659cd7f..72f3e5ad7 100644
	--- a/test/ci/includes_for_ci/material_list.hh
	+++ b/test/ci/includes_for_ci/material_list.hh
	@@ -1,56 +1,56 @@
	/**
	* @file material_list.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Feb 08 2021
	*
	* @brief List of materials and all includes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_MATERIAL_LIST_HH__
	#define __AKANTU_MATERIAL_LIST_HH__

	#include "aka_config.hh"

	/* -------------------------------------------------------------------------- */
	/* Material includes */
	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_includes.hh"
	-#include "material_non_local_includes.hh"
	#include "material_core_includes.hh"
	+#include "material_non_local_includes.hh"

	/* -------------------------------------------------------------------------- */
	/* Material list */
	/* -------------------------------------------------------------------------- */
	-#define AKANTU_MATERIAL_LIST \
	- AKANTU_COHESIVE_MATERIAL_LIST \
	- AKANTU_DAMAGE_NON_LOCAL_MATERIAL_LIST \
	- AKANTU_CORE_MATERIAL_LIST \
	+#define AKANTU_MATERIAL_LIST \
	+ AKANTU_COHESIVE_MATERIAL_LIST \
	+ AKANTU_DAMAGE_NON_LOCAL_MATERIAL_LIST \
	+ AKANTU_CORE_MATERIAL_LIST

	// leave an empty line after the list

	#endif /* __AKANTU_MATERIAL_LIST_HH__ */
	diff --git a/test/ci/ompi_init.supp b/test/ci/ompi_init.supp
	new file mode 100644
	index 000000000..8442657ca
	--- /dev/null
	+++ b/test/ci/ompi_init.supp
	@@ -0,0 +1,1107 @@
	+{
	+ getCommunicator
	+ Memcheck:Param
	+ socketcall.getsockopt(optlen)
	+ fun:getsockopt
	+ fun:pmix_ptl_base_set_timeout
	+ fun:pmix_ptl_base_make_connection
	+ obj:/usr/lib/x86_64-linux-gnu/pmix2/lib/libpmix.so.2.5.0
	+ fun:PMIx_Init
	+ fun:ext3x_client_init
	+ obj:/usr/lib/x86_64-linux-gnu/openmpi/lib/openmpi3/mca_ess_singleton.so
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Param
	+ socketcall.getsockopt(optlen_out)
	+ fun:getsockopt
	+ fun:pmix_ptl_base_set_timeout
	+ fun:pmix_ptl_base_make_connection
	+ obj:/usr/lib/x86_64-linux-gnu/pmix2/lib/libpmix.so.2.5.0
	+ fun:PMIx_Init
	+ fun:ext3x_client_init
	+ obj:/usr/lib/x86_64-linux-gnu/openmpi/lib/openmpi3/mca_ess_singleton.so
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Param
	+ setsockopt(optlen)
	+ fun:setsockopt
	+ fun:pmix_ptl_base_make_connection
	+ obj:/usr/lib/x86_64-linux-gnu/pmix2/lib/libpmix.so.2.5.0
	+ fun:PMIx_Init
	+ fun:ext3x_client_init
	+ obj:/usr/lib/x86_64-linux-gnu/openmpi/lib/openmpi3/mca_ess_singleton.so
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ fun:mca_base_framework_components_register
	+ fun:mca_base_framework_register
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_finalize
	+ fun:ompi_mpi_finalize
	+ fun:~MPICommunicatorData
	+ fun:~MPICommunicatorData
	+ fun:_ZN6akantu19MPICommunicatorDataD0Ev
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ fun:mca_base_framework_components_register
	+ fun:mca_base_framework_register
	+ fun:mca_base_framework_open
	+ obj:*
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libmpi.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ fun:mca_base_framework_components_register
	+ fun:mca_base_framework_register
	+ fun:mca_base_framework_open
	+ obj:*
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libmpi.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:calloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:ompi_mtl_base_select
	+ obj:*
	+ fun:mca_pml_base_select
	+ fun:ompi_mpi_init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ fun:call_init.part.0
	+ fun:call_init
	+ fun:_dl_init
	+ fun:_dl_catch_exception
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+ fun:_dl_catch_error
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:__vasprintf_internal
	+ fun:__asprintf_chk
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_finalize
	+ fun:ompi_mpi_finalize
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:__vasprintf_internal
	+ fun:__asprintf_chk
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_finalize
	+ fun:ompi_mpi_finalize
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_finalize
	+ fun:ompi_mpi_finalize
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:call_init.part.0
	+ fun:call_init
	+ fun:_dl_init
	+ fun:_dl_catch_exception
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+ fun:_dl_catch_error
	+ fun:_dlerror_run
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ fun:mca_base_framework_components_register
	+ fun:mca_base_framework_register
	+ fun:mca_base_framework_open
	+ obj:*
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libmpi.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ fun:call_init.part.0
	+ fun:call_init
	+ fun:_dl_init
	+ fun:_dl_catch_exception
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+ fun:_dl_catch_error
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:__vasprintf_internal
	+ fun:__asprintf_chk
	+ fun:opal_hwloc_base_get_locality_string
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:hwloc_bitmap_alloc
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:calloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:ompi_proc_complete_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:malloc
	+ obj:*
	+ fun:ompi_op_base_op_select
	+ fun:ompi_op_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: definite
	+ fun:calloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:strdup
	+ fun:event_config_avoid_method
	+ fun:opal_event_init
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:strdup
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:ompi_pml_v_output_open
	+ obj:/usr/lib/x86_64-linux-gnu/libmpi.so.40.30.0
	+ fun:mca_base_framework_components_open
	+ obj:/usr/lib/x86_64-linux-gnu/libmpi.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:calloc
	+ fun:event_get_supported_methods
	+ fun:opal_event_init
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:strdup
	+ fun:_dl_load_cache_lookup
	+ fun:_dl_map_object
	+ fun:openaux
	+ fun:_dl_catch_exception
	+ fun:_dl_map_object_deps
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:_dl_new_object
	+ fun:_dl_map_object_from_fd
	+ fun:_dl_map_object
	+ fun:openaux
	+ fun:_dl_catch_exception
	+ fun:_dl_map_object_deps
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ obj:/usr/lib/x86_64-linux-gnu/libevent_pthreads-2.1.so.7.0.1
	+ fun:event_global_setup_locks_
	+ fun:evthread_use_pthreads
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ obj:/usr/lib/x86_64-linux-gnu/libevent_pthreads-2.1.so.7.0.1
	+ fun:evsig_global_setup_locks_
	+ fun:event_global_setup_locks_
	+ fun:evthread_use_pthreads
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ obj:/usr/lib/x86_64-linux-gnu/libevent_pthreads-2.1.so.7.0.1
	+ fun:evutil_secure_rng_global_setup_locks_
	+ fun:event_global_setup_locks_
	+ fun:evthread_use_pthreads
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:mca_base_component_repository_open
	+ fun:mca_base_component_find
	+ fun:mca_base_framework_components_register
	+ fun:mca_base_framework_register
	+ fun:mca_base_framework_open
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:event_config_avoid_method
	+ fun:opal_event_init
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:calloc
	+ fun:event_config_new
	+ fun:opal_event_init
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_framework_open
	+ fun:opal_init
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ fun:hwloc_bitmap_alloc
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+ fun:ompi_mpi_init
	+ fun:PMPI_Init
	+ fun:MPICommunicatorData
	+ fun:make_unique<akantu::MPICommunicatorData>
	+ fun:_ZN6akantu12CommunicatorC1ERKNS0_14private_memberE
	+ fun:make_unique<akantu::Communicator, int&, char**&, akantu::Communicator::private_member>
	+ fun:_ZN6akantu12Communicator21getStaticCommunicatorEv
	+ fun:main
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:calloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:calloc
	+ fun:_dl_check_map_versions
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+ fun:_dl_catch_error
	+ fun:_dlerror_run
	+ fun:dlopen@@GLIBC_2.2.5
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_component_repository_open
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:malloc
	+ fun:add_to_global_resize
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+ fun:_dl_catch_error
	+ fun:_dlerror_run
	+ fun:dlopen@@GLIBC_2.2.5
	+ obj:/usr/lib/x86_64-linux-gnu/libopen-pal.so.40.30.0
	+ fun:mca_base_component_repository_open
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: reachable
	+ fun:calloc
	+ fun:_dl_new_object
	+ fun:_dl_map_object_from_fd
	+ fun:_dl_map_object
	+ fun:openaux
	+ fun:_dl_catch_exception
	+ fun:_dl_map_object_deps
	+ fun:dl_open_worker
	+ fun:_dl_catch_exception
	+ fun:_dl_open
	+ fun:dlopen_doit
	+ fun:_dl_catch_exception
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:calloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:malloc
	+ fun:strdup
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+}
	+{
	+ <insert_a_suppression_name_here>
	+ Memcheck:Leak
	+ match-leak-kinds: indirect
	+ fun:realloc
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:*
	+ obj:/usr/lib/x86_64-linux-gnu/libhwloc.so.15.5.0
	+ fun:hwloc_topology_load
	+ fun:opal_hwloc_base_get_topology
	+ fun:orte_ess_base_proc_binding
	+ obj:*
	+ fun:orte_init
	+}
	diff --git a/test/ci/scripts/clang-tidy2code-quality.py b/test/ci/scripts/clang-tidy2code-quality.py
	deleted file mode 100644
	index 1a8e5841e..000000000
	--- a/test/ci/scripts/clang-tidy2code-quality.py
	+++ /dev/null
	@@ -1,92 +0,0 @@
	-#!/usr/bin/env python3
	-"""clang-tidy2code-quality.py: Conversion of clang-tidy output 2
	-code-quality"""
	-
	-__author__ = "Nicolas Richart"
	-__credits__ = [
	- "Nicolas Richart <nicolas.richart@epfl.ch>",
	-]
	-__copyright__ = "Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale" \
	- " de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
	- " en Mécanique des Solides)"
	-__license__ = "LGPLv3"
	-
	-import re
	-import os
	-import hashlib
	-import json
	-import sys
	-
	-
	-# 7-bit C1 ANSI sequences
	-ansi_escape = re.compile(r'''
	- \x1B # ESC
	- (?: # 7-bit C1 Fe (except CSI)
	- [@-Z\\-_]
	- \| # or [ for CSI, followed by a control sequence
	- \[
	- [0-?]* # Parameter bytes
	- [ -/]* # Intermediate bytes
	- [@-~] # Final byte
	- )
	-''', re.VERBOSE)
	-
	-re_log_parse = re.compile(
	- r'(?P<file>.\.(cc\|hh)):(?P<line>[0-9]+):(?P<column>[0-9]+): warning: (?P<detail>.) \[(?P<type>.*)\]' # noqa
	-)
	-
	-
	-categories = {
	- "bugprone": "Bug Risk",
	- "modernize": "Clarity",
	- "mpi": "Bug Risk",
	- "openmp": "Bug Risk",
	- "performance": "Performance",
	- "readability": "Clarity",
	-}
	-
	-issues = {}
	-
	-with open('clang-tidy-all-out.log', 'r') as log:
	- for line in log:
	- clean_line = ansi_escape.sub('', line)
	- match = re_log_parse.match(clean_line)
	- if match:
	- line_dict = match.groupdict()
	- line_dict['file'] = os.path.relpath(line_dict['file'])
	-
	- line_dict['fingerprint'] = hashlib.md5(
	- '{file}:{line}:{column}:{type}'.format(**line_dict).encode()
	- ).hexdigest()
	-
	- issue = {
	- 'type': 'issue',
	- 'description': line_dict['detail'],
	- 'fingerprint': line_dict['fingerprint'],
	- 'location': {
	- "path": line_dict['file'],
	- "lines": {
	- "begin": int(line_dict['line']),
	- "end": int(line_dict['line']),
	- },
	- "positions": {
	- "begin": {
	- "line": int(line_dict['line']),
	- "column": int(line_dict['column']),
	- },
	- },
	-
	- },
	- 'severity': 'minor',
	- }
	-
	- category = line_dict['type'].split('-')[0]
	- if category in categories:
	- issue['category'] = categories[category]
	-
	- # use a dictionnary to avoid duplicates
	- issues[issue['fingerprint']] = issue
	-
	-issues = list(issues.values())
	-
	-json.dump(issues, sys.stdout)
	diff --git a/test/ci/scripts/codequality/__init__.py b/test/ci/scripts/codequality/__init__.py
	new file mode 100644
	index 000000000..cb8f71fe8
	--- /dev/null
	+++ b/test/ci/scripts/codequality/__init__.py
	@@ -0,0 +1,35 @@
	+#!/usr/bin/env python3
	+import json as _cq_json
	+import sys as _cq_sys
	+try:
	+ from termcolor import colored as _cq_colored
	+except ImportError:
	+ def _cq_colored(text, color): # pylint: disable=unused-argument
	+ """fallback function for termcolor.colored"""
	+ return text
	+
	+def print_debug(message):
	+ '''helper function to print debug messages'''
	+ print(f'Debug: {_cq_colored(message, "red")}',
	+ file=_cq_sys.stderr, flush=True)
	+
	+def print_info(message):
	+ '''helper function to print info messages'''
	+ print(f'Info: {_cq_colored(message, "blue")}',
	+ file=_cq_sys.stderr, flush=True)
	+
	+def run(cmd, **kwargs):
	+ from .issue_generator_clang_tidy import ClangTidyIssueGenerator # NOQA
	+ from .issue_generator_clang_format import ClangFormatIssueGenerator # NOQA
	+ from .issue_generator_warnings import WarningsIssueGenerator # NOQA
	+
	+ if cmd == 'clang_tidy':
	+ tool = ClangTidyIssueGenerator(**kwargs)
	+ elif cmd == 'clang_format':
	+ tool = ClangFormatIssueGenerator(**kwargs)
	+ elif cmd == 'warnings':
	+ tool = WarningsIssueGenerator(**kwargs)
	+
	+ tool.generate_issues()
	+
	+ print(_cq_json.dumps(tool.issues))
	diff --git a/test/ci/scripts/codequality/issue_generator.py b/test/ci/scripts/codequality/issue_generator.py
	new file mode 100644
	index 000000000..5f26d87fe
	--- /dev/null
	+++ b/test/ci/scripts/codequality/issue_generator.py
	@@ -0,0 +1,123 @@
	+#!/usr/bin/env python3
	+
	+from . import print_debug, print_info
	+import hashlib
	+import os
	+import re
	+import copy
	+
	+
	+class IssueGenerator:
	+ """Interface for the issue generators"""
	+
	+ def __init__(self, **kwargs):
	+ self._files = kwargs.pop('file_list', [])
	+
	+ excludes = kwargs.pop('excludes', None)
	+ if excludes is None:
	+ excludes = []
	+
	+ extensions = kwargs.pop('extensions', None)
	+ if extensions is None:
	+ extensions = ['.cc', '.hh']
	+
	+ self._extensions = [
	+ re.compile(r"\{}$".format(extension)) for extension in extensions
	+ ]
	+
	+ self._exclude_patterns = [
	+ re.compile(exclude) for exclude in excludes
	+ ]
	+
	+ self._issues = {}
	+ self._filter_file_list()
	+
	+ def _filter_file_list(self):
	+ file_list = copy.copy(self._files)
	+ self._files = []
	+ for filename in file_list:
	+ filename = os.path.relpath(filename)
	+ need_exclude = self._need_exclude(filename)
	+ if need_exclude:
	+ print_debug(f'exluding file: {filename}')
	+ continue
	+ print_info(f'adding file: {filename}')
	+ self._files.append(filename)
	+
	+ def _need_exclude(self, filename):
	+ need_exclude = False
	+ for pattern in self._exclude_patterns:
	+ match = pattern.search(filename)
	+ need_exclude \|= bool(match)
	+
	+ match_extension = False
	+ for extension in self._extensions:
	+ match = extension.search(filename)
	+ match_extension \|= bool(match)
	+
	+ need_exclude \|= not match_extension
	+ return need_exclude
	+
	+ def add_issue(self, unfmt_issue):
	+ """add an issue to the list if not already present"""
	+ issue = self._format_issue(unfmt_issue)
	+
	+ filepath = issue['location']['path']
	+ if self._need_exclude(filepath):
	+ return
	+
	+ if issue['fingerprint'] in self._issues:
	+ return
	+
	+ self._issues[issue['fingerprint']] = issue
	+
	+ @property
	+ def issues(self):
	+ """get the list of registered issues"""
	+ return list(self._issues.values())
	+
	+ def _format_issue(self, unfmt_issue):
	+ filepath = os.path.relpath(unfmt_issue['file'])
	+ issue = {
	+ 'type': 'issue',
	+ 'check_name': unfmt_issue['name'],
	+ 'description': (
	+ f'''[{unfmt_issue['name']}] {unfmt_issue['description']}'''),
	+ 'location': {
	+ "path": filepath,
	+ "lines": {
	+ "begin": unfmt_issue['line'],
	+ "end": unfmt_issue['line'],
	+ },
	+ "positions": {
	+ "begin": {
	+ "line": unfmt_issue['line'],
	+ "column": unfmt_issue['column'],
	+ },
	+ 'end': {
	+ "line": unfmt_issue['line'],
	+ "column": unfmt_issue['column'],
	+ },
	+ },
	+ },
	+ }
	+
	+ if 'end_line' in unfmt_issue:
	+ issue['location']['positions']['end'] = {
	+ "line": unfmt_issue['end_line'],
	+ "column": unfmt_issue['column'],
	+ }
	+ issue['location']['lines']['end'] = unfmt_issue['end_line']
	+
	+ issue['fingerprint'] = hashlib.md5(
	+ '{file}:{line}:{column}:{type}'.format(
	+ file=filepath,
	+ line=unfmt_issue['line'],
	+ column=unfmt_issue['column'],
	+ type=unfmt_issue['name']).encode()).hexdigest()
	+
	+ issue['categories'], issue['severity'] = \
	+ self._get_classifiaction(unfmt_issue)
	+
	+ print_debug(issue)
	+ return issue
	diff --git a/test/ci/scripts/codequality/issue_generator_clang_format.py b/test/ci/scripts/codequality/issue_generator_clang_format.py
	new file mode 100644
	index 000000000..296f86c7b
	--- /dev/null
	+++ b/test/ci/scripts/codequality/issue_generator_clang_format.py
	@@ -0,0 +1,54 @@
	+#!/usr/bin/env python3
	+
	+from . import print_debug, print_info
	+from .issue_generator_clang_tool import ClangToolIssueGenerator
	+import os
	+import re
	+import copy
	+import difflib
	+import subprocess
	+
	+
	+class ClangFormatIssueGenerator(ClangToolIssueGenerator):
	+ """issue generator for clang format"""
	+
	+ def __init__(self, **kwargs):
	+ kwargs['clang_tool_executable'] = kwargs.pop('clang_format_executable',
	+ 'clang-format')
	+ super().__init__('clang-format', **kwargs)
	+
	+ def _get_classifiaction(self, issue):
	+ return (['Style'], 'info')
	+
	+ def generate_issues(self):
	+ issue = {}
	+ for filename in self._files:
	+ with open(filename, 'r') as fh:
	+ unformated_file = fh.readlines()
	+
	+ command = copy.copy(self._command)
	+ command.append(filename)
	+ formated_file = list(self._run_command(command))
	+
	+ # diffs = difflib.unified_diff(unformated_file, formated_file, n=0)
	+
	+ # print(diffs)
	+ # for diff in diffs:
	+ # print(diff, end='')
	+
	+ s = difflib.SequenceMatcher(None, unformated_file, formated_file)
	+ for tag, i1, i2, j1, j2 in s.get_opcodes():
	+ if tag != 'equal':
	+ diff = list(
	+ difflib.unified_diff(
	+ unformated_file[i1:i2],
	+ formated_file[j1:j2]))
	+ issue = {
	+ 'name': f'''clang-format:{tag}''',
	+ 'description': ''.join(diff[3:]),
	+ 'file': filename,
	+ 'line': i1,
	+ 'column': 1,
	+ 'end_line': i2,
	+ }
	+ self.add_issue(issue)
	diff --git a/test/ci/scripts/codequality/issue_generator_clang_tidy.py b/test/ci/scripts/codequality/issue_generator_clang_tidy.py
	new file mode 100644
	index 000000000..0ad5412ee
	--- /dev/null
	+++ b/test/ci/scripts/codequality/issue_generator_clang_tidy.py
	@@ -0,0 +1,105 @@
	+#!/usr/bin/env python3
	+
	+from . import print_debug, print_info
	+from .issue_generator_clang_tool import ClangToolIssueGenerator
	+import os
	+import re
	+import copy
	+import json
	+import subprocess
	+
	+
	+class ClangTidyIssueGenerator(ClangToolIssueGenerator):
	+ """issue generator for clang tidy"""
	+
	+ # 7-bit C1 ANSI sequences
	+ ANSI_ESCAPE = re.compile(r'''
	+ \x1B # ESC
	+ (?: # 7-bit C1 Fe (except CSI)
	+ [@-Z\\-_]
	+ \| # or [ for CSI, followed by a control sequence
	+ \[
	+ [0-?]* # Parameter bytes
	+ [ -/]* # Intermediate bytes
	+ [@-~] # Final byte
	+ )
	+ ''', re.VERBOSE)
	+
	+ ISSUE_PARSE = re.compile(r'(?P<file>.\.(cc\|hh)):(?P<line>[0-9]+):(?P<column>[0-9]+): (warning\|error): (?P<description>.) \[(?P<name>.*)\]') # NOQA pylint: disable=line-too-long
	+
	+ CLASSIFICATIONS = {
	+ 'bugprone': {
	+ 'categories': ['Bug Risk'],
	+ 'severity': 'major',
	+ },
	+ 'modernize': {
	+ 'categories': ['Clarity', 'Compatibility', 'Style'],
	+ 'severity': 'info'
	+ },
	+ 'mpi': {
	+ 'categories': ['Bug Risk', 'Performance'],
	+ 'severity': 'critical',
	+ },
	+ 'openmp': {
	+ 'categories': ['Bug Risk', 'Performance'],
	+ 'severity': 'critical',
	+ },
	+ 'performance': {
	+ 'categories': ['Performance'],
	+ 'severity': 'minor',
	+ },
	+ 'readability': {
	+ 'categories': ['Clarity', 'Style'],
	+ 'severity': 'info'
	+ },
	+ }
	+
	+ def __init__(self, **kwargs):
	+ kwargs['clang_tool_executable'] = kwargs.pop('clang_tidy_executable',
	+ 'clang-tidy')
	+ super().__init__('clang-tidy',
	+ need_compiledb=True, **kwargs)
	+
	+ def _get_classifiaction(self, issue):
	+ type_ = issue['type']
	+ categories = ['Bug Risk']
	+ severity = 'blocker'
	+
	+ if type_ in self.CLASSIFICATIONS:
	+ categories = self.CLASSIFICATIONS[type_]['categories']
	+ severity = self.CLASSIFICATIONS[type_]['severity']
	+ elif type_[0] == 'clang':
	+ if type_[1] == 'diagnostic':
	+ categories = ['Bug Risk']
	+ severity = 'blocker'
	+ elif type_[1] == 'analyzer':
	+ categories = ['Bug Risk']
	+ severity = 'major'
	+
	+ return (categories, severity)
	+
	+ def generate_issues(self):
	+ issue = {}
	+ for filename in self._files:
	+ command = copy.copy(self._command)
	+ command.append(filename)
	+ for line in self._run_command(command):
	+ line = line.rstrip()
	+ match = self.ISSUE_PARSE.match(line)
	+ if match:
	+ if len(issue) != 0:
	+ self.add_issue(issue)
	+ issue = match.groupdict()
	+ issue['type'] = issue['name']
	+ issue['name'] = f'''clang-tidy:{issue['name']}'''
	+
	+ print_debug(f'[clang-tidy] new issue: {line}')
	+ elif issue:
	+ if 'content' in issue:
	+ issue['content'].append(line)
	+ print_debug(f'[clang-tidy] more extra content: {line}')
	+ else:
	+ issue['content'] = [line]
	+ print_debug(f'[clang-tidy] extra content: {line}')
	+ if len(issue) != 0:
	+ self.add_issue(issue)
	diff --git a/test/ci/scripts/codequality/issue_generator_clang_tool.py b/test/ci/scripts/codequality/issue_generator_clang_tool.py
	new file mode 100644
	index 000000000..b1ef4d100
	--- /dev/null
	+++ b/test/ci/scripts/codequality/issue_generator_clang_tool.py
	@@ -0,0 +1,74 @@
	+#!/usr/bin/env python3
	+
	+from . import print_debug, print_info
	+from .issue_generator import IssueGenerator
	+import os
	+import re
	+import copy
	+import json
	+import subprocess
	+
	+
	+class ClangToolIssueGenerator(IssueGenerator):
	+ """issue generator for clang tidy"""
	+
	+ # 7-bit C1 ANSI sequences
	+ ANSI_ESCAPE = re.compile(r'''
	+ \x1B # ESC
	+ (?: # 7-bit C1 Fe (except CSI)
	+ [@-Z\\-_]
	+ \| # or [ for CSI, followed by a control sequence
	+ \[
	+ [0-?]* # Parameter bytes
	+ [ -/]* # Intermediate bytes
	+ [@-~] # Final byte
	+ )
	+ ''', re.VERBOSE)
	+
	+ def __init__(self, tool, **kwargs):
	+ self._tool = tool
	+ opts = copy.copy(kwargs)
	+ super().__init__(**kwargs)
	+
	+ compiledb_path = opts.pop('compiledb_path')
	+ arguments = opts.pop('arguments', None)
	+ clang_tool = opts.pop('clang_tool_executable', tool)
	+
	+ self._command = [clang_tool]
	+
	+ if 'need_compiledb' in opts and opts['need_compiledb']:
	+ self._command.extend(['-p', compiledb_path])
	+ if arguments is not None:
	+ self._command.extend(arguments)
	+
	+ if len(self._files) == 0 and compiledb_path:
	+ self._get_files_from_compile_db(compiledb_path)
	+
	+ def _get_files_from_compile_db(self, compiledb_path):
	+ file_list = []
	+ with open(os.path.join(
	+ compiledb_path,
	+ 'compile_commands.json'), 'r') as compiledb_fh:
	+ compiledb = json.load(compiledb_fh)
	+ for entry in compiledb:
	+ file_list.append(entry['file'])
	+ self._files = file_list
	+ self._filter_file_list()
	+
	+ def _run_command(self, command):
	+ print_info(f'''[{self._tool}] command: {' '.join(command)}''')
	+ popen = subprocess.Popen(command,
	+ stdout=subprocess.PIPE,
	+ stderr=subprocess.DEVNULL,
	+ universal_newlines=True)
	+
	+ for stdout_line in iter(popen.stdout.readline, ""):
	+ clean_line = self.ANSI_ESCAPE.sub('', stdout_line)
	+ yield clean_line
	+
	+ popen.stdout.close()
	+
	+ return_code = popen.wait()
	+ if return_code:
	+ print_debug(
	+ f"[{self._tool}] {command} ReturnCode {return_code}")
	diff --git a/test/ci/scripts/codequality/issue_generator_warnings.py b/test/ci/scripts/codequality/issue_generator_warnings.py
	new file mode 100644
	index 000000000..b39eb3461
	--- /dev/null
	+++ b/test/ci/scripts/codequality/issue_generator_warnings.py
	@@ -0,0 +1,81 @@
	+#!/usr/bin/env python3
	+"""clang-tidy2code-quality.py: Conversion of clang-tidy output 2
	+code-quality"""
	+
	+__author__ = "Nicolas Richart"
	+__credits__ = [
	+ "Nicolas Richart <nicolas.richart@epfl.ch>",
	+]
	+__copyright__ = "Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale" \
	+ " de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
	+ " en Mécanique des Solides)"
	+__license__ = "LGPLv3"
	+
	+from . import print_debug, print_info
	+from .issue_generator import IssueGenerator
	+import re
	+import sys
	+import warning_parser as warn
	+
	+
	+class WarningsIssueGenerator(IssueGenerator):
	+ '''
	+ Main class to run and convert the results of clang-tidy to the code-quality
	+ format
	+ '''
	+ CLASSIFICATIONS = {
	+ 'gcc': {
	+ 'uninitialized': {
	+ 'categories': ['Bug Risk'],
	+ 'severity': 'major',
	+ },
	+ 'sign-compare': {
	+ 'categories': ['Bug Risk'],
	+ 'severity': 'minor'
	+ },
	+ },
	+ }
	+
	+ def __init__(self, **kwargs):
	+ super().__init__(**kwargs)
	+ files = kwargs.pop('files')
	+
	+ self._input_files = {}
	+ compiler_re = re.compile(".build.(gcc\|clang)-err\.log")
	+
	+ for _file in files:
	+ match = compiler_re.search(_file)
	+ if match:
	+ self._input_files[match.group(1)] = _file
	+ else:
	+ print_info(f"Skipped {_file}, could not determine compiler")
	+
	+ def generate_issues(self):
	+ '''parse warning files'''
	+
	+ for compiler, _file in self._input_files.items():
	+ warnings = warn.get_warnings(_file, compiler)
	+ for warning in warnings:
	+ issue = {
	+ 'name': f'warning:{compiler}-{warning.get_category()}',
	+ 'description': warning.get_message(),
	+ 'file': warning.get_filepath(),
	+ 'line': warning.get_line(),
	+ 'column': warning.get_column(),
	+ 'raw': warning,
	+ }
	+
	+ self.add_issue(issue)
	+
	+ def _get_classifiaction(self, warning):
	+ categories = ['Clarity']
	+ severity = 'info'
	+
	+ if warning.get_tool() in self.CLASSIFICATIONS:
	+ classifications = self.CLASSIFICATIONS[warning.get_tool()]
	+ if warning.get_category() in classifications:
	+ cat = warning.get_category()
	+ categories = classifications[cat]['categories']
	+ severity = classifications[cat]['severity']
	+
	+ return (categories, severity)
	diff --git a/test/ci/scripts/cq b/test/ci/scripts/cq
	new file mode 100755
	index 000000000..87cb98dac
	--- /dev/null
	+++ b/test/ci/scripts/cq
	@@ -0,0 +1,59 @@
	+#!/usr/bin/env python3
	+
	+import click
	+import codequality
	+
	+@click.group()
	+@click.option('-x', '--exclude', default=[], multiple=True)
	+@click.option('-e', '--extensions', default='.cc, .hh')
	+@click.option('-f', '--file-list', default=None)
	+@click.pass_context
	+def cq(ctx, exclude, extensions, file_list):
	+ ctx.obj['excludes'] = exclude
	+ ctx.obj['extensions'] = [ext.strip() for ext in extensions.split(',')]
	+ if file_list is not None:
	+ with open(file_list, 'r') as fh:
	+ ctx.obj['file_list'] = [file_.strip() for file_ in fh.readlines()]
	+
	+@cq.command(context_settings=dict(
	+ ignore_unknown_options=True,
	+))
	+@click.option('-p', '--compiledb-path', default='.')
	+@click.option('-c', '--clang-tidy-executable', default='clang-tidy')
	+@click.argument('clang_tidy_args', nargs=-1, type=click.UNPROCESSED)
	+@click.pass_context
	+def clang_tidy(ctx, compiledb_path, clang_tidy_executable,
	+ clang_tidy_args):
	+ codequality.run('clang_tidy',
	+ compiledb_path=compiledb_path,
	+ clang_tidy_executable=clang_tidy_executable,
	+ arguments=clang_tidy_args,
	+ **ctx.obj)
	+
	+@cq.command(context_settings=dict(
	+ ignore_unknown_options=True,
	+))
	+@click.option('-p', '--compiledb-path', default='.')
	+@click.option('-c', '--clang-format-executable', default='clang-format')
	+@click.argument('clang_format_args', nargs=-1, type=click.UNPROCESSED)
	+@click.pass_context
	+def clang_format(ctx, compiledb_path, clang_format_executable,
	+ clang_format_args):
	+ codequality.run('clang_format',
	+ compiledb_path=compiledb_path,
	+ clang_format_executable=clang_format_executable,
	+ arguments=clang_format_args,
	+ **ctx.obj)
	+
	+@cq.command(context_settings=dict(
	+ ignore_unknown_options=True,
	+))
	+@click.argument('files', nargs=-1, type=click.UNPROCESSED)
	+@click.pass_context
	+def warnings(ctx, files):
	+ codequality.run('warnings',
	+ files=files,
	+ **ctx.obj)
	+
	+if __name__ == '__main__':
	+ cq(obj={})
	diff --git a/test/ci/ubuntu:lts/Dockerfile b/test/ci/ubuntu:lts/Dockerfile
	index b1a78720e..51f94b297 100644
	--- a/test/ci/ubuntu:lts/Dockerfile
	+++ b/test/ci/ubuntu:lts/Dockerfile
	@@ -1,29 +1,31 @@
	FROM ubuntu:xenial
	MAINTAINER Nicolas Richart <nicolas.richart@epfl.ch>

	ENV TZ=Europe/Zurich
	RUN ln -snf /usr/share/zoneinfo/$TZ /etc/localtime && echo $TZ > /etc/timezone

	# Install akantu dependencies
	RUN apt-get -qq update && apt-get -qq -y install \
	g++ gfortran cmake \
	openmpi-bin libmumps-dev libscotch-dev \
	libboost-dev libopenblas-dev libcgal-dev \
	python3 python3-dev python3-numpy python3-scipy python3-pip \
	&& rm -rf /var/lib/apt/lists/*

	RUN pip3 install mpi4py

	# Install test utilities
	RUN apt-get -qq update && apt-get -qq -y install \
	- python3-yaml python3-pytest ccache \
	- gmsh curl git xsltproc \
	+ python3-yaml python3-pytest python3-termcolor python3-click \
	+ ccache gmsh curl git xsltproc \
	gcovr binutils \
	&& rm -rf /var/lib/apt/lists/*

	+RUN pip3 install warning_parser
	+
	COPY .openmpi /root/.openmpi

	# for debug
	RUN apt-get -qq update && apt-get -qq -y install \
	gdb valgrind \
	&& rm -rf /var/lib/apt/lists/*
	diff --git a/test/test_common/test_array.cc b/test/test_common/test_array.cc
	index 9b89586af..f156f0267 100644
	--- a/test/test_common/test_array.cc
	+++ b/test/test_common/test_array.cc
	@@ -1,292 +1,292 @@
	/**
	* @file test_array.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Nov 09 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Test the arry class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <aka_array.hh>
	#include <aka_types.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <memory>
	#include <typeindex>
	#include <typeinfo>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	class NonTrivial {
	public:
	NonTrivial() = default;
	NonTrivial(int a) : a(a){};

	bool operator==(const NonTrivial & rhs) { return a == rhs.a; }
	int a{0};
	};

	bool operator==(const int & a, const NonTrivial & rhs) { return a == rhs.a; }

	std::ostream & operator<<(std::ostream & stream, const NonTrivial & _this) {
	stream << _this.a;
	return stream;
	}

	/* -------------------------------------------------------------------------- */
	using TestTypes = ::testing::Types<Real, UInt, NonTrivial>;
	/* -------------------------------------------------------------------------- */

	::testing::AssertionResult AssertType(const char * /a_expr/,
	const char * /b_expr/,
	const std::type_info & a,
	const std::type_info & b) {
	if (std::type_index(a) == std::type_index(b))
	return ::testing::AssertionSuccess();

	return ::testing::AssertionFailure()
	<< debug::demangle(a.name()) << " != " << debug::demangle(b.name())
	<< ") are different";
	}

	/* -------------------------------------------------------------------------- */

	template <typename T> class ArrayConstructor : public ::testing::Test {
	protected:
	using type = T;

	void SetUp() override { type_str = debug::demangle(typeid(T).name()); }

	template <typename... P> decltype(auto) construct(P &&... params) {
	return std::make_unique<Array<T>>(std::forward<P>(params)...);
	}

	protected:
	std::string type_str;
	};

	TYPED_TEST_SUITE(ArrayConstructor, TestTypes, );

	TYPED_TEST(ArrayConstructor, ConstructDefault1) {
	auto array = this->construct();
	EXPECT_EQ(0, array->size());
	EXPECT_EQ(1, array->getNbComponent());
	EXPECT_STREQ("", array->getID().c_str());
	}

	TYPED_TEST(ArrayConstructor, ConstructDefault2) {
	auto array = this->construct(1000);
	EXPECT_EQ(1000, array->size());
	EXPECT_EQ(1, array->getNbComponent());
	EXPECT_STREQ("", array->getID().c_str());
	}

	TYPED_TEST(ArrayConstructor, ConstructDefault3) {
	auto array = this->construct(1000, 10);
	EXPECT_EQ(1000, array->size());
	EXPECT_EQ(10, array->getNbComponent());
	EXPECT_STREQ("", array->getID().c_str());
	}

	TYPED_TEST(ArrayConstructor, ConstructDefault4) {
	auto array = this->construct(1000, 10, "test");
	EXPECT_EQ(1000, array->size());
	EXPECT_EQ(10, array->getNbComponent());
	EXPECT_STREQ("test", array->getID().c_str());
	}

	TYPED_TEST(ArrayConstructor, ConstructDefault5) {
	auto array = this->construct(1000, 10, 1);
	EXPECT_EQ(1000, array->size());
	EXPECT_EQ(10, array->getNbComponent());
	EXPECT_EQ(1, array->operator()(10, 6));
	EXPECT_STREQ("", array->getID().c_str());
	}

	// TYPED_TEST(ArrayConstructor, ConstructDefault6) {
	// typename TestFixture::type defaultv[2] = {0, 1};

	// auto array = this->construct(1000, 2, defaultv);
	// EXPECT_EQ(1000, array->size());
	// EXPECT_EQ(2, array->getNbComponent());
	// EXPECT_EQ(1, array->operator()(10, 1));
	// EXPECT_EQ(0, array->operator()(603, 0));
	// EXPECT_STREQ("", array->getID().c_str());
	// }

	/* -------------------------------------------------------------------------- */
	template <typename T> class ArrayFixture : public ArrayConstructor<T> {
	public:
	void SetUp() override {
	ArrayConstructor<T>::SetUp();
	array = this->construct(1000, 10);
	}

	void TearDown() override { array.reset(nullptr); }

	protected:
	std::unique_ptr<Array<T>> array;
	};

	TYPED_TEST_SUITE(ArrayFixture, TestTypes, );

	TYPED_TEST(ArrayFixture, Copy) {
	Array<typename TestFixture::type> copy(*this->array);

	EXPECT_EQ(1000, copy.size());
	EXPECT_EQ(10, copy.getNbComponent());
	EXPECT_NE(this->array->storage(), copy.storage());
	}

	TYPED_TEST(ArrayFixture, Set) {
	auto & arr = *(this->array);
	arr.set(12);
	EXPECT_EQ(12, arr(156, 5));
	EXPECT_EQ(12, arr(520, 7));
	EXPECT_EQ(12, arr(999, 9));
	}

	TYPED_TEST(ArrayFixture, Resize) {
	auto & arr = *(this->array);

	auto * ptr = arr.storage();

	arr.resize(0);
	EXPECT_EQ(0, arr.size());
	EXPECT_TRUE(arr.storage() == nullptr or arr.storage() == ptr);
	EXPECT_LE(0, arr.getAllocatedSize());

	arr.resize(3000);
	EXPECT_EQ(3000, arr.size());
	EXPECT_LE(3000, arr.getAllocatedSize());

	ptr = arr.storage();

	arr.resize(0);
	EXPECT_EQ(0, arr.size());
	EXPECT_TRUE(arr.storage() == nullptr or arr.storage() == ptr);
	EXPECT_LE(0, arr.getAllocatedSize());
	}

	TYPED_TEST(ArrayFixture, PushBack) {
	auto & arr = *(this->array);

	auto * ptr = arr.storage();

	arr.resize(0);
	EXPECT_EQ(0, arr.size());
	EXPECT_TRUE(arr.storage() == nullptr or arr.storage() == ptr);
	EXPECT_LE(0, arr.getAllocatedSize());

	arr.resize(3000);
	EXPECT_EQ(3000, arr.size());
	EXPECT_LE(3000, arr.getAllocatedSize());

	ptr = arr.storage();

	arr.resize(0);
	EXPECT_EQ(0, arr.size());
	EXPECT_TRUE(arr.storage() == nullptr or arr.storage() == ptr);
	EXPECT_LE(0, arr.getAllocatedSize());
	}

	TYPED_TEST(ArrayFixture, ViewVector) {
	auto && view = make_view(*this->array, 10);
	EXPECT_NO_THROW(view.begin());
	{
	auto it = view.begin();
	EXPECT_EQ(10, it->size());
	EXPECT_PRED_FORMAT2(AssertType, typeid(*it),
	typeid(Vector<typename TestFixture::type>));
	EXPECT_PRED_FORMAT2(AssertType, typeid(it[0]),
	typeid(VectorProxy<typename TestFixture::type>));
	}
	}

	TYPED_TEST(ArrayFixture, ViewMatrix) {
	{
	auto && view = make_view(*this->array, 2, 5);

	EXPECT_NO_THROW(view.begin());
	{
	auto it = view.begin();
	EXPECT_EQ(10, it->size());
	EXPECT_EQ(2, it->size(0));
	EXPECT_EQ(5, it->size(1));

	EXPECT_PRED_FORMAT2(AssertType, typeid(*it),
	typeid(Matrix<typename TestFixture::type>));
	EXPECT_PRED_FORMAT2(AssertType, typeid(it[0]),
	typeid(MatrixProxy<typename TestFixture::type>));
	}
	}
	}

	TYPED_TEST(ArrayFixture, ViewVectorWrong) {
	auto && view = make_view(*this->array, 11);
	EXPECT_THROW(view.begin(), debug::ArrayException);
	}

	TYPED_TEST(ArrayFixture, ViewMatrixWrong) {
	auto && view = make_view(*this->array, 3, 7);
	EXPECT_THROW(view.begin(), debug::ArrayException);
	}

	TYPED_TEST(ArrayFixture, ViewMatrixIter) {
	std::size_t count = 0;
	for (auto && mat : make_view(*this->array, 10, 10)) {
	EXPECT_EQ(100, mat.size());
	EXPECT_EQ(10, mat.size(0));
	EXPECT_EQ(10, mat.size(1));
	EXPECT_PRED_FORMAT2(AssertType, typeid(mat),
	typeid(Matrix<typename TestFixture::type>));

	++count;
	}

	EXPECT_EQ(100, count);
	}

	TYPED_TEST(ArrayFixture, ConstViewVector) {
	const auto & carray = *this->array;
	auto && view = make_view(carray, 10);
	EXPECT_NO_THROW(view.begin());
	{
	auto it = view.begin();
	EXPECT_EQ(10, it->size());
	EXPECT_PRED_FORMAT2(AssertType, typeid(*it),
	typeid(Vector<typename TestFixture::type>));
	EXPECT_PRED_FORMAT2(AssertType, typeid(it[0]),
	typeid(VectorProxy<typename TestFixture::type>));
	}
	}

	} // namespace
	diff --git a/test/test_common/test_csr.cc b/test/test_common/test_csr.cc
	index ca2eb48aa..f1f570196 100644
	--- a/test/test_common/test_csr.cc
	+++ b/test/test_common/test_csr.cc
	@@ -1,103 +1,103 @@
	/**
	* @file test_csr.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sun Dec 03 2017
	*
	* @brief Test the CSR (compressed sparse row) data structure
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_csr.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class TestCsrFixture : public ::testing::Test {
	protected:
	void SetUp() override {
	csr.resizeRows(N);
	csr.clearRows();

	for (UInt i = 0; i < N; ++i) {
	UInt nb_cols(UInt(rand() * double(N) / (RAND_MAX + 1.)));
	nb_cols_per_row.push_back(nb_cols);
	for (UInt j = 0; j < nb_cols; ++j) {
	++csr.rowOffset(i);
	}
	}

	csr.countToCSR();
	csr.resizeCols();

	csr.beginInsertions();
	for (UInt i = 0; i < N; ++i) {
	UInt nb_cols = nb_cols_per_row[i];
	for (UInt j = 0; j < nb_cols; ++j) {
	csr.insertInRow(i, nb_cols - j);
	}
	}
	csr.endInsertions();
	}

	std::vector<UInt> nb_cols_per_row;
	CSR<UInt> csr;
	size_t N = 1000;
	};

	TEST_F(TestCsrFixture, CheckInsertion) { EXPECT_EQ(N, this->csr.getNbRows()); }

	TEST_F(TestCsrFixture, Iteration) {
	for (UInt i = 0; i < this->csr.getNbRows(); ++i) {
	auto it = this->csr.begin(i);
	auto end = this->csr.end(i);
	UInt nb_cols = this->nb_cols_per_row[i];
	for (; it != end; ++it) {
	EXPECT_EQ(nb_cols, *it);
	nb_cols--;
	}

	EXPECT_EQ(0, nb_cols);
	}
	}

	TEST_F(TestCsrFixture, ReverseIteration) {
	for (UInt i = 0; i < csr.getNbRows(); ++i) {
	auto it = csr.rbegin(i);
	auto end = csr.rend(i);

	UInt nb_cols = nb_cols_per_row[i];
	UInt j = nb_cols;

	for (; it != end; --it) {
	EXPECT_EQ((nb_cols - j + 1), *it);
	j--;
	}

	EXPECT_EQ(0, j);
	}
	}
	diff --git a/test/test_common/test_grid.cc b/test/test_common/test_grid.cc
	index c6c501073..c54c5724b 100644
	--- a/test/test_common/test_grid.cc
	+++ b/test/test_common/test_grid.cc
	@@ -1,85 +1,85 @@
	/**
	* @file test_grid.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Nov 02 2018
	*
	* @brief Test the grid object
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_grid_dynamic.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	const UInt spatial_dimension = 2;
	akantu::initialize(argc, argv);

	Mesh circle(spatial_dimension);
	circle.read("circle.msh");

	const auto & l = circle.getLocalLowerBounds();
	const auto & u = circle.getLocalUpperBounds();

	Real spacing[spatial_dimension] = {0.2, 0.2};

	Vector<Real> s(spacing, spatial_dimension);

	Vector<Real> c = u;
	c += l;
	c /= 2.;

	SpatialGrid<Element> grid(spatial_dimension, s, c);

	Vector<Real> bary(spatial_dimension);
	Element el;
	el.ghost_type = _not_ghost;

	for (auto & type : circle.elementTypes(spatial_dimension)) {
	UInt nb_element = circle.getNbElement(type);
	el.type = type;

	for (UInt e = 0; e < nb_element; ++e) {
	el.element = e;
	circle.getBarycenter(el, bary);
	grid.insert(el, bary);
	}
	}

	std::cout << grid << std::endl;
	Mesh mesh(spatial_dimension, "save");
	grid.saveAsMesh(mesh);
	mesh.write("grid.msh");

	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_common/test_tensors.cc b/test/test_common/test_tensors.cc
	index 531f862cc..8af7dcaa3 100644
	--- a/test/test_common/test_tensors.cc
	+++ b/test/test_common/test_tensors.cc
	@@ -1,594 +1,594 @@
	/**
	* @file test_tensors.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Tue Feb 05 2019
	*
	* @brief test the tensors types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_array.hh"
	#include "aka_iterators.hh"
	#include "aka_types.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <gtest/gtest.h>
	#include <memory>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	/* -------------------------------------------------------------------------- */
	class TensorConstructorFixture : public ::testing::Test {
	public:
	void SetUp() override {
	for (auto & r : reference) {
	r = rand(); // google-test seeds srand()
	}
	}
	void TearDown() override {}

	template <typename V> void compareToRef(const V & v) {
	for (int i = 0; i < size_; ++i) {
	EXPECT_DOUBLE_EQ(reference[i], v.storage()[i]);
	}
	}

	protected:
	const int size_{24};
	const std::array<int, 2> mat_size{{4, 6}};
	// const std::array<int, 3> tens3_size{{4, 2, 3}};
	std::array<double, 24> reference;
	};

	/* -------------------------------------------------------------------------- */
	class TensorFixture : public TensorConstructorFixture {
	public:
	TensorFixture()
	: vref(reference.data(), size_),
	mref(reference.data(), mat_size[0], mat_size[1]) {}

	protected:
	Vector<double> vref;
	Matrix<double> mref;
	};

	/* -------------------------------------------------------------------------- */
	// Vector ----------------------------------------------------------------------
	TEST_F(TensorConstructorFixture, VectorDefaultConstruct) {
	Vector<double> v;
	EXPECT_EQ(0, v.size());
	EXPECT_EQ(nullptr, v.storage());
	EXPECT_EQ(false, v.isWrapped());
	}

	TEST_F(TensorConstructorFixture, VectorConstruct1) {
	double r = rand();
	Vector<double> v(size_, r);
	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(false, v.isWrapped());

	for (int i = 0; i < size_; ++i) {
	EXPECT_DOUBLE_EQ(r, v(i));
	EXPECT_DOUBLE_EQ(r, v[i]);
	}
	}

	TEST_F(TensorConstructorFixture, VectorConstructWrapped) {
	Vector<double> v(reference.data(), size_);
	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(true, v.isWrapped());

	for (int i = 0; i < size_; ++i) {
	EXPECT_DOUBLE_EQ(reference[i], v(i));
	EXPECT_DOUBLE_EQ(reference[i], v[i]);
	}
	}

	TEST_F(TensorConstructorFixture, VectorConstructInitializer) {
	Vector<double> v{0., 1., 2., 3., 4., 5.};
	EXPECT_EQ(6, v.size());
	EXPECT_EQ(false, v.isWrapped());

	for (int i = 0; i < 6; ++i) {
	EXPECT_DOUBLE_EQ(i, v(i));
	}
	}

	TEST_F(TensorConstructorFixture, VectorConstructCopy1) {
	Vector<double> vref(reference.data(), reference.size());
	Vector<double> v(vref);
	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(false, v.isWrapped());
	compareToRef(v);
	}

	TEST_F(TensorConstructorFixture, VectorConstructCopy2) {
	Vector<double> vref(reference.data(), reference.size());
	Vector<double> v(vref, false);
	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(true, v.isWrapped());
	compareToRef(v);
	}

	TEST_F(TensorConstructorFixture, VectorConstructProxy1) {
	VectorProxy<double> vref(reference.data(), reference.size());
	EXPECT_EQ(size_, vref.size());
	compareToRef(vref);

	Vector<double> v(vref);
	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(true, v.isWrapped());
	compareToRef(v);
	}

	TEST_F(TensorConstructorFixture, VectorConstructProxy2) {
	Vector<double> vref(reference.data(), reference.size());
	VectorProxy<double> v(vref);
	EXPECT_EQ(size_, v.size());
	compareToRef(v);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, VectorEqual) {
	Vector<double> v;

	v = vref;
	compareToRef(v);

	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(false, v.isWrapped());
	}

	TEST_F(TensorFixture, VectorEqualProxy) {
	VectorProxy<double> vref_proxy(vref);
	Vector<double> v;

	v = vref;
	compareToRef(v);

	EXPECT_EQ(size_, v.size());
	EXPECT_EQ(false, v.isWrapped());
	}

	TEST_F(TensorFixture, VectorEqualProxy2) {
	Vector<double> v_store(size_, 0.);
	VectorProxy<double> v(v_store);

	v = vref;
	compareToRef(v);
	compareToRef(v_store);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, VectorSet) {
	Vector<double> v(vref);
	compareToRef(v);

	double r = rand();
	v.set(r);

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(r, v[i]);
	}

	TEST_F(TensorFixture, VectorClear) {
	Vector<double> v(vref);
	compareToRef(v);

	v.zero();

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0, v[i]);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, VectorDivide) {
	Vector<double> v;
	double r = rand();
	v = vref / r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] / r, v[i]);
	}

	TEST_F(TensorFixture, VectorMultiply1) {
	Vector<double> v;
	double r = rand();
	v = vref * r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, v[i]);
	}

	TEST_F(TensorFixture, VectorMultiply2) {
	Vector<double> v;
	double r = rand();
	v = r * vref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, v[i]);
	}

	TEST_F(TensorFixture, VectorAddition) {
	Vector<double> v;
	v = vref + vref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * 2., v[i]);
	}

	TEST_F(TensorFixture, VectorSubstract) {
	Vector<double> v;
	v = vref - vref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0., v[i]);
	}

	TEST_F(TensorFixture, VectorDivideEqual) {
	Vector<double> v(vref);
	double r = rand();
	v /= r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] / r, v[i]);
	}

	TEST_F(TensorFixture, VectorMultiplyEqual1) {
	Vector<double> v(vref);
	double r = rand();
	v *= r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, v[i]);
	}

	TEST_F(TensorFixture, VectorMultiplyEqual2) {
	Vector<double> v(vref);
	v *= v;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * reference[i], v[i]);
	}

	TEST_F(TensorFixture, VectorAdditionEqual) {
	Vector<double> v(vref);
	v += vref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * 2., v[i]);
	}

	TEST_F(TensorFixture, VectorSubstractEqual) {
	Vector<double> v(vref);
	v -= vref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0., v[i]);
	}

	/* -------------------------------------------------------------------------- */
	// Matrix ----------------------------------------------------------------------

	TEST_F(TensorConstructorFixture, MatrixDefaultConstruct) {
	Matrix<double> m;
	EXPECT_EQ(0, m.size());
	EXPECT_EQ(0, m.rows());
	EXPECT_EQ(0, m.cols());
	EXPECT_EQ(nullptr, m.storage());
	EXPECT_EQ(false, m.isWrapped());
	}

	TEST_F(TensorConstructorFixture, MatrixConstruct1) {
	double r = rand();
	Matrix<double> m(mat_size[0], mat_size[1], r);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(false, m.isWrapped());

	for (int i = 0; i < mat_size[0]; ++i) {
	for (int j = 0; j < mat_size[1]; ++j) {
	EXPECT_EQ(r, m(i, j));
	EXPECT_EQ(r, m[i + j * mat_size[0]]);
	}
	}
	}

	TEST_F(TensorConstructorFixture, MatrixConstructWrapped) {
	Matrix<double> m(reference.data(), mat_size[0], mat_size[1]);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(true, m.isWrapped());

	for (int i = 0; i < mat_size[0]; ++i) {
	for (int j = 0; j < mat_size[1]; ++j) {
	EXPECT_DOUBLE_EQ(reference[i + j * mat_size[0]], m(i, j));
	}
	}
	compareToRef(m);
	}

	TEST_F(TensorConstructorFixture, MatrixConstructInitializer) {
	Matrix<double> m{{0., 1., 2.}, {3., 4., 5.}};
	EXPECT_EQ(6, m.size());
	EXPECT_EQ(2, m.rows());
	EXPECT_EQ(3, m.cols());

	EXPECT_EQ(false, m.isWrapped());

	int c = 0;
	for (int i = 0; i < 2; ++i) {
	for (int j = 0; j < 3; ++j, ++c) {
	EXPECT_DOUBLE_EQ(c, m(i, j));
	}
	}
	}

	TEST_F(TensorConstructorFixture, MatrixConstructCopy1) {
	Matrix<double> mref(reference.data(), mat_size[0], mat_size[1]);
	Matrix<double> m(mref);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(false, m.isWrapped());
	compareToRef(m);
	}

	TEST_F(TensorConstructorFixture, MatrixConstructCopy2) {
	Matrix<double> mref(reference.data(), mat_size[0], mat_size[1]);
	Matrix<double> m(mref);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(false, m.isWrapped());
	compareToRef(m);
	}

	TEST_F(TensorConstructorFixture, MatrixConstructProxy1) {
	MatrixProxy<double> mref(reference.data(), mat_size[0], mat_size[1]);
	EXPECT_EQ(size_, mref.size());
	EXPECT_EQ(mat_size[0], mref.size(0));
	EXPECT_EQ(mat_size[1], mref.size(1));
	compareToRef(mref);

	Matrix<double> m(mref);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(true, m.isWrapped());
	compareToRef(m);
	}

	TEST_F(TensorConstructorFixture, MatrixConstructProxy2) {
	Matrix<double> mref(reference.data(), mat_size[0], mat_size[1]);
	MatrixProxy<double> m(mref);
	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.size(0));
	EXPECT_EQ(mat_size[1], m.size(1));
	compareToRef(m);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, MatrixEqual) {
	Matrix<double> m;

	m = mref;
	compareToRef(m);

	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(false, m.isWrapped());
	}

	TEST_F(TensorFixture, MatrixEqualProxy1) {
	MatrixProxy<double> mref_proxy(mref);
	Matrix<double> m;

	m = mref;
	compareToRef(m);

	EXPECT_EQ(size_, m.size());
	EXPECT_EQ(mat_size[0], m.rows());
	EXPECT_EQ(mat_size[1], m.cols());
	EXPECT_EQ(false, m.isWrapped());
	}

	TEST_F(TensorFixture, MatrixEqualProxy2) {
	Matrix<double> m_store(mat_size[0], mat_size[1], 0.);
	MatrixProxy<double> m(m_store);

	m = mref;
	compareToRef(m);
	compareToRef(m_store);
	}

	TEST_F(TensorFixture, MatrixEqualSlice) {
	Matrix<double> m(mat_size[0], mat_size[1], 0.);

	for (unsigned int i = 0; i < m.cols(); ++i)
	m(i) = Vector<Real>(mref(i));

	compareToRef(m);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, MatrixSet) {
	Matrix<double> m(mref);
	compareToRef(m);

	double r = rand();
	m.set(r);

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(r, m[i]);
	}

	TEST_F(TensorFixture, MatrixClear) {
	Matrix<double> m(mref);
	compareToRef(m);

	m.zero();

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0, m[i]);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TensorFixture, MatrixDivide) {
	Matrix<double> m;
	double r = rand();
	m = mref / r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] / r, m[i]);
	}

	TEST_F(TensorFixture, MatrixMultiply1) {
	Matrix<double> m;
	double r = rand();
	m = mref * r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, m[i]);
	}

	TEST_F(TensorFixture, MatrixMultiply2) {
	Matrix<double> m;
	double r = rand();
	m = r * mref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, m[i]);
	}

	TEST_F(TensorFixture, MatrixAddition) {
	Matrix<double> m;
	m = mref + mref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * 2., m[i]);
	}

	TEST_F(TensorFixture, MatrixSubstract) {
	Matrix<double> m;
	m = mref - mref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0., m[i]);
	}

	TEST_F(TensorFixture, MatrixDivideEqual) {
	Matrix<double> m(mref);
	double r = rand();
	m /= r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] / r, m[i]);
	}

	TEST_F(TensorFixture, MatrixMultiplyEqual1) {
	Matrix<double> m(mref);
	double r = rand();
	m *= r;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * r, m[i]);
	}

	TEST_F(TensorFixture, MatrixAdditionEqual) {
	Matrix<double> m(mref);
	m += mref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(reference[i] * 2., m[i]);
	}

	TEST_F(TensorFixture, MatrixSubstractEqual) {
	Matrix<double> m(mref);
	m -= mref;

	for (int i = 0; i < size_; ++i)
	EXPECT_DOUBLE_EQ(0., m[i]);
	}

	TEST_F(TensorFixture, MatrixIterator) {
	Matrix<double> m(mref);

	UInt col_count = 0;
	for (auto && col : m) {
	Vector<Real> col_hand(m.storage() + col_count * m.rows(), m.rows());
	Vector<Real> col_wrap(col);

	auto comp = (col_wrap - col_hand).norm<L_inf>();
	EXPECT_DOUBLE_EQ(0., comp);
	++col_count;
	}
	}

	TEST_F(TensorFixture, MatrixIteratorZip) {
	Matrix<double> m1(mref);
	Matrix<double> m2(mref);

	UInt col_count = 0;
	for (auto && col : zip(m1, m2)) {
	Vector<Real> col1(std::get<0>(col));
	Vector<Real> col2(std::get<1>(col));

	auto comp = (col1 - col2).norm<L_inf>();
	EXPECT_DOUBLE_EQ(0., comp);
	++col_count;
	}
	}

	#if defined(AKANTU_USE_LAPACK)
	TEST_F(TensorFixture, MatrixEigs) {
	Matrix<double> m{{0, 1, 0, 0}, {1., 0, 0, 0}, {0, 1, 0, 1}, {0, 0, 4, 0}};

	Matrix<double> eig_vects(4, 4);
	Vector<double> eigs(4);
	m.eig(eigs, eig_vects);

	Vector<double> eigs_ref{2, 1., -1., -2};
	auto lambda_v = m * eig_vects;

	for (int i = 0; i < 4; ++i) {
	EXPECT_NEAR(eigs_ref(i), eigs(i), 1e-14);
	for (int j = 0; j < 4; ++j) {
	EXPECT_NEAR(lambda_v(i)(j), eigs(i) * eig_vects(i)(j), 1e-14);
	}
	}
	}
	#endif

	/* -------------------------------------------------------------------------- */

	} // namespace
	diff --git a/test/test_common/test_types.cc b/test/test_common/test_types.cc
	index ae0e23e24..09ca3ad93 100644
	--- a/test/test_common/test_types.cc
	+++ b/test/test_common/test_types.cc
	@@ -1,356 +1,356 @@
	/**
	* @file test_types.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 15 2015
	* @date last modification: Wed Jun 14 2017
	*
	* @brief Test the types declared in aka_types.hh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_types.hh"

	#include <iostream>
	#include <sstream>
	#include <stdexcept>

	using namespace akantu;

	const Real tolerance = 1e-15;

	std::string itoa(UInt a) {
	std::stringstream sstr;
	sstr << a;
	return sstr.str();
	}

	UInt testcounter = 0;

	struct wrap_error : std::runtime_error {
	wrap_error(const std::string & msg) : std::runtime_error(msg) {}
	};

	struct size_error : std::runtime_error {
	size_error(const std::string & msg) : std::runtime_error(msg) {}
	};

	struct data_error : std::runtime_error {
	data_error(const std::string & msg, UInt i)
	: std::runtime_error(msg), index(i) {}
	UInt index;
	};

	template <class type>
	void compare_storages_with_ref(const type & a, Real * ref, UInt size, UInt line,
	const std::string & txt) {
	std::cout << std::setw(3) << (testcounter++) << ": " << std::setw(10) << txt
	<< " - " << a << " - wrapped: " << std::boolalpha << a.isWrapped()
	<< std::endl;

	if (a.size() != size)
	throw size_error("the size is not correct " + itoa(a.size()) +
	" instead of " + itoa(size) +
	" [Test at line: " + itoa(line) + "]");

	Real * a_ptr = a.storage();
	for (UInt i = 0; i < a.size(); ++i) {
	if (!((std::abs(a_ptr[i]) < tolerance && std::abs(ref[i]) < tolerance) \|\|
	std::abs((a_ptr[i] - ref[i]) / a_ptr[i]) < tolerance)) {
	std::stringstream txt;
	txt << " std::abs(" << a_ptr[i] << " - " << ref[i]
	<< " [= " << std::abs(a_ptr[i] - ref[i]) << "] ) > " << tolerance;
	throw data_error("storage differs at index " + itoa(i) +
	" [Test at line: " + itoa(line) + "]" + txt.str(),
	i);
	}
	}

	if (a_ptr == ref && !a.isWrapped())
	throw wrap_error(
	"the storage should be wrapped but it is not [Test at line: " +
	itoa(line) + "]");
	if (a_ptr != ref && a.isWrapped())
	throw wrap_error(
	"the storage should not be wrapped but it is [Test at line: " +
	itoa(line) + "]");
	}

	#define COMPARE(a, aref, txt) \
	compare_storages_with_ref(a, aref, sizeof(aref) / sizeof(aref[0]), __LINE__, \
	txt)
	#define COMPARE_STORAGE(a, aref, txt) \
	compare_storages_with_ref(a, aref.storage(), aref.size(), __LINE__, txt)

	const UInt ref_size = 10;

	// clang-format off
	/* -------------------------------------------------------------------------- */
	void test_constructor() {
	std::cout << "=== Test constructors ===" << std::endl;
	Real ref1[ref_size] = { 0. };
	Real ref2[ref_size] = { 1563.58, 1563.58, 1563.58, 1563.58, 1563.58, 1563.58, 1563.58, 1563.58, 1563.58, 1563.58 };
	Real ref3[ref_size] = { 23.1594, 79.6184, 77.9052, 47.9922, 12.8674, 37.1445, 64.8991, 80.3364, 98.4064, 73.7858 };

	std::cout << "-- Vectors: " << std::endl;
	Vector<Real> v0 = { 23.1594, 79.6184, 77.9052, 47.9922, 12.8674, 37.1445, 64.8991, 80.3364, 98.4064, 73.7858 };
	; COMPARE ( v0, ref3, "init_list" );
	Vector<Real> v1(ref_size); COMPARE ( v1, ref1, "normal" );
	Vector<Real> v2(ref_size, 1563.58); COMPARE ( v2, ref2, "defval" );
	Vector<Real> v3(ref3, ref_size); COMPARE ( v3, ref3, "wrapped" );
	Vector<Real> v3dcw(v3); COMPARE ( v3dcw, ref3, "wdeepcopy" );
	Vector<Real> v3scw(v3, false); COMPARE ( v3scw, ref3, "wshallow" );
	Vector<Real> v3dc(v3dcw); COMPARE_STORAGE( v3dc, v3dcw, "deepcopy" );
	Vector<Real> v3sc(v3dcw, false); COMPARE_STORAGE( v3sc, v3dcw, "shallow" );
	VectorProxy<Real> vp1(ref3, ref_size);
	Vector<Real> v4(vp1); COMPARE ( v4, ref3, "proxyptr" );
	VectorProxy<Real> vp2(v3dcw);
	Vector<Real> v5(vp2); COMPARE_STORAGE( v5, v3dcw, "proxyvdc" );
	VectorProxy<Real> vp3(v3scw);
	Vector<Real> v6(vp3); COMPARE ( v6, ref3, "proxyvsc" );

	/* ------------------------------------------------------------------------ */
	std::cout << "-- Matrices: " << std::endl;
	Matrix<Real> m0 = {{23.1594, 37.1445},
	{79.6184, 64.8991},
	{77.9052, 80.3364},
	{47.9922, 98.4064},
	{12.8674, 73.7858}};
	COMPARE ( m0, ref3 , "init_list" );
	Matrix<Real> m1(5, 2); COMPARE ( m1, ref1 , "normal" );
	Matrix<Real> m1t(2, 5); COMPARE ( m1t, ref1 , "tnormal" );
	Matrix<Real> m2(5, 2, 1563.58); COMPARE ( m2, ref2 , "defval" );
	Matrix<Real> m2t(2, 5, 1563.58); COMPARE ( m2t, ref2 , "tdefval" );
	Matrix<Real> m3(ref3, 5, 2); COMPARE ( m3, ref3 , "wrapped" );
	Matrix<Real> m3t(ref3, 2, 5); COMPARE ( m3t, ref3 , "twrapped" );
	Matrix<Real> m3dcw(m3); COMPARE ( m3dcw, ref3 , "wdeepcopy" );
	Matrix<Real> m3scw(m3, false); COMPARE ( m3scw, ref3 , "wshallow" );
	Matrix<Real> m3dc(m3dcw); COMPARE_STORAGE( m3dc, m3dcw , "deepcopy" );
	Matrix<Real> m3sc(m3dcw, false); COMPARE_STORAGE( m3sc, m3dcw , "shallow" );
	Matrix<Real> m3tdcw(m3t); COMPARE (m3tdcw, ref3 , "twdeepcopy");
	Matrix<Real> m3tscw(m3t, false); COMPARE (m3tscw, ref3 , "twshallow" );
	Matrix<Real> m3tdc(m3tdcw); COMPARE_STORAGE( m3tdc, m3tdcw, "tdeepcopy" );
	Matrix<Real> m3tsc(m3tdcw, false); COMPARE_STORAGE( m3tsc, m3tdcw, "tshallow" );
	MatrixProxy<Real> mp1(ref3, 5, 2);
	Matrix<Real> m4(mp1); COMPARE ( m4, ref3, "proxyptr" );
	MatrixProxy<Real> mp2(m3dcw);
	Matrix<Real> m5(mp2); COMPARE_STORAGE( m5, m3dcw, "proxyvdc" );
	MatrixProxy<Real> mp3(m3scw);
	Matrix<Real> m6(mp3); COMPARE ( m6, ref3, "proxyvsc" );
	MatrixProxy<Real> mp1t(ref3, 2, 5);
	Matrix<Real> m4t(mp1t); COMPARE ( m4t, ref3, "tproxyptr" );
	MatrixProxy<Real> mp2t(m3tdcw);
	Matrix<Real> m5t(mp2t); COMPARE_STORAGE( m5t, m3tdcw, "tproxyvdc" );
	MatrixProxy<Real> mp3t(m3tscw);
	Matrix<Real> m6t(mp3t); COMPARE ( m6t, ref3, "tproxyvsc" );
	}

	/* -------------------------------------------------------------------------- */
	void test_equal_and_accessors() {
	std::cout << "=== Test operator=() ===" << std::endl;
	Real ref[ref_size] = { 23.1594, 79.6184, 77.9052, 47.9922, 12.8674, 37.1445, 64.8991, 80.3364, 98.4064, 73.7858 };
	Real mod[ref_size] = { 98.7982, 72.1227, 19.7815, 57.6722, 47.1088, 14.9865, 13.3171, 62.7973, 33.9493, 98.3052 };

	std::cout << "-- Vectors: " << std::endl;
	Vector<Real> v (ref, ref_size);
	Vector<Real> vm(mod, ref_size);
	Vector<Real> vref1(v);
	Vector<Real> v1;
	v1 = vref1; COMPARE_STORAGE(v1, vref1, "simple=" );
	for (UInt i = 0; i < ref_size; ++i) v1 (i) = mod[i]; COMPARE (v1, mod, "s_acces" );
	COMPARE_STORAGE(vref1, v, "refcheck1");

	Vector<Real> v2 = vref1; COMPARE_STORAGE(v2, vref1, "construc=");
	for (UInt i = 0; i < ref_size; ++i) v2 (i) = mod[i]; COMPARE (v2, mod, "c_acces" );
	COMPARE_STORAGE(vref1, v, "refcheck2");

	Vector<Real> vref2(vref1, false);
	Vector<Real> v1w;
	v1w = vref2; COMPARE_STORAGE(v1w, vref1, "w_simple=" );
	for (UInt i = 0; i < ref_size; ++i) v1w(i) = mod[i]; COMPARE (v1w, mod, "ws_acces" );
	try { COMPARE(vref2, ref, "refcheck3"); } catch(wrap_error &) {}

	Vector<Real> v2w = vref2; COMPARE_STORAGE(v2w, vref1, "w_constru=");
	for (UInt i = 0; i < ref_size; ++i) v2w(i) = mod[i]; COMPARE (v2w, mod, "wc_acces" );
	try { COMPARE(vref2, ref, "refcheck4"); } catch(wrap_error &) {}

	VectorProxy<Real> vp1(vref1);
	Vector<Real> v3;
	v3 = vp1; COMPARE_STORAGE(v3, vref1, "p_simple=" );
	for (UInt i = 0; i < ref_size; ++i) v3(i) = mod[i]; COMPARE (v3, mod, "ps_acces" );
	COMPARE_STORAGE(vref1, v, "refcheck5");

	Vector<Real> v4 = vp1; COMPARE_STORAGE(v4, vref1, "p_constru=");
	for (UInt i = 0; i < ref_size; ++i) v4(i) = mod[i];
	try { COMPARE(v4, mod, "pc_acces" ); } catch (wrap_error &) {}

	COMPARE(vref1, mod, "refcheck6");
	try { COMPARE(vref2, mod, "refcheck7"); } catch(wrap_error &) {}

	vref2 = v;

	VectorProxy<Real> vp2(vref2);
	Vector<Real> v3w;
	v3w = vp2; COMPARE_STORAGE(v3w, vref1, "pw_simpl=");
	for (UInt i = 0; i < ref_size; ++i) v3w(i) = mod[i]; COMPARE (v3w, mod, "pws_acces");
	try { COMPARE(vref2, ref, "refcheck8"); } catch(wrap_error &) {}

	Vector<Real> v4w = vp2; COMPARE_STORAGE( v4w, vref1, "pw_constr=");
	for (UInt i = 0; i < ref_size; ++i) v4w(i) = mod[i];
	try { COMPARE(v4w, mod, "pwc_acces"); } catch (wrap_error &) {}
	COMPARE_STORAGE(v4w, vref2, "refcheck9");
	try { COMPARE(vref2, mod, "refcheck10"); } catch(wrap_error &) {}

	vref1 = v;

	Real store[ref_size] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
	Vector<Real> vs(store, 10);
	VectorProxy<Real> vp3(vs);
	vp3 = vref1;
	try { COMPARE(vref1, store, "vp_equal_v"); } catch(wrap_error &) {}

	// Vector<Real> vref3(vm);
	// VectorProxy<Real> vp4 = vref3;
	// vp3 = vp4;
	// try { COMPARE(vs, mod, "vp_equal_vp"); } catch(wrap_error &) {}

	/* ------------------------------------------------------------------------ */
	std::cout << "-- Matrices: " << std::endl;

	Matrix<Real> m (ref, 5, 2);
	Matrix<Real> mt(ref, 2, 5);

	Matrix<Real> m1 (5, 2);
	Matrix<Real> m1t(2, 5);

	for (UInt i = 0; i < 5; ++i) {
	for (UInt j = 0; j < 2; ++j) {
	m1(i, j) = ref[i + j*5];
	m1t(j, i) = ref[j + i*2];
	}
	}
	COMPARE_STORAGE( m1, m, "access" );
	COMPARE_STORAGE(m1t, m, "t_access");

	Matrix<Real> mm (mod, 5, 2);
	Matrix<Real> mmt(mod, 2, 5);

	Matrix<Real> m2(m);
	Matrix<Real> m3(m);
	for (UInt j = 0; j < 2; ++j) {
	Vector<Real> v = m2(j);
	for (UInt i = 0; i < 5; ++i)
	v(i) = mm(i, j);
	}
	COMPARE_STORAGE(m2, mm, "slicing");

	for (UInt j = 0; j < 2; ++j)
	m3(j) = mm(j);

	COMPARE_STORAGE(m3, mm, "slic_slic");
	COMPARE(mm, mod, "refcheck");


	Real mod_1[ref_size] = { 98.7982, 72.1227, 197.815, 57.6722, 47.1088, 14.9865, 13.3171, 627.973, 33.9493, 98.3052 };

	Matrix<Real> m4 (mm);
	m4 (2,0) = 197.815;
	m4 (2,1) = 627.973;
	COMPARE(m4, mod_1, "partial");

	Matrix<Real> m4t(mmt);
	m4t(0,1) = 197.815;
	m4t(1,3) = 627.973;
	COMPARE(m4t, mod_1, "t_partial");
	}

	/* -------------------------------------------------------------------------- */
	void test_simple_operators() {
	std::cout << "=== Test simple operation ===" << std::endl;
	Real ref[ref_size] = { 23.1594, 79.6184, 77.9052, 47.9922, 12.8674, 37.1445, 64.8991, 80.3364, 98.4064, 73.7858 };
	Real mod[ref_size] = { 98.7982, 72.1227, 19.7815, 57.6722, 47.1088, 14.9865, 13.3171, 62.7973, 33.9493, 98.3052 };

	Real ref_div[ref_size] = { 1.163905920192984e+00, 4.001326766509196e+00,
	3.915227661071464e+00, 2.411910744798472e+00,
	6.466680068348578e-01, 1.866745401547894e+00,
	3.261589104432606e+00, 4.037410795054780e+00,
	4.945542265554328e+00, 3.708201829329581e+00 };
	Real ref_tim[ref_size] = { 4.608257412000000e+02, 1.584246923200000e+03,
	1.550157669600000e+03, 9.549487955999999e+02,
	2.560355252000000e+02, 7.391012610000000e+02,
	1.291362291800000e+03, 1.598533687200000e+03,
	1.958090547200000e+03, 1.468189848400000e+03 };
	Real ref_p_mod[ref_size] = { 1.219576000000000e+02, 1.517411000000000e+02,
	9.768670000000000e+01, 1.056644000000000e+02,
	5.997620000000001e+01, 5.213100000000000e+01,
	7.821620000000000e+01, 1.431337000000000e+02,
	1.323557000000000e+02, 1.720910000000000e+02 };
	Real ref_m_mod[ref_size] = { -7.563879999999999e+01, 7.495699999999999e+00,
	5.812369999999999e+01, -9.680000000000000e+00,
	-3.424140000000000e+01, 2.215800000000000e+01,
	5.158200000000001e+01, 1.753910000000000e+01,
	6.445710000000000e+01, -2.451940000000000e+01 };
	std::cout << "-- Vectors: " << std::endl;
	Vector<Real> v (ref, ref_size);
	Vector<Real> vm(mod, ref_size);
	Vector<Real> vref(v);
	Vector<Real> vmod(vm);

	Vector<Real> v1 = vref / 19.898; COMPARE(v1, ref_div, "v / s" );
	Vector<Real> v2 = vref * 19.898; COMPARE(v2, ref_tim, "v * s" );
	Vector<Real> v3 = 19.898 * vref; COMPARE(v3, ref_tim, "s * v" );
	Vector<Real> v4 = vref + vmod; COMPARE(v4, ref_p_mod, "v1 + v2" );
	Vector<Real> v5 = vref - vmod; COMPARE(v5, ref_m_mod, "v1 - v2" );
	Vector<Real> v6 = vref; v6 = 19.898; COMPARE(v6, ref_tim, "v = s" );
	Vector<Real> v7 = vref; v7 /= 19.898; COMPARE(v7, ref_div, "v /= s" );
	Vector<Real> v8 = vref; v8 += vmod; COMPARE(v8, ref_p_mod, "v1 += v2");
	Vector<Real> v9 = vref; v9 -= vmod; COMPARE(v9, ref_m_mod, "v1 -= v2");

	std::cout << "-- Matrices: " << std::endl;
	Matrix<Real> m (ref, 5, 2);
	Matrix<Real> mm(mod, 5, 2);
	Matrix<Real> mref(m);
	Matrix<Real> mmod(mm);

	Matrix<Real> m1 = mref / 19.898; COMPARE(m1, ref_div, "m / s" );
	Matrix<Real> m2 = mref * 19.898; COMPARE(m2, ref_tim, "m * s" );
	Matrix<Real> m3 = 19.898 * mref; COMPARE(m3, ref_tim, "s * m" );
	Matrix<Real> m4 = mref + mmod; COMPARE(m4, ref_p_mod, "m1 + m2" );
	Matrix<Real> m5 = mref - mmod; COMPARE(m5, ref_m_mod, "m1 - m2" );
	Matrix<Real> m6 = mref; m6 = 19.898; COMPARE(m6, ref_tim, "m = s" );
	Matrix<Real> m7 = mref; m7 /= 19.898; COMPARE(m7, ref_div, "m /= s" );
	Matrix<Real> m8 = mref; m8 += mmod; COMPARE(m8, ref_p_mod, "m1 += m2");
	Matrix<Real> m9 = mref; m9 -= mmod; COMPARE(m9, ref_m_mod, "m1 -= m2");
	}
	// clang-format on

	/* -------------------------------------------------------------------------- */
	int main() {
	test_constructor();
	test_equal_and_accessors();
	test_simple_operators();

	return 0;
	}
	diff --git a/test/test_common/test_voigt_helper.cc b/test/test_common/test_voigt_helper.cc
	index e9445d361..a587b1927 100644
	--- a/test/test_common/test_voigt_helper.cc
	+++ b/test/test_common/test_voigt_helper.cc
	@@ -1,164 +1,164 @@
	/**
	* @file test_voigt_helper.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 27 2019
	* @date last modification: Wed Nov 18 2020
	*
	* @brief unit tests for VoigtHelper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <aka_voigthelper.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	template <class Dim_v> class VoigtHelperFixture : public ::testing::Test {
	protected:
	using voigt_h = VoigtHelper<Dim_v::value>;
	constexpr static UInt dim = Dim_v::value;

	VoigtHelperFixture() {
	switch (this->dim) {
	case 1: {
	indices.push_back({0, 0});
	matrix = Matrix<Real>{{10}};
	vector = Vector<Real>{10};
	vector_factor = Vector<Real>{10};
	break;
	}
	case 2: {
	indices.push_back({0, 0});
	indices.push_back({1, 1});
	indices.push_back({0, 1});

	matrix = Matrix<Real>{{10, 33}, {0, 56}};
	vector = Vector<Real>{10, 56, 33};
	vector_factor = Vector<Real>{10, 56, 2 * 33};
	break;
	}
	case 3: {
	indices.push_back({0, 0});
	indices.push_back({1, 1});
	indices.push_back({2, 2});
	indices.push_back({1, 2});
	indices.push_back({0, 2});
	indices.push_back({0, 1});

	matrix = Matrix<Real>{{10, 33, 20}, {0, 56, 27}, {0, 0, 98}};
	vector = Vector<Real>{10, 56, 98, 27, 20, 33};
	vector_factor = Vector<Real>{10, 56, 98, 2 * 27, 2 * 20, 2 * 33};
	break;
	}
	}
	}

	void SetUp() override {}

	std::vector<std::pair<UInt, UInt>> indices;
	Matrix<Real> matrix;
	Vector<Real> vector;
	Vector<Real> vector_factor;
	};

	template <UInt dim>
	using spatial_dimension_t = std::integral_constant<UInt, dim>;

	using TestTypes =
	::testing::Types<spatial_dimension_t<1>, spatial_dimension_t<2>,
	spatial_dimension_t<3>>;
	TYPED_TEST_SUITE(VoigtHelperFixture, TestTypes, );

	TYPED_TEST(VoigtHelperFixture, Size) {
	using voigt_h = typename TestFixture::voigt_h;
	switch (this->dim) {
	case 1:
	EXPECT_EQ(voigt_h::size, 1);
	break;
	case 2:
	EXPECT_EQ(voigt_h::size, 3);
	break;
	case 3:
	EXPECT_EQ(voigt_h::size, 6);
	break;
	}
	}

	TYPED_TEST(VoigtHelperFixture, Indicies) {
	using voigt_h = typename TestFixture::voigt_h;

	for (UInt I = 0; I < voigt_h::size; ++I) {
	EXPECT_EQ(this->indices[I].first, voigt_h::vec[I][0]);
	EXPECT_EQ(this->indices[I].second, voigt_h::vec[I][1]);
	}
	}

	TYPED_TEST(VoigtHelperFixture, Factors) {
	using voigt_h = typename TestFixture::voigt_h;
	for (UInt I = 0; I < voigt_h::size; ++I) {
	if (I < this->dim) {
	EXPECT_EQ(voigt_h::factors[I], 1);
	} else {
	EXPECT_EQ(voigt_h::factors[I], 2);
	}
	}
	}

	TYPED_TEST(VoigtHelperFixture, MatrixToVoight) {
	using voigt_h = typename TestFixture::voigt_h;

	auto voigt = voigt_h::matrixToVoigt(this->matrix);

	for (UInt I = 0; I < voigt_h::size; ++I) {
	EXPECT_EQ(voigt(I), this->vector(I));
	}
	}

	TYPED_TEST(VoigtHelperFixture, MatrixToVoightFactors) {
	using voigt_h = typename TestFixture::voigt_h;

	auto voigt = voigt_h::matrixToVoigtWithFactors(this->matrix);

	for (UInt I = 0; I < voigt_h::size; ++I) {
	EXPECT_EQ(voigt(I), this->vector_factor(I));
	}
	}

	TYPED_TEST(VoigtHelperFixture, VoightToMatrix) {
	using voigt_h = typename TestFixture::voigt_h;

	auto matrix = voigt_h::voigtToMatrix(this->vector);

	for (UInt i = 0; i < this->dim; ++i) {
	for (UInt j = 0; j < this->dim; ++j) {
	EXPECT_EQ(matrix(i, j), this->matrix(std::min(i, j), std::max(i, j)));
	}
	}
	}
	diff --git a/test/test_fe_engine/test_facet_element_mapping.cc b/test/test_fe_engine/test_facet_element_mapping.cc
	index 5864f3be9..88c976dcd 100644
	--- a/test/test_fe_engine/test_facet_element_mapping.cc
	+++ b/test/test_fe_engine/test_facet_element_mapping.cc
	@@ -1,128 +1,128 @@
	/**
	* @file test_facet_element_mapping.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Nov 02 2018
	*
	* @brief Test of the MeshData class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_error.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	#include <string>

	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	using namespace std;

	int main(int argc, char * argv[]) {
	// Testing the subelement-to-element mappings
	UInt spatial_dimension(3);

	akantu::initialize(argc, argv);

	Mesh mesh(spatial_dimension, "my_mesh");
	mesh.read("./cube_physical_names.msh");

	typedef Array<std::vector<Element>> ElemToSubelemMapping;
	typedef Array<Element> SubelemToElemMapping;

	std::cout << "ELEMENT-SUBELEMENT MAPPING:" << std::endl;

	for (auto ghost_type : ghost_types) {
	std::cout << " "
	<< "Ghost type: " << ghost_type << std::endl;
	for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {

	const SubelemToElemMapping & subelement_to_element =
	mesh.getSubelementToElement(type, ghost_type);
	std::cout << " "
	<< " "
	<< "Element type: " << type << std::endl;

	std::cout << " "
	<< " "
	<< " "
	<< "subelement_to_element:" << std::endl;
	subelement_to_element.printself(std::cout, 8);

	for (UInt i(0); i < subelement_to_element.size(); ++i) {
	std::cout << " ";
	for (UInt j(0); j < mesh.getNbFacetsPerElement(type); ++j) {
	if (subelement_to_element(i, j) != ElementNull) {
	std::cout << subelement_to_element(i, j);
	std::cout << ", ";
	} else {
	std::cout << "ElementNull"
	<< ", ";
	}
	}
	std::cout << "for element " << i << std::endl;
	}
	}

	for (auto & type : mesh.elementTypes(spatial_dimension - 1, ghost_type)) {
	const ElemToSubelemMapping & element_to_subelement =
	mesh.getElementToSubelement(type, ghost_type);
	std::cout << " "
	<< " "
	<< "Element type: " << type << std::endl;

	std::cout << " "
	<< " "
	<< " "
	<< "element_to_subelement:" << std::endl;
	element_to_subelement.printself(std::cout, 8);

	for (UInt i(0); i < element_to_subelement.size(); ++i) {
	const std::vector<Element> & vec = element_to_subelement(i);
	std::cout << " ";
	std::cout << "item " << i << ": [ ";
	if (vec.size() > 0) {
	for (UInt j(0); j < vec.size(); ++j) {
	if (vec[j] != ElementNull) {
	std::cout << vec[j] << ", ";
	} else {
	std::cout << "ElementNull"
	<< ", ";
	}
	}
	} else {
	std::cout << "empty, ";
	}
	std::cout << "]"
	<< ", " << std::endl;
	}
	std::cout << std::endl;
	}
	}

	return 0;
	}
	diff --git a/test/test_fe_engine/test_fe_engine_fixture.hh b/test/test_fe_engine/test_fe_engine_fixture.hh
	index c58211439..07378f5b9 100644
	--- a/test/test_fe_engine/test_fe_engine_fixture.hh
	+++ b/test/test_fe_engine/test_fe_engine_fixture.hh
	@@ -1,114 +1,114 @@
	/**
	* @file test_fe_engine_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Fixture for feengine tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <element_class.hh>
	#include <fe_engine.hh>
	#include <integrator_gauss.hh>
	#include <shape_lagrange.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_FE_ENGINE_FIXTURE_HH_
	#define AKANTU_TEST_FE_ENGINE_FIXTURE_HH_

	using namespace akantu;

	/// Generic class for FEEngine tests
	template <typename type_, template <ElementKind> class shape_t,
	ElementKind kind = _ek_regular>
	class TestFEMBaseFixture : public ::testing::Test {
	public:
	static constexpr const ElementType type = type_::value;
	static constexpr const size_t dim = ElementClass<type>::getSpatialDimension();
	using FEM = FEEngineTemplate<IntegratorGauss, shape_t, kind>;

	/// Setup reads mesh corresponding to element type and initializes an FEEngine
	void SetUp() override {
	const auto dim = this->dim;
	mesh = std::make_unique<Mesh>(dim);

	std::stringstream meshfilename;
	meshfilename << type << ".msh";
	this->readMesh(meshfilename.str());

	lower = mesh->getLowerBounds();
	upper = mesh->getUpperBounds();

	nb_element = this->mesh->getNbElement(type);

	fem = std::make_unique<FEM>(*mesh, dim, "my_fem");
	nb_quadrature_points_total =
	GaussIntegrationElement<type>::getNbQuadraturePoints() * nb_element;

	SCOPED_TRACE(std::to_string(type));
	}

	void TearDown() override {
	fem.reset(nullptr);
	mesh.reset(nullptr);
	}

	/// Should be reimplemented if further treatment of the mesh is needed
	virtual void readMesh(std::string file_name) { mesh->read(file_name); }

	protected:
	std::unique_ptr<FEM> fem;
	std::unique_ptr<Mesh> mesh;
	UInt nb_element;
	UInt nb_quadrature_points_total;
	Vector<Real> lower;
	Vector<Real> upper;
	};

	template <typename type_, template <ElementKind> class shape_t,
	ElementKind kind>
	constexpr const ElementType TestFEMBaseFixture<type_, shape_t, kind>::type;

	template <typename type_, template <ElementKind> class shape_t,
	ElementKind kind>
	constexpr const size_t TestFEMBaseFixture<type_, shape_t, kind>::dim;

	/* -------------------------------------------------------------------------- */
	/// Base class for test with Lagrange FEEngine and regular elements
	template <typename type_>
	using TestFEMFixture = TestFEMBaseFixture<type_, ShapeLagrange, _ek_regular>;

	/* -------------------------------------------------------------------------- */

	using fe_engine_types = gtest_list_t<TestElementTypes>;

	TYPED_TEST_SUITE(TestFEMFixture, fe_engine_types, );

	#endif /* AKANTU_TEST_FE_ENGINE_FIXTURE_HH_ */
	diff --git a/test/test_fe_engine/test_fe_engine_gauss_integration.cc b/test/test_fe_engine/test_fe_engine_gauss_integration.cc
	index bf89c1160..0be08610b 100644
	--- a/test/test_fe_engine/test_fe_engine_gauss_integration.cc
	+++ b/test/test_fe_engine/test_fe_engine_gauss_integration.cc
	@@ -1,155 +1,156 @@
	/**
	* @file test_fe_engine_gauss_integration.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 24 2016
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test integration on elements, this test consider that mesh is a cube
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	namespace {
	/* -------------------------------------------------------------------------- */
	template <size_t t> using degree_t = std::integral_constant<size_t, t>;

	/* -------------------------------------------------------------------------- */
	using TestDegreeTypes = std::tuple<degree_t<0>, degree_t<1>, degree_t<2>,
	degree_t<3>, degree_t<4>, degree_t<5>>;

	std::array<Polynomial<5>, 3> global_polys{
	{{0.40062394, 0.13703225, 0.51731446, 0.87830084, 0.5410543, 0.71842292},
	{0.41861835, 0.11080576, 0.49874043, 0.49077504, 0.85073835, 0.66259755},
	{0.92620845, 0.7503478, 0.62962232, 0.31662719, 0.64069644, 0.30878135}}};

	template <typename T>
	class TestGaussIntegrationFixture
	: public TestFEMFixture<std::tuple_element_t<0, T>> {
	protected:
	using parent = TestFEMFixture<std::tuple_element_t<0, T>>;
	static constexpr size_t degree{std::tuple_element_t<1, T>::value};

	public:
	TestGaussIntegrationFixture() : integration_points_pos(0, parent::dim) {}

	void SetUp() override {
	parent::SetUp();
	this->fem->initShapeFunctions();

	auto integration_points =
	this->fem->getIntegrator().template getIntegrationPoints <
	parent::type,
	degree == 0 ? 1 : degree > ();

	nb_integration_points = integration_points.cols();

	auto shapes_size = ElementClass<parent::type>::getShapeSize();
	Array<Real> shapes(0, shapes_size);
	this->fem->getShapeFunctions()
	.template computeShapesOnIntegrationPoints<parent::type>(
	this->mesh->getNodes(), integration_points, shapes, _not_ghost);

	auto vect_size = this->nb_integration_points * this->nb_element;
	integration_points_pos.resize(vect_size);
	this->fem->getShapeFunctions()
	.template interpolateOnIntegrationPoints<parent::type>(
	this->mesh->getNodes(), integration_points_pos, this->dim, shapes);

	for (size_t d = 0; d < this->dim; ++d) {
	polys[d] = global_polys[d].extract(degree);
	}
	}

	void testIntegrate() {
	std::stringstream sstr;
	sstr << this->type << ":" << this->degree;
	SCOPED_TRACE(sstr.str().c_str());

	auto vect_size = this->nb_integration_points * this->nb_element;
	Array<Real> polynomial(vect_size);
	size_t dim = parent::dim;

	for (size_t d = 0; d < dim; ++d) {
	auto poly = this->polys[d];
	for (auto && pair :
	zip(polynomial, make_view(this->integration_points_pos, dim))) {
	auto && p = std::get<0>(pair);
	auto & x = std::get<1>(pair);
	p = poly(x(d));
	}

	auto res =
	this->fem->getIntegrator()
	.template integrate<parent::type, (degree == 0 ? 1 : degree)>(
	polynomial);
	auto expect = poly.integrate(this->lower(d), this->upper(d));

	for (size_t o = 0; o < dim; ++o) {
	if (o == d)
	continue;
	expect *= this->upper(d) - this->lower(d);
	}

	EXPECT_NEAR(expect, res, 5e-14);
	}
	}

	protected:
	UInt nb_integration_points;
	std::array<Array<Real>, parent::dim> polynomial;
	Array<Real> integration_points_pos;
	std::array<Polynomial<5>, 3> polys;
	};

	template <typename T> constexpr size_t TestGaussIntegrationFixture<T>::degree;

	/* -------------------------------------------------------------------------- */
	/* Tests */
	/* -------------------------------------------------------------------------- */
	TYPED_TEST_SUITE_P(TestGaussIntegrationFixture);

	TYPED_TEST_P(TestGaussIntegrationFixture, ArbitraryOrder) {
	this->testIntegrate();
	}

	REGISTER_TYPED_TEST_SUITE_P(TestGaussIntegrationFixture, ArbitraryOrder);

	using TestTypes = gtest_list_t<
	tuple_split_t<50, cross_product_t<TestElementTypes, TestDegreeTypes>>>;

	-INSTANTIATE_TYPED_TEST_SUITE_P(Split1, TestGaussIntegrationFixture, TestTypes, );
	+INSTANTIATE_TYPED_TEST_SUITE_P(Split1, TestGaussIntegrationFixture,
	+ TestTypes, );

	using TestTypesTail = gtest_list_t<
	tuple_split_tail_t<50, cross_product_t<TestElementTypes, TestDegreeTypes>>>;

	INSTANTIATE_TYPED_TEST_SUITE_P(Split2, TestGaussIntegrationFixture,
	TestTypesTail, );
	} // namespace
	diff --git a/test/test_fe_engine/test_fe_engine_precomputation.cc b/test/test_fe_engine/test_fe_engine_precomputation.cc
	index b1f5f2fe8..0778ecb98 100644
	--- a/test/test_fe_engine/test_fe_engine_precomputation.cc
	+++ b/test/test_fe_engine/test_fe_engine_precomputation.cc
	@@ -1,115 +1,115 @@
	/**
	* @file test_fe_engine_precomputation.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_aka_array.hh"
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <pybind11/embed.h>
	#include <pybind11/numpy.h>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	namespace py = pybind11;
	using namespace py::literals;

	template <class T> decltype(auto) make_proxy(Array<T> & array) {
	return detail::ArrayProxy<T>(array);
	}

	template <typename type_>
	class TestFEMPyFixture : public TestFEMFixture<type_> {
	using parent = TestFEMFixture<type_>;

	public:
	void SetUp() override {
	parent::SetUp();

	const auto & connectivities = this->mesh->getConnectivity(this->type);
	const auto & nodes = this->mesh->getNodes().begin(this->dim);
	coordinates = std::make_unique<Array<Real>>(
	connectivities.size(), connectivities.getNbComponent() * this->dim);

	for (auto && tuple :
	zip(make_view(connectivities, connectivities.getNbComponent()),
	make_view(*coordinates, this->dim,
	connectivities.getNbComponent()))) {
	const auto & conn = std::get<0>(tuple);
	const auto & X = std::get<1>(tuple);
	for (auto s : arange(conn.size())) {
	Vector<Real>(X(s)) = Vector<Real>(nodes[conn(s)]);
	}
	}
	}

	void TearDown() override {
	parent::TearDown();
	coordinates.reset(nullptr);
	}

	protected:
	std::unique_ptr<Array<Real>> coordinates;
	};

	TYPED_TEST_SUITE(TestFEMPyFixture, fe_engine_types, );

	TYPED_TEST(TestFEMPyFixture, Precompute) {
	SCOPED_TRACE(std::to_string(this->type));
	this->fem->initShapeFunctions();
	const auto & N = this->fem->getShapeFunctions().getShapes(this->type);
	const auto & B =
	this->fem->getShapeFunctions().getShapesDerivatives(this->type);
	const auto & j = this->fem->getIntegrator().getJacobians(this->type);

	// Array<Real> ref_N(this->nb_quadrature_points_total, N.getNbComponent());
	// Array<Real> ref_B(this->nb_quadrature_points_total, B.getNbComponent());
	Array<Real> ref_j(this->nb_quadrature_points_total, j.getNbComponent());
	auto ref_N(N);
	auto ref_B(B);
	py::module py_engine = py::module::import("py_engine");
	auto py_shape = py_engine.attr("Shapes")(py::str(std::to_string(this->type)));
	auto kwargs = py::dict("N"_a = ref_N, "B"_a = ref_B, "j"_a = ref_j,
	"X"_a = *this->coordinates,
	"Q"_a = this->fem->getIntegrationPoints(this->type));

	auto ret = py_shape.attr("precompute")(**kwargs);
	auto check = [&](auto & ref_A, auto & A, const auto & id) {
	SCOPED_TRACE(std::to_string(this->type) + " " + id);
	for (auto && n : zip(make_view(ref_A, ref_A.getNbComponent()),
	make_view(A, A.getNbComponent()))) {
	auto diff = (std::get<0>(n) - std::get<1>(n)).template norm<L_inf>();
	EXPECT_NEAR(0., diff, 1e-10);
	}
	};
	check(ref_N, N, "N");
	check(ref_B, B, "B");
	check(ref_j, j, "j");
	}
	diff --git a/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_2.cc b/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_2.cc
	index c48285fed..d355b65a9 100644
	--- a/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_2.cc
	+++ b/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_2.cc
	@@ -1,154 +1,154 @@
	/**
	* @file test_fe_engine_precomputation_bernoulli_2.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Jan 25 2018
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "integrator_gauss.hh"
	#include "shape_structural.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <functional>
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	Matrix<Real> globalToLocalRotation(Real theta) {
	// clang-format off
	return {{ std::cos(theta), std::sin(theta), 0},
	{-std::sin(theta), std::cos(theta), 0},
	{ 0, 0, 1}};
	// clang-format on
	}

	Vector<Real> axialReference(Real xq) {
	return {(1. - xq) / 2, 0, 0, (1. + xq) / 2, 0, 0};
	}

	Vector<Real> bendingReference(Real xq) {
	return {0,
	1. / 4. * Math::pow<2>(xq - 1) * (xq + 2),
	1. / 4. * Math::pow<2>(xq - 1) * (xq + 1),
	0,
	1. / 4. * Math::pow<2>(xq + 1) * (2 - xq),
	1. / 4. * Math::pow<2>(xq + 1) * (xq - 1)};
	}

	Vector<Real> bendingRotationReference(Real xq) {
	return {0, 3. / 4. * (xq * xq - 1), 1. / 4. * (3 * xq * xq - 2 * xq - 1),
	0, 3. / 4. * (1 - xq * xq), 1. / 4. * (3 * xq * xq + 2 * xq - 1)};
	}

	bool testBending(const Array<Real> & shape_functions, UInt shape_line_index,
	std::function<Vector<Real>(Real)> reference) {
	Real xq = -1. / std::sqrt(3.);

	// Testing values for bending rotations shapes on quadrature points
	for (auto && N : make_view(shape_functions, 3, 6)) {
	auto Nt = N.transpose();
	Vector<Real> N_bending = Nt(shape_line_index);
	auto bending_reference = reference(xq);
	if (!Math::are_vector_equal(6, N_bending.storage(),
	bending_reference.storage()))
	return false;
	xq *= -1;
	}

	std::cout.flush();
	return true;
	}

	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);
	// debug::setDebugLevel(dblTest);

	constexpr ElementType type = _bernoulli_beam_2;
	UInt dim = ElementClass<type>::getSpatialDimension();

	Mesh mesh(dim);
	// creating nodes
	Vector<Real> node = {0, 0};
	mesh.getNodes().push_back(node);
	node = {3. / 5., 4. / 5.};
	mesh.getNodes().push_back(node);
	node = {2 * 3. / 5., 0};
	mesh.getNodes().push_back(node);

	mesh.addConnectivityType(type);
	auto & connectivity = mesh.getConnectivity(type);

	// creating elements
	Vector<UInt> elem = {0, 1};
	connectivity.push_back(elem);
	elem = {1, 2};
	connectivity.push_back(elem);
	elem = {0, 2};
	connectivity.push_back(elem);

	using FE = FEEngineTemplate<IntegratorGauss, ShapeStructural, _ek_structural>;
	using ShapeStruct = ShapeStructural<_ek_structural>;

	auto fem = std::make_unique<FE>(mesh, dim, "test_fem");

	fem->initShapeFunctions();

	auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());

	Array<Real> angles;
	angles.push_back(std::atan(4. / 3.));
	angles.push_back(-std::atan(4. / 3.));
	angles.push_back(0);

	/// Testing the rotation matrices
	for (auto && tuple : zip(make_view(shape.getRotations(type), 3, 3), angles)) {
	auto && rotation = std::get<0>(tuple);
	auto theta = std::get<1>(tuple);
	auto reference = globalToLocalRotation(theta);

	if (!Math::are_vector_equal(9, reference.storage(), rotation.storage()))
	return 1;
	}

	auto & shape_functions = shape.getShapes(type);

	if (!testBending(shape_functions, 0, axialReference))
	return 1;
	// if (!testBending(shape_functions, 1, bendingReference))
	// return 1;
	// if (!testBending(shape_functions, 2, bendingRotationReference))
	// return 1;

	std::cout.flush();

	finalize();

	return 0;
	}
	diff --git a/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_3.cc b/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_3.cc
	index e676e35bf..b820e4431 100644
	--- a/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_3.cc
	+++ b/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_3.cc
	@@ -1,107 +1,107 @@
	/**
	* @file test_fe_engine_precomputation_bernoulli_3.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jan 24 2018
	* @date last modification: Wed Sep 12 2018
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "integrator_gauss.hh"
	#include "shape_structural.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <functional>
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	/**
	* Reference: p. 285, example 5.7 - A First Course in the Finite Elements Method
	* Logan, 6th Edition, 2016
	* ISBN-13: 978-1-305-63734-4
	*/
	Matrix<Real> rotationReference() {
	return {{3. / 13, 4. / 13, 12. / 13},
	{-4. / 5, 3. / 5, 0},
	{-36. / 65, -48. / 65, 5. / 13}};
	}

	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);
	// debug::setDebugLevel(dblTest);

	constexpr ElementType type = _bernoulli_beam_3;
	UInt dim = ElementClass<type>::getSpatialDimension();

	Mesh mesh(dim);

	// Pushing nodes
	Vector<Real> node = {0, 0, 0};
	mesh.getNodes().push_back(node);
	node = {3, 4, 12};
	mesh.getNodes().push_back(node);

	// Pushing connectivity
	mesh.addConnectivityType(type);
	auto & connectivity = mesh.getConnectivity(type);
	Vector<UInt> elem = {0, 1};
	connectivity.push_back(elem);

	// Pushing normals
	auto & normals = mesh.registerElementalData<Real>("extra_normal")
	.alloc(0, dim, type, _not_ghost);
	Vector<Real> normal = {-36. / 65, -48. / 65, 5. / 13};
	normals.push_back(normal);
	normals.push_back(normal);

	using FE = FEEngineTemplate<IntegratorGauss, ShapeStructural, _ek_structural>;
	using ShapeStruct = ShapeStructural<_ek_structural>;

	auto fem = std::make_unique<FE>(mesh, dim, "test_fem");

	fem->initShapeFunctions();

	auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());

	Matrix<Real> rot_ref = rotationReference();
	Matrix<Real> solution(6, 6);
	solution.block(rot_ref, 0, 0);
	solution.block(rot_ref, 3, 3);

	for (auto && rot : make_view(shape.getRotations(type), 6, 6)) {
	if (!Math::are_vector_equal(6 * 6, solution.storage(), rot.storage()))
	return 1;
	}

	/// TODO check shape functions and shape derivatives

	finalize();

	return 0;
	}
	diff --git a/test/test_fe_engine/test_fe_engine_precomputation_structural.cc b/test/test_fe_engine/test_fe_engine_precomputation_structural.cc
	index 8432b740f..e3edfe698 100644
	--- a/test/test_fe_engine/test_fe_engine_precomputation_structural.cc
	+++ b/test/test_fe_engine/test_fe_engine_precomputation_structural.cc
	@@ -1,127 +1,127 @@
	/**
	* @file test_fe_engine_precomputation_structural.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Jan 26 2018
	* @date last modification: Wed Sep 12 2018
	*
	* @brief test of the structural precomputations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "integrator_gauss.hh"
	#include "shape_structural.hh"
	#include "test_fe_engine_structural_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	// Need a special fixture for the extra normal
	class TestBernoulliB3
	: public TestFEMStructuralFixture<element_type_t<_bernoulli_beam_3>> {
	using parent = TestFEMStructuralFixture<element_type_t<_bernoulli_beam_3>>;

	public:
	/// Load the mesh and provide extra normal direction
	void readMesh(std::string filename) override {
	parent::readMesh(filename);
	auto & normals = this->mesh->getElementalData<Real>("extra_normal")
	.alloc(0, dim, type, _not_ghost);
	Vector<Real> normal = {-36. / 65, -48. / 65, 5. / 13};
	normals.push_back(normal);
	}
	};

	/* -------------------------------------------------------------------------- */
	/// Type alias
	using TestBernoulliB2 =
	TestFEMStructuralFixture<element_type_t<_bernoulli_beam_2>>;
	using TestDKT18 =
	TestFEMStructuralFixture<element_type_t<_discrete_kirchhoff_triangle_18>>;
	/* -------------------------------------------------------------------------- */

	/// Solution for 2D rotation matrices
	Matrix<Real> globalToLocalRotation(Real theta) {
	auto c = std::cos(theta);
	auto s = std::sin(theta);
	return {{c, s, 0}, {-s, c, 0}, {0, 0, 1}};
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestBernoulliB2, PrecomputeRotations) {
	this->fem->initShapeFunctions();
	using ShapeStruct = ShapeStructural<_ek_structural>;
	auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
	auto & rot = shape.getRotations(type);

	Real a = std::atan(4. / 3);
	std::vector<Real> angles = {a, -a, 0};

	Math::setTolerance(1e-15);

	for (auto && tuple : zip(make_view(rot, ndof, ndof), angles)) {
	auto rotation = std::get<0>(tuple);
	auto angle = std::get<1>(tuple);
	auto rotation_error = (rotation - globalToLocalRotation(angle)).norm<L_2>();
	EXPECT_NEAR(rotation_error, 0., Math::getTolerance());
	}
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestBernoulliB3, PrecomputeRotations) {
	this->fem->initShapeFunctions();
	using ShapeStruct = ShapeStructural<_ek_structural>;
	auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
	auto & rot = shape.getRotations(type);

	Matrix<Real> ref = {{3. / 13, 4. / 13, 12. / 13},
	{-4. / 5, 3. / 5, 0},
	{-36. / 65, -48. / 65, 5. / 13}};
	Matrix<Real> solution{ndof, ndof};
	solution.block(ref, 0, 0);
	solution.block(ref, dim, dim);

	// The default tolerance is too much, really
	Math::setTolerance(1e-15);

	for (auto & rotation : make_view(rot, ndof, ndof)) {
	auto rotation_error = (rotation - solution).norm<L_2>();
	EXPECT_NEAR(rotation_error, 0., Math::getTolerance());
	}
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestDKT18, DISABLED_PrecomputeRotations) {
	this->fem->initShapeFunctions();
	using ShapeStruct = ShapeStructural<_ek_structural>;
	auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
	auto & rot = shape.getRotations(type);

	for (auto & rotation : make_view(rot, ndof, ndof)) {
	std::cout << rotation << "\n";
	}
	std::cout.flush();
	}
	diff --git a/test/test_fe_engine/test_fe_engine_structural_fixture.hh b/test/test_fe_engine/test_fe_engine_structural_fixture.hh
	index 78d8eb0a3..17bd9db32 100644
	--- a/test/test_fe_engine/test_fe_engine_structural_fixture.hh
	+++ b/test/test_fe_engine/test_fe_engine_structural_fixture.hh
	@@ -1,65 +1,65 @@
	/**
	* @file test_fe_engine_structural_fixture.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jun 12 2019
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_io_msh_struct.hh"
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_FE_ENGINE_STRUCTURAL_FIXTURE_HH_
	#define AKANTU_TEST_FE_ENGINE_STRUCTURAL_FIXTURE_HH_

	using namespace akantu;

	/// Base class for structural FEEngine tests with structural elements
	template <typename type_>
	class TestFEMStructuralFixture
	: public TestFEMBaseFixture<type_, ShapeStructural, _ek_structural> {
	using parent = TestFEMBaseFixture<type_, ShapeStructural, _ek_structural>;

	public:
	static const UInt ndof = ElementClass<parent::type>::getNbDegreeOfFreedom();

	/// Need to tell the mesh to load structural elements
	void readMesh(std::string file_name) override {
	this->mesh->read(file_name, _miot_gmsh_struct);
	}
	};

	template <typename type_> const UInt TestFEMStructuralFixture<type_>::ndof;

	// using types = gtest_list_t<TestElementTypes>;

	// TYPED_TEST_SUITE(TestFEMFixture, types);

	#endif /* AKANTU_TEST_FE_ENGINE_STRUCTURAL_FIXTURE_HH_ */
	diff --git a/test/test_fe_engine/test_gradient.cc b/test/test_fe_engine/test_gradient.cc
	index 7eb6d6965..98f746aa8 100644
	--- a/test/test_fe_engine/test_gradient.cc
	+++ b/test/test_fe_engine/test_gradient.cc
	@@ -1,104 +1,104 @@
	/**
	* @file test_gradient.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Feb 19 2018
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	* @section DESCRIPTION
	*
	* This code is computing the gradient of a linear field and check that it gives
	* a constant result. It also compute the gradient the coordinates of the mesh
	* and check that it gives the identity
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TYPED_TEST(TestFEMFixture, GradientPoly) {
	this->fem->initShapeFunctions();
	Real alpha[2][3] = {{13, 23, 31}, {11, 7, 5}};

	const auto dim = this->dim;
	const auto type = this->type;

	const auto & position = this->fem->getMesh().getNodes();
	Array<Real> const_val(this->fem->getMesh().getNbNodes(), 2, "const_val");
	for (auto && pair : zip(make_view(position, dim), make_view(const_val, 2))) {
	auto & pos = std::get<0>(pair);
	auto & const_ = std::get<1>(pair);

	const_.set(0.);

	for (UInt d = 0; d < dim; ++d) {
	const_(0) += alpha[0][d] * pos(d);
	const_(1) += alpha[1][d] * pos(d);
	}
	}

	/// compute the gradient
	Array<Real> grad_on_quad(this->nb_quadrature_points_total, 2 * dim,
	"grad_on_quad");
	this->fem->gradientOnIntegrationPoints(const_val, grad_on_quad, 2, type);

	/// check the results
	for (auto && grad : make_view(grad_on_quad, 2, dim)) {
	for (UInt d = 0; d < dim; ++d) {
	EXPECT_NEAR(grad(0, d), alpha[0][d], 5e-13);
	EXPECT_NEAR(grad(1, d), alpha[1][d], 5e-13);
	}
	}
	}

	TYPED_TEST(TestFEMFixture, GradientPositions) {
	this->fem->initShapeFunctions();
	const auto dim = this->dim;
	const auto type = this->type;

	UInt nb_quadrature_points =
	this->fem->getNbIntegrationPoints(type) * this->nb_element;
	Array<Real> grad_coord_on_quad(nb_quadrature_points, dim * dim,
	"grad_coord_on_quad");

	const auto & position = this->mesh->getNodes();
	this->fem->gradientOnIntegrationPoints(position, grad_coord_on_quad, dim,
	type);

	auto I = Matrix<Real>::eye(UInt(dim));

	for (auto && grad : make_view(grad_coord_on_quad, dim, dim)) {
	auto diff = (I - grad).template norm<L_inf>();

	EXPECT_NEAR(0., diff, 2e-14);
	}
	}
	diff --git a/test/test_fe_engine/test_integrate.cc b/test/test_fe_engine/test_integrate.cc
	index 819d78be8..c2b506c12 100644
	--- a/test/test_fe_engine/test_integrate.cc
	+++ b/test/test_fe_engine/test_integrate.cc
	@@ -1,74 +1,74 @@
	/**
	* @file test_integrate.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Peter Spijker <peter.spijker@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Feb 19 2018
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TYPED_TEST(TestFEMFixture, IntegrateConstant) {
	this->fem->initShapeFunctions();

	const auto type = this->type;

	const auto & position = this->fem->getMesh().getNodes();

	Array<Real> const_val(position.size(), 2, "const_val");
	Array<Real> val_on_quad(this->nb_quadrature_points_total, 2, "val_on_quad");

	Vector<Real> value{1, 2};
	for (auto && const_ : make_view(const_val, 2)) {
	const_ = value;
	}

	// interpolate function on quadrature points
	this->fem->interpolateOnIntegrationPoints(const_val, val_on_quad, 2, type);

	// integrate function on elements
	Array<Real> int_val_on_elem(this->nb_element, 2, "int_val_on_elem");
	this->fem->integrate(val_on_quad, int_val_on_elem, 2, type);

	// get global integration value
	Vector<Real> sum{0., 0.};

	for (auto && int_ : make_view(int_val_on_elem, 2)) {
	sum += int_;
	}

	auto diff = (value - sum).template norm<L_inf>();
	EXPECT_NEAR(0, diff, 1e-14);
	}
	diff --git a/test/test_fe_engine/test_interpolate.cc b/test/test_fe_engine/test_interpolate.cc
	index f96ac62e2..18bf77992 100644
	--- a/test/test_fe_engine/test_interpolate.cc
	+++ b/test/test_fe_engine/test_interpolate.cc
	@@ -1,73 +1,73 @@
	/**
	* @file test_interpolate.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Nov 14 2017
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	namespace {

	TYPED_TEST(TestFEMFixture, InterpolateConstant) {
	const auto type = this->type;

	const auto & position = this->fem->getMesh().getNodes();

	Array<Real> const_val(position.size(), 2, "const_val");
	Array<Real> val_on_quad(this->nb_quadrature_points_total, 2, "val_on_quad");

	Vector<Real> value{1, 2};
	for (auto && const_ : make_view(const_val, 2)) {
	const_ = value;
	}

	// interpolate function on quadrature points
	this->fem->interpolateOnIntegrationPoints(const_val, val_on_quad, 2, type);

	for (auto && int_ : make_view(val_on_quad, 2)) {
	auto diff = (value - int_).template norm<L_inf>();
	EXPECT_NEAR(0, diff, 1e-14);
	}
	}

	// TYPED_TEST(TestFEMFixture, InterpolatePosition) {
	// const auto dim = this->dim;
	// const auto type = this->type;
	// const auto & position = this->fem->getMesh().getNodes();

	// Array<Real> coord_on_quad(this->nb_quadrature_points_total, dim,
	// "coord_on_quad");

	// this->fem->interpolateOnIntegrationPoints(position, coord_on_quad, dim,
	// type);
	// }

	} // namespace
	diff --git a/test/test_fe_engine/test_interpolate_bernoulli_beam_2.cc b/test/test_fe_engine/test_interpolate_bernoulli_beam_2.cc
	index fb8d11e49..9388b3d4a 100644
	--- a/test/test_fe_engine/test_interpolate_bernoulli_beam_2.cc
	+++ b/test/test_fe_engine/test_interpolate_bernoulli_beam_2.cc
	@@ -1,119 +1,119 @@
	/**
	* @file test_interpolate_bernoulli_beam_2.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sat Jan 23 2016
	*
	* @brief Test of the interpolation on the type _bernoulli_beam_2
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "fe_engine.hh"
	#include "fe_engine_template.hh"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"
	#include "shape_linked.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main() {

	Mesh beams(2);

	/* --------------------------------------------------------------------------
	*/
	// Defining the mesh

	Array<Real> & nodes = const_cast<Array<Real> &>(beams.getNodes());
	nodes.resize(4);

	beams.addConnectivityType(_bernoulli_beam_2);
	Array<UInt> & connectivity =
	const_cast<Array<UInt> &>(beams.getConnectivity(_bernoulli_beam_2));
	connectivity.resize(3);

	for (UInt i = 0; i < 4; ++i) {

	nodes(i, 0) = (i + 1) * 2;
	nodes(i, 1) = 1;
	}
	for (UInt i = 0; i < 3; ++i) {

	connectivity(i, 0) = i;
	connectivity(i, 1) = i + 1;
	}
	akantu::MeshIOMSH mesh_io;
	mesh_io.write("b_beam_2.msh", beams);

	/* --------------------------------------------------------------------------
	*/
	// Interpolation

	FEEngineTemplate<IntegratorGauss, ShapeLinked> * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLinked>(beams, 2);

	fem->initShapeFunctions();

	Array<Real> displ_on_nodes(4, 3);
	Array<Real> displ_on_quad(0, 3);

	for (UInt i = 0; i < 4; ++i) {

	displ_on_nodes(i, 0) = (i + 1) * 2; // Definition of the displacement
	displ_on_nodes(i, 1) = 0;
	displ_on_nodes(i, 2) = 0;
	}

	fem->getShapeFunctions().interpolateOnControlPoints<_bernoulli_beam_2>(
	displ_on_nodes, displ_on_quad, 3, _not_ghost, NULL, false, 0, 0, 0);

	fem->getShapeFunctions().interpolateOnControlPoints<_bernoulli_beam_2>(
	displ_on_nodes, displ_on_quad, 3, _not_ghost, NULL, false, 1, 1, 1);

	fem->getShapeFunctions().interpolateOnControlPoints<_bernoulli_beam_2>(
	displ_on_nodes, displ_on_quad, 3, _not_ghost, NULL, true, 2, 2, 1);

	fem->getShapeFunctions().interpolateOnControlPoints<_bernoulli_beam_2>(
	displ_on_nodes, displ_on_quad, 3, _not_ghost, NULL, false, 3, 2, 3);

	fem->getShapeFunctions().interpolateOnControlPoints<_bernoulli_beam_2>(
	displ_on_nodes, displ_on_quad, 3, _not_ghost, NULL, true, 4, 3, 3);

	Real * don = displ_on_nodes.storage();
	Real * doq = displ_on_quad.storage();

	std::ofstream my_file("out.txt");
	my_file << don << std::endl;
	my_file << doq << std::endl;

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_fe_engine/test_inverse_map.cc b/test/test_fe_engine/test_inverse_map.cc
	index dfeaf3adc..bf1f42a6a 100644
	--- a/test/test_fe_engine/test_inverse_map.cc
	+++ b/test/test_fe_engine/test_inverse_map.cc
	@@ -1,71 +1,71 @@
	/**
	* @file test_inverse_map.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Mar 13 2018
	*
	* @brief test of the fem class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_fe_engine_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TYPED_TEST(TestFEMFixture, InverseMap) {
	this->fem->initShapeFunctions();

	Matrix<Real> quad =
	GaussIntegrationElement<TestFixture::type>::getQuadraturePoints();

	const auto & position = this->fem->getMesh().getNodes();

	/// get the quadrature points coordinates
	Array<Real> coord_on_quad(quad.cols() * this->nb_element, this->dim,
	"coord_on_quad");

	this->fem->interpolateOnIntegrationPoints(position, coord_on_quad, this->dim,
	this->type);

	Vector<Real> natural_coords(this->dim);

	auto length = (this->upper - this->lower).template norm<L_inf>();

	for (auto && enum_ :
	enumerate(make_view(coord_on_quad, this->dim, quad.cols()))) {
	auto el = std::get<0>(enum_);
	const auto & quads_coords = std::get<1>(enum_);

	for (auto q : arange(quad.cols())) {
	Vector<Real> quad_coord = quads_coords(q);
	Vector<Real> ref_quad_coord = quad(q);
	this->fem->inverseMap(quad_coord, el, this->type, natural_coords);

	auto dis_normalized = ref_quad_coord.distance(natural_coords) / length;
	EXPECT_NEAR(0., dis_normalized, 3.5e-11);
	}
	}
	}
	diff --git a/test/test_fe_engine/test_mesh_boundary.cc b/test/test_fe_engine/test_mesh_boundary.cc
	index feb6ba6f1..0d89d89f6 100644
	--- a/test/test_fe_engine/test_mesh_boundary.cc
	+++ b/test/test_fe_engine/test_mesh_boundary.cc
	@@ -1,66 +1,66 @@
	/**
	* @file test_mesh_boundary.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sun Aug 13 2017
	*
	* @brief Thest the element groups
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	UInt spatialDimension(3);

	akantu::initialize(argc, argv);

	Mesh mesh(spatialDimension, "mesh_names");

	std::cout << "Loading the mesh." << std::endl;

	mesh.read("./cube_physical_names.msh");

	std::cout << "Examining mesh:" << std::endl;

	// Inspection of the number of boundaries
	UInt nb_boundaries = mesh.getNbElementGroups(spatialDimension - 1);
	AKANTU_DEBUG_INFO(nb_boundaries << " boundaries advertised by Mesh.");
	if (nb_boundaries == 0) {
	std::cout << "No boundary detected!" << std::endl;
	return 1;
	}

	std::cout << (dynamic_cast<GroupManager >(&mesh)) << std::endl;

	akantu::finalize();

	return 0;
	}
	diff --git a/test/test_fe_engine/test_mesh_data.cc b/test/test_fe_engine/test_mesh_data.cc
	index 6e9c746c4..15cbeccbc 100644
	--- a/test/test_fe_engine/test_mesh_data.cc
	+++ b/test/test_fe_engine/test_mesh_data.cc
	@@ -1,87 +1,87 @@
	/**
	* @file test_mesh_data.cc
	*
	* @author Dana Christen <dana.christen@gmail.com>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Jul 13 2015
	*
	* @brief Test of the MeshData class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	#include <string>

	#define QUOTES(x) #x
	#define ADD_QUOTES(x) QUOTES(x)

	#define CAT(x, y) x##_##y
	#define CONCAT(x, y) CAT(x, y)

	//#define TYPE std::string
	//#define VALUE1 "abc"
	//#define VALUE2 "qwe"

	#define ELEMENT _triangle_6
	#define NAME CONCAT(TYPE, data)

	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	using namespace std;

	int main() {

	std::cout << "Testing with type " << ADD_QUOTES(TYPE) << " and values "
	<< ADD_QUOTES(VALUE1) << "," << ADD_QUOTES(VALUE2) << "..."
	<< std::endl;
	MeshData mesh_data;

	ElementType elem_type = ELEMENT;

	const std::string name = ADD_QUOTES(NAME);

	Array<TYPE> & vec =
	mesh_data.getElementalDataArrayAlloc<TYPE>(name, elem_type);
	// XXX TO DELETE
	// vec.copy(mesh_data.getElementalDataArrayAlloc<TYPE>(name, elem_type));

	TYPE value[2] = {VALUE1, VALUE2};

	vec.push_back(value[0]);
	vec.push_back(value[1]);

	for (UInt i(0); i < 2; i++) {
	AKANTU_DEBUG_ASSERT(vec(i) == value[i], "The Array accessed through the "
	"getElementDataArray method does "
	"not contain the right value.");
	}

	std::cout << vec << std::endl;
	std::cout << mesh_data.getTypeCode(name) << std::endl;

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_geometry/test_geometry_intersection.cc b/test/test_geometry/test_geometry_intersection.cc
	index 6dd8020e1..4303d9bf6 100644
	--- a/test/test_geometry/test_geometry_intersection.cc
	+++ b/test/test_geometry/test_geometry_intersection.cc
	@@ -1,132 +1,132 @@
	/**
	* @file test_geometry_intersection.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Tests the intersection module
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"
	#include "geom_helper_functions.hh"
	#include "mesh_geom_factory.hh"
	#include "tree_type_helper.hh"

	#include "mesh_geom_common.hh"

	#include <iostream>
	#include <iterator>

	#include <CGAL/Exact_spherical_kernel_3.h>
	#include <CGAL/Spherical_kernel_intersections.h>
	#include <CGAL/intersections.h>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	typedef cgal::Cartesian K;
	typedef IntersectionTypeHelper<TreeTypeHelper<Triangle<K>, K>,
	K::Segment_3>::intersection_type result_type;

	typedef cgal::Spherical SK;
	typedef boost::variant<std::pair<SK::Circular_arc_point_3, UInt>> sk_inter_res;
	/*typedef CGAL::cpp11::result_of<SK::Intersect_3(SK::Line_arc_3,
	SK::Sphere_3,
	std::back_insert_iterator<
	std::list<sk_inter_res> >)>::type sk_res;*/

	typedef std::pair<SK::Circular_arc_point_3, UInt> pair_type;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("", argc, argv);
	debug::setDebugLevel(dblWarning);

	Mesh mesh(2);
	mesh.read("test_geometry_triangle.msh");

	MeshGeomFactory<2, _triangle_3, Triangle<K>, K> factory(mesh);
	factory.constructData();

	const TreeTypeHelper<Triangle<K>, K>::tree & tree = factory.getTree();

	K::Point_3 a(0., 0.25, 0.), b(1., 0.25, 0.);
	K::Segment_3 line(a, b);

	K::Point_3 begin(a), intermediate(0.25, 0.25, 0.), end(0.75, 0.25, 0.);
	K::Segment_3 result_0(begin, intermediate), result_1(intermediate, end);

	std::list<result_type> list_of_intersections;
	tree.all_intersections(line, std::back_inserter(list_of_intersections));

	const result_type & intersection_0 = list_of_intersections.back();
	const result_type & intersection_1 = list_of_intersections.front();

	if (!intersection_0 \|\| !intersection_1)
	return EXIT_FAILURE;

	/// -> first is the intersection ; ->second is the primitive id
	if (const K::Segment_3 * segment =
	boost::get<K::Segment_3>(&(intersection_0->first))) {
	if (!compareSegments(*segment, result_0)) {
	return EXIT_FAILURE;
	}
	} else
	return EXIT_FAILURE;

	if (const K::Segment_3 * segment =
	boost::get<K::Segment_3>(&(intersection_1->first))) {
	if (!compareSegments(*segment, result_1)) {
	return EXIT_FAILURE;
	}
	} else
	return EXIT_FAILURE;

	SK::Sphere_3 sphere(SK::Point_3(0, 0, 0), 3.);
	SK::Segment_3 seg(SK::Point_3(0, 0, 0), SK::Point_3(2., 2., 2.));
	SK::Line_arc_3 arc(seg);

	std::list<sk_inter_res> s_results;
	CGAL::intersection(arc, sphere, std::back_inserter(s_results));

	if (pair_type * pair = boost::get<pair_type>(&s_results.front())) {
	std::cout << "xi = " << to_double(pair->first.x())
	<< ", yi = " << to_double(pair->first.y()) << std::endl;
	if (!comparePoints(pair->first, SK::Circular_arc_point_3(1.0, 1.0, 1.0)))
	return EXIT_FAILURE;
	} else
	return EXIT_FAILURE;

	MeshGeomFactory<2, _triangle_3, Line_arc<SK>, SK> Sfactory(mesh);
	Sfactory.constructData();

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_geometry/test_geometry_predicates.cc b/test/test_geometry/test_geometry_predicates.cc
	index 5f6044010..c1c219aef 100644
	--- a/test/test_geometry/test_geometry_predicates.cc
	+++ b/test/test_geometry/test_geometry_predicates.cc
	@@ -1,89 +1,89 @@
	/**
	* @file test_geometry_predicates.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jan 31 2018
	*
	* @brief Tests the geometry predicates
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"
	#include "geom_helper_functions.hh"

	#include "mesh_geom_common.hh"

	#include <iostream>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	typedef cgal::Cartesian K;
	typedef K::Point_3 Point;
	typedef K::Segment_3 Segment;

	int main(int argc, char * argv[]) {
	initialize("", argc, argv);
	debug::setDebugLevel(dblWarning);

	Point a(0, 1, 0);
	Point b(0, 1, 1);

	Segment seg1(a, b);
	Segment seg2(b, a);

	if (!compareSegments(seg1, seg2))
	return EXIT_FAILURE;

	// Testing sort + unique on list of segments
	std::vector<std::pair<K::Segment_3, UInt>> pair_list;
	pair_list.push_back(std::make_pair(seg1, 1));
	pair_list.push_back(std::make_pair(seg2, 2));

	segmentPairsLess sorter;
	std::sort(pair_list.begin(), pair_list.end(), sorter);
	std::vector<std::pair<K::Segment_3, UInt>>::iterator it =
	std::unique(pair_list.begin(), pair_list.end(), compareSegmentPairs);

	if (it - pair_list.begin() != 1) {
	std::cout << pair_list.size() << std::endl;
	return EXIT_FAILURE;
	}

	// Testing insertion in set
	std::set<std::pair<K::Segment_3, UInt>, segmentPairsLess> pair_set;
	pair_set.insert(pair_set.begin(), std::make_pair(seg1, 1));
	pair_set.insert(pair_set.begin(), std::make_pair(seg2, 2));

	if (pair_set.size() != 1) {
	std::cout << pair_set.size() << std::endl;
	return EXIT_FAILURE;
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_geometry/test_segment_intersection_tetrahedron_4.cc b/test/test_geometry/test_segment_intersection_tetrahedron_4.cc
	index 78877d7a2..185aae1cb 100644
	--- a/test/test_geometry/test_segment_intersection_tetrahedron_4.cc
	+++ b/test/test_geometry/test_segment_intersection_tetrahedron_4.cc
	@@ -1,144 +1,144 @@
	/**
	* @file test_segment_intersection_tetrahedron_4.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Tue Mar 13 2018
	*
	* @brief Tests the intersection module with _tetrahedron_4 elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"
	#include "mesh_segment_intersector.hh"

	#include "mesh_geom_common.hh"

	#include <iostream>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	typedef cgal::Cartesian K;
	typedef K::Point_3 Point;
	typedef K::Segment_3 Segment;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("", argc, argv);
	debug::setDebugLevel(dblError);

	Mesh mesh(3), interface_mesh(3, "interface_mesh");
	mesh.read("test_geometry_tetrahedron.msh");

	MeshSegmentIntersector<3, _tetrahedron_4> intersector(mesh, interface_mesh);
	intersector.constructData();

	// Testing a segment going through the cube
	Point point(1., 1., 1.);
	Segment segment(CGAL::ORIGIN, point);

	intersector.computeIntersectionQuery(segment);

	std::cout << "number of seg_2 : " << interface_mesh.getNbElement(_segment_2)
	<< std::endl;
	if (interface_mesh.getNbElement(_segment_2) != 2)
	return EXIT_FAILURE;

	Vector<Real> bary(2), bary1(2), bary2(2);

	Element test{_segment_2, 0, _not_ghost};
	interface_mesh.getBarycenter(test, bary1);

	test.element = 1;
	interface_mesh.getBarycenter(test, bary2);

	Real first_bary[] = {1. / 6., 1. / 6., 1. / 6.};
	Real second_bary[] = {2. / 3., 2. / 3., 2. / 3.};

	// We don't know the order of the elements, so here we test permutations
	if (!((Math::are_vector_equal(3, bary1.storage(), first_bary) &&
	Math::are_vector_equal(3, bary2.storage(), second_bary)) \|\|
	(Math::are_vector_equal(3, bary1.storage(), second_bary) &&
	Math::are_vector_equal(3, bary2.storage(), first_bary))))
	return EXIT_FAILURE;

	// Testing a segment completely inside one element
	Point a(0.05, 0.05, 0.05), b(0.06, 0.06, 0.06);
	Segment inside_segment(a, b);

	intersector.computeIntersectionQuery(inside_segment);
	test.element = interface_mesh.getNbElement(_segment_2) - 1;
	interface_mesh.getBarycenter(test, bary);
	Real third_bary[] = {0.055, 0.055, 0.055};

	if (!Math::are_vector_equal(3, bary.storage(), third_bary))
	return EXIT_FAILURE;

	// Testing a segment whose end points are inside elements
	Point c(0.1, 0.1, 0.1), d(0.9, 0.9, 0.9);
	Segment crossing_segment(c, d);

	intersector.computeIntersectionQuery(crossing_segment);
	UInt el1 = interface_mesh.getNbElement(_segment_2) - 2;
	UInt el2 = el1 + 1;

	test.element = el1;
	interface_mesh.getBarycenter(test, bary1);
	test.element = el2;
	interface_mesh.getBarycenter(test, bary2);

	Real fourth_bary[] = {13. / 60., 13. / 60., 13. / 60.};
	Real fifth_bary[] = {37. / 60., 37. / 60., 37. / 60.};

	// We don't know the order of the elements, so here we test permutations
	if (!((Math::are_vector_equal(3, bary1.storage(), fourth_bary) &&
	Math::are_vector_equal(3, bary2.storage(), fifth_bary)) \|\|
	(Math::are_vector_equal(3, bary1.storage(), fifth_bary) &&
	Math::are_vector_equal(3, bary2.storage(), fourth_bary))))
	return EXIT_FAILURE;

	// Testing a segment along the edge of elements
	Point e(1, 0, 0), f(0, 1, 0);
	Segment edge_segment(e, f);

	UInt current_nb_elements = interface_mesh.getNbElement(_segment_2);

	intersector.computeIntersectionQuery(edge_segment);

	if (interface_mesh.getNbElement(_segment_2) != current_nb_elements + 1)
	return EXIT_FAILURE;

	test.element = interface_mesh.getNbElement(_segment_2) - 1;
	interface_mesh.getBarycenter(test, bary);
	Real sixth_bary[] = {0.5, 0.5, 0};

	if (!Math::are_vector_equal(3, bary.storage(), sixth_bary))
	return EXIT_FAILURE;

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_geometry/test_segment_intersection_triangle_3.cc b/test/test_geometry/test_segment_intersection_triangle_3.cc
	index c336c80e3..08266bc2e 100644
	--- a/test/test_geometry/test_segment_intersection_triangle_3.cc
	+++ b/test/test_geometry/test_segment_intersection_triangle_3.cc
	@@ -1,137 +1,137 @@
	/**
	* @file test_segment_intersection_triangle_3.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Fri Feb 27 2015
	* @date last modification: Tue Mar 13 2018
	*
	* @brief Tests the interface mesh generation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"

	#include "geom_helper_functions.hh"
	#include "mesh_geom_common.hh"
	#include "mesh_segment_intersector.hh"
	#include "mesh_sphere_intersector.hh"

	#include <iostream>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	typedef cgal::Cartesian K;
	typedef cgal::Spherical SK;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("", argc, argv);
	debug::setDebugLevel(dblError);

	Math::setTolerance(1e-10);

	Mesh mesh(2), interface_mesh(2, "interface_mesh");
	mesh.read("test_geometry_triangle.msh");

	MeshSegmentIntersector<2, _triangle_3> intersector(mesh, interface_mesh);
	intersector.constructData();

	// Testing a segment going out of the mesh
	K::Point_3 a(0, 0.25, 0), b(1, 0.25, 0), c(0.25, 0, 0), d(0.25, 1, 0);

	K::Segment_3 h_interface(a, b), v_interface(c, d);

	std::list<K::Segment_3> interface_list;
	interface_list.push_back(h_interface);
	interface_list.push_back(v_interface);

	intersector.computeIntersectionQueryList(interface_list);

	if (interface_mesh.getNbElement(_segment_2) != 4)
	return EXIT_FAILURE;

	Vector<Real> bary(2);
	Element test{_segment_2, 0, _not_ghost};

	interface_mesh.getBarycenter(test, bary);
	Real first_bary[] = {0.125, 0.25};

	if (!Math::are_vector_equal(2, bary.storage(), first_bary))
	return EXIT_FAILURE;

	// Testing a segment completely inside an element
	K::Point_3 e(0.1, 0.33, 0), f(0.1, 0.67, 0);
	K::Segment_3 inside_segment(e, f);
	intersector.computeIntersectionQuery(inside_segment);

	test.element = interface_mesh.getNbElement(_segment_2) - 1;
	interface_mesh.getBarycenter(test, bary);

	Real second_bary[] = {0.1, 0.5};

	if (!Math::are_vector_equal(2, bary.storage(), second_bary))
	return EXIT_FAILURE;

	#if 0
	// cgal::Spherical kernel testing the addition of nodes
	std::cout << "initial mesh size = " << mesh.getNodes().size() << " nodes" << std::endl;

	SK::Sphere_3 sphere(SK::Point_3(0, 1, 0), 0.2*0.2);
	SK::Sphere_3 sphere2(SK::Point_3(1, 0, 0), 0.4999999999);
	MeshSphereIntersector<2, _triangle_3> intersector_sphere(mesh);
	intersector_sphere.constructData();

	std::list<SK::Sphere_3> sphere_list;
	sphere_list.push_back(sphere);
	sphere_list.push_back(sphere2);

	intersector_sphere.computeIntersectionQueryList(sphere_list);
	std::cout << "final mesh size = " << mesh.getNodes().size() << std::endl;

	const Array<UInt> new_node_triangle_3 = intersector_sphere.getNewNodePerElem();
	const Array<Real> & nodes = mesh.getNodes();
	std::cout << "New nodes :" << std::endl;
	std::cout << "node 5, x=" << nodes(4,0) << ", y=" << nodes(4,1) << std::endl;
	std::cout << "node 6, x=" << nodes(5,0) << ", y=" << nodes(5,1) << std::endl;
	std::cout << "node 7, x=" << nodes(6,0) << ", y=" << nodes(6,1) << std::endl;

	if ( (new_node_triangle_3(0,0) != 1) \|\| (new_node_triangle_3(1,0) != 2)){
	for(UInt k=0; k != new_node_triangle_3.size(); ++k){
	std::cout << new_node_triangle_3(k,0) << " new nodes in element " << k << ", node(s): "
	<< new_node_triangle_3(k,1) << ", " << new_node_triangle_3(k,3)
	<< ", on segment(s):" << new_node_triangle_3(k,2) << ", "
	<< new_node_triangle_3(k,4) << std::endl;
	}
	return EXIT_FAILURE;
	}
	#endif

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_gtest_main.cc b/test/test_gtest_main.cc
	index 7c92f45aa..f999cdd80 100644
	--- a/test/test_gtest_main.cc
	+++ b/test/test_gtest_main.cc
	@@ -1,84 +1,84 @@
	/**
	* @file test_gtest_main.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Nov 09 2017
	* @date last modification: Tue Dec 10 2019
	*
	* @brief Main function for gtest tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "communicator.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#if defined(AKANTU_TEST_USE_PYBIND11)
	#include <pybind11/embed.h>
	namespace py = pybind11;
	#endif
	/* -------------------------------------------------------------------------- */

	namespace {
	class AkaEnvironment : public ::testing::Environment {
	public:
	AkaEnvironment(int & argc, char **& argv) : argc(argc), argv(argv) {}
	// Override this to define how to set up the environment.
	void SetUp() override {
	::akantu::initialize(argc, argv);

	#if defined(AKANTU_USE_PYBIND11)
	// py::initialize_interpreter();
	#endif
	}
	// Override this to define how to tear down the environment.
	void TearDown() override {
	::akantu::finalize();
	#if defined(AKANTU_USE_PYBIND11)
	// py::finalize_interpreter();
	#endif
	}

	protected:
	int & argc;
	char **& argv;
	};
	} // namespace

	int main(int argc, char ** argv) {
	#if defined(AKANTU_TEST_USE_PYBIND11)
	py::scoped_interpreter guard{};
	#endif

	::testing::InitGoogleTest(&argc, argv);
	::testing::AddGlobalTestEnvironment(new AkaEnvironment(argc, argv));

	::testing::TestEventListeners & listeners =
	::testing::UnitTest::GetInstance()->listeners();
	if (::akantu::Communicator::getStaticCommunicator().whoAmI() != 0) {
	delete listeners.Release(listeners.default_result_printer());
	}

	return RUN_ALL_TESTS();
	}
	diff --git a/test/test_gtest_utils.hh b/test/test_gtest_utils.hh
	index 0f5b6269d..e98e8c6c8 100644
	--- a/test/test_gtest_utils.hh
	+++ b/test/test_gtest_utils.hh
	@@ -1,260 +1,259 @@
	/**
	* @file test_gtest_utils.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Fri Jan 10 2020
	*
	* @brief Utils to help write tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_iterators.hh"
	/* -------------------------------------------------------------------------- */
	#include <boost/preprocessor.hpp>
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_GTEST_UTILS_HH_
	#define AKANTU_TEST_GTEST_UTILS_HH_

	#if !defined(TYPED_TEST_SUITE)
	#define TYPED_TEST_SUITE(...) TYPED_TEST_CASE(__VA_ARGS__)
	#endif

	#if !defined(TYPED_TEST_SUITE_P)
	#define TYPED_TEST_SUITE_P(...) TYPED_TEST_CASE_P(__VA_ARGS__)
	#endif

	#if !defined(REGISTER_TYPED_TEST_SUITE_P)
	#define REGISTER_TYPED_TEST_SUITE_P(...) REGISTER_TYPED_TEST_CASE_P(__VA_ARGS__)
	#endif

	#if !defined(INSTANTIATE_TYPED_TEST_SUITE_P)
	#define INSTANTIATE_TYPED_TEST_SUITE_P(...) \
	INSTANTIATE_TYPED_TEST_CASE_P(__VA_ARGS__)
	#endif

	namespace {

	/* -------------------------------------------------------------------------- */
	template <::akantu::ElementType t>
	using element_type_t = std::integral_constant<::akantu::ElementType, t>;

	/* -------------------------------------------------------------------------- */
	template <typename... T> struct gtest_list {};

	template <typename... Ts> struct gtest_list<std::tuple<Ts...>> {
	using type = ::testing::Types<Ts...>;
	};

	template <typename... T> using gtest_list_t = typename gtest_list<T...>::type;

	/* -------------------------------------------------------------------------- */
	-//template <typename... T> struct tuple_concat {};
	+// template <typename... T> struct tuple_concat {};

	-template <typename... Ts>
	-struct tuple_concat {
	+template <typename... Ts> struct tuple_concat {
	using type = decltype(std::tuple_cat(std::declval<Ts>()...));
	};

	template <typename... T>
	using tuple_concat_t = typename tuple_concat<T...>::type;

	/* -------------------------------------------------------------------------- */
	template <template <typename> class Pred, typename... Ts>
	struct tuple_filter {};

	template <template <typename> class Pred, typename T>
	struct tuple_filter<Pred, std::tuple<T>> {
	using type = std::conditional_t<Pred<T>::value, std::tuple<T>, std::tuple<>>;
	};

	template <template <typename> class Pred, typename T, typename... Ts>
	struct tuple_filter<Pred, std::tuple<T, Ts...>> {
	using type =
	tuple_concat_t<typename tuple_filter<Pred, std::tuple<T>>::type,
	typename tuple_filter<Pred, std::tuple<Ts...>>::type>;
	};

	template <template <typename> class Pred, typename... Ts>
	using tuple_filter_t = typename tuple_filter<Pred, Ts...>::type;

	/* -------------------------------------------------------------------------- */
	template <size_t N, typename... Ts> struct tuple_split {};

	template <size_t N, typename T, typename... Ts>
	struct tuple_split<N, std::tuple<T, Ts...>> {
	protected:
	using split = tuple_split<N - 1, std::tuple<Ts...>>;

	public:
	using type = tuple_concat_t<std::tuple<T>, typename split::type>;
	using type_tail = typename split::type_tail;
	};

	template <typename T, typename... Ts>
	struct tuple_split<1, std::tuple<T, Ts...>> {
	using type = std::tuple<T>;
	using type_tail = std::tuple<Ts...>;
	};

	template <size_t N, typename... T>
	using tuple_split_t = typename tuple_split<N, T...>::type;

	template <size_t N, typename... T>
	using tuple_split_tail_t = typename tuple_split<N, T...>::type_tail;

	/* -------------------------------------------------------------------------- */
	template <typename... T> struct cross_product {};

	template <typename... T2s>
	struct cross_product<std::tuple<>, std::tuple<T2s...>> {
	using type = std::tuple<>;
	};

	template <typename T1, typename... T1s, typename... T2s>
	struct cross_product<std::tuple<T1, T1s...>, std::tuple<T2s...>> {
	using type = tuple_concat_t<
	std::tuple<std::tuple<T1, T2s>...>,
	typename cross_product<std::tuple<T1s...>, std::tuple<T2s...>>::type>;
	};

	template <typename... T>
	using cross_product_t = typename cross_product<T...>::type;
	/* -------------------------------------------------------------------------- */

	} // namespace

	#define OP_CAT(s, data, elem) BOOST_PP_CAT(_element_type, elem)

	// creating a type instead of a using helps to debug
	#define AKANTU_DECLARE_ELEMENT_TYPE_STRUCT(r, data, elem) \
	struct BOOST_PP_CAT(_element_type, elem) \
	: public element_type_t<::akantu::elem> {};

	BOOST_PP_SEQ_FOR_EACH(AKANTU_DECLARE_ELEMENT_TYPE_STRUCT, _,
	AKANTU_ALL_ELEMENT_TYPE)

	#undef AKANTU_DECLARE_ELEMENT_TYPE_STRUCT

	using TestElementTypesAll = std::tuple<BOOST_PP_SEQ_ENUM(
	BOOST_PP_SEQ_TRANSFORM(OP_CAT, _, AKANTU_ek_regular_ELEMENT_TYPE))>;

	#if defined(AKANTU_COHESIVE_ELEMENT)
	using TestCohesiveElementTypes = std::tuple<BOOST_PP_SEQ_ENUM(
	BOOST_PP_SEQ_TRANSFORM(OP_CAT, _, AKANTU_ek_cohesive_ELEMENT_TYPE))>;
	#endif

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	using TestElementTypesStructural = std::tuple<BOOST_PP_SEQ_ENUM(
	BOOST_PP_SEQ_TRANSFORM(OP_CAT, _, AKANTU_ek_structural_ELEMENT_TYPE))>;
	#endif

	using TestAllDimensions = std::tuple<std::integral_constant<unsigned int, 1>,
	std::integral_constant<unsigned int, 2>,
	std::integral_constant<unsigned int, 3>>;

	template <typename T, ::akantu::ElementType type>
	using is_element = aka::bool_constant<T::value == type>;

	template <typename T>
	using not_is_point_1 = aka::negation<is_element<T, ::akantu::_point_1>>;

	using TestElementTypes = tuple_filter_t<not_is_point_1, TestElementTypesAll>;

	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	using StructuralTestElementTypes =
	tuple_filter_t<not_is_point_1, TestElementTypesStructural>;
	#endif

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	template <size_t degree> class Polynomial {
	public:
	Polynomial() = default;

	Polynomial(std::initializer_list<double> && init) {
	for (auto && pair : akantu::zip(init, constants))
	std::get<1>(pair) = std::get<0>(pair);
	}

	double operator()(double x) {
	double res = 0.;
	for (auto && vals : akantu::enumerate(constants)) {
	double a;
	int k;
	std::tie(k, a) = vals;
	res += a * std::pow(x, k);
	}
	return res;
	}

	Polynomial extract(size_t pdegree) {
	Polynomial<degree> extract(*this);
	for (size_t d = pdegree + 1; d < degree + 1; ++d)
	extract.constants[d] = 0;
	return extract;
	}

	auto integral() {
	Polynomial<degree + 1> integral_;
	integral_.set(0, 0.);
	;
	for (size_t d = 0; d < degree + 1; ++d) {
	integral_.set(1 + d, get(d) / double(d + 1));
	}
	return integral_;
	}

	auto integrate(double a, double b) {
	auto primitive = integral();
	return (primitive(b) - primitive(a));
	}

	double get(int i) const { return constants[i]; }

	void set(int i, double a) { constants[i] = a; }

	protected:
	std::array<double, degree + 1> constants;
	};

	template <size_t degree>
	std::ostream & operator<<(std::ostream & stream, const Polynomial<degree> & p) {
	for (size_t d = 0; d < degree + 1; ++d) {
	if (d != 0)
	stream << " + ";

	stream << p.get(degree - d);
	if (d != degree)
	stream << "x ^ " << degree - d;
	}
	return stream;
	}

	/* -------------------------------------------------------------------------- */

	#endif /* AKANTU_TEST_GTEST_UTILS_HH_ */
	diff --git a/test/test_io/test_dumper/test_dumper.cc b/test/test_io/test_dumper/test_dumper.cc
	index fd6a34f42..77c453dcb 100644
	--- a/test/test_io/test_dumper/test_dumper.cc
	+++ b/test/test_io/test_dumper/test_dumper.cc
	@@ -1,161 +1,162 @@
	/**
	* @file test_dumper.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue May 21 2019
	*
	* @brief test dumper
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper_paraview.hh"
	#include "dumper_nodal_field.hh"
	#include "dumper_text.hh"
	#include "dumper_variable.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("input_file.dat", argc, argv);

	UInt spatial_dimension = 3;
	Mesh mesh(spatial_dimension);
	mesh.read("test_dumper.msh");

	SolidMechanicsModel model(mesh);
	auto && mat_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	model.setMaterialSelector(mat_selector);

	model.initFull();
	model.assembleInternalForces();

	Real time_step = 0.1;

	const Array<Real> & coord = mesh.getNodes();
	Array<Real> & disp = model.getDisplacement();
	Array<bool> & bound = model.getBlockedDOFs();

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	Real dist = 0.;
	for (UInt d = 0; d < spatial_dimension; ++d) {
	dist += coord(n, d) * coord(n, d);
	}
	dist = sqrt(dist);

	for (UInt d = 0; d < spatial_dimension; ++d) {
	disp(n, d) = (d + 1) * dist;
	bound(n, d) = bool((n % 2) + d);
	}
	}

	// dump boundary bottom as reference
	model.setGroupDirectory("paraview", "Bottom");
	model.setGroupBaseName("paraview_bottom", "Bottom");
	model.addDumpGroupField("displacement", "Bottom");
	model.addDumpGroupField("blocked_dofs", "Bottom");

	UInt nbp = 3;
	DumperParaview prvdumper("paraview_bottom_parallel", "paraview", false);
	iohelper::Dumper & prvdpr = prvdumper.getDumper();
	for (UInt p = 0; p < nbp; ++p) {
	prvdpr.setParallelContext(p, nbp, 0);
	if (p != 0) {
	prvdumper.unRegisterField("connectivities");
	prvdumper.unRegisterField("element_type");
	prvdumper.unRegisterField("positions");
	prvdumper.unRegisterField("displacement");
	}
	prvdumper.registerFilteredMesh(
	mesh, mesh.getElementGroup("Bottom").getElements(),
	mesh.getElementGroup("Bottom").getNodeGroup().getNodes());
	prvdumper.registerField(
	"displacement",
	std::make_shared<dumpers::NodalField<Real, true>>(
	model.getDisplacement(), 0, 0,
	&(mesh.getElementGroup("Bottom").getNodeGroup().getNodes())));
	prvdumper.dump(0);
	}

	DumperText txtdumper("text_bottom", iohelper::_tdm_csv);
	txtdumper.setDirectory("paraview");
	txtdumper.setPrecision(8);
	txtdumper.setTimeStep(time_step);
	txtdumper.registerFilteredMesh(
	mesh, mesh.getElementGroup("Bottom").getElements(),
	mesh.getElementGroup("Bottom").getNodeGroup().getNodes());
	txtdumper.registerField(
	"displacement",
	std::make_shared<dumpers::NodalField<Real, true>>(
	model.getDisplacement(), 0, 0,
	&(mesh.getElementGroup("Bottom").getNodeGroup().getNodes())));
	txtdumper.registerField(
	"blocked_dofs",
	std::make_shared<dumpers::NodalField<bool, true>>(
	model.getBlockedDOFs(), 0, 0,
	&(mesh.getElementGroup("Bottom").getNodeGroup().getNodes())));

	Real pot_energy = 1.2345567891;
	Vector<Real> gforces(2, 1.);
	txtdumper.registerVariable(
	- "potential_energy", std::make_shared<dumpers::Variable<Real>>(pot_energy));
	+ "potential_energy",
	+ std::make_shared<dumpers::Variable<Real>>(pot_energy));
	txtdumper.registerVariable(
	"global_forces",
	std::make_shared<dumpers::Variable<Vector<Real>>>(gforces));

	// dump a first time before the main loop
	model.dumpGroup("Bottom");
	txtdumper.dump();

	Real time = 0.;
	for (UInt i = 1; i < 5; ++i) {
	pot_energy += 2.;
	gforces(0) += 0.1;
	gforces(1) += 0.2;

	// pre -> cor

	// increment time after all steps of integration
	time += time_step;

	// dump after time increment
	if (i % 2 == 0) {
	txtdumper.dump(time, i);
	model.dumpGroup("Bottom");

	// parallel test
	for (UInt p = 0; p < nbp; ++p) {
	prvdpr.setParallelContext(p, nbp, 0);
	prvdumper.dump(i);
	}
	}
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_io/test_parser/test_parser.cc b/test/test_io/test_parser/test_parser.cc
	index 4e85c0cb3..87f03b77f 100644
	--- a/test/test_io/test_parser/test_parser.cc
	+++ b/test/test_io/test_parser/test_parser.cc
	@@ -1,76 +1,76 @@
	/**
	* @file test_parser.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sun Jul 09 2017
	*
	* @brief test the input file parser
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_random_generator.hh"
	#include "parser.hh"

	#include <iostream>

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("input_file.dat", argc, argv);

	const Parser & p = getStaticParser();

	std::cout << RandomGenerator<UInt>::seed() << "==123456" << std::endl;

	std::cout << p << std::endl;

	Real toto = p.getParameter("toto");
	std::cout << toto;
	Real ref = 2 * M_PI + std::max(2., 50.);
	if (std::abs(toto - ref) > std::numeric_limits<Real>::epsilon()) {
	std::cout << "!=" << ref << std::endl;
	return 1;
	}

	std::cout << "==" << ref << std::endl;

	Vector<Real> vect = p.getParameter("vect");
	std::cout << vect << std::endl;

	Matrix<Real> mat = p.getParameter("mat");
	std::cout << mat << std::endl;

	RandomParameter<Real> rand1 = p.getParameter("rand1");
	std::cout << rand1 << std::endl;

	RandomParameter<Real> rand2 = p.getParameter("rand2");
	std::cout << rand2 << std::endl;

	RandomParameter<Real> rand3 = p.getParameter("rand3");
	std::cout << rand3 << std::endl;

	finalize();
	return 0;
	}
	diff --git a/test/test_mesh/test_mesh_periodic.cc b/test/test_mesh/test_mesh_periodic.cc
	index 9c80849e0..963e02c83 100644
	--- a/test/test_mesh/test_mesh_periodic.cc
	+++ b/test/test_mesh/test_mesh_periodic.cc
	@@ -1,143 +1,143 @@
	/**
	* @file test_mesh_periodic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Feb 12 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test makePeriodic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	//#include "mesh_partition_scotch.hh"
	#include "periodic_node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include "dumpable_inline_impl.hh"
	//#include "dumper_element_partition.hh"
	#include "dumper_iohelper_paraview.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char ** argv) {
	initialize(argc, argv);

	constexpr UInt dim = 3;

	auto prank = Communicator::getStaticCommunicator().whoAmI();
	// auto psize = Communicator::getStaticCommunicator().getNbProc();

	Mesh mesh(dim);
	if (prank == 0) {
	mesh.read("cube_periodic.msh");
	}

	MeshAccessor mesh_accessor(mesh);
	// mesh_accessor.wipePeriodicInfo();
	// mesh.makePeriodic(_z);

	// if (prank == 0) {
	// MeshPartitionScotch partition(mesh, dim);
	// partition.partitionate(psize);
	// }

	UInt offset = 0;
	for (auto && type : mesh.elementTypes()) {
	auto & g_ids = mesh.getDataPointer<UInt>("global_ids", type);
	for (auto && data : enumerate(g_ids)) {
	std::get<1>(data) = offset + std::get<0>(data);
	}
	offset += g_ids.size();
	}

	mesh.distribute();

	mesh.makePeriodic(_x);
	mesh.makePeriodic(_y);
	mesh.makePeriodic(_z);

	auto * dumper = new DumperParaview("periodic", "./paraview");
	mesh.registerExternalDumper(*dumper, "periodic", true);
	mesh.addDumpMesh(mesh);
	if (mesh.isDistributed()) {
	mesh.addDumpFieldExternalToDumper(
	"periodic", "node_type",
	const_cast<const Mesh &>(mesh).getNodesFlags());
	}
	mesh.dump();

	Array<Int> periodic(mesh.getNbNodes(), 1, 0.);
	Array<Int> masters(mesh.getNbNodes(), 1, 0.);
	Array<Int> global_ids(mesh.getNbNodes(), 1, 0.);
	UInt prev_node = -1;
	UInt value = 0;
	const auto & periodic_ms = mesh.getPeriodicMasterSlaves();
	for (auto & pair : periodic_ms) {
	if (prev_node != pair.first) {
	++value;
	}

	prev_node = pair.first;
	periodic(pair.first) = value;
	periodic(pair.second) = value;

	masters(pair.first) = 1;
	global_ids(pair.first) = mesh.getNodeGlobalId(pair.second);

	auto it = periodic_ms.find(pair.second);
	if (it != periodic_ms.end()) {
	AKANTU_EXCEPTION(pair.second << " is slave of " << pair.first
	<< " and master of " << it->second);
	}
	}
	mesh.addDumpFieldExternalToDumper("periodic", "periodic", periodic);
	mesh.addDumpFieldExternalToDumper("periodic", "masters", masters);
	mesh.addDumpFieldExternalToDumper("periodic", "global_ids", global_ids);
	mesh.addDumpFieldExternalToDumper("periodic", "element_global_ids",
	mesh.getData<UInt>("global_ids"));

	mesh.dump();

	Array<Int> data(mesh.getNbNodes(), 1, 0.);
	mesh.addDumpFieldExternalToDumper("periodic", "data", data);
	for (auto node : arange(mesh.getNbNodes())) {
	if (mesh.isPeriodicMaster(node)) {
	data(node) = 1 * (prank + 1);
	if (mesh.isMasterNode(node) or mesh.isLocalNode(node)) {
	data(node) = 10 * (prank + 1);
	}
	}
	}

	mesh.dump();

	// SimpleUIntDataAccessor<Int> data_accessor(data,
	// SynchronizationTag::_user_1);
	// mesh.getPeriodicNodeSynchronizer().synchronizeOnce(data_accessor,
	// SynchronizationTag::_user_1);
	mesh.dump();
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_20.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_20.cc
	index 3aebe1106..1082cf689 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_20.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_20.cc
	@@ -1,150 +1,150 @@
	/**
	* @file test_buildfacets_hexahedron_20.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with hexahedrons
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type = _hexahedron_20;

	Mesh mesh(spatial_dimension);
	mesh.read("hexahedron_20.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// std::cout << mesh_facets << std::endl;

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel3 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3(i)[j].type << " " << el_to_subel3(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type_facet);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 6; ++j) {
	std::cout << subel_to_el3(i, j).type << " " << subel_to_el3(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_8.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_8.cc
	index 0610e7b6b..0d7dd4617 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_8.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_hexahedron_8.cc
	@@ -1,150 +1,150 @@
	/**
	* @file test_buildfacets_hexahedron_8.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with hexahedrons
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type = _hexahedron_8;

	Mesh mesh(spatial_dimension);
	mesh.read("hexahedron_8.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// std::cout << mesh_facets << std::endl;

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel3 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3(i)[j].type << " " << el_to_subel3(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type_facet);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 6; ++j) {
	std::cout << subel_to_el3(i, j).type << " " << subel_to_el3(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_linear.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_linear.cc
	index 214ee1049..0f96ad7ab 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_linear.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_linear.cc
	@@ -1,133 +1,133 @@
	/**
	* @file test_buildfacets_mixed2d_linear.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with quadrangles
	* and triangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type1 = _quadrangle_4;
	const ElementType type2 = _triangle_3;

	Mesh mesh(spatial_dimension);
	mesh.read("mixed2d_linear.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type1);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2_1 =
	mesh_facets.getSubelementToElement(type1);
	const Array<Element> & subel_to_el2_2 =
	mesh_facets.getSubelementToElement(type2);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2_1.size(); ++i) {
	std::cout << type1 << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2_1(i, j).type << " "
	<< subel_to_el2_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < subel_to_el2_2.size(); ++i) {
	std::cout << type2 << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2_2(i, j).type << " "
	<< subel_to_el2_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_quadratic.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_quadratic.cc
	index 77ee43d3e..d9ef56d6f 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_quadratic.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed2d_quadratic.cc
	@@ -1,133 +1,133 @@
	/**
	* @file test_buildfacets_mixed2d_quadratic.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with quadrangles
	* and triangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type1 = _quadrangle_8;
	const ElementType type2 = _triangle_6;

	Mesh mesh(spatial_dimension);
	mesh.read("mixed2d_quadratic.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type1);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2_1 =
	mesh_facets.getSubelementToElement(type1);
	const Array<Element> & subel_to_el2_2 =
	mesh_facets.getSubelementToElement(type2);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2_1.size(); ++i) {
	std::cout << type1 << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2_1(i, j).type << " "
	<< subel_to_el2_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < subel_to_el2_2.size(); ++i) {
	std::cout << type2 << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2_2(i, j).type << " "
	<< subel_to_el2_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_linear.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_linear.cc
	index cab9ed2e9..ee2c04488 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_linear.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_linear.cc
	@@ -1,181 +1,181 @@
	/**
	* @file test_buildfacets_mixed3d_linear.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with hexahedrons
	* and pentahedrons
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type1 = _hexahedron_8;
	const ElementType type2 = _pentahedron_6;

	Mesh mesh(spatial_dimension);
	mesh.read("mixed3d_linear.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet1 = mesh.getFacetType(type1);
	const ElementType type_facet2 = mesh.getFacetType(type2);
	const ElementType type_subfacet = mesh.getFacetType(type_facet1);
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel3_1 =
	mesh_facets.getElementToSubelement(type_facet1);
	const Array<std::vector<Element>> & el_to_subel3_2 =
	mesh_facets.getElementToSubelement(type_facet2);
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3_1.size(); ++i) {
	std::cout << type_facet1 << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3_1(i)[j].type << " "
	<< el_to_subel3_1(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < el_to_subel3_2.size(); ++i) {
	std::cout << type_facet2 << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3_2(i)[j].type << " "
	<< el_to_subel3_2(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3_1 =
	mesh_facets.getSubelementToElement(type1);
	const Array<Element> & subel_to_el3_2 =
	mesh_facets.getSubelementToElement(type2);
	const Array<Element> & subel_to_el2_1 =
	mesh_facets.getSubelementToElement(type_facet1);
	const Array<Element> & subel_to_el2_2 =
	mesh_facets.getSubelementToElement(type_facet2);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3_1.size(); ++i) {
	std::cout << type1 << " " << i << " connected to ";
	for (UInt j = 0; j < 6; ++j) {
	std::cout << subel_to_el3_1(i, j).type << " "
	<< subel_to_el3_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < subel_to_el3_2.size(); ++i) {
	std::cout << type2 << " " << i << " connected to ";
	for (UInt j = 0; j < 5; ++j) {
	std::cout << subel_to_el3_2(i, j).type << " "
	<< subel_to_el3_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2_1.size(); ++i) {
	std::cout << type_facet1 << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2_1(i, j).type << " "
	<< subel_to_el2_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < subel_to_el2_2.size(); ++i) {
	std::cout << type_facet2 << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2_2(i, j).type << " "
	<< subel_to_el2_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_quadratic.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_quadratic.cc
	index 62e5eaa94..e0b950663 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_quadratic.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_mixed3d_quadratic.cc
	@@ -1,182 +1,182 @@
	/**
	* @file test_buildfacets_mixed3d_quadratic.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with hexahedrons
	* and pentahedrons
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type1 = _hexahedron_20;
	const ElementType type2 = _pentahedron_15;

	Mesh mesh(spatial_dimension);
	mesh.read("mixed3d_quadratic.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet1 = mesh.getFacetType(type1);
	const ElementType type_facet2 = mesh.getFacetType(type2);
	const ElementType type_subfacet = mesh.getFacetType(type_facet1);
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel3_1 =
	mesh_facets.getElementToSubelement(type_facet1);
	const Array<std::vector<Element>> & el_to_subel3_2 =
	mesh_facets.getElementToSubelement(type_facet2);
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3_1.size(); ++i) {
	std::cout << type_facet1 << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3_1(i)[j].type << " "
	<< el_to_subel3_1(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < el_to_subel3_2.size(); ++i) {
	std::cout << type_facet2 << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3_2(i)[j].type << " "
	<< el_to_subel3_2(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3_1 =
	mesh_facets.getSubelementToElement(type1);
	const Array<Element> & subel_to_el3_2 =
	mesh_facets.getSubelementToElement(type2);
	const Array<Element> & subel_to_el2_1 =
	mesh_facets.getSubelementToElement(type_facet1);
	const Array<Element> & subel_to_el2_2 =
	mesh_facets.getSubelementToElement(type_facet2);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3_1.size(); ++i) {
	std::cout << type1 << " " << i << " connected to ";
	for (UInt j = 0; j < 6; ++j) {
	std::cout << subel_to_el3_1(i, j).type << " "
	<< subel_to_el3_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt i = 0; i < subel_to_el3_2.size(); ++i) {
	std::cout << type2 << " " << i << " connected to ";
	for (UInt j = 0; j < 5; ++j) {
	std::cout << subel_to_el3_2(i, j).type << " "
	<< subel_to_el3_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2_1.size(); ++i) {
	std::cout << type_facet1 << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2_1(i, j).type << " "
	<< subel_to_el2_1(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2_2.size(); ++i) {
	std::cout << type_facet2 << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2_2(i, j).type << " "
	<< subel_to_el2_2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_15.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_15.cc
	index 671a51fbe..83027c537 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_15.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_15.cc
	@@ -1,154 +1,152 @@
	/**
	* @file test_buildfacets_pentahedron_15.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type = _pentahedron_15;

	Mesh mesh(spatial_dimension);
	mesh.read("pentahedron_15.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	Vector<const ElementType> types_facet(mesh.getAllFacetTypes(type));
	const ElementType type_subfacet = mesh.getFacetType(types_facet(0));
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	for (UInt ft = 0; ft < types_facet.size(); ++ft) {
	ElementType type_facet = types_facet(ft);
	- auto && el_to_subel3 =
	- mesh_facets.getElementToSubelement(type_facet);
	+ auto && el_to_subel3 = mesh_facets.getElementToSubelement(type_facet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3(i)[j].type << " "
	<< el_to_subel3(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}
	}

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3 =
	mesh_facets.getSubelementToElement(type);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el3.getNbComponent(); ++j) {
	std::cout << subel_to_el3(i, j).type << " " << subel_to_el3(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt ft = 0; ft < types_facet.size(); ++ft) {
	ElementType type_facet = types_facet(ft);
	- auto && subel_to_el2 =
	- mesh_facets.getSubelementToElement(type_facet);
	+ auto && subel_to_el2 = mesh_facets.getSubelementToElement(type_facet);

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el2.getNbComponent(); ++j) {
	std::cout << subel_to_el2(i, j).type << " "
	<< subel_to_el2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}
	}

	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el1.getNbComponent(); ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_6.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_6.cc
	index ad15df1a7..516ae6eab 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_6.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_pentahedron_6.cc
	@@ -1,154 +1,151 @@
	/**
	* @file test_buildfacets_pentahedron_6.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type = _pentahedron_6;

	Mesh mesh(spatial_dimension);
	mesh.read("pentahedron_6.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	Vector<const ElementType> types_facet(mesh.getAllFacetTypes(type));
	const ElementType type_subfacet = mesh.getFacetType(types_facet(0));
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	for (UInt ft = 0; ft < types_facet.size(); ++ft) {
	ElementType type_facet = types_facet(ft);
	- auto && el_to_subel3 =
	- mesh_facets.getElementToSubelement(type_facet);
	+ auto && el_to_subel3 = mesh_facets.getElementToSubelement(type_facet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3(i)[j].type << " "
	<< el_to_subel3(i)[j].element << ", ";
	}
	std::cout << " " << std::endl;
	}
	}

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	- auto && subel_to_el3 =
	- mesh_facets.getSubelementToElement(type);
	+ auto && subel_to_el3 = mesh_facets.getSubelementToElement(type);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el3.getNbComponent(); ++j) {
	std::cout << subel_to_el3(i, j).type << " " << subel_to_el3(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	for (UInt ft = 0; ft < types_facet.size(); ++ft) {
	ElementType type_facet = types_facet(ft);
	- auto && subel_to_el2 =
	- mesh_facets.getSubelementToElement(type_facet);
	+ auto && subel_to_el2 = mesh_facets.getSubelementToElement(type_facet);

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el2.getNbComponent(); ++j) {
	std::cout << subel_to_el2(i, j).type << " "
	<< subel_to_el2(i, j).element << ", ";
	}
	std::cout << " " << std::endl;
	}
	}

	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < subel_to_el1.getNbComponent(); ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_4.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_4.cc
	index d9836686e..dac8d1620 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_4.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_4.cc
	@@ -1,120 +1,120 @@
	/**
	* @file test_buildfacets_quadrangle_4.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with quadrangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type = _quadrangle_4;

	Mesh mesh(spatial_dimension);
	mesh.read("quadrangle_4.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_8.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_8.cc
	index 11bc1c7b0..5c0c45d76 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_8.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_quadrangle_8.cc
	@@ -1,120 +1,120 @@
	/**
	* @file test_buildfacets_quadrangle_8.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with quadrangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type = _quadrangle_8;

	Mesh mesh(spatial_dimension);
	mesh.read("quadrangle_8.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_tetrahedron_10.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_tetrahedron_10.cc
	index ce3608b50..78397077d 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_tetrahedron_10.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_tetrahedron_10.cc
	@@ -1,149 +1,149 @@
	/**
	* @file test_buildfacets_tetrahedron_10.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 3;
	const ElementType type = _tetrahedron_10;

	Mesh mesh(spatial_dimension);
	mesh.read("tetrahedron_10.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// std::cout << mesh_facets << std::endl;

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);
	const ElementType type_subsubfacet = mesh.getFacetType(type_subfacet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel3 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_subfacet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subsubfacet);

	std::cout << "ElementToSubelement3" << std::endl;
	for (UInt i = 0; i < el_to_subel3.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel3(i)[j].type << " " << el_to_subel3(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel2(i).size(); ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subsubfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el3 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type_facet);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_subfacet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement3" << std::endl;
	for (UInt i = 0; i < subel_to_el3.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 4; ++j) {
	std::cout << subel_to_el3(i, j).type << " " << subel_to_el3(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_3.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_3.cc
	index 5af6b3f78..b006f2707 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_3.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_3.cc
	@@ -1,119 +1,119 @@
	/**
	* @file test_buildfacets_triangle_3.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Test to check the building of the facets. Mesh with triangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type = _triangle_3;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle_3.msh");
	const auto & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */
	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_6.cc b/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_6.cc
	index 06613981a..67e66ec60 100644
	--- a/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_6.cc
	+++ b/test/test_mesh_utils/test_buildfacets/test_buildfacets_triangle_6.cc
	@@ -1,120 +1,120 @@
	/**
	* @file test_buildfacets_triangle_6.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Thu Nov 09 2017
	*
	* @brief Test to check the building of the facets. Mesh with triangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const UInt spatial_dimension = 2;
	const ElementType type = _triangle_6;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle_6.msh");
	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");

	const ElementType type_facet = mesh.getFacetType(type);
	const ElementType type_subfacet = mesh.getFacetType(type_facet);

	/* ------------------------------------------------------------------------ */
	/* Element to Subelement testing */
	/* ------------------------------------------------------------------------ */

	const Array<std::vector<Element>> & el_to_subel2 =
	mesh_facets.getElementToSubelement(type_facet);
	const Array<std::vector<Element>> & el_to_subel1 =
	mesh_facets.getElementToSubelement(type_subfacet);

	std::cout << "ElementToSubelement2" << std::endl;
	for (UInt i = 0; i < el_to_subel2.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << el_to_subel2(i)[j].type << " " << el_to_subel2(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "ElementToSubelement1" << std::endl;
	for (UInt i = 0; i < el_to_subel1.size(); ++i) {
	std::cout << type_subfacet << " " << i << " connected to ";
	for (UInt j = 0; j < el_to_subel1(i).size(); ++j) {
	std::cout << el_to_subel1(i)[j].type << " " << el_to_subel1(i)[j].element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	/* ------------------------------------------------------------------------ */
	/* Subelement to Element testing */
	/* ------------------------------------------------------------------------ */

	const Array<Element> & subel_to_el2 =
	mesh_facets.getSubelementToElement(type);
	const Array<Element> & subel_to_el1 =
	mesh_facets.getSubelementToElement(type_facet);

	std::cout << " " << std::endl;
	std::cout << "SubelementToElement2" << std::endl;
	for (UInt i = 0; i < subel_to_el2.size(); ++i) {
	std::cout << type << " " << i << " connected to ";
	for (UInt j = 0; j < 3; ++j) {
	std::cout << subel_to_el2(i, j).type << " " << subel_to_el2(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	std::cout << "SubelementToElement1" << std::endl;
	for (UInt i = 0; i < subel_to_el1.size(); ++i) {
	std::cout << type_facet << " " << i << " connected to ";
	for (UInt j = 0; j < 2; ++j) {
	std::cout << subel_to_el1(i, j).type << " " << subel_to_el1(i, j).element
	<< ", ";
	}
	std::cout << " " << std::endl;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh.cc b/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh.cc
	index c9cc4731c..53a1625d6 100644
	--- a/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh.cc
	+++ b/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh.cc
	@@ -1,54 +1,54 @@
	/**
	* @file test_mesh_io_msh.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu Jul 15 2010
	* @date last modification: Fri Jan 15 2016
	*
	* @brief unit test for the MeshIOMSH class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);
	akantu::MeshIOMSH mesh_io;
	akantu::Mesh mesh(3);

	mesh_io.read("./cube.msh", mesh);

	std::cout << mesh << std::endl;

	mesh_io.write("./cube.out", mesh);

	akantu::finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh_physical_names.cc b/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh_physical_names.cc
	index dd08e5e41..ebea0cb68 100644
	--- a/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh_physical_names.cc
	+++ b/test/test_mesh_utils/test_mesh_io/test_mesh_io_msh_physical_names.cc
	@@ -1,61 +1,61 @@
	/**
	* @file test_mesh_io_msh_physical_names.cc
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Nov 02 2018
	*
	* @brief unit test for the MeshIOMSH physical names class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "aka_common.hh"
	#include "mesh.hh"
	#include <iostream>
	#include <sstream>

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	UInt spatialDimension(3);

	akantu::initialize(argc, argv);

	Mesh mesh(spatialDimension);

	mesh.read("./cube_physical_names.msh");
	std::stringstream sstr;

	for (auto type : mesh.elementTypes()) {
	const Array<std::string> & name_vec =
	mesh.getData<std::string>("physical_names", type);
	for (UInt i(0); i < name_vec.size(); i++) {
	std::cout << "Element " << i << " (of type " << type
	<< ") has physical name " << name_vec(i) << "." << std::endl;
	}
	}

	akantu::finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_mesh_iterators.cc b/test/test_mesh_utils/test_mesh_iterators.cc
	index a17321c8c..bda4d005b 100644
	--- a/test/test_mesh_utils/test_mesh_iterators.cc
	+++ b/test/test_mesh_utils/test_mesh_iterators.cc
	@@ -1,75 +1,75 @@
	/**
	* @file test_mesh_iterators.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Jun 13 2019
	*
	* @brief Test the mesh iterators
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "element_group.hh"
	#include "mesh.hh"
	#include "mesh_iterators.hh"
	#include "node_group.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	Mesh mesh(3);
	const Mesh & cmesh = mesh;
	mesh.read("iterators_mesh.msh");

	std::cout << "ElementGroups" << std::endl;
	for (auto && element_group : mesh.iterateElementGroups()) {
	std::cout << element_group.getName() << " " << element_group.getDimension()
	<< std::endl;
	}

	std::cout << "NodeGroups" << std::endl;
	for (auto && node_group : cmesh.iterateNodeGroups()) {
	std::cout << node_group.getName() << std::endl;
	}

	std::cout << "enumerate(ElementGroups)" << std::endl;
	for (auto && element_group : enumerate(mesh.iterateElementGroups())) {
	std::cout << std::get<0>(element_group) << " "
	<< std::get<1>(element_group).getName() << std::endl;
	}

	// for (auto && node_group :
	// counting(NodeGroupsIterable(cmesh))) {
	// std::cout << std::get<0>(node_group) << " " <<
	// std::get<1>(node_group).getName() << std::endl;
	// }

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_mesh_data.cc b/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_mesh_data.cc
	index 8d4697d66..c5eddb71a 100644
	--- a/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_mesh_data.cc
	+++ b/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_mesh_data.cc
	@@ -1,117 +1,117 @@
	/**
	* @file test_mesh_partitionate_mesh_data.cc
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Nov 02 2018
	*
	* @brief test of manual partitioner
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_partition_mesh_data.hh"
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_elemental_field.hh"
	#include "dumper_paraview.hh"
	#endif // AKANTU_USE_IOHELPER
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt dim = 2;
	UInt nb_partitions = 8;
	akantu::Mesh mesh(dim);
	mesh.read("quad.msh");

	ElementTypeMapArray<UInt> partition;
	UInt nb_component = 1;

	GhostType gt = _not_ghost;
	for (auto & type : mesh.elementTypes(dim, gt)) {
	UInt nb_element = mesh.getNbElement(type, gt);
	partition.alloc(nb_element, nb_component, type, gt);
	Array<UInt> & type_partition_reference = partition(type, gt);
	for (UInt i(0); i < nb_element; ++i) {
	Vector<Real> barycenter(dim);
	Element element{type, i, gt};
	mesh.getBarycenter(element, barycenter);

	Real real_proc = barycenter[0] * nb_partitions;
	if (std::abs(real_proc - round(real_proc)) <
	10 * std::numeric_limits<Real>::epsilon()) {
	type_partition_reference(i) = round(real_proc);
	} else {
	std::cout << "*";
	type_partition_reference(i) = floor(real_proc);
	}
	std::cout << "Assigned proc " << type_partition_reference(i)
	<< " to elem " << i << " (type " << type
	<< ", barycenter x-coordinate " << barycenter[0] << ")"
	<< std::endl;
	}
	}

	akantu::MeshPartitionMeshData * partitioner =
	new akantu::MeshPartitionMeshData(mesh, dim);
	partitioner->setPartitionMapping(partition);
	partitioner->partitionate(nb_partitions);

	for (auto & type : mesh.elementTypes(dim, gt)) {
	UInt nb_element = mesh.getNbElement(type, gt);
	const Array<UInt> & type_partition_reference = partition(type, gt);
	const Array<UInt> & type_partition = partitioner->getPartitions()(type, gt);
	for (UInt i(0); i < nb_element; ++i) {
	if (not(type_partition(i) == type_partition_reference(i))) {
	std::cout << "Incorrect partitioning" << std::endl;
	return 1;
	}
	}
	}

	#ifdef DEBUG_TEST
	DumperParaview dumper("test-mesh-data-partition");
	dumpers::Field * field1 =
	new dumpers::ElementalField<UInt>(partitioner->getPartitions(), dim);
	dumpers::Field * field2 = new dumpers::ElementalField<UInt>(partition, dim);
	dumper.registerMesh(mesh, dim);
	dumper.registerField("partitions", field1);
	dumper.registerField("partitions_ref", field2);
	dumper.dump();
	#endif

	delete partitioner;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_scotch.cc b/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_scotch.cc
	index 253fa2700..b2868f25f 100644
	--- a/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_scotch.cc
	+++ b/test/test_mesh_utils/test_mesh_partitionate/test_mesh_partitionate_scotch.cc
	@@ -1,75 +1,75 @@
	/**
	* @file test_mesh_partitionate_scotch.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Sep 12 2010
	* @date last modification: Fri Nov 02 2018
	*
	* @brief test of internal facet extraction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_partition_scotch.hh"
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_elemental_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif // AKANTU_USE_IOHELPER

	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);
	debug::setDebugLevel(akantu::dblDump);

	int dim = 2;

	Mesh mesh(dim);
	mesh.read("triangle.msh");

	MeshPartitionScotch partition(mesh, dim);
	partition.partitionate(8);

	#ifdef AKANTU_USE_IOHELPER
	DumperParaview dumper("test-scotch-partition");
	auto field = std::make_shared<dumpers::ElementalField<UInt>>(
	partition.getPartitions(), dim);
	dumper.registerMesh(mesh, dim);
	dumper.registerField("partitions", field);
	dumper.dump();
	#endif // AKANTU_USE_IOHELPER

	partition.reorder();
	mesh.write("triangle_reorder.msh");

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_pbc_tweak/test_pbc_tweak.cc b/test/test_mesh_utils/test_pbc_tweak/test_pbc_tweak.cc
	index 2d8ac8555..87db5f0d6 100644
	--- a/test/test_mesh_utils/test_pbc_tweak/test_pbc_tweak.cc
	+++ b/test/test_mesh_utils/test_pbc_tweak/test_pbc_tweak.cc
	@@ -1,71 +1,71 @@
	/**
	* @file test_pbc_tweak.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Dec 07 2016
	*
	* @brief test of internal facet extraction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	int dim = 3;

	initialize("material.dat", argc, argv);
	debug::setDebugLevel(akantu::dblInfo);

	Mesh mesh(dim);
	mesh.read("cube.msh");

	SolidMechanicsModel model(mesh);
	/* --------------------------------------------------------------------------
	*/
	model.initFull();
	/* --------------------------------------------------------------------------
	*/
	// model.setPBC(1,1,1);
	// model.initPBC();
	model.assembleMassLumped();
	/* --------------------------------------------------------------------------
	*/

	model.setBaseName("test-pbc-tweak");
	model.addDumpField("mass");
	model.dump();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_purify_mesh.cc b/test/test_mesh_utils/test_purify_mesh.cc
	index e48adc491..bcc365970 100644
	--- a/test/test_mesh_utils/test_purify_mesh.cc
	+++ b/test/test_mesh_utils/test_purify_mesh.cc
	@@ -1,62 +1,62 @@
	/**
	* @file test_purify_mesh.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test the purifyMesh function from MeshUtils
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);

	Mesh mesh(2);

	mesh.read("purify_mesh.msh");

	MeshUtils::purifyMesh(mesh);

	mesh.write("purify_mesh_after.msh");

	if (mesh.getNbNodes() != 21)
	AKANTU_ERROR(
	"The purified mesh does not contain the good number of nodes.");

	if (mesh.getNbElement(_quadrangle_8) != 4)
	AKANTU_ERROR(
	"The purified mesh does not contain the good number of element.");

	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_mesh_utils/test_segment_nodetype/test_segment_nodetype.cc b/test/test_mesh_utils/test_segment_nodetype/test_segment_nodetype.cc
	index 12c9024bf..7eeb127d9 100644
	--- a/test/test_mesh_utils/test_segment_nodetype/test_segment_nodetype.cc
	+++ b/test/test_mesh_utils/test_segment_nodetype/test_segment_nodetype.cc
	@@ -1,98 +1,98 @@
	/**
	* @file test_segment_nodetype.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Sep 18 2015
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test to verify that the node type is correctly associated to
	* the segments in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_synchronizer.hh"
	#include "mesh_utils.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt spatial_dimension = 3;
	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	// partition the mesh
	if (prank == 0) {
	mesh.read("mesh.msh");
	}

	mesh.distribute();

	// compute the node types for each segment
	Mesh & mesh_facets = mesh.initMeshFacets();
	MeshUtils::buildSegmentToNodeType(mesh, mesh_facets);

	// verify that the number of segments per node type makes sense
	std::map<Int, UInt> nb_facets_per_nodetype;
	UInt nb_segments = 0;

	for (auto ghost_type : ghost_types) {
	const Array<Int> & segment_to_nodetype =
	mesh_facets.getData<Int>("segment_to_nodetype", _segment_2, ghost_type);

	// count the number of segments per node type
	for (auto & stn : segment_to_nodetype) {
	if (nb_facets_per_nodetype.find(stn) == nb_facets_per_nodetype.end())
	nb_facets_per_nodetype[stn] = 1;
	else
	++nb_facets_per_nodetype[stn];
	}
	nb_segments += segment_to_nodetype.size();
	}

	// checking the solution
	if (nb_segments != 24)
	AKANTU_ERROR("The number of segments is wrong");

	if (prank == 0) {
	if (nb_facets_per_nodetype[-1] != 3 \|\| nb_facets_per_nodetype[-2] != 9 \|\|
	nb_facets_per_nodetype[-3] != 12)
	AKANTU_ERROR("The segments of processor 0 have the wrong node type");

	if (nb_facets_per_nodetype.size() > 3)
	AKANTU_ERROR("Processor 0 cannot have any slave segment");
	}

	if (prank == psize - 1 &&
	nb_facets_per_nodetype.find(-2) != nb_facets_per_nodetype.end())
	AKANTU_ERROR("The last processor must not have any master facets");

	finalize();
	return 0;
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.cc b/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.cc
	index 14e981590..0c9760c92 100644
	--- a/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.cc
	@@ -1,138 +1,138 @@
	/**
	* @file patch_test_linear_anisotropic_explicit.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Till Junge <till.junge@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Tue May 14 2019
	* @date last modification: Thu Oct 29 2020
	*
	* @brief patch test for elastic material in solid mechanics model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "patch_test_linear_solid_mechanics_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	// Stiffness tensor, rotated by hand

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, AnisotropicExplicit) {
	Real C[3][3][3][3] = {
	{{{112.93753505, 1.85842452538e-10, -4.47654358027e-10},
	{1.85847317471e-10, 54.2334345331, -3.69840984824},
	{-4.4764768395e-10, -3.69840984824, 56.848605217}},
	{{1.85847781609e-10, 25.429294233, -3.69840984816},
	{25.429294233, 3.31613847493e-10, -8.38797920011e-11},
	{-3.69840984816, -8.38804581349e-11, -1.97875715813e-10}},
	{{-4.47654358027e-10, -3.69840984816, 28.044464917},
	{-3.69840984816, 2.09374961813e-10, 9.4857455224e-12},
	{28.044464917, 9.48308098714e-12, -2.1367885239e-10}}},
	{{{1.85847781609e-10, 25.429294233, -3.69840984816},
	{25.429294233, 3.31613847493e-10, -8.38793479119e-11},
	{-3.69840984816, -8.38795699565e-11, -1.97876381947e-10}},
	{{54.2334345331, 3.31617400207e-10, 2.09372075233e-10},
	{3.3161562385e-10, 115.552705733, -3.15093728886e-10},
	{2.09372075233e-10, -3.15090176173e-10, 54.2334345333}},
	{{-3.69840984824, -8.38795699565e-11, 9.48219280872e-12},
	{-8.38795699565e-11, -3.1509195253e-10, 25.4292942335},
	{9.48441325477e-12, 25.4292942335, 3.69840984851}}},
	{{{-4.47653469848e-10, -3.69840984816, 28.044464917},
	{-3.69840984816, 2.09374073634e-10, 9.48752187924e-12},
	{28.044464917, 9.48552347779e-12, -2.1367885239e-10}},
	{{-3.69840984824, -8.3884899027e-11, 9.48219280872e-12},
	{-8.3884899027e-11, -3.150972816e-10, 25.4292942335},
	{9.48041645188e-12, 25.4292942335, 3.69840984851}},
	{{56.848605217, -1.97875493768e-10, -2.13681516925e-10},
	{-1.97877270125e-10, 54.2334345333, 3.69840984851},
	{-2.13683293282e-10, 3.69840984851, 112.93753505}}}};

	if (this->dim == 2) {
	for (UInt i = 0; i < this->dim; ++i) {
	for (UInt j = 0; j < this->dim; ++j) {
	for (UInt k = 0; k < this->dim; ++k) {
	for (UInt l = 0; l < this->dim; ++l) {
	C[i][j][k][l] = 0;
	}
	}
	}
	}
	C[0][0][0][0] = C[1][1][1][1] = 112.93753504999995;
	C[0][0][1][1] = C[1][1][0][0] = 51.618263849999984;
	C[0][1][0][1] = C[1][0][0][1] = C[0][1][1][0] = C[1][0][1][0] =
	22.814123549999987;
	}

	if (this->dim == 1) {
	C[0][0][0][0] = 105.092023;
	}
	this->initModel(_explicit_lumped_mass,
	"material_anisotropic_" + std::to_string(this->dim) + ".dat");

	const auto & coordinates = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();

	// set the position of all nodes to the static solution
	for (auto && tuple : zip(make_view(coordinates, this->dim),
	make_view(displacement, this->dim))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}

	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	auto ekin = this->model->getEnergy("kinetic");
	EXPECT_NEAR(0, ekin, 1e-16);

	auto & mat = this->model->getMaterial(0);

	this->checkDOFs(displacement);
	this->checkGradient(mat.getGradU(this->type), displacement);

	this->result_tolerance = 1e-11;
	this->checkResults(
	[&](const Matrix<Real> & pstrain) {
	auto strain = (pstrain + pstrain.transpose()) / 2.;
	decltype(strain) stress(this->dim, this->dim);

	for (UInt i = 0; i < this->dim; ++i) {
	for (UInt j = 0; j < this->dim; ++j) {
	stress(i, j) = 0;
	for (UInt k = 0; k < this->dim; ++k) {
	for (UInt l = 0; l < this->dim; ++l) {
	stress(i, j) += C[i][j][k][l] * strain(k, l);
	}
	}
	}
	}
	return stress;
	},
	mat.getStress(this->type), displacement);
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_anisotropic_implicit.cc b/test/test_model/patch_tests/patch_test_linear_anisotropic_implicit.cc
	index 88faf78f3..e4134fe6c 100644
	--- a/test/test_model/patch_tests/patch_test_linear_anisotropic_implicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_anisotropic_implicit.cc
	@@ -1,131 +1,131 @@
	/**
	* @file patch_test_linear_anisotropic_implicit.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Till Junge <till.junge@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
	*
	* @date creation: Tue May 14 2019
	* @date last modification: Thu Oct 29 2020
	*
	* @brief patch test for elastic material in solid mechanics model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "patch_test_linear_solid_mechanics_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	// Stiffness tensor, rotated by hand

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, AnisotropicStatic) {
	Real C[3][3][3][3] = {
	{{{112.93753505, 1.85842452538e-10, -4.47654358027e-10},
	{1.85847317471e-10, 54.2334345331, -3.69840984824},
	{-4.4764768395e-10, -3.69840984824, 56.848605217}},
	{{1.85847781609e-10, 25.429294233, -3.69840984816},
	{25.429294233, 3.31613847493e-10, -8.38797920011e-11},
	{-3.69840984816, -8.38804581349e-11, -1.97875715813e-10}},
	{{-4.47654358027e-10, -3.69840984816, 28.044464917},
	{-3.69840984816, 2.09374961813e-10, 9.4857455224e-12},
	{28.044464917, 9.48308098714e-12, -2.1367885239e-10}}},
	{{{1.85847781609e-10, 25.429294233, -3.69840984816},
	{25.429294233, 3.31613847493e-10, -8.38793479119e-11},
	{-3.69840984816, -8.38795699565e-11, -1.97876381947e-10}},
	{{54.2334345331, 3.31617400207e-10, 2.09372075233e-10},
	{3.3161562385e-10, 115.552705733, -3.15093728886e-10},
	{2.09372075233e-10, -3.15090176173e-10, 54.2334345333}},
	{{-3.69840984824, -8.38795699565e-11, 9.48219280872e-12},
	{-8.38795699565e-11, -3.1509195253e-10, 25.4292942335},
	{9.48441325477e-12, 25.4292942335, 3.69840984851}}},
	{{{-4.47653469848e-10, -3.69840984816, 28.044464917},
	{-3.69840984816, 2.09374073634e-10, 9.48752187924e-12},
	{28.044464917, 9.48552347779e-12, -2.1367885239e-10}},
	{{-3.69840984824, -8.3884899027e-11, 9.48219280872e-12},
	{-8.3884899027e-11, -3.150972816e-10, 25.4292942335},
	{9.48041645188e-12, 25.4292942335, 3.69840984851}},
	{{56.848605217, -1.97875493768e-10, -2.13681516925e-10},
	{-1.97877270125e-10, 54.2334345333, 3.69840984851},
	{-2.13683293282e-10, 3.69840984851, 112.93753505}}}};

	if (this->dim == 2) {
	for (UInt i = 0; i < this->dim; ++i) {
	for (UInt j = 0; j < this->dim; ++j) {
	for (UInt k = 0; k < this->dim; ++k) {
	for (UInt l = 0; l < this->dim; ++l) {
	C[i][j][k][l] = 0;
	}
	}
	}
	}
	C[0][0][0][0] = C[1][1][1][1] = 112.93753504999995;
	C[0][0][1][1] = C[1][1][0][0] = 51.618263849999984;
	C[0][1][0][1] = C[1][0][0][1] = C[0][1][1][0] = C[1][0][1][0] =
	22.814123549999987;
	}

	if (this->dim == 1) {
	C[0][0][0][0] = 105.092023;
	}

	this->initModel(_static,
	"material_anisotropic_" + std::to_string(this->dim) + ".dat");

	auto & solver = this->model->getNonLinearSolver();
	solver.set("max_iterations", 2);
	solver.set("threshold", 2e-4);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	this->model->solveStep();

	auto & mat = this->model->getMaterial(0);

	const auto & displacement = this->model->getDisplacement();
	this->checkDOFs(displacement);
	this->checkGradient(mat.getGradU(this->type), displacement);

	this->result_tolerance = 1e-11;
	this->checkResults(
	[&](const Matrix<Real> & pstrain) {
	auto strain = (pstrain + pstrain.transpose()) / 2.;
	decltype(strain) stress(this->dim, this->dim);

	for (UInt i = 0; i < this->dim; ++i) {
	for (UInt j = 0; j < this->dim; ++j) {
	stress(i, j) = 0;
	for (UInt k = 0; k < this->dim; ++k) {
	for (UInt l = 0; l < this->dim; ++l) {
	stress(i, j) += C[i][j][k][l] * strain(k, l);
	}
	}
	}
	}
	return stress;
	},
	mat.getStress(this->type), displacement);
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_elastic_explicit.cc b/test/test_model/patch_tests/patch_test_linear_elastic_explicit.cc
	index c0a9845b6..9943fdbdf 100644
	--- a/test/test_model/patch_tests/patch_test_linear_elastic_explicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_elastic_explicit.cc
	@@ -1,100 +1,100 @@
	/**
	* @file patch_test_linear_elastic_explicit.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Thu Oct 29 2020
	*
	* @brief patch test solid mechanics explicit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_solid_mechanics_fixture.hh"
	/* -------------------------------------------------------------------------- */

	TYPED_TEST(TestPatchTestSMMLinear, Explicit) {
	std::string filename = "material_check_stress_plane_stress.dat";
	if (this->plane_strain)
	filename = "material_check_stress_plane_strain.dat";

	this->initModel(_explicit_lumped_mass, filename);

	const auto & coordinates = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();
	// set the position of all nodes to the static solution
	for (auto && tuple : zip(make_view(coordinates, this->dim),
	make_view(displacement, this->dim))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}
	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	auto ekin = this->model->getEnergy("kinetic");
	EXPECT_NEAR(0, ekin, 1e-16);

	this->checkAll();

	#define debug 0
	#if debug
	this->model->setBaseName(std::to_string(this->type) + "_explicit");
	this->model->addDumpField("stress");
	this->model->addDumpField("grad_u");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpFieldVector("displacement");
	this->model->dump();
	#endif
	-
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, ExplicitFiniteDeformation) {
	- std::string filename = "material_check_stress_plane_stress_finite_deformation.dat";
	+ std::string filename =
	+ "material_check_stress_plane_stress_finite_deformation.dat";
	if (this->plane_strain) {
	filename = "material_check_stress_plane_strain_finite_deformation.dat";
	} else {
	SUCCEED();
	return;
	}

	this->initModel(_explicit_lumped_mass, filename);

	const auto & coordinates = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();
	// set the position of all nodes to the static solution
	for (auto && tuple : zip(make_view(coordinates, this->dim),
	make_view(displacement, this->dim))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}
	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	auto ekin = this->model->getEnergy("kinetic");
	EXPECT_NEAR(0, ekin, 1e-16);

	this->checkAll();
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_elastic_implicit.cc b/test/test_model/patch_tests/patch_test_linear_elastic_implicit.cc
	index 9932bc8f6..133f44e36 100644
	--- a/test/test_model/patch_tests/patch_test_linear_elastic_implicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_elastic_implicit.cc
	@@ -1,172 +1,168 @@
	/**
	* @file patch_test_linear_elastic_implicit.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Tue Mar 24 2020
	*
	* @brief Patch test for SolidMechanics implicit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_solid_mechanics_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TYPED_TEST(TestPatchTestSMMLinear, Implicit) {
	std::string filename = "material_check_stress_plane_stress.dat";
	if (this->plane_strain)
	filename = "material_check_stress_plane_strain.dat";

	this->initModel(_implicit_dynamic, filename);

	const auto & coordinates = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();
	// set the position of all nodes to the static solution
	for (auto && tuple : zip(make_view(coordinates, this->dim),
	make_view(displacement, this->dim))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}
	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	auto ekin = this->model->getEnergy("kinetic");
	EXPECT_NEAR(0, ekin, 1e-16);

	this->checkAll();

	#define debug 0
	#if debug
	this->model->setBaseName(std::to_string(this->type) + "_implicit");
	this->model->addDumpField("stress");
	this->model->addDumpField("grad_u");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpFieldVector("displacement");
	this->model->dump();
	#endif
	-
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, Static) {
	std::string filename = "material_check_stress_plane_stress.dat";
	if (this->plane_strain)
	filename = "material_check_stress_plane_strain.dat";

	this->initModel(_static, filename);

	auto & solver = this->model->getNonLinearSolver();
	solver.set("max_iterations", 2);
	solver.set("threshold", 2e-4);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	this->model->solveStep();

	this->checkAll();

	#define debug 0
	#if debug
	this->model->setBaseName(std::to_string(this->type) + "_static");
	this->model->addDumpField("stress");
	this->model->addDumpField("grad_u");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpFieldVector("displacement");
	this->model->dump();
	#endif
	-
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, ImplicitFiniteDeformation) {
	std::string filename =
	"material_check_stress_plane_stress_finite_deformation.dat";
	if (this->plane_strain)
	filename = "material_check_stress_plane_strain_finite_deformation.dat";
	else {
	SUCCEED();
	return;
	}

	this->initModel(_implicit_dynamic, filename);

	const auto & coordinates = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();
	// set the position of all nodes to the static solution
	for (auto && tuple : zip(make_view(coordinates, this->dim),
	make_view(displacement, this->dim))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}
	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	auto ekin = this->model->getEnergy("kinetic");
	EXPECT_NEAR(0, ekin, 1e-16);

	this->checkAll();

	-
	#define debug 0
	#if debug
	this->model->setBaseName(std::to_string(this->type) + "_implicit_finit_def");
	this->model->addDumpField("stress");
	this->model->addDumpField("grad_u");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpFieldVector("displacement");
	this->model->dump();
	#endif
	-
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestPatchTestSMMLinear, StaticFiniteDeformation) {
	std::string filename =
	"material_check_stress_plane_stress_finite_deformation.dat";
	if (this->plane_strain) {
	filename = "material_check_stress_plane_strain_finite_deformation.dat";
	} else {
	SUCCEED();
	return;
	}
	this->initModel(_static, filename);

	auto & solver = this->model->getNonLinearSolver();
	solver.set("max_iterations", 2);
	solver.set("threshold", 2e-4);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	this->model->solveStep();

	this->checkAll();
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_fixture.hh b/test/test_model/patch_tests/patch_test_linear_fixture.hh
	index d0b2ce86c..048646c96 100644
	--- a/test/test_model/patch_tests/patch_test_linear_fixture.hh
	+++ b/test/test_model/patch_tests/patch_test_linear_fixture.hh
	@@ -1,185 +1,185 @@
	/**
	* @file patch_test_linear_fixture.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Sun Jun 02 2019
	*
	* @brief Fixture for linear patch tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_group.hh"
	#include "mesh_utils.hh"
	#include "model.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PATCH_TEST_LINEAR_FIXTURE_HH_
	#define AKANTU_PATCH_TEST_LINEAR_FIXTURE_HH_

	//#define DEBUG_TEST

	using namespace akantu;

	template <typename type_, typename M>
	class TestPatchTestLinear : public ::testing::Test {
	public:
	static constexpr ElementType type = type_::value;
	static constexpr size_t dim = ElementClass<type>::getSpatialDimension();

	virtual void SetUp() {
	mesh = std::make_unique<Mesh>(dim);
	mesh->read(std::to_string(type) + ".msh");
	MeshUtils::buildFacets(*mesh);
	mesh->createBoundaryGroupFromGeometry();

	model = std::make_unique<M>(*mesh);
	}

	virtual void TearDown() {
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	virtual void initModel(const AnalysisMethod & method,
	const std::string & material_file) {
	debug::setDebugLevel(dblError);
	getStaticParser().parse(material_file);

	this->model->initFull(_analysis_method = method);
	this->applyBC();

	if (method != _static)
	this->model->setTimeStep(0.8 * this->model->getStableTimeStep());
	}

	virtual void applyBC() {
	auto & boundary = this->model->getBlockedDOFs();

	for (auto & eg : mesh->iterateElementGroups()) {
	for (const auto & node : eg.getNodeGroup()) {
	for (UInt s = 0; s < boundary.getNbComponent(); ++s) {
	boundary(node, s) = true;
	}
	}
	}
	}

	virtual void applyBConDOFs(const Array<Real> & dofs) {
	const auto & coordinates = this->mesh->getNodes();
	for (auto & eg : this->mesh->iterateElementGroups()) {
	for (const auto & node : eg.getNodeGroup()) {
	this->setLinearDOF(dofs.begin(dofs.getNbComponent())[node],
	coordinates.begin(this->dim)[node]);
	}
	}
	}

	template <typename V> Matrix<Real> prescribed_gradient(const V & dof) {
	Matrix<Real> gradient(dof.getNbComponent(), dim);

	for (UInt i = 0; i < gradient.rows(); ++i) {
	for (UInt j = 0; j < gradient.cols(); ++j) {
	gradient(i, j) = alpha(i, j + 1);
	}
	}
	return gradient;
	}

	template <typename Gradient, typename DOFs>
	void checkGradient(const Gradient & gradient, const DOFs & dofs) {
	auto pgrad = prescribed_gradient(dofs);

	for (auto & grad :
	make_view(gradient, gradient.getNbComponent() / dim, dim)) {
	auto diff = grad - pgrad;
	auto gradient_error =
	diff.template norm<L_inf>() / grad.template norm<L_inf>();

	EXPECT_NEAR(0, gradient_error, gradient_tolerance);
	}
	}

	template <typename presult_func_t, typename Result, typename DOFs>
	void checkResults(presult_func_t && presult_func, const Result & results,
	const DOFs & dofs) {
	auto presult = presult_func(prescribed_gradient(dofs));
	for (auto & result :
	make_view(results, results.getNbComponent() / dim, dim)) {
	auto diff = result - presult;
	auto result_error =
	diff.template norm<L_inf>() / presult.template norm<L_inf>();

	EXPECT_NEAR(0, result_error, result_tolerance);
	}
	}

	template <typename V1, typename V2>
	void setLinearDOF(V1 && dof, V2 && coord) {
	for (UInt i = 0; i < dof.size(); ++i) {
	dof(i) = this->alpha(i, 0);
	for (UInt j = 0; j < coord.size(); ++j) {
	dof(i) += this->alpha(i, j + 1) * coord(j);
	}
	}
	}

	template <typename V> void checkDOFs(V && dofs) {
	const auto & coordinates = mesh->getNodes();
	Vector<Real> ref_dof(dofs.getNbComponent());

	for (auto && tuple : zip(make_view(coordinates, dim),
	make_view(dofs, dofs.getNbComponent()))) {
	setLinearDOF(ref_dof, std::get<0>(tuple));
	auto diff = std::get<1>(tuple) - ref_dof;
	auto dofs_error = diff.template norm<L_inf>();

	EXPECT_NEAR(0, dofs_error, dofs_tolerance);
	}
	}

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<M> model;
	Matrix<Real> alpha{{0.01, 0.02, 0.03, 0.04},
	{0.05, 0.06, 0.07, 0.08},
	{0.09, 0.10, 0.11, 0.12}};

	Real gradient_tolerance{1e-13};
	Real result_tolerance{1e-13};
	Real dofs_tolerance{1e-15};
	};

	template <typename type_, typename M>
	constexpr ElementType TestPatchTestLinear<type_, M>::type;

	template <typename tuple_, typename M>
	constexpr size_t TestPatchTestLinear<tuple_, M>::dim;

	#endif /* AKANTU_PATCH_TEST_LINEAR_FIXTURE_HH_ */
	diff --git a/test/test_model/patch_tests/patch_test_linear_heat_transfer_explicit.cc b/test/test_model/patch_tests/patch_test_linear_heat_transfer_explicit.cc
	index 434543f98..5b51dd68f 100644
	--- a/test/test_model/patch_tests/patch_test_linear_heat_transfer_explicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_heat_transfer_explicit.cc
	@@ -1,52 +1,52 @@
	/**
	* @file patch_test_linear_heat_transfer_explicit.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Wed Jan 31 2018
	*
	* @brief HeatTransfer patch test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_heat_transfer_fixture.hh"
	/* -------------------------------------------------------------------------- */

	TYPED_TEST(TestPatchTestHTMLinear, Explicit) {
	this->initModel(_explicit_lumped_mass, "heat_transfer_input.dat");

	const auto & coordinates = this->mesh->getNodes();
	auto & temperature = this->model->getTemperature();
	// set the position of all nodes to the static solution
	for (auto && tuple :
	zip(make_view(coordinates, this->dim), make_view(temperature, 1))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}

	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	this->checkAll();
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_heat_transfer_fixture.hh b/test/test_model/patch_tests/patch_test_linear_heat_transfer_fixture.hh
	index 04e17e7f8..98dec7a62 100644
	--- a/test/test_model/patch_tests/patch_test_linear_heat_transfer_fixture.hh
	+++ b/test/test_model/patch_tests/patch_test_linear_heat_transfer_fixture.hh
	@@ -1,79 +1,79 @@
	/**
	* @file patch_test_linear_heat_transfer_fixture.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Wed Nov 18 2020
	*
	* @brief HeatTransfer patch tests fixture
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "heat_transfer_model.hh"
	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_fixture.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PATCH_TEST_LINEAR_HEAT_TRANSFER_FIXTURE_HH_
	#define AKANTU_PATCH_TEST_LINEAR_HEAT_TRANSFER_FIXTURE_HH_

	/* -------------------------------------------------------------------------- */
	template <typename type>
	class TestPatchTestHTMLinear
	: public TestPatchTestLinear<type, HeatTransferModel> {
	using parent = TestPatchTestLinear<type, HeatTransferModel>;

	public:
	void applyBC() override {
	parent::applyBC();
	auto & temperature = this->model->getTemperature();
	this->applyBConDOFs(temperature);
	}

	void initModel(const AnalysisMethod & method,
	const std::string & material_file) override {
	TestPatchTestLinear<type, HeatTransferModel>::initModel(method,
	material_file);
	if (method != _static)
	this->model->setTimeStep(0.5 * this->model->getStableTimeStep());
	}

	void checkAll() {
	auto & temperature = this->model->getTemperature();
	Matrix<Real> C = this->model->get("conductivity");
	this->checkDOFs(temperature);
	this->checkGradient(this->model->getTemperatureGradient(this->type),
	temperature);
	this->checkResults(
	[&](const Matrix<Real> & grad_T) { return C * grad_T.transpose(); },
	this->model->getKgradT(this->type), temperature);
	}
	};

	using htm_types = gtest_list_t<TestElementTypes>;

	TYPED_TEST_SUITE(TestPatchTestHTMLinear, htm_types, );

	#endif /* AKANTU_PATCH_TEST_LINEAR_HEAT_TRANSFER_FIXTURE_HH_ */
	diff --git a/test/test_model/patch_tests/patch_test_linear_heat_transfer_implicit.cc b/test/test_model/patch_tests/patch_test_linear_heat_transfer_implicit.cc
	index db20f25aa..697b91eee 100644
	--- a/test/test_model/patch_tests/patch_test_linear_heat_transfer_implicit.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_heat_transfer_implicit.cc
	@@ -1,54 +1,54 @@
	/**
	* @file patch_test_linear_heat_transfer_implicit.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Wed Feb 28 2018
	*
	* @brief HeatTransfer patch test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_heat_transfer_fixture.hh"
	/* -------------------------------------------------------------------------- */

	TYPED_TEST(TestPatchTestHTMLinear, Implicit) {
	this->initModel(_implicit_dynamic, "heat_transfer_input.dat");

	const auto & coordinates = this->mesh->getNodes();
	auto & temperature = this->model->getTemperature();

	// set the position of all nodes to the static solution
	for (auto && tuple :
	zip(make_view(coordinates, this->dim), make_view(temperature, 1))) {
	this->setLinearDOF(std::get<1>(tuple), std::get<0>(tuple));
	}

	for (UInt s = 0; s < 100; ++s) {
	this->model->solveStep();
	}

	this->checkAll();
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_heat_transfer_static.cc b/test/test_model/patch_tests/patch_test_linear_heat_transfer_static.cc
	index e68bade48..ea8757c5e 100644
	--- a/test/test_model/patch_tests/patch_test_linear_heat_transfer_static.cc
	+++ b/test/test_model/patch_tests/patch_test_linear_heat_transfer_static.cc
	@@ -1,48 +1,48 @@
	/**
	* @file patch_test_linear_heat_transfer_static.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief HeatTransfer patch test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_heat_transfer_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */

	TYPED_TEST(TestPatchTestHTMLinear, Static) {
	this->initModel(_static, "heat_transfer_input.dat");

	auto & solver = this->model->getNonLinearSolver();
	solver.set("max_iterations", 2);
	solver.set("threshold", 2e-4);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	this->model->solveStep();
	this->checkAll();
	}
	diff --git a/test/test_model/patch_tests/patch_test_linear_solid_mechanics_fixture.hh b/test/test_model/patch_tests/patch_test_linear_solid_mechanics_fixture.hh
	index 56ee38b0d..676768afa 100644
	--- a/test/test_model/patch_tests/patch_test_linear_solid_mechanics_fixture.hh
	+++ b/test/test_model/patch_tests/patch_test_linear_solid_mechanics_fixture.hh
	@@ -1,156 +1,156 @@
	/**
	* @file patch_test_linear_solid_mechanics_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jan 30 2018
	* @date last modification: Wed Nov 18 2020
	*
	* @brief SolidMechanics patch tests fixture
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "patch_test_linear_fixture.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_PATCH_TEST_LINEAR_SOLID_MECHANICS_FIXTURE_HH_
	#define AKANTU_PATCH_TEST_LINEAR_SOLID_MECHANICS_FIXTURE_HH_

	/* -------------------------------------------------------------------------- */
	template <typename tuple_>
	class TestPatchTestSMMLinear
	: public TestPatchTestLinear<std::tuple_element_t<0, tuple_>,
	SolidMechanicsModel> {
	using parent =
	TestPatchTestLinear<std::tuple_element_t<0, tuple_>, SolidMechanicsModel>;

	public:
	static constexpr bool plane_strain = std::tuple_element_t<1, tuple_>::value;

	void applyBC() override {
	parent::applyBC();
	auto & displacement = this->model->getDisplacement();
	this->applyBConDOFs(displacement);
	}

	void checkForces() {
	auto & mat = this->model->getMaterial(0);
	auto & internal_forces = this->model->getInternalForce();
	auto & external_forces = this->model->getExternalForce();
	auto dim = this->dim;

	Matrix<Real> sigma =
	make_view(mat.getStress(this->type), dim, dim).begin()[0];

	external_forces.zero();
	if (dim > 1) {
	for (auto & eg : this->mesh->iterateElementGroups()) {
	this->model->applyBC(BC::Neumann::FromHigherDim(sigma), eg.getName());
	}
	} else {
	external_forces(0) = -sigma(0, 0);
	external_forces(1) = sigma(0, 0);
	}

	Real force_norm_inf = -std::numeric_limits<Real>::max();

	Vector<Real> total_force(dim);
	total_force.zero();

	for (auto && f : make_view(internal_forces, dim)) {
	total_force += f;
	force_norm_inf = std::max(force_norm_inf, f.template norm<L_inf>());
	}

	EXPECT_NEAR(0, total_force.template norm<L_inf>() / force_norm_inf, 1e-9);

	for (auto && tuple : zip(make_view(internal_forces, dim),
	make_view(external_forces, dim))) {
	auto && f_int = std::get<0>(tuple);
	auto && f_ext = std::get<1>(tuple);
	auto f = f_int + f_ext;
	EXPECT_NEAR(0, f.template norm<L_inf>() / force_norm_inf, 1e-9);
	}
	}

	void checkAll() {
	auto & displacement = this->model->getDisplacement();
	auto & mat = this->model->getMaterial(0);

	this->checkDOFs(displacement);
	this->checkGradient(mat.getGradU(this->type), displacement);
	this->checkResults(
	[&](const Matrix<Real> & pstrain) {
	Real nu = this->model->getMaterial(0).get("nu");
	Real E = this->model->getMaterial(0).get("E");

	auto strain = (pstrain + pstrain.transpose()) / 2.;
	auto trace = strain.trace();

	auto lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
	auto mu = E / (2 * (1 + nu));

	if (not this->plane_strain) {
	lambda = nu * E / (1 - nu * nu);
	}

	decltype(strain) stress(this->dim, this->dim);

	if (this->dim == 1) {
	stress(0, 0) = E * strain(0, 0);
	} else {
	for (UInt i = 0; i < this->dim; ++i)
	for (UInt j = 0; j < this->dim; ++j)
	stress(i, j) =
	(i == j) * lambda * trace + 2 * mu * strain(i, j);
	}

	return stress;
	},
	mat.getStress(this->type), displacement);
	this->checkForces();
	}
	};

	template <typename tuple_>
	constexpr bool TestPatchTestSMMLinear<tuple_>::plane_strain;

	template <typename T> struct invalid_plan_stress : std::true_type {};
	template <typename type, typename bool_c>
	struct invalid_plan_stress<std::tuple<type, bool_c>>
	: aka::bool_constant<ElementClass<type::value>::getSpatialDimension() !=
	2 and
	not bool_c::value> {};

	using true_false =
	std::tuple<aka::bool_constant<true>, aka::bool_constant<false>>;

	template <typename T> using valid_types = aka::negation<invalid_plan_stress<T>>;

	using model_types = gtest_list_t<
	tuple_filter_t<valid_types, cross_product_t<TestElementTypes, true_false>>>;

	TYPED_TEST_SUITE(TestPatchTestSMMLinear, model_types, );

	#endif /* AKANTU_PATCH_TEST_LINEAR_SOLID_MECHANICS_FIXTURE_HH_ */
	diff --git a/test/test_model/patch_tests/test_lumped_mass.cc b/test/test_model/patch_tests/test_lumped_mass.cc
	index b8c0aa087..f10ef3908 100644
	--- a/test/test_model/patch_tests/test_lumped_mass.cc
	+++ b/test/test_model/patch_tests/test_lumped_mass.cc
	@@ -1,103 +1,103 @@
	/**
	* @file test_lumped_mass.cc
	*
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Dec 05 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test the lumping of the mass matrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <tuple>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	template <typename tuple_>
	class TestLumpedMassesFixture : public ::testing::Test {
	public:
	static constexpr ElementType type = tuple_::value;
	static constexpr size_t dim = ElementClass<type>::getSpatialDimension();

	void SetUp() override {
	debug::setDebugLevel(dblError);
	getStaticParser().parse("material_lumped.dat");

	std::stringstream element_type;
	element_type << type;

	mesh = std::make_unique<Mesh>(dim);
	mesh->read(element_type.str() + ".msh");

	SCOPED_TRACE(element_type.str().c_str());

	model = std::make_unique<SolidMechanicsModel>(*mesh);

	model->initFull(_analysis_method = _explicit_lumped_mass);
	}

	void TearDown() override {
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<SolidMechanicsModel> model;
	};

	template <typename T> constexpr ElementType TestLumpedMassesFixture<T>::type;
	template <typename T> constexpr size_t TestLumpedMassesFixture<T>::dim;

	using mass_types = gtest_list_t<TestElementTypes>;

	TYPED_TEST_SUITE(TestLumpedMassesFixture, mass_types, );

	TYPED_TEST(TestLumpedMassesFixture, TestLumpedMass) {
	this->model->assembleMassLumped();

	auto rho = this->model->getMaterial(0).getRho();
	auto & fem = this->model->getFEEngine();
	auto nb_element = this->mesh->getNbElement(this->type);
	auto nb_quadrature_points =
	fem.getNbIntegrationPoints(this->type) * nb_element;

	Array<Real> rho_on_quad(nb_quadrature_points, 1, rho, "rho_on_quad");
	auto mass = fem.integrate(rho_on_quad, this->type);
	const auto & masses = this->model->getMass();

	Vector<Real> sum(this->dim, 0.);
	for (auto & mass : make_view(masses, this->dim)) {
	sum += mass;
	}

	for (UInt s = 0; s < sum.size(); ++s)
	EXPECT_NEAR(0., (mass - sum[s]) / mass, 2e-15);
	}
	diff --git a/test/test_model/test_common/test_dof_manager.cc b/test/test_model/test_common/test_dof_manager.cc
	index 61baaadbf..f038faf45 100644
	--- a/test/test_model/test_common/test_dof_manager.cc
	+++ b/test/test_model/test_common/test_dof_manager.cc
	@@ -1,302 +1,302 @@
	/**
	* @file test_dof_manager.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 26 2019
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test the dof managers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <dof_manager.hh>
	#include <mesh_partition_scotch.hh>
	#include <mesh_utils.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <numeric>
	#include <string>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	enum DOFManagerType { _dmt_default, _dmt_petsc };
	}
	AKANTU_ENUM_HASH(DOFManagerType)

	using namespace akantu;

	// defined as struct to get there names in gtest outputs
	struct dof_manager_default_
	: public std::integral_constant<DOFManagerType, _dmt_default> {};
	struct dof_manager_petsc_
	: public std::integral_constant<DOFManagerType, _dmt_petsc> {};

	using dof_manager_types = ::testing::Types<
	#ifdef AKANTU_USE_PETSC
	dof_manager_petsc_,
	#endif
	dof_manager_default_>;

	namespace std {

	std::string to_string(const DOFManagerType & type) {
	std::unordered_map<DOFManagerType, std::string> map{
	#ifdef AKANTU_USE_PETSC
	{_dmt_petsc, "petsc"},
	#endif
	{_dmt_default, "default"},
	};
	return map.at(type);
	}

	} // namespace std

	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	class DOFManagerTester {
	public:
	DOFManagerTester(std::unique_ptr<DOFManager> dof_manager)
	: dof_manager(std::move(dof_manager)) {}

	DOFManager & operator() { return dof_manager; }
	DOFManager * operator->() { return dof_manager.get(); }
	void getArrayPerDOFs(const ID & id, SolverVector & vector,
	Array<Real> & array) {
	dof_manager->getArrayPerDOFs(id, vector, array);
	}

	SolverVector & residual() { return *dof_manager->residual; }

	private:
	std::unique_ptr<DOFManager> dof_manager;
	};
	} // namespace akantu

	template <class T> class DOFManagerFixture : public ::testing::Test {
	public:
	constexpr static DOFManagerType type = T::value;
	constexpr static UInt dim = 3;
	void SetUp() override {
	mesh = std::make_unique<Mesh>(this->dim);

	auto & communicator = Communicator::getStaticCommunicator();
	if (communicator.whoAmI() == 0) {
	mesh->read("mesh.msh");
	}
	mesh->distribute();

	nb_nodes = this->mesh->getNbNodes();
	nb_total_nodes = this->mesh->getNbGlobalNodes();

	auto && range_nodes = arange(nb_nodes);
	nb_pure_local =
	std::accumulate(range_nodes.begin(), range_nodes.end(), 0,
	[&](auto && init, auto && val) {
	return init + mesh->isLocalOrMasterNode(val);
	});
	}
	void TearDown() override {
	mesh.reset();
	dof1.reset();
	dof2.reset();
	}

	decltype(auto) alloc() {
	std::unordered_map<DOFManagerType, std::string> types{
	- {_dmt_default, "default"}, {_dmt_petsc, "petsc"}};
	+ {_dmt_default, "default"}, {_dmt_petsc, "petsc"}};

	return DOFManagerTester(DOFManagerFactory::getInstance().allocate(
	types[T::value], *mesh, "dof_manager"));
	}

	decltype(auto) registerDOFs(DOFSupportType dst1, DOFSupportType dst2) {
	auto dof_manager = DOFManagerTester(this->alloc());

	auto n1 = dst1 == _dst_nodal ? nb_nodes : nb_pure_local;
	this->dof1 = std::make_unique<Array<Real>>(n1, 3);

	dof_manager->registerDOFs("dofs1", *this->dof1, dst1);

	EXPECT_EQ(dof_manager.residual().size(), nb_total_nodes * 3);

	auto n2 = dst2 == _dst_nodal ? nb_nodes : nb_pure_local;
	this->dof2 = std::make_unique<Array<Real>>(n2, 5);

	dof_manager->registerDOFs("dofs2", *this->dof2, dst2);

	EXPECT_EQ(dof_manager.residual().size(), nb_total_nodes * 8);
	return dof_manager;
	}

	protected:
	Int nb_nodes{0}, nb_total_nodes{0}, nb_pure_local{0};
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<Array<Real>> dof1;
	std::unique_ptr<Array<Real>> dof2;
	};

	template <class T> constexpr DOFManagerType DOFManagerFixture<T>::type;
	template <class T> constexpr UInt DOFManagerFixture<T>::dim;

	TYPED_TEST_SUITE(DOFManagerFixture, dof_manager_types, );

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, Construction) {
	auto dof_manager = this->alloc();
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, DoubleConstruction) {
	auto dof_manager = this->alloc();
	dof_manager = this->alloc();
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, RegisterGenericDOF1) {
	auto dof_manager = this->alloc();

	Array<Real> dofs(this->nb_pure_local, 3);

	dof_manager->registerDOFs("dofs1", dofs, _dst_generic);
	EXPECT_GE(dof_manager.residual().size(), this->nb_total_nodes * 3);
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, RegisterNodalDOF1) {
	auto dof_manager = this->alloc();

	Array<Real> dofs(this->nb_nodes, 3);
	dof_manager->registerDOFs("dofs1", dofs, _dst_nodal);
	EXPECT_GE(dof_manager.residual().size(), this->nb_total_nodes * 3);
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, RegisterGenericDOF2) {
	this->registerDOFs(_dst_generic, _dst_generic);
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, RegisterNodalDOF2) {
	this->registerDOFs(_dst_nodal, _dst_nodal);
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, RegisterMixedDOF) {
	auto dof_manager = this->registerDOFs(_dst_nodal, _dst_generic);
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, AssembleVector) {
	auto dof_manager = this->registerDOFs(_dst_nodal, _dst_generic);

	dof_manager.residual().zero();

	for (auto && data :
	enumerate(make_view(*this->dof1, this->dof1->getNbComponent()))) {
	auto n = std::get<0>(data);
	auto & l = std::get<1>(data);
	l.set(1. * this->mesh->isLocalOrMasterNode(n));
	}

	this->dof2->set(2.);

	dof_manager->assembleToResidual("dofs1", *this->dof1);
	dof_manager->assembleToResidual("dofs2", *this->dof2);

	this->dof1->set(0.);
	this->dof2->set(0.);

	dof_manager.getArrayPerDOFs("dofs1", dof_manager.residual(), *this->dof1);
	for (auto && data :
	enumerate(make_view(*this->dof1, this->dof1->getNbComponent()))) {
	if (this->mesh->isLocalOrMasterNode(std::get<0>(data))) {
	const auto & l = std::get<1>(data);
	auto e = (l - Vector<Real>{1., 1., 1.}).norm();
	ASSERT_EQ(e, 0.);
	}
	}

	dof_manager.getArrayPerDOFs("dofs2", dof_manager.residual(), *this->dof2);
	for (auto && l : make_view(*this->dof2, this->dof2->getNbComponent())) {
	auto e = (l - Vector<Real>{2., 2., 2., 2., 2.}).norm();
	ASSERT_EQ(e, 0.);
	}
	}

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(DOFManagerFixture, AssembleMatrixNodal) {
	auto dof_manager = this->registerDOFs(_dst_nodal, _dst_nodal);

	auto && K = dof_manager->getNewMatrix("K", _symmetric);
	K.zero();

	auto && elemental_matrix = std::make_unique<Array<Real>>(
	this->mesh->getNbElement(this->dim), 8 * 3 * 8 * 3);

	for (auto && m : make_view(elemental_matrix, 8 3, 8 * 3)) {
	m.set(1.);
	}

	dof_manager->assembleElementalMatricesToMatrix(
	"K", "dofs1", *elemental_matrix, _hexahedron_8);

	elemental_matrix = std::make_unique<Array<Real>>(
	this->mesh->getNbElement(this->dim), 8 * 5 * 8 * 5);

	for (auto && m : make_view(elemental_matrix, 8 5, 8 * 5)) {
	m.set(1.);
	}

	dof_manager->assembleElementalMatricesToMatrix(
	"K", "dofs2", *elemental_matrix, _hexahedron_8);

	CSR<Element> node_to_elem;
	MeshUtils::buildNode2Elements(*this->mesh, node_to_elem, this->dim);

	dof_manager.residual().zero();

	for (auto && data :
	enumerate(zip(make_view(*this->dof1, this->dof1->getNbComponent()),
	make_view(*this->dof2, this->dof2->getNbComponent())))) {
	auto n = std::get<0>(data);
	auto & l1 = std::get<0>(std::get<1>(data));
	auto & l2 = std::get<1>(std::get<1>(data));
	auto v = 1. * this->mesh->isLocalOrMasterNode(n);
	l1.set(v);
	l2.set(v);
	}

	dof_manager->assembleToResidual("dofs1", *this->dof1);
	dof_manager->assembleToResidual("dofs2", *this->dof2);

	for (auto && n : arange(this->nb_nodes)) {
	if (not this->mesh->isLocalOrMasterNode(n)) {
	}
	}
	}
	diff --git a/test/test_model/test_common/test_model_solver/test_dof_manager_default.cc b/test/test_model/test_common/test_model_solver/test_dof_manager_default.cc
	index da17e643e..c814910f3 100644
	--- a/test/test_model/test_common/test_model_solver/test_dof_manager_default.cc
	+++ b/test/test_model/test_common/test_model_solver/test_dof_manager_default.cc
	@@ -1,131 +1,131 @@
	/**
	* @file test_dof_manager_default.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Feb 26 2016
	* @date last modification: Wed Jan 30 2019
	*
	* @brief Test default dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_default.hh"
	#include "solver_callback.hh"
	#include "sparse_matrix_aij.hh"
	#include "time_step_solver.hh"

	using namespace akantu;

	/**
	* =\o-----o-----o-> F
	* \| \|
	* \|---- L ----\|
	*/
	class MySolverCallback : public SolverCallback {
	public:
	MySolverCallback(Real F, DOFManagerDefault & dof_manager, UInt nb_dofs = 3)
	: dof_manager(dof_manager), dispacement(nb_dofs, 1, "disp"),
	blocked(nb_dofs, 1), forces(nb_dofs, 1), nb_dofs(nb_dofs) {
	dof_manager.registerDOFs("disp", dispacement, _dst_generic);
	dof_manager.registerBlockedDOFs("disp", blocked);

	dispacement.set(0.);
	forces.set(0.);
	blocked.set(false);

	forces(nb_dofs - 1, _x) = F;
	blocked(0, _x) = true;
	}

	void assembleMatrix(const ID & matrix_id) {
	if (matrix_id != "K")
	return;

	auto & K = dynamic_cast<SparseMatrixAIJ &>(dof_manager.getMatrix("K"));
	K.zero();

	for (UInt i = 1; i < nb_dofs - 1; ++i)
	K.add(i, i, 2.);
	for (UInt i = 0; i < nb_dofs - 1; ++i)
	K.add(i, i + 1, -1.);

	K.add(0, 0, 1);
	K.add(nb_dofs - 1, nb_dofs - 1, 1);

	// K *= 1 / L_{el}
	K *= nb_dofs - 1;
	}

	MatrixType getMatrixType(const ID & matrix_id) {
	if (matrix_id == "K")
	return _symmetric;
	return _mt_not_defined;
	}
	void assembleLumpedMatrix(const ID &) {}

	void assembleResidual() { dof_manager.assembleToResidual("disp", forces); }

	void predictor() {}
	void corrector() {}

	DOFManagerDefault & dof_manager;
	Array<Real> dispacement;
	Array<bool> blocked;
	Array<Real> forces;

	UInt nb_dofs;
	};

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	DOFManagerDefault dof_manager("test_dof_manager");
	MySolverCallback callback(10., dof_manager, 11);

	NonLinearSolver & nls =
	dof_manager.getNewNonLinearSolver("my_nls", NonLinearSolverType::_linear);
	TimeStepSolver & tss = dof_manager.getNewTimeStepSolver(
	"my_tss", TimeStepSolverType::_static, nls, callback);
	tss.setIntegrationScheme("disp", IntegrationSchemeType::_pseudo_time);
	tss.solveStep(callback);

	dof_manager.getMatrix("K").saveMatrix("K_dof_manager_default.mtx");

	Array<Real>::const_scalar_iterator disp_it = callback.dispacement.begin();
	Array<Real>::const_scalar_iterator force_it = callback.forces.begin();
	Array<bool>::const_scalar_iterator blocked_it = callback.blocked.begin();
	std::cout << std::setw(8) << "disp"
	<< " " << std::setw(8) << "force"
	<< " " << std::setw(8) << "blocked" << std::endl;

	for (; disp_it != callback.dispacement.end();
	++disp_it, ++force_it, ++blocked_it) {
	std::cout << std::setw(8) << disp_it << " " << std::setw(8) << force_it
	<< " " << std::setw(8) << std::boolalpha << *blocked_it
	<< std::endl;
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_common/test_model_solver/test_model_solver.cc b/test/test_model/test_common/test_model_solver/test_model_solver.cc
	index 0d8eb11bd..67dec144c 100644
	--- a/test/test_model/test_common/test_model_solver/test_model_solver.cc
	+++ b/test/test_model/test_common/test_model_solver/test_model_solver.cc
	@@ -1,178 +1,178 @@
	/**
	* @file test_model_solver.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Apr 13 2016
	* @date last modification: Tue Apr 23 2019
	*
	* @brief Test default dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_random_generator.hh"
	#include "dof_manager.hh"
	#include "dof_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "model_solver.hh"
	#include "non_linear_solver.hh"
	#include "sparse_matrix.hh"

	/* -------------------------------------------------------------------------- */
	#include "test_model_solver_my_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	static void genMesh(Mesh & mesh, UInt nb_nodes);
	static void printResults(MyModel & model, UInt nb_nodes);

	Real F = -10;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt prank = Communicator::getStaticCommunicator().whoAmI();

	std::cout << std::setprecision(7);

	ID dof_manager_type = "default";
	#if defined(DOF_MANAGER_TYPE)
	dof_manager_type = DOF_MANAGER_TYPE;
	#endif

	UInt global_nb_nodes = 100;
	Mesh mesh(1);

	RandomGenerator<UInt>::seed(1);

	if (prank == 0) {
	genMesh(mesh, global_nb_nodes);
	}

	// std::cout << prank << RandGenerator<Real>::seed() << std::endl;
	mesh.distribute();

	MyModel model(F, mesh, false, dof_manager_type);

	model.getNewSolver("static", TimeStepSolverType::_static,
	NonLinearSolverType::_newton_raphson);
	model.setIntegrationScheme("static", "disp",
	IntegrationSchemeType::_pseudo_time);

	NonLinearSolver & solver = model.getDOFManager().getNonLinearSolver("static");
	solver.set("max_iterations", 2);

	model.solveStep();

	printResults(model, global_nb_nodes);

	finalize();
	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	void genMesh(Mesh & mesh, UInt nb_nodes) {
	MeshAccessor mesh_accessor(mesh);
	Array<Real> & nodes = mesh_accessor.getNodes();
	Array<UInt> & conn = mesh_accessor.getConnectivity(_segment_2);

	nodes.resize(nb_nodes);
	mesh_accessor.setNbGlobalNodes(nb_nodes);

	for (UInt n = 0; n < nb_nodes; ++n) {
	nodes(n, _x) = n * (1. / (nb_nodes - 1));
	}

	conn.resize(nb_nodes - 1);
	for (UInt n = 0; n < nb_nodes - 1; ++n) {
	conn(n, 0) = n;
	conn(n, 1) = n + 1;
	}
	mesh_accessor.makeReady();
	}

	/* -------------------------------------------------------------------------- */
	void printResults(MyModel & model, UInt /nb_nodes/) {
	// if (model.mesh.isDistributed()) {
	// UInt prank = model.mesh.getCommunicator().whoAmI();
	// auto & sync = dynamic_cast<DOFManagerDefault &>(model.getDOFManager())
	// .getSynchronizer();

	// if (prank == 0) {
	// Array<Real> global_displacement(nb_nodes);
	// Array<Real> global_forces(nb_nodes);
	// Array<bool> global_blocked(nb_nodes);

	// sync.gather(model.forces, global_forces);
	// sync.gather(model.displacement, global_displacement);
	// sync.gather(model.blocked, global_blocked);

	// auto force_it = global_forces.begin();
	// auto disp_it = global_displacement.begin();
	// auto blocked_it = global_blocked.begin();

	// std::cout << "node"
	// << ", " << std::setw(8) << "disp"
	// << ", " << std::setw(8) << "force"
	// << ", " << std::setw(8) << "blocked" << std::endl;

	// UInt node = 0;
	// for (; disp_it != global_displacement.end();
	// ++disp_it, ++force_it, ++blocked_it, ++node) {
	// std::cout << node << ", " << std::setw(8) << *disp_it << ", "
	// << std::setw(8) << *force_it << ", " << std::setw(8)
	// << *blocked_it << std::endl;

	// std::cout << std::flush;
	// }
	// } else {
	// sync.gather(model.forces);
	// sync.gather(model.displacement);
	// sync.gather(model.blocked);
	// }
	// } else {
	auto force_it = model.forces.begin();
	auto disp_it = model.displacement.begin();
	auto blocked_it = model.blocked.begin();

	std::cout << "node"
	<< ", " << std::setw(8) << "disp"
	<< ", " << std::setw(8) << "force"
	<< ", " << std::setw(8) << "blocked" << std::endl;

	UInt node = 0;
	for (; disp_it != model.displacement.end();
	++disp_it, ++force_it, ++blocked_it, ++node) {
	std::cout << node << ", " << std::setw(8) << *disp_it << ", "
	<< std::setw(8) << *force_it << ", " << std::setw(8)
	<< *blocked_it << std::endl;

	std::cout << std::flush;
	}
	// }
	}
	diff --git a/test/test_model/test_common/test_model_solver/test_model_solver_dynamic.cc b/test/test_model/test_common/test_model_solver/test_model_solver_dynamic.cc
	index 9b27bc55c..8a5381e1f 100644
	--- a/test/test_model/test_common/test_model_solver/test_model_solver_dynamic.cc
	+++ b/test/test_model/test_common/test_model_solver/test_model_solver_dynamic.cc
	@@ -1,247 +1,247 @@
	/**
	* @file test_model_solver_dynamic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Apr 13 2016
	* @date last modification: Wed Aug 14 2019
	*
	* @brief Test default dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "element_group.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include "dumpable_inline_impl.hh"
	#include "dumper_element_partition.hh"
	#include "dumper_iohelper_paraview.hh"
	/* -------------------------------------------------------------------------- */
	#include "test_model_solver_my_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	#ifndef EXPLICIT
	#define EXPLICIT true
	#endif

	using namespace akantu;

	class Sinusoidal : public BC::Dirichlet::DirichletFunctor {
	public:
	Sinusoidal(MyModel & model, Real amplitude, Real pulse_width, Real t)
	: model(model), A(amplitude), k(2 * M_PI / pulse_width),
	t(t), v{std::sqrt(model.E / model.rho)} {}

	void operator()(UInt n, Vector<bool> & /flags/, Vector<Real> & disp,
	const Vector<Real> & coord) const {
	auto x = coord(_x);
	model.velocity(n, _x) = k * v * A * sin(k * (x - v * t));
	disp(_x) = A * cos(k * (x - v * t));
	}

	private:
	MyModel & model;
	Real A{1.};
	Real k{2 * M_PI};
	Real t{1.};
	Real v{1.};
	};

	static void genMesh(Mesh & mesh, UInt nb_nodes);

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt prank = Communicator::getStaticCommunicator().whoAmI();
	UInt global_nb_nodes = 201;
	UInt max_steps = 400;
	Real time_step = 0.001;
	Mesh mesh(1);
	Real F = -9.81;
	bool _explicit = EXPLICIT;
	const Real pulse_width = 0.2;
	const Real A = 0.01;

	ID dof_manager_type = "default";
	#if defined(DOF_MANAGER_TYPE)
	dof_manager_type = DOF_MANAGER_TYPE;
	#endif

	if (prank == 0)
	genMesh(mesh, global_nb_nodes);

	mesh.distribute();

	// mesh.makePeriodic(_x);

	MyModel model(F, mesh, _explicit, dof_manager_type);

	model.forces.zero();
	model.blocked.zero();

	model.applyBC(Sinusoidal(model, A, pulse_width, 0.), "all");
	model.applyBC(BC::Dirichlet::FlagOnly(_x), "border");

	if (!_explicit) {
	model.getNewSolver("dynamic", TimeStepSolverType::_dynamic,
	NonLinearSolverType::_newton_raphson);
	model.setIntegrationScheme("dynamic", "disp",
	IntegrationSchemeType::_trapezoidal_rule_2,
	IntegrationScheme::_displacement);
	} else {
	model.getNewSolver("dynamic", TimeStepSolverType::_dynamic_lumped,
	NonLinearSolverType::_lumped);
	model.setIntegrationScheme("dynamic", "disp",
	IntegrationSchemeType::_central_difference,
	IntegrationScheme::_acceleration);
	}

	model.setTimeStep(time_step);

	if (prank == 0) {
	std::cout << std::scientific;
	std::cout << std::setw(14) << "time"
	<< "," << std::setw(14) << "wext"
	<< "," << std::setw(14) << "epot"
	<< "," << std::setw(14) << "ekin"
	<< "," << std::setw(14) << "total"
	<< "," << std::setw(14) << "max_disp"
	<< "," << std::setw(14) << "min_disp" << std::endl;
	}
	Real wext = 0.;

	model.getDOFManager().zeroResidual();
	model.assembleResidual();

	Real epot = 0; // model.getPotentialEnergy();
	Real ekin = 0; // model.getKineticEnergy();
	Real einit = ekin + epot;
	Real etot = ekin + epot - wext - einit;

	Real max_disp = 0., min_disp = 0.;
	for (auto && disp : model.displacement) {
	max_disp = std::max(max_disp, disp);
	min_disp = std::min(min_disp, disp);
	}

	if (prank == 0) {
	std::cout << std::setw(14) << 0. << "," << std::setw(14) << wext << ","
	<< std::setw(14) << epot << "," << std::setw(14) << ekin << ","
	<< std::setw(14) << etot << "," << std::setw(14) << max_disp
	<< "," << std::setw(14) << min_disp << std::endl;
	}

	#if EXPLICIT == false
	NonLinearSolver & solver =
	model.getDOFManager().getNonLinearSolver("dynamic");

	solver.set("max_iterations", 20);
	#endif

	auto && dumper = std::make_shared<DumperParaview>("dynamic", "./paraview");
	mesh.registerExternalDumper(dumper, "dynamic", true);
	mesh.addDumpMesh(mesh);

	mesh.addDumpFieldExternalToDumper("dynamic", "displacement",
	model.displacement);
	mesh.addDumpFieldExternalToDumper("dynamic", "velocity", model.velocity);
	mesh.addDumpFieldExternalToDumper("dynamic", "forces", model.forces);
	mesh.addDumpFieldExternalToDumper("dynamic", "internal_forces",
	model.internal_forces);
	mesh.addDumpFieldExternalToDumper("dynamic", "acceleration",
	model.acceleration);

	mesh.dump();

	for (UInt i = 1; i < max_steps + 1; ++i) {
	model.applyBC(Sinusoidal(model, A, pulse_width, time_step * (i - 1)),
	"border");

	model.solveStep("dynamic");
	mesh.dump();

	epot = model.getPotentialEnergy();
	ekin = model.getKineticEnergy();
	wext += model.getExternalWorkIncrement();
	etot = ekin + epot - wext - einit;

	Real max_disp = 0., min_disp = 0.;
	for (auto && disp : model.displacement) {
	max_disp = std::max(max_disp, disp);
	min_disp = std::min(min_disp, disp);
	}

	if (prank == 0) {
	std::cout << std::setw(14) << time_step * i << "," << std::setw(14)
	<< wext << "," << std::setw(14) << epot << "," << std::setw(14)
	<< ekin << "," << std::setw(14) << etot << "," << std::setw(14)
	<< max_disp << "," << std::setw(14) << min_disp << std::endl;
	}
	}

	// output.close();
	finalize();
	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	void genMesh(Mesh & mesh, UInt nb_nodes) {
	MeshAccessor mesh_accessor(mesh);
	Array<Real> & nodes = mesh_accessor.getNodes();
	Array<UInt> & conn = mesh_accessor.getConnectivity(_segment_2);

	nodes.resize(nb_nodes);

	auto & all = mesh.createNodeGroup("all_nodes");

	for (UInt n = 0; n < nb_nodes; ++n) {
	nodes(n, _x) = n * (1. / (nb_nodes - 1));
	all.add(n);
	}

	mesh.createElementGroupFromNodeGroup("all", "all_nodes");

	conn.resize(nb_nodes - 1);
	for (UInt n = 0; n < nb_nodes - 1; ++n) {
	conn(n, 0) = n;
	conn(n, 1) = n + 1;
	}

	Array<UInt> & conn_points = mesh_accessor.getConnectivity(_point_1);
	conn_points.resize(2);

	conn_points(0, 0) = 0;
	conn_points(1, 0) = nb_nodes - 1;

	auto & border = mesh.createElementGroup("border", 0);
	border.add({_point_1, 0, _not_ghost}, true);
	border.add({_point_1, 1, _not_ghost}, true);

	mesh_accessor.makeReady();
	}
	diff --git a/test/test_model/test_common/test_model_solver/test_model_solver_dynamic_petsc.cc b/test/test_model/test_common/test_model_solver/test_model_solver_dynamic_petsc.cc
	index d4b5b81e2..d54f37248 100644
	--- a/test/test_model/test_common/test_model_solver/test_model_solver_dynamic_petsc.cc
	+++ b/test/test_model/test_common/test_model_solver/test_model_solver_dynamic_petsc.cc
	@@ -1,839 +1,839 @@
	/**
	* @file test_model_solver_dynamic_petsc.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Jan 06 2019
	* @date last modification: Wed Mar 13 2019
	*
	* @brief Test default dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "element_group.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include "boundary_condition_functor.hh"
	#include "mpi_communicator_data.hh"
	/* -------------------------------------------------------------------------- */
	#include "dumpable_inline_impl.hh"
	#include "dumper_element_partition.hh"
	#include "dumper_iohelper_paraview.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	#include <petscmat.h>
	#include <petscsnes.h>
	#include <petscvec.h>
	/* -------------------------------------------------------------------------- */

	#ifndef EXPLICIT
	#define EXPLICIT true
	#endif

	template <typename func>
	void CHECK_ERR_CXX(func && func_, PetscErrorCode ierr) {
	if (PetscUnlikely(ierr != 0)) {
	const char * desc;
	PetscErrorMessage(ierr, &desc, nullptr);
	AKANTU_EXCEPTION("Error in PETSc call to \'" << func_ << "\': " << desc);
	}
	}

	using namespace akantu;

	static void genMesh(Mesh & mesh, UInt nb_nodes);

	class MyModel {
	public:
	MyModel(Real F, Mesh & mesh, bool lumped)
	: nb_dofs(mesh.getNbNodes()), nb_elements(mesh.getNbElement(_segment_2)),
	lumped(lumped), E(1.), A(1.), rho(1.), mesh(mesh),
	displacement(nb_dofs, 1, "disp"), velocity(nb_dofs, 1, "velo"),
	acceleration(nb_dofs, 1, "accel"), blocked(nb_dofs, 1, "blocked"),
	forces(nb_dofs, 1, "force_ext"),
	internal_forces(nb_dofs, 1, "force_int"),
	stresses(nb_elements, 1, "stress"), strains(nb_elements, 1, "strain"),
	initial_lengths(nb_elements, 1, "L0") {

	auto n_global = mesh.getNbGlobalNodes();
	int n_local = 0;

	std::vector<PetscInt> nodes_global_ids(nb_dofs);
	for (auto && data : enumerate(nodes_global_ids)) {
	auto n = std::get<0>(data);
	n_local += mesh.isLocalOrMasterNode(n);
	std::get<1>(data) = mesh.getNodeGlobalId(n);
	}

	mpi_comm = dynamic_cast<MPICommunicatorData &>(
	mesh.getCommunicator().getCommunicatorData())
	.getMPICommunicator();

	MeshAccessor mesh_accessor(mesh);

	ierr = ISLocalToGlobalMappingCreate(
	mpi_comm, 1, mesh.getNbNodes(), nodes_global_ids.data(),
	PETSC_COPY_VALUES, &petsc_local_to_global);
	CHECK_ERR_CXX("ISLocalToGlobalMappingCreate", ierr);

	auto setName = [](auto && Obj, auto && name) {
	PetscObjectSetName(reinterpret_cast<PetscObject>(Obj), name);
	};

	ierr = VecCreate(mpi_comm, &rhs);
	ierr = VecSetSizes(rhs, n_local, n_global);
	ierr = VecSetFromOptions(rhs);
	ierr = VecSetLocalToGlobalMapping(rhs, petsc_local_to_global);
	setName(rhs, "rhs");

	ierr = VecDuplicate(rhs, &x);
	ierr = VecDuplicate(rhs, &x_save);
	ierr = VecDuplicate(rhs, &dx);
	ierr = VecDuplicate(rhs, &f_int);
	ierr = VecDuplicate(rhs, &f_dirichlet);
	setName(x, "x");
	setName(x_save, "x save");
	setName(dx, "dx");
	setName(f_int, "f_int");
	setName(f_dirichlet, "f_dirichlet");

	ierr = MatCreate(mpi_comm, &M);
	ierr = MatSetSizes(M, n_local, n_local, n_global, n_global);
	ierr = MatSetFromOptions(M);
	ierr = MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE);
	ierr = MatSetOption(M, MAT_ROW_ORIENTED, PETSC_TRUE);
	ierr = MatSetUp(M);
	ierr = MatSetLocalToGlobalMapping(M, petsc_local_to_global,
	petsc_local_to_global);
	setName(M, "M");

	assembleMass();

	ierr = MatDuplicate(M, MAT_DO_NOT_COPY_VALUES, &K);
	setName(K, "K");
	ierr = MatDuplicate(M, MAT_DO_NOT_COPY_VALUES, &J);
	setName(J, "J");

	ierr = SNESCreate(mpi_comm, &snes);
	ierr = SNESSetFromOptions(snes);
	ierr = SNESSetFunction(snes, rhs, MyModel::FormFunction, this);
	ierr = SNESSetJacobian(snes, J, J, MyModel::FormJacobian, this);

	PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INDEX);

	displacement.set(0.);
	velocity.set(0.);
	acceleration.set(0.);

	forces.set(0.);
	blocked.set(false);
	blocked(0, 0) = true;
	blocked(nb_dofs - 1, 0) = true;
	displacement(0, 0) = 0;
	displacement(nb_dofs - 1, 0) = 1;

	for (auto && data :
	zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
	make_view(this->initial_lengths))) {
	const auto & conn = std::get<0>(data);
	auto & L = std::get<1>(data);

	auto p1 = this->mesh.getNodes()(conn(0), _x);
	auto p2 = this->mesh.getNodes()(conn(1), _x);

	L = std::abs(p2 - p1);
	}
	}

	// static PetscErrorCode SNESMonitor(SNES snes,PetscInt its,PetscReal
	// fnorm,void *ctx) {
	// auto & _this = reinterpret_cast<MyModel >(ctx);
	// //SNESMonitorDefault(snes, its, fnorm, PETSC_VIEWER_STDOUT_WORLD);
	// }

	static PetscErrorCode FormFunction(SNES /snes/, Vec /dx/, Vec /f/,
	void * ctx) {
	auto & _this = reinterpret_cast<MyModel >(ctx);
	_this.assembleResidual();
	return 0;
	}

	static PetscErrorCode FormJacobian(SNES /snes/, Vec /dx/, Mat /J/,
	Mat /P/, void * ctx) {
	auto & _this = reinterpret_cast<MyModel >(ctx);
	_this.assembleJacobian();
	return 0;
	}

	~MyModel() {
	ierr = MatDestroy(&M);
	ierr = MatDestroy(&K);
	ierr = MatDestroy(&J);

	ierr = VecDestroy(&rhs);
	ierr = VecDestroy(&x);
	ierr = VecDestroy(&dx);
	ierr = VecDestroy(&x_save);
	ierr = VecDestroy(&f_int);

	PetscFinalize();
	}

	void solveStep() {
	std::cout << "solveStep" << std::endl;
	copy(x_save, displacement);

	ierr = SNESSolve(snes, NULL, dx);
	CHECK_ERR_CXX("SNESSolve", ierr);

	setSolutionToDisplacement();
	assembleResidual();
	}

	void applyBC() {
	std::vector<PetscInt> rows;
	for (auto && data : enumerate(blocked)) {
	if (std::get<1>(data)) {
	rows.push_back(std::get<0>(data));
	}
	}

	copy(x, displacement);
	ierr = MatZeroRowsColumnsLocal(J, rows.size(), rows.data(), 1., x,
	f_dirichlet);
	VecView(f_dirichlet, PETSC_VIEWER_STDOUT_WORLD);
	CHECK_ERR_CXX("MatZeroRowsColumnsLocal", ierr);
	}

	void setSolutionToDisplacement() {
	std::cout << "setSolutionToDisplacement" << std::endl;
	ierr = VecWAXPY(x, 1, x_save, dx);
	copy(displacement, x);
	}

	void assembleJacobian() {
	std::cout << "assembleJacobian" << std::endl;
	setSolutionToDisplacement();

	assembleStiffness();

	ierr = MatZeroEntries(J);
	CHECK_ERR_CXX("MatZeroEntries", ierr);

	ierr = MatAXPY(J, 1., K, SAME_NONZERO_PATTERN);
	CHECK_ERR_CXX("MatAXPY", ierr);

	MatView(J, PETSC_VIEWER_STDOUT_WORLD);
	applyBC();
	MatView(J, PETSC_VIEWER_STDOUT_WORLD);
	}

	void assembleMass() {
	std::cout << "assembleMass" << std::endl;
	ierr = MatZeroEntries(M);
	CHECK_ERR_CXX("MatZeroEntries", ierr);

	Array<Real> m_all_el(this->nb_elements, 4);

	Matrix<Real> m(2, 2);
	m(0, 0) = m(1, 1) = 2;
	m(0, 1) = m(1, 0) = 1;

	// under integrated
	// m(0, 0) = m(1, 1) = 3./2.;
	// m(0, 1) = m(1, 0) = 3./2.;

	// lumping the mass matrix
	// m(0, 0) += m(0, 1);
	// m(1, 1) += m(1, 0);
	// m(0, 1) = m(1, 0) = 0;

	for (auto && data :
	zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
	make_view(m_all_el, 2, 2))) {
	const auto & conn = std::get<0>(data);
	auto & m_el = std::get<1>(data);
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	Real L = std::abs(p2 - p1);

	m_el = m;
	m_el = rho A * L / 6.;

	Vector<Int> conn_int(conn.size());
	for (auto && data : zip(conn_int, conn)) {
	std::get<0>(data) = std::get<1>(data);
	}

	ierr = MatSetValuesLocal(M, conn_int.size(), conn_int.storage(),
	conn_int.size(), conn_int.storage(), m.storage(),
	ADD_VALUES);
	}

	ierr = MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY);
	ierr = MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY);
	ierr = MatSetOption(M, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);

	PetscViewer viewer;
	ierr = PetscViewerASCIIOpen(mpi_comm, "M.mtx", &viewer);
	PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATRIXMARKET);
	ierr = MatView(M, viewer);
	PetscViewerPopFormat(viewer);
	ierr = PetscViewerDestroy(&viewer);
	// this->getDOFManager().assembleElementalMatricesToMatrix(
	// "M", "disp", m_all_el, _segment_2);

	is_mass_assembled = true;
	}

	// MatrixType getMatrixType(const ID &) { return _symmetric; }

	// void assembleMatrix(const ID & matrix_id) {
	// if (matrix_id == "K") {
	// if (not is_stiffness_assembled)
	// this->assembleStiffness();
	// } else if (matrix_id == "M") {
	// if (not is_mass_assembled)
	// this->assembleMass();
	// } else if (matrix_id == "C") {
	// // pass, no damping matrix
	// } else {
	// AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
	// << matrix_id);
	// }
	// }

	void assembleLumpedMatrix(const ID & matrix_id) {
	std::cout << "assembleLumpedMatrix" << std::endl;
	AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
	<< matrix_id);
	}

	void assembleStiffness() {
	std::cout << "assembleStiffness" << std::endl;
	// SparseMatrix & K = this->getDOFManager().getMatrix("K");
	// K.zero();
	ierr = MatZeroEntries(K);
	CHECK_ERR_CXX("MatZeroEntries", ierr);

	Matrix<Real> k(2, 2);
	k(0, 0) = k(1, 1) = 1;
	k(0, 1) = k(1, 0) = -1;

	Array<Real> k_all_el(this->nb_elements, 4);

	auto k_it = k_all_el.begin(2, 2);
	auto cit = this->mesh.getConnectivity(_segment_2).begin(2);
	auto cend = this->mesh.getConnectivity(_segment_2).end(2);

	for (; cit != cend; ++cit, ++k_it) {
	const auto & conn = *cit;
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	Real L = std::abs(p2 - p1);

	auto & k_el = *k_it;
	k_el = k;
	k_el = E A / L;

	Vector<Int> conn_int(conn.size());
	for (auto && data : zip(conn_int, conn)) {
	std::get<0>(data) = std::get<1>(data);
	}

	ierr = MatSetValuesLocal(K, conn_int.size(), conn_int.storage(),
	conn_int.size(), conn_int.storage(),
	k_el.storage(), ADD_VALUES);
	}

	ierr = MatAssemblyBegin(K, MAT_FINAL_ASSEMBLY);
	CHECK_ERR_CXX("MatAssemblyBegin", ierr);

	ierr = MatAssemblyEnd(K, MAT_FINAL_ASSEMBLY);
	CHECK_ERR_CXX("MatAssemblyEnd", ierr);

	ierr = MatSetOption(K, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);
	CHECK_ERR_CXX("MatSetOption", ierr);

	PetscViewer viewer;
	ierr = PetscViewerASCIIOpen(mpi_comm, "K.mtx", &viewer);
	CHECK_ERR_CXX("PetscViewerASCIIOpen", ierr);

	PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATRIXMARKET);
	ierr = MatView(K, viewer);
	CHECK_ERR_CXX("MatView", ierr);

	PetscViewerPopFormat(viewer);
	ierr = PetscViewerDestroy(&viewer);
	CHECK_ERR_CXX("PetscViewerDestroy", ierr);

	// this->getDOFManager().assembleElementalMatricesToMatrix(
	// "K", "disp", k_all_el, _segment_2);

	is_stiffness_assembled = true;
	}

	void copy(Array<Real> & y, Vec x) {
	std::cout << "copy <-" << std::endl;
	const PetscScalar * x_local;
	ierr = VecGetArrayRead(x, &x_local);

	for (auto && data : zip(y, range(x_local + 0, x_local + y.size()))) {
	std::get<0>(data) = std::get<1>(data);
	}
	ierr = VecRestoreArrayRead(x, &x_local);

	// VecView(x, PETSC_VIEWER_STDOUT_WORLD);
	// std::cout << y.getID() << " " << Vector<Real>(y.storage(), y.size())
	// << std::endl;
	}

	void print(const Array<Real> & x) const {
	std::cout << x.getID() << " " << Vector<Real>(x.storage(), x.size())
	<< std::endl;
	}

	void copy(Vec x, const Array<Real> & y) {
	std::cout << "copy ->" << std::endl;
	PetscScalar * x_local;
	ierr = VecGetArray(x, &x_local);

	for (auto && data : zip(y, range(x_local + 0, x_local + y.size()))) {
	std::get<1>(data) = std::get<0>(data);
	}
	ierr = VecRestoreArray(x, &x_local);

	// std::cout << y.getID() << " " << Vector<Real>(y.storage(), y.size())
	// << std::endl;
	// VecView(x, PETSC_VIEWER_STDOUT_WORLD);
	}

	void assembleResidual() {
	std::cout << "assembleResidual" << std::endl;
	// this->getDOFManager().assembleToResidual("disp", forces);
	setSolutionToDisplacement();
	copy(rhs, forces);
	// VecAXPY(rhs, -1., f_dirichlet);

	print(displacement);
	this->assembleResidual(_not_ghost);
	// this->synchronize(SynchronizationTag::_user_1);

	// this->getDOFManager().assembleToResidual("disp", internal_forces, -1.);
	VecAXPY(rhs, 1., f_int);

	for (auto && data : enumerate(blocked)) {
	if (std::get<1>(data)) {
	VecSetValueLocal(rhs, std::get<0>(data), 0., INSERT_VALUES);
	}
	}
	VecAssemblyBegin(rhs);
	VecAssemblyEnd(rhs);

	VecView(rhs, PETSC_VIEWER_STDOUT_WORLD);
	}

	void assembleResidual(GhostType ghost_type) {
	std::cout << "assembleResidual" << std::endl;
	VecZeroEntries(f_int);

	auto cit = this->mesh.getConnectivity(_segment_2, ghost_type).begin(2);
	auto cend = this->mesh.getConnectivity(_segment_2, ghost_type).end(2);

	auto strain_it = this->strains.begin();
	auto stress_it = this->stresses.begin();
	auto L_it = this->initial_lengths.begin();

	for (; cit != cend; ++cit, ++strain_it, ++stress_it, ++L_it) {
	const auto & conn = *cit;
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real u1 = this->displacement(n1, _x);
	Real u2 = this->displacement(n2, _x);

	strain_it = (u2 - u1) / L_it;
	stress_it = E *strain_it;
	Real f_n = A * *stress_it;

	std::cout << n1 << "[" << u1 << "]"
	<< " <-> " << n2 << "[" << u2 << "]"
	<< " : " << f_n << std::endl;

	ierr = VecSetValueLocal(f_int, n1, -f_n, ADD_VALUES);
	ierr = VecSetValueLocal(f_int, n2, f_n, ADD_VALUES);
	}

	ierr = VecAssemblyBegin(f_int);
	ierr = VecAssemblyEnd(f_int);
	// this->getDOFManager().assembleElementalArrayLocalArray(
	// forces_internal_el, internal_forces, _segment_2, ghost_type);
	}

	Real getPotentialEnergy() {
	std::cout << "getPotentialEnergy" << std::endl;
	copy(x, displacement);
	Vec Ax;

	ierr = VecDuplicate(x, &Ax);
	ierr = MatMult(K, x, Ax);
	PetscScalar res;
	ierr = VecDot(x, Ax, &res);

	return res / 2.;
	}

	Real getKineticEnergy() {
	std::cout << "getKineticEnergy" << std::endl;
	return 0;
	}

	// Real getExternalWorkIncrement() {
	// Real res = 0;

	// auto it = velocity.begin();
	// auto end = velocity.end();
	// auto if_it = internal_forces.begin();
	// auto ef_it = forces.begin();
	// auto b_it = blocked.begin();

	// for (UInt node = 0; it != end; ++it, ++if_it, ++ef_it, ++b_it, ++node) {
	// if (mesh.isLocalOrMasterNode(node))
	// res += (b_it ? -if_it : ef_it) *it;
	// }

	// mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);

	// return res * this->getTimeStep();
	// }

	// void predictor() {}
	// void corrector() {}

	// /* ------------------------------------------------------------------------
	// */ UInt getNbData(const Array<Element> & elements,
	// const SynchronizationTag &) const {
	// return elements.size() * sizeof(Real);
	// }

	// void packData(CommunicationBuffer & buffer, const Array<Element> &
	// elements,
	// const SynchronizationTag & tag) const {
	// if (tag == SynchronizationTag::_user_1) {
	// for (const auto & el : elements) {
	// buffer << this->stresses(el.element);
	// }
	// }
	// }

	// void unpackData(CommunicationBuffer & buffer, const Array<Element> &
	// elements,
	// const SynchronizationTag & tag) {
	// if (tag == SynchronizationTag::_user_1) {
	// auto cit = this->mesh.getConnectivity(_segment_2, _ghost).begin(2);

	// for (const auto & el : elements) {
	// Real stress;
	// buffer >> stress;

	// Real f = A * stress;

	// Vector<UInt> conn = cit[el.element];
	// this->internal_forces(conn(0), _x) += -f;
	// this->internal_forces(conn(1), _x) += f;
	// }
	// }
	// }

	Real getExternalWorkIncrement() {
	std::cout << "getExternalWorkIncrement" << std::endl;
	return 0.;
	}

	template <class Functor> void applyBC(Functor && func, const ID & group_id) {
	auto & group = mesh.getElementGroup(group_id).getNodeGroup().getNodes();

	auto blocked_dofs = make_view(blocked, 1).begin();
	auto disps = make_view(displacement, 1).begin();
	auto poss = make_view(mesh.getNodes(), 1).begin();
	for (auto && node : group) {
	auto disp = Vector<Real>(disps[node]);
	auto pos = Vector<Real>(poss[node]);
	auto flags = Vector<bool>(blocked_dofs[node]);
	func(node, flags, disp, pos);
	}
	}

	const Mesh & getMesh() const { return mesh; }

	UInt getSpatialDimension() const { return 1; }

	auto & getBlockedDOFs() { return blocked; }

	void setTimeStep(Real dt) {
	std::cout << "setTimeStep" << std::endl;
	this->dt = dt;
	}

	private:
	PetscErrorCode ierr{0};
	MPI_Comm mpi_comm;
	ISLocalToGlobalMapping petsc_local_to_global;

	UInt nb_dofs;
	UInt nb_elements;

	bool lumped;

	bool is_stiffness_assembled{false};
	bool is_mass_assembled{false};
	bool is_lumped_mass_assembled{false};

	Mat K{nullptr}, J{nullptr}, M{nullptr};
	Vec rhs{nullptr}, x{nullptr}, x_save{nullptr}, dx{nullptr}, f_int{nullptr},
	f_dirichlet{nullptr};

	SNES snes;

	Real dt{0};
	Array<Real> save_displacement;

	public:
	Real E, A, rho;

	Mesh & mesh;
	Array<Real> displacement;
	Array<Real> velocity;
	Array<Real> acceleration;
	Array<bool> blocked;
	Array<Real> forces;
	Array<Real> internal_forces;

	Array<Real> stresses;
	Array<Real> strains;

	Array<Real> initial_lengths;
	};

	/* -------------------------------------------------------------------------- */
	class Sinusoidal : public BC::Dirichlet::DirichletFunctor {
	public:
	Sinusoidal(MyModel & model, Real amplitude, Real pulse_width, Real t)
	: model(model), A(amplitude), k(2 * M_PI / pulse_width),
	t(t), v{std::sqrt(model.E / model.rho)} {}

	void operator()(UInt n, Vector<bool> & /flags/, Vector<Real> & disp,
	const Vector<Real> & coord) const {
	auto x = coord(_x);
	model.velocity(n, _x) = k * v * A * sin(k * (x - v * t));
	disp(_x) = A * cos(k * (x - v * t));
	}

	private:
	MyModel & model;
	Real A{1.};
	Real k{2 * M_PI};
	Real t{1.};
	Real v{1.};
	};

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	PetscInitialize(&argc, &argv, nullptr, nullptr);

	UInt prank = Communicator::getStaticCommunicator().whoAmI();
	UInt global_nb_nodes = 3;
	UInt max_steps = 400;
	Real time_step = 0.001;
	Mesh mesh(1);
	Real F = -9.81;
	bool _explicit = EXPLICIT;
	// const Real pulse_width = 0.2;
	const Real A = 0.01;

	if (prank == 0)
	genMesh(mesh, global_nb_nodes);

	mesh.distribute();

	// mesh.makePeriodic(_x);

	MyModel model(F, mesh, _explicit);

	// model.forces.zero();
	// model.blocked.zero();

	// model.applyBC(Sinusoidal(model, A, pulse_width, 0.), "all");
	// model.applyBC(BC::Dirichlet::FlagOnly(_x), "border");

	// if (!_explicit) {
	// model.getNewSolver("dynamic", TimeStepSolverType::_dynamic,
	// NonLinearSolverType::_newton_raphson);
	// model.setIntegrationScheme("dynamic", "disp",
	// IntegrationSchemeType::_trapezoidal_rule_2,
	// IntegrationScheme::_displacement);
	// } else {
	// model.getNewSolver("dynamic", TimeStepSolverType::_dynamic_lumped,
	// NonLinearSolverType::_lumped);
	// model.setIntegrationScheme("dynamic", "disp",
	// IntegrationSchemeType::_central_difference,
	// IntegrationScheme::_acceleration);
	// }

	model.setTimeStep(time_step);

	if (prank == 0) {
	std::cout << std::scientific;
	std::cout << std::setw(14) << "time"
	<< "," << std::setw(14) << "wext"
	<< "," << std::setw(14) << "epot"
	<< "," << std::setw(14) << "ekin"
	<< "," << std::setw(14) << "total"
	<< "," << std::setw(14) << "max_disp"
	<< "," << std::setw(14) << "min_disp" << std::endl;
	}
	Real wext = 0.;

	// model.getDOFManager().clearResidual();
	// model.assembleResidual();

	Real epot = 0; // model.getPotentialEnergy();
	Real ekin = 0; // model.getKineticEnergy();
	Real einit = ekin + epot;
	Real etot = ekin + epot - wext - einit;

	Real max_disp = 0., min_disp = 0.;
	for (auto && disp : model.displacement) {
	max_disp = std::max(max_disp, disp);
	min_disp = std::min(min_disp, disp);
	}

	if (prank == 0) {
	std::cout << std::setw(14) << 0. << "," << std::setw(14) << wext << ","
	<< std::setw(14) << epot << "," << std::setw(14) << ekin << ","
	<< std::setw(14) << etot << "," << std::setw(14) << max_disp
	<< "," << std::setw(14) << min_disp << std::endl;
	}

	// #if EXPLICIT == false
	// NonLinearSolver & solver =
	// model.getDOFManager().getNonLinearSolver("dynamic");

	// solver.set("max_iterations", 20);
	// #endif

	auto * dumper = new DumperParaview("dynamic", "./paraview");
	mesh.registerExternalDumper(*dumper, "dynamic", true);
	mesh.addDumpMesh(mesh);

	mesh.addDumpFieldExternalToDumper("dynamic", "displacement",
	model.displacement);
	mesh.addDumpFieldExternalToDumper("dynamic", "velocity", model.velocity);
	mesh.addDumpFieldExternalToDumper("dynamic", "forces", model.forces);
	mesh.addDumpFieldExternalToDumper("dynamic", "acceleration",
	model.acceleration);

	mesh.dump();
	max_steps = 1;
	for (UInt i = 1; i < max_steps + 1; ++i) {
	// model.applyBC(Sinusoidal(model, A, pulse_width, time_step * (i - 1)),
	// "border");

	model.solveStep();
	mesh.dump();

	epot = model.getPotentialEnergy();
	ekin = model.getKineticEnergy();
	wext += model.getExternalWorkIncrement();
	etot = ekin + epot - wext - einit;

	Real max_disp = 0., min_disp = 0.;
	for (auto && disp : model.displacement) {
	max_disp = std::max(max_disp, disp);
	min_disp = std::min(min_disp, disp);
	}

	if (prank == 0) {
	std::cout << std::setw(14) << time_step * i << "," << std::setw(14)
	<< wext << "," << std::setw(14) << epot << "," << std::setw(14)
	<< ekin << "," << std::setw(14) << etot << "," << std::setw(14)
	<< max_disp << "," << std::setw(14) << min_disp << std::endl;
	}
	}

	// output.close();
	// finalize();
	// PetscFinalize();

	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	void genMesh(Mesh & mesh, UInt nb_nodes) {
	MeshAccessor mesh_accessor(mesh);
	Array<Real> & nodes = mesh_accessor.getNodes();
	Array<UInt> & conn = mesh_accessor.getConnectivity(_segment_2);

	nodes.resize(nb_nodes);

	// auto & all = mesh.createNodeGroup("all_nodes");

	for (UInt n = 0; n < nb_nodes; ++n) {
	nodes(n, _x) = n * (1. / (nb_nodes - 1));
	// all.add(n);
	}

	// mesh.createElementGroupFromNodeGroup("all", "all_nodes");

	conn.resize(nb_nodes - 1);
	for (UInt n = 0; n < nb_nodes - 1; ++n) {
	conn(n, 0) = n;
	conn(n, 1) = n + 1;
	}

	// Array<UInt> & conn_points = mesh_accessor.getConnectivity(_point_1);
	// conn_points.resize(2);

	// conn_points(0, 0) = 0;
	// conn_points(1, 0) = nb_nodes - 1;

	// auto & border = mesh.createElementGroup("border", 0);
	// border.add({_point_1, 0, _not_ghost}, true);
	// border.add({_point_1, 1, _not_ghost}, true);

	mesh_accessor.makeReady();
	}
	diff --git a/test/test_model/test_common/test_model_solver/test_model_solver_my_model.hh b/test/test_model/test_common/test_model_solver/test_model_solver_my_model.hh
	index 03f3e4980..b1f750ae0 100644
	--- a/test/test_model/test_common/test_model_solver/test_model_solver_my_model.hh
	+++ b/test/test_model/test_common/test_model_solver/test_model_solver_my_model.hh
	@@ -1,453 +1,453 @@
	/**
	* @file test_model_solver_my_model.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Apr 13 2016
	* @date last modification: Fri Jun 26 2020
	*
	* @brief Test default dof manager
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "boundary_condition.hh"
	#include "communicator.hh"
	#include "data_accessor.hh"
	#include "dof_manager_default.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "model_solver.hh"
	#include "periodic_node_synchronizer.hh"
	#include "solver_vector_default.hh"
	#include "sparse_matrix.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	#ifndef AKANTU_TEST_MODEL_SOLVER_MY_MODEL_HH_
	#define AKANTU_TEST_MODEL_SOLVER_MY_MODEL_HH_

	/**
	* =\o-----o-----o-> F
	* \| \|
	* \|---- L ----\|
	*/
	class MyModel : public ModelSolver,
	public BoundaryCondition<MyModel>,
	public DataAccessor<Element> {
	public:
	MyModel(Real F, Mesh & mesh, bool lumped,
	const ID & dof_manager_type = "default")
	: ModelSolver(mesh, ModelType::_model, "model_solver"),
	nb_dofs(mesh.getNbNodes()), nb_elements(mesh.getNbElement(_segment_2)),
	lumped(lumped), E(1.), A(1.), rho(1.), mesh(mesh),
	displacement(nb_dofs, 1, "disp"), velocity(nb_dofs, 1, "velo"),
	acceleration(nb_dofs, 1, "accel"), blocked(nb_dofs, 1, "blocked"),
	forces(nb_dofs, 1, "force_ext"),
	internal_forces(nb_dofs, 1, "force_int"),
	stresses(nb_elements, 1, "stress"), strains(nb_elements, 1, "strain"),
	initial_lengths(nb_elements, 1, "L0") {

	this->initDOFManager(dof_manager_type);

	this->initBC(*this, displacement, forces);

	this->getDOFManager().registerDOFs("disp", displacement, _dst_nodal);
	this->getDOFManager().registerDOFsDerivative("disp", 1, velocity);
	this->getDOFManager().registerDOFsDerivative("disp", 2, acceleration);
	this->getDOFManager().registerBlockedDOFs("disp", blocked);

	displacement.set(0.);
	velocity.set(0.);
	acceleration.set(0.);

	forces.set(0.);
	blocked.set(false);

	UInt global_nb_nodes = mesh.getNbGlobalNodes();
	for (auto && n : arange(nb_dofs)) {
	auto global_id = mesh.getNodeGlobalId(n);
	if (global_id == (global_nb_nodes - 1))
	forces(n, _x) = F;

	if (global_id == 0)
	blocked(n, _x) = true;
	}

	auto cit = this->mesh.getConnectivity(_segment_2).begin(2);
	auto cend = this->mesh.getConnectivity(_segment_2).end(2);
	auto L_it = this->initial_lengths.begin();

	for (; cit != cend; ++cit, ++L_it) {
	const Vector<UInt> & conn = *cit;
	UInt n1 = conn(0);
	UInt n2 = conn(1);
	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	*L_it = std::abs(p2 - p1);
	}

	this->registerDataAccessor(*this);
	this->registerSynchronizer(
	const_cast<ElementSynchronizer &>(this->mesh.getElementSynchronizer()),
	SynchronizationTag::_user_1);
	}

	void assembleLumpedMass() {
	auto & M = this->getDOFManager().getLumpedMatrix("M");
	M.zero();

	this->assembleLumpedMass(_not_ghost);
	if (this->mesh.getNbElement(_segment_2, _ghost) > 0)
	this->assembleLumpedMass(_ghost);

	is_lumped_mass_assembled = true;
	}

	void assembleLumpedMass(GhostType ghost_type) {
	Array<Real> M(nb_dofs, 1, 0.);

	Array<Real> m_all_el(this->mesh.getNbElement(_segment_2, ghost_type), 2);

	for (auto && data :
	zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
	make_view(m_all_el, 2))) {
	const auto & conn = std::get<0>(data);
	auto & m_el = std::get<1>(data);

	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	Real L = std::abs(p2 - p1);

	Real M_n = rho * A * L / 2;
	m_el(0) = m_el(1) = M_n;
	}

	this->getDOFManager().assembleElementalArrayLocalArray(
	m_all_el, M, _segment_2, ghost_type);

	this->getDOFManager().assembleToLumpedMatrix("disp", M, "M");
	}

	void assembleMass() {
	SparseMatrix & M = this->getDOFManager().getMatrix("M");
	M.zero();

	Array<Real> m_all_el(this->nb_elements, 4);

	Matrix<Real> m(2, 2);
	m(0, 0) = m(1, 1) = 2;
	m(0, 1) = m(1, 0) = 1;

	// under integrated
	// m(0, 0) = m(1, 1) = 3./2.;
	// m(0, 1) = m(1, 0) = 3./2.;

	// lumping the mass matrix
	// m(0, 0) += m(0, 1);
	// m(1, 1) += m(1, 0);
	// m(0, 1) = m(1, 0) = 0;

	for (auto && data :
	zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
	make_view(m_all_el, 2, 2))) {
	const auto & conn = std::get<0>(data);
	auto & m_el = std::get<1>(data);
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	Real L = std::abs(p2 - p1);

	m_el = m;
	m_el = rho A * L / 6.;
	}

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"M", "disp", m_all_el, _segment_2);

	is_mass_assembled = true;
	}

	MatrixType getMatrixType(const ID &) override { return _symmetric; }

	void assembleMatrix(const ID & matrix_id) override {
	if (matrix_id == "K") {
	if (not is_stiffness_assembled)
	this->assembleStiffness();
	} else if (matrix_id == "M") {
	if (not is_mass_assembled)
	this->assembleMass();
	} else if (matrix_id == "C") {
	// pass, no damping matrix
	} else {
	AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
	<< matrix_id);
	}
	}

	void assembleLumpedMatrix(const ID & matrix_id) override {
	if (matrix_id == "M") {
	if (not is_lumped_mass_assembled)
	this->assembleLumpedMass();
	} else {
	AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
	<< matrix_id);
	}
	}

	void assembleStiffness() {
	SparseMatrix & K = this->getDOFManager().getMatrix("K");
	K.zero();

	Matrix<Real> k(2, 2);
	k(0, 0) = k(1, 1) = 1;
	k(0, 1) = k(1, 0) = -1;

	Array<Real> k_all_el(this->nb_elements, 4);

	auto k_it = k_all_el.begin(2, 2);
	auto cit = this->mesh.getConnectivity(_segment_2).begin(2);
	auto cend = this->mesh.getConnectivity(_segment_2).end(2);

	for (; cit != cend; ++cit, ++k_it) {
	const auto & conn = *cit;
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real p1 = this->mesh.getNodes()(n1, _x);
	Real p2 = this->mesh.getNodes()(n2, _x);

	Real L = std::abs(p2 - p1);

	auto & k_el = *k_it;
	k_el = k;
	k_el = E A / L;
	}

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "disp", k_all_el, _segment_2);

	is_stiffness_assembled = true;
	}

	void assembleResidual() override {
	this->getDOFManager().assembleToResidual("disp", forces);
	internal_forces.zero();

	this->assembleResidualInternal(_not_ghost);

	this->synchronize(SynchronizationTag::_user_1);

	this->getDOFManager().assembleToResidual("disp", internal_forces, -1.);
	}

	void assembleResidualInternal(GhostType ghost_type) {
	Array<Real> forces_internal_el(
	this->mesh.getNbElement(_segment_2, ghost_type), 2);

	auto cit = this->mesh.getConnectivity(_segment_2, ghost_type).begin(2);
	auto cend = this->mesh.getConnectivity(_segment_2, ghost_type).end(2);

	auto f_it = forces_internal_el.begin(2);

	auto strain_it = this->strains.begin();
	auto stress_it = this->stresses.begin();
	auto L_it = this->initial_lengths.begin();

	for (; cit != cend; ++cit, ++f_it, ++strain_it, ++stress_it, ++L_it) {
	const auto & conn = *cit;
	UInt n1 = conn(0);
	UInt n2 = conn(1);

	Real u1 = this->displacement(n1, _x);
	Real u2 = this->displacement(n2, _x);

	strain_it = (u2 - u1) / L_it;
	stress_it = E *strain_it;
	Real f_n = A * *stress_it;
	Vector<Real> & f = *f_it;

	f(0) = -f_n;
	f(1) = f_n;
	}

	this->getDOFManager().assembleElementalArrayLocalArray(
	forces_internal_el, internal_forces, _segment_2, ghost_type);
	}

	Real getPotentialEnergy() {
	Real res = 0;

	if (not lumped) {
	res = this->mulVectMatVect(this->displacement, "K", this->displacement);
	} else {
	auto strain_it = this->strains.begin();
	auto stress_it = this->stresses.begin();
	auto strain_end = this->strains.end();
	auto L_it = this->initial_lengths.begin();

	for (; strain_it != strain_end; ++strain_it, ++stress_it, ++L_it) {
	res += strain_it stress_it A * *L_it;
	}

	mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);
	}

	return res / 2.;
	}

	Real getKineticEnergy() {
	Real res = 0;
	if (not lumped) {
	res = this->mulVectMatVect(this->velocity, "M", this->velocity);
	} else {
	Array<Real> & m = dynamic_cast<SolverVectorDefault &>(
	this->getDOFManager().getLumpedMatrix("M"));
	auto it = velocity.begin();
	auto end = velocity.end();
	auto m_it = m.begin();

	for (UInt node = 0; it != end; ++it, ++m_it, ++node) {
	if (mesh.isLocalOrMasterNode(node))
	res += m_it it *it;
	}

	mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);
	}

	return res / 2.;
	}

	Real getExternalWorkIncrement() {
	Real res = 0;

	auto it = velocity.begin();
	auto end = velocity.end();
	auto if_it = internal_forces.begin();
	auto ef_it = forces.begin();
	auto b_it = blocked.begin();

	for (UInt node = 0; it != end; ++it, ++if_it, ++ef_it, ++b_it, ++node) {
	if (mesh.isLocalOrMasterNode(node))
	res += (b_it ? -if_it : ef_it) *it;
	}

	mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);

	return res * this->getTimeStep();
	}

	Real mulVectMatVect(const Array<Real> & x, const ID & A_id,
	const Array<Real> & y) {
	Array<Real> Ay(nb_dofs);
	this->getDOFManager().assembleMatMulVectToArray("disp", A_id, y, Ay);

	Real res = 0.;
	for (auto && data : zip(arange(nb_dofs), make_view(Ay), make_view(x))) {
	res += std::get<2>(data) * std::get<1>(data) *
	mesh.isLocalOrMasterNode(std::get<0>(data));
	}

	mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);
	return res;
	}

	/* ------------------------------------------------------------------------ */
	UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag &) const override {
	return elements.size() * sizeof(Real);
	}

	void packData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) const override {
	if (tag == SynchronizationTag::_user_1) {
	for (const auto & el : elements) {
	buffer << this->stresses(el.element);
	}
	}
	}

	void unpackData(CommunicationBuffer & buffer, const Array<Element> & elements,
	const SynchronizationTag & tag) override {
	if (tag == SynchronizationTag::_user_1) {
	auto cit = this->mesh.getConnectivity(_segment_2, _ghost).begin(2);

	for (const auto & el : elements) {
	Real stress;
	buffer >> stress;

	Real f = A * stress;

	Vector<UInt> conn = cit[el.element];
	this->internal_forces(conn(0), _x) += -f;
	this->internal_forces(conn(1), _x) += f;
	}
	}
	}

	const Mesh & getMesh() const { return mesh; }

	UInt getSpatialDimension() const { return 1; }

	auto & getBlockedDOFs() { return blocked; }

	private:
	UInt nb_dofs;
	UInt nb_elements;

	bool lumped;

	bool is_stiffness_assembled{false};
	bool is_mass_assembled{false};
	bool is_lumped_mass_assembled{false};

	public:
	Real E, A, rho;

	Mesh & mesh;
	Array<Real> displacement;
	Array<Real> velocity;
	Array<Real> acceleration;
	Array<bool> blocked;
	Array<Real> forces;
	Array<Real> internal_forces;

	Array<Real> stresses;
	Array<Real> strains;

	Array<Real> initial_lengths;
	};

	#endif /* AKANTU_TEST_MODEL_SOLVER_MY_MODEL_HH_ */

	} // namespace akantu
	diff --git a/test/test_model/test_common/test_non_local_toolbox/my_model.hh b/test/test_model/test_common/test_non_local_toolbox/my_model.hh
	index 3e78a2df5..4dba337a2 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/my_model.hh
	+++ b/test/test_model/test_common/test_non_local_toolbox/my_model.hh
	@@ -1,125 +1,124 @@
	/**
	* @file my_model.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Sep 11 2017
	* @date last modification: Fri Jun 26 2020
	*
	* @brief A dummy model for tests purposes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss.hh"
	#include "model.hh"
	#include "non_local_manager.hh"
	#include "non_local_manager_callback.hh"
	#include "non_local_neighborhood_base.hh"
	#include "shape_lagrange.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class MyModel : public Model, public NonLocalManagerCallback {
	using MyFEEngineType = FEEngineTemplate<IntegratorGauss, ShapeLagrange>;

	public:
	MyModel(Mesh & mesh, UInt spatial_dimension)
	: Model(mesh, ModelType::_model, spatial_dimension),
	manager(this, this) {
	registerFEEngineObject<MyFEEngineType>("FEEngine", mesh, spatial_dimension);
	manager.registerNeighborhood("test_region", "test_region");

	getFEEngine().initShapeFunctions();
	manager.initialize();
	}

	void initModel() override {}

	MatrixType getMatrixType(const ID &) override { return _mt_not_defined; }
	std::tuple<ID, TimeStepSolverType>
	getDefaultSolverID(const AnalysisMethod & /method/) override {
	return std::make_tuple("test", TimeStepSolverType::_static);
	}

	void assembleMatrix(const ID &) override {}
	void assembleLumpedMatrix(const ID &) override {}
	void assembleResidual() override {}

	void onNodesAdded(const Array<UInt> &, const NewNodesEvent &) override {}

	void onNodesRemoved(const Array<UInt> &, const Array<UInt> &,
	const RemovedNodesEvent &) override {}
	void onElementsAdded(const Array<Element> &,
	const NewElementsEvent &) override {}
	void onElementsRemoved(const Array<Element> &,
	const ElementTypeMapArray<UInt> &,
	const RemovedElementsEvent &) override {}
	void onElementsChanged(const Array<Element> &, const Array<Element> &,
	const ElementTypeMapArray<UInt> &,
	const ChangedElementsEvent &) override {}

	- void insertIntegrationPointsInNeighborhoods(
	- GhostType ghost_type) override {
	+ void insertIntegrationPointsInNeighborhoods(GhostType ghost_type) override {
	ElementTypeMapArray<Real> quadrature_points_coordinates(
	"quadrature_points_coordinates_tmp_nl", this->id);
	quadrature_points_coordinates.initialize(this->getFEEngine(),
	_nb_component = spatial_dimension,
	_ghost_type = ghost_type);

	IntegrationPoint q;
	q.ghost_type = ghost_type;
	q.global_num = 0;

	auto & neighborhood = manager.getNeighborhood("test_region");

	for (auto & type : quadrature_points_coordinates.elementTypes(
	spatial_dimension, ghost_type)) {
	q.type = type;
	auto & quads = quadrature_points_coordinates(type, ghost_type);
	this->getFEEngine().computeIntegrationPointsCoordinates(quads, type,
	ghost_type);
	auto quad_it = quads.begin(quads.getNbComponent());
	auto quad_end = quads.end(quads.getNbComponent());
	q.num_point = 0;
	for (; quad_it != quad_end; ++quad_it) {
	neighborhood.insertIntegrationPoint(q, *quad_it);
	++q.num_point;
	++q.global_num;
	}
	}
	}

	void computeNonLocalStresses(GhostType) override {}

	void updateLocalInternal(ElementTypeMapReal &, GhostType,
	ElementKind) override {}

	void updateNonLocalInternal(ElementTypeMapReal &, GhostType,
	ElementKind) override {}

	const auto & getNonLocalManager() const { return manager; }

	private:
	NonLocalManager manager;
	};
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_build_neighborhood_parallel.cc b/test/test_model/test_common/test_non_local_toolbox/test_build_neighborhood_parallel.cc
	index b975f7bf7..15ab6531e 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_build_neighborhood_parallel.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_build_neighborhood_parallel.cc
	@@ -1,190 +1,190 @@
	/**
	* @file test_build_neighborhood_parallel.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Wed Jan 30 2019
	*
	* @brief test in parallel for the class NonLocalNeighborhood
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_iohelper_paraview.hh"
	#include "non_local_neighborhood_base.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize("material_parallel_test.dat", argc, argv);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	// some configuration variables
	const UInt spatial_dimension = 2;

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	if (prank == 0) {
	mesh.read("parallel_test.msh");
	}

	mesh.distribute();

	/// model creation
	SolidMechanicsModel model(mesh);

	/// dump the ghost elements before the non-local part is intialized
	DumperParaview dumper_ghost("ghost_elements");
	dumper_ghost.registerMesh(mesh, spatial_dimension, _ghost);
	if (psize > 1) {
	dumper_ghost.dump();
	}

	/// creation of material selector
	auto && mat_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	model.setMaterialSelector(mat_selector);

	/// dump material index in paraview
	model.addDumpField("partitions");
	model.dump();

	/// model initialization changed to use our material
	model.initFull();

	/// dump the ghost elements after ghosts for non-local have been added
	if (psize > 1)
	dumper_ghost.dump();

	model.addDumpField("grad_u");
	model.addDumpField("grad_u non local");
	model.addDumpField("material_index");

	/// apply constant strain field everywhere in the plate
	Matrix<Real> applied_strain(spatial_dimension, spatial_dimension);
	applied_strain.zero();
	for (UInt i = 0; i < spatial_dimension; ++i)
	applied_strain(i, i) = 2.;

	ElementType element_type = _triangle_3;
	GhostType ghost_type = _not_ghost;
	/// apply constant grad_u field in all elements
	for (UInt m = 0; m < model.getNbMaterials(); ++m) {
	auto & mat = model.getMaterial(m);
	auto & grad_u = const_cast<Array<Real> &>(
	mat.getInternal<Real>("grad_u")(element_type, ghost_type));
	auto grad_u_it = grad_u.begin(spatial_dimension, spatial_dimension);
	auto grad_u_end = grad_u.end(spatial_dimension, spatial_dimension);
	for (; grad_u_it != grad_u_end; ++grad_u_it)
	(grad_u_it) = -1. applied_strain;
	}

	/// double the strain in the center: find the closed gauss point to the center
	/// compute the quadrature points
	ElementTypeMapReal quad_coords("quad_coords");
	quad_coords.initialize(mesh, _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_with_nb_element = true);
	model.getFEEngine().computeIntegrationPointsCoordinates(quad_coords);

	Vector<Real> center(spatial_dimension, 0.);
	Real min_distance = 2;
	IntegrationPoint q_min;
	for (auto type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {
	UInt nb_elements = mesh.getNbElement(type, _not_ghost);
	UInt nb_quads = model.getFEEngine().getNbIntegrationPoints(type);
	Array<Real> & coords = quad_coords(type, _not_ghost);
	auto coord_it = coords.begin(spatial_dimension);
	for (UInt e = 0; e < nb_elements; ++e) {
	for (UInt q = 0; q < nb_quads; ++q, ++coord_it) {
	Real dist = center.distance(*coord_it);
	if (dist < min_distance) {
	min_distance = dist;
	q_min.element = e;
	q_min.num_point = q;
	q_min.global_num = nb_elements * nb_quads + q;
	q_min.type = type;
	}
	}
	}
	}

	Real global_min = min_distance;
	comm.allReduce(global_min, SynchronizerOperation::_min);

	if (Math::are_float_equal(global_min, min_distance)) {
	UInt mat_index = model.getMaterialByElement(q_min.type, _not_ghost)
	.begin()[q_min.element];
	Material & mat = model.getMaterial(mat_index);
	UInt nb_quads = model.getFEEngine().getNbIntegrationPoints(q_min.type);
	UInt local_el_index =
	model.getMaterialLocalNumbering(q_min.type, _not_ghost)
	.begin()[q_min.element];
	UInt local_num = (local_el_index * nb_quads) + q_min.num_point;
	Array<Real> & grad_u = const_cast<Array<Real> &>(
	mat.getInternal<Real>("grad_u")(q_min.type, _not_ghost));
	Array<Real>::iterator<Matrix<Real>> grad_u_it =
	grad_u.begin(spatial_dimension, spatial_dimension);
	grad_u_it += local_num;
	Matrix<Real> & g_u = *grad_u_it;
	g_u += applied_strain;
	}

	/// compute the non-local strains
	model.assembleInternalForces();
	model.dump();

	/// damage the element with higher grad_u completely, so that it is
	/// not taken into account for the averaging
	if (Math::are_float_equal(global_min, min_distance)) {
	UInt mat_index = model.getMaterialByElement(q_min.type, _not_ghost)
	.begin()[q_min.element];
	Material & mat = model.getMaterial(mat_index);
	UInt nb_quads = model.getFEEngine().getNbIntegrationPoints(q_min.type);
	UInt local_el_index =
	model.getMaterialLocalNumbering(q_min.type, _not_ghost)
	.begin()[q_min.element];
	UInt local_num = (local_el_index * nb_quads) + q_min.num_point;
	Array<Real> & damage = const_cast<Array<Real> &>(
	mat.getInternal<Real>("damage")(q_min.type, _not_ghost));
	Real * dam_ptr = damage.storage();
	dam_ptr += local_num;
	*dam_ptr = 0.9;
	}

	/// compute the non-local strains
	model.assembleInternalForces();
	model.dump();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_material.cc b/test/test_model/test_common/test_non_local_toolbox/test_material.cc
	index 654f808c3..9aba193e4 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_material.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_material.cc
	@@ -1,57 +1,57 @@
	/**
	* @file test_material.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Wed Jan 30 2019
	*
	* @brief Implementation of test material for the non-local neighborhood base
	* test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_material.hh"

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	TestMaterial<dim>::TestMaterial(SolidMechanicsModel & model, const ID & id)
	: Parent(model, id), grad_u_nl("grad_u non local", *this) {
	this->is_non_local = true;
	this->grad_u_nl.initialize(dim * dim);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void TestMaterial<dim>::registerNonLocalVariables() {
	this->model.getNonLocalManager().registerNonLocalVariable(
	this->gradu.getName(), grad_u_nl.getName(), dim * dim);

	this->model.getNonLocalManager()
	.getNeighborhood(this->getNeighborhoodName())
	.registerNonLocalVariable(grad_u_nl.getName());
	}

	/* -------------------------------------------------------------------------- */
	// Instantiate the material for the 3 dimensions
	INSTANTIATE_MATERIAL(test_material, TestMaterial);
	/* -------------------------------------------------------------------------- */
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_material.hh b/test/test_model/test_common/test_non_local_toolbox/test_material.hh
	index 9b0130132..9d76af8c0 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_material.hh
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_material.hh
	@@ -1,73 +1,73 @@
	/**
	* @file test_material.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jan 30 2019
	*
	* @brief test material for the non-local neighborhood base test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_damage.hh"
	#include "material_damage_non_local.hh"

	#ifndef TEST_MATERIAL_HH_
	#define TEST_MATERIAL_HH_

	using namespace akantu;

	template <UInt dim>
	class TestMaterial
	: public MaterialDamageNonLocal<dim, MaterialDamage<dim, MaterialElastic>> {
	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructor */
	/* ------------------------------------------------------------------------ */
	public:
	using Parent =
	MaterialDamageNonLocal<dim, MaterialDamage<dim, MaterialElastic>>;

	TestMaterial(SolidMechanicsModel & model, const ID & id);

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void registerNonLocalVariables() override final;

	void computeNonLocalStress(ElementType, GhostType) override final{};

	void computeNonLocalStresses(GhostType) override final{};

	protected:
	ID getNeighborhoodName() override { return "test_region"; }

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	private:
	InternalField<Real> grad_u_nl;
	};

	#endif /* TEST_MATERIAL_HH_ */
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_material_damage.cc b/test/test_model/test_common/test_non_local_toolbox/test_material_damage.cc
	index b64e75bfa..611e420d4 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_material_damage.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_material_damage.cc
	@@ -1,59 +1,59 @@
	/**
	* @file test_material_damage.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Wed Jan 30 2019
	*
	* @brief Implementation of test material damage
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_material_damage.hh"
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	TestMaterialDamage<dim>::TestMaterialDamage(SolidMechanicsModel & model,
	const ID & id)
	: Parent(model, id), grad_u_nl("grad_u non local", *this) {
	this->is_non_local = true;
	this->grad_u_nl.initialize(dim * dim);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void TestMaterialDamage<dim>::registerNonLocalVariables() {
	this->model.getNonLocalManager().registerNonLocalVariable(
	this->gradu.getName(), grad_u_nl.getName(), dim * dim);

	this->model.getNonLocalManager()
	.getNeighborhood(this->getNeighborhoodName())
	.registerNonLocalVariable(grad_u_nl.getName());
	}

	/* -------------------------------------------------------------------------- */
	// Instantiate the material for the 3 dimensions
	INSTANTIATE_MATERIAL(test_material, TestMaterialDamage);
	/* -------------------------------------------------------------------------- */
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_material_damage.hh b/test/test_model/test_common/test_non_local_toolbox/test_material_damage.hh
	index 6b1c38081..b08564b0a 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_material_damage.hh
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_material_damage.hh
	@@ -1,75 +1,75 @@
	/**
	* @file test_material_damage.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jan 30 2019
	*
	* @brief test material damage for the non-local remove damage test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_damage.hh"
	#include "material_damage_non_local.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef TEST_MATERIAL_DAMAGE_HH_
	#define TEST_MATERIAL_DAMAGE_HH_

	using namespace akantu;

	template <UInt dim>
	class TestMaterialDamage
	: public MaterialDamageNonLocal<dim, MaterialDamage<dim, MaterialElastic>> {

	using Parent =
	MaterialDamageNonLocal<dim, MaterialDamage<dim, MaterialElastic>>;

	/* ------------------------------------------------------------------------ */
	/* Constructor/Destructor */
	/* ------------------------------------------------------------------------ */
	public:
	TestMaterialDamage(SolidMechanicsModel & model, const ID & id);
	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void registerNonLocalVariables() override final;

	void computeNonLocalStress(ElementType, GhostType) override final{};

	void insertQuadsInNeighborhoods(GhostType ghost_type);

	protected:
	// ID getNeighborhoodName() override { return "test_region"; }

	/* ------------------------------------------------------------------------ */
	/* Members */
	/* ------------------------------------------------------------------------ */
	private:
	InternalField<Real> grad_u_nl;
	};

	#endif /* TEST_MATERIAL_DAMAGE_HH_ */
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_non_local_averaging.cc b/test/test_model/test_common/test_non_local_toolbox/test_non_local_averaging.cc
	index 6db9ae1fe..323134218 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_non_local_averaging.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_non_local_averaging.cc
	@@ -1,112 +1,112 @@
	/**
	* @file test_non_local_averaging.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Sun Jun 16 2019
	*
	* @brief test for non-local averaging of strain
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "non_local_manager.hh"
	#include "non_local_neighborhood.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize("material_avg.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;
	ElementType element_type = _quadrangle_4;
	GhostType ghost_type = _not_ghost;

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	mesh.read("plate.msh");

	/// model creation
	SolidMechanicsModel model(mesh);

	/// creation of material selector
	auto && mat_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	model.setMaterialSelector(mat_selector);

	/// model initialization changed to use our material
	model.initFull();

	/// dump material index in paraview
	model.addDumpField("material_index");
	model.addDumpField("grad_u");
	model.addDumpField("grad_u non local");
	model.dump();

	/// apply constant strain field everywhere in the plate
	Matrix<Real> applied_strain(spatial_dimension, spatial_dimension);
	applied_strain.zero();
	for (UInt i = 0; i < spatial_dimension; ++i)
	applied_strain(i, i) = 2.;

	/// apply constant grad_u field in all elements
	for (auto & mat : model.getMaterials()) {
	auto & grad_us =
	mat.getInternal<Real>("eigen_grad_u")(element_type, ghost_type);
	for (auto & grad_u :
	make_view(grad_us, spatial_dimension, spatial_dimension)) {
	grad_u = -1. * applied_strain;
	}
	}

	/// compute the non-local strains
	model.assembleInternalForces();
	model.dump();

	/// verify the result: non-local averaging over constant field must
	/// yield same constant field
	Real test_result = 0.;
	Matrix<Real> difference(spatial_dimension, spatial_dimension, 0.);

	for (auto & mat : model.getMaterials()) {
	auto & grad_us_nl =
	mat.getInternal<Real>("grad_u non local")(element_type, ghost_type);
	for (auto & grad_u_nl :
	make_view(grad_us_nl, spatial_dimension, spatial_dimension)) {
	difference = grad_u_nl - applied_strain;
	test_result += difference.norm<L_2>();
	}
	}

	if (test_result > 10.e-13) {
	AKANTU_EXCEPTION("the total norm is: " << test_result);
	}

	return 0;
	}
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_non_local_neighborhood_base.cc b/test/test_model/test_common/test_non_local_toolbox/test_non_local_neighborhood_base.cc
	index 42c36be2a..80c52dc20 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_non_local_neighborhood_base.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_non_local_neighborhood_base.cc
	@@ -1,82 +1,82 @@
	/**
	* @file test_non_local_neighborhood_base.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Wed Jan 30 2019
	*
	* @brief test for the class NonLocalNeighborhoodBase
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "my_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize("material.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	mesh.read("plate.msh");

	/// model creation
	MyModel model(mesh, spatial_dimension);
	const auto & manager = model.getNonLocalManager();
	const auto & neighborhood = manager.getNeighborhood("test_region");

	/// save the pair of quadrature points and the coords of all neighbors
	std::string output_1 = "quadrature_pairs";
	std::string output_2 = "neighborhoods";
	neighborhood.savePairs(output_1);
	neighborhood.saveNeighborCoords(output_2);

	/// print results to screen for validation
	std::ifstream quad_pairs;
	quad_pairs.open("quadrature_pairs.0");

	std::string current_line;
	while (getline(quad_pairs, current_line))
	std::cout << current_line << std::endl;

	quad_pairs.close();

	std::ifstream neighborhoods;
	neighborhoods.open("neighborhoods.0");
	while (getline(neighborhoods, current_line))
	std::cout << current_line << std::endl;
	neighborhoods.close();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_pair_computation.cc b/test/test_model/test_common/test_non_local_toolbox/test_pair_computation.cc
	index e5a4390f8..d9a481f8c 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_pair_computation.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_pair_computation.cc
	@@ -1,225 +1,229 @@
	/**
	* @file test_pair_computation.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 25 2015
	* @date last modification: Fri Jul 10 2020
	*
	* @brief test the weight computation with and without grid
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "non_local_manager.hh"
	#include "non_local_neighborhood.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material_damage.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	typedef std::vector<std::pair<IntegrationPoint, IntegrationPoint>> PairList;

	/* -------------------------------------------------------------------------- */
	void computePairs(SolidMechanicsModel & model, PairList * pair_list);
	int main(int argc, char * argv[]) {
	akantu::initialize("material_remove_damage.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	if (prank == 0) {
	mesh.read("pair_test.msh");
	}
	mesh.distribute();

	/// model creation
	SolidMechanicsModel model(mesh);

	/// creation of material selector
	auto && mat_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	model.setMaterialSelector(mat_selector);

	/// model initialization changed to use our material
	model.initFull();

	/// dump material index in paraview
	model.addDumpField("material_index");
	model.dump();

	/// compute the pairs by looping over all the quadrature points
	std::array<PairList, 2> pair_list;
	computePairs(model, pair_list.data());

	const auto & pairs_mat_1_not_ghost =
	- model.getNonLocalManager().getNeighborhood("mat_1").getPairLists(_not_ghost);
	+ model.getNonLocalManager().getNeighborhood("mat_1").getPairLists(
	+ _not_ghost);
	const auto & pairs_mat_1_ghost =
	model.getNonLocalManager().getNeighborhood("mat_1").getPairLists(_ghost);
	const auto & pairs_mat_2_not_ghost =
	- model.getNonLocalManager().getNeighborhood("mat_2").getPairLists(_not_ghost);
	+ model.getNonLocalManager().getNeighborhood("mat_2").getPairLists(
	+ _not_ghost);
	const auto & pairs_mat_2_ghost =
	model.getNonLocalManager().getNeighborhood("mat_2").getPairLists(_ghost);

	/// compare the number of pairs
	- UInt nb_not_ghost_pairs_grid = pairs_mat_1_not_ghost.size() + pairs_mat_2_not_ghost.size();
	- UInt nb_ghost_pairs_grid = pairs_mat_1_ghost.size() + pairs_mat_2_ghost.size();
	+ UInt nb_not_ghost_pairs_grid =
	+ pairs_mat_1_not_ghost.size() + pairs_mat_2_not_ghost.size();
	+ UInt nb_ghost_pairs_grid =
	+ pairs_mat_1_ghost.size() + pairs_mat_2_ghost.size();
	UInt nb_not_ghost_pairs_no_grid = pair_list[0].size();
	UInt nb_ghost_pairs_no_grid = pair_list[1].size();

	if ((nb_not_ghost_pairs_grid != nb_not_ghost_pairs_no_grid) \|\|
	(nb_ghost_pairs_grid != nb_ghost_pairs_no_grid)) {
	std::cout << "The number of pairs is not correct: TEST FAILED!!!"
	<< std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	for (UInt i = 0; i < pairs_mat_1_not_ghost.size(); ++i) {
	PairList::const_iterator it = std::find(
	pair_list[0].begin(), pair_list[0].end(), (pairs_mat_1_not_ghost)[i]);
	if (it == pair_list[0].end()) {
	std::cout << "The pairs are not correct" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	for (UInt i = 0; i < pairs_mat_2_not_ghost.size(); ++i) {
	PairList::const_iterator it = std::find(
	pair_list[0].begin(), pair_list[0].end(), (pairs_mat_2_not_ghost)[i]);
	if (it == pair_list[0].end()) {
	std::cout << "The pairs are not correct" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	for (UInt i = 0; i < pairs_mat_1_ghost.size(); ++i) {
	PairList::const_iterator it = std::find(
	pair_list[1].begin(), pair_list[1].end(), (pairs_mat_1_ghost)[i]);
	if (it == pair_list[1].end()) {
	std::cout << "The pairs are not correct" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	for (UInt i = 0; i < pairs_mat_2_ghost.size(); ++i) {
	PairList::const_iterator it = std::find(
	pair_list[1].begin(), pair_list[1].end(), (pairs_mat_2_ghost)[i]);
	if (it == pair_list[1].end()) {
	std::cout << "The pairs are not correct" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	finalize();

	return 0;
	}

	/* -------------------------------------------------------------------------- */
	void computePairs(SolidMechanicsModel & model, PairList * pair_list) {
	ElementKind kind = _ek_regular;
	Mesh & mesh = model.getMesh();
	UInt spatial_dimension = model.getSpatialDimension();
	/// compute the quadrature points
	ElementTypeMapReal quad_coords("quad_coords");
	quad_coords.initialize(mesh, _nb_component = spatial_dimension,
	_spatial_dimension = spatial_dimension,
	_with_nb_element = true);
	model.getFEEngine().computeIntegrationPointsCoordinates(quad_coords);

	/// loop in a n^2 way over all the quads to generate the pairs
	Real neighborhood_radius = 0.5;

	IntegrationPoint q1;
	IntegrationPoint q2;
	GhostType ghost_type_1 = _not_ghost;
	q1.ghost_type = ghost_type_1;
	Vector<Real> q1_coords(spatial_dimension);
	Vector<Real> q2_coords(spatial_dimension);

	for (auto type_1 : mesh.elementTypes(spatial_dimension, _not_ghost, kind)) {
	q1.type = type_1;
	UInt nb_elements_1 = mesh.getNbElement(type_1, ghost_type_1);
	UInt nb_quads_1 = model.getFEEngine().getNbIntegrationPoints(type_1);
	Array<Real> & quad_coords_1 = quad_coords(q1.type, q1.ghost_type);
	auto coord_it_1 = quad_coords_1.begin(spatial_dimension);
	for (UInt e_1 = 0; e_1 < nb_elements_1; ++e_1) {
	q1.element = e_1;
	UInt mat_index_1 = model.getMaterialByElement(q1.type, q1.ghost_type)
	.begin()[q1.element];
	for (UInt q_1 = 0; q_1 < nb_quads_1; ++q_1) {
	q1.global_num = nb_quads_1 * e_1 + q_1;
	q1.num_point = q_1;
	q1_coords = coord_it_1[q1.global_num];
	/// loop over all other quads and create pairs for this given quad
	for (auto ghost_type_2 : ghost_types) {
	q2.ghost_type = ghost_type_2;

	for (auto type_2 :
	mesh.elementTypes(spatial_dimension, ghost_type_2, kind)) {

	q2.type = type_2;
	UInt nb_elements_2 = mesh.getNbElement(type_2, ghost_type_2);
	UInt nb_quads_2 =
	model.getFEEngine().getNbIntegrationPoints(type_2);
	Array<Real> & quad_coords_2 = quad_coords(q2.type, q2.ghost_type);
	auto coord_it_2 = quad_coords_2.begin(spatial_dimension);
	for (UInt e_2 = 0; e_2 < nb_elements_2; ++e_2) {
	q2.element = e_2;
	UInt mat_index_2 =
	model.getMaterialByElement(q2.type, q2.ghost_type)
	.begin()[q2.element];
	for (UInt q_2 = 0; q_2 < nb_quads_2; ++q_2) {
	q2.global_num = nb_quads_2 * e_2 + q_2;
	q2.num_point = q_2;
	q2_coords = coord_it_2[q2.global_num];
	Real distance = q1_coords.distance(q2_coords);
	if (mat_index_1 != mat_index_2)
	continue;
	else if (distance <=
	neighborhood_radius + Math::getTolerance() &&
	(q2.ghost_type == _ghost \|\|
	(q2.ghost_type == _not_ghost &&
	q1.global_num <=
	q2.global_num))) { // storing only half lists
	pair_list[q2.ghost_type].push_back(std::make_pair(q1, q2));
	}
	}
	}
	}
	}
	}
	}
	}
	}
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_remove_damage_weight_function.cc b/test/test_model/test_common/test_non_local_toolbox/test_remove_damage_weight_function.cc
	index b8c2cbaab..6f114cb0c 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_remove_damage_weight_function.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_remove_damage_weight_function.cc
	@@ -1,192 +1,192 @@
	/**
	* @file test_remove_damage_weight_function.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 07 2015
	* @date last modification: Wed Nov 27 2019
	*
	* @brief Test the damage weight funcion for non local computations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "non_local_manager.hh"
	#include "non_local_neighborhood.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize("material_remove_damage.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;
	ElementType element_type = _quadrangle_4;
	GhostType ghost_type = _not_ghost;

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	mesh.read("plate.msh");

	/// model creation
	SolidMechanicsModel model(mesh);
	/// creation of material selector
	auto && mat_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	model);
	model.setMaterialSelector(mat_selector);

	/// model initialization changed to use our material
	model.initFull();
	/// dump material index in paraview
	model.addDumpField("material_index");
	model.addDumpField("grad_u");
	model.addDumpField("grad_u non local");
	model.addDumpField("damage");
	model.dump();

	/// apply constant strain field in all elements except element 3 and 15
	Matrix<Real> applied_strain(spatial_dimension, spatial_dimension);
	applied_strain.zero();
	for (UInt i = 0; i < spatial_dimension; ++i)
	applied_strain(i, i) = 2.;

	/// apply different strain in element 3 and 15
	Matrix<Real> modified_strain(spatial_dimension, spatial_dimension);
	modified_strain.zero();
	for (UInt i = 0; i < spatial_dimension; ++i)
	modified_strain(i, i) = 1.;

	/// apply constant grad_u field in all elements
	for (UInt m = 0; m < model.getNbMaterials(); ++m) {
	Material & mat = model.getMaterial(m);
	Array<Real> & grad_u = const_cast<Array<Real> &>(
	mat.getInternal<Real>("eigen_grad_u")(element_type, ghost_type));

	auto grad_u_it = grad_u.begin(spatial_dimension, spatial_dimension);
	auto grad_u_end = grad_u.end(spatial_dimension, spatial_dimension);
	UInt element_counter = 0;
	for (; grad_u_it != grad_u_end; ++grad_u_it, ++element_counter)
	if (element_counter == 12 \|\| element_counter == 13 \|\|
	element_counter == 14 \|\| element_counter == 15)
	(grad_u_it) = -1. modified_strain;
	else
	(grad_u_it) = -1. applied_strain;
	}

	/// compute the non-local strains
	model.assembleInternalForces();
	model.dump();
	/// save the weights in a file
	auto & neighborhood_1 = model.getNonLocalManager().getNeighborhood("mat_1");
	auto & neighborhood_2 = model.getNonLocalManager().getNeighborhood("mat_2");
	neighborhood_1.saveWeights("before_0");
	neighborhood_2.saveWeights("before_1");
	for (UInt n = 0; n < 2; ++n) {
	/// print results to screen for validation
	std::stringstream sstr;
	sstr << "before_" << n << ".0";
	std::ifstream weights;
	weights.open(sstr.str());
	std::string current_line;
	while (getline(weights, current_line))
	std::cout << current_line << std::endl;
	weights.close();
	}

	/// apply damage to not have the elements with lower strain impact the
	/// averaging
	for (UInt m = 0; m < model.getNbMaterials(); ++m) {
	auto & mat =
	dynamic_cast<MaterialDamage<spatial_dimension> &>(model.getMaterial(m));

	auto & damage = const_cast<Array<Real> &>(
	mat.getInternal<Real>("damage")(element_type, ghost_type));

	auto dam_it = damage.begin();
	auto dam_end = damage.end();
	UInt element_counter = 0;
	for (; dam_it != dam_end; ++dam_it, ++element_counter)
	if (element_counter == 12 \|\| element_counter == 13 \|\|
	element_counter == 14 \|\| element_counter == 15)
	*dam_it = 0.9;
	}

	/// compute the non-local strains
	model.assembleInternalForces();
	neighborhood_1.saveWeights("after_0");
	neighborhood_2.saveWeights("after_1");
	for (UInt n = 0; n < 2; ++n) {
	/// print results to screen for validation
	std::stringstream sstr;
	sstr << "after_" << n << ".0";
	std::ifstream weights;
	weights.open(sstr.str());
	std::string current_line;
	while (getline(weights, current_line))
	std::cout << current_line << std::endl;
	weights.close();
	}

	model.dump();

	/// verify the result: non-local averaging over constant field must
	/// yield same constant field
	Real test_result = 0.;
	Matrix<Real> difference(spatial_dimension, spatial_dimension, 0.);
	Matrix<Real> difference_in_damaged_elements(spatial_dimension,
	spatial_dimension, 0.);
	for (UInt m = 0; m < model.getNbMaterials(); ++m) {
	difference_in_damaged_elements.zero();
	auto & mat = model.getMaterial(m);
	auto & grad_u_nl = const_cast<Array<Real> &>(
	mat.getInternal<Real>("grad_u non local")(element_type, ghost_type));

	auto grad_u_nl_it = grad_u_nl.begin(spatial_dimension, spatial_dimension);
	auto grad_u_nl_end = grad_u_nl.end(spatial_dimension, spatial_dimension);
	UInt element_counter = 0;
	for (; grad_u_nl_it != grad_u_nl_end; ++grad_u_nl_it, ++element_counter) {
	if (element_counter == 12 \|\| element_counter == 13 \|\|
	element_counter == 14 \|\| element_counter == 15)
	difference_in_damaged_elements += (*grad_u_nl_it);
	else
	difference = (*grad_u_nl_it) - applied_strain;
	test_result += difference.norm<L_2>();
	}
	difference_in_damaged_elements *= (1 / 4.);
	difference_in_damaged_elements -= (1.41142 * modified_strain);
	test_result += difference_in_damaged_elements.norm<L_2>();
	}

	if (test_result > 10.e-5) {
	std::cout << "the total norm is: " << test_result << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_common/test_non_local_toolbox/test_weight_computation.cc b/test/test_model/test_common/test_non_local_toolbox/test_weight_computation.cc
	index 459512160..252b9ba96 100644
	--- a/test/test_model/test_common/test_non_local_toolbox/test_weight_computation.cc
	+++ b/test/test_model/test_common/test_non_local_toolbox/test_weight_computation.cc
	@@ -1,69 +1,69 @@
	/**
	* @file test_weight_computation.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sat Sep 26 2015
	* @date last modification: Wed Jan 30 2019
	*
	* @brief test for the weight computation with base weight function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "my_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	akantu::initialize("material_weight_computation.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;

	// mesh creation and read
	Mesh mesh(spatial_dimension);
	mesh.read("plate.msh");

	/// model creation
	MyModel model(mesh, spatial_dimension);

	/// save the weights in a file
	const auto & neighborhood =
	model.getNonLocalManager().getNeighborhood("test_region");

	neighborhood.saveWeights("weights");
	/// print results to screen for validation
	std::ifstream weights;
	weights.open("weights.0");
	std::string current_line;
	while (getline(weights, current_line))
	std::cout << current_line << std::endl;

	weights.close();
	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_contact_mechanics_model/test_coupler/test_contact_coupling.cc b/test/test_model/test_contact_mechanics_model/test_coupler/test_contact_coupling.cc
	index 3aab210d9..a49008ae8 100644
	--- a/test/test_model/test_contact_mechanics_model/test_coupler/test_contact_coupling.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_coupler/test_contact_coupling.cc
	@@ -1,77 +1,75 @@
	/**
	* @file test_contact_coupling.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Thu May 16 2019
	*
	* @brief Test for contact mechanics model class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_contact.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	-int main(int argc, char *argv[]) {
	+int main(int argc, char * argv[]) {

	const UInt spatial_dimension = 2;
	initialize("material.dat", argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read("coupling.msh");
	-
	+
	CouplerSolidContact coupler(mesh);

	auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	solid.initFull(_analysis_method = _static);
	contact.initFull(_analysis_method = _implicit_contact);

	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "bot_body");
	solid.applyBC(BC::Dirichlet::IncrementValue(0.001, _y), "bot_body");

	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "top");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "top");
	-
	+
	coupler.initFull(_analysis_method = _implicit_contact);

	coupler.setBaseName("coupling");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("external_force");
	coupler.addDumpField("internal_force");
	coupler.addDumpField("grad_u");
	coupler.addDumpField("stress");
	-
	+
	coupler.solveStep();

	contact.dump();

	-
	return 0;
	}
	-
	diff --git a/test/test_model/test_contact_mechanics_model/test_coupler/test_coupled_stiffness.cc b/test/test_model/test_contact_mechanics_model/test_coupler/test_coupled_stiffness.cc
	index 1338dbeae..a0ef09068 100644
	--- a/test/test_model/test_contact_mechanics_model/test_coupler/test_coupled_stiffness.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_coupler/test_coupled_stiffness.cc
	@@ -1,139 +1,140 @@
	/**
	* @file test_coupled_stiffness.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri May 24 2019
	* @date last modification: Wed Oct 02 2019
	*
	* @brief Test for contact mechanics model class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	-#include "solid_mechanics_model.hh"
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_contact.hh"
	#include "non_linear_solver.hh"
	+#include "solid_mechanics_model.hh"
	#include "sparse_matrix.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	-int main(int argc, char *argv[]) {
	+int main(int argc, char * argv[]) {

	Real max_displacement = 0.01;

	const UInt spatial_dimension = 2;
	initialize("material_stiffness.dat", argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read("flat_on_flat.msh");
	-
	+
	CouplerSolidContact coupler(mesh);

	- auto & solid = coupler.getSolidMechanicsModel();
	+ auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	auto && selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	"physical_names", solid);
	solid.setMaterialSelector(selector);
	-
	- solid.initFull( _analysis_method = _static);
	+
	+ solid.initFull(_analysis_method = _static);
	contact.initFull(_analysis_method = _implicit_contact);

	- auto &&surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	+ auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);
	-
	+
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "bottom");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "bottom");
	-
	+
	solid.applyBC(BC::Dirichlet::IncrementValue(-max_displacement, _y), "top");
	-
	+
	coupler.initFull(_analysis_method = _implicit_contact);

	- auto &solver = coupler.getNonLinearSolver();
	+ auto & solver = coupler.getNonLinearSolver();
	solver.set("max_iterations", 1000);
	solver.set("threshold", 1e-2);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);
	-
	+
	coupler.setBaseName("test-coupled-stiffness");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpFieldVector("contact_force");
	coupler.addDumpFieldVector("external_force");
	coupler.addDumpFieldVector("internal_force");
	coupler.addDumpField("gaps");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("grad_u");
	coupler.addDumpField("stress");

	-
	- auto & before_assembly =
	- const_cast<SparseMatrix &>(coupler.getDOFManager().getNewMatrix("K", _symmetric));
	-
	+ auto & before_assembly = const_cast<SparseMatrix &>(
	+ coupler.getDOFManager().getNewMatrix("K", _symmetric));
	+
	solid.assembleStiffnessMatrix();

	auto & solid_assembly =
	- const_cast<SparseMatrix &>(coupler.getDOFManager().getMatrix("K"));
	+ const_cast<SparseMatrix &>(coupler.getDOFManager().getMatrix("K"));
	solid_assembly.saveMatrix("solid_assembly.mtx");

	auto & displacement = solid.getDisplacement();
	-
	+
	contact.search(displacement);
	contact.assembleStiffnessMatrix();

	auto contact_map = contact.getContactMap();
	auto nb_contacts = contact_map.size();
	-
	+
	auto & contact_assembly =
	- const_cast<SparseMatrix &>(coupler.getDOFManager().getMatrix("K"));
	+ const_cast<SparseMatrix &>(coupler.getDOFManager().getMatrix("K"));
	contact_assembly.saveMatrix("contact_assembly.mtx");

	solid.assembleInternalForces();
	contact.assembleInternalForces();

	coupler.dump();
	-
	+
	Array<Real> & contact_force = contact.getInternalForce();

	for (UInt n : arange(contact_force.size())) {
	std::cerr << contact_force(n, 1) << std::endl;
	}
	-
	+
	if (solid_assembly.size() == contact_assembly.size() and nb_contacts > 0) {
	- std::cerr << "size of stiffness matrix of solid = " << solid_assembly.size() << std::endl;
	- std::cerr << "size of stiffness matrix of coupled = " << contact_assembly.size() << std::endl;
	+ std::cerr << "size of stiffness matrix of solid = "
	+ << solid_assembly.size() << std::endl;
	+ std::cerr << "size of stiffness matrix of coupled = "
	+ << contact_assembly.size() << std::endl;
	std::cerr << "number of contacts = " << nb_contacts << std::endl;

	for (auto & pair : contact_map) {
	- std::cerr << "Node " << pair.first << " in contact with " << pair.second.master <<
	- " of gap " << pair.second.gap << std::endl;
	+ std::cerr << "Node " << pair.first << " in contact with "
	+ << pair.second.master << " of gap " << pair.second.gap
	+ << std::endl;
	}
	return EXIT_FAILURE;
	}
	-
	+
	return EXIT_SUCCESS;
	}
	-
	diff --git a/test/test_model/test_contact_mechanics_model/test_detector/test_detection.cc b/test/test_model/test_contact_mechanics_model/test_detector/test_detection.cc
	index 351ae4aa9..fac8b9379 100644
	--- a/test/test_model/test_contact_mechanics_model/test_detector/test_detection.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_detector/test_detection.cc
	@@ -1,62 +1,56 @@
	/**
	* @file test_detection.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Generic test for detection between different element types
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "test_detection_fixture.hh"
	/* -------------------------------------------------------------------------- */

	-
	TYPED_TEST(TestCMMDFixture, Implicit) {

	this->analysis_method = _static;
	this->detection_type = _implicit_contact;

	this->testImplicit();

	this->checkGap();
	-
	}

	-
	TYPED_TEST(TestCMMDFixture, Explicit) {

	this->analysis_method = _static;
	this->detection_type = _explicit_contact;

	this->testExplicit();

	this->checkGap();
	-
	}
	-
	-
	diff --git a/test/test_model/test_contact_mechanics_model/test_detector/test_detection_fixture.hh b/test/test_model/test_contact_mechanics_model/test_detector/test_detection_fixture.hh
	index 72011760d..e96f1571c 100644
	--- a/test/test_model/test_contact_mechanics_model/test_detector/test_detection_fixture.hh
	+++ b/test/test_model/test_contact_mechanics_model/test_detector/test_detection_fixture.hh
	@@ -1,226 +1,212 @@
	/**
	* @file test_detection_fixture.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Dec 11 2020
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Contact detection test fixture
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_mdoel.hh"
	#include "solid_mechanics_model.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_TEST_DETECTION_FIXTURE_HH__
	#define __AKANTU_TEST_DETECTION_FIXTURE_HH__

	using namespace akantu;

	template <::akantu::AnalysisMethod t>
	using analysis_method_t std::integral_constant<::akantu::AnalysisMethod, t>;

	class StrainIncrement : public BC::Functor {
	public:
	StrainIncrement(const Matrix<Real> & strain, BC::Axis dir)
	: strain_inc(strain), dir(dir) {}

	void operator()(UInt /node/, Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	if (std::abs(coord(dir)) < 1e-8) {
	return;
	}

	flags.set(true);
	primal += strain_inc * coord;
	}

	static const BC::Functor::Type type = BC::Functor::_dirichlet;

	private:
	Matrix<Real> strain_inc;
	BC::Axis dir;
	};

	template <typename param_> class TestCMMDFixture : public ::testing::Test {
	public:
	-
	static constexpr ElementType type_1 = std::tuple_element_t<1, param_>::value;
	static constexpr ElementType type_2 = std::tuple_element_t<2, param_>::value;

	void Setup() override {
	mesh = std::make_unique<Mesh>(this->dim);
	if (Communicator::getStaticCommunicator().whoAmI() == 0) {
	ASSERT_NO_THROW({ mesh->read(this->mesh_name); });
	}
	mesh->distribute();
	}

	void TearDown() override {
	solid.reset(nullptr);
	contact.reset(nullptr);
	mesh.reset(nullptr);
	}

	void createModel() {
	solid = std::make_unique<SolidmechanicsModel>(*mesh);
	solid->initFull(_analysis_method = this->analysis_method);
	-
	+
	contact = std::make_unique<ContactMechanicsModel>(*mesh);
	contact->initFull(_analysis_method = this->detection_type);
	auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(*mesh);
	contact->getContactDetector().setSurfaceSelector(surface_selector);
	}

	void setInitialCondition(const Matrix<Real> & strain) {
	for (auto && data :
	zip(make_view(this->mesh->getNodes(), this->dim),
	make_view(this->solid->getDisplacement(), this->dim))) {
	const auto & pos = std::get<0>(data);
	auto & disp = std::get<1>(data);
	disp = strain * pos;
	}
	}

	void steps(const Matrix<Real> & strain) {
	StrainIncrement functor((1. / 300) * strain, this->dim == 1 ? _x : _y);

	for (auto _ [[gnu::unused]] : arange(nb_steps)) {
	this->solid->applyBC(functor, "loading");
	this->solid->applyBC(functor, "fixed");
	this->solid->solveStep();
	}
	}

	void testImplicit() {
	this->createModel();
	auto & mat_el = this->solid->getMaterial("body");

	SCOPED_TRACE(std::to_string(this->dim) + "D - " + std::to_string(type_1) +
	":" + std::to_string(type_2));
	-
	+
	if (this->dim > 1)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_y), "sides");
	if (this->dim > 2)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_z), "sides");

	Real E = mat_el.get("E");
	Real nu = mat_el.get("nu");

	-
	Matrix<Real> strain;
	if (dim == 1) {
	strain = {{1.}};
	} else if (dim == 2) {
	strain = {{-nu, 0.}, {0., 1. - nu}};
	strain *= (1. + nu);
	} else if (dim == 3) {
	strain = {{-nu, 0., 0.}, {0., 1., 0.}, {0., 0., -nu}};
	}
	-
	+
	this->setInitialCondition((1 - 1e-5) * strain);
	this->steps(1e-2 * strain);

	this->contact->search();
	}

	void testExplicit() {
	this->createModel();
	auto & mat_el = this->solid->getMaterial("body");

	SCOPED_TRACE(std::to_string(this->dim) + "D - " + std::to_string(type_1) +
	":" + std::to_string(type_2));
	-
	+
	if (this->dim > 1)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_y), "sides");
	if (this->dim > 2)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_z), "sides");

	Real E = mat_el.get("E");
	Real nu = mat_el.get("nu");

	-
	Matrix<Real> strain;
	if (dim == 1) {
	strain = {{-1.}};
	} else if (dim == 2) {
	strain = {{-nu, 0.}, {0., 1. - nu}};
	strain *= (1. + nu);
	} else if (dim == 3) {
	strain = {{-nu, 0., 0.}, {0., 1., 0.}, {0., 0., -nu}};
	}
	-
	+
	this->setInitialCondition((1 - 1e-5) * strain);
	this->steps(1e-2 * strain);

	this->contact->search();
	-
	}

	- bool checkGap() {
	+ bool checkGap() {}

	- }
	+ bool checkNormal() {}

	- bool checkNormal() {
	-
	- }
	-
	- bool checkCovariantBasis() {
	-
	- }
	-
	-
	+ bool checkCovariantBasis() {}

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<SolidMechanicsModel> solid;
	std::unique_ptr<ContactMechanicsModel> contact;

	- std::string mesh_name{std::to_string(detection_type) + std::to_string(type_1) +
	- (type_1 == type_2 ? "" : std::to_string(type_2)) +
	- ".msh"};
	-
	+ std::string mesh_name{
	+ std::to_string(detection_type) + std::to_string(type_1) +
	+ (type_1 == type_2 ? "" : std::to_string(type_2)) + ".msh"};
	+
	AnalysisMethod analysis_method;
	DetectionType detection_type;
	};

	/* -------------------------------------------------------------------------- */

	-
	using element_types = gtest_list_t<std::tuple<
	- std::tuple<_element_type_segment_2, _element_type_segement_2>,
	- std::tuple< _element_type_triangle_3, _element_type_triangle_3>,
	- std::tuple<_element_type_triangle_3, _element_type_quadrangle_4>,
	- std::tuple<_element_type_quadrangle_4, _element_type_quadrange_4>,
	- std::tuple<_element_type_tetrahedron_6, _element_type_tetrahedron_6> >>;
	-
	+ std::tuple<_element_type_segment_2, _element_type_segement_2>,
	+ std::tuple<_element_type_triangle_3, _element_type_triangle_3>,
	+ std::tuple<_element_type_triangle_3, _element_type_quadrangle_4>,
	+ std::tuple<_element_type_quadrangle_4, _element_type_quadrange_4>,
	+ std::tuple<_element_type_tetrahedron_6, _element_type_tetrahedron_6>>>;

	TYPED_TEST_SUITE(TestCMMDFixture, detection_types)

	#endif
	diff --git a/test/test_model/test_contact_mechanics_model/test_explicit_dynamic.cc b/test/test_model/test_contact_mechanics_model/test_explicit_dynamic.cc
	index 2bfaef378..b8c6fb759 100644
	--- a/test/test_model/test_contact_mechanics_model/test_explicit_dynamic.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_explicit_dynamic.cc
	@@ -1,168 +1,167 @@
	/**
	* @file test_explicit_dynamic.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri Dec 11 2020
	* @date last modification: Sun Jun 06 2021
	*
	* @brief Test for dynamic explicit contact
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_contact.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	-
	/* -------------------------------------------------------------------------- */
	-template<typename T>
	-std::vector<T> arrange(T start, T stop, T step = 1) {
	- std::vector<T> values;
	- for (T value = start; value <= stop; value += step)
	- values.push_back(value);
	- return values;
	+template <typename T> std::vector<T> arrange(T start, T stop, T step = 1) {
	+ std::vector<T> values;
	+ for (T value = start; value <= stop; value += step)
	+ values.push_back(value);
	+ return values;
	}

	-
	int main(int argc, char * argv[]) {

	- UInt max_steps = 2000;
	+ UInt max_steps = 2000;
	Real max_displacement = 1e-2;
	- Real damping_ratio = 0.99;
	+ Real damping_ratio = 0.99;

	- std::string mesh_file = "flat_on_flat.msh";
	+ std::string mesh_file = "flat_on_flat.msh";
	std::string material_file = "material.dat";

	const UInt spatial_dimension = 2;

	initialize(material_file, argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read(mesh_file);

	CouplerSolidContact coupler(mesh);

	auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	auto && material_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	solid);
	solid.setMaterialSelector(material_selector);

	coupler.initFull(_analysis_method = _explicit_lumped_mass);

	auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);

	- solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "upper");
	+ solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "upper");
	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "lower");

	-
	Real time_step = solid.getStableTimeStep();
	time_step *= 0.05;

	coupler.setTimeStep(time_step);

	- std::cout << "Stable time increment : " << time_step << " sec " << std::endl;
	+ std::cout << "Stable time increment : " << time_step << " sec "
	+ << std::endl;

	coupler.setBaseName("explicit-dynamic");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpFieldVector("contact_force");
	coupler.addDumpFieldVector("external_force");
	coupler.addDumpFieldVector("internal_force");
	coupler.addDumpField("gaps");
	coupler.addDumpField("areas");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("strain");
	coupler.addDumpField("stress");

	auto & velocity = solid.getVelocity();
	auto & gaps = contact.getGaps();

	- auto xi = arrange<Real>(0, 1, 1./max_steps);
	-
	+ auto xi = arrange<Real>(0, 1, 1. / max_steps);
	+
	std::vector<Real> displacements;
	std::transform(xi.begin(), xi.end(), std::back_inserter(displacements),
	- [&](Real & p) -> Real {
	- return 0. + (max_displacement)pow(p, 3)(10-15p+ 6pow(p,2)); });
	-
	+ [&](Real & p) -> Real {
	+ return 0. + (max_displacement)pow(p, 3)
	+ (10 - 15 * p + 6 * pow(p, 2));
	+ });
	+
	for (UInt s : arange(max_steps)) {

	- solid.applyBC(BC::Dirichlet::FixedValue(-displacements[s], _y), "loading");
	- solid.applyBC(BC::Dirichlet::FixedValue(displacements[s], _y), "fixed");
	+ solid.applyBC(BC::Dirichlet::FixedValue(-displacements[s], _y), "loading");
	+ solid.applyBC(BC::Dirichlet::FixedValue(displacements[s], _y), "fixed");

	coupler.solveStep();
	-
	- for(auto && tuple : zip(gaps,
	- make_view(velocity, spatial_dimension))){
	+
	+ for (auto && tuple : zip(gaps, make_view(velocity, spatial_dimension))) {
	auto & gap = std::get<0>(tuple);
	auto & vel = std::get<1>(tuple);
	- if(gap > 0) {
	- vel *= damping_ratio;
	+ if (gap > 0) {
	+ vel *= damping_ratio;
	}
	}

	-
	if (s % 100 == 0) {
	coupler.dump();
	}
	}

	coupler.dump();

	- const ElementType element_type = _quadrangle_4;
	- const Array<Real> & stress_vect = solid.getMaterial("upper").getStress(element_type);
	-
	+ const ElementType element_type = _quadrangle_4;
	+ const Array<Real> & stress_vect =
	+ solid.getMaterial("upper").getStress(element_type);
	+
	auto stress_it = stress_vect.begin(spatial_dimension, spatial_dimension);
	auto stress_end = stress_vect.end(spatial_dimension, spatial_dimension);

	Real stress_tolerance = 1e-2;

	Matrix<Real> presc_stress{{0, 0}, {0, 7e5}};
	-
	+
	for (; stress_it != stress_end; ++stress_it) {
	const auto & stress = *stress_it;

	- Real stress_error = (std::abs(stress(1, 1)) - presc_stress(1, 1))/(presc_stress(1, 1));
	-
	- // if error is more than 1%
	+ Real stress_error =
	+ (std::abs(stress(1, 1)) - presc_stress(1, 1)) / (presc_stress(1, 1));
	+
	+ // if error is more than 1%
	if (std::abs(stress_error) > stress_tolerance) {
	std::cerr << "stress error: " << stress_error << " > " << stress_tolerance
	<< std::endl;
	std::cerr << "stress: " << stress << std::endl
	<< "prescribed stress: " << presc_stress << std::endl;
	return EXIT_FAILURE;
	}
	}
	-
	+
	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_contact_mechanics_model/test_explicit_friction.cc b/test/test_model/test_contact_mechanics_model/test_explicit_friction.cc
	index ca696ce3e..a6fe45a51 100644
	--- a/test/test_model/test_contact_mechanics_model/test_explicit_friction.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_explicit_friction.cc
	@@ -1,176 +1,179 @@
	/**
	* @file test_explicit_friction.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jun 06 2021
	* @date last modification: Sun Jun 06 2021
	*
	* @brief Test contact mechanics with friction
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	#include "coupler_solid_contact.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	-
	/* -------------------------------------------------------------------------- */
	-template<typename T>
	-std::vector<T> arrange(T start, T stop, T step = 1) {
	- std::vector<T> values;
	- for (T value = start; value <= stop; value += step)
	- values.push_back(value);
	- return values;
	+template <typename T> std::vector<T> arrange(T start, T stop, T step = 1) {
	+ std::vector<T> values;
	+ for (T value = start; value <= stop; value += step)
	+ values.push_back(value);
	+ return values;
	}

	-
	int main(int argc, char * argv[]) {

	- UInt max_normal_steps = 2500;
	- UInt max_shear_steps = 7500;
	- Real max_shear_displacement = 1e-1;
	+ UInt max_normal_steps = 2500;
	+ UInt max_shear_steps = 7500;
	+ Real max_shear_displacement = 1e-1;
	Real max_normal_displacement = 2e-2;
	- Real damping_ratio = 0.99;
	+ Real damping_ratio = 0.99;

	- std::string mesh_file = "sliding-block-2D.msh";
	+ std::string mesh_file = "sliding-block-2D.msh";
	std::string material_file = "material-friction.dat";

	const UInt spatial_dimension = 2;

	initialize(material_file, argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read(mesh_file);

	CouplerSolidContact coupler(mesh);

	auto & solid = coupler.getSolidMechanicsModel();
	auto & contact = coupler.getContactMechanicsModel();

	auto && material_selector =
	std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	solid);
	solid.setMaterialSelector(material_selector);

	coupler.initFull(_analysis_method = _explicit_lumped_mass);

	auto && surface_selector = std::make_shared<PhysicalSurfaceSelector>(mesh);
	contact.getContactDetector().setSurfaceSelector(surface_selector);

	solid.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "lower");
	- solid.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "lower");
	-
	+ solid.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "lower");
	+
	Real time_step = solid.getStableTimeStep();
	time_step *= 0.05;

	coupler.setTimeStep(time_step);

	- std::cout << "Stable time increment : " << time_step << " sec " << std::endl;
	+ std::cout << "Stable time increment : " << time_step << " sec "
	+ << std::endl;

	coupler.setBaseName("explicit-friction");
	coupler.addDumpFieldVector("displacement");
	coupler.addDumpFieldVector("normals");
	coupler.addDumpFieldVector("contact_force");
	coupler.addDumpFieldVector("tangential_force");
	coupler.addDumpFieldVector("external_force");
	coupler.addDumpFieldVector("internal_force");
	coupler.addDumpField("gaps");
	coupler.addDumpField("areas");
	coupler.addDumpField("blocked_dofs");
	coupler.addDumpField("strain");
	coupler.addDumpField("stress");
	coupler.addDumpField("contact_state");

	auto & velocity = solid.getVelocity();
	auto & gaps = contact.getGaps();

	- auto xi = arrange<Real>(0, 1, 1./max_shear_steps);
	-
	+ auto xi = arrange<Real>(0, 1, 1. / max_shear_steps);
	+
	std::vector<Real> shear_displacements;
	std::transform(xi.begin(), xi.end(), std::back_inserter(shear_displacements),
	- [&](Real & p) -> Real {
	- return 0. + (max_shear_displacement)pow(p, 3)(10-15p+ 6pow(p,2)); });
	+ [&](Real & p) -> Real {
	+ return 0. + (max_shear_displacement)pow(p, 3)
	+ (10 - 15 * p + 6 * pow(p, 2));
	+ });

	+ auto normal_xi = arrange<Real>(0, 1, 1. / max_normal_steps);

	- auto normal_xi = arrange<Real>(0, 1, 1./max_normal_steps);
	-
	std::vector<Real> normal_displacements;
	- std::transform(normal_xi.begin(), normal_xi.end(), std::back_inserter(normal_displacements),
	- [&](Real & p) -> Real {
	- return 0. + (max_normal_displacement)pow(p, 3)(10-15p+ 6pow(p,2)); });
	+ std::transform(normal_xi.begin(), normal_xi.end(),
	+ std::back_inserter(normal_displacements),
	+ [&](Real & p) -> Real {
	+ return 0. + (max_normal_displacement)pow(p, 3)
	+ (10 - 15 * p + 6 * pow(p, 2));
	+ });

	auto max_steps = max_normal_steps + max_shear_steps;

	- auto & contact_nodes = surface_selector->getSlaveList();
	+ auto & contact_nodes = surface_selector->getSlaveList();
	auto & tangential_traction = contact.getTangentialTractions();

	for (UInt s : arange(max_steps)) {

	- if (s < max_normal_steps){
	- solid.applyBC(BC::Dirichlet::FixedValue(-normal_displacements[s], _y), "loading");
	- }
	- else {
	- solid.applyBC(BC::Dirichlet::FixedValue(shear_displacements[s - max_normal_steps], _x), "loading");
	+ if (s < max_normal_steps) {
	+ solid.applyBC(BC::Dirichlet::FixedValue(-normal_displacements[s], _y),
	+ "loading");
	+ } else {
	+ solid.applyBC(BC::Dirichlet::FixedValue(
	+ shear_displacements[s - max_normal_steps], _x),
	+ "loading");
	}

	coupler.solveStep();
	-
	- for(auto && tuple : zip(gaps,
	- make_view(velocity, spatial_dimension))){
	+
	+ for (auto && tuple : zip(gaps, make_view(velocity, spatial_dimension))) {
	auto & gap = std::get<0>(tuple);
	auto & vel = std::get<1>(tuple);
	- if(gap > 0) {
	- vel *= damping_ratio;
	+ if (gap > 0) {
	+ vel *= damping_ratio;
	}
	}

	-
	if (s % 100 == 0) {
	coupler.dump();
	}

	- auto sum = std::accumulate(tangential_traction.begin(), tangential_traction.end(), 0.0);
	+ auto sum = std::accumulate(tangential_traction.begin(),
	+ tangential_traction.end(), 0.0);
	auto num_tang_traction = std::abs(sum) / contact_nodes.size();

	- Real exp_tang_traction = 0.3*1.4e6;
	+ Real exp_tang_traction = 0.3 * 1.4e6;

	- Real error = std::abs(num_tang_traction - exp_tang_traction) / exp_tang_traction;
	+ Real error =
	+ std::abs(num_tang_traction - exp_tang_traction) / exp_tang_traction;

	- if (error > 1e-3 and num_tang_traction > exp_tang_traction){
	+ if (error > 1e-3 and num_tang_traction > exp_tang_traction) {
	std::cerr << error << "----" << num_tang_traction << std::endl;
	return EXIT_FAILURE;
	}
	-
	}

	coupler.dump();
	-
	+
	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_contact_mechanics_model/test_resolution/test_explicit_resolution.cc b/test/test_model/test_contact_mechanics_model/test_resolution/test_explicit_resolution.cc
	index 23253e289..a92784701 100644
	--- a/test/test_model/test_contact_mechanics_model/test_resolution/test_explicit_resolution.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_resolution/test_explicit_resolution.cc
	@@ -1,54 +1,52 @@
	/**
	* @file test_explicit_resolution.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Thu Jan 17 2019
	*
	* @brief Test for explicit contact resolution
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "contact_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	const UInt spatial_dimension = 2;

	-int main(int argc, char *argv[])
	-{
	+int main(int argc, char * argv[]) {
	initialize("options.dat", argc, argv);

	Mesh mesh(spatial_dimension);
	- //mesh.read("explicit_2d.msh");
	-
	+ // mesh.read("explicit_2d.msh");
	+
	ContactMechanicsModel model(mesh);
	model.initFull(_analysis_method = _static);

	std::cout << model;
	-
	+
	finalize();
	return EXIT_SUCCESS;
	}
	-
	diff --git a/test/test_model/test_contact_mechanics_model/test_resolution/test_resolution.cc b/test/test_model/test_contact_mechanics_model/test_resolution/test_resolution.cc
	index d4ba1d080..f21844783 100644
	--- a/test/test_model/test_contact_mechanics_model/test_resolution/test_resolution.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_resolution/test_resolution.cc
	@@ -1,93 +1,82 @@
	/**
	* @file test_resolution.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed May 08 2019
	* @date last modification: Wed May 08 2019
	*
	* @brief Test the resolution class common function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "resolution.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.hh>
	-#include <type_traits>
	-#include <tuple>
	#include <random>
	+#include <tuple>
	+#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */

	-class TestResolutionFixture : public::testing::Test {
	+class TestResolutionFixture : public ::testing::Test {
	public:
	-
	-
	void SetUp() override {
	mesh = std::make_unique<Mesh>(spatial_dimension);
	model = std::make_unique<Model>(*mesh);
	resolution = std::make_unique<Resolution>(*model, "resolution");
	}

	void TearDown() override {
	resolution.reset(nullptr);
	model.reset(nullptr);
	mesh.reset(nullptr);
	}
	-
	+
	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<ContactMechanicsModel> model;
	std::unique_ptr<Resolution> resolution;
	};

	-
	TYPED_TEST(TestResolutionFixture, TestComputeN) {

	Vector<Real> shapes(nb_nodes_master);
	Vector<Real> projection(spatial_diemnsion - 1);

	-#define GET_SHAPES_NATURAL(type) \
	+#define GET_SHAPES_NATURAL(type) \
	ElementClass<type>::computeShapes(projection, shapes)
	AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPES_NATURAL);
	-#undef GET_SHAPES_NATURAL
	+#undef GET_SHAPES_NATURAL

	Vector<Real> n(conn.size() * spatial_dimension);
	resolution->computeN(n, shapes, normal);
	-
	-
	-}
	-
	-
	-TYPED_TEST(TestResolutionFixture, TestComputeDalpha) {
	-
	}

	+TYPED_TEST(TestResolutionFixture, TestComputeDalpha) {}

	-TYPED_TEST(TestResolutionFixture, TestComputeNalpha) {
	-
	-}
	+TYPED_TEST(TestResolutionFixture, TestComputeNalpha) {}
	diff --git a/test/test_model/test_contact_mechanics_model/test_selector/test_selection.cc b/test/test_model/test_contact_mechanics_model/test_selector/test_selection.cc
	index 63590fb43..e90a50056 100644
	--- a/test/test_model/test_contact_mechanics_model/test_selector/test_selection.cc
	+++ b/test/test_model/test_contact_mechanics_model/test_selector/test_selection.cc
	@@ -1,47 +1,47 @@
	/**
	* @file test_selection.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Thu Feb 21 2013
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Generic test for surface selection
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_selection_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TYPED_TEST(TestSurfaceSelectionFixture, PhysicalSurface) {

	auto & actual_slave_nodes = this->mesh.getElementgroup("slave").getNodes();
	auto nb_slave_nodes = actual_slave_nodes.size();
	this->checkNbSlaveNodes(nb_slave_nodes);

	auto & actual_master_nodes = this->mesh.getElementgroup("master").getNodes();
	auto nb_master_nodes = actual_master_nodes.size();
	this->checkNbMasterNodes(nb_master_nodes);
	}
	diff --git a/test/test_model/test_contact_mechanics_model/test_selector/test_selection_fixture.hh b/test/test_model/test_contact_mechanics_model/test_selector/test_selection_fixture.hh
	index c993e4000..001ef86c1 100644
	--- a/test/test_model/test_contact_mechanics_model/test_selector/test_selection_fixture.hh
	+++ b/test/test_model/test_contact_mechanics_model/test_selector/test_selection_fixture.hh
	@@ -1,86 +1,80 @@
	/**
	* @file test_selection_fixture.hh
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed May 08 2019
	* @date last modification: Fri Dec 11 2020
	*
	* @brief Generic test for selection of nodes across different surfaces
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "surface_selector.hh"
	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	-
	using namespace akantu;

	template <typename dim_>
	class TestSurfaceSelecionFixture : public ::testing::Test {
	public:
	static constexpr size_t spatial_dimension = dim_::value;
	-
	+
	void Setup() override {
	mesh = std::make_unique<Mesh>(spatial_dimension);
	mesh->read("selection_" + std::string(spatial_dimension) + "D.msh");
	selector = make_unique<PhysicalSurfaceSelector>(*mesh);
	}

	void TearDown() {
	mesh.reset(nullptr);
	selector.reset(nullptr);
	}

	-
	bool checkNbSlaveNodes(UInt & act_slave_nodes) {
	auto & slave_list = this->selectior->getSlaveList();
	auto nb_slave_nodes = slave_list.size();
	EXCEP_EQ(nb_slave_nodes, act_slave_nodes)
	}

	-
	bool checkNbmasterNodes(UInt & act_master_nodes) {
	auto & master_list = this->selectior->getMasterList();
	auto nb_master_nodes = master_list.size();
	EXCEP_EQ(nb_master_nodes, act_master_nodes)
	}
	-
	-
	- protected:
	+
	+protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<PhysicalSurfaceSelector> selector
	};

	-
	using dim_types = gtest_list_t<std::tuple<1, 2, 3>>;

	-
	TYPED_TEST_SUITE(TestSurfaceSelectionFixture, dim_types);
	diff --git a/test/test_model/test_phase_field_model/test_multi_material.cc b/test/test_model/test_phase_field_model/test_multi_material.cc
	index 436374dc9..91f30929c 100644
	--- a/test/test_model/test_phase_field_model/test_multi_material.cc
	+++ b/test/test_model/test_phase_field_model/test_multi_material.cc
	@@ -1,131 +1,127 @@
	/**
	* @file test_multi_material.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Wed Feb 24 2021
	* @date last modification: Sun Feb 28 2021
	*
	* @brief test of the class PhaseFieldModel on the 2d square
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	-#include "non_linear_solver.hh"
	#include "coupler_solid_phasefield.hh"
	-#include "solid_mechanics_model.hh"
	-#include "phase_field_model.hh"
	#include "material.hh"
	#include "material_phasefield.hh"
	+#include "non_linear_solver.hh"
	+#include "phase_field_model.hh"
	+#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	-#include <iostream>
	#include <fstream>
	+#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	const UInt spatial_dimension = 2;

	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel &, Real &);
	/* -------------------------------------------------------------------------- */

	-int main(int argc, char *argv[]) {
	-
	+int main(int argc, char * argv[]) {
	+
	initialize("material_multiple.dat", argc, argv);
	-
	+
	Mesh mesh(spatial_dimension);
	mesh.read("test_two_element.msh");

	CouplerSolidPhaseField coupler(mesh);
	auto & model = coupler.getSolidMechanicsModel();
	auto & phase = coupler.getPhaseFieldModel();

	- auto && mat_selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	- "physical_names", model);
	+ auto && mat_selector =
	+ std::make_shared<MeshDataMaterialSelector<std::string>>("physical_names",
	+ model);
	model.setMaterialSelector(mat_selector);

	model.initFull(_analysis_method = _explicit_lumped_mass);

	Real time_step = model.getStableTimeStep();
	time_step *= 0.8;
	model.setTimeStep(time_step);

	auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
	"physical_names", phase);
	phase.setPhaseFieldSelector(selector);

	phase.initFull(_analysis_method = _static);
	-
	+
	model.setBaseName("multi_material");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpField("damage");
	model.addDumpFieldVector("displacement");
	model.addDumpField("blocked_dofs");
	model.dump();
	-
	+
	UInt nbSteps = 1000;
	Real increment = 1e-4;
	-
	+
	for (UInt s = 0; s < nbSteps; ++s) {
	Real axial_strain = increment * s;
	applyDisplacement(model, axial_strain);

	coupler.solve();
	-
	+
	model.dump();
	}

	finalize();
	return EXIT_SUCCESS;
	-
	}

	-
	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel & model, Real & increment) {
	auto & displacement = model.getDisplacement();

	auto & positions = model.getMesh().getNodes();
	auto & blocked_dofs = model.getBlockedDOFs();

	-
	for (UInt n = 0; n < model.getMesh().getNbNodes(); ++n) {
	if (positions(n, 1) == -1) {
	displacement(n, 1) = 0;
	blocked_dofs(n, 1) = true;
	displacement(n, 0) = 0;
	- blocked_dofs(n ,0) = true;
	- }
	- else if (positions(n, 1) == 1) {
	+ blocked_dofs(n, 0) = true;
	+ } else if (positions(n, 1) == 1) {
	displacement(n, 0) = 0;
	displacement(n, 1) = increment;
	blocked_dofs(n, 0) = true;
	- blocked_dofs(n ,1) = true;
	- }
	- else {
	- displacement(n, 0) = 0;
	- blocked_dofs(n, 0) = true;
	+ blocked_dofs(n, 1) = true;
	+ } else {
	+ displacement(n, 0) = 0;
	+ blocked_dofs(n, 0) = true;
	}
	}
	}
	diff --git a/test/test_model/test_phase_field_model/test_phase_solid_coupling.cc b/test/test_model/test_phase_field_model/test_phase_solid_coupling.cc
	index dfabfa83e..df65ca0a4 100644
	--- a/test/test_model/test_phase_field_model/test_phase_solid_coupling.cc
	+++ b/test/test_model/test_phase_field_model/test_phase_solid_coupling.cc
	@@ -1,278 +1,272 @@
	/**
	* @file test_phase_solid_coupling.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Jan 06 2019
	* @date last modification: Wed Mar 03 2021
	*
	* @brief test of the class PhaseFieldModel on the 2d square
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	-#include "non_linear_solver.hh"
	-#include "solid_mechanics_model.hh"
	-#include "phase_field_model.hh"
	#include "material.hh"
	#include "material_phasefield.hh"
	+#include "non_linear_solver.hh"
	+#include "phase_field_model.hh"
	+#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	-#include <iostream>
	#include <fstream>
	+#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	const UInt spatial_dimension = 2;

	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel &, Real &);
	-void computeStrainOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &, const GhostType &);
	-void computeDamageOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &, const GhostType &);
	+void computeStrainOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &,
	+ const GhostType &);
	+void computeDamageOnQuadPoints(SolidMechanicsModel &, PhaseFieldModel &,
	+ const GhostType &);
	void gradUToEpsilon(const Matrix<Real> &, Matrix<Real> &);
	/* -------------------------------------------------------------------------- */

	-int main(int argc, char *argv[]) {
	+int main(int argc, char * argv[]) {

	std::ofstream os("data.csv");
	os << "#strain stress damage analytical_sigma analytical_damage" << std::endl;
	-
	+
	initialize("material_coupling.dat", argc, argv);
	-
	+
	Mesh mesh(spatial_dimension);
	mesh.read("test_one_element.msh");

	SolidMechanicsModel model(mesh);
	model.initFull(_analysis_method = _static);

	PhaseFieldModel phase(mesh);
	auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
	- "physical_names", phase);
	+ "physical_names", phase);
	phase.setPhaseFieldSelector(selector);
	phase.initFull(_analysis_method = _static);

	-
	model.setBaseName("phase_solid");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpFieldVector("displacement");
	model.addDumpField("damage");
	model.dump();
	-
	+
	UInt nbSteps = 1000;
	Real increment = 1e-4;

	auto & stress = model.getMaterial(0).getArray<Real>("stress", _quadrangle_4);
	auto & damage = model.getMaterial(0).getArray<Real>("damage", _quadrangle_4);

	Real analytical_damage{0.};
	Real analytical_sigma{0.};

	auto & phasefield = phase.getPhaseField(0);
	-
	- const Real E = phasefield.getParam("E");
	- const Real nu = phasefield.getParam("nu");
	- Real c22 = E(1-nu)/((1+nu)(1-2*nu));
	+
	+ const Real E = phasefield.getParam("E");
	+ const Real nu = phasefield.getParam("nu");
	+ Real c22 = E * (1 - nu) / ((1 + nu) * (1 - 2 * nu));

	const Real gc = phasefield.getParam("gc");
	const Real l0 = phasefield.getParam("l0");
	-
	+
	Real error_stress{0.};

	Real error_damage{0.};
	-
	+
	for (UInt s = 0; s < nbSteps; ++s) {
	Real axial_strain = increment * s;
	applyDisplacement(model, axial_strain);

	model.solveStep();
	computeStrainOnQuadPoints(model, phase, _not_ghost);

	phase.solveStep();
	computeDamageOnQuadPoints(model, phase, _not_ghost);

	model.assembleInternalForces();

	- analytical_damage = axial_strainaxial_strainc22/(gc/l0 + axial_strainaxial_strainc22);
	- analytical_sigma = c22axial_strain(1-analytical_damage)*(1-analytical_damage);
	+ analytical_damage = axial_strain * axial_strain * c22 /
	+ (gc / l0 + axial_strain * axial_strain * c22);
	+ analytical_sigma =
	+ c22 * axial_strain * (1 - analytical_damage) * (1 - analytical_damage);

	- error_stress = std::abs(analytical_sigma - stress(0, 3))/analytical_sigma;
	+ error_stress = std::abs(analytical_sigma - stress(0, 3)) / analytical_sigma;

	- error_damage = std::abs(analytical_damage - damage(0))/analytical_damage;
	+ error_damage = std::abs(analytical_damage - damage(0)) / analytical_damage;

	if (error_damage > 1e-8 and error_stress > 1e-8) {
	return EXIT_FAILURE;
	}

	-
	os << axial_strain << " " << stress(0, 3) << " " << damage(0) << " "
	- << analytical_sigma << " " << analytical_damage << " " <<
	- error_stress << " " << error_damage << std::endl;
	+ << analytical_sigma << " " << analytical_damage << " " << error_stress
	+ << " " << error_damage << std::endl;

	model.dump();
	}

	os.close();
	finalize();

	-
	-
	return EXIT_SUCCESS;
	-
	}

	-
	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel & model, Real & increment) {
	auto & displacement = model.getDisplacement();

	auto & positions = model.getMesh().getNodes();
	auto & blocked_dofs = model.getBlockedDOFs();

	-
	for (UInt n = 0; n < model.getMesh().getNbNodes(); ++n) {
	if (positions(n, 1) == -0.5) {
	displacement(n, 0) = 0;
	displacement(n, 1) = 0;
	blocked_dofs(n, 0) = true;
	- blocked_dofs(n ,1) = true;
	- }
	- else {
	+ blocked_dofs(n, 1) = true;
	+ } else {
	displacement(n, 0) = 0;
	displacement(n, 1) = increment;
	blocked_dofs(n, 0) = true;
	- blocked_dofs(n ,1) = true;
	+ blocked_dofs(n, 1) = true;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	-void computeStrainOnQuadPoints(SolidMechanicsModel & solid, PhaseFieldModel & phase,
	- const GhostType & ghost_type) {
	+void computeStrainOnQuadPoints(SolidMechanicsModel & solid,
	+ PhaseFieldModel & phase,
	+ const GhostType & ghost_type) {

	auto & mesh = solid.getMesh();

	- auto nb_materials = solid.getNbMaterials();
	+ auto nb_materials = solid.getNbMaterials();
	auto nb_phasefields = phase.getNbPhaseFields();
	-
	- AKANTU_DEBUG_ASSERT(nb_phasefields == nb_materials,
	- "The number of phasefields and materials should be equal" );

	+ AKANTU_DEBUG_ASSERT(
	+ nb_phasefields == nb_materials,
	+ "The number of phasefields and materials should be equal");

	- for(auto index : arange(nb_materials)) {
	+ for (auto index : arange(nb_materials)) {
	auto & material = solid.getMaterial(index);
	-
	- for(auto index2 : arange(nb_phasefields)) {
	+
	+ for (auto index2 : arange(nb_phasefields)) {
	auto & phasefield = phase.getPhaseField(index2);
	-
	- if(phasefield.getName() == material.getName()){
	-
	- auto & strain_on_qpoints = phasefield.getStrain();
	- auto & gradu_on_qpoints = material.getGradU();
	-
	- for (auto & type: mesh.elementTypes(spatial_dimension, ghost_type)) {
	- auto & strain_on_qpoints_vect = strain_on_qpoints(type, ghost_type);
	- auto & gradu_on_qpoints_vect = gradu_on_qpoints(type, ghost_type);
	- for (auto && values:
	- zip(make_view(strain_on_qpoints_vect, spatial_dimension, spatial_dimension),
	- make_view(gradu_on_qpoints_vect, spatial_dimension, spatial_dimension))) {
	- auto & strain = std::get<0>(values);
	- auto & grad_u = std::get<1>(values);
	- gradUToEpsilon(grad_u, strain);
	- }
	- }
	-
	- break;
	+
	+ if (phasefield.getName() == material.getName()) {
	+
	+ auto & strain_on_qpoints = phasefield.getStrain();
	+ auto & gradu_on_qpoints = material.getGradU();
	+
	+ for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	+ auto & strain_on_qpoints_vect = strain_on_qpoints(type, ghost_type);
	+ auto & gradu_on_qpoints_vect = gradu_on_qpoints(type, ghost_type);
	+ for (auto && values :
	+ zip(make_view(strain_on_qpoints_vect, spatial_dimension,
	+ spatial_dimension),
	+ make_view(gradu_on_qpoints_vect, spatial_dimension,
	+ spatial_dimension))) {
	+ auto & strain = std::get<0>(values);
	+ auto & grad_u = std::get<1>(values);
	+ gradUToEpsilon(grad_u, strain);
	+ }
	+ }
	+
	+ break;
	}
	-
	}
	}
	}

	-
	/* -------------------------------------------------------------------------- */
	-void computeDamageOnQuadPoints(SolidMechanicsModel & solid, PhaseFieldModel & phase,
	- const GhostType & ghost_type) {
	-
	- auto & fem = phase.getFEEngine();
	+void computeDamageOnQuadPoints(SolidMechanicsModel & solid,
	+ PhaseFieldModel & phase,
	+ const GhostType & ghost_type) {
	+
	+ auto & fem = phase.getFEEngine();
	auto & mesh = phase.getMesh();

	- auto nb_materials = solid.getNbMaterials();
	+ auto nb_materials = solid.getNbMaterials();
	auto nb_phasefields = phase.getNbPhaseFields();
	-
	- AKANTU_DEBUG_ASSERT(nb_phasefields == nb_materials,
	- "The number of phasefields and materials should be equal" );

	+ AKANTU_DEBUG_ASSERT(
	+ nb_phasefields == nb_materials,
	+ "The number of phasefields and materials should be equal");

	- for(auto index : arange(nb_materials)) {
	+ for (auto index : arange(nb_materials)) {
	auto & material = solid.getMaterial(index);
	-
	- for(auto index2 : arange(nb_phasefields)) {
	+
	+ for (auto index2 : arange(nb_phasefields)) {
	auto & phasefield = phase.getPhaseField(index2);
	-
	- if(phasefield.getName() == material.getName()){
	-
	-
	- switch (spatial_dimension) {
	- case 1: {
	- auto & mat = static_cast<MaterialPhaseField<1> &>(material);
	- auto & solid_damage = mat.getDamage();
	-
	- for (auto & type: mesh.elementTypes(spatial_dimension, ghost_type)) {
	- auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
	-
	- fem.interpolateOnIntegrationPoints(phase.getDamage(), damage_on_qpoints_vect,
	- 1, type, ghost_type);
	- }
	-
	- break;
	- }
	- case 2: {
	- auto & mat = static_cast<MaterialPhaseField<2> &>(material);
	- auto & solid_damage = mat.getDamage();
	-
	- for (auto & type: mesh.elementTypes(spatial_dimension, ghost_type)) {
	- auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
	-
	- fem.interpolateOnIntegrationPoints(phase.getDamage(), damage_on_qpoints_vect,
	- 1, type, ghost_type);
	- }
	- break;
	- }
	- default:
	- break;
	- }

	+ if (phasefield.getName() == material.getName()) {
	+
	+ switch (spatial_dimension) {
	+ case 1: {
	+ auto & mat = static_cast<MaterialPhaseField<1> &>(material);
	+ auto & solid_damage = mat.getDamage();
	+
	+ for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	+ auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
	+
	+ fem.interpolateOnIntegrationPoints(
	+ phase.getDamage(), damage_on_qpoints_vect, 1, type, ghost_type);
	+ }
	+
	+ break;
	+ }
	+ case 2: {
	+ auto & mat = static_cast<MaterialPhaseField<2> &>(material);
	+ auto & solid_damage = mat.getDamage();
	+
	+ for (auto & type : mesh.elementTypes(spatial_dimension, ghost_type)) {
	+ auto & damage_on_qpoints_vect = solid_damage(type, ghost_type);
	+
	+ fem.interpolateOnIntegrationPoints(
	+ phase.getDamage(), damage_on_qpoints_vect, 1, type, ghost_type);
	+ }
	+ break;
	+ }
	+ default:
	+ break;
	+ }
	}
	}
	}
	-
	}

	-
	/* -------------------------------------------------------------------------- */
	void gradUToEpsilon(const Matrix<Real> & grad_u, Matrix<Real> & epsilon) {
	- for (UInt i=0; i < spatial_dimension; ++i) {
	+ for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j)
	- epsilon(i, j) = 0.5 * (grad_u(i, j) + grad_u(j, i));
	+ epsilon(i, j) = 0.5 * (grad_u(i, j) + grad_u(j, i));
	}
	}
	diff --git a/test/test_model/test_phase_field_model/test_phase_solid_explicit.cc b/test/test_model/test_phase_field_model/test_phase_solid_explicit.cc
	index f5d270816..ac98e50d6 100644
	--- a/test/test_model/test_phase_field_model/test_phase_solid_explicit.cc
	+++ b/test/test_model/test_phase_field_model/test_phase_solid_explicit.cc
	@@ -1,154 +1,154 @@
	/**
	* @file test_phase_solid_explicit.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Sun Feb 28 2021
	* @date last modification: Fri Jun 25 2021
	*
	* @brief test of the class PhaseFieldModel on the 2d square
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "coupler_solid_phasefield.hh"
	#include "non_linear_solver.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	const UInt spatial_dimension = 2;

	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel &, Real &);
	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {

	std::ofstream os("data-explicit.csv");
	os << "#strain stress damage analytical_sigma analytical_damage error_stress "
	"error_damage"
	<< std::endl;

	initialize("material_coupling.dat", argc, argv);

	Mesh mesh(spatial_dimension);
	mesh.read("test_one_element.msh");

	CouplerSolidPhaseField coupler(mesh);
	auto & model = coupler.getSolidMechanicsModel();
	auto & phase = coupler.getPhaseFieldModel();

	model.initFull(_analysis_method = _explicit_lumped_mass);

	Real time_factor = 0.8;
	Real stable_time_step = model.getStableTimeStep() * time_factor;
	model.setTimeStep(stable_time_step);

	auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
	"physical_names", phase);
	phase.setPhaseFieldSelector(selector);
	phase.initFull(_analysis_method = _static);

	model.setBaseName("phase_solid");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpFieldVector("displacement");
	model.addDumpField("damage");
	model.dump();

	UInt nbSteps = 1000;
	Real increment = 1e-4;

	auto & stress = model.getMaterial(0).getArray<Real>("stress", _quadrangle_4);
	auto & damage = model.getMaterial(0).getArray<Real>("damage", _quadrangle_4);

	Real analytical_damage{0.};
	Real analytical_sigma{0.};

	auto & phasefield = phase.getPhaseField(0);

	const Real E = phasefield.getParam("E");
	const Real nu = phasefield.getParam("nu");
	Real c22 = E * (1 - nu) / ((1 + nu) * (1 - 2 * nu));

	const Real gc = phasefield.getParam("gc");
	const Real l0 = phasefield.getParam("l0");

	Real error_stress{0.};
	Real error_damage{0.};

	for (UInt s = 0; s < nbSteps; ++s) {
	Real axial_strain = increment * s;
	applyDisplacement(model, axial_strain);

	coupler.solve("explicit_lumped", "static");

	analytical_damage = axial_strain * axial_strain * c22 /
	(gc / l0 + axial_strain * axial_strain * c22);
	analytical_sigma =
	c22 * axial_strain * (1 - analytical_damage) * (1 - analytical_damage);

	error_stress = std::abs(analytical_sigma - stress(0, 3)) / analytical_sigma;

	error_damage = std::abs(analytical_damage - damage(0)) / analytical_damage;

	if (error_damage > 1e-8 and error_stress > 1e-8) {
	return EXIT_FAILURE;
	}

	os << axial_strain << " " << stress(0, 3) << " " << damage(0) << " "
	<< analytical_sigma << " " << analytical_damage << " " << error_stress
	<< " " << error_damage << std::endl;

	model.dump();
	}

	os.close();
	finalize();

	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	void applyDisplacement(SolidMechanicsModel & model, Real & increment) {
	auto & displacement = model.getDisplacement();

	auto & positions = model.getMesh().getNodes();
	auto & blocked_dofs = model.getBlockedDOFs();

	for (UInt n = 0; n < model.getMesh().getNbNodes(); ++n) {
	if (positions(n, 1) == -0.5) {
	displacement(n, 0) = 0;
	displacement(n, 1) = 0;
	blocked_dofs(n, 0) = true;
	blocked_dofs(n, 1) = true;
	} else {
	displacement(n, 0) = 0;
	displacement(n, 1) = increment;
	blocked_dofs(n, 0) = true;
	blocked_dofs(n, 1) = true;
	}
	}
	}
	diff --git a/test/test_model/test_phase_field_model/test_phasefield_selector.cc b/test/test_model/test_phase_field_model/test_phasefield_selector.cc
	index 7f62938e2..c38bf58ee 100644
	--- a/test/test_model/test_phase_field_model/test_phasefield_selector.cc
	+++ b/test/test_model/test_phase_field_model/test_phasefield_selector.cc
	@@ -1,70 +1,68 @@
	/**
	* @file test_phasefield_selector.cc
	*
	* @author Mohit Pundir <mohit.pundir@epfl.ch>
	*
	* @date creation: Fri May 01 2015
	* @date last modification: Wed Apr 28 2021
	*
	* @brief Test for phasefield selector
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "aka_common.hh"
	#include "phase_field_model.hh"
	#include "phasefield_exponential.hh"

	using namespace akantu;

	-int main(int argc, char *argv[]){
	+int main(int argc, char * argv[]) {

	initialize("phasefield_selector.dat", argc, argv);

	Math::setTolerance(1e-8);

	Mesh mesh(1);
	mesh.read("phasefield_selector.msh");

	PhaseFieldModel model(mesh);
	auto && selector = std::make_shared<MeshDataPhaseFieldSelector<std::string>>(
	- "physical_names", model);
	+ "physical_names", model);
	model.setPhaseFieldSelector(selector);

	model.initFull();

	PhaseField & chocolate = model.getPhaseField("chocolate");
	PhaseField & chewing_gum = model.getPhaseField("chewing-gum");
	PhaseField & candy = model.getPhaseField("candy");
	-

	UInt chocolate_element = chocolate.getElementFilter(_segment_2)(0, 0);
	UInt chewing_gum_element = chewing_gum.getElementFilter(_segment_2)(0, 0);
	UInt candy_element = candy.getElementFilter(_segment_2)(0, 0);
	-
	- if (chocolate_element != 0 \|\| chewing_gum_element != 1 \|\| candy_element != 2 ) {
	+
	+ if (chocolate_element != 0 \|\| chewing_gum_element != 1 \|\|
	+ candy_element != 2) {
	return EXIT_FAILURE;
	}
	-
	+
	return EXIT_SUCCESS;
	}
	-
	-
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive.cc
	index c0f246d38..b45935dfd 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive.cc
	@@ -1,135 +1,135 @@
	/**
	* @file test_cohesive.cc
	*
	* @author Tobias Brink <tobias.brink@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jan 10 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Generic test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "test_cohesive_fixture.hh"
	/* -------------------------------------------------------------------------- */

	TYPED_TEST(TestSMMCFixture, ExtrinsicModeI) {
	if (this->mesh->getCommunicator().getNbProc() > 1 and this->dim == 1) {
	SUCCEED();
	return;
	}
	getStaticParser().parse("material_0.dat");
	this->is_extrinsic = true;
	this->analysis_method = _explicit_lumped_mass;

	this->testModeI();
	this->checkInsertion();

	auto & mat_co = this->model->getMaterial("insertion");
	Real G_c = mat_co.get("G_c");

	// if (this->dim != 3)
	this->checkDissipated(G_c);
	}

	TYPED_TEST(TestSMMCFixture, ExtrinsicModeIFiniteDef) {
	if (this->dim == 1) {
	SUCCEED();
	return;
	}
	getStaticParser().parse("material_0_finite_def.dat");
	this->is_extrinsic = true;
	this->analysis_method = _explicit_lumped_mass;

	this->testModeI();
	this->checkInsertion();

	auto & mat_co = this->model->getMaterial("insertion");
	Real G_c = mat_co.get("G_c");

	// if (this->dim != 3)
	this->checkDissipated(G_c);
	}

	TYPED_TEST(TestSMMCFixture, ExtrinsicModeII) {
	if (this->mesh->getCommunicator().getNbProc() > 1 and this->dim == 1) {
	SUCCEED();
	return;
	}
	getStaticParser().parse("material_0.dat");
	this->is_extrinsic = true;
	this->analysis_method = _explicit_lumped_mass;

	this->testModeII();
	this->checkInsertion();

	auto & mat_co = this->model->getMaterial("insertion");
	Real G_c = mat_co.get("G_c");

	// if (this->dim != 3)
	this->checkDissipated(G_c);
	}

	TYPED_TEST(TestSMMCFixture, IntrinsicModeI) {
	if (this->mesh->getCommunicator().getNbProc() > 1 and this->dim == 1) {
	SUCCEED();
	return;
	}
	getStaticParser().parse("material_1.dat");
	this->is_extrinsic = false;
	this->analysis_method = _explicit_lumped_mass;

	this->testModeI();

	this->checkInsertion();

	auto & mat_co = this->model->getMaterial("insertion");
	Real G_c = mat_co.get("G_c");

	// if (this->dim != 3)
	this->checkDissipated(G_c);
	}

	TYPED_TEST(TestSMMCFixture, IntrinsicModeII) {
	if (this->mesh->getCommunicator().getNbProc() > 1 and this->dim == 1) {
	SUCCEED();
	return;
	}

	getStaticParser().parse("material_1.dat");
	this->is_extrinsic = false;
	this->analysis_method = _explicit_lumped_mass;

	this->testModeII();

	this->checkInsertion();

	auto & mat_co = this->model->getMaterial("insertion");
	Real G_c = mat_co.get("G_c");

	// if (this->dim != 3)
	this->checkDissipated(G_c);
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_1d_element/test_cohesive_1d_element.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_1d_element/test_cohesive_1d_element.cc
	index 5c226fab3..520e543c6 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_1d_element/test_cohesive_1d_element.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_1d_element/test_cohesive_1d_element.cc
	@@ -1,104 +1,104 @@
	/**
	* @file test_cohesive_1d_element.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jan 10 2018
	*
	* @brief Test for 1D cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt max_steps = 2000;
	const Real strain_rate = 5;

	UInt spatial_dimension = 1;
	Mesh mesh(spatial_dimension, "mesh");
	mesh.read("bar.msh");

	Math::setTolerance(1e-7);
	SolidMechanicsModelCohesive model(mesh);
	model.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = true);

	auto time_step = model.getStableTimeStep() * 0.01;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	auto posx_max = mesh.getUpperBounds()(_x);
	auto posx_min = mesh.getLowerBounds()(_x);

	/// initial conditions
	const auto & position = mesh.getNodes();
	auto & velocity = model.getVelocity();
	auto nb_nodes = mesh.getNbNodes();

	for (UInt n = 0; n < nb_nodes; ++n)
	velocity(n) = strain_rate * (position(n) - (posx_max + posx_min) / 2.);

	/// boundary conditions
	model.applyBC(BC::Dirichlet::FlagOnly(_x), "left");
	model.applyBC(BC::Dirichlet::FlagOnly(_x), "right");
	auto disp_increment = strain_rate * (posx_max - posx_min) / 2. * time_step;

	model.assembleInternalForces();

	for (UInt s = 1; s <= max_steps; ++s) {
	model.checkCohesiveStress();
	model.solveStep();

	auto nb_cohesive_elements = mesh.getNbElement(_cohesive_1d_2);

	if (s % 10 == 0) {
	std::cout << "passing step " << s << "/" << max_steps
	<< ", number of cohesive elemets:" << nb_cohesive_elements
	<< std::endl;
	}

	/// update external work and boundary conditions
	model.applyBC(BC::Dirichlet::IncrementValue(-disp_increment, _x), "left");
	model.applyBC(BC::Dirichlet::IncrementValue(disp_increment, _x), "right");
	}

	auto Ed = model.getEnergy("dissipated");
	auto Edt = 100. * 3.;

	std::cout << Ed << " " << Edt << std::endl;
	if (std::abs(Ed - Edt) > 0.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_buildfragments/test_cohesive_buildfragments.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_buildfragments/test_cohesive_buildfragments.cc
	index 6672010ab..7c81a31e9 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_buildfragments/test_cohesive_buildfragments.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_buildfragments/test_cohesive_buildfragments.cc
	@@ -1,183 +1,183 @@
	/**
	* @file test_cohesive_buildfragments.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu May 09 2019
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fragment_manager.hh"
	#include "material_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	Math::setTolerance(1e-14);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 200;
	Real strain_rate = 1.e5;
	ElementType type = _quadrangle_4;

	Real L = 0.03;
	Real theoretical_mass = L * L / 20. * 2500;

	ElementType type_facet = Mesh::getFacetType(type);
	ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);

	Mesh mesh(spatial_dimension);
	mesh.read("mesh.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(_analysis_method = _explicit_lumped_mass,
	_is_extrinsic = true);

	Real time_step = model.getStableTimeStep() * 0.05;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	Real disp_increment = strain_rate * L / 2. * time_step;
	model.assembleMassLumped();

	Array<Real> & velocity = model.getVelocity();
	const Array<Real> & position = mesh.getNodes();
	UInt nb_nodes = mesh.getNbNodes();

	/// initial conditions
	for (UInt n = 0; n < nb_nodes; ++n)
	velocity(n, 0) = strain_rate * position(n, 0);

	/// boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0, _x), "Left_side");
	model.applyBC(BC::Dirichlet::FixedValue(0, _x), "Right_side");

	UInt cohesive_index = 1;

	UInt nb_quad_per_facet =
	model.getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);
	MaterialCohesive & mat_cohesive =
	dynamic_cast<MaterialCohesive &>(model.getMaterial(cohesive_index));
	const Array<Real> & damage = mat_cohesive.getDamage(type_cohesive);

	FragmentManager fragment_manager(model, false);
	const Array<Real> & fragment_mass = fragment_manager.getMass();

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {
	model.checkCohesiveStress();
	model.solveStep();

	/// apply boundary conditions
	model.applyBC(BC::Dirichlet::IncrementValue(-disp_increment, _x),
	"Left_side");
	model.applyBC(BC::Dirichlet::IncrementValue(disp_increment, _x),
	"Right_side");

	if (s % 1 == 0) {
	// model.dump();
	std::cout << "passing step " << s << "/" << max_steps << std::endl;

	fragment_manager.computeAllData();

	/// check number of fragments
	UInt nb_fragment_num = fragment_manager.getNbFragment();

	UInt nb_cohesive_elements = mesh.getNbElement(type_cohesive);

	UInt nb_fragment = 1;
	for (UInt el = 0; el < nb_cohesive_elements; ++el) {
	UInt q = 0;
	while (q < nb_quad_per_facet &&
	Math::are_float_equal(damage(el * nb_quad_per_facet + q), 1))
	++q;

	if (q == nb_quad_per_facet) {
	++nb_fragment;
	}
	}

	if (nb_fragment != nb_fragment_num) {
	std::cout << "The number of fragments is wrong!" << std::endl;
	return EXIT_FAILURE;
	}

	/// check mass computation
	Real total_mass = 0.;
	for (UInt frag = 0; frag < nb_fragment_num; ++frag) {
	total_mass += fragment_mass(frag);
	}

	if (!Math::are_float_equal(theoretical_mass, total_mass)) {
	std::cout << "The fragments' mass is wrong!" << std::endl;
	return EXIT_FAILURE;
	}
	}
	}

	model.dump();

	/// check velocities
	UInt nb_fragment = fragment_manager.getNbFragment();
	const Array<Real> & fragment_velocity = fragment_manager.getVelocity();
	const Array<Real> & fragment_center = fragment_manager.getCenterOfMass();

	Real fragment_length = L / nb_fragment;
	Real initial_position = -L / 2. + fragment_length / 2.;

	for (UInt frag = 0; frag < nb_fragment; ++frag) {
	Real theoretical_center = initial_position + fragment_length * frag;

	if (!Math::are_float_equal(fragment_center(frag, 0), theoretical_center)) {
	std::cout << "The fragments' center is wrong!" << std::endl;
	return EXIT_FAILURE;
	}

	Real initial_vel = fragment_center(frag, 0) * strain_rate;

	Math::setTolerance(100);

	if (!Math::are_float_equal(fragment_velocity(frag), initial_vel)) {
	std::cout << "The fragments' velocity is wrong!" << std::endl;
	return EXIT_FAILURE;
	}
	}

	finalize();

	std::cout << "OK: test_cohesive_buildfragments was passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic.cc
	index ee94efbb1..bf4e24cdf 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic.cc
	@@ -1,136 +1,136 @@
	/**
	* @file test_cohesive_extrinsic.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Dec 14 2017
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);
	debug::setDebugLevel(dblWarning);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 1000;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	model.getElementInserter().setLimit(_y, -0.30, -0.20);
	model.updateAutomaticInsertion();

	mesh.setBaseName("test_cohesive_extrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("mass");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.addDumpField("grad_u");
	model.dump();

	Real time_step = model.getStableTimeStep() * 0.05;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	boundary(n, 1) = true;

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99)
	boundary(n, 0) = true;
	}

	/// initial conditions
	Real loading_rate = 0.5;
	Real disp_update = loading_rate * time_step;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 1) = loading_rate * position(n, 1);
	}

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	/// update displacement on extreme nodes
	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	displacement(n, 1) += disp_update * position(n, 1);
	}

	model.checkCohesiveStress();
	model.solveStep();

	if (s % 100 == 0) {
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	model.dump();
	}

	Real Ed = model.getEnergy("dissipated");
	Real Edt = 200 * std::sqrt(2);

	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	finalize();

	std::cout << "OK: test_cohesive_extrinsic was passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_fatigue.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_fatigue.cc
	index 2722d739f..760f84709 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_fatigue.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_fatigue.cc
	@@ -1,244 +1,244 @@
	/**
	* @file test_cohesive_extrinsic_fatigue.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Feb 20 2015
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test for the linear fatigue cohesive law
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear_fatigue.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include <limits>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	// the following class contains an implementation of the 1D linear
	// fatigue cohesive law
	class MaterialFatigue {
	public:
	MaterialFatigue(Real delta_f, Real sigma_c, Real delta_c)
	: delta_f(delta_f), sigma_c(sigma_c), delta_c(delta_c), delta_prec(0),
	traction(sigma_c), delta_max(0),
	stiff_plus(std::numeric_limits<Real>::max()),
	tolerance(Math::getTolerance()){};

	Real computeTraction(Real delta) {
	if (delta - delta_c > -tolerance)
	traction = 0;
	else if (delta_max < tolerance && delta < tolerance)
	traction = sigma_c;
	else {
	Real delta_dot = delta - delta_prec;

	if (delta_dot > -tolerance) {
	stiff_plus *= 1 - delta_dot / delta_f;
	traction += stiff_plus * delta_dot;
	Real max_traction = sigma_c * (1 - delta / delta_c);

	if (traction - max_traction > -tolerance \|\| delta_max < tolerance) {
	traction = max_traction;
	stiff_plus = traction / delta;
	}
	} else {
	Real stiff_minus = traction / delta_prec;
	stiff_plus += (stiff_plus - stiff_minus) * delta_dot / delta_f;
	traction += stiff_minus * delta_dot;
	}
	}

	delta_prec = delta;
	delta_max = std::max(delta, delta_max);
	return traction;
	}

	private:
	const Real delta_f;
	const Real sigma_c;
	const Real delta_c;
	Real delta_prec;
	Real traction;
	Real delta_max;
	Real stiff_plus;
	const Real tolerance;
	};

	void imposeOpening(SolidMechanicsModelCohesive &, Real);
	void arange(Array<Real> &, Real, Real, Real);

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material_fatigue.dat", argc, argv);

	Math::setTolerance(1e-13);

	const UInt spatial_dimension = 2;
	const ElementType type = _quadrangle_4;

	Mesh mesh(spatial_dimension);
	mesh.read("fatigue.msh");

	// init stuff
	const ElementType type_facet = Mesh::getFacetType(type);
	const ElementType type_cohesive =
	FEEngine::getCohesiveElementType(type_facet);

	SolidMechanicsModelCohesive model(mesh);
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	MaterialCohesiveLinearFatigue<2> & numerical_material =
	dynamic_cast<MaterialCohesiveLinearFatigue<2> &>(
	model.getMaterial("cohesive"));

	Real delta_f = numerical_material.getParam("delta_f");
	Real delta_c = numerical_material.getParam("delta_c");
	Real sigma_c = 1;

	const Array<Real> & traction_array =
	numerical_material.getTraction(type_cohesive);

	MaterialFatigue theoretical_material(delta_f, sigma_c, delta_c);

	// model.setBaseName("fatigue");
	// model.addDumpFieldVector("displacement");
	// model.addDumpField("stress");
	// model.dump();

	// stretch material
	Real strain = 1;
	Array<Real> & displacement = model.getDisplacement();
	const Array<Real> & position = mesh.getNodes();

	for (UInt n = 0; n < mesh.getNbNodes(); ++n)
	displacement(n, 0) = position(n, 0) * strain;

	model.assembleInternalForces();
	// model.dump();

	// insert cohesive elements
	model.checkCohesiveStress();

	// create the displacement sequence
	Real increment = 0.01;

	Array<Real> openings;

	arange(openings, 0, 0.5, increment);
	arange(openings, 0.5, 0.1, increment);
	arange(openings, 0.1, 0.7, increment);
	arange(openings, 0.7, 0.3, increment);
	arange(openings, 0.3, 0.6, increment);
	arange(openings, 0.6, 0.3, increment);
	arange(openings, 0.3, 0.7, increment);
	arange(openings, 0.7, 1.3, increment);

	const Array<UInt> & switches = numerical_material.getSwitches(type_cohesive);

	// std::ofstream edis("fatigue_edis.txt");

	// impose openings
	for (UInt i = 0; i < openings.size(); ++i) {

	// compute numerical traction
	imposeOpening(model, openings(i));
	model.assembleInternalForces();
	// model.dump();
	Real numerical_traction = traction_array(0, 0);

	// compute theoretical traction
	Real theoretical_traction =
	theoretical_material.computeTraction(openings(i));

	// test traction
	if (std::abs(numerical_traction - theoretical_traction) > 1e-13)
	AKANTU_ERROR("The numerical traction "
	<< numerical_traction << " and theoretical traction "
	<< theoretical_traction << " are not coincident");

	// edis << model.getEnergy("dissipated") << std::endl;
	}

	if (switches(0) != 7)
	AKANTU_ERROR("The number of switches is wrong");

	std::cout << "OK: the test_cohesive_extrinsic_fatigue passed." << std::endl;
	return 0;
	}

	/* -------------------------------------------------------------------------- */

	void imposeOpening(SolidMechanicsModelCohesive & model, Real opening) {

	UInt spatial_dimension = model.getSpatialDimension();
	Mesh & mesh = model.getFEEngine().getMesh();
	Array<Real> & position = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	UInt nb_nodes = mesh.getNbNodes();

	Array<bool> update(nb_nodes);
	update.zero();

	Mesh::type_iterator it = mesh.firstType(spatial_dimension);
	Mesh::type_iterator end = mesh.lastType(spatial_dimension);

	for (; it != end; ++it) {
	ElementType type = *it;
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	Vector<Real> barycenter(spatial_dimension);

	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter({type, el, _not_ghost}, barycenter);
	if (barycenter(0) > 1) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connectivity(el, n);
	if (!update(node)) {
	displacement(node, 0) = opening + position(node, 0);
	update(node) = true;
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void arange(Array<Real> & openings, Real begin, Real end, Real increment) {
	if (begin < end) {
	for (Real opening = begin; opening < end - increment / 2.;
	opening += increment)
	openings.push_back(opening);
	} else {
	for (Real opening = begin; opening > end + increment / 2.;
	opening -= increment)
	openings.push_back(opening);
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_quadrangle.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_quadrangle.cc
	index ac249d375..119b0faff 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_quadrangle.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_quadrangle.cc
	@@ -1,129 +1,129 @@
	/**
	* @file test_cohesive_extrinsic_quadrangle.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Dec 14 2017
	*
	* @brief Test for extrinsic cohesive elements and quadrangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 1000;

	Mesh mesh(spatial_dimension);
	mesh.read("quadrangle.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));
	model.getElementInserter().setLimit(_y, -0.05, 0.05);
	model.updateAutomaticInsertion();

	Real time_step = model.getStableTimeStep() * 0.05;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	const Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	boundary(n, 1) = true;

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99)
	boundary(n, 0) = true;
	}

	model.assembleInternalForces();

	/// initial conditions
	Real loading_rate = 0.2;
	Real disp_update = loading_rate * time_step;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 1) = loading_rate * position(n, 1);
	}

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	/// update displacement on extreme nodes
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	displacement(n, 1) += disp_update * position(n, 1);
	}

	model.checkCohesiveStress();

	model.solveStep();

	if (s % 1 == 0) {
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	}

	mesh.write("mesh_final.msh");

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 200;

	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.99 \|\| Ed > Edt * 1.01 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	std::cout << "OK: test_cohesive_extrinsic_quadrangle was passed!"
	<< std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_tetrahedron.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_tetrahedron.cc
	index f1f1f716f..76dd30965 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_tetrahedron.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic/test_cohesive_extrinsic_tetrahedron.cc
	@@ -1,240 +1,240 @@
	/**
	* @file test_cohesive_extrinsic_tetrahedron.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Aug 22 2017
	*
	* @brief Test for serial extrinsic cohesive elements for tetrahedron
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	Real function(Real constant, Real x, Real y, Real z) {
	return constant + 2. * x + 3. * y + 4 * z;
	}

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	// const UInt max_steps = 1000;
	// Real increment = 0.005;
	const UInt spatial_dimension = 3;
	Math::setTolerance(1.e-12);

	ElementType type = _tetrahedron_10;
	ElementType type_facet = Mesh::getFacetType(type);
	ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);

	Mesh mesh(spatial_dimension);
	mesh.read("tetrahedron.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	const MaterialCohesiveLinear<3> & mat_cohesive =
	dynamic_cast<const MaterialCohesiveLinear<3> &>(model.getMaterial(1));

	std::cout << mat_cohesive << std::endl;
	std::cout << model.getMaterial(2) << std::endl;

	const Real sigma_c = mat_cohesive.get("sigma_c");
	const Real beta = mat_cohesive.get("beta");

	std::cout << sigma_c << " " << beta << std::endl;

	Array<Real> & position = mesh.getNodes();

	/* ------------------------------------------------------------------------ */
	/* Facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points positions on facets
	const Mesh & mesh_facets = model.getMeshFacets();
	UInt nb_facet = mesh_facets.getNbElement(type_facet);
	UInt nb_quad_per_facet =
	model.getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);
	UInt nb_tot_quad = nb_quad_per_facet * nb_facet;

	Array<Real> quad_facets(nb_tot_quad, spatial_dimension);

	model.getFEEngine("FacetsFEEngine")
	.interpolateOnIntegrationPoints(position, quad_facets, spatial_dimension,
	type_facet);

	/* ------------------------------------------------------------------------ */
	/* End of facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points position of the elements
	UInt nb_quad_per_element = model.getFEEngine().getNbIntegrationPoints(type);
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_tot_quad_el = nb_quad_per_element * nb_element;

	Array<Real> quad_elements(nb_tot_quad_el, spatial_dimension);

	model.getFEEngine().interpolateOnIntegrationPoints(position, quad_elements,
	spatial_dimension, type);

	/// assign some values to stresses
	Array<Real> & stress =
	const_cast<Array<Real> &>(model.getMaterial(0).getStress(type));

	Array<Real>::iterator<Matrix<Real>> stress_it =
	stress.begin(spatial_dimension, spatial_dimension);

	for (UInt q = 0; q < nb_tot_quad_el; ++q, ++stress_it) {

	/// compute values
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	(*stress_it)(i, j) =
	index * function(sigma_c * 5, quad_elements(q, 0),
	quad_elements(q, 1), quad_elements(q, 2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	(stress_it)(i, j) = (stress_it)(j, i);
	}
	}
	}

	/// compute stress on facet quads
	Array<Real> stress_facets(nb_tot_quad, spatial_dimension * spatial_dimension);

	Array<Real>::iterator<Matrix<Real>> stress_facets_it =
	stress_facets.begin(spatial_dimension, spatial_dimension);

	for (UInt q = 0; q < nb_tot_quad; ++q, ++stress_facets_it) {
	/// compute values
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	(*stress_facets_it)(i, j) =
	index * function(sigma_c * 5, quad_facets(q, 0), quad_facets(q, 1),
	quad_facets(q, 2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	(stress_facets_it)(i, j) = (stress_facets_it)(j, i);
	}
	}
	}

	/// insert cohesive elements
	model.checkCohesiveStress();

	/// check insertion stress
	const Array<Real> & normals = model.getFEEngine("FacetsFEEngine")
	.getNormalsOnIntegrationPoints(type_facet);
	const Array<Real> & tangents = model.getTangents(type_facet);
	const Array<Real> & sigma_c_eff =
	mat_cohesive.getInsertionTraction(type_cohesive);

	Vector<Real> normal_stress(spatial_dimension);

	const Array<std::vector<Element>> & coh_element_to_facet =
	mesh_facets.getElementToSubelement(type_facet);

	Array<Real>::iterator<Matrix<Real>> quad_facet_stress =
	stress_facets.begin(spatial_dimension, spatial_dimension);

	Array<Real>::const_iterator<Vector<Real>> quad_normal =
	normals.begin(spatial_dimension);

	Array<Real>::const_iterator<Vector<Real>> quad_tangents =
	tangents.begin(tangents.getNbComponent());

	for (UInt f = 0; f < nb_facet; ++f) {
	const Element & cohesive_element = coh_element_to_facet(f)[1];

	for (UInt q = 0; q < nb_quad_per_facet;
	++q, ++quad_facet_stress, ++quad_normal, ++quad_tangents) {
	if (cohesive_element == ElementNull)
	continue;

	normal_stress.mul<false>(quad_facet_stress, quad_normal);

	Real normal_contrib = normal_stress.dot(*quad_normal);

	Real first_tangent_contrib = 0;

	for (UInt dim = 0; dim < spatial_dimension; ++dim)
	first_tangent_contrib += normal_stress(dim) * (*quad_tangents)(dim);

	Real second_tangent_contrib = 0;

	for (UInt dim = 0; dim < spatial_dimension; ++dim)
	second_tangent_contrib +=
	normal_stress(dim) * (*quad_tangents)(dim + spatial_dimension);

	Real tangent_contrib =
	std::sqrt(first_tangent_contrib * first_tangent_contrib +
	second_tangent_contrib * second_tangent_contrib);

	normal_contrib = std::max(0., normal_contrib);

	Real effective_norm =
	std::sqrt(normal_contrib * normal_contrib +
	tangent_contrib * tangent_contrib / beta / beta);

	if (effective_norm < sigma_c)
	continue;

	if (!Math::are_float_equal(
	effective_norm,
	sigma_c_eff(cohesive_element.element * nb_quad_per_facet + q))) {
	std::cout << "Insertion tractions do not match" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}
	}

	finalize();

	std::cout << "OK: test_cohesive_extrinsic was passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic_implicit/test_assembling_K_cohe_elements.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic_implicit/test_assembling_K_cohe_elements.cc
	index 7404e924e..01132d989 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic_implicit/test_assembling_K_cohe_elements.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_extrinsic_implicit/test_assembling_K_cohe_elements.cc
	@@ -1,172 +1,172 @@
	/**
	* @file test_assembling_K_cohe_elements.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri May 15 2015
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test to check the correct matrix assembling for cohesive elements
	* with degenerated nodes
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	const UInt spatial_dimension = 2;
	Real increment = 0.004;
	bool passed = true;
	Real tol = 1.0e-13;

	Mesh mesh(spatial_dimension);
	mesh.read("quadrangle.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(SolidMechanicsModelCohesiveOptions(_static, true));

	/// CohesiveElementInserter
	model.getElementInserter().setLimit(_y, -0.001, 0.001);
	model.updateAutomaticInsertion();

	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & position = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	// SparseMatrix & K_test = model.getStiffnessMatrix();
	Array<Real> K_verified(0, 3, "K_matrix_verified");
	Array<Real> K_test(0, 3, "K_matrix_test");

	/// load the verified stiffness matrix
	Vector<Real> tmp(3);
	UInt nb_lines;

	std::ifstream infile("K_matrix_verified.dat");
	std::string line;
	if (!infile.good())
	AKANTU_ERROR("Cannot open file K_matrix_verified.dat");
	else {
	for (UInt i = 0; i < 2; ++i) {
	getline(infile, line);
	std::stringstream sstr_data(line);
	if (i == 1) {
	sstr_data >> tmp(0) >> tmp(1) >> tmp(2);
	nb_lines = tmp(2);
	}
	}

	for (UInt i = 0; i < nb_lines; ++i) {
	getline(infile, line);
	std::stringstream sstr_data(line);
	sstr_data >> tmp(0) >> tmp(1) >> tmp(2);
	K_verified.push_back(tmp);
	}
	}
	infile.close();

	/// impose boundary conditions
	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (position(n, 1) < -0.99) {
	boundary(n, 1) = true;
	boundary(n, 0) = true;
	}
	if (position(n, 1) > 0.99 && position(n, 0) < -0.99)
	boundary(n, 1) = true;
	}

	/// solve step
	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (position(n, 1) > 0.99 && position(n, 0) < -0.99)
	displacement(n, 1) += increment;
	}

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 10);
	solver.set("threshold", 1e-13);

	model.solveStep();

	model.getDOFManager().getMatrix("K").saveMatrix("K_matrix_test.dat");

	/// load the stiffness matrix to be tested
	std::ifstream infile2("K_matrix_test.dat");
	if (!infile2.good())
	AKANTU_ERROR("Cannot open file K_matrix_test.dat");
	else {
	for (UInt i = 0; i < 2; ++i) {
	getline(infile2, line);
	std::stringstream sstr_data(line);
	if (i == 1) {
	sstr_data >> tmp(0) >> tmp(1) >> tmp(2);
	nb_lines = tmp(2);
	}
	}

	for (UInt i = 0; i < nb_lines; ++i) {
	getline(infile2, line);
	std::stringstream sstr_data(line);
	sstr_data >> tmp(0) >> tmp(1) >> tmp(2);
	K_test.push_back(tmp);
	}
	}
	infile2.close();

	for (UInt i = 0; i < K_verified.size(); ++i) {
	for (UInt j = 0; j < K_test.size(); ++j) {
	if ((K_test(j, 0) == K_verified(i, 0)) &&
	(K_test(j, 1) == K_verified(i, 1))) {
	if (std::abs(K_verified(i, 2)) < tol) {
	if (std::abs(K_test(j, 2)) > tol)
	passed = false;
	} else {
	Real ratio = (std::abs(K_test(j, 2) - K_verified(i, 2))) /
	(std::abs(K_verified(i, 2)));
	if (ratio > tol)
	passed = false;
	}
	}
	}
	}

	finalize();

	if (passed)
	return EXIT_SUCCESS;
	else
	return EXIT_FAILURE;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_fixture.hh b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_fixture.hh
	index 9623e1e76..80363caf4 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_fixture.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_fixture.hh
	@@ -1,350 +1,347 @@
	/**
	* @file test_cohesive_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Jan 10 2018
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Coehsive element test fixture
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "solid_mechanics_model_cohesive.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_COHESIVE_FIXTURE_HH_
	#define AKANTU_TEST_COHESIVE_FIXTURE_HH_

	using namespace akantu;

	template <::akantu::AnalysisMethod t>
	using analysis_method_t = std::integral_constant<::akantu::AnalysisMethod, t>;

	class StrainIncrement : public BC::Functor {
	public:
	StrainIncrement(const Matrix<Real> & strain, BC::Axis dir)
	: strain_inc(strain), dir(dir) {}

	void operator()(UInt /node/, Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	if (std::abs(coord(dir)) < 1e-8) {
	return;
	}

	flags.set(true);
	primal += strain_inc * coord;
	}

	static const BC::Functor::Type type = BC::Functor::_dirichlet;

	private:
	Matrix<Real> strain_inc;
	BC::Axis dir;
	};

	template <typename param_> class TestSMMCFixture : public ::testing::Test {
	public:
	static constexpr ElementType cohesive_type =
	std::tuple_element_t<0, param_>::value;
	static constexpr ElementType type_1 = std::tuple_element_t<1, param_>::value;
	static constexpr ElementType type_2 = std::tuple_element_t<2, param_>::value;

	static constexpr size_t dim =
	ElementClass<cohesive_type>::getSpatialDimension();

	- void SetUp() {
	+ void SetUp() {
	mesh = std::make_unique<Mesh>(this->dim);
	if (Communicator::getStaticCommunicator().whoAmI() == 0) {
	- mesh->read(this->mesh_name);
	+ mesh->read(this->mesh_name);
	}
	mesh->distribute();
	}

	void TearDown() {
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	void createModel() {
	model = std::make_unique<SolidMechanicsModelCohesive>(*mesh);
	model->initFull(_analysis_method = this->analysis_method,
	_is_extrinsic = this->is_extrinsic);

	auto time_step = this->model->getStableTimeStep() * 0.01;
	this->model->setTimeStep(time_step);

	if (dim == 1) {
	surface = 1;
	group_size = 1;
	return;
	}

	auto facet_type = mesh->getFacetType(this->cohesive_type);

	auto & fe_engine = model->getFEEngineBoundary();
	const auto & group = mesh->getElementGroup("insertion");
	group_size = group.size(_ghost_type = _not_ghost);
	const auto & elements = group.getElements(facet_type);
	- Array<Real> ones(fe_engine.getNbIntegrationPoints(facet_type) *
	- group_size);
	+ Array<Real> ones(fe_engine.getNbIntegrationPoints(facet_type) * group_size);
	ones.set(1.);

	surface = fe_engine.integrate(ones, facet_type, _not_ghost, elements);
	mesh->getCommunicator().allReduce(surface, SynchronizerOperation::_sum);

	-
	-
	mesh->getCommunicator().allReduce(group_size, SynchronizerOperation::_sum);

	#define debug_ 0

	#if debug_
	this->model->addDumpFieldVector("displacement");
	this->model->addDumpFieldVector("velocity");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpField("stress");
	this->model->addDumpField("strain");
	this->model->assembleInternalForces();
	this->model->setBaseNameToDumper("cohesive elements", "cohesive_elements");
	this->model->addDumpFieldVectorToDumper("cohesive elements",
	"displacement");
	this->model->addDumpFieldToDumper("cohesive elements", "damage");
	this->model->addDumpFieldToDumper("cohesive elements", "tractions");
	this->model->addDumpFieldToDumper("cohesive elements", "opening");
	this->model->dump();
	this->model->dump("cohesive elements");
	#endif
	}

	void setInitialCondition(const Matrix<Real> & strain) {
	for (auto && data :
	zip(make_view(this->mesh->getNodes(), this->dim),
	make_view(this->model->getDisplacement(), this->dim))) {
	const auto & pos = std::get<0>(data);
	auto & disp = std::get<1>(data);
	disp = strain * pos;
	}
	}

	bool checkDamaged() {
	UInt nb_damaged = 0;
	auto & damage =
	model->getMaterial("insertion").getArray<Real>("damage", cohesive_type);
	for (auto d : damage) {
	if (d >= .99) {
	++nb_damaged;
	}
	}

	return (nb_damaged == group_size);
	}

	void steps(const Matrix<Real> & strain) {
	StrainIncrement functor((1. / 300) * strain, this->dim == 1 ? _x : _y);

	for (auto _ [[gnu::unused]] : arange(nb_steps)) {
	this->model->applyBC(functor, "loading");
	this->model->applyBC(functor, "fixed");
	if (this->is_extrinsic) {
	this->model->checkCohesiveStress();
	}

	this->model->solveStep();
	#if debug_
	this->model->dump();
	this->model->dump("cohesive elements");
	#endif
	}
	}

	void checkInsertion() {
	auto nb_cohesive_element = this->mesh->getNbElement(cohesive_type);
	mesh->getCommunicator().allReduce(nb_cohesive_element,
	SynchronizerOperation::_sum);

	EXPECT_EQ(nb_cohesive_element, group_size);
	}

	void checkDissipated(Real expected_density) {
	Real edis = this->model->getEnergy("dissipated");

	EXPECT_NEAR(this->surface * expected_density, edis, 5e-1);
	}

	void testModeI() {
	this->createModel();

	auto & mat_el = this->model->getMaterial("body");

	auto speed = mat_el.getPushWaveSpeed(Element());
	auto direction = _y;
	if (dim == 1) {
	direction = _x;
	}
	auto length =
	mesh->getUpperBounds()(direction) - mesh->getLowerBounds()(direction);
	nb_steps = length / speed / model->getTimeStep();

	SCOPED_TRACE(std::to_string(this->dim) + "D - " + std::to_string(type_1) +
	":" + std::to_string(type_2));

	auto & mat_co = this->model->getMaterial("insertion");
	Real sigma_c = mat_co.get("sigma_c");

	Real E = mat_el.get("E");
	Real nu = mat_el.get("nu");

	Matrix<Real> strain;
	if (dim == 1) {
	strain = {{1.}};
	} else if (dim == 2) {
	strain = {{-nu, 0.}, {0., 1. - nu}};
	strain *= (1. + nu);
	} else if (dim == 3) {
	strain = {{-nu, 0., 0.}, {0., 1., 0.}, {0., 0., -nu}};
	}

	strain *= sigma_c / E;

	this->setInitialCondition((1 - 1e-5) * strain);
	this->steps(2e-2 * strain);
	}

	void testModeII() {
	this->createModel();
	auto & mat_el = this->model->getMaterial("body");
	Real speed;
	try {
	speed =
	mat_el.getShearWaveSpeed(Element()); // the slowest speed if exists
	} catch (...) {
	speed = mat_el.getPushWaveSpeed(Element());
	}

	auto direction = _y;
	if (dim == 1)
	direction = _x;
	auto length =
	mesh->getUpperBounds()(direction) - mesh->getLowerBounds()(direction);
	nb_steps = 2 * length / 2. / speed / model->getTimeStep();

	SCOPED_TRACE(std::to_string(this->dim) + "D - " + std::to_string(type_1) +
	":" + std::to_string(type_2));

	if (this->dim > 1)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_y), "sides");
	if (this->dim > 2)
	this->model->applyBC(BC::Dirichlet::FlagOnly(_z), "sides");

	auto & mat_co = this->model->getMaterial("insertion");
	Real sigma_c = mat_co.get("sigma_c");
	Real beta = mat_co.get("beta");
	// Real G_c = mat_co.get("G_c");

	Real E = mat_el.get("E");
	Real nu = mat_el.get("nu");

	Matrix<Real> strain;
	if (dim == 1) {
	strain = {{1.}};
	} else if (dim == 2) {
	strain = {{0., 1.}, {0., 0.}};
	strain *= (1. + nu);
	} else if (dim == 3) {
	strain = {{0., 1., 0.}, {0., 0., 0.}, {0., 0., 0.}};
	strain *= (1. + nu);
	}
	strain = 2 beta * beta * sigma_c / E;

	// nb_steps *= 5;

	this->setInitialCondition((1. - 1e-5) * strain);
	this->steps(0.005 * strain);
	}

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<SolidMechanicsModelCohesive> model;

	std::string mesh_name{std::to_string(cohesive_type) + std::to_string(type_1) +
	(type_1 == type_2 ? "" : std::to_string(type_2)) +
	".msh"};

	bool is_extrinsic;
	AnalysisMethod analysis_method;

	Real surface{0};
	UInt nb_steps{1000};
	UInt group_size{10000};
	};

	/* -------------------------------------------------------------------------- */
	template <typename param_>
	constexpr ElementType TestSMMCFixture<param_>::cohesive_type;
	template <typename param_>
	constexpr ElementType TestSMMCFixture<param_>::type_1;
	template <typename param_>
	constexpr ElementType TestSMMCFixture<param_>::type_2;

	template <typename param_> constexpr size_t TestSMMCFixture<param_>::dim;
	/* -------------------------------------------------------------------------- */

	using IsExtrinsicTypes = std::tuple<std::true_type, std::false_type>;
	using AnalysisMethodTypes =
	std::tuple<analysis_method_t<_explicit_lumped_mass>>;

	using coh_types = gtest_list_t<std::tuple<
	std::tuple<_element_type_cohesive_1d_2, _element_type_segment_2,
	_element_type_segment_2>,
	std::tuple<_element_type_cohesive_2d_4, _element_type_triangle_3,
	_element_type_triangle_3>,
	std::tuple<_element_type_cohesive_2d_4, _element_type_quadrangle_4,
	_element_type_quadrangle_4>,
	std::tuple<_element_type_cohesive_2d_4, _element_type_triangle_3,
	_element_type_quadrangle_4>,
	std::tuple<_element_type_cohesive_2d_6, _element_type_triangle_6,
	_element_type_triangle_6>,
	std::tuple<_element_type_cohesive_2d_6, _element_type_quadrangle_8,
	_element_type_quadrangle_8>,
	std::tuple<_element_type_cohesive_2d_6, _element_type_triangle_6,
	_element_type_quadrangle_8>,
	std::tuple<_element_type_cohesive_3d_6, _element_type_tetrahedron_4,
	_element_type_tetrahedron_4>,
	std::tuple<_element_type_cohesive_3d_12, _element_type_tetrahedron_10,
	_element_type_tetrahedron_10> /*,
	std::tuple<_element_type_cohesive_3d_8, _element_type_hexahedron_8,
	_element_type_hexahedron_8>,
	std::tuple<_element_type_cohesive_3d_16, _element_type_hexahedron_20,
	_element_type_hexahedron_20>*/>>;

	TYPED_TEST_SUITE(TestSMMCFixture, coh_types, );

	#endif /* AKANTU_TEST_COHESIVE_FIXTURE_HH_ */
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_insertion/test_cohesive_insertion_along_physical_surfaces.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_insertion/test_cohesive_insertion_along_physical_surfaces.cc
	index 91928a466..4b5b16f85 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_insertion/test_cohesive_insertion_along_physical_surfaces.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_insertion/test_cohesive_insertion_along_physical_surfaces.cc
	@@ -1,95 +1,95 @@
	/**
	* @file test_cohesive_insertion_along_physical_surfaces.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Aug 07 2015
	* @date last modification: Thu Oct 29 2020
	*
	* @brief Test intrinsic insertion of cohesive elements along physical surfaces
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_cohesive.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {

	initialize("input_file.dat", argc, argv);

	Math::setTolerance(1e-15);

	const UInt spatial_dimension = 3;

	Mesh mesh(spatial_dimension);

	mesh.read("3d_spherical_inclusion.msh");

	SolidMechanicsModelCohesive model(mesh);

	auto && material_selector =
	std::make_shared<MeshDataMaterialCohesiveSelector>(model);
	material_selector->setFallback(model.getMaterialSelector());
	model.setMaterialSelector(material_selector);

	model.initFull();

	std::vector<std::string> surfaces_name = {"interface", "coh1", "coh2",
	"coh3", "coh4", "coh5"};
	UInt nb_surf = surfaces_name.size();

	for (auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_cohesive)) {
	for (UInt i = 0; i < nb_surf; ++i) {

	UInt expected_insertion = mesh.getElementGroup(surfaces_name[i])
	.getElements(mesh.getFacetType(type))
	.size();
	UInt inserted_elements =
	model.getMaterial(surfaces_name[i]).getElementFilter()(type).size();
	if (not(expected_insertion == inserted_elements)) {
	std::cout << "!!! Mismatch in insertion of surface named "
	<< surfaces_name[i] << " --> " << inserted_elements
	<< " inserted elements out of " << expected_insertion
	<< std::endl;
	return 1;
	}
	}
	}

	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic.cc
	index 26d2382fd..0392290d9 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic.cc
	@@ -1,180 +1,180 @@
	/**
	* @file test_cohesive_intrinsic.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Dec 18 2017
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "mesh.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model_cohesive.hh"

	#include "dumper_paraview.hh"

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	static void updateDisplacement(SolidMechanicsModelCohesive &, Array<UInt> &,
	ElementType, Real);

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 350;

	const ElementType type = _triangle_6;

	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	std::cout << mesh << std::endl;
	SolidMechanicsModelCohesive model(mesh);
	model.getElementInserter().setLimit(_x, -0.26, -0.24);

	/// model initialization
	model.initFull();

	mesh.write("mesh_cohesive.msh");

	Real time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	Array<bool> & boundary = model.getBlockedDOFs();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();
	UInt nb_element = mesh.getNbElement(type);

	/// boundary conditions
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	for (UInt n = 0; n < nb_nodes; ++n) {
	boundary(n, dim) = true;
	}
	}

	model.assembleInternalForces();

	model.setBaseName("intrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.addDumpField("external_force");
	model.dump();

	model.setBaseNameToDumper("cohesive elements", "cohesive_elements_triangle");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");
	model.dump("cohesive elements");

	/// update displacement
	Array<UInt> elements;
	Vector<Real> bary(spatial_dimension);
	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter({type, el, _not_ghost}, bary);
	if (bary(0) > -0.25)
	elements.push_back(el);
	}

	Real increment = 0.01;

	updateDisplacement(model, elements, type, increment);

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	model.solveStep();

	updateDisplacement(model, elements, type, increment);

	if (s % 1 == 0) {
	model.dump();
	model.dump("cohesive elements");
	std::cout << "passing step " << s << "/" << max_steps
	<< ", Ed = " << model.getEnergy("dissipated") << std::endl;
	}
	}

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 2 * sqrt(2);

	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	std::cout << "OK: test_cohesive_intrinsic was passed!" << std::endl;
	return EXIT_SUCCESS;
	}

	static void updateDisplacement(SolidMechanicsModelCohesive & model,
	Array<UInt> & elements, ElementType type,
	Real increment) {

	Mesh & mesh = model.getFEEngine().getMesh();
	UInt nb_element = elements.size();
	UInt nb_nodes = mesh.getNbNodes();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> update(nb_nodes);
	update.zero();

	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connectivity(elements(el), n);
	if (!update(node)) {
	displacement(node, 0) += increment;
	// displacement(node, 1) += increment;
	update(node) = true;
	}
	}
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_quadrangle.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_quadrangle.cc
	index 41f6f64ff..c5714ff55 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_quadrangle.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_quadrangle.cc
	@@ -1,207 +1,207 @@
	/**
	* @file test_cohesive_intrinsic_quadrangle.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Dec 18 2017
	*
	* @brief Intrinsic cohesive elements' test for quadrangles
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	static void updateDisplacement(SolidMechanicsModelCohesive &, Array<UInt> &,
	ElementType, Real);

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 350;

	const ElementType type = _quadrangle_4;

	Mesh mesh(spatial_dimension);
	mesh.read("quadrangle.msh");

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// debug::setDebugLevel(dblWarning);

	SolidMechanicsModelCohesive model(mesh);
	model.getElementInserter().setLimit(_x, -0.01, 0.01);
	/// model initialization
	model.initFull();

	Real time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);
	model.assembleMassLumped();

	Array<bool> & boundary = model.getBlockedDOFs();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();
	UInt nb_element = mesh.getNbElement(type);

	/// boundary conditions
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	for (UInt n = 0; n < nb_nodes; ++n) {
	boundary(n, dim) = true;
	}
	}

	model.assembleInternalForces();

	model.setBaseName("intrinsic_quadrangle");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpField("external_force");

	model.setBaseNameToDumper("cohesive elements",
	"cohesive_elements_quadrangle");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");

	model.dump();
	model.dump("cohesive elements");

	/// update displacement
	Array<UInt> elements;
	Vector<Real> bary(spatial_dimension);
	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter({type, el, _not_ghost}, bary);
	if (bary(_x) > 0.)
	elements.push_back(el);
	}

	Real increment = 0.01;

	updateDisplacement(model, elements, type, increment);

	// for (UInt n = 0; n < nb_nodes; ++n) {
	// if (position(n, 1) + displacement(n, 1) > 0) {
	// if (position(n, 0) == 0) {
	// displacement(n, 1) -= 0.25;
	// }
	// if (position(n, 0) == 1) {
	// displacement(n, 1) += 0.25;
	// }
	// }
	// }

	// std::ofstream edis("edis.txt");
	// std::ofstream erev("erev.txt");

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {
	model.solveStep();

	updateDisplacement(model, elements, type, increment);

	if (s % 1 == 0) {
	model.dump();
	model.dump("cohesive elements");
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}

	// // update displacement
	// for (UInt n = 0; n < nb_nodes; ++n) {
	// if (position(n, 1) + displacement(n, 1) > 0) {
	// displacement(n, 0) -= 0.01;
	// }
	// }

	// Real Ed = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getDissipatedEnergy();
	// Real Er = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getReversibleEnergy();

	// edis << s << " "
	// << Ed << std::endl;

	// erev << s << " "
	// << Er << std::endl;
	}

	// edis.close();
	// erev.close();

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 1;

	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}

	finalize();

	std::cout << "OK: test_cohesive_intrinsic_quadrangle was passed!"
	<< std::endl;
	return EXIT_SUCCESS;
	}

	static void updateDisplacement(SolidMechanicsModelCohesive & model,
	Array<UInt> & elements, ElementType type,
	Real increment) {

	Mesh & mesh = model.getFEEngine().getMesh();
	UInt nb_element = elements.size();
	UInt nb_nodes = mesh.getNbNodes();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);

	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> update(nb_nodes);
	update.zero();

	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connectivity(elements(el), n);
	if (!update(node)) {
	displacement(node, 0) += increment;
	// displacement(node, 1) += increment;
	update(node) = true;
	}
	}
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron.cc
	index 8712cc70f..6443d7691 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron.cc
	@@ -1,355 +1,355 @@
	/**
	* @file test_cohesive_intrinsic_tetrahedron.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Dec 18 2017
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class Checker {
	public:
	Checker(const SolidMechanicsModelCohesive & model,
	const Array<UInt> & elements, ElementType type);

	void check(const Vector<Real> & opening, const Matrix<Real> & rotation) {
	checkTractions(opening, rotation);
	checkEquilibrium();
	computeEnergy(opening);
	}

	void updateDisplacement(const Vector<Real> & increment);

	protected:
	void checkTractions(const Vector<Real> & opening,
	const Matrix<Real> & rotation);
	void checkEquilibrium();
	void checkResidual(const Matrix<Real> & rotation);
	void computeEnergy(const Vector<Real> & opening);

	private:
	std::set<UInt> nodes_to_check;
	const SolidMechanicsModelCohesive & model;
	ElementType type;
	// const Array<UInt> & elements;

	const Material & mat_cohesive;

	Real sigma_c;
	const Real beta;
	const Real G_c;
	const Real delta_0;
	const Real kappa;
	Real delta_c;

	const UInt spatial_dimension;

	const ElementType type_facet;
	const ElementType type_cohesive;
	const Array<Real> & traction;
	const Array<Real> & damage;
	const UInt nb_quad_per_el;
	const UInt nb_element;

	const Real beta2_kappa2;
	const Real beta2_kappa;

	Vector<Real> theoretical_traction;
	Vector<Real> traction_old;
	Vector<Real> opening_old;

	Real Ed;
	};

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material_tetrahedron.dat", argc, argv);

	// debug::setDebugLevel(dblDump);
	const UInt spatial_dimension = 3;
	const UInt max_steps = 60;
	const Real increment_constant = 0.01;
	Math::setTolerance(1.e-12);

	const ElementType type = _tetrahedron_10;

	Mesh mesh(spatial_dimension);
	mesh.read("tetrahedron.msh");

	SolidMechanicsModelCohesive model(mesh);
	model.getElementInserter().setLimit(_x, -0.01, 0.01);

	/// model initialization
	model.initFull();

	Array<bool> & boundary = model.getBlockedDOFs();
	boundary.set(true);
	UInt nb_element = mesh.getNbElement(type);

	model.setBaseName("intrinsic_tetrahedron");
	model.addDumpFieldVector("displacement");
	model.addDumpField("internal_force");
	model.dump();

	model.setBaseNameToDumper("cohesive elements",
	"cohesive_elements_tetrahedron");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");
	model.dump("cohesive elements");

	/// find elements to displace
	Array<UInt> elements;
	Vector<Real> bary(spatial_dimension);
	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter({type, el, _not_ghost}, bary);
	if (bary(_x) > 0.01)
	elements.push_back(el);
	}

	/// rotate mesh
	Real angle = 1.;

	// clang-format off
	Matrix<Real> rotation{
	{std::cos(angle), std::sin(angle) * -1., 0.},
	{std::sin(angle), std::cos(angle), 0.},
	{0., 0., 1.}};
	// clang-format on

	Vector<Real> increment_tmp{increment_constant, 2. * increment_constant,
	3. * increment_constant};
	Vector<Real> increment = rotation * increment_tmp;

	auto & position = mesh.getNodes();
	auto position_it = position.begin(spatial_dimension);
	auto position_end = position.end(spatial_dimension);

	for (; position_it != position_end; ++position_it) {
	auto & pos = *position_it;
	pos = rotation * pos;
	}

	model.dump();
	model.dump("cohesive elements");

	/// find nodes to check
	Checker checker(model, elements, type);

	checker.updateDisplacement(increment);

	Real theoretical_Ed = 0;

	Vector<Real> opening(spatial_dimension, 0.);
	Vector<Real> opening_old(spatial_dimension, 0.);

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {
	model.solveStep();

	model.dump();
	model.dump("cohesive elements");

	opening += increment_tmp;
	checker.check(opening, rotation);

	checker.updateDisplacement(increment);
	}

	model.dump();
	model.dump("cohesive elements");

	Real Ed = model.getEnergy("dissipated");
	theoretical_Ed *= 4.;

	std::cout << Ed << " " << theoretical_Ed << std::endl;

	if (!Math::are_float_equal(Ed, theoretical_Ed) \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	finalize();

	std::cout << "OK: test_cohesive_intrinsic_tetrahedron was passed!"
	<< std::endl;
	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	void Checker::updateDisplacement(const Vector<Real> & increment) {
	Mesh & mesh = model.getFEEngine().getMesh();
	const auto & connectivity = mesh.getConnectivity(type);
	auto & displacement = model.getDisplacement();
	Array<bool> update(displacement.size());
	update.zero();

	auto conn_it = connectivity.begin(connectivity.getNbComponent());
	auto conn_end = connectivity.begin(connectivity.getNbComponent());
	for (; conn_it != conn_end; ++conn_it) {
	const auto & conn = *conn_it;
	for (UInt n = 0; n < conn.size(); ++n) {
	UInt node = conn(n);
	if (!update(node)) {
	Vector<Real> node_disp(displacement.storage() +
	node * spatial_dimension,
	spatial_dimension);
	node_disp += increment;
	update(node) = true;
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	Checker::Checker(const SolidMechanicsModelCohesive & model,
	const Array<UInt> & elements, ElementType type)
	: model(model), type(std::move(type)), // elements(elements),
	mat_cohesive(model.getMaterial(1)), sigma_c(mat_cohesive.get("sigma_c")),
	beta(mat_cohesive.get("beta")), G_c(mat_cohesive.get("G_c")),
	delta_0(mat_cohesive.get("delta_0")), kappa(mat_cohesive.get("kappa")),
	spatial_dimension(model.getSpatialDimension()),
	type_facet(Mesh::getFacetType(type)),
	type_cohesive(FEEngine::getCohesiveElementType(type_facet)),
	traction(mat_cohesive.getArray<Real>("tractions", type_cohesive)),
	damage(mat_cohesive.getArray<Real>("damage", type_cohesive)),
	nb_quad_per_el(model.getFEEngine("CohesiveFEEngine")
	.getNbIntegrationPoints(type_cohesive)),
	nb_element(model.getMesh().getNbElement(type_cohesive)),
	beta2_kappa2(beta * beta / kappa / kappa),
	beta2_kappa(beta * beta / kappa) {
	const Mesh & mesh = model.getMesh();
	const auto & connectivity = mesh.getConnectivity(type);
	const auto & position = mesh.getNodes();
	auto conn_it = connectivity.begin(connectivity.getNbComponent());
	for (const auto & element : elements) {
	Vector<UInt> conn_el(conn_it[element]);
	for (UInt n = 0; n < conn_el.size(); ++n) {
	UInt node = conn_el(n);
	if (Math::are_float_equal(position(node, _x), 0.))
	nodes_to_check.insert(node);
	}
	}

	delta_c = 2 * G_c / sigma_c;
	sigma_c *= delta_c / (delta_c - delta_0);
	}

	/* -------------------------------------------------------------------------- */
	void Checker::checkTractions(const Vector<Real> & opening,
	const Matrix<Real> & rotation) {
	auto normal_opening = opening * Vector<Real>{1., 0., 0.};
	auto tangential_opening = opening - normal_opening;
	const Real normal_opening_norm = normal_opening.norm();
	const Real tangential_opening_norm = tangential_opening.norm();
	const Real delta =
	std::max(std::sqrt(tangential_opening_norm * tangential_opening_norm *
	beta2_kappa2 +
	normal_opening_norm * normal_opening_norm),
	0.);

	Real theoretical_damage = std::min(delta / delta_c, 1.);

	theoretical_traction = (tangential_opening * beta2_kappa + normal_opening) *
	sigma_c / delta * (1. - theoretical_damage);
	// adjust damage
	theoretical_damage = std::max((delta - delta_0) / (delta_c - delta_0), 0.);
	theoretical_damage = std::min(theoretical_damage, 1.);

	Vector<Real> theoretical_traction_rotated = rotation * theoretical_traction;

	std::for_each(
	traction.begin(spatial_dimension), traction.end(spatial_dimension),
	[&theoretical_traction_rotated](auto && traction) {
	Real diff =
	Vector<Real>(theoretical_traction_rotated - traction).norm<L_inf>();
	if (diff > 1e-14)
	throw std::domain_error("Tractions are incorrect");
	});

	std::for_each(damage.begin(), damage.end(),
	[&theoretical_damage](auto && damage) {
	if (not Math::are_float_equal(theoretical_damage, damage))
	throw std::domain_error("Damage is incorrect");
	});
	}

	/* -------------------------------------------------------------------------- */
	void Checker::computeEnergy(const Vector<Real> & opening) {
	/// compute energy
	auto Do = opening - opening_old;
	auto Dt = traction_old + theoretical_traction;

	Ed += .5 * Do.dot(Dt);

	opening_old = opening;
	traction_old = theoretical_traction;
	}

	/* -------------------------------------------------------------------------- */
	void Checker::checkEquilibrium() {
	Vector<Real> residual_sum(spatial_dimension, 0.);
	const auto & residual = model.getInternalForce();
	auto res_it = residual.begin(spatial_dimension);
	auto res_end = residual.end(spatial_dimension);
	for (; res_it != res_end; ++res_it)
	residual_sum += *res_it;

	if (!Math::are_float_equal(residual_sum.norm<L_inf>(), 0.))
	throw std::domain_error("System is not in equilibrium!");
	}

	/* -------------------------------------------------------------------------- */
	void Checker::checkResidual(const Matrix<Real> & rotation) {
	Vector<Real> total_force(spatial_dimension, 0.);
	const auto & residual = model.getInternalForce();
	for (auto node : nodes_to_check) {
	Vector<Real> res(residual.begin(spatial_dimension)[node]);
	total_force += res;
	}

	Vector<Real> theoretical_total_force(spatial_dimension);
	theoretical_total_force.mul<false>(rotation, theoretical_traction);
	theoretical_total_force = -1 2 * 2;

	for (UInt s = 0; s < spatial_dimension; ++s) {
	if (!Math::are_float_equal(total_force(s), theoretical_total_force(s))) {
	std::cout << "Total force isn't correct!" << std::endl;
	std::terminate();
	}
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron_fragmentation.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron_fragmentation.cc
	index 13d47b4fe..c3f99da6d 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron_fragmentation.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic/test_cohesive_intrinsic_tetrahedron_fragmentation.cc
	@@ -1,127 +1,127 @@
	/**
	* @file test_cohesive_intrinsic_tetrahedron_fragmentation.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Dec 18 2017
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	// debug::setDebugLevel(dblDump);
	ElementType type = _tetrahedron_10;

	const UInt spatial_dimension = 3;
	const UInt max_steps = 100;

	Mesh mesh(spatial_dimension);
	mesh.read("tetrahedron_full.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull();

	Real time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	model.assembleInternalForces();

	model.setBaseName("intrinsic_tetrahedron_fragmentation");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("grad_u");

	model.setBaseNameToDumper("cohesive elements",
	"cohesive_elements_tetrahedron_fragmentation");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");

	model.dump();
	model.dump("cohesive elements");

	/// update displacement
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes = mesh.getNbNodes();
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Vector<Real> bary(spatial_dimension);

	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> update(nb_nodes);

	for (UInt s = 0; s < max_steps; ++s) {
	Real increment = s / 10.;
	update.zero();

	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter({type, el, _not_ghost}, bary);
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connectivity(el, n);
	if (!update(node)) {
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	displacement(node, dim) = increment * bary(dim);
	update(node) = true;
	}
	}
	}
	}

	if (s % 10 == 0) {
	model.dump();
	model.dump("cohesive elements");
	}
	}

	if (nb_nodes != nb_element * Mesh::getNbNodesPerElement(type)) {
	std::cout << "Wrong number of nodes" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	finalize();
	std::cout << "OK: test_cohesive_intrinsic_tetrahedron was passed!"
	<< std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic_impl/test_cohesive_intrinsic_impl.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic_impl/test_cohesive_intrinsic_impl.cc
	index 8bfd79172..fac80b5c8 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic_impl/test_cohesive_intrinsic_impl.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_intrinsic_impl/test_cohesive_intrinsic_impl.cc
	@@ -1,175 +1,175 @@
	/**
	* @file test_cohesive_intrinsic_impl.cc
	*
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblError);

	const UInt spatial_dimension = 2;
	const ElementType type = _triangle_6;

	Mesh mesh(spatial_dimension);
	mesh.read("implicit.msh");

	CohesiveElementInserter inserter(mesh);
	inserter.setLimit(_y, 0.9, 1.1);
	inserter.insertIntrinsicElements();

	// mesh.write("implicit_cohesive.msh");

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initFull(SolidMechanicsModelCohesiveOptions(_static));

	/// boundary conditions
	Array<bool> & boundary = model.getBlockedDOFs();
	UInt nb_nodes = mesh.getNbNodes();
	Array<Real> & position = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	const ElementType type_facet = mesh.getFacetType(type);

	for (UInt n = 0; n < nb_nodes; ++n) {

	if (std::abs(position(n, 1)) < Math::getTolerance()) {
	boundary(n, 1) = true;
	displacement(n, 1) = 0.0;
	}

	if ((std::abs(position(n, 0)) < Math::getTolerance()) &&
	(position(n, 1) < 1.1)) {
	boundary(n, 0) = true;
	displacement(n, 0) = 0.0;
	}
	if ((std::abs(position(n, 0) - 1) < Math::getTolerance()) &&
	(std::abs(position(n, 1) - 1) < Math::getTolerance())) {
	boundary(n, 0) = true;
	displacement(n, 0) = 0.0;
	}

	if (std::abs(position(n, 1) - 2) < Math::getTolerance()) {
	boundary(n, 1) = true;
	}
	}

	model.setBaseName("intrinsic_impl");
	model.addDumpField("displacement");
	// model.addDumpField("mass" );
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("force");
	model.addDumpField("residual");
	// model.addDumpField("damage" );
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.dump();

	const MaterialCohesive & mat_coh =
	dynamic_cast<const MaterialCohesive &>(model.getMaterial(1));

	ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);

	const Array<Real> & opening = mat_coh.getOpening(type_cohesive);
	// const Array<Real> & traction = mat_coh.getTraction(type_cohesive);

	model.assembleInternalForces();
	const Array<Real> & residual = model.getInternalForce();

	UInt max_step = 1000;
	Real increment = 3. / max_step;
	Real error_tol = 10e-6;

	std::ofstream fout;
	fout.open("output");

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 100);
	solver.set("threshold", 1e-5);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	/// Main loop
	for (UInt nstep = 0; nstep < max_step; ++nstep) {
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (std::abs(position(n, 1) - 2) < Math::getTolerance()) {
	displacement(n, 1) += increment;
	}
	}

	model.solveStep();

	// model.dump();

	Real resid = 0;
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (std::abs(position(n, 1) - 2.) / 2. < Math::getTolerance()) {
	resid += residual(n, 1);
	}
	}

	Real analytical = exp(1) * std::abs(opening(0, 1)) *
	exp(-std::abs(opening(0, 1)) / 0.5) / 0.5;

	// the residual force is comparing with the theoretical value of the
	// cohesive law
	error_tol = std::abs((std::abs(resid) - analytical) / analytical);

	fout << nstep << " " << -resid << " " << analytical << " " << error_tol
	<< std::endl;

	if (error_tol > 1e-3) {
	std::cout << "Relative error: " << error_tol << std::endl;
	std::cout << "Test failed!" << std::endl;
	return EXIT_FAILURE;
	}
	}

	model.dump();

	fout.close();

	finalize();

	std::cout << "Test passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_linear_friction/test_cohesive_friction.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_linear_friction/test_cohesive_friction.cc
	index 1ad4dec21..6950a86ca 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_linear_friction/test_cohesive_friction.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_cohesive_linear_friction/test_cohesive_friction.cc
	@@ -1,241 +1,241 @@
	/**
	* @file test_cohesive_friction.cc
	*
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Thu Jan 14 2016
	* @date last modification: Sun Dec 30 2018
	*
	* @brief testing the correct behavior of the friction law included in
	* the cohesive linear law, in implicit
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include <cmath>
	#include <fstream>
	#include <iomanip>
	#include <iostream>
	#include <string>
	#include <time.h>

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {

	initialize("material.dat", argc, argv);

	Math::setTolerance(1.e-15);
	UInt spatial_dimension = 2;
	const ElementType type = _cohesive_2d_4;

	Mesh mesh(spatial_dimension);

	mesh.read("mesh_cohesive_friction.msh");

	// Create the model
	SolidMechanicsModelCohesive model(mesh);

	// Model initialization
	model.initFull(SolidMechanicsModelCohesiveOptions(_static, true));

	// CohesiveElementInserter inserter(mesh);
	model.limitInsertion(_y, -0.001, 0.001);
	model.updateAutomaticInsertion();

	Real eps = 1e-10;
	Array<Real> & pos = mesh.getNodes();
	Array<Real> & disp = model.getDisplacement();
	Array<bool> & boun = model.getBlockedDOFs();
	const Array<Real> & residual = model.getInternalForce();
	Array<Real> & cohe_opening = const_cast<Array<Real> &>(
	model.getMaterial("interface").getInternal<Real>("opening")(type));
	Array<Real> & friction_force = const_cast<Array<Real> &>(
	model.getMaterial("interface").getInternal<Real>("friction_force")(type));

	// Boundary conditions
	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	if (pos(i, 1) < -0.49 \|\| pos(i, 1) > 0.49) {
	boun(i, 0) = true;
	boun(i, 1) = true;
	}
	}

	bool passed = true;
	Real tolerance = 1e-13;
	Real error;
	bool load_reduction = false;
	Real tol_increase_factor = 1e5;
	Real increment = 1.0e-4;

	model.synchronizeBoundaries();
	model.updateResidual();

	/* -------------------------------------------- */
	/* LOADING PHASE to introduce cohesive elements */
	/* -------------------------------------------- */

	for (UInt nstep = 0; nstep < 100; ++nstep) {

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (pos(n, 1) > 0.49)
	disp(n, 1) += increment;
	}

	model.solveStepCohesive<_scm_newton_raphson_tangent,
	SolveConvergenceCriteria::_increment>(
	tolerance, error, 25, load_reduction, tol_increase_factor);

	if (error > tolerance) {
	AKANTU_ERROR("Convergence not reached in the mode I loading phase");
	passed = false;
	}
	}

	/* --------------------------------------------------------- */
	/* UNLOADING PHASE to bring cohesive elements in compression */
	/* --------------------------------------------------------- */

	for (UInt nstep = 0; nstep < 110; ++nstep) {

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (pos(n, 1) > 0.49)
	disp(n, 1) -= increment;
	}

	model.solveStepCohesive<_scm_newton_raphson_tangent,
	SolveConvergenceCriteria::_increment>(
	tolerance, error, 25, load_reduction, tol_increase_factor);

	if (error > tolerance) {
	AKANTU_ERROR("Convergence not reached in the mode I unloading phase");
	passed = false;
	}
	}

	/* -------------------------------------------------- */
	/* SHEAR PHASE - displacement towards right */
	/* -------------------------------------------------- */

	increment *= 2;

	for (UInt nstep = 0; nstep < 30; ++nstep) {

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (pos(n, 1) > 0.49)
	disp(n, 0) += increment;
	}

	model.solveStepCohesive<_scm_newton_raphson_tangent,
	SolveConvergenceCriteria::_increment>(
	tolerance, error, 25, load_reduction, tol_increase_factor);

	if (error > tolerance) {
	AKANTU_ERROR("Convergence not reached in the shear loading phase");
	passed = false;
	}
	}

	/* ---------------------------------------------------*/
	/* Check the horizontal component of the reaction */
	/* ---------------------------------------------------*/

	// Friction + mode II cohesive behavior
	Real reac_X = 0.;

	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	if (pos(i, 1) > 0.49)
	reac_X += residual(i, 0);
	}
	if (std::abs(reac_X - (-13.987451183762181)) > eps)
	passed = false;

	// Only friction
	Real friction = friction_force(0, 0) + friction_force(1, 0);

	if (std::abs(friction - (-12.517967866999832)) > eps)
	passed = false;

	/* -------------------------------------------------- */
	/* SHEAR PHASE - displacement back to zero */
	/* -------------------------------------------------- */

	for (UInt nstep = 0; nstep < 30; ++nstep) {

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (pos(n, 1) > 0.49)
	disp(n, 0) -= increment;
	}

	model.solveStepCohesive<_scm_newton_raphson_tangent,
	SolveConvergenceCriteria::_increment>(
	tolerance, error, 25, load_reduction, tol_increase_factor);

	if (error > tolerance) {
	AKANTU_ERROR("Convergence not reached in the shear unloading phase");
	passed = false;
	}
	}

	/* ------------------------------------------------------- */
	/* Check the horizontal component of the reaction and */
	/* the residual relative sliding in the cohesive elements */
	/* ------------------------------------------------------- */

	// Friction + mode II cohesive behavior
	reac_X = 0.;

	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	if (pos(i, 1) > 0.49)
	reac_X += residual(i, 0);
	}
	if (std::abs(reac_X - 12.400313187122208) > eps)
	passed = false;

	// Only friction
	friction = 0.;
	friction = friction_force(0, 0) + friction_force(1, 0);

	if (std::abs(friction - 12.523300983293165) > eps)
	passed = false;

	// Residual sliding
	Real sliding[2];
	sliding[0] = cohe_opening(0, 0);
	sliding[1] = cohe_opening(1, 0);

	if (std::abs(sliding[0] - (-0.00044246686809147357)) > eps)
	passed = false;

	if (passed)
	return EXIT_SUCCESS;
	else
	return EXIT_FAILURE;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_fixture.hh b/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_fixture.hh
	index eb61607e2..8647dca80 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_fixture.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_fixture.hh
	@@ -1,314 +1,314 @@
	/**
	* @file test_material_cohesive_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Feb 21 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Test the traction separations laws for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	//#define debug_

	/* -------------------------------------------------------------------------- */
	template <template <UInt> class Mat, typename dim_>
	class TestMaterialCohesiveFixture : public ::testing::Test {
	public:
	static constexpr UInt dim = dim_::value;
	using Material = Mat<dim>;

	void SetUp() override {
	mesh = std::make_unique<Mesh>(dim);
	model = std::make_unique<SolidMechanicsModelCohesive>(*mesh);
	material = std::make_unique<Material>(*model);

	material->SetUps();
	openings = std::make_unique<Array<Real>>(0, dim);
	tractions = std::make_unique<Array<Real>>(0, dim);
	reset();

	gen.seed(::testing::GTEST_FLAG(random_seed));

	normal = getRandomNormal();
	tangents = getRandomTangents();
	}

	void TearDown() override {
	material.reset(nullptr);
	model.reset(nullptr);
	mesh.reset(nullptr);

	openings.reset(nullptr);
	tractions.reset(nullptr);
	}

	void reset() {
	openings->resize(1);
	tractions->resize(1);

	openings->zero();
	tractions->zero();
	}

	/* ------------------------------------------------------------------------ */
	void addOpening(const Vector<Real> & direction, Real start, Real stop,
	UInt nb_steps) {
	for (auto s : arange(nb_steps)) {
	auto opening =
	direction * (start + (stop - start) / Real(nb_steps) * Real(s + 1));
	openings->push_back(opening);
	}
	tractions->resize(openings->size());
	}

	/* ------------------------------------------------------------------------ */
	Vector<Real> getRandomVector() {
	std::uniform_real_distribution<Real> dis;
	Vector<Real> vector(dim);
	for (auto s : arange(dim))
	vector(s) = dis(gen);
	return vector;
	}

	Vector<Real> getRandomNormal() {
	auto normal = getRandomVector();
	normal.normalize();
	#if defined(debug_)
	normal.set(0.);
	normal(0) = 1.;
	#endif
	return normal;
	}

	Matrix<Real> getRandomTangents() {
	auto dim = normal.size();
	Matrix<Real> tangent(dim, dim - 1);
	if (dim == 2) {
	Math::normal2(normal.storage(), tangent(0).storage());
	}

	if (dim == 3) {
	auto v = getRandomVector();
	tangent(0) = (v - v.dot(normal) * normal).normalize();
	Math::normal3(normal.storage(), tangent(0).storage(),
	tangent(1).storage());
	}

	#if defined(debug_)
	if (dim == 2)
	tangent(0) = Vector<Real>{0., 1};
	if (dim == 3)
	tangent = Matrix<Real>{{0., 0.}, {1., 0.}, {0., 1.}};
	#endif

	return tangent;
	}

	/* ------------------------------------------------------------------------ */
	void output_csv() {
	const ::testing::TestInfo * const test_info =
	::testing::UnitTest::GetInstance()->current_test_info();

	std::ofstream cout(std::string(test_info->name()) + ".csv");
	auto print_vect_name = [&](auto name) {
	for (auto s : arange(dim)) {
	if (s != 0) {
	cout << ", ";
	}
	cout << name << "_" << s;
	}
	};
	auto print_vect = [&](const auto & vect) {
	cout << vect.dot(normal);
	if (dim > 1)
	cout << ", " << vect.dot(tangents(0));
	if (dim > 2)
	cout << ", " << vect.dot(tangents(1));
	};

	cout << "delta, ";
	print_vect_name("opening");
	cout << ", ";
	print_vect_name("traction");
	cout << std::endl;

	for (auto && data : zip(make_view(*this->openings, this->dim),
	make_view(*this->tractions, this->dim))) {
	const auto & opening = std::get<0>(data);
	auto & traction = std::get<1>(data);

	cout << this->material->delta(opening, normal) << ", ";
	print_vect(opening);
	cout << ", ";
	print_vect(traction);
	cout << std::endl;
	}
	}

	/* ------------------------------------------------------------------------ */
	Real dissipated() {
	Vector<Real> prev_opening(dim, 0.);
	Vector<Real> prev_traction(dim, 0.);

	Real etot = 0.;
	Real erev = 0.;
	for (auto && data : zip(make_view(*this->openings, this->dim),
	make_view(*this->tractions, this->dim))) {
	const auto & opening = std::get<0>(data);
	const auto & traction = std::get<1>(data);

	etot += (opening - prev_opening).dot(traction + prev_traction) / 2.;
	erev = traction.dot(opening) / 2.;

	prev_opening = opening;
	prev_traction = traction;
	}

	return etot - erev;
	}

	/* ------------------------------------------------------------------------ */
	void checkModeI(Real max_opening, Real expected_dissipated) {
	this->material->insertion_stress_ = this->material->sigma_c_ * normal;
	addOpening(normal, 0., max_opening, 100);

	this->material->computeTractions(openings, normal, tractions);

	for (auto && data : zip(make_view(*this->openings, this->dim),
	make_view(*this->tractions, this->dim))) {
	const auto & opening = std::get<0>(data);
	auto & traction = std::get<1>(data);
	auto T = traction.dot(normal);
	EXPECT_NEAR(0, (traction - T * normal).norm(), 1e-9);

	auto T_expected =
	this->material->tractionModeI(opening, normal).dot(normal);
	EXPECT_NEAR(T_expected, T, 1e-9);
	}

	EXPECT_NEAR(expected_dissipated, dissipated(), 1e-5);
	this->output_csv();
	}

	/* ------------------------------------------------------------------------ */
	void checkModeII(Real max_opening) {
	if (this->dim == 1) {
	SUCCEED();
	return;
	}

	std::uniform_real_distribution<Real> dis;

	auto direction = Vector<Real>(tangents(0));
	auto alpha = dis(gen) + 0.1;
	auto beta = dis(gen) + 0.2;
	#ifndef debug_
	direction = alpha * Vector<Real>(tangents(0));
	if (dim > 2)
	direction += beta * Vector<Real>(tangents(1));

	direction = direction.normalize();
	#endif

	beta = this->material->get("beta");
	this->material->insertion_stress_ =
	beta * this->material->sigma_c_ * direction;

	addOpening(direction, 0., max_opening, 100);

	this->material->computeTractions(openings, normal, tractions);

	for (auto && data : zip(make_view(*this->openings, this->dim),
	make_view(*this->tractions, this->dim))) {
	const auto & opening = std::get<0>(data);
	const auto & traction = std::get<1>(data);

	// In ModeII normal traction should be 0
	ASSERT_NEAR(0, traction.dot(normal), 1e-9);
	// Normal opening is null
	ASSERT_NEAR(0, opening.dot(normal), 1e-16);

	auto T = traction.dot(direction);
	auto T_expected =
	this->material->tractionModeII(opening, normal).dot(direction);

	EXPECT_NEAR(T_expected, T, 1e-9);
	}

	// EXPECT_NEAR(expected_dissipated, dissipated(), 1e-5);
	this->output_csv();
	}

	protected:
	Vector<Real> normal;
	Matrix<Real> tangents;
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<SolidMechanicsModelCohesive> model;
	std::unique_ptr<Material> material;

	std::unique_ptr<Array<Real>> openings;
	std::unique_ptr<Array<Real>> tractions;

	std::mt19937 gen;
	};

	template <template <UInt> class Mat, UInt dim>
	struct TestMaterialCohesive : public Mat<dim> {
	TestMaterialCohesive(SolidMechanicsModel & model)
	: Mat<dim>(model, "test"), insertion_stress_(dim, 0.) {}

	virtual void SetUp() {}
	virtual void resetInternal() {}

	void SetUps() {
	this->initMaterial();
	this->SetUp();
	this->updateInternalParameters();
	this->resetInternals();
	}

	void resetInternals() { this->resetInternal(); }

	virtual void computeTractions(Array<Real> & /openings/,
	const Vector<Real> & /normal/,
	Array<Real> & /tractions/) {}

	Vector<Real> insertion_stress_;
	Real sigma_c_{0};
	bool is_extrinsic{true};
	};

	template <template <UInt> class Mat, typename dim_>
	constexpr UInt TestMaterialCohesiveFixture<Mat, dim_>::dim;
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_linear.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_linear.cc
	index 2225bf121..a0769b005 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_linear.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_materials/test_material_cohesive_linear.cc
	@@ -1,195 +1,195 @@
	/**
	* @file test_material_cohesive_linear.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Feb 21 2018
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Test material cohesive linear
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_material_cohesive_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	/* -------------------------------------------------------------------------- */

	template <UInt dim>
	struct TestMaterialCohesiveLinear
	: public TestMaterialCohesive<MaterialCohesiveLinear, dim> {

	TestMaterialCohesiveLinear(SolidMechanicsModel & model)
	: TestMaterialCohesive<MaterialCohesiveLinear, dim>(model) {}

	void SetUp() override {
	this->is_extrinsic = true;

	this->beta = 2.;
	this->kappa = 2;

	this->G_c = 10.;
	this->sigma_c_ = 1e6;
	this->penalty = 1e11;

	this->delta_c_ = 2. * this->G_c / this->sigma_c_;
	}

	void resetInternal() override {
	normal_opening = Vector<Real>(dim, 0.);
	tangential_opening = Vector<Real>(dim, 0.);
	contact_traction = Vector<Real>(dim, 0.);
	contact_opening = Vector<Real>(dim, 0.);
	}

	void computeTractions(Array<Real> & openings, const Vector<Real> & normal,
	Array<Real> & tractions) override {
	for (auto && data :
	zip(make_view(openings, dim), make_view(tractions, dim))) {
	auto & opening = std::get<0>(data);
	auto & traction = std::get<1>(data);

	this->computeTractionOnQuad(
	traction, opening, normal, delta_max, this->delta_c_,
	this->insertion_stress_, this->sigma_c_, normal_opening,
	tangential_opening, normal_opening_norm, tangential_opening_norm,
	damage, penetration, contact_traction, contact_opening);

	opening += contact_opening;
	traction += contact_traction;
	}
	}

	Real delta(const Vector<Real> & opening, const Vector<Real> & normal) {
	auto beta = this->beta;
	auto kappa = this->kappa;

	auto normal_opening = opening.dot(normal) * normal;
	auto tangential_opening = opening - normal_opening;

	return std::sqrt(std::pow(normal_opening.norm(), 2) +
	std::pow(tangential_opening.norm() * beta / kappa, 2));
	}

	Vector<Real> traction(const Vector<Real> & opening,
	const Vector<Real> & normal) {
	auto delta_c = this->delta_c_;
	auto sigma_c = this->sigma_c_;
	auto beta = this->beta;
	auto kappa = this->kappa;

	auto normal_opening = opening.dot(normal) * normal;
	auto tangential_opening = opening - normal_opening;

	auto delta_ = this->delta(opening, normal);
	if (delta_ < 1e-16) {
	return this->insertion_stress_;
	}

	if (opening.dot(normal) / delta_c < -Math::getTolerance()) {
	ADD_FAILURE() << "This is contact";
	return Vector<Real>(dim, 0.);
	}

	auto T = sigma_c * (delta_c - delta_) / delta_c / delta_ *
	(normal_opening + tangential_opening * beta * beta / kappa);

	return T;
	}

	Vector<Real> tractionModeI(const Vector<Real> & opening,
	const Vector<Real> & normal) {
	return traction(opening, normal);
	}

	Vector<Real> tractionModeII(const Vector<Real> & opening,
	const Vector<Real> & normal) {
	return traction(opening, normal);
	}

	public:
	Real delta_c_{0};

	Real delta_max{0.};
	Real normal_opening_norm{0};
	Real tangential_opening_norm{0};
	Real damage{0};
	bool penetration{false};

	Real etot{0.};
	Real edis{0.};

	Vector<Real> normal_opening;
	Vector<Real> tangential_opening;

	Vector<Real> contact_traction;
	Vector<Real> contact_opening;
	};

	template <typename dim_>
	using TestMaterialCohesiveLinearFixture =
	TestMaterialCohesiveFixture<TestMaterialCohesiveLinear, dim_>;

	using coh_types = gtest_list_t<TestAllDimensions>;

	TYPED_TEST_SUITE(TestMaterialCohesiveLinearFixture, coh_types, );

	TYPED_TEST(TestMaterialCohesiveLinearFixture, ModeI) {
	this->checkModeI(this->material->delta_c_, this->material->get("G_c"));

	Real G_c = this->material->get("G_c");
	EXPECT_NEAR(G_c, this->dissipated(), 1e-6);
	}

	TYPED_TEST(TestMaterialCohesiveLinearFixture, ModeII) {
	this->checkModeII(this->material->delta_c_);

	if (this->dim != 1) {
	Real G_c = this->material->get("G_c");
	Real beta = this->material->get("beta");
	Real dis = beta * G_c;
	EXPECT_NEAR(dis, this->dissipated(), 1e-6);
	}
	}

	TYPED_TEST(TestMaterialCohesiveLinearFixture, Cycles) {
	auto delta_c = this->material->delta_c_;
	auto sigma_c = this->material->sigma_c_;

	this->material->insertion_stress_ = this->normal * sigma_c;

	this->addOpening(this->normal, 0, 0.1 * delta_c, 100);
	this->addOpening(this->normal, 0.1 * delta_c, 0., 100);
	this->addOpening(this->normal, 0., 0.5 * delta_c, 100);
	this->addOpening(this->normal, 0.5 * delta_c, -1.e-5, 100);
	this->addOpening(this->normal, -1.e-5, 0.9 * delta_c, 100);
	this->addOpening(this->normal, 0.9 * delta_c, 0., 100);
	this->addOpening(this->normal, 0., delta_c, 100);

	this->material->computeTractions(*this->openings, this->normal,
	*this->tractions);

	Real G_c = this->material->get("G_c");
	EXPECT_NEAR(G_c, this->dissipated(), 2e-3); // due to contact dissipation at 0
	this->output_csv();
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_facet_stress_synchronizer/test_cohesive_facet_stress_synchronizer.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_facet_stress_synchronizer/test_cohesive_facet_stress_synchronizer.cc
	index cef8f089e..8ffbbb4d5 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_facet_stress_synchronizer/test_cohesive_facet_stress_synchronizer.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_facet_stress_synchronizer/test_cohesive_facet_stress_synchronizer.cc
	@@ -1,214 +1,214 @@
	/**
	* @file test_cohesive_facet_stress_synchronizer.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Test for facet stress synchronizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	Real function(Real constant, Real x, Real y, Real z) {
	return constant + 2. * x + 3. * y + 4 * z;
	}

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt spatial_dimension = 3;

	ElementType type = _tetrahedron_10;
	ElementType type_facet = Mesh::getFacetType(type);
	Math::setTolerance(1.e-11);

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("tetrahedron.msh");

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	}

	SolidMechanicsModelCohesive model(mesh);
	model.initParallel(partition, NULL, true);
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	Array<Real> & position = mesh.getNodes();

	/* ------------------------------------------------------------------------ */
	/* Facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points positions on facets
	const Mesh & mesh_facets = model.getMeshFacets();
	UInt nb_facet = mesh_facets.getNbElement(type_facet);
	UInt nb_quad_per_facet =
	model.getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);
	UInt nb_tot_quad = nb_quad_per_facet * nb_facet;

	Array<Real> quad_facets(nb_tot_quad, spatial_dimension);

	model.getFEEngine("FacetsFEEngine")
	.interpolateOnIntegrationPoints(position, quad_facets, spatial_dimension,
	type_facet);

	/* ------------------------------------------------------------------------ */
	/* End of facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points position of the elements
	UInt nb_quad_per_element = model.getFEEngine().getNbIntegrationPoints(type);
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_tot_quad_el = nb_quad_per_element * nb_element;

	Array<Real> quad_elements(nb_tot_quad_el, spatial_dimension);

	model.getFEEngine().interpolateOnIntegrationPoints(position, quad_elements,
	spatial_dimension, type);

	/// assign some values to stresses
	Array<Real> & stress =
	const_cast<Array<Real> &>(model.getMaterial(0).getStress(type));

	Array<Real>::iterator<Matrix<Real>> stress_it =
	stress.begin(spatial_dimension, spatial_dimension);

	for (UInt q = 0; q < nb_tot_quad_el; ++q, ++stress_it) {

	/// compute values
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	(*stress_it)(i, j) = function(index, quad_elements(q, 0),
	quad_elements(q, 1), quad_elements(q, 2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	(stress_it)(i, j) = (stress_it)(j, i);
	}
	}

	// stress_it->clear();
	// for (UInt i = 0; i < spatial_dimension; ++i)
	// (stress_it)(i, i) = sigma_c 5;
	}

	/// compute and communicate stress on facets
	model.checkCohesiveStress();

	/* ------------------------------------------------------------------------ */
	/* Check facet stress */
	/* ------------------------------------------------------------------------ */

	const Array<Real> & facet_stress = model.getStressOnFacets(type_facet);
	const Array<bool> & facet_check =
	model.getElementInserter().getCheckFacets(type_facet);
	const Array<std::vector<Element>> & elements_to_facet =
	model.getMeshFacets().getElementToSubelement(type_facet);

	Array<Real>::iterator<Vector<Real>> quad_facet_it =
	quad_facets.begin(spatial_dimension);
	Array<Real>::const_iterator<Matrix<Real>> facet_stress_it =
	facet_stress.begin(spatial_dimension, spatial_dimension * 2);

	Matrix<Real> current_stress(spatial_dimension, spatial_dimension);

	for (UInt f = 0; f < nb_facet; ++f) {

	if (!facet_check(f) \|\| (elements_to_facet(f)[0].ghost_type == _not_ghost &&
	elements_to_facet(f)[1].ghost_type == _not_ghost)) {
	quad_facet_it += nb_quad_per_facet;
	facet_stress_it += nb_quad_per_facet;
	continue;
	}

	for (UInt q = 0; q < nb_quad_per_facet;
	++q, ++quad_facet_it, ++facet_stress_it) {
	/// compute current_stress
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	current_stress(i, j) =
	function(index, (quad_facet_it)(0), (quad_facet_it)(1),
	(*quad_facet_it)(2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	current_stress(i, j) = current_stress(j, i);
	}
	}

	/// compare it to interpolated one
	for (UInt s = 0; s < 2; ++s) {
	Matrix<Real> stress_to_check(facet_stress_it->storage() +
	s * spatial_dimension *
	spatial_dimension,
	spatial_dimension, spatial_dimension);

	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	if (!Math::are_float_equal(stress_to_check(i, j),
	current_stress(i, j))) {
	std::cout << "Stress doesn't match" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}
	}
	}
	}
	}

	finalize();
	if (prank == 0)
	std::cout << "OK: test_cohesive_facet_stress_synchronizer passed!"
	<< std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_buildfragments/test_cohesive_parallel_buildfragments.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_buildfragments/test_cohesive_parallel_buildfragments.cc
	index 4d4fd89a8..75e501935 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_buildfragments/test_cohesive_parallel_buildfragments.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_buildfragments/test_cohesive_parallel_buildfragments.cc
	@@ -1,457 +1,457 @@
	/**
	* @file test_cohesive_parallel_buildfragments.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test to build fragments in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <fstream>
	#include <functional>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */
	#include "fragment_manager.hh"
	#include "material_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	void verticalInsertionLimit(SolidMechanicsModelCohesive &);
	void displaceElements(SolidMechanicsModelCohesive &, const Real, const Real);
	bool isInertiaEqual(const Vector<Real> &, const Vector<Real> &);
	void rotateArray(Array<Real> & array, Real angle);
	UInt getNbBigFragments(FragmentManager &, UInt);

	const UInt spatial_dimension = 3;
	const UInt total_nb_fragment = 4;
	const Real rotation_angle = M_PI / 4.;
	const Real global_tolerance = 1.e-9;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	Math::setTolerance(global_tolerance);

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("mesh.msh");

	/// partition the mesh
	MeshUtils::purifyMesh(mesh);
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	}

	SolidMechanicsModelCohesive model(mesh);
	model.initParallel(partition, NULL, true);

	delete partition;

	/// model initialization
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	mesh.computeBoundingBox();
	Real L = mesh.getUpperBounds()(0) - mesh.getLowerBounds()(0);
	Real h = mesh.getUpperBounds()(1) - mesh.getLowerBounds()(1);
	Real rho = model.getMaterial("bulk").getParam<Real>("rho");

	Real theoretical_mass = L * h * h * rho;
	Real frag_theo_mass = theoretical_mass / total_nb_fragment;

	UInt nb_element =
	mesh.getNbElement(spatial_dimension, _not_ghost, _ek_regular);
	comm.allReduce(&nb_element, 1, _so_sum);
	UInt nb_element_per_fragment = nb_element / total_nb_fragment;

	FragmentManager fragment_manager(model);

	fragment_manager.computeAllData();
	getNbBigFragments(fragment_manager, nb_element_per_fragment + 1);

	model.setBaseName("extrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("stress");
	model.addDumpField("partitions");
	model.addDumpField("fragments");
	model.addDumpField("fragments mass");
	model.addDumpField("moments of inertia");
	model.addDumpField("elements per fragment");
	model.dump();

	model.setBaseNameToDumper("cohesive elements", "cohesive_elements_test");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");
	model.dump("cohesive elements");

	/// set check facets
	verticalInsertionLimit(model);

	model.assembleMassLumped();
	model.synchronizeBoundaries();

	/// impose initial displacement
	Array<Real> & displacement = model.getDisplacement();
	Array<Real> & velocity = model.getVelocity();
	const Array<Real> & position = mesh.getNodes();
	UInt nb_nodes = mesh.getNbNodes();

	for (UInt n = 0; n < nb_nodes; ++n) {
	displacement(n, 0) = position(n, 0) * 0.1;
	velocity(n, 0) = position(n, 0);
	}

	rotateArray(mesh.getNodes(), rotation_angle);
	// rotateArray(displacement, rotation_angle);
	// rotateArray(velocity, rotation_angle);

	model.updateResidual();
	model.checkCohesiveStress();
	model.dump();
	model.dump("cohesive elements");

	const Array<Real> & fragment_mass = fragment_manager.getMass();
	const Array<Real> & fragment_center = fragment_manager.getCenterOfMass();

	Real el_size = L / total_nb_fragment;
	Real lim = -L / 2 + el_size * 0.99;

	/// define theoretical inertia moments
	Vector<Real> small_frag_inertia(spatial_dimension);
	small_frag_inertia(0) = frag_theo_mass * (h * h + h * h) / 12.;
	small_frag_inertia(1) = frag_theo_mass * (el_size * el_size + h * h) / 12.;
	small_frag_inertia(2) = frag_theo_mass * (el_size * el_size + h * h) / 12.;

	std::sort(small_frag_inertia.storage(),
	small_frag_inertia.storage() + spatial_dimension,
	std::greater<Real>());

	const Array<Real> & inertia_moments = fragment_manager.getMomentsOfInertia();
	Array<Real>::const_iterator<Vector<Real>> inertia_moments_begin =
	inertia_moments.begin(spatial_dimension);

	/// displace one fragment each time
	for (UInt frag = 1; frag <= total_nb_fragment; ++frag) {
	if (prank == 0)
	std::cout << "Generating fragment: " << frag << std::endl;

	fragment_manager.computeAllData();

	/// check number of big fragments
	UInt nb_big_fragment =
	getNbBigFragments(fragment_manager, nb_element_per_fragment + 1);

	model.dump();
	model.dump("cohesive elements");

	if (frag < total_nb_fragment) {
	if (nb_big_fragment != 1) {
	AKANTU_ERROR(
	"The number of big fragments is wrong: " << nb_big_fragment);
	return EXIT_FAILURE;
	}
	} else {
	if (nb_big_fragment != 0) {
	AKANTU_ERROR(
	"The number of big fragments is wrong: " << nb_big_fragment);
	return EXIT_FAILURE;
	}
	}

	/// check number of fragments
	UInt nb_fragment_num = fragment_manager.getNbFragment();

	if (nb_fragment_num != frag) {
	AKANTU_ERROR("The number of fragments is wrong! Numerical: "
	<< nb_fragment_num << " Theoretical: " << frag);
	return EXIT_FAILURE;
	}

	/// check mass computation
	if (frag < total_nb_fragment) {
	Real total_mass = 0.;
	UInt small_fragments = 0;

	for (UInt f = 0; f < nb_fragment_num; ++f) {
	const Vector<Real> & current_inertia = inertia_moments_begin[f];

	if (Math::are_float_equal(fragment_mass(f, 0), frag_theo_mass)) {

	/// check center of mass
	if (fragment_center(f, 0) > (L * frag / total_nb_fragment - L / 2)) {
	AKANTU_ERROR("Fragment center is wrong!");
	return EXIT_FAILURE;
	}

	/// check moment of inertia
	if (!isInertiaEqual(current_inertia, small_frag_inertia)) {
	AKANTU_ERROR("Inertia moments are wrong");
	return EXIT_FAILURE;
	}

	++small_fragments;
	total_mass += frag_theo_mass;
	} else {
	/// check the moment of inertia for the biggest fragment
	Real big_frag_mass = frag_theo_mass * (total_nb_fragment - frag + 1);
	Real big_frag_size = el_size * (total_nb_fragment - frag + 1);

	Vector<Real> big_frag_inertia(spatial_dimension);
	big_frag_inertia(0) = big_frag_mass * (h * h + h * h) / 12.;
	big_frag_inertia(1) =
	big_frag_mass * (big_frag_size * big_frag_size + h * h) / 12.;
	big_frag_inertia(2) =
	big_frag_mass * (big_frag_size * big_frag_size + h * h) / 12.;

	std::sort(big_frag_inertia.storage(),
	big_frag_inertia.storage() + spatial_dimension,
	std::greater<Real>());

	if (!isInertiaEqual(current_inertia, big_frag_inertia)) {
	AKANTU_ERROR("Inertia moments are wrong");
	return EXIT_FAILURE;
	}
	}
	}

	if (small_fragments != nb_fragment_num - 1) {
	AKANTU_ERROR("The number of small fragments is wrong!");
	return EXIT_FAILURE;
	}

	if (!Math::are_float_equal(total_mass,
	small_fragments * frag_theo_mass)) {
	AKANTU_ERROR("The mass of small fragments is wrong!");
	return EXIT_FAILURE;
	}
	}

	/// displace fragments
	rotateArray(mesh.getNodes(), -rotation_angle);
	// rotateArray(displacement, -rotation_angle);
	displaceElements(model, lim, el_size * 2);
	rotateArray(mesh.getNodes(), rotation_angle);
	// rotateArray(displacement, rotation_angle);

	model.updateResidual();

	lim += el_size;
	}

	model.dump();
	model.dump("cohesive elements");

	/// check centers
	const Array<Real> & fragment_velocity = fragment_manager.getVelocity();

	Real initial_position = -L / 2. + el_size / 2.;

	for (UInt frag = 0; frag < total_nb_fragment; ++frag) {
	Real theoretical_center = initial_position + el_size * frag;

	UInt f_index = 0;
	while (
	f_index < total_nb_fragment &&
	!Math::are_float_equal(fragment_center(f_index, 0), theoretical_center))
	++f_index;

	if (f_index == total_nb_fragment) {
	AKANTU_ERROR("The fragments' center is wrong!");
	return EXIT_FAILURE;
	}

	f_index = 0;
	while (f_index < total_nb_fragment &&
	!Math::are_float_equal(fragment_velocity(f_index, 0),
	theoretical_center))
	++f_index;

	if (f_index == total_nb_fragment) {
	AKANTU_ERROR("The fragments' velocity is wrong!");
	return EXIT_FAILURE;
	}
	}

	finalize();

	if (prank == 0)
	std::cout << "OK: test_cohesive_buildfragments was passed!" << std::endl;
	return EXIT_SUCCESS;
	}

	void verticalInsertionLimit(SolidMechanicsModelCohesive & model) {
	UInt spatial_dimension = model.getSpatialDimension();
	const Mesh & mesh_facets = model.getMeshFacets();
	const Array<Real> & position = mesh_facets.getNodes();

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {
	GhostType ghost_type = *gt;

	Mesh::type_iterator it =
	mesh_facets.firstType(spatial_dimension - 1, ghost_type);
	Mesh::type_iterator end =
	mesh_facets.lastType(spatial_dimension - 1, ghost_type);
	for (; it != end; ++it) {
	ElementType type = *it;

	Array<bool> & check_facets =
	model.getElementInserter().getCheckFacets(type, ghost_type);

	const Array<UInt> & connectivity =
	mesh_facets.getConnectivity(type, ghost_type);
	UInt nb_nodes_per_facet = connectivity.getNbComponent();

	for (UInt f = 0; f < check_facets.getSize(); ++f) {
	if (!check_facets(f))
	continue;

	UInt nb_aligned_nodes = 1;
	Real first_node_pos = position(connectivity(f, 0), 0);

	for (; nb_aligned_nodes < nb_nodes_per_facet; ++nb_aligned_nodes) {
	Real other_node_pos = position(connectivity(f, nb_aligned_nodes), 0);

	if (!Math::are_float_equal(first_node_pos, other_node_pos))
	break;
	}

	if (nb_aligned_nodes != nb_nodes_per_facet) {
	check_facets(f) = false;
	}
	}
	}
	}
	}

	void displaceElements(SolidMechanicsModelCohesive & model, const Real lim,
	const Real amount) {
	UInt spatial_dimension = model.getSpatialDimension();
	Array<Real> & displacement = model.getDisplacement();
	Mesh & mesh = model.getMesh();
	UInt nb_nodes = mesh.getNbNodes();
	Array<bool> displaced(nb_nodes);
	displaced.zero();
	Vector<Real> barycenter(spatial_dimension);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {
	GhostType ghost_type = *gt;

	Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
	Mesh::type_iterator end = mesh.lastType(spatial_dimension, ghost_type);
	for (; it != end; ++it) {
	ElementType type = *it;
	const Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);
	UInt nb_element = connectivity.getSize();
	UInt nb_nodes_per_element = connectivity.getNbComponent();

	Array<UInt>::const_vector_iterator conn_el =
	connectivity.begin(nb_nodes_per_element);

	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter(el, type, barycenter.storage(), ghost_type);

	if (barycenter(0) < lim) {
	const Vector<UInt> & conn = conn_el[el];

	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = conn(n);
	if (!displaced(node)) {
	displacement(node, 0) -= amount;
	displaced(node) = true;
	}
	}
	}
	}
	}
	}
	}

	bool isInertiaEqual(const Vector<Real> & a, const Vector<Real> & b) {
	UInt nb_terms = a.size();
	UInt equal_terms = 0;

	while (equal_terms < nb_terms &&
	std::abs(a(equal_terms) - b(equal_terms)) / a(equal_terms) <
	Math::getTolerance())
	++equal_terms;

	return equal_terms == nb_terms;
	}

	void rotateArray(Array<Real> & array, Real angle) {
	UInt spatial_dimension = array.getNbComponent();

	Real rotation_values[] = {std::cos(angle),
	std::sin(angle),
	0,
	-std::sin(angle),
	std::cos(angle),
	0,
	0,
	0,
	1};
	Matrix<Real> rotation(rotation_values, spatial_dimension, spatial_dimension);

	RVector displaced_node(spatial_dimension);
	auto node_it = array.begin(spatial_dimension);
	auto node_end = array.end(spatial_dimension);

	for (; node_it != node_end; ++node_it) {
	displaced_node.mul<false>(rotation, *node_it);
	*node_it = displaced_node;
	}
	}

	UInt getNbBigFragments(FragmentManager & fragment_manager,
	UInt minimum_nb_elements) {
	fragment_manager.computeNbElementsPerFragment();
	const Array<UInt> & nb_elements_per_fragment =
	fragment_manager.getNbElementsPerFragment();
	UInt nb_fragment = fragment_manager.getNbFragment();
	UInt nb_big_fragment = 0;

	for (UInt frag = 0; frag < nb_fragment; ++frag) {
	if (nb_elements_per_fragment(frag) >= minimum_nb_elements) {
	++nb_big_fragment;
	}
	}

	return nb_big_fragment;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic.cc
	index 43fa07e70..76d2f7bcc 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic.cc
	@@ -1,188 +1,188 @@
	/**
	* @file test_cohesive_parallel_extrinsic.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief parallel test for cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt max_steps = 500;

	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("mesh.msh");

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	// debug::setDebugLevel(dblDump);
	partition->partitionate(psize);
	// debug::setDebugLevel(dblWarning);
	}

	SolidMechanicsModelCohesive model(mesh);

	model.initParallel(partition, NULL, true);

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// debug::setDebugLevel(dblWarning);

	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));
	model.limitInsertion(_y, -0.30, -0.20);
	model.updateAutomaticInsertion();

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh_facets << std::endl;
	// debug::setDebugLevel(dblWarning);

	Real time_step = model.getStableTimeStep() * 0.1;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	boundary(n, 1) = true;

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99)
	boundary(n, 0) = true;
	}

	/// initial conditions
	Real loading_rate = 0.5;
	Real disp_update = loading_rate * time_step;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 1) = loading_rate * position(n, 1);
	}

	model.synchronizeBoundaries();
	model.updateResidual();

	model.setBaseName("extrinsic_parallel");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("residual");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.addDumpField("partitions");
	// model.getDumper().getDumper().setMode(iohelper::BASE64);
	model.dump();

	model.setBaseNameToDumper("cohesive elements",
	"extrinsic_parallel_cohesive_elements");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");
	model.dump("cohesive elements");

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	/// update displacement on extreme nodes
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	displacement(n, 1) += disp_update * position(n, 1);
	}

	model.checkCohesiveStress();
	model.solveStep();

	// model.dump();
	if (s % 10 == 0) {
	if (prank == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}

	// // update displacement
	// for (UInt n = 0; n < nb_nodes; ++n) {
	// if (position(n, 1) + displacement(n, 1) > 0) {
	// displacement(n, 0) -= 0.01;
	// }
	// }

	// Real Ed = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getDissipatedEnergy();
	// Real Er = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getReversibleEnergy();

	// edis << s << " "
	// << Ed << std::endl;

	// erev << s << " "
	// << Er << std::endl;
	}

	model.dump();
	model.dump("cohesive elements");

	// edis.close();
	// erev.close();

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 200 * sqrt(2);

	if (prank == 0) {
	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.999 \|\| Ed > Edt * 1.001 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron.cc
	index de3c6a1d3..1fd5e4839 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron.cc
	@@ -1,245 +1,245 @@
	/**
	* @file test_cohesive_parallel_extrinsic_tetrahedron.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Tue May 08 2012
	* @date last modification: Thu Mar 22 2018
	*
	* @brief 3D extrinsic cohesive elements test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	#include "solid_mechanics_model_cohesive.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	Real function(Real constant, Real x, Real y, Real z) {
	return constant + 2. * x + 3. * y + 4 * z;
	}

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	// const UInt max_steps = 1000;
	// Real increment = 0.005;
	const UInt spatial_dimension = 3;
	Math::setTolerance(1.e-12);

	ElementType type = _tetrahedron_10;
	ElementType type_facet = Mesh::getFacetType(type);
	ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("tetrahedron.msh");

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	}

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initParallel(partition, NULL, true);
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	const MaterialCohesiveLinear<3> & mat_cohesive =
	dynamic_cast<const MaterialCohesiveLinear<3> &>(model.getMaterial(1));

	const Real sigma_c =
	mat_cohesive.getParam<RandomInternalField<Real, FacetInternalField>>(
	"sigma_c");
	const Real beta = mat_cohesive.getParam<Real>("beta");
	// const Real G_cI = mat_cohesive.getParam<Real>("G_cI");

	Array<Real> & position = mesh.getNodes();

	/* ------------------------------------------------------------------------ */
	/* Facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points positions on facets
	const Mesh & mesh_facets = model.getMeshFacets();
	UInt nb_facet = mesh_facets.getNbElement(type_facet);
	UInt nb_quad_per_facet =
	model.getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);
	UInt nb_tot_quad = nb_quad_per_facet * nb_facet;

	Array<Real> quad_facets(nb_tot_quad, spatial_dimension);

	model.getFEEngine("FacetsFEEngine")
	.interpolateOnIntegrationPoints(position, quad_facets, spatial_dimension,
	type_facet);

	/* ------------------------------------------------------------------------ */
	/* End of facet part */
	/* ------------------------------------------------------------------------ */

	/// compute quadrature points position of the elements
	UInt nb_quad_per_element = model.getFEEngine().getNbIntegrationPoints(type);
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_tot_quad_el = nb_quad_per_element * nb_element;

	Array<Real> quad_elements(nb_tot_quad_el, spatial_dimension);

	model.getFEEngine().interpolateOnIntegrationPoints(position, quad_elements,
	spatial_dimension, type);

	/// assign some values to stresses
	Array<Real> & stress =
	const_cast<Array<Real> &>(model.getMaterial(0).getStress(type));

	Array<Real>::iterator<Matrix<Real>> stress_it =
	stress.begin(spatial_dimension, spatial_dimension);

	for (UInt q = 0; q < nb_tot_quad_el; ++q, ++stress_it) {

	/// compute values
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	(*stress_it)(i, j) =
	index * function(sigma_c * 5, quad_elements(q, 0),
	quad_elements(q, 1), quad_elements(q, 2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	(stress_it)(i, j) = (stress_it)(j, i);
	}
	}
	}

	/// compute stress on facet quads
	Array<Real> stress_facets(nb_tot_quad, spatial_dimension * spatial_dimension);

	Array<Real>::iterator<Matrix<Real>> stress_facets_it =
	stress_facets.begin(spatial_dimension, spatial_dimension);

	for (UInt q = 0; q < nb_tot_quad; ++q, ++stress_facets_it) {
	/// compute values
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = i; j < spatial_dimension; ++j) {
	UInt index = i * spatial_dimension + j;
	(*stress_facets_it)(i, j) =
	index * function(sigma_c * 5, quad_facets(q, 0), quad_facets(q, 1),
	quad_facets(q, 2));
	}
	}

	/// fill symmetrical part
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < i; ++j) {
	(stress_facets_it)(i, j) = (stress_facets_it)(j, i);
	}
	}
	}

	/// insert cohesive elements
	model.checkCohesiveStress();

	/// check insertion stress
	const Array<Real> & normals = model.getFEEngine("FacetsFEEngine")
	.getNormalsOnIntegrationPoints(type_facet);
	const Array<Real> & tangents = model.getTangents(type_facet);
	const Array<Real> & sigma_c_eff =
	mat_cohesive.getInsertionTraction(type_cohesive);

	Vector<Real> normal_stress(spatial_dimension);

	const Array<std::vector<Element>> & coh_element_to_facet =
	mesh_facets.getElementToSubelement(type_facet);

	Array<Real>::iterator<Matrix<Real>> quad_facet_stress =
	stress_facets.begin(spatial_dimension, spatial_dimension);

	Array<Real>::const_iterator<Vector<Real>> quad_normal =
	normals.begin(spatial_dimension);

	Array<Real>::const_iterator<Vector<Real>> quad_tangents =
	tangents.begin(tangents.getNbComponent());

	for (UInt f = 0; f < nb_facet; ++f) {
	const Element & cohesive_element = coh_element_to_facet(f)[1];

	for (UInt q = 0; q < nb_quad_per_facet;
	++q, ++quad_facet_stress, ++quad_normal, ++quad_tangents) {
	if (cohesive_element == ElementNull)
	continue;

	normal_stress.mul<false>(quad_facet_stress, quad_normal);

	Real normal_contrib = normal_stress.dot(*quad_normal);

	Real first_tangent_contrib = 0;

	for (UInt dim = 0; dim < spatial_dimension; ++dim)
	first_tangent_contrib += normal_stress(dim) * (*quad_tangents)(dim);

	Real second_tangent_contrib = 0;

	for (UInt dim = 0; dim < spatial_dimension; ++dim)
	second_tangent_contrib +=
	normal_stress(dim) * (*quad_tangents)(dim + spatial_dimension);

	Real tangent_contrib =
	std::sqrt(first_tangent_contrib * first_tangent_contrib +
	second_tangent_contrib * second_tangent_contrib);

	normal_contrib = std::max(0., normal_contrib);

	Real effective_norm =
	std::sqrt(normal_contrib * normal_contrib +
	tangent_contrib * tangent_contrib / beta / beta);

	if (effective_norm < sigma_c)
	continue;

	if (!Math::are_float_equal(
	effective_norm,
	sigma_c_eff(cohesive_element.element * nb_quad_per_facet + q))) {
	std::cout << "Insertion tractions do not match" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}
	}
	finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron_displacement.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron_displacement.cc
	index 92e8e2f14..58c16d7dc 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron_displacement.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic/test_cohesive_parallel_extrinsic_tetrahedron_displacement.cc
	@@ -1,405 +1,405 @@
	/**
	* @file test_cohesive_parallel_extrinsic_tetrahedron_displacement.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Displacement test for 3D cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "material_cohesive_linear.hh"
	#include "solid_mechanics_model_cohesive.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	bool checkDisplacement(SolidMechanicsModelCohesive & model, ElementType type,
	std::ofstream & error_output, UInt step,
	bool barycenters);

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	const UInt max_steps = 500;
	Math::setTolerance(1.e-12);

	UInt spatial_dimension = 3;
	ElementType type = _tetrahedron_10;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("tetrahedron.msh");

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	// debug::setDebugLevel(dblDump);
	partition->partitionate(psize);
	// debug::setDebugLevel(dblWarning);
	}

	SolidMechanicsModelCohesive model(mesh);

	model.initParallel(partition, NULL, true);

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh << std::endl;
	// debug::setDebugLevel(dblWarning);

	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true));

	/* ------------------------------------------------------------------------ */
	/* Facet part */
	/* ------------------------------------------------------------------------ */

	// Array<Real> limits(spatial_dimension, 2);
	// limits(0, 0) = -0.01;
	// limits(0, 1) = 0.01;
	// limits(1, 0) = -100;
	// limits(1, 1) = 100;
	// limits(2, 0) = -100;
	// limits(2, 1) = 100;

	// model.enableFacetsCheckOnArea(limits);

	/* ------------------------------------------------------------------------ */
	/* End of facet part */
	/* ------------------------------------------------------------------------ */

	// debug::setDebugLevel(dblDump);
	// std::cout << mesh_facets << std::endl;
	// debug::setDebugLevel(dblWarning);

	Real time_step = model.getStableTimeStep() * 0.1;
	model.setTimeStep(time_step);
	std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99) {
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	boundary(n, dim) = true;
	}
	}

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99) {
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	boundary(n, dim) = true;
	}
	}
	}

	// #if defined (AKANTU_DEBUG_TOOLS)
	// Vector<Real> facet_center(spatial_dimension);
	// facet_center(0) = 0;
	// facet_center(1) = -0.16666667;
	// facet_center(2) = 0.5;

	// debug::element_manager.setMesh(mesh);
	// debug::element_manager.addModule(debug::_dm_material_cohesive);
	// debug::element_manager.addModule(debug::_dm_debug_tools);
	// //debug::element_manager.addModule(debug::_dm_integrator);
	// #endif

	/// initial conditions
	Real loading_rate = 1;
	Real disp_update = loading_rate * time_step;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 0) = loading_rate * position(n, 0);
	velocity(n, 1) = loading_rate * position(n, 0);
	}

	model.synchronizeBoundaries();
	model.updateResidual();

	std::stringstream paraview_output;
	paraview_output << "extrinsic_parallel_tetrahedron_" << psize;

	model.setBaseName(paraview_output.str());
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("velocity");
	model.addDumpFieldVector("acceleration");
	model.addDumpFieldVector("residual");
	model.addDumpFieldTensor("stress");
	model.addDumpFieldTensor("grad_u");
	model.addDumpField("partitions");
	// model.getDumper().getDumper().setMode(iohelper::BASE64);
	model.dump();

	model.setBaseNameToDumper("cohesive elements",
	paraview_output.str() + "_cohesive_elements");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");
	model.dump("cohesive elements");

	std::stringstream error_stream;
	error_stream << "error"
	<< ".csv";
	std::ofstream error_output;
	error_output.open(error_stream.str().c_str());
	error_output << "# Step, Average, Max, Min" << std::endl;

	if (checkDisplacement(model, type, error_output, 0, true)) {
	}

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	/// update displacement on extreme nodes
	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99) {
	displacement(n, 0) += disp_update * position(n, 0);
	displacement(n, 1) += disp_update * position(n, 0);
	}
	}

	model.checkCohesiveStress();

	model.solveStep();

	if (s % 100 == 0) {
	if (prank == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}
	}

	model.dump();
	model.dump("cohesive elements");

	if (!checkDisplacement(model, type, error_output, max_steps, false)) {
	finalize();
	return EXIT_FAILURE;
	}

	finalize();
	return EXIT_SUCCESS;
	}

	bool checkDisplacement(SolidMechanicsModelCohesive & model, ElementType type,
	std::ofstream & error_output, UInt step,
	bool barycenters) {

	Mesh & mesh = model.getMesh();
	UInt spatial_dimension = mesh.getSpatialDimension();
	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	const Array<Real> & displacement = model.getDisplacement();
	UInt nb_element = mesh.getNbElement(type);
	UInt nb_nodes_per_elem = Mesh::getNbNodesPerElement(type);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	if (psize == 1) {
	std::stringstream displacement_file;
	displacement_file << "displacement/displacement_" << std::setfill('0')
	<< std::setw(6) << step;
	std::ofstream displacement_output;
	displacement_output.open(displacement_file.str().c_str());

	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt n = 0; n < nb_nodes_per_elem; ++n) {
	UInt node = connectivity(el, n);

	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	displacement_output << std::setprecision(15)
	<< displacement(node, dim) << " ";
	}
	displacement_output << std::endl;
	}
	}

	displacement_output.close();

	if (barycenters) {
	std::stringstream barycenter_file;
	barycenter_file << "displacement/barycenters";
	std::ofstream barycenter_output;
	barycenter_output.open(barycenter_file.str().c_str());

	Element element(type, 0);
	Vector<Real> bary(spatial_dimension);

	for (UInt el = 0; el < nb_element; ++el) {
	element.element = el;
	mesh.getBarycenter(element, bary);

	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	barycenter_output << std::setprecision(15) << bary(dim) << " ";
	}
	barycenter_output << std::endl;
	}

	barycenter_output.close();
	}
	} else {

	if (barycenters)
	return true;

	/// read data
	std::stringstream displacement_file;
	displacement_file << "displacement/displacement_" << std::setfill('0')
	<< std::setw(6) << step;
	std::ifstream displacement_input;
	displacement_input.open(displacement_file.str().c_str());

	Array<Real> displacement_serial(0, spatial_dimension);
	Vector<Real> disp_tmp(spatial_dimension);

	while (displacement_input.good()) {
	for (UInt i = 0; i < spatial_dimension; ++i)
	displacement_input >> disp_tmp(i);

	displacement_serial.push_back(disp_tmp);
	}

	std::stringstream barycenter_file;
	barycenter_file << "displacement/barycenters";
	std::ifstream barycenter_input;
	barycenter_input.open(barycenter_file.str().c_str());

	Array<Real> barycenter_serial(0, spatial_dimension);

	while (barycenter_input.good()) {
	for (UInt dim = 0; dim < spatial_dimension; ++dim)
	barycenter_input >> disp_tmp(dim);

	barycenter_serial.push_back(disp_tmp);
	}

	Element element(type, 0);
	Vector<Real> bary(spatial_dimension);

	Array<Real>::iterator<Vector<Real>> it;
	Array<Real>::iterator<Vector<Real>> begin =
	barycenter_serial.begin(spatial_dimension);
	Array<Real>::iterator<Vector<Real>> end =
	barycenter_serial.end(spatial_dimension);

	Array<Real>::const_iterator<Vector<Real>> disp_it;
	Array<Real>::iterator<Vector<Real>> disp_serial_it;

	Vector<Real> difference(spatial_dimension);
	Array<Real> error;

	/// compute error
	for (UInt el = 0; el < nb_element; ++el) {
	element.element = el;
	mesh.getBarycenter(element, bary);

	/// find element
	for (it = begin; it != end; ++it) {
	UInt matched_dim = 0;

	while (matched_dim < spatial_dimension &&
	Math::are_float_equal(bary(matched_dim), (*it)(matched_dim)))
	++matched_dim;

	if (matched_dim == spatial_dimension)
	break;
	}

	if (it == end) {
	std::cout << "Element barycenter not found!" << std::endl;
	return false;
	}

	UInt matched_el = it - begin;

	disp_serial_it = displacement_serial.begin(spatial_dimension) +
	matched_el * nb_nodes_per_elem;

	for (UInt n = 0; n < nb_nodes_per_elem; ++n, ++disp_serial_it) {
	UInt node = connectivity(el, n);
	if (!mesh.isLocalOrMasterNode(node))
	continue;

	disp_it = displacement.begin(spatial_dimension) + node;

	difference = *disp_it;
	difference -= *disp_serial_it;

	error.push_back(difference.norm());
	}
	}

	/// compute average error
	Real average_error = std::accumulate(error.begin(), error.end(), 0.);
	comm.allReduce(&average_error, 1, _so_sum);

	UInt error_size = error.getSize();
	comm.allReduce(&error_size, 1, _so_sum);

	average_error /= error_size;

	/// compute maximum and minimum
	Real max_error = *std::max_element(error.begin(), error.end());
	comm.allReduce(&max_error, 1, _so_max);

	Real min_error = *std::min_element(error.begin(), error.end());
	comm.allReduce(&min_error, 1, _so_min);

	/// output data
	if (prank == 0) {
	error_output << step << ", " << average_error << ", " << max_error << ", "
	<< min_error << std::endl;
	}

	if (max_error > 1.e-9) {
	std::cout << "Displacement error is too big!" << std::endl;
	return false;
	}
	}

	return true;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic_IG_TG/test_cohesive_parallel_extrinsic_IG_TG.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic_IG_TG/test_cohesive_parallel_extrinsic_IG_TG.cc
	index 63459ad60..e596ba687 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic_IG_TG/test_cohesive_parallel_extrinsic_IG_TG.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_extrinsic_IG_TG/test_cohesive_parallel_extrinsic_IG_TG.cc
	@@ -1,317 +1,317 @@
	/**
	* @file test_cohesive_parallel_extrinsic_IG_TG.cc
	*
	* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Jul 24 2020
	*
	* @brief Test for considering different cohesive properties for
	* intergranular (IG) and transgranular (TG) fractures in extrinsic
	* cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "material_cohesive_linear.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class MultiGrainMaterialSelector : public DefaultMaterialCohesiveSelector {
	public:
	MultiGrainMaterialSelector(const SolidMechanicsModelCohesive & model,
	const ID & transgranular_id,
	const ID & intergranular_id)
	: DefaultMaterialCohesiveSelector(model),
	transgranular_id(transgranular_id), intergranular_id(intergranular_id),
	model(model), mesh(model.getMesh()), mesh_facets(model.getMeshFacets()),
	spatial_dimension(model.getSpatialDimension()), nb_IG(0), nb_TG(0) {}

	UInt operator()(const Element & element) {
	if (mesh_facets.getSpatialDimension(element.type) ==
	(spatial_dimension - 1)) {
	const std::vector<Element> & element_to_subelement =
	mesh_facets.getElementToSubelement(element.type, element.ghost_type)(
	element.element);

	const Element & el1 = element_to_subelement[0];
	const Element & el2 = element_to_subelement[1];

	UInt grain_id1 =
	mesh.getData<UInt>("tag_0", el1.type, el1.ghost_type)(el1.element);
	if (el2 != ElementNull) {
	UInt grain_id2 =
	mesh.getData<UInt>("tag_0", el2.type, el2.ghost_type)(el2.element);
	if (grain_id1 == grain_id2) {
	// transgranular = 0 indicator
	nb_TG++;
	return model.getMaterialIndex(transgranular_id);
	} else {
	// intergranular = 1 indicator
	nb_IG++;
	return model.getMaterialIndex(intergranular_id);
	}
	} else {
	// transgranular = 0 indicator
	nb_TG++;
	return model.getMaterialIndex(transgranular_id);
	}
	} else {
	return DefaultMaterialCohesiveSelector::operator()(element);
	}
	}

	private:
	ID transgranular_id, intergranular_id;
	const SolidMechanicsModelCohesive & model;
	const Mesh & mesh;
	const Mesh & mesh_facets;
	UInt spatial_dimension;

	UInt nb_IG;
	UInt nb_TG;
	};

	/* -------------------------------------------------------------------------- */
	void limitInsertion(SolidMechanicsModelCohesive & model) {

	Real tolerance = 0.1;

	const Mesh & mesh = model.getMesh();
	const Mesh & mesh_facets = model.getMeshFacets();
	CohesiveElementInserter & inserter = model.getElementInserter();

	UInt spatial_dimension = mesh.getSpatialDimension();
	Vector<Real> bary_facet(spatial_dimension);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {
	GhostType ghost_type = *gt;

	Mesh::type_iterator it =
	mesh_facets.firstType(spatial_dimension - 1, ghost_type);
	Mesh::type_iterator end =
	mesh_facets.lastType(spatial_dimension - 1, ghost_type);
	for (; it != end; ++it) {
	ElementType type = *it;
	Array<bool> & f_check = inserter.getCheckFacets(type, ghost_type);
	UInt nb_facet = mesh_facets.getNbElement(type, ghost_type);

	for (UInt f = 0; f < nb_facet; ++f) {
	if (f_check(f)) {

	mesh_facets.getBarycenter(f, type, bary_facet.storage(), ghost_type);

	if (!(bary_facet(0) > -tolerance && bary_facet(0) < tolerance) &&
	!(bary_facet(1) > -tolerance && bary_facet(1) < tolerance))
	f_check(f) = false;
	}
	}
	}
	}

	model.updateAutomaticInsertion();
	}

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	const UInt spatial_dimension = 2;
	const UInt max_steps = 600;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	mesh.read("square.msh");
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	}

	SolidMechanicsModelCohesive model(mesh);

	/// model initialization
	model.initParallel(partition, NULL, true);

	delete partition;

	MultiGrainMaterialSelector material_selector(model, "TG_cohesive",
	"IG_cohesive");
	model.setMaterialSelector(material_selector);
	model.initFull(
	SolidMechanicsModelCohesiveOptions(_explicit_lumped_mass, true, false));

	Real time_step = model.getStableTimeStep() * 0.1;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	limitInsertion(model);

	// std::cout << mesh << std::endl;

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();

	/// boundary conditions
	for (UInt n = 0; n < nb_nodes; ++n) {
	if (position(n, 1) > 0.99 \|\| position(n, 1) < -0.99)
	boundary(n, 1) = true;

	if (position(n, 0) > 0.99 \|\| position(n, 0) < -0.99)
	boundary(n, 0) = true;
	}

	model.synchronizeBoundaries();
	model.updateResidual();

	model.setBaseName("extrinsic");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("residual");
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.addDumpField("partitions");

	model.setBaseNameToDumper("cohesive elements", "extrinsic_cohesive");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.addDumpFieldToDumper("cohesive elements", "damage");

	model.dump();
	model.dump("cohesive elements");

	/// initial conditions
	Real loading_rate = 0.1;
	// bar_height = 2
	Real VI = loading_rate * 2 * 0.5;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 1) = loading_rate * position(n, 1);
	velocity(n, 0) = loading_rate * position(n, 0);
	}

	// std::ofstream edis("edis.txt");
	// std::ofstream erev("erev.txt");

	// Array<Real> & residual = model.getResidual();
	// model.dump();
	// const Array<Real> & stress = model.getMaterial(0).getStress(type);
	Real dispy = 0;
	// UInt nb_coh_elem = 0;

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {
	dispy += VI * time_step;
	/// update displacement on extreme nodes
	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (position(n, 1) > 0.99) {
	displacement(n, 1) = dispy;
	velocity(n, 1) = VI;
	}
	if (position(n, 1) < -0.99) {
	displacement(n, 1) = -dispy;
	velocity(n, 1) = -VI;
	}
	if (position(n, 0) > 0.99) {
	displacement(n, 0) = dispy;
	velocity(n, 0) = VI;
	}
	if (position(n, 0) < -0.99) {
	displacement(n, 0) = -dispy;
	velocity(n, 0) = -VI;
	}
	}

	model.checkCohesiveStress();

	model.solveStep();

	if (s % 10 == 0) {
	if (prank == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;

	// model.dump();
	// model.dump("cohesive elements");
	}

	// Real Ed = model.getEnergy("dissipated");

	// edis << s << " "
	// << Ed << std::endl;

	// erev << s << " "
	// << Er << std::endl;
	}

	model.dump();
	model.dump("cohesive elements");

	// edis.close();
	// erev.close();

	// mesh.write("mesh_final.msh");

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 40;

	if (prank == 0)
	std::cout << Ed << " " << Edt << std::endl;

	if (Ed < Edt * 0.99 \|\| Ed > Edt * 1.01 \|\| std::isnan(Ed)) {
	if (prank == 0)
	std::cout << "The dissipated energy is incorrect" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	// for (UInt n = 0; n < position.getSize(); ++n) {
	// for (UInt s = 0; s < spatial_dimension; ++s) {
	// position(n, s) += displacement(n, s);
	// }
	// }

	finalize();

	if (prank == 0)
	std::cout << "OK: test_cohesive_extrinsic_IG_TG was passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_insertion_along_physical_surfaces.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_insertion_along_physical_surfaces.cc
	index 0f949b872..fb0dbcdca 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_insertion_along_physical_surfaces.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_insertion_along_physical_surfaces.cc
	@@ -1,134 +1,134 @@
	/**
	* @file test_cohesive_parallel_insertion_along_physical_surfaces.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Test parallel intrinsic insertion of cohesive elements along physical
	* surfaces
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_cohesive.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model_cohesive.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {

	initialize("input_file.dat", argc, argv);

	Math::setTolerance(1e-15);

	const UInt spatial_dimension = 3;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();
	akantu::MeshPartition * partition = NULL;

	if (prank == 0) {

	mesh.read("3d_spherical_inclusion.msh");

	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	}
	SolidMechanicsModelCohesive model(mesh);
	model.initParallel(partition);
	mesh.createGroupsFromMeshData<std::string>("physical_names");
	model.initFull(SolidMechanicsModelCohesiveOptions(_static));

	std::vector<std::string> surfaces_name = {"interface", "coh1", "coh2",
	"coh3", "coh4", "coh5"};
	UInt nb_surf = surfaces_name.size();

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	std::string ghost_str;

	if (*gt == 1)
	ghost_str = "ghost";
	else
	ghost_str = "not ghost";

	Mesh::type_iterator it =
	mesh.firstType(spatial_dimension, *gt, _ek_cohesive);
	Mesh::type_iterator end =
	mesh.lastType(spatial_dimension, *gt, _ek_cohesive);

	for (; it != end; ++it) {

	Array<UInt> & material_id = mesh.getMeshFacets().getData<UInt>(
	"physical_names")(mesh.getFacetType(it), gt);

	for (UInt i = 0; i < nb_surf; ++i) {

	UInt expected_insertion = 0;

	for (UInt m = 0; m < material_id.getSize(); ++m) {
	if (material_id(m) ==
	model.SolidMechanicsModel::getMaterialIndex(surfaces_name[i]))
	++expected_insertion;
	}

	UInt inserted_elements;

	inserted_elements = model.getMaterial(surfaces_name[i])
	.getElementFilter()(it, gt)
	.getSize();
	if (expected_insertion != inserted_elements) {
	std::cerr << std::endl
	<< "!!! Mismatch in insertion of surface named "
	<< surfaces_name[i] << " in proc n° " << prank << " --> "
	<< inserted_elements << " inserted elements of type "
	<< ghost_str << " out of " << expected_insertion
	<< std::endl;
	return EXIT_FAILURE;
	}
	}
	}
	}

	model.assembleStiffnessMatrix();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_intrinsic_implicit_insertion.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_intrinsic_implicit_insertion.cc
	index c5af557f5..d00b4c34a 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_intrinsic_implicit_insertion.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_insertion/test_cohesive_parallel_intrinsic_implicit_insertion.cc
	@@ -1,308 +1,308 @@
	/**
	* @file test_cohesive_parallel_intrinsic_implicit_insertion.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Verifying the proper insertion and synchronization of intrinsic
	* cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "material_cohesive.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model_cohesive.hh"
	/* -------------------------------------------------------------------------- */
	using namespace akantu;
	std::ofstream output;

	/* -------------------------------------------------------------------------- */
	void printMeshContent(Mesh & mesh) {

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();
	comm.barrier();
	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	Mesh::type_iterator first =
	mesh.firstType(_all_dimensions, *gt, _ek_not_defined);
	Mesh::type_iterator last =
	mesh.lastType(_all_dimensions, *gt, _ek_not_defined);

	for (; first != last; ++first) {
	UInt nb_element = mesh.getNbElement(first, gt);
	output << std::endl
	<< "Element type: " << first << ", " << gt << ": " << nb_element
	<< " in the mesh of processor " << prank << std::endl;
	Array<UInt> & conn = mesh.getConnectivity(first, gt);
	for (UInt i = 0; i < conn.getSize(); ++i) {
	output << "Element no " << i << " ";
	for (UInt j = 0; j < conn.getNbComponent(); ++j) {
	output << conn(i, j) << " ";
	}
	output << std::endl;
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void printNodeList(Mesh & mesh) {

	Array<double> & nodes = mesh.getNodes();

	output << "Number of nodes: " << mesh.getNbNodes() << std::endl;
	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	output << "Node # " << i << ", x-coord: " << nodes(i, 0)
	<< ", y-coord: " << nodes(i, 1)
	<< ", of type: " << mesh.getNodeType(i) << std::endl;
	}
	output << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void getGlobalIDs(Mesh & mesh) {

	const Array<UInt> & glob_id = mesh.getGlobalNodesIds();
	if (&glob_id) {
	output << "Global nodes ID: " << std::endl;
	for (UInt i = 0; i < glob_id.getSize(); ++i) {
	output << i << " " << glob_id(i) << std::endl;
	}
	}
	output << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void printSynchroinfo(Mesh & mesh, const DistributedSynchronizer & synch) {

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();
	Int psize = comm.getNbProc();

	if (comm.getNbProc() == 1)
	return;

	for (Int p = 0; p < psize; ++p) {

	if (p == prank)
	continue;
	output << "From processor " << prank << " to processor " << p << std::endl;
	const Array<Element> & sele = *(synch.getSendElement() + p);
	output << " Sending element(s): " << std::endl;
	for (UInt i = 0; i < sele.getSize(); ++i) {
	output << sele(i) << std::endl;
	}

	const Array<Element> & rele = *(synch.getReceiveElement() + p);
	output << " Receiving element(s): " << std::endl;
	for (UInt i = 0; i < rele.getSize(); ++i) {
	output << rele(i) << std::endl;
	}
	}
	output << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	void printDOF(SolidMechanicsModelCohesive & model) {

	const auto & comm = Communicator::getStaticCommunicator();
	if (comm.getNbProc() == 1)
	return;
	Int prank = comm.whoAmI();

	const DOFSynchronizer & dof = model.getDOFSynchronizer();

	output << "Number of global dofs " << dof.getNbGlobalDOFs()
	<< " for processor " << prank << std::endl;

	const Array<UInt> & dof_global_ids = dof.getDOFGlobalIDs();

	for (UInt i = 0; i < dof_global_ids.getSize(); ++i) {

	output << "Local dof " << i << ", global id: " << dof_global_ids(i)
	<< std::endl;
	}
	output << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {

	std::string input_file = "input_file_iii.dat";
	std::string mesh_file = "2d_basic_interface.msh";
	std::string dir = "output_dir/";

	initialize(input_file, argc, argv);

	debug::setDebugLevel(dbl0);

	const UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();
	akantu::MeshPartition * partition = NULL;

	std::stringstream filename;
	filename << dir.c_str() << "output_from_proc_" << prank << "_out_of_" << psize
	<< ".out";
	output.open(filename.str());

	if (prank == 0) {

	mesh.read(mesh_file);
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);

	const ElementTypeMapArray<UInt> & partitions = partition->getPartitions();

	output << "The root processor read the mesh." << std::endl
	<< "Only GMSH physical objects are created in the mesh."
	<< std::endl;

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	Mesh::type_iterator first = mesh.firstType(_all_dimensions, *gt);
	Mesh::type_iterator last = mesh.lastType(_all_dimensions, *gt);

	for (; first != last; ++first) {

	output << "Element type: " << first << " ghost type: " << gt
	<< std::endl;
	UInt nb_element = mesh.getNbElement(first, gt);
	output << nb_element << " to partitionate between " << psize
	<< " processsors" << std::endl;

	Array<UInt> part = partitions(first, gt);

	for (UInt i = 0; i < part.getSize(); ++i) {
	output << i << " " << part(i) << std::endl;
	}
	}
	}

	output << "Nodes are also read and set with type -1 (normal node)"
	<< std::endl;
	printNodeList(mesh);
	}

	SolidMechanicsModelCohesive model(mesh);

	output << "Before initParallel(), non-root processors have empty Mesh object"
	<< std::endl;
	printMeshContent(mesh);

	model.initParallel(partition);

	output << "After initParallel(), Mesh object on each processor is a local "
	"partionated mesh containing ghost elements"
	<< std::endl;
	printMeshContent(mesh);

	output << "Nodes are also partionated and new node types are defined:"
	<< std::endl;
	printNodeList(mesh);
	output << "-3: pure ghost node -> not a local node" << std::endl
	<< "-2: master node -> node shared with other processor(s) -> local "
	"and global node"
	<< std::endl
	<< ">0: slave node -> -> node shared with other processor(s) -> only "
	"local node (its id is the rank of the processor owning the master "
	"node)"
	<< std::endl;

	output
	<< "Each local node has a corresponding global id used during assembly: "
	<< std::endl;
	getGlobalIDs(mesh);

	Mesh & mesh_facets = mesh.getMeshFacets();

	output << "Within cohesive element model, initParallel() creates a second "
	"Mesh object usually called mesh_facet"
	<< std::endl
	<< "This Mesh object contains all sub-dimensional elements where "
	"potential cohesive element can be inserted"
	<< std::endl;
	printMeshContent(mesh_facets);

	const DistributedSynchronizer & synch_model = model.getSynchronizer();
	output << "The distributed synchronizer of solid mechanics model is used to "
	"synchronize fields with ghost element:"
	<< std::endl;
	printSynchroinfo(mesh, synch_model);

	mesh.createGroupsFromMeshData<std::string>("physical_names");
	model.initFull(SolidMechanicsModelCohesiveOptions(_static));

	output << "In case of insertion along physical objects, cohesive elements "
	"are created during initFull()"
	<< std::endl;
	output << "Elements list after insertion" << std::endl;
	printMeshContent(mesh);

	output << "Node list after insertion: (Total number of nodes "
	<< mesh.getNbNodes() << ")" << std::endl;
	printNodeList(mesh);

	output << "Node global ids after insertion: (Total number of nodes "
	<< mesh.getNbGlobalNodes() << ")" << std::endl;
	getGlobalIDs(mesh);

	const DistributedSynchronizer & coh_synch_model =
	*(model.getCohesiveSynchronizer());
	output << "Solid mechanics model cohesive has its own distributed "
	"synchronizer to handle ghost cohesive element:"
	<< std::endl;
	printSynchroinfo(mesh, coh_synch_model);

	output << "A synchronizer dedicated to degrees of freedom (DOFs) is used by "
	"the solver to build matrices in parallel:"
	<< std::endl
	<< "This DOFSynchronizer is built based on nodes global id "
	<< std::endl;
	printDOF(model);

	output.close();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic.cc
	index e60e1dd73..1198a4ee0 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic.cc
	@@ -1,176 +1,176 @@
	/**
	* @file test_cohesive_parallel_intrinsic.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief parallel test for intrinsic cohesive elements
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model_cohesive.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material.dat", argc, argv);

	const UInt max_steps = 350;

	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("mesh.msh");

	// /// insert cohesive elements
	// CohesiveElementInserter inserter(mesh);
	// inserter.setLimit('x', -0.26, -0.24);
	// inserter.insertIntrinsicElements();

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	// debug::setDebugLevel(dblDump);
	partition->partitionate(psize);
	// debug::setDebugLevel(dblWarning);
	}

	SolidMechanicsModelCohesive model(mesh);

	model.initParallel(partition);

	model.initFull();

	model.limitInsertion(_x, -0.26, -0.24);
	model.insertIntrinsicElements();

	debug::setDebugLevel(dblDump);
	std::cout << mesh << std::endl;
	debug::setDebugLevel(dblWarning);

	Real time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);
	// std::cout << "Time step: " << time_step << std::endl;

	model.assembleMassLumped();

	Array<Real> & position = mesh.getNodes();
	Array<Real> & velocity = model.getVelocity();
	Array<bool> & boundary = model.getBlockedDOFs();
	// Array<Real> & displacement = model.getDisplacement();
	// const Array<Real> & residual = model.getResidual();

	UInt nb_nodes = mesh.getNbNodes();
	Real epsilon = std::numeric_limits<Real>::epsilon();

	for (UInt n = 0; n < nb_nodes; ++n) {
	if (std::abs(position(n, 0) - 1.) < epsilon)
	boundary(n, 0) = true;
	}

	model.synchronizeBoundaries();
	model.updateResidual();

	model.setBaseName("intrinsic_parallel");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("residual");
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.addDumpField("partitions");
	model.addDumpField("force");
	model.dump();

	model.setBaseNameToDumper("cohesive elements",
	"cohesive_elements_parallel_intrinsic");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.dump("cohesive elements");

	/// initial conditions
	Real loading_rate = .2;
	for (UInt n = 0; n < nb_nodes; ++n) {
	velocity(n, 0) = loading_rate * position(n, 0);
	}

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	model.solveStep();

	if (s % 20 == 0) {
	model.dump();
	model.dump("cohesive elements");
	if (prank == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	}

	// // update displacement
	// for (UInt n = 0; n < nb_nodes; ++n) {
	// if (position(n, 1) + displacement(n, 1) > 0) {
	// displacement(n, 0) -= 0.01;
	// }
	// }

	// Real Ed = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getDissipatedEnergy();
	// Real Er = dynamic_cast<MaterialCohesive&>
	// (model.getMaterial(1)).getReversibleEnergy();

	// edis << s << " "
	// << Ed << std::endl;

	// erev << s << " "
	// << Er << std::endl;
	}

	// edis.close();
	// erev.close();

	Real Ed = model.getEnergy("dissipated");

	Real Edt = 2 * sqrt(2);

	if (prank == 0) {
	std::cout << Ed << " " << Edt << std::endl;

	if (std::abs((Ed - Edt) / Edt) > 0.01 \|\| std::isnan(Ed)) {
	std::cout << "The dissipated energy is incorrect" << std::endl;
	return EXIT_FAILURE;
	}
	}

	finalize();
	if (prank == 0)
	std::cout << "OK: Test passed!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic_tetrahedron.cc b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic_tetrahedron.cc
	index 25cea47a5..6b243974e 100644
	--- a/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic_tetrahedron.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_cohesive/test_parallel_cohesive/test_cohesive_parallel_intrinsic/test_cohesive_parallel_intrinsic_tetrahedron.cc
	@@ -1,714 +1,714 @@
	/**
	* @file test_cohesive_parallel_intrinsic_tetrahedron.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Wed Nov 08 2017
	*
	* @brief Test for 3D intrinsic cohesive elements simulation in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dumper_paraview.hh"
	#include "material_cohesive.hh"
	#include "solid_mechanics_model_cohesive.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	void updateDisplacement(SolidMechanicsModelCohesive & model,
	const ElementTypeMapArray<UInt> & elements,
	Vector<Real> & increment);

	bool checkTractions(SolidMechanicsModelCohesive & model, Vector<Real> & opening,
	Vector<Real> & theoretical_traction,
	Matrix<Real> & rotation);

	void findNodesToCheck(const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements,
	Array<UInt> & nodes_to_check, Int psize);

	bool checkEquilibrium(const Mesh & mesh, const Array<Real> & residual);

	bool checkResidual(const Array<Real> & residual, const Vector<Real> & traction,
	const Array<UInt> & nodes_to_check,
	const Matrix<Real> & rotation);

	void findElementsToDisplace(const Mesh & mesh,
	ElementTypeMapArray<UInt> & elements);

	int main(int argc, char * argv[]) {
	initialize("material_tetrahedron.dat", argc, argv);

	const UInt spatial_dimension = 3;
	const UInt max_steps = 60;
	const Real increment_constant = 0.01;
	ElementType type = _tetrahedron_10;
	Math::setTolerance(1.e-10);

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	UInt nb_nodes_to_check_serial = 0;
	UInt total_nb_nodes = 0;
	UInt nb_elements_check_serial = 0;

	akantu::MeshPartition * partition = NULL;
	if (prank == 0) {
	// Read the mesh
	mesh.read("tetrahedron.msh");

	/// count nodes with zero position
	const Array<Real> & position = mesh.getNodes();
	for (UInt n = 0; n < position.getSize(); ++n) {
	if (std::abs(position(n, 0) - 0.) < 1e-6)
	++nb_nodes_to_check_serial;
	}

	// /// insert cohesive elements
	// CohesiveElementInserter inserter(mesh);
	// inserter.setLimit(0, -0.01, 0.01);
	// inserter.insertIntrinsicElements();

	/// find nodes to check in serial
	ElementTypeMapArray<UInt> elements_serial("elements_serial", "");
	findElementsToDisplace(mesh, elements_serial);
	nb_elements_check_serial = elements_serial(type).getSize();

	total_nb_nodes = mesh.getNbNodes() + nb_nodes_to_check_serial;

	/// partition the mesh
	partition = new MeshPartitionScotch(mesh, spatial_dimension);
	debug::setDebugLevel(dblDump);
	partition->partitionate(psize);
	debug::setDebugLevel(dblInfo);
	}

	comm.broadcast(&nb_nodes_to_check_serial, 1, 0);
	comm.broadcast(&nb_elements_check_serial, 1, 0);

	SolidMechanicsModelCohesive model(mesh);

	model.initParallel(partition);
	model.initFull();

	model.limitInsertion(_x, -0.01, 0.01);
	model.insertIntrinsicElements();

	{
	comm.broadcast(&total_nb_nodes, 1, 0);

	Array<Int> nb_local_nodes(psize);
	nb_local_nodes.zero();

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (mesh.isLocalOrMasterNode(n))
	++nb_local_nodes(prank);
	}

	comm.allGather(nb_local_nodes.storage(), 1);

	UInt total_nb_nodes_parallel =
	std::accumulate(nb_local_nodes.begin(), nb_local_nodes.end(), 0);

	Array<UInt> global_nodes_list(total_nb_nodes_parallel);

	UInt first_global_node = std::accumulate(nb_local_nodes.begin(),
	nb_local_nodes.begin() + prank, 0);

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	if (mesh.isLocalOrMasterNode(n)) {
	global_nodes_list(first_global_node) = mesh.getNodeGlobalId(n);
	++first_global_node;
	}
	}

	comm.allGatherV(global_nodes_list.storage(), nb_local_nodes.storage());

	if (prank == 0)
	std::cout << "Maximum node index: "
	<< *(std::max_element(global_nodes_list.begin(),
	global_nodes_list.end()))
	<< std::endl;

	Array<UInt> repeated_nodes;
	repeated_nodes.resize(0);

	for (UInt n = 0; n < total_nb_nodes_parallel; ++n) {
	UInt appearances =
	std::count(global_nodes_list.begin() + n, global_nodes_list.end(),
	global_nodes_list(n));

	if (appearances > 1) {
	std::cout << "Node " << global_nodes_list(n) << " appears "
	<< appearances << " times" << std::endl;

	std::cout << " in position: " << n;

	repeated_nodes.push_back(global_nodes_list(n));

	UInt * node_position = global_nodes_list.storage() + n;

	for (UInt i = 1; i < appearances; ++i) {
	node_position =
	std::find(node_position + 1,
	global_nodes_list.storage() + total_nb_nodes_parallel,
	global_nodes_list(n));

	UInt current_index = node_position - global_nodes_list.storage();

	std::cout << ", " << current_index;
	}
	std::cout << std::endl << std::endl;
	}
	}

	for (UInt n = 0; n < mesh.getNbNodes(); ++n) {
	UInt global_node = mesh.getNodeGlobalId(n);

	if (std::find(repeated_nodes.begin(), repeated_nodes.end(),
	global_node) != repeated_nodes.end()) {
	std::cout << "Repeated global node " << global_node
	<< " corresponds to local node " << n << std::endl;
	}
	}

	if (total_nb_nodes != total_nb_nodes_parallel) {
	if (prank == 0) {
	std::cout << "Error: total number of nodes is wrong in parallel"
	<< std::endl;
	std::cout << "Serial: " << total_nb_nodes
	<< " Parallel: " << total_nb_nodes_parallel << std::endl;
	}
	finalize();
	return EXIT_FAILURE;
	}
	}

	model.updateResidual();

	model.setBaseName("intrinsic_parallel_tetrahedron");
	model.addDumpFieldVector("displacement");
	model.addDumpField("residual");
	model.addDumpField("partitions");
	model.dump();

	model.setBaseNameToDumper("cohesive elements",
	"cohesive_elements_parallel_tetrahedron");
	model.addDumpFieldVectorToDumper("cohesive elements", "displacement");
	model.dump("cohesive elements");

	/// find elements to displace
	ElementTypeMapArray<UInt> elements("elements", "");
	findElementsToDisplace(mesh, elements);

	UInt nb_elements_check = elements(type).getSize();
	comm.allReduce(&nb_elements_check, 1, _so_sum);

	if (nb_elements_check != nb_elements_check_serial) {
	if (prank == 0) {
	std::cout << "Error: number of elements to check is wrong" << std::endl;
	std::cout << "Serial: " << nb_elements_check_serial
	<< " Parallel: " << nb_elements_check << std::endl;
	}
	finalize();
	return EXIT_FAILURE;
	}

	/// find nodes to check
	Array<UInt> nodes_to_check;
	findNodesToCheck(mesh, elements, nodes_to_check, psize);

	Vector<Int> nodes_to_check_size(psize);
	nodes_to_check_size(prank) = nodes_to_check.getSize();
	comm.allGather(nodes_to_check_size.storage(), 1);

	UInt nodes_to_check_global_size = std::accumulate(
	nodes_to_check_size.storage(), nodes_to_check_size.storage() + psize, 0);

	if (nodes_to_check_global_size != nb_nodes_to_check_serial) {
	if (prank == 0) {
	std::cout << "Error: number of nodes to check is wrong in parallel"
	<< std::endl;
	std::cout << "Serial: " << nb_nodes_to_check_serial
	<< " Parallel: " << nodes_to_check_global_size << std::endl;
	}
	finalize();
	return EXIT_FAILURE;
	}

	/// rotate mesh
	Real angle = 1.;

	Matrix<Real> rotation(spatial_dimension, spatial_dimension);
	rotation.zero();
	rotation(0, 0) = std::cos(angle);
	rotation(0, 1) = std::sin(angle) * -1.;
	rotation(1, 0) = std::sin(angle);
	rotation(1, 1) = std::cos(angle);
	rotation(2, 2) = 1.;

	Vector<Real> increment_tmp(spatial_dimension);
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	increment_tmp(dim) = (dim + 1) * increment_constant;
	}

	Vector<Real> increment(spatial_dimension);
	increment.mul<false>(rotation, increment_tmp);

	Array<Real> & position = mesh.getNodes();
	Array<Real> position_tmp(position);

	Array<Real>::iterator<Vector<Real>> position_it =
	position.begin(spatial_dimension);
	Array<Real>::iterator<Vector<Real>> position_end =
	position.end(spatial_dimension);
	Array<Real>::iterator<Vector<Real>> position_tmp_it =
	position_tmp.begin(spatial_dimension);

	for (; position_it != position_end; ++position_it, ++position_tmp_it)
	position_it->mul<false>(rotation, *position_tmp_it);

	model.dump();
	model.dump("cohesive elements");

	updateDisplacement(model, elements, increment);

	Real theoretical_Ed = 0;

	Vector<Real> opening(spatial_dimension);
	Vector<Real> traction(spatial_dimension);
	Vector<Real> opening_old(spatial_dimension);
	Vector<Real> traction_old(spatial_dimension);

	opening.zero();
	traction.zero();
	opening_old.zero();
	traction_old.zero();

	Vector<Real> Dt(spatial_dimension);
	Vector<Real> Do(spatial_dimension);

	const Array<Real> & residual = model.getResidual();

	/// Main loop
	for (UInt s = 1; s <= max_steps; ++s) {

	model.updateResidual();

	opening += increment_tmp;
	if (checkTractions(model, opening, traction, rotation) \|\|
	checkEquilibrium(mesh, residual) \|\|
	checkResidual(residual, traction, nodes_to_check, rotation)) {
	finalize();
	return EXIT_FAILURE;
	}

	/// compute energy
	Do = opening;
	Do -= opening_old;

	Dt = traction_old;
	Dt += traction;

	theoretical_Ed += .5 * Do.dot(Dt);

	opening_old = opening;
	traction_old = traction;

	updateDisplacement(model, elements, increment);

	if (s % 10 == 0) {
	if (prank == 0)
	std::cout << "passing step " << s << "/" << max_steps << std::endl;
	model.dump();
	model.dump("cohesive elements");
	}
	}

	model.dump();
	model.dump("cohesive elements");

	Real Ed = model.getEnergy("dissipated");

	theoretical_Ed *= 4.;

	if (prank == 0)
	std::cout << "Dissipated energy: " << Ed
	<< ", theoretical value: " << theoretical_Ed << std::endl;

	if (!Math::are_float_equal(Ed, theoretical_Ed) \|\| std::isnan(Ed)) {

	if (prank == 0)
	std::cout << "Error: the dissipated energy is incorrect" << std::endl;

	finalize();
	return EXIT_FAILURE;
	}

	finalize();
	if (prank == 0)
	std::cout << "OK: Test passed!" << std::endl;
	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */

	void updateDisplacement(SolidMechanicsModelCohesive & model,
	const ElementTypeMapArray<UInt> & elements,
	Vector<Real> & increment) {

	UInt spatial_dimension = model.getSpatialDimension();
	Mesh & mesh = model.getFEEngine().getMesh();
	UInt nb_nodes = mesh.getNbNodes();

	Array<Real> & displacement = model.getDisplacement();
	Array<bool> update(nb_nodes);
	update.zero();

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	GhostType ghost_type = *gt;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
	Mesh::type_iterator last = mesh.lastType(spatial_dimension, ghost_type);

	for (; it != last; ++it) {
	ElementType type = *it;

	const Array<UInt> & elem = elements(type, ghost_type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);
	UInt nb_nodes_per_element = connectivity.getNbComponent();

	for (UInt el = 0; el < elem.getSize(); ++el) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	UInt node = connectivity(elem(el), n);
	if (!update(node)) {
	Vector<Real> node_disp(displacement.storage() +
	node * spatial_dimension,
	spatial_dimension);
	node_disp += increment;
	update(node) = true;
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	bool checkTractions(SolidMechanicsModelCohesive & model, Vector<Real> & opening,
	Vector<Real> & theoretical_traction,
	Matrix<Real> & rotation) {
	UInt spatial_dimension = model.getSpatialDimension();
	const Mesh & mesh = model.getMesh();

	const MaterialCohesive & mat_cohesive =
	dynamic_cast<const MaterialCohesive &>(model.getMaterial(1));

	Real sigma_c =
	mat_cohesive.getParam<RandomInternalField<Real, FacetInternalField>>(
	"sigma_c");
	const Real beta = mat_cohesive.getParam<Real>("beta");
	const Real G_cI = mat_cohesive.getParam<Real>("G_c");
	// Real G_cII = mat_cohesive.getParam<Real>("G_cII");
	const Real delta_0 = mat_cohesive.getParam<Real>("delta_0");
	const Real kappa = mat_cohesive.getParam<Real>("kappa");
	Real delta_c = 2 * G_cI / sigma_c;
	sigma_c *= delta_c / (delta_c - delta_0);

	Vector<Real> normal_opening(spatial_dimension);
	normal_opening.zero();
	normal_opening(0) = opening(0);
	Real normal_opening_norm = normal_opening.norm();

	Vector<Real> tangential_opening(spatial_dimension);
	tangential_opening.zero();
	for (UInt dim = 1; dim < spatial_dimension; ++dim)
	tangential_opening(dim) = opening(dim);

	Real tangential_opening_norm = tangential_opening.norm();

	Real beta2_kappa2 = beta * beta / kappa / kappa;
	Real beta2_kappa = beta * beta / kappa;

	Real delta = std::sqrt(tangential_opening_norm * tangential_opening_norm *
	beta2_kappa2 +
	normal_opening_norm * normal_opening_norm);

	delta = std::max(delta, delta_0);

	Real theoretical_damage = std::min(delta / delta_c, 1.);

	if (Math::are_float_equal(theoretical_damage, 1.))
	theoretical_traction.zero();
	else {
	theoretical_traction = tangential_opening;
	theoretical_traction *= beta2_kappa;
	theoretical_traction += normal_opening;
	theoretical_traction = sigma_c / delta (1. - theoretical_damage);
	}

	Vector<Real> theoretical_traction_rotated(spatial_dimension);
	theoretical_traction_rotated.mul<false>(rotation, theoretical_traction);

	// adjust damage
	theoretical_damage = std::max((delta - delta_0) / (delta_c - delta_0), 0.);
	theoretical_damage = std::min(theoretical_damage, 1.);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	GhostType ghost_type = *gt;
	Mesh::type_iterator it =
	mesh.firstType(spatial_dimension, ghost_type, _ek_cohesive);
	Mesh::type_iterator last =
	mesh.lastType(spatial_dimension, ghost_type, _ek_cohesive);

	for (; it != last; ++it) {
	ElementType type = *it;

	const Array<Real> & traction = mat_cohesive.getTraction(type, ghost_type);
	const Array<Real> & damage = mat_cohesive.getDamage(type, ghost_type);

	UInt nb_quad_per_el =
	model.getFEEngine("CohesiveFEEngine").getNbIntegrationPoints(type);
	UInt nb_element = model.getMesh().getNbElement(type, ghost_type);
	UInt tot_nb_quad = nb_element * nb_quad_per_el;

	for (UInt q = 0; q < tot_nb_quad; ++q) {
	for (UInt dim = 0; dim < spatial_dimension; ++dim) {
	if (!Math::are_float_equal(
	std::abs(theoretical_traction_rotated(dim)),
	std::abs(traction(q, dim)))) {
	std::cout << "Error: tractions are incorrect" << std::endl;
	return 1;
	}
	}

	if (ghost_type == _not_ghost)
	if (!Math::are_float_equal(theoretical_damage, damage(q))) {
	std::cout << "Error: damage is incorrect" << std::endl;
	return 1;
	}
	}
	}
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */

	void findNodesToCheck(const Mesh & mesh,
	const ElementTypeMapArray<UInt> & elements,
	Array<UInt> & nodes_to_check, Int psize) {

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	nodes_to_check.resize(0);

	Array<UInt> global_nodes_to_check;

	UInt spatial_dimension = mesh.getSpatialDimension();
	const Array<Real> & position = mesh.getNodes();

	UInt nb_nodes = position.getSize();

	Array<bool> checked_nodes(nb_nodes);
	checked_nodes.zero();

	Mesh::type_iterator it = mesh.firstType(spatial_dimension);
	Mesh::type_iterator last = mesh.lastType(spatial_dimension);

	for (; it != last; ++it) {
	ElementType type = *it;

	const Array<UInt> & elem = elements(type);
	const Array<UInt> & connectivity = mesh.getConnectivity(type);
	UInt nb_nodes_per_elem = connectivity.getNbComponent();

	for (UInt el = 0; el < elem.getSize(); ++el) {

	UInt element = elem(el);
	Vector<UInt> conn_el(connectivity.storage() + nb_nodes_per_elem * element,
	nb_nodes_per_elem);

	for (UInt n = 0; n < nb_nodes_per_elem; ++n) {
	UInt node = conn_el(n);
	if (std::abs(position(node, 0) - 0.) < 1.e-6 && !checked_nodes(node)) {
	checked_nodes(node) = true;
	nodes_to_check.push_back(node);
	global_nodes_to_check.push_back(mesh.getNodeGlobalId(node));
	}
	}
	}
	}

	std::vector<CommunicationRequest *> requests;

	for (Int p = prank + 1; p < psize; ++p) {
	requests.push_back(comm.asyncSend(global_nodes_to_check.storage(),
	global_nodes_to_check.getSize(), p,
	prank));
	}

	Array<UInt> recv_nodes;

	for (Int p = 0; p < prank; ++p) {
	CommunicationStatus status;
	comm.probe<UInt>(p, p, status);

	UInt recv_nodes_size = recv_nodes.getSize();
	recv_nodes.resize(recv_nodes_size + status.getSize());

	comm.receive(recv_nodes.storage() + recv_nodes_size, status.getSize(), p,
	p);
	}

	comm.waitAll(requests);
	comm.freeCommunicationRequest(requests);

	for (UInt i = 0; i < recv_nodes.getSize(); ++i) {
	Array<UInt>::iterator<UInt> node_position =
	std::find(global_nodes_to_check.begin(), global_nodes_to_check.end(),
	recv_nodes(i));

	if (node_position != global_nodes_to_check.end()) {
	UInt index = node_position - global_nodes_to_check.begin();
	nodes_to_check.erase(index);
	global_nodes_to_check.erase(index);
	}
	}
	}

	/* -------------------------------------------------------------------------- */

	bool checkEquilibrium(const Mesh & mesh, const Array<Real> & residual) {

	UInt spatial_dimension = residual.getNbComponent();

	Vector<Real> residual_sum(spatial_dimension);
	residual_sum.zero();

	Array<Real>::const_iterator<Vector<Real>> res_it =
	residual.begin(spatial_dimension);

	for (UInt n = 0; n < residual.getSize(); ++n, ++res_it) {
	if (mesh.isLocalOrMasterNode(n))
	residual_sum += *res_it;
	}

	const auto & comm = Communicator::getStaticCommunicator();
	comm.allReduce(residual_sum.storage(), spatial_dimension, _so_sum);

	for (UInt s = 0; s < spatial_dimension; ++s) {
	if (!Math::are_float_equal(residual_sum(s), 0.)) {

	if (comm.whoAmI() == 0)
	std::cout << "Error: system is not in equilibrium!" << std::endl;

	return 1;
	}
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */

	bool checkResidual(const Array<Real> & residual, const Vector<Real> & traction,
	const Array<UInt> & nodes_to_check,
	const Matrix<Real> & rotation) {

	UInt spatial_dimension = residual.getNbComponent();

	Vector<Real> total_force(spatial_dimension);
	total_force.zero();

	for (UInt n = 0; n < nodes_to_check.getSize(); ++n) {
	UInt node = nodes_to_check(n);

	Vector<Real> res(residual.storage() + node * spatial_dimension,
	spatial_dimension);

	total_force += res;
	}

	const auto & comm = Communicator::getStaticCommunicator();
	comm.allReduce(total_force.storage(), spatial_dimension, _so_sum);

	Vector<Real> theoretical_total_force(spatial_dimension);
	theoretical_total_force.mul<false>(rotation, traction);
	theoretical_total_force = -1 2 * 2;

	for (UInt s = 0; s < spatial_dimension; ++s) {
	if (!Math::are_float_equal(total_force(s), theoretical_total_force(s))) {

	if (comm.whoAmI() == 0)
	std::cout << "Error: total force isn't correct!" << std::endl;

	return 1;
	}
	}

	return 0;
	}

	/* -------------------------------------------------------------------------- */

	void findElementsToDisplace(const Mesh & mesh,
	ElementTypeMapArray<UInt> & elements) {
	UInt spatial_dimension = mesh.getSpatialDimension();

	mesh.initElementTypeMapArray(elements, 1, spatial_dimension);

	Vector<Real> bary(spatial_dimension);

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	GhostType ghost_type = *gt;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
	Mesh::type_iterator last = mesh.lastType(spatial_dimension, ghost_type);

	for (; it != last; ++it) {
	ElementType type = *it;

	Array<UInt> & elem = elements(type, ghost_type);
	UInt nb_element = mesh.getNbElement(type, ghost_type);

	for (UInt el = 0; el < nb_element; ++el) {
	mesh.getBarycenter(el, type, bary.storage(), ghost_type);
	if (bary(0) > 0.0001)
	elem.push_back(el);
	}
	}
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_element_matrix.cc b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_element_matrix.cc
	index 262ad1a44..5d8ea800d 100644
	--- a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_element_matrix.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_element_matrix.cc
	@@ -1,100 +1,100 @@
	/**
	* @file test_embedded_element_matrix.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Wed Mar 25 2015
	* @date last modification: Wed Sep 12 2018
	*
	* @brief test of the class EmbeddedInterfaceModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "embedded_interface_model.hh"
	#include "sparse_matrix_aij.hh"
	#include "sparse_solver.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	debug::setDebugLevel(dblWarning);
	initialize("embedded_element.dat", argc, argv);

	constexpr UInt dim = 2;
	constexpr ElementType type = _segment_2;
	const Real height = 0.4;

	Mesh mesh(dim);
	mesh.read("triangle.msh");

	Mesh reinforcement_mesh(dim, "reinforcement_mesh");
	auto & nodes = reinforcement_mesh.getNodes();
	nodes.push_back(Vector<Real>({0, height}));
	nodes.push_back(Vector<Real>({1, height}));

	reinforcement_mesh.addConnectivityType(type);
	auto & connectivity = reinforcement_mesh.getConnectivity(type);
	connectivity.push_back(Vector<UInt>({0, 1}));

	Array<std::string> names_vec(1, 1, "reinforcement", "reinforcement_names");
	reinforcement_mesh.getElementalData<std::string>("physical_names")
	.alloc(1, 1, type);
	reinforcement_mesh.getData<std::string>("physical_names")(type).copy(
	names_vec);

	EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);

	model.initFull(_analysis_method = _static);

	if (model.getInterfaceMesh().getNbElement(type) != 1)
	return EXIT_FAILURE;

	if (model.getInterfaceMesh().getSpatialDimension() != 2)
	return EXIT_FAILURE;

	try { // matrix should be singular
	model.solveStep();
	} catch (debug::SingularMatrixException & e) {
	std::cerr << "Matrix is singular, relax, everything is fine :)"
	<< std::endl;
	} catch (debug::Exception & e) {
	std::cerr << "Unexpceted error: " << e.what() << std::endl;
	throw e;
	}

	SparseMatrixAIJ & K =
	dynamic_cast<SparseMatrixAIJ &>(model.getDOFManager().getMatrix("K"));
	K.saveMatrix("stiffness.mtx");

	Math::setTolerance(1e-8);

	// Testing the assembled stiffness matrix
	if (!Math::are_float_equal(K(0, 0), 1. - height) \|\|
	!Math::are_float_equal(K(0, 2), height - 1.) \|\|
	!Math::are_float_equal(K(2, 0), height - 1.) \|\|
	!Math::are_float_equal(K(2, 2), 1. - height))
	return EXIT_FAILURE;

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model.cc b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model.cc
	index d09ed6a04..f70af8382 100644
	--- a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model.cc
	@@ -1,109 +1,109 @@
	/**
	* @file test_embedded_interface_model.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Wed Mar 25 2015
	* @date last modification: Wed Feb 06 2019
	*
	* @brief Embedded model test based on potential energy
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <iostream>

	#include "aka_common.hh"
	#include "embedded_interface_model.hh"
	#include "sparse_matrix.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	debug::setDebugLevel(dblWarning);
	initialize("material.dat", argc, argv);

	UInt dim = 2;
	Math::setTolerance(1e-7);

	// Mesh here is a 1x1 patch
	Mesh mesh(dim);
	mesh.read("embedded_mesh.msh");

	Array<Real> nodes_vec(2, dim, "reinforcement_nodes");
	nodes_vec.storage()[0] = 0;
	nodes_vec.storage()[1] = 0.5;
	nodes_vec.storage()[2] = 1;
	nodes_vec.storage()[3] = 0.5;

	Array<UInt> conn_vec(1, 2, "reinforcement_connectivity");
	conn_vec.storage()[0] = 0;
	conn_vec.storage()[1] = 1;

	Array<std::string> names_vec(1, 1, "reinforcement", "reinforcement_names");

	Mesh reinforcement_mesh(dim, "reinforcement_mesh");
	reinforcement_mesh.getNodes().copy(nodes_vec);
	reinforcement_mesh.addConnectivityType(_segment_2);
	reinforcement_mesh.getConnectivity(_segment_2).copy(conn_vec);
	reinforcement_mesh.getElementalData<std::string>("physical_names")
	.alloc(1, 1, _segment_2);
	reinforcement_mesh.getData<std::string>("physical_names")(_segment_2)
	.copy(names_vec);

	EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);
	model.initFull(_analysis_method = _static);

	Array<Real> & nodes = mesh.getNodes();
	Array<Real> & forces = model.getExternalForce();
	Array<bool> & bound = model.getBlockedDOFs();

	forces(2, 0) = -250;
	forces(5, 0) = -500;
	forces(8, 0) = -250;

	for (UInt i = 0; i < mesh.getNbNodes(); i++) {
	if (Math::are_float_equal(nodes(i, 0), 0.))
	bound(i, 0) = true;
	if (Math::are_float_equal(nodes(i, 1), 0.))
	bound(i, 1) = true;
	}

	model.addDumpFieldVector("displacement");
	model.addDumpFieldTensor("stress");

	model.setBaseNameToDumper("reinforcement", "reinforcement");
	model.addDumpFieldTensorToDumper("reinforcement", "stress_embedded");

	model.solveStep();

	model.getDOFManager().getMatrix("K").saveMatrix("matrix_test");

	model.dump();

	Real pot_energy = model.getEnergy("potential");

	if (std::abs(pot_energy - 7.37343e-06) > 1e-5)
	return EXIT_FAILURE;

	finalize();
	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
	index 157677a5b..448d2160e 100644
	--- a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
	@@ -1,236 +1,236 @@
	/**
	* @file test_embedded_interface_model_prestress.cc
	*
	* @author Zineb Fouad <zineb.fouad@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Tue Apr 28 2015
	* @date last modification: Fri Jun 14 2019
	*
	* @brief Embedded model test for prestressing (bases on stress norm)
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "aka_common.hh"
	#include "embedded_interface_model.hh"

	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	#define YG 0.483644859
	#define I_eq 0.012488874
	#define A_eq (1e-2 + 1. / 7. * 1.)

	/* -------------------------------------------------------------------------- */

	struct StressSolution : public BC::Neumann::FromHigherDim {
	Real M;
	Real I;
	Real yg;
	Real pre_stress;

	StressSolution(UInt dim, Real M, Real I, Real yg = 0, Real pre_stress = 0)
	: BC::Neumann::FromHigherDim(Matrix<Real>(dim, dim)), M(M), I(I), yg(yg),
	pre_stress(pre_stress) {}

	virtual ~StressSolution() {}

	void operator()(const IntegrationPoint & /quad_point/, Vector<Real> & dual,
	const Vector<Real> & coord,
	const Vector<Real> & normals) const {
	UInt dim = coord.size();

	if (dim < 2)
	AKANTU_ERROR("Solution not valid for 1D");

	Matrix<Real> stress(dim, dim);
	stress.zero();
	stress(0, 0) = this->stress(coord(1));
	dual.mul<false>(stress, normals);
	}

	inline Real stress(Real height) const {
	return -M / I * (height - yg) + pre_stress;
	}

	inline Real neutral_axis() const { return -I * pre_stress / M + yg; }
	};

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("prestress.dat", argc, argv);
	debug::setDebugLevel(dblError);

	Math::setTolerance(1e-6);

	const UInt dim = 2;

	/* --------------------------------------------------------------------------
	*/

	Mesh mesh(dim);
	mesh.read("embedded_mesh_prestress.msh");
	// mesh.createGroupsFromMeshData<std::string>("physical_names");

	Mesh reinforcement_mesh(dim, "reinforcement_mesh");
	try {
	reinforcement_mesh.read("embedded_mesh_prestress_reinforcement.msh");
	} catch (debug::Exception & e) {
	}

	// reinforcement_mesh.createGroupsFromMeshData<std::string>("physical_names");

	EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);
	model.initFull(EmbeddedInterfaceModelOptions(_static));

	/* --------------------------------------------------------------------------
	*/
	/* Computation of analytical residual */
	/* --------------------------------------------------------------------------
	*/

	/*
	* q = 1000 N/m
	* L = 20 m
	* a = 1 m
	*/

	Real steel_area = model.getMaterial("reinforcement").get("area");
	Real pre_stress = model.getMaterial("reinforcement").get("pre_stress");
	Real stress_norm = 0.;

	StressSolution concrete_stress = nullptr, steel_stress = nullptr;

	Real pre_force = pre_stress * steel_area;
	Real pre_moment = -pre_force * (YG - 0.25);
	Real neutral_axis = YG - I_eq / A_eq * pre_force / pre_moment;

	concrete_stress = new StressSolution(dim, pre_moment, 7. * I_eq, YG,
	-pre_force / (7. * A_eq));
	steel_stress = new StressSolution(dim, pre_moment, I_eq, YG,
	pre_stress - pre_force / A_eq);

	stress_norm =
	std::abs(concrete_stress->stress(1)) * (1 - neutral_axis) * 0.5 +
	std::abs(concrete_stress->stress(0)) * neutral_axis * 0.5 +
	std::abs(steel_stress->stress(0.25)) * steel_area;

	model.applyBC(*concrete_stress, "XBlocked");
	auto end_node = *mesh.getElementGroup("EndNode").getNodeGroup().begin();

	Vector<Real> end_node_force = model.getExternalForce().begin(dim)[end_node];
	end_node_force(0) += steel_stress->stress(0.25) * steel_area;

	Array<Real> analytical_residual(mesh.getNbNodes(), dim,
	"analytical_residual");
	analytical_residual.copy(model.getExternalForce());
	model.getExternalForce().zero();

	delete concrete_stress;
	delete steel_stress;

	/* --------------------------------------------------------------------------
	*/

	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "XBlocked");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "YBlocked");

	try {
	model.solveStep();
	} catch (debug::Exception & e) {
	std::cerr << e.what() << std::endl;
	return EXIT_FAILURE;
	}

	/* --------------------------------------------------------------------------
	*/
	/* Computation of FEM residual norm */
	/* --------------------------------------------------------------------------
	*/

	ElementGroup & xblocked = mesh.getElementGroup("XBlocked");
	NodeGroup & boundary_nodes = xblocked.getNodeGroup();
	NodeGroup::const_node_iterator nodes_it = boundary_nodes.begin(),
	nodes_end = boundary_nodes.end();
	model.assembleInternalForces();
	Array<Real> residual(mesh.getNbNodes(), dim, "my_residual");
	residual.copy(model.getInternalForce());
	residual -= model.getExternalForce();

	auto com_res = residual.begin(dim);
	auto position = mesh.getNodes().begin(dim);

	Real res_sum = 0.;
	UInt lower_node = -1;
	UInt upper_node = -1;
	Real lower_dist = 1;
	Real upper_dist = 1;

	for (; nodes_it != nodes_end; ++nodes_it) {
	UInt node_number = *nodes_it;
	const Vector<Real> res = com_res[node_number];
	const Vector<Real> pos = position[node_number];

	if (!Math::are_float_equal(pos(1), 0.25)) {
	if ((std::abs(pos(1) - 0.25) < lower_dist) && (pos(1) < 0.25)) {
	lower_dist = std::abs(pos(1) - 0.25);
	lower_node = node_number;
	}

	if ((std::abs(pos(1) - 0.25) < upper_dist) && (pos(1) > 0.25)) {
	upper_dist = std::abs(pos(1) - 0.25);
	upper_node = node_number;
	}
	}

	for (UInt i = 0; i < dim; i++) {
	if (!Math::are_float_equal(pos(1), 0.25)) {
	res_sum += std::abs(res(i));
	}
	}
	}

	const Vector<Real> upper_res = com_res[upper_node],
	lower_res = com_res[lower_node];
	const Vector<Real> end_node_res = com_res[end_node];
	Vector<Real> delta = upper_res - lower_res;
	delta *= lower_dist / (upper_dist + lower_dist);
	Vector<Real> concrete_residual = lower_res + delta;
	Vector<Real> steel_residual = end_node_res - concrete_residual;

	for (UInt i = 0; i < dim; i++) {
	res_sum += std::abs(concrete_residual(i));
	res_sum += std::abs(steel_residual(i));
	}

	Real relative_error = std::abs(res_sum - stress_norm) / stress_norm;

	if (relative_error > 1e-3) {
	std::cerr << "Relative error = " << relative_error << std::endl;
	return EXIT_FAILURE;
	}

	finalize();
	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_kinetic_energy.cc b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_kinetic_energy.cc
	index 392f65c60..07fe244e6 100644
	--- a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_kinetic_energy.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_kinetic_energy.cc
	@@ -1,91 +1,91 @@
	/**
	* @file test_solid_mechanics_model_kinetic_energy.cc
	*
	* @author Tobias Brink <tobias.brink@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Mon Feb 26 2018
	*
	* @brief test kinetic energy
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	* @section description
	*
	* This test uses a linear elastic material with density = 1, Young's modulus =
	* 1, and Poisson's ratio = 0 and imposes a uniform velocity of 1. The volume of
	* the mesh is 1 and thus we have a mass of 1 and therefore a kinetic energy of
	* 0.5mv² = 0.5. The kind of constitutive law should not matter for this test,
	* so we use linear elastic. We perform 5 timesteps and check the solution every
	* time.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "../test_solid_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	void test_body(SolidMechanicsModel & model, AnalysisMethod analysis_method) {
	const auto spatial_dimension = model.getSpatialDimension();

	getStaticParser().parse("test_solid_mechanics_model_"
	"kinetic_energy_material.dat");

	model.initFull(_analysis_method = analysis_method);
	model.assembleMassLumped();

	/// impose initial velocity of 1, it should remain constant
	auto & velo = model.getVelocity();

	for (auto && velov : make_view(velo, spatial_dimension)) {
	velov(_x) = 1;
	}

	/// set up timestep
	auto time_step = model.getStableTimeStep() * 0.8;
	model.setTimeStep(time_step);

	/// run five times and look at the kinetic energy
	for (uint i = 0; i < 5; ++i) {

	/// make a step
	model.solveStep();

	/// compare energy to analytical solution
	const Real E_ref = 0.5;
	auto E_kin = model.getEnergy("kinetic");

	EXPECT_NEAR(E_ref, E_kin, 1e-8);
	}
	}

	TYPED_TEST(TestSMMFixture, KineticEnergyImplicit) {
	test_body(*(this->model), _implicit_dynamic);
	}

	TYPED_TEST(TestSMMFixture, KineticEnergyExplicit) {
	test_body(*(this->model), _explicit_lumped_mass);
	}

	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_linear_elastic_potential_energy.cc b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_linear_elastic_potential_energy.cc
	index f838eae4b..a3f8704a1 100644
	--- a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_linear_elastic_potential_energy.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_linear_elastic_potential_energy.cc
	@@ -1,118 +1,118 @@
	/**
	* @file test_solid_mechanics_model_linear_elastic_potential_energy.cc
	*
	* @author Tobias Brink <tobias.brink@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Sun Mar 11 2018
	*
	* @brief test potential energy of the linear elasticity model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	* @section description
	*
	* This test uses a linear elastic material with density = 1, Young's
	* modulus = 1, and Poisson's ratio = 0 and applies a linear
	* displacement from 0 to ε in x direction. The resulting potential
	* energy density should be 0.5Yε² = ε²/2. Since the mesh always has
	* a volume of 1, the energy density equals the total energy. We test
	* 3 different strains.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "../test_solid_mechanics_model_fixture.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	TYPED_TEST(TestSMMFixture, LinearElasticPotentialEnergy) {
	const auto spatial_dimension = this->spatial_dimension;

	this->initModel("test_solid_mechanics_model_linear_elastic_"
	"potential_energy_material.dat",
	_static);

	const auto & lower = this->mesh->getLowerBounds();
	const auto & upper = this->mesh->getUpperBounds();
	auto length = upper(_x) - lower(_x);

	const auto & pos = this->mesh->getNodes();
	auto & disp = this->model->getDisplacement();
	auto & boun = this->model->getBlockedDOFs();

	std::vector<Real> strains{0.0, 0.1, 0.2, 0.3};

	for (auto && eps : strains) {
	/// boundary conditions
	for (auto && pair : zip(make_view(pos, spatial_dimension),
	make_view(disp, spatial_dimension),
	make_view(boun, spatial_dimension))) {
	const auto & posv = std::get<0>(pair);
	auto & dispv = std::get<1>(pair);
	auto & bounv = std::get<2>(pair);
	auto reduced_x = (posv(_x) - lower(_x)) / length;
	dispv(_x) = reduced_x * eps;
	bounv(_x) = true;

	if (posv(_x) < (lower(_x) + 1e-6)) {
	if ((spatial_dimension > 1) and (posv(_y) < (lower(_y) + 1e-6))) {
	bounv(_y) = true;

	if ((spatial_dimension > 2) and (posv(_z) < (lower(_z) + 1e-6))) {
	bounv(_z) = true;
	}
	}
	}
	}

	if (this->dump_paraview) {
	this->model->dump();
	}
	/// "solve" a step (solution is imposed)
	try {
	this->model->solveStep();
	} catch (...) {
	const auto & A = this->model->getDOFManager().getMatrix("J");
	auto prank = this->mesh->getCommunicator().whoAmI();
	A.saveMatrix("solver_mumps" + std::to_string(prank) + ".mtx");
	throw;
	}

	if (this->dump_paraview) {
	const auto & A = this->model->getDOFManager().getMatrix("J");
	auto prank = this->mesh->getCommunicator().whoAmI();
	A.saveMatrix("solver_mumps" + std::to_string(prank) + ".mtx");
	}

	/// compare energy to analytical solution
	auto E_ref = 0.5 * eps * eps;
	auto E_pot = this->model->getEnergy("potential");

	EXPECT_NEAR(E_ref, E_pot, 1e-8);
	}
	}

	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_dynamics.cc b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_dynamics.cc
	index b20aa2d68..8af11bee3 100644
	--- a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_dynamics.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_dynamics.cc
	@@ -1,159 +1,159 @@
	/**
	* @file test_solid_mechanics_model_work_dynamics.cc
	*
	* @author Tobias Brink <tobias.brink@epfl.ch>
	*
	* @date creation: Fri Dec 15 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test work in dynamic simulations
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	* @section description
	*
	* Assuming that the kinetic energy and the potential energy of the
	* linear elastic material are bug free, the work in a dynamic
	* simulation must equal the change in internal energy (first law of
	* thermodynamics). Work in dynamics is an infinitesimal work Fds,
	* thus we need to integrate it and compare at the end. In this test,
	* we use one Dirichlet boundary condition (with u = 0.0, 0.01, and
	* -0.01) and one Neumann boundary condition for F on the opposite
	* side. Then we do a few steps to get reference energies for work and
	* internal energy. After more steps, the change in both work and
	* internal energy must be equal.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "../test_solid_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	template <typename type_>
	class TestSMMFixtureWorkDynamic : public TestSMMFixture<type_> {
	public:
	void SetUp() override {
	this->mesh_file =
	"../../patch_tests/data/bar" + std::to_string(this->type) + ".msh";
	TestSMMFixture<type_>::SetUp();

	getStaticParser().parse("test_solid_mechanics_model_"
	"work_material.dat");

	/// model initialization
	this->model->initFull();

	/// Create a node group for Neumann BCs.
	auto & apply_force_grp = this->mesh->createNodeGroup("apply_force");
	auto & fixed_grp = this->mesh->createNodeGroup("fixed");

	const auto & pos = this->mesh->getNodes();
	const auto & lower = this->mesh->getLowerBounds();
	const auto & upper = this->mesh->getUpperBounds();

	UInt i = 0;
	for (auto && posv : make_view(pos, this->spatial_dimension)) {
	if (posv(_x) > upper(_x) - 1e-6) {
	apply_force_grp.add(i);
	} else if (posv(_x) < lower(_x) + 1e-6) {
	fixed_grp.add(i);
	}
	++i;
	}

	this->mesh->createElementGroupFromNodeGroup("el_apply_force", "apply_force",
	this->spatial_dimension - 1);
	this->mesh->createElementGroupFromNodeGroup("el_fixed", "fixed",
	this->spatial_dimension - 1);

	Vector<Real> surface_traction(this->spatial_dimension);
	surface_traction(_x) = 0.5;
	if (this->spatial_dimension == 1) {
	// TODO: this is a hack to work
	// around non-implemented
	// BC::Neumann::FromTraction for 1D
	auto & force = this->model->getExternalForce();

	for (auto && pair : zip(make_view(pos, this->spatial_dimension),
	make_view(force, this->spatial_dimension))) {
	auto & posv = std::get<0>(pair);
	auto & forcev = std::get<1>(pair);
	if (posv(_x) > upper(_x) - 1e-6) {
	forcev(_x) = surface_traction(_x);
	}
	}
	} else {
	this->model->applyBC(BC::Neumann::FromTraction(surface_traction),
	"el_apply_force");
	}

	/// set up timestep
	auto time_step = this->model->getStableTimeStep() * 0.1;
	this->model->setTimeStep(time_step);
	}
	};

	TYPED_TEST_SUITE(TestSMMFixtureWorkDynamic, gtest_element_types, );

	/* TODO: this is currently disabled for terrible results and performance
	TYPED_TEST(TestSMMFixtureBar, WorkImplicit) {
	test_body((this->model), (this->mesh), _implicit_dynamic, 500);
	}
	*/
	// model.assembleMassLumped();
	TYPED_TEST(TestSMMFixtureWorkDynamic, WorkExplicit) {
	/// Do the sim
	std::vector<Real> displacements{0.00, 0.01, -0.01};

	for (auto && u : displacements) {
	this->model->applyBC(BC::Dirichlet::FixedValue(u, _x), "el_fixed");

	// First, "equilibrate" a bit to get a reference state of total
	// energy and work. This is needed when we have a Dirichlet with
	// finite displacement on one side.
	for (UInt i = 0; i < 25; ++i) {
	this->model->solveStep();
	}
	// Again, work reported by Akantu is infinitesimal (dW) and we
	// need to integrate a while to get a decent value.
	double Etot0 =
	this->model->getEnergy("potential") + this->model->getEnergy("kinetic");
	double W = 0.0;
	for (UInt i = 0; i < 200; ++i) {
	/// Solve.
	this->model->solveStep();

	const auto dW = this->model->getEnergy("external work");

	W += dW;
	}
	// Finally check.
	const auto Epot = this->model->getEnergy("potential");
	const auto Ekin = this->model->getEnergy("kinetic");

	EXPECT_NEAR(W, Ekin + Epot - Etot0, 5e-2);
	// Sadly not very exact for such a coarse mesh.
	}
	}
	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_quasistatic.cc b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_quasistatic.cc
	index 968309099..77bfe11b8 100644
	--- a/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_quasistatic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_energies/test_solid_mechanics_model_work_quasistatic.cc
	@@ -1,147 +1,147 @@
	/**
	* @file test_solid_mechanics_model_work_quasistatic.cc
	*
	* @author Tobias Brink <tobias.brink@epfl.ch>
	*
	* @date creation: Wed Nov 29 2017
	* @date last modification: Wed Dec 04 2019
	*
	* @brief test work in quasistatic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	* @section description
	*
	* Assuming that the potential energy of a linear elastic material
	* works correctly, the work in a static simulation must equal the
	* potential energy of the material. Since the work in static is an
	* infinitesimal work Fds, we need to integrate by increasing F from 0
	* to F_final in steps. This test uses one Dirichlet boundary
	* condition (with u = 0.0, 0.1, and -0.1) and one Neumann boundary
	* condition for F on the opposite side. The final work must be the
	* same for all u.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "../test_solid_mechanics_model_fixture.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	TYPED_TEST(TestSMMFixture, WorkQuasistatic) {
	const auto spatial_dimension = this->spatial_dimension;

	getStaticParser().parse("test_solid_mechanics_model_"
	"work_material.dat");

	/// model initialization
	this->model->initFull(_analysis_method = _static);

	/// Create a node group for Neumann BCs.
	auto & apply_force_grp = this->mesh->createNodeGroup("apply_force");
	auto & fixed_grp = this->mesh->createNodeGroup("fixed");

	const auto & pos = this->mesh->getNodes();
	auto & flags = this->model->getBlockedDOFs();
	auto & lower = this->mesh->getLowerBounds();
	auto & upper = this->mesh->getUpperBounds();

	UInt i = 0;
	for (auto && data : zip(make_view(pos, spatial_dimension),
	make_view(flags, spatial_dimension))) {
	const auto & posv = std::get<0>(data);
	auto & flag = std::get<1>(data);
	if (posv(_x) > upper(_x) - 1e-6) {
	apply_force_grp.add(i);
	} else if (posv(_x) < lower(_x) + 1e-6) {
	fixed_grp.add(i);

	if ((spatial_dimension > 1) and (posv(_y) < lower(_y) + 1e-6)) {
	flag(_y) = true;
	if ((spatial_dimension > 2) and (posv(_z) < lower(_z) + 1e-6)) {
	flag(_z) = true;
	}
	}
	}
	++i;
	}

	this->mesh->createElementGroupFromNodeGroup("el_apply_force", "apply_force",
	spatial_dimension - 1);
	this->mesh->createElementGroupFromNodeGroup("el_fixed", "fixed",
	spatial_dimension - 1);

	std::vector<Real> displacements{0.0, 0.1, -0.1};
	for (auto && u : displacements) {
	this->model->applyBC(BC::Dirichlet::FixedValue(u, _x), "el_fixed");

	Vector<Real> surface_traction(spatial_dimension);
	Real work = 0.0;
	Real Epot;
	static const UInt N = 100;
	for (UInt i = 0; i <= N; ++i) {
	this->model->getExternalForce().zero(); // reset external forces to zero

	surface_traction(_x) = (1.0 * i) / N;

	if (spatial_dimension == 1) {
	// \TODO: this is a hack to work
	// around non-implemented
	// BC::Neumann::FromTraction for 1D
	auto & force = this->model->getExternalForce();
	for (auto && pair : zip(make_view(pos, spatial_dimension),
	make_view(force, spatial_dimension))) {
	auto & posv = std::get<0>(pair);
	auto & forcev = std::get<1>(pair);
	if (posv(_x) > upper(_x) - 1e-6) {
	forcev(_x) = surface_traction(_x);
	}
	}
	} else {
	this->model->applyBC(BC::Neumann::FromTraction(surface_traction),
	"el_apply_force");
	}

	/// Solve.
	this->model->solveStep();

	Epot = this->model->getEnergy("potential");
	// In static, this is infinitesimal work!
	auto Fds = this->model->getEnergy("external work");

	work += Fds; // integrate

	/// Check that no work was done for zero force.
	if (i == 0) {
	EXPECT_NEAR(work, 0.0, 1e-12);
	}
	}

	// Due to the finite integration steps, we make a rather large error
	// in our work integration, thus the allowed delta is 1e-2.
	EXPECT_NEAR(work, Epot, 1e-2);
	}
	}

	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_material_selector.cc b/test/test_model/test_solid_mechanics_model/test_material_selector.cc
	index 2a452b25b..8f6c15ea0 100644
	--- a/test/test_model/test_solid_mechanics_model/test_material_selector.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_material_selector.cc
	@@ -1,64 +1,64 @@
	/**
	* @file test_material_selector.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Fri May 01 2015
	* @date last modification: Tue Dec 05 2017
	*
	* @brief Test for material selector
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "aka_common.hh"
	#include "solid_mechanics_model.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material_selector.dat", argc, argv);

	Math::setTolerance(1e-8);

	Mesh mesh(1);
	mesh.read("material_selector.msh");

	SolidMechanicsModel model(mesh);
	auto && selector = std::make_shared<MeshDataMaterialSelector<std::string>>(
	"physical_names", model);
	model.setMaterialSelector(selector);

	model.initFull();

	Material & chocolate = model.getMaterial("chocolate");
	Material & chewing_gum = model.getMaterial("chewing-gum");
	Material & candy = model.getMaterial("candy");

	UInt chocolate_element = chocolate.getElementFilter(_segment_2)(0, 0);
	UInt chewing_gum_element = chewing_gum.getElementFilter(_segment_2)(0, 0);
	UInt candy_element = candy.getElementFilter(_segment_2)(0, 0);

	if (chocolate_element != 0 \|\| chewing_gum_element != 1 \|\| candy_element != 2)
	return EXIT_FAILURE;

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.cc b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.cc
	index 178c7fe7c..67cf644b9 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.cc
	@@ -1,107 +1,107 @@
	/**
	* @file local_material_damage.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri May 03 2019
	*
	* @brief Specialization of the material class for the damage material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "local_material_damage.hh"
	#include "solid_mechanics_model.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	LocalMaterialDamage::LocalMaterialDamage(SolidMechanicsModel & model,
	const ID & id)
	: Material(model, id), damage("damage", *this) {
	AKANTU_DEBUG_IN();

	this->registerParam("E", E, 0., _pat_parsable, "Young's modulus");
	this->registerParam("nu", nu, 0.5, _pat_parsable, "Poisson's ratio");
	this->registerParam("lambda", lambda, _pat_readable,
	"First Lamé coefficient");
	this->registerParam("mu", mu, _pat_readable, "Second Lamé coefficient");
	this->registerParam("kapa", kpa, _pat_readable, "Bulk coefficient");
	this->registerParam("Yd", Yd, 50., _pat_parsmod);
	this->registerParam("Sd", Sd, 5000., _pat_parsmod);

	damage.initialize(1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::initMaterial() {
	AKANTU_DEBUG_IN();
	Material::initMaterial();

	lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
	mu = E / (2 * (1 + nu));
	kpa = lambda + 2. / 3. * mu;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::computeStress(ElementType el_type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	auto dam = damage(el_type, ghost_type).begin();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type);

	computeStressOnQuad(grad_u, sigma, *dam);
	++dam;

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void LocalMaterialDamage::computePotentialEnergy(ElementType el_type) {
	AKANTU_DEBUG_IN();

	Material::computePotentialEnergy(el_type);

	Real * epot = potential_energy(el_type).storage();

	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, _not_ghost);
	computePotentialEnergyOnQuad(grad_u, sigma, *epot);
	epot++;
	MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.hh b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.hh
	index f2be79e3a..685a724a0 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage.hh
	@@ -1,127 +1,127 @@
	/**
	* @file local_material_damage.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri May 03 2019
	*
	* @brief Material isotropic elastic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_LOCAL_MATERIAL_DAMAGE_HH_
	#define AKANTU_LOCAL_MATERIAL_DAMAGE_HH_

	namespace akantu {

	class LocalMaterialDamage : public Material {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	LocalMaterialDamage(SolidMechanicsModel & model, const ID & id = "");

	virtual ~LocalMaterialDamage(){};

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	void initMaterial();

	/// constitutive law for all element of a type
	void computeStress(ElementType el_type, GhostType ghost_type = _not_ghost);

	/// constitutive law for a given quadrature point
	inline void computeStressOnQuad(Matrix<Real> & grad_u, Matrix<Real> & sigma,
	Real & damage);

	/// compute tangent stiffness
	virtual void computeTangentStiffness(__attribute__((unused))
	ElementType el_type,
	__attribute__((unused))
	Array<Real> & tangent_matrix,
	__attribute__((unused))
	GhostType ghost_type = _not_ghost){};

	/// compute the potential energy for all elements
	void computePotentialEnergy(ElementType el_type);

	/// compute the potential energy for on element
	inline void computePotentialEnergyOnQuad(Matrix<Real> & grad_u,
	Matrix<Real> & sigma, Real & epot);

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:
	/// compute the celerity of wave in the material
	inline Real getCelerity(const Element & element) const;

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Damage, damage, Real);

	private:
	/// the young modulus
	Real E;

	/// Poisson coefficient
	Real nu;

	/// First Lamé coefficient
	Real lambda;

	/// Second Lamé coefficient (shear modulus)
	Real mu;

	/// resistance to damage
	Real Yd;

	/// damage threshold
	Real Sd;

	/// Bulk modulus
	Real kpa;

	/// damage internal variable
	InternalField<Real> damage;
	};

	/* -------------------------------------------------------------------------- */
	/* inline functions */
	/* -------------------------------------------------------------------------- */
	#include "local_material_damage_inline_impl.hh"

	} // namespace akantu

	#endif /* AKANTU_LOCAL_MATERIAL_DAMAGE_HH_ */
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage_inline_impl.hh b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage_inline_impl.hh
	index 62bee5ea5..53cf33433 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage_inline_impl.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/local_material_damage_inline_impl.hh
	@@ -1,80 +1,80 @@
	/**
	* @file local_material_damage_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Sep 11 2017
	*
	* @brief Implementation of the inline functions of the material damage
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	inline void LocalMaterialDamage::computeStressOnQuad(Matrix<Real> & grad_u,
	Matrix<Real> & sigma,
	Real & dam) {

	Real trace = grad_u.trace();

	/// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
	/// u_{ij} + \nabla u_{ji})
	auto && epsilon = (grad_u + grad_u.transpose()) / 2.;

	sigma = Matrix<Real>::eye(spatial_dimension) * trace * lambda + mu * epsilon;

	Real Y = 0;
	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	Y += sigma(i, j) * epsilon(i, j);
	}
	}
	Y *= 0.5;

	Real Fd = Y - Yd - Sd * dam;

	if (Fd > 0)
	dam = (Y - Yd) / Sd;
	dam = std::min(dam, 1.);

	sigma *= 1 - dam;
	}

	/* -------------------------------------------------------------------------- */
	inline void LocalMaterialDamage::computePotentialEnergyOnQuad(
	Matrix<Real> & grad_u, Matrix<Real> & sigma, Real & epot) {
	epot = 0.;
	for (UInt i = 0, t = 0; i < spatial_dimension; ++i)
	for (UInt j = 0; j < spatial_dimension; ++j, ++t)
	epot += sigma(i, j) * (grad_u(i, j) - (i == j));
	epot *= .5;
	}

	/* -------------------------------------------------------------------------- */
	inline Real LocalMaterialDamage::getCelerity(__attribute__((unused))
	const Element & element) const {
	return (std::sqrt(E / rho));
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_damage_materials.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_damage_materials.cc
	index b7720ea07..1a5608d09 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_damage_materials.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_damage_materials.cc
	@@ -1,246 +1,246 @@
	/**
	* @file test_damage_materials.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Tests for damage materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_material_fixtures.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_marigo.hh>
	#include <material_mazars.hh>
	#include <py_aka_array.hh>
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <gtest/gtest.h>
	#include <pybind11/embed.h>
	#include <pybind11/numpy.h>
	#include <pybind11/stl.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace py = pybind11;
	using namespace py::literals;

	using mat_types = ::testing::Types<
	// Traits<MaterialMarigo, 1>, Traits<MaterialMarigo, 2>,
	// Traits<MaterialMarigo, 3>,
	Traits<MaterialMazars, 1>, Traits<MaterialMazars, 2>,
	Traits<MaterialMazars, 3>>;

	/*****************************************************************/

	template <> void FriendMaterial<MaterialMazars<1>>::setParams() {
	K0.setDefaultValue(1e-4);
	At = 1.0;
	Bt = 5e3;
	Ac = 0.8;
	Bc = 1391.3;
	beta = 1.;
	E = 25e9;
	nu = 0.2;

	updateInternalParameters();
	}

	template <> void FriendMaterial<MaterialMazars<2>>::setParams() {
	K0.setDefaultValue(1e-4);
	At = 1.0;
	Bt = 5e3;
	Ac = 0.8;
	Bc = 1391.3;
	beta = 1.;
	E = 25e9;
	nu = 0.2;
	plane_stress = true;
	updateInternalParameters();
	}

	template <> void FriendMaterial<MaterialMazars<3>>::setParams() {
	K0.setDefaultValue(1e-4);
	At = 1.0;
	Bt = 5e3;
	Ac = 0.8;
	Bc = 1391.3;
	beta = 1.;
	E = 25e9;
	nu = 0.2;

	updateInternalParameters();
	}

	template <> void FriendMaterial<MaterialMazars<1>>::testComputeStress() {
	Array<Real> epsilons(1001, 1);
	Array<Real> sigmas(1001, 1);
	Array<Real> damages(1001, 1);

	for (auto && data : enumerate(epsilons)) {
	std::get<1>(data) = 2e-6 * std::get<0>(data);
	}
	Real _K0 = K0;
	py::module py_engine = py::module::import("py_mazars");

	auto kwargs_mat_params =
	py::dict("K0"_a = _K0, "At"_a = At, "Bt"_a = Bt, "Ac"_a = Ac, "Bc"_a = Bc,
	"E"_a = E, "nu"_a = nu);
	auto kwargs = py::dict("epsilons"_a = epsilons, "sigmas"_a = sigmas,
	"damages"_a = damages);

	auto py_mazars = py_engine.attr("Mazars")(**kwargs_mat_params);
	// auto Gf_py = py_mazars.attr("compute")(**kwargs);

	Real dam = 0.;
	Real dam_ref = 0.;
	Real ehat = 0.;

	for (auto && epsilon : epsilons) {
	Matrix<Real> strain(this->spatial_dimension, this->spatial_dimension, 0.);
	Matrix<Real> sigma(this->spatial_dimension, this->spatial_dimension, 0.);
	strain(0, 0) = epsilon;

	computeStressOnQuad(strain, sigma, dam, ehat);

	Real sigma_ref;
	auto py_data =
	py_mazars.attr("compute_step")(epsilon, sigma_ref, dam_ref, false);
	std::tie(sigma_ref, dam_ref) = py::cast<std::pair<double, double>>(py_data);

	EXPECT_NEAR(sigma(0, 0), sigma_ref, 1e-5);
	EXPECT_NEAR(dam, dam_ref, 1e-10);
	}
	}

	template <> void FriendMaterial<MaterialMazars<2>>::testComputeStress() {
	Array<Real> epsilons(1001, 1);
	Array<Real> sigmas(1001, 1);
	Array<Real> damages(1001, 1);

	for (auto && data : enumerate(epsilons)) {
	std::get<1>(data) = 2e-6 * std::get<0>(data);
	}
	Real _K0 = K0;
	py::module py_engine = py::module::import("py_mazars");

	auto kwargs_mat_params =
	py::dict("K0"_a = _K0, "At"_a = At, "Bt"_a = Bt, "Ac"_a = Ac, "Bc"_a = Bc,
	"E"_a = E, "nu"_a = nu);
	auto kwargs = py::dict("epsilons"_a = epsilons, "sigmas"_a = sigmas,
	"damages"_a = damages);

	auto py_mazars = py_engine.attr("Mazars")(**kwargs_mat_params);
	// auto Gf_py = py_mazars.attr("compute")(**kwargs);

	Real dam = 0.;
	Real dam_ref = 0.;
	Real ehat = 0.;

	for (auto && epsilon : epsilons) {
	Matrix<Real> strain(this->spatial_dimension, this->spatial_dimension, 0.);
	Matrix<Real> sigma(this->spatial_dimension, this->spatial_dimension, 0.);
	strain(0, 0) = epsilon;
	strain(1, 1) = -this->nu * epsilon;

	computeStressOnQuad(strain, sigma, dam, ehat);

	Real sigma_ref;
	auto py_data =
	py_mazars.attr("compute_step")(epsilon, sigma_ref, dam_ref, false);
	std::tie(sigma_ref, dam_ref) = py::cast<std::pair<double, double>>(py_data);

	EXPECT_NEAR(sigma(0, 0), sigma_ref, 1e-5);
	EXPECT_NEAR(dam, dam_ref, 1e-10);
	}
	}

	template <> void FriendMaterial<MaterialMazars<3>>::testComputeStress() {
	Array<Real> epsilons(1001, 1);
	Array<Real> sigmas(1001, 1);
	Array<Real> damages(1001, 1);

	for (auto && data : enumerate(epsilons)) {
	std::get<1>(data) = 2e-6 * std::get<0>(data);
	}
	Real _K0 = K0;
	py::module py_engine = py::module::import("py_mazars");

	auto kwargs_mat_params =
	py::dict("K0"_a = _K0, "At"_a = At, "Bt"_a = Bt, "Ac"_a = Ac, "Bc"_a = Bc,
	"E"_a = E, "nu"_a = nu);
	auto kwargs = py::dict("epsilons"_a = epsilons, "sigmas"_a = sigmas,
	"damages"_a = damages);

	auto py_mazars = py_engine.attr("Mazars")(**kwargs_mat_params);
	// auto Gf_py = py_mazars.attr("compute")(**kwargs);

	Real dam = 0.;
	Real dam_ref = 0.;
	Real ehat = 0.;

	for (auto && epsilon : epsilons) {
	Matrix<Real> strain(this->spatial_dimension, this->spatial_dimension, 0.);
	Matrix<Real> sigma(this->spatial_dimension, this->spatial_dimension, 0.);
	strain(0, 0) = epsilon;
	strain(1, 1) = strain(2, 2) = -this->nu * epsilon;

	computeStressOnQuad(strain, sigma, dam, ehat);

	Real sigma_ref;
	auto py_data =
	py_mazars.attr("compute_step")(epsilon, sigma_ref, dam_ref, false);
	std::tie(sigma_ref, dam_ref) = py::cast<std::pair<double, double>>(py_data);

	EXPECT_NEAR(sigma(0, 0), sigma_ref, 1e-5);
	EXPECT_NEAR(dam, dam_ref, 1e-10);
	}
	}

	namespace {

	template <typename T>
	class TestDamageMaterialFixture : public ::TestMaterialFixture<T> {};

	TYPED_TEST_SUITE(TestDamageMaterialFixture, mat_types, );

	TYPED_TEST(TestDamageMaterialFixture, ComputeStress) {
	this->material->testComputeStress();
	}
	TYPED_TEST(TestDamageMaterialFixture, DISABLED_EnergyDensity) {
	this->material->testEnergyDensity();
	}
	TYPED_TEST(TestDamageMaterialFixture, DISABLED_ComputeTangentModuli) {
	this->material->testComputeTangentModuli();
	}
	TYPED_TEST(TestDamageMaterialFixture, DISABLED_ComputeCelerity) {
	this->material->testCelerity();
	}
	} // namespace
	/*****************************************************************/
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_elastic_materials.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_elastic_materials.cc
	index 33dd2f615..78ec6baca 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_elastic_materials.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_elastic_materials.cc
	@@ -1,887 +1,887 @@
	/**
	* @file test_elastic_materials.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Enrico Milanese <enrico.milanese@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Tests the Elastic materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	#include "test_material_fixtures.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_elastic.hh>
	#include <material_elastic_orthotropic.hh>
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	using mat_types =
	::testing::Types<Traits<MaterialElastic, 1>, Traits<MaterialElastic, 2>,
	Traits<MaterialElastic, 3>,

	Traits<MaterialElasticOrthotropic, 2>,
	Traits<MaterialElasticOrthotropic, 3>,

	Traits<MaterialElasticLinearAnisotropic, 2>,
	Traits<MaterialElasticLinearAnisotropic, 3>>;

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<1>>::setParams() {
	Real E = 3.;
	Real rho = 2;
	setParam("E", E);
	setParam("rho", rho);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<1>>::testComputeStress() {
	Matrix<Real> eps = {{2}};
	Matrix<Real> sigma(1, 1);
	Real sigma_th = 2;
	this->computeStressOnQuad(eps, sigma, sigma_th);

	auto solution = E * eps(0, 0) + sigma_th;
	EXPECT_NEAR(sigma(0, 0), solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<1>>::testEnergyDensity() {
	Real eps = 2, sigma = 2;
	Real epot = 0;
	this->computePotentialEnergyOnQuad({{eps}}, {{sigma}}, epot);
	Real solution = 2;
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElastic<1>>::testComputeTangentModuli() {
	Matrix<Real> tangent(1, 1);
	this->computeTangentModuliOnQuad(tangent);
	EXPECT_NEAR(tangent(0, 0), E, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<1>>::testCelerity() {
	auto wave_speed = this->getCelerity(Element());
	auto solution = std::sqrt(E / rho);
	EXPECT_NEAR(wave_speed, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<2>>::setParams() {
	Real E = 1.;
	Real nu = .3;
	Real rho = 2;
	setParam("E", E);
	setParam("nu", nu);
	setParam("rho", rho);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<2>>::testComputeStress() {
	Real bulk_modulus_K = E / (3 * (1 - 2 * nu));
	Real shear_modulus_mu = E / (2 * (1 + nu));

	auto rotation_matrix = getRandomRotation();

	auto grad_u = this->getComposedStrain(1.).block(0, 0, 2, 2);

	auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);

	Matrix<Real> sigma_rot(2, 2);
	this->computeStressOnQuad(grad_u_rot, sigma_rot, sigma_th);

	auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);

	auto identity = Matrix<Real>::eye(2, 1.);

	auto strain = 0.5 * (grad_u + grad_u.transpose());
	auto deviatoric_strain = strain - 1. / 3. * strain.trace() * identity;

	auto sigma_expected = 2 * shear_modulus_mu * deviatoric_strain +
	(sigma_th + 2. * bulk_modulus_K) * identity;

	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>() / sigma_expected.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-13);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<2>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2}, {2, 4}};
	Matrix<Real> eps = {{1, 0}, {0, 1}};
	Real epot = 0;
	Real solution = 2.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElastic<2>>::testComputeTangentModuli() {
	Matrix<Real> tangent(3, 3);

	/* Plane Strain */
	// clang-format off
	Matrix<Real> solution = {
	{1 - nu, nu, 0},
	{nu, 1 - nu, 0},
	{0, 0, (1 - 2 * nu) / 2},
	};
	// clang-format on
	solution = E / ((1 + nu) (1 - 2 * nu));

	this->computeTangentModuliOnQuad(tangent);
	Real tangent_error = (tangent - solution).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);

	/* Plane Stress */
	this->plane_stress = true;
	this->updateInternalParameters();
	// clang-format off
	solution = {
	{1, nu, 0},
	{nu, 1, 0},
	{0, 0, (1 - nu) / 2},
	};
	// clang-format on
	solution = E / (1 - nu nu);

	this->computeTangentModuliOnQuad(tangent);
	tangent_error = (tangent - solution).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<2>>::testCelerity() {
	auto push_wave_speed = this->getPushWaveSpeed(Element());
	auto celerity = this->getCelerity(Element());

	Real K = E / (3 * (1 - 2 * nu));
	Real mu = E / (2 * (1 + nu));
	Real sol = std::sqrt((K + 4. / 3 * mu) / rho);

	EXPECT_NEAR(push_wave_speed, sol, 1e-14);
	EXPECT_NEAR(celerity, sol, 1e-14);

	auto shear_wave_speed = this->getShearWaveSpeed(Element());

	sol = std::sqrt(mu / rho);

	EXPECT_NEAR(shear_wave_speed, sol, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<3>>::setParams() {
	Real E = 1.;
	Real nu = .3;
	Real rho = 2;
	setParam("E", E);
	setParam("nu", nu);
	setParam("rho", rho);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<3>>::testComputeStress() {
	Real bulk_modulus_K = E / 3. / (1 - 2. * nu);
	Real shear_modulus_mu = 0.5 * E / (1 + nu);

	Matrix<Real> rotation_matrix = getRandomRotation();

	auto grad_u = this->getComposedStrain(1.);

	auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);

	Matrix<Real> sigma_rot(3, 3);
	this->computeStressOnQuad(grad_u_rot, sigma_rot, sigma_th);

	auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);

	Matrix<Real> identity(3, 3);
	identity.eye();

	Matrix<Real> strain = 0.5 * (grad_u + grad_u.transpose());
	Matrix<Real> deviatoric_strain = strain - 1. / 3. * strain.trace() * identity;

	Matrix<Real> sigma_expected = 2 * shear_modulus_mu * deviatoric_strain +
	(sigma_th + 3. * bulk_modulus_K) * identity;

	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<3>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
	Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
	Real epot = 0;
	Real solution = 5.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElastic<3>>::testComputeTangentModuli() {
	Matrix<Real> tangent(6, 6);

	// clang-format off
	Matrix<Real> solution = {
	{1 - nu, nu, nu, 0, 0, 0},
	{nu, 1 - nu, nu, 0, 0, 0},
	{nu, nu, 1 - nu, 0, 0, 0},
	{0, 0, 0, (1 - 2 * nu) / 2, 0, 0},
	{0, 0, 0, 0, (1 - 2 * nu) / 2, 0},
	{0, 0, 0, 0, 0, (1 - 2 * nu) / 2},
	};
	// clang-format on
	solution = E / ((1 + nu) (1 - 2 * nu));

	this->computeTangentModuliOnQuad(tangent);
	Real tangent_error = (tangent - solution).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElastic<3>>::testCelerity() {
	auto push_wave_speed = this->getPushWaveSpeed(Element());
	auto celerity = this->getCelerity(Element());

	Real K = E / (3 * (1 - 2 * nu));
	Real mu = E / (2 * (1 + nu));
	Real sol = std::sqrt((K + 4. / 3 * mu) / rho);

	EXPECT_NEAR(push_wave_speed, sol, 1e-14);
	EXPECT_NEAR(celerity, sol, 1e-14);

	auto shear_wave_speed = this->getShearWaveSpeed(Element());

	sol = std::sqrt(mu / rho);

	EXPECT_NEAR(shear_wave_speed, sol, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::setParams() {
	// Note: for this test material and canonical basis coincide
	Vector<Real> n1 = {1, 0};
	Vector<Real> n2 = {0, 1};
	Real E1 = 1.;
	Real E2 = 2.;
	Real nu12 = 0.1;
	Real G12 = 2.;
	Real rho = 2.5;

	*this->dir_vecs[0] = n1;
	*this->dir_vecs[1] = n2;
	this->E1 = E1;
	this->E2 = E2;
	this->nu12 = nu12;
	this->G12 = G12;
	this->rho = rho;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeStress() {
	UInt Dim = 2;
	// material frame of reference is rotate by rotation_matrix starting from
	// canonical basis
	Matrix<Real> rotation_matrix = getRandomRotation();

	// canonical basis as expressed in the material frame of reference, as
	// required by MaterialElasticOrthotropic class (it is simply given by the
	// columns of the rotation_matrix; the lines give the material basis expressed
	// in the canonical frame of reference)
	*this->dir_vecs[0] = rotation_matrix(0);
	*this->dir_vecs[1] = rotation_matrix(1);

	// set internal Cijkl matrix expressed in the canonical frame of reference
	this->updateInternalParameters();

	// gradient in material frame of reference
	auto grad_u = this->getComposedStrain(2.).block(0, 0, 2, 2);

	// gradient in canonical basis (we need to rotate back to the canonical
	// basis)
	auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);

	// stress in the canonical basis
	Matrix<Real> sigma_rot(2, 2);
	this->computeStressOnQuad(grad_u_rot, sigma_rot);

	// stress in the material reference (we need to apply the rotation)
	auto sigma = this->applyRotation(sigma_rot, rotation_matrix);

	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real gamma = 1 / (1 - nu12 * nu21);

	Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
	C_expected(0, 0) = gamma * E1;
	C_expected(1, 1) = gamma * E2;
	C_expected(2, 2) = G12;

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;

	// epsilon is computed directly in the material frame of reference
	Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());

	// sigma_expected is computed directly in the material frame of reference
	Matrix<Real> sigma_expected(Dim, Dim);
	for (UInt i = 0; i < Dim; ++i) {
	for (UInt j = 0; j < Dim; ++j) {
	sigma_expected(i, i) += C_expected(i, j) * epsilon(j, j);
	}
	}

	sigma_expected(0, 1) = sigma_expected(1, 0) =
	C_expected(2, 2) * 2 * epsilon(0, 1);

	// sigmas are checked in the material frame of reference
	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-13);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<2>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2}, {2, 4}};
	Matrix<Real> eps = {{1, 0}, {0, 1}};
	Real epot = 0;
	Real solution = 2.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<2>>::testComputeTangentModuli() {
	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real gamma = 1 / (1 - nu12 * nu21);

	Matrix<Real> C_expected(3, 3);
	C_expected(0, 0) = gamma * E1;
	C_expected(1, 1) = gamma * E2;
	C_expected(2, 2) = G12;

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;

	Matrix<Real> tangent(3, 3);
	this->computeTangentModuliOnQuad(tangent);

	Real tangent_error = (tangent - C_expected).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */

	template <> void FriendMaterial<MaterialElasticOrthotropic<2>>::testCelerity() {
	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real gamma = 1 / (1 - nu12 * nu21);

	Matrix<Real> C_expected(3, 3);
	C_expected(0, 0) = gamma * E1;
	C_expected(1, 1) = gamma * E2;
	C_expected(2, 2) = G12;

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * nu21;

	Vector<Real> eig_expected(3);
	C_expected.eig(eig_expected);

	auto celerity_expected = std::sqrt(eig_expected(0) / rho);

	auto celerity = this->getCelerity(Element());

	EXPECT_NEAR(celerity_expected, celerity, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::setParams() {
	Vector<Real> n1 = {1, 0, 0};
	Vector<Real> n2 = {0, 1, 0};
	Vector<Real> n3 = {0, 0, 1};
	Real E1 = 1.;
	Real E2 = 2.;
	Real E3 = 3.;
	Real nu12 = 0.1;
	Real nu13 = 0.2;
	Real nu23 = 0.3;
	Real G12 = 2.;
	Real G13 = 3.;
	Real G23 = 1.;
	Real rho = 2.3;

	*this->dir_vecs[0] = n1;
	*this->dir_vecs[1] = n2;
	*this->dir_vecs[2] = n3;
	this->E1 = E1;
	this->E2 = E2;
	this->E3 = E3;
	this->nu12 = nu12;
	this->nu13 = nu13;
	this->nu23 = nu23;
	this->G12 = G12;
	this->G13 = G13;
	this->G23 = G23;
	this->rho = rho;
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeStress() {
	UInt Dim = 3;

	// material frame of reference is rotate by rotation_matrix starting from
	// canonical basis
	Matrix<Real> rotation_matrix = getRandomRotation();

	// canonical basis as expressed in the material frame of reference, as
	// required by MaterialElasticOrthotropic class (it is simply given by the
	// columns of the rotation_matrix; the lines give the material basis expressed
	// in the canonical frame of reference)
	*this->dir_vecs[0] = rotation_matrix(0);
	*this->dir_vecs[1] = rotation_matrix(1);
	*this->dir_vecs[2] = rotation_matrix(2);

	// set internal Cijkl matrix expressed in the canonical frame of reference
	this->updateInternalParameters();

	// gradient in material frame of reference
	auto grad_u = this->getComposedStrain(2.);

	// gradient in canonical basis (we need to rotate back to the canonical
	// basis)
	auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);

	// stress in the canonical basis
	Matrix<Real> sigma_rot(3, 3);
	this->computeStressOnQuad(grad_u_rot, sigma_rot);

	// stress in the material reference (we need to apply the rotation)
	auto sigma = this->applyRotation(sigma_rot, rotation_matrix);

	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real nu31 = nu13 * E3 / E1;
	Real nu32 = nu23 * E3 / E2;
	Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
	2 * nu21 * nu32 * nu13);

	Matrix<Real> C_expected(6, 6);
	C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
	C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
	C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
	C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
	C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);

	C_expected(3, 3) = G23;
	C_expected(4, 4) = G13;
	C_expected(5, 5) = G12;

	// epsilon is computed directly in the material frame of reference
	Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());

	// sigma_expected is computed directly in the material frame of reference
	Matrix<Real> sigma_expected(Dim, Dim);
	for (UInt i = 0; i < Dim; ++i) {
	for (UInt j = 0; j < Dim; ++j) {
	sigma_expected(i, i) += C_expected(i, j) * epsilon(j, j);
	}
	}

	sigma_expected(0, 1) = C_expected(5, 5) * 2 * epsilon(0, 1);
	sigma_expected(0, 2) = C_expected(4, 4) * 2 * epsilon(0, 2);
	sigma_expected(1, 2) = C_expected(3, 3) * 2 * epsilon(1, 2);
	sigma_expected(1, 0) = sigma_expected(0, 1);
	sigma_expected(2, 0) = sigma_expected(0, 2);
	sigma_expected(2, 1) = sigma_expected(1, 2);

	// sigmas are checked in the material frame of reference
	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-13);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<3>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
	Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
	Real epot = 0;
	Real solution = 5.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticOrthotropic<3>>::testComputeTangentModuli() {
	// Note: for this test material and canonical basis coincide
	UInt Dim = 3;

	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real nu31 = nu13 * E3 / E1;
	Real nu32 = nu23 * E3 / E2;
	Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
	2 * nu21 * nu32 * nu13);

	Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
	C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
	C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
	C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
	C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
	C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);

	C_expected(3, 3) = G23;
	C_expected(4, 4) = G13;
	C_expected(5, 5) = G12;

	Matrix<Real> tangent(6, 6);
	this->computeTangentModuliOnQuad(tangent);

	Real tangent_error = (tangent - C_expected).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialElasticOrthotropic<3>>::testCelerity() {
	// Note: for this test material and canonical basis coincide
	UInt Dim = 3;
	// construction of Cijkl engineering tensor in the material frame of
	// reference
	// ref: http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php#Sect3_2_13
	Real nu21 = nu12 * E2 / E1;
	Real nu31 = nu13 * E3 / E1;
	Real nu32 = nu23 * E3 / E2;
	Real gamma = 1 / (1 - nu12 * nu21 - nu23 * nu32 - nu31 * nu13 -
	2 * nu21 * nu32 * nu13);

	Matrix<Real> C_expected(2 * Dim, 2 * Dim, 0);
	C_expected(0, 0) = gamma * E1 * (1 - nu23 * nu32);
	C_expected(1, 1) = gamma * E2 * (1 - nu13 * nu31);
	C_expected(2, 2) = gamma * E3 * (1 - nu12 * nu21);

	C_expected(1, 0) = C_expected(0, 1) = gamma * E1 * (nu21 + nu31 * nu23);
	C_expected(2, 0) = C_expected(0, 2) = gamma * E1 * (nu31 + nu21 * nu32);
	C_expected(2, 1) = C_expected(1, 2) = gamma * E2 * (nu32 + nu12 * nu31);

	C_expected(3, 3) = G23;
	C_expected(4, 4) = G13;
	C_expected(5, 5) = G12;

	Vector<Real> eig_expected(6);
	C_expected.eig(eig_expected);

	auto celerity_expected = std::sqrt(eig_expected(0) / rho);

	auto celerity = this->getCelerity(Element());

	EXPECT_NEAR(celerity_expected, celerity, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::setParams() {
	Matrix<Real> C = {
	{1.0, 0.3, 0.4},
	{0.3, 2.0, 0.1},
	{0.4, 0.1, 1.5},
	};

	for (auto i = 0u; i < C.rows(); ++i)
	for (auto j = 0u; j < C.cols(); ++j)
	this->Cprime(i, j) = C(i, j);

	this->rho = 2.7;

	// material frame of reference is rotate by rotation_matrix starting from
	// canonical basis
	Matrix<Real> rotation_matrix = getRandomRotation();

	// canonical basis as expressed in the material frame of reference, as
	// required by MaterialElasticLinearAnisotropic class (it is simply given by
	// the columns of the rotation_matrix; the lines give the material basis
	// expressed in the canonical frame of reference)
	*this->dir_vecs[0] = rotation_matrix(0);
	*this->dir_vecs[1] = rotation_matrix(1);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testComputeStress() {
	Matrix<Real> C = {
	{1.0, 0.3, 0.4},
	{0.3, 2.0, 0.1},
	{0.4, 0.1, 1.5},
	};

	Matrix<Real> rotation_matrix(2, 2);

	rotation_matrix(0) = *this->dir_vecs[0];
	rotation_matrix(1) = *this->dir_vecs[1];

	// gradient in material frame of reference
	auto grad_u = this->getComposedStrain(1.).block(0, 0, 2, 2);

	// gradient in canonical basis (we need to rotate back to the canonical
	// basis)
	auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);

	// stress in the canonical basis
	Matrix<Real> sigma_rot(2, 2);
	this->computeStressOnQuad(grad_u_rot, sigma_rot);

	// stress in the material reference (we need to apply the rotation)
	auto sigma = this->applyRotation(sigma_rot, rotation_matrix);

	// epsilon is computed directly in the material frame of reference
	Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
	Vector<Real> epsilon_voigt(3);
	epsilon_voigt(0) = epsilon(0, 0);
	epsilon_voigt(1) = epsilon(1, 1);
	epsilon_voigt(2) = 2 * epsilon(0, 1);

	// sigma_expected is computed directly in the material frame of reference
	Vector<Real> sigma_voigt = C * epsilon_voigt;
	Matrix<Real> sigma_expected(2, 2);
	sigma_expected(0, 0) = sigma_voigt(0);
	sigma_expected(1, 1) = sigma_voigt(1);
	sigma_expected(0, 1) = sigma_expected(1, 0) = sigma_voigt(2);

	// sigmas are checked in the material frame of reference
	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-13);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2}, {2, 4}};
	Matrix<Real> eps = {{1, 0}, {0, 1}};
	Real epot = 0;
	Real solution = 2.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<
	MaterialElasticLinearAnisotropic<2>>::testComputeTangentModuli() {
	Matrix<Real> tangent(3, 3);
	this->computeTangentModuliOnQuad(tangent);

	Real tangent_error = (tangent - C).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<2>>::testCelerity() {
	Vector<Real> eig_expected(3);
	C.eig(eig_expected);

	auto celerity_expected = std::sqrt(eig_expected(0) / this->rho);
	auto celerity = this->getCelerity(Element());

	EXPECT_NEAR(celerity_expected, celerity, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::setParams() {
	// Note: for this test material and canonical basis coincide
	Matrix<Real> C = {
	{1.0, 0.3, 0.4, 0.3, 0.2, 0.1}, {0.3, 2.0, 0.1, 0.2, 0.3, 0.2},
	{0.4, 0.1, 1.5, 0.1, 0.4, 0.3}, {0.3, 0.2, 0.1, 2.4, 0.1, 0.4},
	{0.2, 0.3, 0.4, 0.1, 0.9, 0.1}, {0.1, 0.2, 0.3, 0.4, 0.1, 1.2},
	};

	for (auto i = 0u; i < C.rows(); ++i)
	for (auto j = 0u; j < C.cols(); ++j)
	this->Cprime(i, j) = C(i, j);

	this->rho = 2.9;

	// material frame of reference is rotate by rotation_matrix starting from
	// canonical basis
	Matrix<Real> rotation_matrix = getRandomRotation();

	// canonical basis as expressed in the material frame of reference, as
	// required by MaterialElasticLinearAnisotropic class (it is simply given by
	// the columns of the rotation_matrix; the lines give the material basis
	// expressed in the canonical frame of reference)
	*this->dir_vecs[0] = rotation_matrix(0);
	*this->dir_vecs[1] = rotation_matrix(1);
	*this->dir_vecs[2] = rotation_matrix(2);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testComputeStress() {
	Matrix<Real> C = {
	{1.0, 0.3, 0.4, 0.3, 0.2, 0.1}, {0.3, 2.0, 0.1, 0.2, 0.3, 0.2},
	{0.4, 0.1, 1.5, 0.1, 0.4, 0.3}, {0.3, 0.2, 0.1, 2.4, 0.1, 0.4},
	{0.2, 0.3, 0.4, 0.1, 0.9, 0.1}, {0.1, 0.2, 0.3, 0.4, 0.1, 1.2},
	};

	Matrix<Real> rotation_matrix(3, 3);

	rotation_matrix(0) = *this->dir_vecs[0];
	rotation_matrix(1) = *this->dir_vecs[1];
	rotation_matrix(2) = *this->dir_vecs[2];

	// gradient in material frame of reference
	auto grad_u = this->getComposedStrain(2.);

	// gradient in canonical basis (we need to rotate back to the canonical
	// basis)
	auto grad_u_rot = this->reverseRotation(grad_u, rotation_matrix);

	// stress in the canonical basis
	Matrix<Real> sigma_rot(3, 3);
	this->computeStressOnQuad(grad_u_rot, sigma_rot);

	// stress in the material reference (we need to apply the rotation)
	auto sigma = this->applyRotation(sigma_rot, rotation_matrix);

	// epsilon is computed directly in the material frame of reference
	Matrix<Real> epsilon = 0.5 * (grad_u + grad_u.transpose());
	Vector<Real> epsilon_voigt(6);
	epsilon_voigt(0) = epsilon(0, 0);
	epsilon_voigt(1) = epsilon(1, 1);
	epsilon_voigt(2) = epsilon(2, 2);
	epsilon_voigt(3) = 2 * epsilon(1, 2);
	epsilon_voigt(4) = 2 * epsilon(0, 2);
	epsilon_voigt(5) = 2 * epsilon(0, 1);

	// sigma_expected is computed directly in the material frame of reference
	Vector<Real> sigma_voigt = C * epsilon_voigt;
	Matrix<Real> sigma_expected(3, 3);
	sigma_expected(0, 0) = sigma_voigt(0);
	sigma_expected(1, 1) = sigma_voigt(1);
	sigma_expected(2, 2) = sigma_voigt(2);
	sigma_expected(1, 2) = sigma_expected(2, 1) = sigma_voigt(3);
	sigma_expected(0, 2) = sigma_expected(2, 0) = sigma_voigt(4);
	sigma_expected(0, 1) = sigma_expected(1, 0) = sigma_voigt(5);

	// sigmas are checked in the material frame of reference
	auto diff = sigma - sigma_expected;
	Real stress_error = diff.norm<L_inf>();
	EXPECT_NEAR(stress_error, 0., 1e-13);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testEnergyDensity() {
	Matrix<Real> sigma = {{1, 2, 3}, {2, 4, 5}, {3, 5, 6}};
	Matrix<Real> eps = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
	Real epot = 0;
	Real solution = 5.5;
	this->computePotentialEnergyOnQuad(eps, sigma, epot);
	EXPECT_NEAR(epot, solution, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<
	MaterialElasticLinearAnisotropic<3>>::testComputeTangentModuli() {
	Matrix<Real> tangent(6, 6);
	this->computeTangentModuliOnQuad(tangent);

	Real tangent_error = (tangent - C).norm<L_2>();
	EXPECT_NEAR(tangent_error, 0, 1e-14);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	void FriendMaterial<MaterialElasticLinearAnisotropic<3>>::testCelerity() {
	Vector<Real> eig_expected(6);
	C.eig(eig_expected);

	auto celerity_expected = std::sqrt(eig_expected(0) / this->rho);

	auto celerity = this->getCelerity(Element());

	EXPECT_NEAR(celerity_expected, celerity, 1e-14);
	}

	/* -------------------------------------------------------------------------- */

	namespace {

	template <typename T>
	class TestElasticMaterialFixture : public ::TestMaterialFixture<T> {};

	TYPED_TEST_SUITE(TestElasticMaterialFixture, mat_types, );

	TYPED_TEST(TestElasticMaterialFixture, ComputeStress) {
	this->material->testComputeStress();
	}

	TYPED_TEST(TestElasticMaterialFixture, EnergyDensity) {
	this->material->testEnergyDensity();
	}

	TYPED_TEST(TestElasticMaterialFixture, ComputeTangentModuli) {
	this->material->testComputeTangentModuli();
	}

	TYPED_TEST(TestElasticMaterialFixture, ComputeCelerity) {
	this->material->testCelerity();
	}

	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_finite_def_materials.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_finite_def_materials.cc
	index f8be98d4a..bef92967d 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_finite_def_materials.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_finite_def_materials.cc
	@@ -1,89 +1,89 @@
	/**
	* @file test_finite_def_materials.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Test finite deformation materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	#include "test_material_fixtures.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_neohookean.hh>
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	using mat_types = ::testing::Types<Traits<MaterialNeohookean, 1>,
	Traits<MaterialNeohookean, 2>,
	Traits<MaterialNeohookean, 3>>;

	/*****************************************************************/

	template <> void FriendMaterial<MaterialNeohookean<3>>::testComputeStress() {
	AKANTU_TO_IMPLEMENT();
	}

	/*****************************************************************/
	template <>
	void FriendMaterial<MaterialNeohookean<3>>::testComputeTangentModuli() {
	AKANTU_TO_IMPLEMENT();
	}

	/*****************************************************************/

	template <> void FriendMaterial<MaterialNeohookean<3>>::testEnergyDensity() {
	AKANTU_TO_IMPLEMENT();
	}

	/*****************************************************************/

	namespace {

	template <typename T>
	class TestFiniteDefMaterialFixture : public ::TestMaterialFixture<T> {};

	TYPED_TEST_SUITE(TestFiniteDefMaterialFixture, mat_types, );

	TYPED_TEST(TestFiniteDefMaterialFixture, DISABLED_ComputeStress) {
	this->material->testComputeStress();
	}
	TYPED_TEST(TestFiniteDefMaterialFixture, DISABLED_EnergyDensity) {
	this->material->testEnergyDensity();
	}
	TYPED_TEST(TestFiniteDefMaterialFixture, DISABLED_ComputeTangentModuli) {
	this->material->testComputeTangentModuli();
	}
	TYPED_TEST(TestFiniteDefMaterialFixture, DISABLED_DefComputeCelerity) {
	this->material->testCelerity();
	}
	} // namespace
	/*****************************************************************/
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_finite_deformation.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_finite_deformation.cc
	index 1739a1071..896b25148 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_finite_deformation.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_finite_deformation.cc
	@@ -1,141 +1,139 @@
	/**
	* @file test_finite_deformation.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Nov 11 2019
	* @date last modification: Wed May 27 2020
	*
	* @brief Test for dinite deformation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	-
	TEST(TestFiniteDeformation, NotUnit) {
	getStaticParser().parse("material_finite_deformation.dat");

	const double pi = std::atan(1) * 4;
	constexpr int dim = 3;

	Mesh mesh(dim);
	mesh.read("1_tetrahedron.msh");

	SolidMechanicsModel model(mesh);
	model.initFull(_analysis_method = _static);

	#if DEBUG_TEST
	model.addDumpField("displacement");
	model.addDumpField("internal_force");
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.dump();
	#endif

	Matrix<Real> alpha{{0.00, 0.02, 0.03, 0.04},
	{0.00, 0.06, 0.07, 0.08},
	{0.00, 0.10, 0.11, 0.12}};

	auto impose_disp = [&] {
	model.getDisplacement().zero();
	- for (auto data : zip(make_view(mesh.getNodes(), dim),
	- make_view(model.getDisplacement(), dim),
	- make_view(model.getBlockedDOFs(), dim))) {
	+ for (auto data : zip(make_view(mesh.getNodes(), dim),
	+ make_view(model.getDisplacement(), dim),
	+ make_view(model.getBlockedDOFs(), dim))) {
	auto & pos = std::get<0>(data);
	auto & dis = std::get<1>(data);
	auto & blocked = std::get<2>(data);

	blocked.set(true);
	-
	+
	dis += Vector<Real>(alpha(0));
	for (auto p : arange(dim)) {
	- dis += Vector<Real>(alpha(1+p)) * pos(p);
	+ dis += Vector<Real>(alpha(1 + p)) * pos(p);
	}
	}
	};

	impose_disp();
	model.solveStep();
	#if DEBUG_TEST
	model.dump();
	#endif

	auto stesses0 = model.getMaterial(0).getStress();
	auto displacement0 = model.getDisplacement();
	auto internal_force0 = model.getInternalForce();

	auto theta = pi / 4;
	Matrix<Real> R{{1., 0., 0.},
	{0., std::cos(theta), -std::sin(theta)},
	{0., std::sin(theta), std::cos(theta)}};

	impose_disp();
	for (auto data : zip(make_view(mesh.getNodes(), dim),
	make_view(model.getDisplacement(), dim))) {
	auto & X = std::get<0>(data);
	auto & u = std::get<1>(data);
	u = R * (X + u) - X;
	}

	model.solveStep();
	#if DEBUG_TEST
	model.dump();
	#endif

	for (auto data : zip(make_view(mesh.getNodes(), dim),
	make_view(model.getDisplacement(), dim),
	make_view(displacement0, dim),
	make_view(model.getInternalForce(), dim),
	make_view(internal_force0, dim))) {
	auto pos = std::get<0>(data);
	Vector<Real> refdis(dim, 0.);

	refdis += Vector<Real>(alpha(0));
	for (auto p : arange(dim)) {
	- refdis += Vector<Real>(alpha(1+p)) * pos(p);
	+ refdis += Vector<Real>(alpha(1 + p)) * pos(p);
	}

	auto dis = std::get<1>(data);
	auto dis0 = std::get<2>(data);

	auto err = refdis.distance(dis0);
	- EXPECT_NEAR(err, 0, 1e-14);
	+ EXPECT_NEAR(err, 0, 1e-14);

	auto err1 = dis.distance(R * (pos + dis0) - pos);
	- EXPECT_NEAR(err1, 0, 1e-14);
	+ EXPECT_NEAR(err1, 0, 1e-14);

	auto f = std::get<3>(data);
	auto f0 = std::get<4>(data);

	auto err3 = f.distance(R * f0);
	- EXPECT_NEAR(err3, 0, 1e-5);
	-
	+ EXPECT_NEAR(err3, 0, 1e-5);
	}
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_interpolate_stress.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_interpolate_stress.cc
	index 7548dc0cd..9fe106177 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_interpolate_stress.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_interpolate_stress.cc
	@@ -1,183 +1,183 @@
	/**
	* @file test_interpolate_stress.cc
	*
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Sep 08 2020
	*
	* @brief Test for the stress interpolation function
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include <fstream>
	#include <iostream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "integrator_gauss.hh"
	#include "mesh_utils.hh"
	#include "shape_lagrange.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	Real function(Real x, Real y, Real z) { return 100. + 2. * x + 3. * y + 4 * z; }

	int main(int argc, char * argv[]) {
	initialize("material_interpolate.dat", argc, argv);

	debug::setDebugLevel(dblWarning);

	const UInt spatial_dimension = 3;
	const ElementType type = _tetrahedron_10;

	Mesh mesh(spatial_dimension);
	mesh.read("interpolation.msh");
	const ElementType type_facet = mesh.getFacetType(type);

	Mesh & mesh_facets = mesh.initMeshFacets("mesh_facets");
	MeshUtils::buildAllFacets(mesh, mesh_facets);

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull();

	Array<Real> & position = mesh.getNodes();
	UInt nb_facet = mesh_facets.getNbElement(type_facet);
	UInt nb_element = mesh.getNbElement(type);

	/// compute quadrature points positions on facets
	typedef FEEngineTemplate<IntegratorGauss, ShapeLagrange> MyFEEngineType;

	model.registerFEEngineObject<MyFEEngineType>("FacetsFEEngine", mesh_facets,
	spatial_dimension - 1);
	model.getFEEngine("FacetsFEEngine").initShapeFunctions();

	UInt nb_quad_per_facet =
	model.getFEEngine("FacetsFEEngine").getNbIntegrationPoints(type_facet);
	UInt nb_tot_quad = nb_quad_per_facet * nb_facet;

	Array<Real> quad_facets(nb_tot_quad, spatial_dimension);

	model.getFEEngine("FacetsFEEngine")
	.interpolateOnIntegrationPoints(position, quad_facets, spatial_dimension,
	type_facet);

	auto && facet_to_element = mesh_facets.getSubelementToElement(type);
	UInt nb_facet_per_elem = facet_to_element.getNbComponent();

	ElementTypeMapArray<Real> element_quad_facet;
	element_quad_facet.alloc(nb_element * nb_facet_per_elem * nb_quad_per_facet,
	spatial_dimension, type);

	ElementTypeMapArray<Real> interpolated_stress("interpolated_stress", "");
	interpolated_stress.initialize(
	mesh, _nb_component = spatial_dimension * spatial_dimension,
	_spatial_dimension = spatial_dimension);

	Array<Real> & interp_stress = interpolated_stress(type);
	interp_stress.resize(nb_element * nb_facet_per_elem * nb_quad_per_facet);

	Array<Real> & el_q_facet = element_quad_facet(type);

	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt f = 0; f < nb_facet_per_elem; ++f) {
	UInt global_facet = facet_to_element(el, f).element;

	for (UInt q = 0; q < nb_quad_per_facet; ++q) {
	for (UInt s = 0; s < spatial_dimension; ++s) {
	el_q_facet(el * nb_facet_per_elem * nb_quad_per_facet +
	f * nb_quad_per_facet + q,
	s) = quad_facets(global_facet * nb_quad_per_facet + q, s);
	}
	}
	}
	}

	/// compute quadrature points position of the elements
	UInt nb_quad_per_element = model.getFEEngine().getNbIntegrationPoints(type);
	UInt nb_tot_quad_el = nb_quad_per_element * nb_element;

	Array<Real> quad_elements(nb_tot_quad_el, spatial_dimension);

	model.getFEEngine().interpolateOnIntegrationPoints(position, quad_elements,
	spatial_dimension, type);

	/// assign some values to stresses
	Array<Real> & stress =
	const_cast<Array<Real> &>(model.getMaterial(0).getStress(type));

	for (UInt q = 0; q < nb_tot_quad_el; ++q) {
	for (UInt s = 0; s < spatial_dimension * spatial_dimension; ++s) {
	stress(q, s) = s * function(quad_elements(q, 0), quad_elements(q, 1),
	quad_elements(q, 2));
	}
	}

	/// interpolate stresses on facets' quadrature points
	model.getMaterial(0).initElementalFieldInterpolation(element_quad_facet);
	model.getMaterial(0).interpolateStress(interpolated_stress);

	Real tolerance = 1.e-10;

	/// check results
	for (UInt el = 0; el < nb_element; ++el) {
	for (UInt f = 0; f < nb_facet_per_elem; ++f) {

	for (UInt q = 0; q < nb_quad_per_facet; ++q) {
	for (UInt s = 0; s < spatial_dimension * spatial_dimension; ++s) {

	Real x = el_q_facet(el * nb_facet_per_elem * nb_quad_per_facet +
	f * nb_quad_per_facet + q,
	0);
	Real y = el_q_facet(el * nb_facet_per_elem * nb_quad_per_facet +
	f * nb_quad_per_facet + q,
	1);
	Real z = el_q_facet(el * nb_facet_per_elem * nb_quad_per_facet +
	f * nb_quad_per_facet + q,
	2);

	Real theoretical = s * function(x, y, z);

	Real numerical =
	interp_stress(el * nb_facet_per_elem * nb_quad_per_facet +
	f * nb_quad_per_facet + q,
	s);

	if (std::abs(theoretical - numerical) > tolerance) {
	std::cout << "Theoretical and numerical values aren't coincident!"
	<< std::endl;
	return EXIT_FAILURE;
	}
	}
	}
	}
	}

	std::cout << "OK: Stress interpolation test passed." << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_local_material.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_local_material.cc
	index 186129640..326728e2b 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_local_material.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_local_material.cc
	@@ -1,134 +1,134 @@
	/**
	* @file test_local_material.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jun 05 2019
	*
	* @brief test of the class SolidMechanicsModel with custom local damage on a
	* notched plate
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	#include "local_material_damage.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	akantu::initialize("material.dat", argc, argv);
	UInt max_steps = 1100;

	const UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("mesh_section_gap.msh");

	/// model initialization
	MaterialFactory::getInstance().registerAllocator(
	"local_damage",
	[](UInt, const ID &, SolidMechanicsModel & model,
	const ID & id) -> std::unique_ptr<Material> {
	return std::make_unique<LocalMaterialDamage>(model, id);
	});

	SolidMechanicsModel model(mesh);
	model.initFull();

	std::cout << model.getMaterial(0) << std::endl;

	model.addDumpField("damage");

	model.addDumpField("strain");
	model.addDumpField("stress");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.dump();

	Real time_step = model.getStableTimeStep();
	model.setTimeStep(time_step / 2.5);

	/// Dirichlet boundary conditions
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "Fixed");
	// model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "Fixed");
	Matrix<Real> stress(2, 2);
	stress.eye(5e7);
	model.applyBC(BC::Neumann::FromHigherDim(stress), "Traction");

	for (UInt s = 0; s < max_steps; ++s)
	model.solveStep();

	model.dump();

	// This should throw a bad_cast if not the proper material
	auto & mat =
	dynamic_cast<LocalMaterialDamage &>(model.getMaterial("concrete"));
	const auto & filter = mat.getElementFilter();
	for (auto & type : filter.elementTypes(spatial_dimension)) {
	std::cout << mat.getDamage(type) << std::endl;
	}

	// This part of the test is to mesh dependent and as nothing to do with the
	// fact that we can create a user defined material or not

	// const auto & lower_bounds = mesh.getLowerBounds();
	// const auto & upper_bounds = mesh.getUpperBounds();
	// Real L = upper_bounds(_x) - lower_bounds(_x);
	// Real H = upper_bounds(_y) - lower_bounds(_y);

	// const auto & filter = model.getMaterial("concrete").getElementFilter();

	// Vector<Real> barycenter(spatial_dimension);

	// for (auto & type : filter.elementTypes(spatial_dimension)) {
	// UInt nb_elem = mesh.getNbElement(type);
	// const UInt nb_gp = model.getFEEngine().getNbIntegrationPoints(type);
	// const auto & material_damage_array =
	// model.getMaterial(0).getArray<Real>("damage", type);
	// UInt cpt = 0;
	// for (auto nel : arange(nb_elem)) {
	// mesh.getBarycenter({type, nel, _not_ghost}, barycenter);
	// if ((std::abs(barycenter(_x) - (L / 2) + 0.025) < 0.025) &&
	// (std::abs(barycenter(_y) - (H / 2) + 0.045) < 0.045)) {
	// if (material_damage_array(cpt, 0) < 0.9) {
	// std::terminate();
	// } else {
	// std::cout << "element " << nel << " is correctly broken" <<
	// std::endl;
	// }
	// }

	// cpt += nb_gp;
	// }
	// }

	akantu::finalize();
	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_elasto_plastic_linear_isotropic_hardening/test_material_elasto_plastic_linear_isotropic_hardening.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_elasto_plastic_linear_isotropic_hardening/test_material_elasto_plastic_linear_isotropic_hardening.cc
	index 400bbaebc..e7e2e080e 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_elasto_plastic_linear_isotropic_hardening/test_material_elasto_plastic_linear_isotropic_hardening.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_elasto_plastic_linear_isotropic_hardening/test_material_elasto_plastic_linear_isotropic_hardening.cc
	@@ -1,93 +1,93 @@
	/**
	* @file test_material_elasto_plastic_linear_isotropic_hardening.cc
	*
	* @author Jaehyun Cho <jaehyun.cho@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue May 21 2019
	*
	* @brief test for material type elasto plastic linear isotropic hardening
	* using tension-compression test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	initialize("test_material_elasto_plastic_linear_isotropic_hardening.dat",
	argc, argv);

	const UInt spatial_dimension = 2;
	const Real u_increment = 0.1;
	const UInt steps = 20;

	Mesh mesh(spatial_dimension);
	mesh.read("test_material_elasto_plastic_linear_isotropic_hardening.msh");

	SolidMechanicsModel model(mesh);
	model.initFull(_analysis_method = _static);

	auto & solver = model.getNonLinearSolver("static");
	solver.set("max_iterations", 300);
	solver.set("threshold", 1e-5);

	model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "left");
	model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "bottom");

	std::cout.precision(4);
	for (UInt i = 0; i < steps; ++i) {

	model.applyBC(BC::Dirichlet::FixedValue(i * u_increment, _x), "right");

	try {
	model.solveStep();
	} catch (debug::NLSNotConvergedException & e) {
	std::cout << e.niter << " " << e.error << std::endl;
	throw;
	}
	Real strainxx = i * u_increment / 10.;

	const Array<UInt> & edge_nodes =
	mesh.getElementGroup("right").getNodeGroup().getNodes();
	Array<Real> & residual = model.getInternalForce();
	Real reaction = 0;

	for (UInt n = 0; n < edge_nodes.size(); n++) {
	reaction -= residual(edge_nodes(n), 0);
	}

	std::cout << strainxx << "," << reaction << std::endl;
	}

	finalize();
	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_fixtures.hh b/test/test_model/test_solid_mechanics_model/test_materials/test_material_fixtures.hh
	index a32953d27..462a9dc09 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_fixtures.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_fixtures.hh
	@@ -1,215 +1,215 @@
	/**
	* @file test_material_fixtures.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Fri Dec 13 2019
	*
	* @brief Fixture for material tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <material_elastic.hh>
	#include <solid_mechanics_model.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <random>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	template <typename T> class FriendMaterial : public T {
	public:
	~FriendMaterial() = default;

	FriendMaterial(SolidMechanicsModel & model, const ID & id = "material")
	: T(model, id) {
	gen.seed(::testing::GTEST_FLAG(random_seed));
	}

	virtual void testComputeStress() { AKANTU_TO_IMPLEMENT(); };
	virtual void testComputeTangentModuli() { AKANTU_TO_IMPLEMENT(); };
	virtual void testEnergyDensity() { AKANTU_TO_IMPLEMENT(); };
	virtual void testCelerity() { AKANTU_TO_IMPLEMENT(); }

	virtual void setParams() {}
	virtual void SetUp() {
	this->setParams();
	this->initMaterial();
	}

	virtual void TearDown() {}

	inline Matrix<Real> getDeviatoricStrain(Real intensity);
	inline Matrix<Real> getHydrostaticStrain(Real intensity);
	inline Matrix<Real> getComposedStrain(Real intensity);

	inline const Matrix<Real> reverseRotation(Matrix<Real> mat,
	Matrix<Real> rotation_matrix) {
	Matrix<Real> R = rotation_matrix;
	Matrix<Real> m2 = mat * R;
	Matrix<Real> m1 = R.transpose();
	return m1 * m2;
	};

	inline const Matrix<Real> applyRotation(Matrix<Real> mat,
	const Matrix<Real> rotation_matrix) {
	Matrix<Real> R = rotation_matrix;
	Matrix<Real> m2 = mat * R.transpose();
	Matrix<Real> m1 = R;
	return m1 * m2;
	};

	inline Vector<Real> getRandomVector();
	inline Matrix<Real> getRandomRotation();

	protected:
	std::mt19937 gen;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T>
	Matrix<Real> FriendMaterial<T>::getDeviatoricStrain(Real intensity) {
	Matrix<Real> dev = {{0., 1., 2.}, {1., 0., 3.}, {2., 3., 0.}};
	dev *= intensity;
	return dev;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T>
	Matrix<Real> FriendMaterial<T>::getHydrostaticStrain(Real intensity) {
	Matrix<Real> dev = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
	dev *= intensity;
	return dev;
	}

	/* -------------------------------------------------------------------------- */

	template <typename T>
	Matrix<Real> FriendMaterial<T>::getComposedStrain(Real intensity) {
	Matrix<Real> s = FriendMaterial<T>::getHydrostaticStrain(intensity) +
	FriendMaterial<T>::getDeviatoricStrain(intensity);
	s *= intensity;
	return s;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> Vector<Real> FriendMaterial<T>::getRandomVector() {
	auto dim = this->spatial_dimension;
	std::uniform_real_distribution<Real> dis;
	Vector<Real> vector(dim, 0.);
	while (vector.norm() < 1e-9) {
	for (auto s : arange(dim))
	vector(s) = dis(gen);
	}
	return vector;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T> Matrix<Real> FriendMaterial<T>::getRandomRotation() {
	auto dim = this->spatial_dimension;

	Matrix<Real> rotation(dim, dim);
	Vector<Real> v1 = rotation(0);
	v1 = getRandomVector().normalize();
	if (dim == 2) {
	Vector<Real> v1_ = {v1(0), v1(1), 0};
	Vector<Real> v2_(3);
	Vector<Real> v3_ = {0, 0, 1};
	v2_.crossProduct(v3_, v1_);

	Vector<Real> v2 = rotation(1);
	v2(0) = v2_(0);
	v2(1) = v2_(1);
	}

	if (dim == 3) {
	auto v2 = getRandomVector();
	v2 = (v2 - v2.dot(v1) * v1).normalize();

	Vector<Real> v3(3);
	v3.crossProduct(v1, v2);

	rotation(1) = v2;
	rotation(2) = v3;
	}

	//#define debug_
	#if defined(debug_)
	if (dim == 2)
	rotation = Matrix<Real>{{1., 0.}, {0., 1.}};
	if (dim == 3)
	rotation = Matrix<Real>{{1., 0., 0.}, {0., 1., 0.}, {0., 0., 1.}};
	#endif

	rotation = rotation.transpose();

	return rotation;
	}

	/* -------------------------------------------------------------------------- */
	template <typename T, class Model>
	class TestMaterialBaseFixture : public ::testing::Test {
	public:
	using mat_class = typename T::mat_class;

	void SetUp() override {
	constexpr auto spatial_dimension = T::Dim;
	mesh = std::make_unique<Mesh>(spatial_dimension);
	model = std::make_unique<Model>(*mesh);
	material = std::make_unique<friend_class>(*model);
	material->SetUp();
	}

	void TearDown() override {
	material->TearDown();
	material.reset(nullptr);
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	using friend_class = FriendMaterial<mat_class>;

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<Model> model;
	std::unique_ptr<friend_class> material;
	};

	/* -------------------------------------------------------------------------- */
	template <template <UInt> class T, UInt _Dim> struct Traits {
	using mat_class = T<_Dim>;
	static constexpr UInt Dim = _Dim;
	};

	/* -------------------------------------------------------------------------- */
	template <typename T>
	using TestMaterialFixture = TestMaterialBaseFixture<T, SolidMechanicsModel>;

	/* -------------------------------------------------------------------------- */
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_mazars.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_mazars.cc
	index e7532cd3c..455b811db 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_mazars.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_mazars.cc
	@@ -1,290 +1,290 @@
	/**
	* @file test_material_mazars.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Thu Oct 08 2015
	* @date last modification: Wed Jun 05 2019
	*
	* @brief test for material mazars, dissymmetric
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_accessor.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	debug::setDebugLevel(akantu::dblWarning);

	akantu::initialize("material_mazars.dat", argc, argv);
	const UInt spatial_dimension = 3;

	// ElementType type = _quadrangle_4;
	ElementType type = _hexahedron_8;

	Mesh mesh(spatial_dimension);

	MeshAccessor mesh_accessor(mesh);

	Array<Real> & nodes = mesh_accessor.getNodes();
	Array<UInt> & connectivity = mesh_accessor.getConnectivity(type);

	const Real width = 1;
	UInt nb_dof = 0;

	connectivity.resize(1);

	if (type == _hexahedron_8) {
	nb_dof = 8;
	nodes.resize(nb_dof);

	nodes(0, 0) = 0.;
	nodes(0, 1) = 0.;
	nodes(0, 2) = 0.;

	nodes(1, 0) = width;
	nodes(1, 1) = 0.;
	nodes(1, 2) = 0.;

	nodes(2, 0) = width;
	nodes(2, 1) = width;
	nodes(2, 2) = 0;

	nodes(3, 0) = 0;
	nodes(3, 1) = width;
	nodes(3, 2) = 0;

	nodes(4, 0) = 0.;
	nodes(4, 1) = 0.;
	nodes(4, 2) = width;

	nodes(5, 0) = width;
	nodes(5, 1) = 0.;
	nodes(5, 2) = width;

	nodes(6, 0) = width;
	nodes(6, 1) = width;
	nodes(6, 2) = width;

	nodes(7, 0) = 0;
	nodes(7, 1) = width;
	nodes(7, 2) = width;

	connectivity(0, 0) = 0;
	connectivity(0, 1) = 1;
	connectivity(0, 2) = 2;
	connectivity(0, 3) = 3;
	connectivity(0, 4) = 4;
	connectivity(0, 5) = 5;
	connectivity(0, 6) = 6;
	connectivity(0, 7) = 7;
	} else if (type == _quadrangle_4) {
	nb_dof = 4;
	nodes.resize(nb_dof);

	nodes(0, 0) = 0.;
	nodes(0, 1) = 0.;

	nodes(1, 0) = width;
	nodes(1, 1) = 0;

	nodes(2, 0) = width;
	nodes(2, 1) = width;

	nodes(3, 0) = 0.;
	nodes(3, 1) = width;

	connectivity(0, 0) = 0;
	connectivity(0, 1) = 1;
	connectivity(0, 2) = 2;
	connectivity(0, 3) = 3;
	}

	mesh_accessor.makeReady();

	SolidMechanicsModel model(mesh);
	model.initFull();
	Material & mat = model.getMaterial(0);
	std::cout << mat << std::endl;

	/// boundary conditions
	Array<Real> & disp = model.getDisplacement();
	Array<Real> & velo = model.getVelocity();
	Array<bool> & boun = model.getBlockedDOFs();

	for (UInt i = 0; i < nb_dof; ++i) {
	boun(i, 0) = true;
	}

	Real time_step = model.getStableTimeStep() * .5;
	// Real time_step = 1e-5;

	std::cout << "Time Step = " << time_step
	<< "s - nb elements : " << mesh.getNbElement(type) << std::endl;
	model.setTimeStep(time_step);

	std::ofstream energy;
	energy.open("energies_and_scalar_mazars.csv");
	energy << "id,rtime,epot,ekin,u,wext,kin+pot,D,strain_xx,strain_yy,stress_xx,"
	"stress_yy,edis,tot"
	<< std::endl;

	/// Set dumper
	model.setBaseName("uniaxial_comp-trac_mazars");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpField("damage");
	model.addDumpField("strain");
	model.addDumpField("stress");
	model.addDumpField("partitions");
	model.dump();

	const Array<Real> & strain = mat.getGradU(type);
	const Array<Real> & stress = mat.getStress(type);
	const Array<Real> & damage = mat.getArray<Real>("damage", type);

	/* ------------------------------------------------------------------------ */
	/* Main loop */
	/* ------------------------------------------------------------------------ */
	Real wext = 0.;
	Real sigma_max = 0, sigma_min = 0;

	Real max_disp;
	Real stress_xx_compression_1;
	UInt nb_steps = 7e5 / 150;

	Real adisp = 0;
	for (UInt s = 0; s < nb_steps; ++s) {
	if (s == 0) {
	max_disp = 0.003;
	adisp = -(max_disp * 8. / nb_steps) / 2.;
	std::cout << "Step " << s << " compression: " << max_disp << std::endl;
	}

	if (s == (2 * nb_steps / 8)) {
	stress_xx_compression_1 = stress(0, 0);
	max_disp = 0 + max_disp;
	adisp = max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " discharge" << std::endl;
	}

	if (s == (3 * nb_steps / 8)) {
	max_disp = 0.004;
	adisp = -max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " compression: " << max_disp << std::endl;
	}

	if (s == (4 * nb_steps / 8)) {
	if (stress(0, 0) < stress_xx_compression_1) {
	std::cout << "after this second compression step softening should have "
	"started"
	<< std::endl;
	return EXIT_FAILURE;
	}
	max_disp = 0.0015 + max_disp;
	adisp = max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " discharge tension: " << max_disp
	<< std::endl;
	}

	if (s == (5 * nb_steps / 8)) {
	max_disp = 0. + 0.0005;
	adisp = -max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " discharge" << std::endl;
	}

	if (s == (6 * nb_steps / 8)) {
	max_disp = 0.0035 - 0.001;
	adisp = max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " tension: " << max_disp << std::endl;
	}

	if (s == (7 * nb_steps / 8)) {
	// max_disp = max_disp;
	adisp = -max_disp * 8. / nb_steps;
	std::cout << "Step " << s << " discharge" << std::endl;
	}

	for (UInt i = 0; i < nb_dof; ++i) {
	if (std::abs(nodes(i, 0) - width) <
	std::numeric_limits<Real>::epsilon()) {
	disp(i, 0) += adisp;
	velo(i, 0) = adisp / time_step;
	}
	}

	std::cout << "S: " << s << "/" << nb_steps << " inc disp: " << adisp
	<< " disp: " << std::setw(5) << disp(2, 0) << "\r" << std::flush;

	model.solveStep();

	Real epot = model.getEnergy("potential");
	Real ekin = model.getEnergy("kinetic");
	Real edis = model.getEnergy("dissipated");
	wext += model.getEnergy("external work");

	sigma_max = std::max(sigma_max, stress(0, 0));
	sigma_min = std::min(sigma_min, stress(0, 0));
	if (s % 10 == 0)
	energy << s << "," // 1
	<< s * time_step << "," // 2
	<< epot << "," // 3
	<< ekin << "," // 4
	<< disp(2, 0) << "," // 5
	<< wext << "," // 6
	<< epot + ekin << "," // 7
	<< damage(0) << "," // 8
	<< strain(0, 0) << "," // 9
	<< strain(0, 3) << "," // 11
	<< stress(0, 0) << "," // 10
	<< stress(0, 3) << "," // 10
	<< edis << "," // 12
	<< epot + ekin + edis // 13
	<< std::endl;

	if (s % 100 == 0)
	model.dump();
	}

	std::cout << std::endl
	<< "sigma_max = " << sigma_max << ", sigma_min = " << sigma_min
	<< std::endl;
	/// Verif the maximal/minimal stress values
	if ((std::abs(sigma_max) > std::abs(sigma_min)) or
	(std::abs(sigma_max - 6.24e6) > 1e5) or
	(std::abs(sigma_min + 2.943e7) > 1e6))
	return EXIT_FAILURE;
	energy.close();

	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.cc
	index 79846b81a..0bcff4bf8 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.cc
	@@ -1,96 +1,96 @@
	/**
	* @file custom_non_local_test_material.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Mar 01 2015
	* @date last modification: Mon Sep 11 2017
	*
	* @brief Custom material to test the non local implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#include "custom_non_local_test_material.hh"

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	CustomNonLocalTestMaterial<dim>::CustomNonLocalTestMaterial(
	SolidMechanicsModel & model, const ID & id)
	: MyNonLocalParent(model, id), local_damage("local_damage", *this),
	damage("damage", *this) {
	// Initialize the internal field by specifying the number of components
	this->local_damage.initialize(1);
	this->damage.initialize(1);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void CustomNonLocalTestMaterial<dim>::registerNonLocalVariables() {
	/// register the non-local variable in the manager
	this->model.getNonLocalManager().registerNonLocalVariable(
	this->local_damage.getName(), this->damage.getName(), 1);

	this->model.getNonLocalManager()
	.getNeighborhood(this->name)
	.registerNonLocalVariable(damage.getName());
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim> void CustomNonLocalTestMaterial<dim>::initMaterial() {
	MyNonLocalParent::initMaterial();
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void CustomNonLocalTestMaterial<dim>::computeStress(ElementType el_type,
	GhostType ghost_type) {
	MyNonLocalParent::computeStress(el_type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <UInt dim>
	void CustomNonLocalTestMaterial<dim>::computeNonLocalStress(
	ElementType el_type, GhostType ghost_type) {
	Array<Real>::const_scalar_iterator dam =
	this->damage(el_type, ghost_type).begin();
	Array<Real>::matrix_iterator stress =
	this->stress(el_type, ghost_type).begin(dim, dim);
	Array<Real>::matrix_iterator stress_end =
	this->stress(el_type, ghost_type).end(dim, dim);

	// compute the damage and update the stresses
	for (; stress != stress_end; ++stress, ++dam) {
	stress = (1. - *dam);
	}
	}

	/* -------------------------------------------------------------------------- */
	// Instantiate the material for the 3 dimensions
	INSTANTIATE_MATERIAL(custom_non_local_test_material,
	CustomNonLocalTestMaterial);
	/* -------------------------------------------------------------------------- */
	} // namespace akantu
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.hh b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.hh
	index 75d2e4f7c..83c24ef76 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/custom_non_local_test_material.hh
	@@ -1,81 +1,81 @@
	/**
	* @file custom_non_local_test_material.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Jun 26 2020
	*
	* @brief Custom material to test the non local implementation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_elastic.hh"
	#include "material_non_local.hh"
	/* -------------------------------------------------------------------------- */

	#ifndef CUSTOM_NON_LOCAL_TEST_MATERIAL_HH_
	#define CUSTOM_NON_LOCAL_TEST_MATERIAL_HH_

	namespace akantu {

	template <UInt dim>
	class CustomNonLocalTestMaterial
	: public MaterialNonLocal<dim, MaterialElastic<dim>> {
	public:
	using MyNonLocalParent = MaterialNonLocal<dim, MaterialElastic<dim>>;

	CustomNonLocalTestMaterial(SolidMechanicsModel & model, const ID & id);

	/* ------------------------------------------------------------------------ */
	void initMaterial() override;

	void computeNonLocalStress(ElementType el_type, GhostType ghost_type);
	void computeStress(ElementType el_type, GhostType ghost_type) override;

	protected:
	void registerNonLocalVariables() override;

	/* ------------------------------------------------------------------------ */
	void computeNonLocalStresses(GhostType ghost_type) override {
	AKANTU_DEBUG_IN();

	for (auto & type : this->element_filter.elementTypes(dim, ghost_type)) {
	computeNonLocalStress(type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	public:
	void setDamage(Real dam) { this->local_damage.setDefaultValue(dam); }

	protected:
	InternalField<Real> local_damage;
	InternalField<Real> damage;
	};

	} // namespace akantu

	#endif /* CUSTOM_NON_LOCAL_TEST_MATERIAL_HH_ */
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_damage_non_local.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_damage_non_local.cc
	index b37abae23..3bc68d7f8 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_damage_non_local.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_damage_non_local.cc
	@@ -1,117 +1,117 @@
	/**
	* @file test_material_damage_non_local.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Clement Roux <clement.roux@epfl.ch>
	*
	* @date creation: Wed Aug 04 2010
	* @date last modification: Thu Dec 14 2017
	*
	* @brief test for non-local damage materials on a 2D plate with a section gap
	* the sample should break at the notch
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	debug::setDebugLevel(dblWarning);

	akantu::initialize("material_damage_non_local.dat", argc, argv);
	UInt max_steps = 1100;

	const UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("mesh_section_gap.msh");

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull();

	Real time_step = model.getStableTimeStep();
	model.setTimeStep(time_step / 2.5);

	std::cout << model << std::endl;

	model.applyBC(BC::Dirichlet::FixedValue(0.0), "Fixed");

	// Boundary condition (Neumann)
	Matrix<Real> stress(2, 2);
	stress.eye(5e8);
	model.applyBC(BC::Neumann::FromHigherDim(stress), "Traction");

	model.setBaseName("damage_non_local");
	model.addDumpFieldVector("displacement");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.addDumpField("damage");
	model.addDumpField("stress");
	model.addDumpField("strain");
	model.dump();

	for (UInt s = 0; s < max_steps; ++s) {
	model.solveStep();

	// if(s % 100 == 0) std::cout << "Step " << s+1 << "/" << max_steps
	// <<std::endl; if(s % 100 == 0) model.dump();
	}

	model.dump();

	const auto & lower_bounds = mesh.getLowerBounds();
	const auto & upper_bounds = mesh.getUpperBounds();
	Real L = upper_bounds(0) - lower_bounds(0);
	Real H = upper_bounds(1) - lower_bounds(1);

	const auto & mat = model.getMaterial(0);
	const auto & filter = mat.getElementFilter();
	Vector<Real> barycenter(spatial_dimension);

	for (auto & type : filter.elementTypes(spatial_dimension)) {
	UInt nb_elem = mesh.getNbElement(type);
	const UInt nb_gp = model.getFEEngine().getNbIntegrationPoints(type);
	auto & material_damage_array = mat.getArray<Real>("damage", type);
	UInt cpt = 0;
	for (UInt nel = 0; nel < nb_elem; ++nel) {
	mesh.getBarycenter({type, nel, _not_ghost}, barycenter);
	if ((std::abs(barycenter(0) - (L / 2) + 0.025) < 0.025) &&
	(std::abs(barycenter(1) - (H / 2) + 0.025) < 0.025)) {
	if (material_damage_array(cpt, 0) < 0.9) {
	std::terminate();
	}
	}
	cpt += nb_gp;
	}
	}

	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_non_local.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_non_local.cc
	index 2e0622964..34ea1a015 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_non_local.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_non_local/test_material_non_local.cc
	@@ -1,104 +1,104 @@
	/**
	* @file test_material_non_local.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Aug 31 2011
	* @date last modification: Thu Mar 22 2018
	*
	* @brief test of the main part of the non local materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "custom_non_local_test_material.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize("material.dat", argc, argv);

	// some configuration variables
	const UInt spatial_dimension = 2;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	// mesh creation and read
	if (prank == 0) {
	mesh.read("mesh.msh");
	}
	mesh.distribute();

	/// model creation
	SolidMechanicsModel model(mesh);

	/// model initialization changed to use our material
	model.initFull();

	CustomNonLocalTestMaterial<spatial_dimension> & mat =
	dynamic_cast<CustomNonLocalTestMaterial<spatial_dimension> &>(
	model.getMaterial("test"));

	if (prank == 0)
	std::cout << mat << std::endl;

	// Setting up the dumpers + first dump
	model.setBaseName("non_local_material");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.addDumpField("partitions");
	model.addDumpField("stress");
	model.addDumpField("stress");
	model.addDumpField("local_damage");
	model.addDumpField("damage");

	model.assembleInternalForces();
	model.dump();

	// Array<Real> & damage = mat.getArray("local_damage", _quadrangle_4);
	Array<Real> & damage = mat.getArray<Real>("local_damage", _triangle_3);

	RandomGenerator<UInt> gen;

	for (UInt i = 0; i < 1; ++i) {
	UInt g = (gen() / Real(RandomGenerator<UInt>::max() -
	RandomGenerator<UInt>::min())) *
	damage.size();
	std::cout << prank << " -> " << g << std::endl;
	damage(g) = 1.;
	}

	model.assembleInternalForces();
	model.dump();

	akantu::finalize();
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_orthotropic.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_orthotropic.cc
	index 2eb53d280..6c0d747da 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_orthotropic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_orthotropic.cc
	@@ -1,101 +1,101 @@
	/**
	* @file test_material_orthotropic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu May 09 2019
	*
	* @brief test of the class SolidMechanicsModel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	// akantu::initialize("orthotropic.dat", argc, argv);
	akantu::initialize("orthotropic.dat", argc, argv);
	UInt max_steps = 1000;
	Real epot, ekin;

	Mesh mesh(2);
	mesh.read("square.msh");
	mesh.createBoundaryGroupFromGeometry();

	SolidMechanicsModel model(mesh);

	/// model initialization
	model.initFull();

	Real time_step = model.getStableTimeStep();
	model.setTimeStep(time_step / 10.);

	model.assembleMassLumped();

	std::cout << model << std::endl;

	// Boundary condition (Neumann)
	Matrix<Real> stress(2, 2);
	stress.eye(Real(1e3));
	model.applyBC(BC::Neumann::FromHigherDim(stress), "boundary_0");

	model.setBaseName("square-orthotrope");
	model.addDumpFieldVector("displacement");
	model.addDumpField("mass");
	model.addDumpField("velocity");
	model.addDumpField("acceleration");
	model.addDumpFieldVector("external_force");
	model.addDumpFieldVector("internal_force");
	model.addDumpField("stress");
	model.addDumpField("grad_u");
	model.dump();

	std::ofstream energy;
	energy.open("energy.csv");
	energy << "id,epot,ekin,tot" << std::endl;

	for (UInt s = 0; s < max_steps; ++s) {
	model.solveStep();

	epot = model.getEnergy("potential");
	ekin = model.getEnergy("kinetic");

	std::cerr << "passing step " << s << "/" << max_steps << std::endl;
	energy << s << "," << epot << "," << ekin << "," << epot + ekin
	<< std::endl;

	if (s % 100 == 0)
	model.dump();
	}

	energy.close();

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_thermal.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_thermal.cc
	index 670d4e6f1..8dfe2b79a 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_thermal.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_thermal.cc
	@@ -1,106 +1,106 @@
	/**
	* @file test_material_thermal.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Test the thermal material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_thermal.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material_fixtures.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	using mat_types =
	::testing::Types<Traits<MaterialThermal, 1>, Traits<MaterialThermal, 2>,
	Traits<MaterialThermal, 3>>;

	/* -------------------------------------------------------------------------- */
	template <> void FriendMaterial<MaterialThermal<3>>::testComputeStress() {
	Real E = 1.;
	Real nu = .3;
	Real alpha = 2;
	setParam("E", E);
	setParam("nu", nu);
	setParam("alpha", alpha);

	Real deltaT = 1;
	Real sigma = 0;
	this->computeStressOnQuad(sigma, deltaT);
	Real solution = -E / (1 - 2 * nu) * alpha * deltaT;
	auto error = std::abs(sigma - solution);
	ASSERT_NEAR(error, 0, 1e-14);
	}

	template <> void FriendMaterial<MaterialThermal<2>>::testComputeStress() {
	Real E = 1.;
	Real nu = .3;
	Real alpha = 2;
	setParam("E", E);
	setParam("nu", nu);
	setParam("alpha", alpha);

	Real deltaT = 1;
	Real sigma = 0;
	this->computeStressOnQuad(sigma, deltaT);
	Real solution = -E / (1 - 2 * nu) * alpha * deltaT;
	auto error = std::abs(sigma - solution);
	ASSERT_NEAR(error, 0, 1e-14);
	}

	template <> void FriendMaterial<MaterialThermal<1>>::testComputeStress() {
	Real E = 1.;
	Real nu = .3;
	Real alpha = 2;
	setParam("E", E);
	setParam("nu", nu);
	setParam("alpha", alpha);

	Real deltaT = 1;
	Real sigma = 0;
	this->computeStressOnQuad(sigma, deltaT);
	Real solution = -E * alpha * deltaT;
	auto error = std::abs(sigma - solution);
	ASSERT_NEAR(error, 0, 1e-14);
	}

	namespace {

	template <typename T>
	class TestMaterialThermalFixture : public ::TestMaterialFixture<T> {};

	TYPED_TEST_SUITE(TestMaterialThermalFixture, mat_types, );

	TYPED_TEST(TestMaterialThermalFixture, ThermalComputeStress) {
	this->material->testComputeStress();
	}
	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation.cc
	index f7235b84a..2cd8a5e0e 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation.cc
	@@ -1,171 +1,171 @@
	/**
	* @file test_material_standard_linear_solid_deviatoric_relaxation.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Vladislav Yastrebov <vladislav.yastrebov@epfl.ch>
	*
	* @date creation: Mon Aug 09 2010
	* @date last modification: Sat Dec 19 2020
	*
	* @brief test of the viscoelastic material: relaxation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	#include <sstream>
	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	akantu::initialize("material_standard_linear_solid_deviatoric_relaxation.dat",
	argc, argv);
	akantu::debug::setDebugLevel(akantu::dblWarning);

	// sim data
	Real T = 10.;
	Real eps = 0.001;

	const UInt dim = 2;
	Real sim_time = 25.;
	Real time_factor = 0.1;

	Real tolerance = 1e-7;

	Mesh mesh(dim);
	mesh.read("test_material_standard_linear_solid_deviatoric_relaxation.msh");

	const ElementType element_type = _quadrangle_4;
	SolidMechanicsModel model(mesh);

	/* ------------------------------------------------------------------------ */
	/* Initialization */
	/* ------------------------------------------------------------------------ */
	model.initFull();
	std::cout << model.getMaterial(0) << std::endl;

	model.assembleMassLumped();

	std::stringstream filename_sstr;
	filename_sstr
	<< "test_material_standard_linear_solid_deviatoric_relaxation.out";
	std::ofstream output_data;
	output_data.open(filename_sstr.str().c_str());
	output_data << "#[1]-time [2]-sigma_analytic [3+]-sigma_measurements"
	<< std::endl;

	Material & mat = model.getMaterial(0);

	const Array<Real> & stress = mat.getStress(element_type);

	Real Eta = mat.get("Eta");
	Real EV = mat.get("Ev");
	Real Einf = mat.get("Einf");
	Real nu = mat.get("nu");
	Real Ginf = Einf / (2 * (1 + nu));
	Real G = EV / (2 * (1 + nu));
	Real G0 = G + Ginf;
	Real gamma = G / G0;
	Real tau = Eta / EV;
	Real gammainf = Ginf / G0;

	UInt nb_nodes = mesh.getNbNodes();
	const Array<Real> & coordinate = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();

	/// Setting time step
	Real time_step = model.getStableTimeStep() * time_factor;
	std::cout << "Time Step = " << time_step << "s" << std::endl;
	model.setTimeStep(time_step);

	UInt max_steps = sim_time / time_step;
	UInt out_interval = 1;

	Real time = 0.;

	/* ------------------------------------------------------------------------ */
	/* Main loop */
	/* ------------------------------------------------------------------------ */
	for (UInt s = 0; s <= max_steps; ++s) {

	if (s % 1000 == 0)
	std::cerr << "passing step " << s << "/" << max_steps << std::endl;

	time = s * time_step;
	// impose displacement
	Real epsilon = 0.;
	if (time < T) {
	epsilon = eps * time / T;
	} else {
	epsilon = eps;
	}
	for (UInt n = 0; n < nb_nodes; ++n) {
	displacement(n, 0) = epsilon * coordinate(n, 1);
	displacement(n, 1) = epsilon * coordinate(n, 0);
	}

	// compute stress
	model.assembleInternalForces();

	// print output
	if (s % out_interval == 0) {
	// analytical solution
	Real solution = 0.;
	if (time < T) {
	solution = 2 * G0 * eps / T *
	(gammainf * time + gamma * tau * (1 - exp(-time / tau)));
	} else {
	solution = 2 * G0 * eps *
	(gammainf + gamma * tau / T *
	(exp((T - time) / tau) - exp(-time / tau)));
	}
	output_data << s * time_step << " " << solution;

	// data output
	Array<Real>::const_matrix_iterator stress_it = stress.begin(dim, dim);
	Array<Real>::const_matrix_iterator stress_end = stress.end(dim, dim);
	for (; stress_it != stress_end; ++stress_it) {
	output_data << " " << (stress_it)(0, 1) << " " << (stress_it)(1, 0);

	// test error
	Real rel_error_1 = std::abs(((*stress_it)(0, 1) - solution) / solution);
	Real rel_error_2 = std::abs(((*stress_it)(1, 0) - solution) / solution);
	if (rel_error_1 > tolerance \|\| rel_error_2 > tolerance) {
	std::cerr << "Relative error: " << rel_error_1 << " " << rel_error_2
	<< std::endl;
	return EXIT_FAILURE;
	}
	}
	output_data << std::endl;
	}
	}

	finalize();

	std::cout << "Test successful!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation_tension.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
	index 38e3e9470..fad4b3cc7 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic/test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
	@@ -1,181 +1,181 @@
	/**
	* @file test_material_standard_linear_solid_deviatoric_relaxation_tension.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Mon Aug 09 2010
	* @date last modification: Sat Dec 19 2020
	*
	* @brief test of the viscoelastic material: relaxation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	#include <sstream>
	/* -------------------------------------------------------------------------- */
	#include "solid_mechanics_model.hh"

	using namespace akantu;

	int main(int argc, char * argv[]) {
	akantu::initialize("material_standard_linear_solid_deviatoric_relaxation.dat",
	argc, argv);

	// sim data
	Real T = 10.;
	Real eps = 0.001;

	// const UInt dim = 3;
	const UInt dim = 2;
	Real sim_time = 25.;
	// Real sim_time = 250.;
	Real time_factor = 0.1;

	Real tolerance = 1e-5;

	Mesh mesh(dim);
	mesh.read("test_material_standard_linear_solid_deviatoric_relaxation.msh");
	// mesh_io.read("hexa_structured.msh",mesh);
	// const ElementType element_type = _hexahedron_8;
	const ElementType element_type = _quadrangle_4;
	SolidMechanicsModel model(mesh);

	/* ------------------------------------------------------------------------ */
	/* Initialization */
	/* ------------------------------------------------------------------------ */
	model.initFull();
	std::cout << model.getMaterial(0) << std::endl;

	model.assembleMassLumped();

	model.assembleInternalForces();
	model.getMaterial(0).setToSteadyState();

	std::stringstream filename_sstr;
	filename_sstr << "test_material_standard_linear_solid_deviatoric_relaxation_"
	"tension.out";
	std::ofstream output_data;
	output_data.open(filename_sstr.str().c_str());
	output_data << "#[1]-time [2]-sigma_analytic [3+]-sigma_measurements"
	<< std::endl;

	Material & mat = model.getMaterial(0);
	const Array<Real> & stress = mat.getStress(element_type);

	Real Eta = mat.get("Eta");
	Real EV = mat.get("Ev");
	Real Einf = mat.get("Einf");
	Real E0 = mat.get("E");

	Real kpa = mat.get("kapa");
	Real mu = mat.get("mu");

	Real gamma = EV / E0;
	Real gammainf = Einf / E0;

	Real tau = Eta / EV;
	std::cout << "relaxation time = " << tau << std::endl;

	UInt nb_nodes = mesh.getNbNodes();
	const Array<Real> & coordinate = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();

	/// Setting time step
	Real time_step = model.getStableTimeStep() * time_factor;
	std::cout << "Time Step = " << time_step << "s" << std::endl;
	model.setTimeStep(time_step);

	UInt max_steps = sim_time / time_step;
	UInt out_interval = 1;

	Real time = 0.;

	/* ------------------------------------------------------------------------ */
	/* Main loop */
	/* ------------------------------------------------------------------------ */
	for (UInt s = 0; s <= max_steps; ++s) {

	if (s % 1000 == 0)
	std::cerr << "passing step " << s << "/" << max_steps << std::endl;

	time = s * time_step;
	// impose displacement
	Real epsilon = 0.;
	if (time < T) {
	epsilon = eps * time / T;
	} else {
	epsilon = eps;
	}

	for (UInt n = 0; n < nb_nodes; ++n) {
	for (UInt d = 0; d < dim; ++d)
	displacement(n, d) = epsilon * coordinate(n, d);
	}

	// compute stress
	model.assembleInternalForces();

	// print output
	if (s % out_interval == 0) {
	// analytical solution
	Real epskk = dim * eps;
	Real solution = 0.;
	if (time < T) {
	solution =
	2 * mu * (eps - epskk / 3.) / T *
	(gammainf * time + gamma * tau * (1 - exp(-time / tau))) +
	gammainf * kpa * epskk * time / T;
	} else {
	solution =
	2 * mu * (eps - epskk / 3.) *
	(gammainf +
	gamma * tau / T * (exp((T - time) / tau) - exp(-time / tau))) +
	gammainf * kpa * epskk;
	}
	output_data << s * time_step << " " << solution;

	// data output
	Array<Real>::const_matrix_iterator stress_it = stress.begin(dim, dim);
	Array<Real>::const_matrix_iterator stress_end = stress.end(dim, dim);
	for (; stress_it != stress_end; ++stress_it) {
	output_data << " " << (*stress_it)(1, 1);

	// test error
	Real rel_error_1 = std::abs(((*stress_it)(1, 1) - solution) / solution);
	if (rel_error_1 > tolerance) {
	std::cerr << "Relative error: " << rel_error_1 << std::endl;
	return EXIT_FAILURE;
	}
	}
	output_data << std::endl;
	}
	}

	finalize();

	std::cout << "Test successful!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic_maxwell/test_material_viscoelastic_maxwell_relaxation.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic_maxwell/test_material_viscoelastic_maxwell_relaxation.cc
	index c144a964d..692c80fa3 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic_maxwell/test_material_viscoelastic_maxwell_relaxation.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_material_viscoelastic_maxwell/test_material_viscoelastic_maxwell_relaxation.cc
	@@ -1,196 +1,196 @@
	/**
	* @file test_material_viscoelastic_maxwell_relaxation.cc
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	*
	* @date creation: Tue Nov 20 2018
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test of the viscoelastic material: relaxation
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	#include <sstream>
	/* -------------------------------------------------------------------------- */
	#include "material_viscoelastic_maxwell.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	#include "sparse_matrix.hh"

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */

	int main(int argc, char * argv[]) {
	akantu::initialize("material_viscoelastic_maxwell.dat", argc, argv);

	// sim data
	Real eps = 0.1;

	const UInt dim = 2;
	Real sim_time = 100.;
	Real T = 10.;
	Real tolerance = 1e-6;
	Mesh mesh(dim);
	mesh.read("test_material_viscoelastic_maxwell.msh");

	const ElementType element_type = _quadrangle_4;
	SolidMechanicsModel model(mesh);

	/* ------------------------------------------------------------------------ */
	/* Initialization */
	/* ------------------------------------------------------------------------ */
	model.initFull(_analysis_method = _static);
	std::cout << model.getMaterial(0) << std::endl;

	std::stringstream filename_sstr;
	filename_sstr << "test_material_viscoelastic_maxwell.out";
	std::ofstream output_data;
	output_data.open(filename_sstr.str().c_str());

	Material & mat = model.getMaterial(0);

	const Array<Real> & stress = mat.getStress(element_type);

	Vector<Real> Eta = mat.get("Eta");
	Vector<Real> Ev = mat.get("Ev");
	Real Einf = mat.get("Einf");
	Real nu = mat.get("nu");
	Real lambda = Eta(0) / Ev(0);
	Real pre_mult = 1 / (1 + nu) / (1 - 2 * nu);
	Real time_step = 0.1;

	UInt nb_nodes = mesh.getNbNodes();
	const Array<Real> & coordinate = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> & blocked = model.getBlockedDOFs();

	/// Setting time step

	model.setTimeStep(time_step);

	UInt max_steps = sim_time / time_step + 1;
	Real time = 0.;

	auto & solver = model.getNonLinearSolver();
	solver.set("max_iterations", 200);
	solver.set("threshold", 1e-7);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	/* ------------------------------------------------------------------------ */
	/* Main loop */
	/* ------------------------------------------------------------------------ */
	for (UInt s = 0; s <= max_steps; ++s) {

	std::cout << "Time Step = " << time_step << "s" << std::endl;
	std::cout << "Time = " << time << std::endl;

	// impose displacement
	Real epsilon = 0;
	if (time < T) {
	epsilon = eps * time / T;
	} else {
	epsilon = eps;
	}

	for (UInt n = 0; n < nb_nodes; ++n) {
	if (Math::are_float_equal(coordinate(n, 0), 0.0)) {
	displacement(n, 0) = 0;
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 1), 0.0)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = 0;
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 0), 0.001)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	} else if (Math::are_float_equal(coordinate(n, 1), 0.001)) {
	displacement(n, 0) = epsilon * coordinate(n, 0);
	blocked(n, 0) = true;
	displacement(n, 1) = epsilon * coordinate(n, 1);
	blocked(n, 1) = true;
	}
	}

	try {
	model.solveStep();
	} catch (debug::Exception & e) {
	}

	Int nb_iter = solver.get("nb_iterations");
	Real error = solver.get("error");
	bool converged = solver.get("converged");

	if (converged) {
	std::cout << "Converged in " << nb_iter << " iterations" << std::endl;
	} else {
	std::cout << "Didn't converge after " << nb_iter
	<< " iterations. Error is " << error << std::endl;
	return EXIT_FAILURE;
	}

	// analytical solution
	Real solution_11 = 0.;
	if (time < T) {
	solution_11 = pre_mult * eps / T *
	(Einf * time + lambda * Ev(0) * (1 - exp(-time / lambda)));
	} else {
	solution_11 =
	pre_mult * eps *
	(Einf + lambda * Ev(0) / T *
	(exp((T - time) / lambda) - exp(-time / lambda)));
	}

	// data output
	output_data << s * time_step << " " << epsilon << " " << solution_11;
	Array<Real>::const_matrix_iterator stress_it = stress.begin(dim, dim);
	Array<Real>::const_matrix_iterator stress_end = stress.end(dim, dim);
	for (; stress_it != stress_end; ++stress_it) {
	output_data << " " << (*stress_it)(0, 0);
	// test error
	Real rel_error_11 =
	std::abs(((*stress_it)(0, 0) - solution_11) / solution_11);
	if (rel_error_11 > tolerance) {
	std::cerr << "Relative error: " << rel_error_11 << std::endl;
	return EXIT_FAILURE;
	}
	}
	output_data << std::endl;
	time += time_step;
	}
	output_data.close();
	finalize();

	std::cout << "Test successful!" << std::endl;
	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_multi_material_elastic.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_multi_material_elastic.cc
	index 6229906a0..6dcd6dfad 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_multi_material_elastic.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_multi_material_elastic.cc
	@@ -1,124 +1,124 @@
	/**
	* @file test_multi_material_elastic.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Mar 03 2017
	* @date last modification: Thu May 09 2019
	*
	* @brief Test with 2 elastic materials
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include "non_linear_solver.hh"
	#include <solid_mechanics_model.hh>

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("test_multi_material_elastic.dat", argc, argv);

	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);

	mesh.read("test_multi_material_elastic.msh");

	SolidMechanicsModel model(mesh);

	auto && mat_sel = std::make_shared<MeshDataMaterialSelector<std::string>>(
	"physical_names", model);
	model.setMaterialSelector(mat_sel);

	model.initFull(_analysis_method = _static);

	model.applyBC(BC::Dirichlet::FlagOnly(_y), "ground");
	model.applyBC(BC::Dirichlet::FlagOnly(_x), "corner");

	Vector<Real> trac(spatial_dimension, 0.);
	trac(_y) = 1.;
	model.applyBC(BC::Neumann::FromTraction(trac), "air");

	model.addDumpField("external_force");
	model.addDumpField("internal_force");
	model.addDumpField("blocked_dofs");
	model.addDumpField("displacement");
	model.addDumpField("stress");
	model.addDumpField("grad_u");

	// model.dump();
	auto & solver = model.getNonLinearSolver("static");
	solver.set("max_iterations", 1);
	solver.set("threshold", 1e-8);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	model.solveStep();
	// model.dump();

	std::map<std::string, Matrix<Real>> ref_strain;
	ref_strain["strong"] = Matrix<Real>(spatial_dimension, spatial_dimension, 0.);
	ref_strain["strong"](_y, _y) = .5;

	ref_strain["weak"] = Matrix<Real>(spatial_dimension, spatial_dimension, 0.);
	ref_strain["weak"](_y, _y) = 1;

	Matrix<Real> ref_stress(spatial_dimension, spatial_dimension, 0.);
	ref_stress(_y, _y) = 1.;

	std::vector<std::string> mats = {"strong", "weak"};

	typedef Array<Real>::const_matrix_iterator mat_it;
	auto check = [](mat_it it, mat_it end, const Matrix<Real> & ref) -> bool {
	for (; it != end; ++it) {
	Real dist = (*it - ref).norm<L_2>();

	// std::cout << *it << " " << dist << " " << (dist < 1e-10 ? "OK" : "Not
	// OK") << std::endl;

	if (dist > 1e-10)
	return false;
	}

	return true;
	};

	for (auto & type : mesh.elementTypes(spatial_dimension)) {
	for (auto mat_id : mats) {
	auto & stress = model.getMaterial(mat_id).getStress(type);
	auto & grad_u = model.getMaterial(mat_id).getGradU(type);

	auto sit = stress.begin(spatial_dimension, spatial_dimension);
	auto send = stress.end(spatial_dimension, spatial_dimension);

	auto git = grad_u.begin(spatial_dimension, spatial_dimension);
	auto gend = grad_u.end(spatial_dimension, spatial_dimension);

	if (!check(sit, send, ref_stress))
	AKANTU_ERROR("The stresses are not correct");
	if (!check(git, gend, ref_strain[mat_id]))
	AKANTU_ERROR("The grad_u are not correct");
	}
	}

	finalize();

	return 0;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_materials/test_plastic_materials.cc b/test/test_model/test_solid_mechanics_model/test_materials/test_plastic_materials.cc
	index fa993c305..e144af29b 100644
	--- a/test/test_model/test_solid_mechanics_model/test_materials/test_plastic_materials.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_materials/test_plastic_materials.cc
	@@ -1,194 +1,194 @@
	/**
	* @file test_plastic_materials.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	*
	* @date creation: Fri Nov 17 2017
	* @date last modification: Tue Jan 19 2021
	*
	* @brief Tests the plastic material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "material_linear_isotropic_hardening.hh"
	#include "solid_mechanics_model.hh"
	#include "test_material_fixtures.hh"
	#include <gtest/gtest.h>
	#include <type_traits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	using mat_types = ::testing::Types<
	// Traits<MaterialLinearIsotropicHardening, 1>,
	// Traits<MaterialLinearIsotropicHardening, 2>,
	Traits<MaterialLinearIsotropicHardening, 3>>;

	/* -------------------------------------------------------------------------- */

	template <>
	void FriendMaterial<MaterialLinearIsotropicHardening<3>>::testComputeStress() {

	Real E = 1.;
	// Real nu = .3;
	Real nu = 0.;
	Real rho = 1.;
	Real sigma_0 = 1.;
	Real h = 0.;
	Real bulk_modulus_K = E / 3. / (1 - 2. * nu);
	Real shear_modulus_mu = 0.5 * E / (1 + nu);

	setParam("E", E);
	setParam("nu", nu);
	setParam("rho", rho);
	setParam("sigma_y", sigma_0);
	setParam("h", h);

	auto rotation_matrix = getRandomRotation();

	Real max_strain = 10.;
	Real strain_steps = 100;
	Real dt = max_strain / strain_steps;
	std::vector<double> steps(strain_steps);
	std::iota(steps.begin(), steps.end(), 0.);

	Matrix<Real> previous_grad_u_rot(3, 3, 0.);
	Matrix<Real> previous_sigma(3, 3, 0.);
	Matrix<Real> previous_sigma_rot(3, 3, 0.);
	Matrix<Real> inelastic_strain_rot(3, 3, 0.);
	Matrix<Real> inelastic_strain(3, 3, 0.);
	Matrix<Real> previous_inelastic_strain(3, 3, 0.);
	Matrix<Real> previous_inelastic_strain_rot(3, 3, 0.);
	Matrix<Real> sigma_rot(3, 3, 0.);
	Real iso_hardening = 0.;
	Real previous_iso_hardening = 0.;

	// hydrostatic loading (should not plastify)
	for (auto && i : steps) {
	auto t = i * dt;

	auto grad_u = this->getHydrostaticStrain(t);
	auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);

	this->computeStressOnQuad(grad_u_rot, previous_grad_u_rot, sigma_rot,
	previous_sigma_rot, inelastic_strain_rot,
	previous_inelastic_strain_rot, iso_hardening,
	previous_iso_hardening, 0., 0.);

	auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);

	Matrix<Real> sigma_expected =
	t * 3. * bulk_modulus_K * Matrix<Real>::eye(3, 1.);

	Real stress_error = (sigma - sigma_expected).norm<L_inf>();

	ASSERT_NEAR(stress_error, 0., 1e-13);
	ASSERT_NEAR(inelastic_strain_rot.norm<L_inf>(), 0., 1e-13);

	previous_grad_u_rot = grad_u_rot;
	previous_sigma_rot = sigma_rot;
	previous_inelastic_strain_rot = inelastic_strain_rot;
	previous_iso_hardening = iso_hardening;
	}

	// deviatoric loading (should plastify)
	// stress at onset of plastication
	Real beta = sqrt(42);
	Real t_P = sigma_0 / 2. / shear_modulus_mu / beta;
	Matrix<Real> sigma_P = sigma_0 / beta * this->getDeviatoricStrain(1.);

	for (auto && i : steps) {

	auto t = i * dt;
	auto grad_u = this->getDeviatoricStrain(t);
	auto grad_u_rot = this->applyRotation(grad_u, rotation_matrix);
	Real iso_hardening{0.};
	Real previous_iso_hardening{0.};

	this->computeStressOnQuad(grad_u_rot, previous_grad_u_rot, sigma_rot,
	previous_sigma_rot, inelastic_strain_rot,
	previous_inelastic_strain_rot, iso_hardening,
	previous_iso_hardening, 0., 0.);

	auto sigma = this->reverseRotation(sigma_rot, rotation_matrix);
	auto inelastic_strain =
	this->reverseRotation(inelastic_strain_rot, rotation_matrix);

	if (t < t_P) {

	Matrix<Real> sigma_expected =
	shear_modulus_mu * (grad_u + grad_u.transpose());

	Real stress_error = (sigma - sigma_expected).norm<L_inf>();
	ASSERT_NEAR(stress_error, 0., 1e-13);
	ASSERT_NEAR(inelastic_strain_rot.norm<L_inf>(), 0., 1e-13);
	} else if (t > t_P + dt) {
	// skip the transition from non plastic to plastic

	auto delta_lambda_expected =
	dt / t * previous_sigma.doubleDot(grad_u + grad_u.transpose()) / 2.;
	auto delta_inelastic_strain_expected =
	delta_lambda_expected * 3. / 2. / sigma_0 * previous_sigma;
	auto inelastic_strain_expected =
	delta_inelastic_strain_expected + previous_inelastic_strain;
	ASSERT_NEAR((inelastic_strain - inelastic_strain_expected).norm<L_inf>(),
	0., 1e-13);
	auto delta_sigma_expected =
	2. * shear_modulus_mu *
	(0.5 * dt / t * (grad_u + grad_u.transpose()) -
	delta_inelastic_strain_expected);

	auto delta_sigma = sigma - previous_sigma;
	ASSERT_NEAR((delta_sigma_expected - delta_sigma).norm<L_inf>(), 0.,
	1e-13);
	}
	previous_sigma = sigma;
	previous_sigma_rot = sigma_rot;
	previous_grad_u_rot = grad_u_rot;
	previous_inelastic_strain = inelastic_strain;
	previous_inelastic_strain_rot = inelastic_strain_rot;
	}
	}

	namespace {

	template <typename T>
	class TestPlasticMaterialFixture : public ::TestMaterialFixture<T> {};

	TYPED_TEST_SUITE(TestPlasticMaterialFixture, mat_types, );

	TYPED_TEST(TestPlasticMaterialFixture, ComputeStress) {
	this->material->testComputeStress();
	}
	TYPED_TEST(TestPlasticMaterialFixture, DISABLED_EnergyDensity) {
	this->material->testEnergyDensity();
	}
	TYPED_TEST(TestPlasticMaterialFixture, DISABLED_ComputeTangentModuli) {
	this->material->testComputeTangentModuli();
	}
	TYPED_TEST(TestPlasticMaterialFixture, DISABLED_ComputeCelerity) {
	this->material->testCelerity();
	}
	} // namespace

	/*****************************************************************/
	diff --git a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_dynamics.cc b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_dynamics.cc
	index 1c6dec0ea..79eae42d7 100644
	--- a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_dynamics.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_dynamics.cc
	@@ -1,323 +1,323 @@
	/**
	* @file test_solid_mechanics_model_dynamics.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Nov 29 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief test of the class SolidMechanicsModel on the 3d cube
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "boundary_condition_functor.hh"
	#include "test_solid_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	namespace {

	const Real A = 1e-1;
	const Real E = 1.;
	const Real poisson = 3. / 10;
	const Real lambda = E * poisson / (1 + poisson) / (1 - 2 * poisson);
	const Real mu = E / 2 / (1. + poisson);
	const Real rho = 1.;
	const Real cp = std::sqrt((lambda + 2 * mu) / rho);
	const Real cs = std::sqrt(mu / rho);
	const Real c = std::sqrt(E / rho);

	const Vector<Real> k = {.5, 0., 0.};
	const Vector<Real> psi1 = {0., 0., 1.};
	const Vector<Real> psi2 = {0., 1., 0.};
	const Real knorm = k.norm();

	/* -------------------------------------------------------------------------- */
	template <UInt dim> struct Verification {};

	/* -------------------------------------------------------------------------- */
	template <> struct Verification<1> {
	void displacement(Vector<Real> & disp, const Vector<Real> & coord,
	Real current_time) {
	const auto & x = coord(_x);
	const Real omega = c * k[0];
	disp(_x) = A * cos(k[0] * x - omega * current_time);
	}

	void velocity(Vector<Real> & vel, const Vector<Real> & coord,
	Real current_time) {
	const auto & x = coord(_x);
	const Real omega = c * k[0];
	vel(_x) = omega * A * sin(k[0] * x - omega * current_time);
	}
	};

	/* -------------------------------------------------------------------------- */
	template <> struct Verification<2> {
	void displacement(Vector<Real> & disp, const Vector<Real> & X,
	Real current_time) {
	Vector<Real> kshear = {k[1], k[0]};
	Vector<Real> kpush = {k[0], k[1]};

	const Real omega_p = knorm * cp;
	const Real omega_s = knorm * cs;

	Real phase_p = X.dot(kpush) - omega_p * current_time;
	Real phase_s = X.dot(kpush) - omega_s * current_time;

	disp = A * (kpush * cos(phase_p) + kshear * cos(phase_s));
	}

	void velocity(Vector<Real> & vel, const Vector<Real> & X, Real current_time) {
	Vector<Real> kshear = {k[1], k[0]};
	Vector<Real> kpush = {k[0], k[1]};

	const Real omega_p = knorm * cp;
	const Real omega_s = knorm * cs;

	Real phase_p = X.dot(kpush) - omega_p * current_time;
	Real phase_s = X.dot(kpush) - omega_s * current_time;

	vel =
	A * (kpush * omega_p * cos(phase_p) + kshear * omega_s * cos(phase_s));
	}
	};

	/* -------------------------------------------------------------------------- */
	template <> struct Verification<3> {
	void displacement(Vector<Real> & disp, const Vector<Real> & coord,
	Real current_time) {
	const auto & X = coord;
	Vector<Real> kpush = k;
	Vector<Real> kshear1(3);
	Vector<Real> kshear2(3);
	kshear1.crossProduct(k, psi1);
	kshear2.crossProduct(k, psi2);

	const Real omega_p = knorm * cp;
	const Real omega_s = knorm * cs;

	Real phase_p = X.dot(kpush) - omega_p * current_time;
	Real phase_s = X.dot(kpush) - omega_s * current_time;

	disp = A * (kpush * cos(phase_p) + kshear1 * cos(phase_s) +
	kshear2 * cos(phase_s));
	}

	void velocity(Vector<Real> & vel, const Vector<Real> & coord,
	Real current_time) {
	const auto & X = coord;
	Vector<Real> kpush = k;
	Vector<Real> kshear1(3);
	Vector<Real> kshear2(3);
	kshear1.crossProduct(k, psi1);
	kshear2.crossProduct(k, psi2);

	const Real omega_p = knorm * cp;
	const Real omega_s = knorm * cs;

	Real phase_p = X.dot(kpush) - omega_p * current_time;
	Real phase_s = X.dot(kpush) - omega_s * current_time;

	vel =
	A * (kpush * omega_p * cos(phase_p) + kshear1 * omega_s * cos(phase_s) +
	kshear2 * omega_s * cos(phase_s));
	}
	};

	/* -------------------------------------------------------------------------- */
	template <ElementType _type>
	class SolutionFunctor : public BC::Dirichlet::DirichletFunctor {
	public:
	SolutionFunctor(Real current_time, SolidMechanicsModel & model)
	: current_time(current_time), model(model) {}

	public:
	static constexpr UInt dim = ElementClass<_type>::getSpatialDimension();

	inline void operator()(UInt node, Vector<bool> & flags, Vector<Real> & primal,
	const Vector<Real> & coord) const {
	flags(0) = true;
	auto & vel = model.getVelocity();
	auto it = vel.begin(model.getSpatialDimension());
	Vector<Real> v = it[node];

	Verification<dim> verif;
	verif.displacement(primal, coord, current_time);
	verif.velocity(v, coord, current_time);
	}

	private:
	Real current_time;
	SolidMechanicsModel & model;
	};

	/* -------------------------------------------------------------------------- */
	// This fixture uses somewhat finer meshes representing bars.
	template <typename type_, typename analysis_method_>
	class TestSMMFixtureBar : public TestSMMFixture<type_> {
	using parent = TestSMMFixture<type_>;

	public:
	void SetUp() override {
	this->mesh_file =
	"../patch_tests/data/bar" + std::to_string(this->type) + ".msh";
	parent::SetUp();

	auto analysis_method = analysis_method_::value;
	this->initModel("test_solid_mechanics_model_"
	"dynamics_material.dat",
	analysis_method);

	const auto & position = this->mesh->getNodes();
	auto & displacement = this->model->getDisplacement();
	auto & velocity = this->model->getVelocity();

	constexpr auto dim = parent::spatial_dimension;

	Verification<dim> verif;

	for (auto && tuple :
	zip(make_view(position, dim), make_view(displacement, dim),
	make_view(velocity, dim))) {
	verif.displacement(std::get<1>(tuple), std::get<0>(tuple), 0.);
	verif.velocity(std::get<2>(tuple), std::get<0>(tuple), 0.);
	}

	if (this->dump_paraview)
	this->model->dump();

	/// boundary conditions
	this->model->applyBC(SolutionFunctor<parent::type>(0., *this->model), "BC");

	wave_velocity = 1.; // sqrt(E/rho) = sqrt(1/1) = 1
	simulation_time = 5 / wave_velocity;
	time_step = this->model->getTimeStep();

	max_steps = simulation_time / time_step; // 100
	}

	void solveStep() {
	constexpr auto dim = parent::spatial_dimension;
	Real current_time = 0.;
	const auto & position = this->mesh->getNodes();
	const auto & displacement = this->model->getDisplacement();
	UInt nb_nodes = this->mesh->getNbNodes();
	UInt nb_global_nodes = this->mesh->getNbGlobalNodes();

	max_error = -1.;

	Array<Real> displacement_solution(nb_nodes, dim);
	Verification<dim> verif;

	auto ndump = 50;
	auto dump_freq = max_steps / ndump;

	for (UInt s = 0; s < this->max_steps;
	++s, current_time += this->time_step) {
	if (s % dump_freq == 0 && this->dump_paraview)
	this->model->dump();

	/// boundary conditions
	this->model->applyBC(
	SolutionFunctor<parent::type>(current_time, *this->model), "BC");

	// compute the disp solution
	for (auto && tuple : zip(make_view(position, dim),
	make_view(displacement_solution, dim))) {
	verif.displacement(std::get<1>(tuple), std::get<0>(tuple),
	current_time);
	}

	// compute the error solution
	Real disp_error = 0.;
	auto n = 0;
	for (auto && tuple : zip(make_view(displacement, dim),
	make_view(displacement_solution, dim))) {
	if (this->mesh->isLocalOrMasterNode(n)) {
	auto diff = std::get<1>(tuple) - std::get<0>(tuple);
	disp_error += diff.dot(diff);
	}
	++n;
	}

	this->mesh->getCommunicator().allReduce(disp_error,
	SynchronizerOperation::_sum);

	disp_error = sqrt(disp_error) / nb_global_nodes;
	max_error = std::max(disp_error, max_error);

	this->model->solveStep();
	}
	}

	protected:
	Real time_step;
	Real wave_velocity;
	Real simulation_time;
	UInt max_steps;
	Real max_error{-1};
	};

	template <AnalysisMethod t>
	using analysis_method_t = std::integral_constant<AnalysisMethod, t>;

	using TestTypes = gtest_list_t<TestElementTypes>;

	template <typename type_>
	using TestSMMFixtureBarExplicit =
	TestSMMFixtureBar<type_, analysis_method_t<_explicit_lumped_mass>>;

	TYPED_TEST_SUITE(TestSMMFixtureBarExplicit, TestTypes, );

	/* -------------------------------------------------------------------------- */
	TYPED_TEST(TestSMMFixtureBarExplicit, Dynamics) {
	this->solveStep();
	EXPECT_NEAR(this->max_error, 0., 2e-3);
	// std::cout << "max error: " << max_error << std::endl;
	}

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_IMPLICIT)
	template <typename type_>
	using TestSMMFixtureBarImplicit =
	TestSMMFixtureBar<type_, analysis_method_t<_implicit_dynamic>>;

	TYPED_TEST_SUITE(TestSMMFixtureBarImplicit, TestTypes, );

	TYPED_TEST(TestSMMFixtureBarImplicit, Dynamics) {
	if (this->type == _segment_2 and
	(this->mesh->getCommunicator().getNbProc() > 2)) {
	// The error are just to high after (hopefully because of the two small test
	// case)
	SUCCEED();
	return;
	}
	this->solveStep();
	EXPECT_NEAR(this->max_error, 0., 2e-3);
	}
	#endif

	} // namespace
	diff --git a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_fixture.hh b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_fixture.hh
	index e76f956e1..d819616b2 100644
	--- a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_fixture.hh
	+++ b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_fixture.hh
	@@ -1,131 +1,132 @@
	/**
	* @file test_solid_mechanics_model_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Wed Nov 18 2020
	*
	* @brief Main solif mechanics test file
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	+#include "mesh_utils.hh"
	#include "solid_mechanics_model.hh"
	#include "test_gtest_utils.hh"
	-#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_SOLID_MECHANICS_MODEL_FIXTURE_HH_
	#define AKANTU_TEST_SOLID_MECHANICS_MODEL_FIXTURE_HH_

	using namespace akantu;

	// This fixture uses very small meshes with a volume of 1.
	template <typename type_> class TestSMMFixture : public ::testing::Test {
	public:
	static constexpr ElementType type = type_::value;
	static constexpr size_t spatial_dimension =
	ElementClass<type>::getSpatialDimension();

	void SetUp() override {
	this->mesh = std::make_unique<Mesh>(this->spatial_dimension);
	auto prank = Communicator::getStaticCommunicator().whoAmI();
	if (prank == 0) {
	this->mesh->read(this->mesh_file);
	- if(spatial_dimension > 1 and mesh->getNbElement(spatial_dimension - 1) == 0) {
	+ if (spatial_dimension > 1 and
	+ mesh->getNbElement(spatial_dimension - 1) == 0) {
	MeshUtils::buildFacets(*this->mesh);
	}
	}

	mesh->distribute();

	SCOPED_TRACE(std::to_string(this->type).c_str());

	model = std::make_unique<SolidMechanicsModel>(*mesh, _all_dimensions,
	std::to_string(this->type));
	}

	void initModel(const ID & input, const AnalysisMethod & analysis_method) {
	getStaticParser().parse(input);
	this->model->initFull(_analysis_method = analysis_method);

	if (analysis_method != _static) {
	auto time_step = this->model->getStableTimeStep() / 10.;
	this->model->setTimeStep(time_step);
	}
	// std::cout << "timestep: " << time_step << std::endl;

	if (this->dump_paraview) {
	std::stringstream base_name;
	base_name << "bar" << analysis_method << this->type;
	this->model->setBaseName(base_name.str());
	this->model->addDumpFieldVector("displacement");
	this->model->addDumpFieldVector("blocked_dofs");
	if (analysis_method != _static) {
	this->model->addDumpField("velocity");
	this->model->addDumpField("acceleration");
	}
	if (this->mesh->isDistributed()) {
	this->model->addDumpField("partitions");
	}
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpField("stress");
	this->model->addDumpField("strain");
	}
	}

	void TearDown() override {
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	protected:
	std::string mesh_file{std::to_string(this->type) + ".msh"};
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<SolidMechanicsModel> model;
	bool dump_paraview{false};
	};

	template <typename type_> constexpr ElementType TestSMMFixture<type_>::type;
	template <typename type_>
	constexpr size_t TestSMMFixture<type_>::spatial_dimension;

	template <typename T>
	using is_not_pentahedron =
	aka::negation<aka::disjunction<is_element<T, _pentahedron_6>,
	is_element<T, _pentahedron_15>>>;

	using TestElementTypesFiltered =
	tuple_filter_t<is_not_pentahedron, TestElementTypes>;

	// using gtest_element_types = gtest_list_t<TestElementTypesFiltered>;
	using gtest_element_types = gtest_list_t<TestElementTypes>;

	TYPED_TEST_SUITE(TestSMMFixture, gtest_element_types, );

	#endif /* AKANTU_TEST_SOLID_MECHANICS_MODEL_FIXTURE_HH_ */
	diff --git a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_eigenstrain.cc b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_eigenstrain.cc
	index 99eb66964..107adfade 100644
	--- a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_eigenstrain.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_eigenstrain.cc
	@@ -1,202 +1,202 @@
	/**
	* @file test_solid_mechanics_model_material_eigenstrain.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sat Apr 16 2011
	* @date last modification: Sat Dec 19 2020
	*
	* @brief test the internal field prestrain
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_utils.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	Real alpha[3][4] = {{0.01, 0.02, 0.03, 0.04},
	{0.05, 0.06, 0.07, 0.08},
	{0.09, 0.10, 0.11, 0.12}};

	/* -------------------------------------------------------------------------- */
	template <ElementType type> static Matrix<Real> prescribed_strain() {
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
	Matrix<Real> strain(spatial_dimension, spatial_dimension);

	for (UInt i = 0; i < spatial_dimension; ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	strain(i, j) = alpha[i][j + 1];
	}
	}
	return strain;
	}

	template <ElementType type>
	static Matrix<Real> prescribed_stress(Matrix<Real> prescribed_eigengradu) {
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
	Matrix<Real> stress(spatial_dimension, spatial_dimension);

	// plane strain in 2d
	Matrix<Real> strain(spatial_dimension, spatial_dimension);
	Matrix<Real> pstrain;
	pstrain = prescribed_strain<type>();
	Real nu = 0.3;
	Real E = 2.1e11;
	Real trace = 0;

	/// symetric part of the strain tensor
	for (UInt i = 0; i < spatial_dimension; ++i)
	for (UInt j = 0; j < spatial_dimension; ++j)
	strain(i, j) = 0.5 * (pstrain(i, j) + pstrain(j, i));

	// elastic strain is equal to elastic strain minus the eigenstrain
	strain -= prescribed_eigengradu;
	for (UInt i = 0; i < spatial_dimension; ++i)
	trace += strain(i, i);

	Real lambda = nu * E / ((1 + nu) * (1 - 2 * nu));
	Real mu = E / (2 * (1 + nu));

	if (spatial_dimension == 1) {
	stress(0, 0) = E * strain(0, 0);
	} else {
	for (UInt i = 0; i < spatial_dimension; ++i)
	for (UInt j = 0; j < spatial_dimension; ++j) {
	stress(i, j) = (i == j) * lambda * trace + 2 * mu * strain(i, j);
	}
	}

	return stress;
	}

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize("material_elastic_plane_strain.dat", argc, argv);

	UInt dim = 3;
	const ElementType element_type = _tetrahedron_4;

	Matrix<Real> prescribed_eigengradu(dim, dim);
	prescribed_eigengradu.set(0.1);

	/// load mesh
	Mesh mesh(dim);
	mesh.read("cube_3d_tet_4.msh");

	/// declaration of model
	SolidMechanicsModel model(mesh);
	/// model initialization
	model.initFull(_analysis_method = _static);

	// model.getNewSolver("static", TimeStepSolverType::_static,
	// NonLinearSolverType::_newton_raphson_modified);
	auto & solver = model.getNonLinearSolver("static");
	solver.set("threshold", 2e-4);
	solver.set("max_iterations", 2);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	const Array<Real> & coordinates = mesh.getNodes();
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> & boundary = model.getBlockedDOFs();
	MeshUtils::buildFacets(mesh);

	mesh.createBoundaryGroupFromGeometry();

	// Loop over (Sub)Boundar(ies)
	for (auto & group : mesh.iterateElementGroups()) {
	for (const auto & n : group.getNodeGroup()) {
	std::cout << "Node " << n << std::endl;
	for (UInt i = 0; i < dim; ++i) {
	displacement(n, i) = alpha[i][0];
	for (UInt j = 0; j < dim; ++j) {
	displacement(n, i) += alpha[i][j + 1] * coordinates(n, j);
	}
	boundary(n, i) = true;
	}
	}
	}

	/* ------------------------------------------------------------------------ */
	/* Apply eigenstrain in each element */
	/* ------------------------------------------------------------------------ */
	Array<Real> & eigengradu_vect =
	model.getMaterial(0).getInternal<Real>("eigen_grad_u")(element_type);
	auto eigengradu_it = eigengradu_vect.begin(dim, dim);
	auto eigengradu_end = eigengradu_vect.end(dim, dim);

	for (; eigengradu_it != eigengradu_end; ++eigengradu_it) {
	*eigengradu_it = prescribed_eigengradu;
	}

	/* ------------------------------------------------------------------------ */
	/* Static solve */
	/* ------------------------------------------------------------------------ */
	model.solveStep();

	std::cout << "Converged in " << Int(solver.get("nb_iterations")) << " ("
	<< Real(solver.get("error")) << ")" << std::endl;

	/* ------------------------------------------------------------------------ */
	/* Checks */
	/* ------------------------------------------------------------------------ */
	const Array<Real> & stress_vect =
	model.getMaterial(0).getStress(element_type);

	auto stress_it = stress_vect.begin(dim, dim);
	auto stress_end = stress_vect.end(dim, dim);

	Matrix<Real> presc_stress;
	presc_stress = prescribed_stress<element_type>(prescribed_eigengradu);

	Real stress_tolerance = 1e-13;

	for (; stress_it != stress_end; ++stress_it) {
	const auto & stress = *stress_it;
	Matrix<Real> diff(dim, dim);

	diff = stress;
	diff -= presc_stress;
	Real stress_error = diff.norm<L_inf>() / stress.norm<L_inf>();

	if (stress_error > stress_tolerance) {
	std::cerr << "stress error: " << stress_error << " > " << stress_tolerance
	<< std::endl;
	std::cerr << "stress: " << stress << std::endl
	<< "prescribed stress: " << presc_stress << std::endl;
	return EXIT_FAILURE;
	} // else {
	// std::cerr << "stress error: " << stress_error
	// << " < " << stress_tolerance << std::endl;
	// }
	}

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_large_rotation.cc b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_large_rotation.cc
	index 278fe0227..d948c46b5 100644
	--- a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_large_rotation.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_material_large_rotation.cc
	@@ -1,122 +1,122 @@
	/**
	* @file test_solid_mechanics_model_material_large_rotation.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 27 2019
	*
	* @brief test the internal field prestrain
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "mesh_utils.hh"
	#include "non_linear_solver.hh"
	#include "solid_mechanics_model.hh"
	#include "sparse_matrix_aij.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize("material_elastic.dat", argc, argv);

	UInt dim = 3;

	/// load mesh
	Mesh mesh(dim);
	mesh.read("cube_3d_tet_4.msh");

	/// declaration of model
	SolidMechanicsModel model(mesh);

	/// model initialization
	// model.initFull(_analysis_method=akantu._explicit_lumped_mass)
	model.initFull(_analysis_method = _implicit_dynamic);
	// model.initFull(_analysis_method = akantu._implicit_dynamic)

	auto & solver = model.getNonLinearSolver();
	solver.set("threshold", 1e-4);
	solver.set("max_iterations", 100);
	solver.set("convergence_type", SolveConvergenceCriteria::_residual);

	model.setBaseName("waves");
	model.addDumpFieldVector("displacement");
	model.addDumpFieldVector("acceleration");
	model.addDumpFieldVector("velocity");
	model.addDumpFieldVector("internal_force");
	model.addDumpFieldVector("external_force");
	model.addDumpField("strain");
	model.addDumpField("stress");
	model.addDumpField("blocked_dofs");

	/* ------------------------------------------------------------------------ */
	// get mass center
	/* ------------------------------------------------------------------------ */

	model.assembleMass();
	auto & M = model.getDOFManager().getMatrix("M");
	Array<Real> _mass(M.size(), 1);
	_mass.zero();
	std::cout << "AAAA " << M.size() << std::endl;
	std::cout << "AAAA " << _mass.size() << std::endl;

	for (UInt i = 0; i < M.size(); ++i) {
	for (UInt j = 0; j < M.size(); ++j) {
	- std::cout << i << ", " << j <<std::endl;
	+ std::cout << i << ", " << j << std::endl;
	_mass[i] += M(i, j);
	}
	}
	std::array<Real, 3> mass_center{0., 0., 0.};
	std::cout << "AAAA " << _mass.size() << std::endl;
	Real total_mass = 0.;
	for (UInt i = 0; i < _mass.size(); ++i) {
	for (UInt j = 0; j < 3; ++j) {
	mass_center[j] += _mass(i * 3 + j);
	total_mass += _mass(i * 3 + j);
	}
	}
	mass_center[0] /= total_mass / 3.;
	mass_center[1] /= total_mass / 3.;
	mass_center[2] /= total_mass / 3.;
	std::cout << "total mass" << total_mass << std::endl;
	std::cout << mass_center[0] << " " << mass_center[1] << " " << mass_center[2]
	<< std::endl;

	/* ---------------------------------------------------------------------- */
	/* Dynamic evolution */
	/* ---------------------------------------------------------------------- */
	model.dump();

	model.solveStep();
	model.dump();

	std::cout << "Converged in " << Int(solver.get("nb_iterations")) << " ("
	<< Real(solver.get("error")) << ")" << std::endl;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_reassign_material.cc b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_reassign_material.cc
	index 0d0b467c6..0ed52e2a8 100644
	--- a/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_reassign_material.cc
	+++ b/test/test_model/test_solid_mechanics_model/test_solid_mechanics_model_reassign_material.cc
	@@ -1,196 +1,196 @@
	/**
	* @file test_solid_mechanics_model_reassign_material.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Mar 11 2021
	*
	* @brief test the function reassign material
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_grid_dynamic.hh"
	-#include "mesh_iterators.hh"
	#include "communicator.hh"
	#include "material.hh"
	+#include "mesh_iterators.hh"
	#include "mesh_utils.hh"
	#include "solid_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class StraightInterfaceMaterialSelector : public MaterialSelector {
	public:
	StraightInterfaceMaterialSelector(SolidMechanicsModel & model,
	UInt horizontal, Real & pos_interface,
	const std::string & mat_1_material,
	const std::string & mat_2_material)
	: model(model), horizontal(horizontal), pos_interface(pos_interface),
	mat_1_material(mat_1_material), mat_2_material(mat_2_material) {
	Mesh & mesh = model.getMesh();
	UInt spatial_dimension = mesh.getSpatialDimension();

	/// store barycenters of all elements
	barycenters.initialize(mesh, _spatial_dimension = spatial_dimension,
	_nb_component = spatial_dimension,
	_with_nb_element = true);

	for_each_element(mesh, [&](auto && el) {
	Vector<Real> bary(barycenters.get(el));
	mesh.getBarycenter(el, bary);
	});
	}

	void setMaterials() {
	mat_ids[0] = model.getMaterialIndex(mat_1_material);
	mat_ids[1] = model.getMaterialIndex(mat_2_material);
	}

	UInt operator()(const Element & elem) override {
	if (not materials_set) {
	setMaterials();
	}
	const Vector<Real> bary = barycenters.get(elem);
	/// check for a given element on which side of the material interface plane
	/// the bary center lies and assign corresponding material
	if (bary(horizontal) < pos_interface) {
	return mat_ids[0];
	}
	return mat_ids[1];
	}

	bool isConditonVerified() {
	/// check if material has been (re)-assigned correctly
	auto & mesh = model.getMesh();
	auto spatial_dimension = mesh.getSpatialDimension();
	for (const auto & type : mesh.elementTypes(spatial_dimension)) {
	auto & mat_indexes = model.getMaterialByElement(type);
	for (auto && data :
	enumerate(make_view(barycenters(type), spatial_dimension))) {
	auto elem = std::get<0>(data);
	auto & bary = std::get<1>(data);
	/// compare element_index_by material to material index that should be
	/// assigned due to the geometry of the interface
	UInt mat_index;
	if (bary(horizontal) < pos_interface) {
	mat_index = mat_ids[0];
	} else {
	mat_index = mat_ids[1];
	}

	if (mat_indexes(elem) != mat_index) {
	/// wrong material index, make test fail
	return false;
	}
	}
	}
	return true;
	}

	void moveInterface(Real & pos_new, UInt horizontal_new) {
	/// update position and orientation of material interface plane
	pos_interface = pos_new;
	horizontal = horizontal_new;
	model.reassignMaterial();
	}

	protected:
	SolidMechanicsModel & model;
	ElementTypeMapArray<Real> barycenters;
	std::array<UInt, 2> mat_ids;
	UInt horizontal;
	Real pos_interface;
	bool materials_set{false};
	std::string mat_1_material;
	std::string mat_2_material;
	};

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {

	bool test_passed;

	debug::setDebugLevel(dblWarning);
	initialize("two_materials.dat", argc, argv);

	/// specify position and orientation of material interface plane
	Real pos_interface = 0.;

	UInt spatial_dimension = 3;

	const auto & comm = Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	Mesh mesh(spatial_dimension);

	if (prank == 0) {
	mesh.read("cube_two_materials.msh");
	}
	mesh.distribute();

	/// model creation
	SolidMechanicsModel model(mesh);

	/// assign the two different materials using the
	/// StraightInterfaceMaterialSelector

	auto && mat_selector = std::make_shared<StraightInterfaceMaterialSelector>(
	model, _x, pos_interface, "mat_1", "mat_2");

	model.setMaterialSelector(mat_selector);
	model.initFull(_analysis_method = _static);
	MeshUtils::buildFacets(mesh);

	/// check if different materials have been assigned correctly
	test_passed = mat_selector->isConditonVerified();
	if (not test_passed) {
	AKANTU_ERROR("materials not correctly assigned");
	return EXIT_FAILURE;
	}

	model.addDumpField("material_index");
	/// change orientation of material interface plane

	model.dump();
	mat_selector->moveInterface(pos_interface, _y);
	model.dump();

	/// test if material has been reassigned correctly
	test_passed = mat_selector->isConditonVerified();
	if (not test_passed) {
	AKANTU_ERROR("materials not correctly reassigned");
	return EXIT_FAILURE;
	}

	finalize();

	if (prank == 0)
	std::cout << "OK: test passed!" << std::endl;

	return EXIT_SUCCESS;
	}

	/* -------------------------------------------------------------------------- */
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_2.cc b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_2.cc
	index 00b3acd6f..f1a5d1772 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_2.cc
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_2.cc
	@@ -1,115 +1,115 @@
	/**
	* @file test_structural_mechanics_model_bernoulli_beam_2.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Feb 25 2021
	*
	* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_structural_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	class TestStructBernoulli2
	: public TestStructuralFixture<element_type_t<_bernoulli_beam_2>> {
	using parent = TestStructuralFixture<element_type_t<_bernoulli_beam_2>>;

	public:
	void addMaterials() override {
	mat.E = 3e10;
	mat.I = 0.0025;
	mat.A = 0.01;

	this->model->addMaterial(mat);

	mat.E = 3e10;
	mat.I = 0.00128;
	mat.A = 0.01;

	this->model->addMaterial(mat);
	}

	void assignMaterials() override {
	auto & materials = this->model->getElementMaterial(parent::type);
	materials(0) = 0;
	materials(1) = 1;
	}

	void setDirichletBCs() override {
	auto boundary = this->model->getBlockedDOFs().begin(parent::ndof);
	// clang-format off
	*boundary = {true, true, true}; ++boundary;
	*boundary = {false, true, false}; ++boundary;
	*boundary = {false, true, false}; ++boundary;
	// clang-format on
	}

	void setNeumannBCs() override {
	- Real M = 3600; // Nm
	+ Real M = 3600; // Nm
	Real q = 6000; // kN/m
	- Real L = 10; // m
	+ Real L = 10; // m
	auto & forces = this->model->getExternalForce();
	forces(2, 2) = -M; // moment on last node
	#if 1 // as long as integration is not available
	forces(0, 1) = -q * L / 2;
	forces(0, 2) = -q * L * L / 12;
	forces(1, 1) = -q * L / 2;
	forces(1, 2) = q * L * L / 12;
	#else
	auto & group = mesh.createElementGroup("lin_force");
	group.add({type, 0, _not_ghost});
	Vector<Real> lin_force = {0, q, 0};
	// a linear force is not actually a boundary condition
	// it is equivalent to a volume force
	model.applyBC(BC::Neumann::FromSameDim(lin_force), group);
	#endif
	forces(2, 0) = mat.E * mat.A / 18;
	}

	protected:
	StructuralMaterial mat;
	};

	/* -------------------------------------------------------------------------- */

	TEST_F(TestStructBernoulli2, TestDisplacements) {
	model->solveStep();
	auto d1 = model->getDisplacement()(1, 2);
	auto d2 = model->getDisplacement()(2, 2);
	auto d3 = model->getDisplacement()(1, 0);

	Real tol = Math::getTolerance();

	EXPECT_NEAR(d1, 5.6 / 4800, tol); // first rotation
	EXPECT_NEAR(d2, -3.7 / 4800, tol); // second rotation
	EXPECT_NEAR(d3, 10. / 18, tol); // axial deformation
	}
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_3.cc b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_3.cc
	index 1a0e4040b..f24169ec4 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_3.cc
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_3.cc
	@@ -1,101 +1,99 @@
	/**
	* @file test_structural_mechanics_model_bernoulli_beam_3.cc
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Feb 25 2021
	*
	* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_structural_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class TestStructBernoulli3Static
	: public TestStructuralFixture<element_type_t<_bernoulli_beam_3>> {
	using parent = TestStructuralFixture<element_type_t<_bernoulli_beam_3>>;

	public:
	- void readMesh(std::string filename) override {
	- parent::readMesh(filename);
	- }
	+ void readMesh(std::string filename) override { parent::readMesh(filename); }

	void setNormals() override {
	- auto &normals = this->mesh->getData<Real>("extra_normal", parent::type);
	+ auto & normals = this->mesh->getData<Real>("extra_normal", parent::type);
	normals(0, _z) = 1;
	normals(1, _z) = 1;
	}

	void addMaterials() override {
	StructuralMaterial mat;
	mat.E = 1;
	mat.Iz = 1;
	mat.Iy = 1;
	mat.A = 1;
	mat.GJ = 1;
	this->model->addMaterial(mat);
	}

	void setDirichletBCs() override {
	// Boundary conditions (blocking all DOFs of nodes 2 & 3)
	auto boundary = ++this->model->getBlockedDOFs().begin(parent::ndof);
	// clang-format off
	*boundary = {true, true, true, true, true, true}; ++boundary;
	*boundary = {true, true, true, true, true, true}; ++boundary;
	// clang-format on
	}

	void setNeumannBCs() override {
	// Forces
	Real P = 1; // N
	auto & forces = this->model->getExternalForce();
	forces.zero();
	forces(0, 2) = -P; // vertical force on first node
	}

	void assignMaterials() override {
	model->getElementMaterial(parent::type).set(0);
	}
	};

	/* -------------------------------------------------------------------------- */
	TEST_F(TestStructBernoulli3Static, TestDisplacements) {
	model->solveStep();
	auto vz = model->getDisplacement()(0, 2);
	auto thy = model->getDisplacement()(0, 4);
	auto thx = model->getDisplacement()(0, 3);
	auto thz = model->getDisplacement()(0, 5);

	Real tol = Math::getTolerance();

	EXPECT_NEAR(vz, -5. / 48, tol);
	EXPECT_NEAR(thy, -std::sqrt(2) / 8, tol);
	EXPECT_NEAR(thz, 0, tol);
	EXPECT_NEAR(thx, 0, tol);
	}
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_dynamics.cc b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_dynamics.cc
	index 3388a6f98..f2f05e8da 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_dynamics.cc
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_bernoulli_beam_dynamics.cc
	@@ -1,370 +1,369 @@
	/**
	* @file test_structural_mechanics_model_bernoulli_beam_dynamics.cc
	*
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Mon Mar 15 2021
	*
	* @brief Test for _bernouilli_beam in dynamic
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_structural_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "dof_manager.hh"
	#include "mesh_accessor.hh"
	#include "non_linear_solver_newton_raphson.hh"
	#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <iostream>
	#include <limits>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	static Real analytical_solution(Real time, Real L, Real rho, Real E,
	__attribute__((unused)) Real A, Real I,
	Real F) {
	Real omega = M_PI * M_PI / L / L * sqrt(E * I / rho);
	Real sum = 0.;
	UInt i = 5;
	for (UInt n = 1; n <= i; n += 2) {
	sum += (1. - cos(n * n * omega * time)) / pow(n, 4);
	}

	return 2. * F * pow(L, 3) / pow(M_PI, 4) / E / I * sum;
	}

	template <class Type>
	class TestStructBernoulliDynamic : public TestStructuralFixture<Type> {
	using parent = TestStructuralFixture<Type>;

	public:
	const UInt nb_element{40};
	const Real L{2};
	const Real le{L / nb_element};

	const UInt nb_nodes{nb_element + 1};
	const Real F{1e4};

	StructuralMaterial mat;

	void readMesh(std::string /filename/) override {
	MeshAccessor mesh_accessor(*this->mesh);
	auto & nodes = mesh_accessor.getNodes();
	nodes.resize(nb_nodes);

	nodes.set(0.);

	for (auto && data : enumerate(make_view(nodes, this->spatial_dimension))) {
	auto & node = std::get<1>(data);
	UInt i = std::get<0>(data);
	node[_x] = i * le;
	}

	this->mesh->addConnectivityType(parent::type);
	auto & connectivities = mesh_accessor.getConnectivity(parent::type);
	connectivities.resize(nb_element);
	for (auto && data : enumerate(make_view(connectivities, 2))) {
	UInt i = std::get<0>(data);
	auto & connectivity = std::get<1>(data);

	connectivity = {i, i + 1};
	}

	mesh_accessor.makeReady();
	}

	void setNormals() override {
	if (this->spatial_dimension != 3) {
	return;
	}
	auto & normals =
	this->mesh->template getData<Real>("extra_normal", parent::type);
	normals.resize(nb_element);

	for (auto && normal : make_view(normals, this->spatial_dimension)) {
	normal = {0., 0., 1.};
	}
	}

	AnalysisMethod getAnalysisMethod() const override {
	return _implicit_dynamic;
	}

	void addMaterials() override {
	this->mat.E = 1e9;
	this->mat.rho = 10;
	this->mat.I = 1;
	this->mat.Iz = 1;
	this->mat.Iy = 1;
	this->mat.A = 1;
	this->mat.GJ = 1;

	this->model->addMaterial(mat);
	}

	void setDirichletBCs() override {
	auto & boundary = this->model->getBlockedDOFs();
	boundary.set(false);

	boundary(0, _x) = true;
	boundary(0, _y) = true;

	boundary(nb_nodes - 1, _y) = true;

	if (this->spatial_dimension == 3) {
	boundary(0, _z) = true;
	boundary(nb_nodes - 1, _z) = true;
	}
	}

	void setNeumannBCs() override {
	auto node_to_print = nb_nodes / 2;
	// Forces
	auto & forces = this->model->getExternalForce();
	forces.zero();
	forces(node_to_print, _y) = F;
	}

	void assignMaterials() override {
	this->model->getElementMaterial(parent::type).set(0);
	}
	};

	using beam_types = gtest_list_t<std::tuple<element_type_t<_bernoulli_beam_2>,
	element_type_t<_bernoulli_beam_3>>>;

	TYPED_TEST_SUITE(TestStructBernoulliDynamic, beam_types, );

	template <class Type>
	void getElementMassMatrix(const StructuralMaterial & /material/, Real /l/,
	Matrix<Real> & /M/) {}

	template <class Type>
	void getElementStifnessMatrix(const StructuralMaterial & /material/,
	Real /l/, Matrix<Real> & /M/) {}

	template <>
	void getElementMassMatrix<element_type_t<_bernoulli_beam_2>>(
	const StructuralMaterial & material, Real l, Matrix<Real> & M) {
	auto A = material.A;
	auto rho = material.rho;
	// clang-format off
	M = rho * A * l / 420. * Matrix<Real>({
	{140, 0, 0, 70, 0, 0},
	{ 0, 156, 22l, 0, 54, -13l},
	{ 0, 22l, 4ll, 0, 13l, -3ll},
	{ 70, 0, 0, 140, 0, 0},
	{ 0, 54, 13l, 0, 156, -22l},
	{ 0,-13l, -3ll, 0, -22l, 4ll}});
	// clang-format on
	}

	template <>
	void getElementStifnessMatrix<element_type_t<_bernoulli_beam_2>>(
	const StructuralMaterial & material, Real l, Matrix<Real> & K) {
	auto E = material.E;
	auto A = material.A;
	auto I = material.I;

	auto l_2 = l * l;
	auto l_3 = l * l * l;
	// clang-format off
	K = Matrix<Real>({
	{ EA/l, 0, 0, -EA/l, 0, 0},
	{ 0, 12EI/l_3, 6EI/l_2, 0, -12EI/l_3, 6EI/l_2},
	{ 0, 6EI/l_2, 4EI/l, 0, -6EI/l_2, 2EI/l},
	{-EA/l, 0, 0, EA/l, 0, 0},
	{ 0, -12EI/l_3, -6EI/l_2, 0, 12EI/l_3, -6EI/l_2},
	{ 0, 6EI/l_2, 2EI/l, 0, -6EI/l_2, 4EI/l}});
	// clang-format on
	}

	template <>
	void getElementMassMatrix<element_type_t<_bernoulli_beam_3>>(
	const StructuralMaterial & material, Real l, Matrix<Real> & M) {
	auto A = material.A;
	auto rho = material.rho;
	// clang-format off
	M = rho * A * l / 420. * Matrix<Real>({
	{140, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0},
	{ 0, 156, 0, 0, 0, 22l, 0, 54, 0, 0, 0, -13l},
	{ 0, 0, 156, 0, -22l, 0, 0, 0, 54, 0, 13l, 0},
	{ 0, 0, 0, 140, 0, 0, 0, 0, 0, 70, 0, 0},
	{ 0, 0, -22l, 0, 4ll, 0, 0, 0, -13l, 0, -3ll, 0},
	{ 0, 22l, 0, 0, 0, 4ll, 0, 13l, 0, 0, 0, -3ll},
	{ 70, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0},
	{ 0, 54, 0, 0, 0, 13l, 0, 156, 0, 0, 0, -22l},
	{ 0, 0, 54, 0, -13l, 0, 0, 0, 156, 0, 22l, 0},
	{ 0, 0, 0, 70, 0, 0, 0, 0, 0, 140, 0, 0},
	{ 0, 0, 13l, 0, -3ll, 0, 0, 0, 22l, 0, 4ll, 0},
	{ 0, -13l, 0, 0, 0, -3ll, 0, -22l, 0, 0, 0, 4ll}});
	// clang-format on
	}

	template <>
	void getElementStifnessMatrix<element_type_t<_bernoulli_beam_3>>(
	const StructuralMaterial & material, Real l, Matrix<Real> & K) {
	auto E = material.E;
	auto A = material.A;
	auto Iy = material.Iy;
	auto Iz = material.Iz;
	auto GJ = material.GJ;

	auto a1 = E * A / l;
	auto b1 = 12 * E * Iz / l / l / l;
	auto b2 = 6 * E * Iz / l / l;
	auto b3 = 4 * E * Iz / l;
	auto b4 = 2 * E * Iz / l;

	auto c1 = 12 * E * Iy / l / l / l;
	auto c2 = 6 * E * Iy / l / l;
	auto c3 = 4 * E * Iy / l;
	auto c4 = 2 * E * Iy / l;

	auto d1 = GJ / l;

	// clang-format off
	K = Matrix<Real>({
	{ a1, 0, 0, 0, 0, 0, -a1, 0, 0, 0, 0, 0},
	{ 0, b1, 0, 0, 0, b2, 0, -b1, 0, 0, 0, b2},
	{ 0, 0, c1, 0, -c2, 0, 0, 0, -c1, 0, -c2, 0},
	{ 0, 0, 0, d1, 0, 0, 0, 0, 0, -d1, 0, 0},
	{ 0, 0, -c2, 0, c3, 0, 0, 0, c2, 0, c4, 0},
	{ 0, b2, 0, 0, 0, b3, 0, -b2, 0, 0, 0, b4},
	{ -a1, 0, 0, 0, 0, 0, a1, 0, 0, 0, 0, 0},
	{ 0, -b1, 0, 0, 0, -b2, 0, b1, 0, 0, 0, -b2},
	{ 0, 0, -c1, 0, c2, 0, 0, 0, c1, 0, c2, 0},
	{ 0, 0, 0, -d1, 0, 0, 0, 0, 0, d1, 0, 0},
	{ 0, 0, -c2, 0, c4, 0, 0, 0, c2, 0, c3, 0},
	{ 0, b2, 0, 0, 0, b4, 0, -b2, 0, 0, 0, b3}});
	// clang-format on
	}

	TYPED_TEST(TestStructBernoulliDynamic, TestBeamMatrices) {
	this->model->assembleMatrix("M");
	this->model->assembleMatrix("K");

	const auto & K = this->model->getDOFManager().getMatrix("K");
	const auto & M = this->model->getDOFManager().getMatrix("M");

	Matrix<Real> Ka(this->nb_nodes * this->ndof, this->nb_nodes * this->ndof, 0.);
	Matrix<Real> Ma(this->nb_nodes * this->ndof, this->nb_nodes * this->ndof, 0.);

	Matrix<Real> Ke(this->ndof * 2, this->ndof * 2);
	Matrix<Real> Me(this->ndof * 2, this->ndof * 2);

	getElementMassMatrix<TypeParam>(this->mat, this->le, Me);
	getElementStifnessMatrix<TypeParam>(this->mat, this->le, Ke);

	auto assemble = [&](auto && nodes, auto && M, auto && Me) {
	auto n1 = nodes[0];
	auto n2 = nodes[1];
	for (auto i : arange(this->ndof)) {
	for (auto j : arange(this->ndof)) {
	M(n1 * this->ndof + i, n1 * this->ndof + j) += Me(i, j);
	M(n2 * this->ndof + i, n2 * this->ndof + j) +=
	Me(this->ndof + i, this->ndof + j);
	M(n1 * this->ndof + i, n2 * this->ndof + j) += Me(i, this->ndof + j);
	M(n2 * this->ndof + i, n1 * this->ndof + j) += Me(this->ndof + i, j);
	}
	}
	};

	auto && connectivities = this->mesh->getConnectivity(this->type);

	for (auto && connectivity : make_view(connectivities, 2)) {
	assemble(connectivity, Ka, Ke);
	assemble(connectivity, Ma, Me);
	}

	auto tol = 1e-13;

	auto Ka_max = Ka.template norm<L_inf>();
	auto Ma_max = Ma.template norm<L_inf>();

	for (auto i : arange(Ka.rows())) {
	for (auto j : arange(Ka.cols())) {
	EXPECT_NEAR(Ka(i, j), K(i, j), tol * Ka_max);
	EXPECT_NEAR(Ma(i, j), M(i, j), tol * Ma_max);
	}
	}
	}

	TYPED_TEST(TestStructBernoulliDynamic, TestBeamOscilation) {
	Real time_step = 1e-6;
	this->model->setTimeStep(time_step);

	auto & solver = this->model->getNonLinearSolver();
	solver.set("max_iterations", 100);
	solver.set("threshold", 1e-8);
	solver.set("convergence_type", SolveConvergenceCriteria::_solution);

	auto node_to_print = this->nb_nodes / 2;
	auto & d = this->model->getDisplacement()(node_to_print, _y);

	std::ofstream pos;
	std::string filename = "position" + std::to_string(this->type) + ".csv";
	pos.open(filename);
	if (not pos.good()) {
	AKANTU_ERROR("Cannot open file \"position.csv\"");
	}
	pos << "id,time,position,solution" << std::endl;

	//#define debug
	#ifdef debug
	this->model->addDumpFieldVector("displacement");
	this->model->addDumpField("blocked_dofs");
	this->model->addDumpFieldVector("external_force");
	this->model->addDumpFieldVector("internal_force");
	this->model->addDumpFieldVector("acceleration");
	this->model->addDumpFieldVector("velocity");
	this->model->dump();
	#endif

	this->model->getDisplacement().set(0.);

	Real tol = 1e-6;
	Real time = 0.;
	for (UInt s = 1; s < 300; ++s) {
	EXPECT_NO_THROW(this->model->solveStep());

	time = s * time_step;

	auto da = analytical_solution(time, this->L, this->mat.rho, this->mat.E,
	this->mat.A, this->mat.Iy, this->F);

	pos << s << "," << time << "," << d << "," << da << std::endl;

	#ifdef debug
	this->model->dump();
	#endif
	EXPECT_NEAR(d, da, tol);
	}
	-
	}
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_discrete_kirchhoff_triangle_18.cc b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_discrete_kirchhoff_triangle_18.cc
	index 62124a4ef..fb93700cc 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_discrete_kirchhoff_triangle_18.cc
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_discrete_kirchhoff_triangle_18.cc
	@@ -1,113 +1,113 @@
	/**
	* @file test_structural_mechanics_model_discrete_kirchhoff_triangle_18.cc
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Thu Feb 25 2021
	*
	* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "sparse_matrix.hh"
	#include "test_structural_mechanics_model_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	class TestStructDKT18 : public TestStructuralFixture<
	element_type_t<_discrete_kirchhoff_triangle_18>> {
	using parent =
	TestStructuralFixture<element_type_t<_discrete_kirchhoff_triangle_18>>;

	public:
	void addMaterials() override {
	mat.E = 1;
	mat.t = 1;
	mat.nu = 0.3;

	this->model->addMaterial(mat);
	}

	void assignMaterials() override {
	auto & materials = this->model->getElementMaterial(parent::type);
	std::fill(materials.begin(), materials.end(), 0);
	}

	void setDirichletBCs() override {
	this->model->getBlockedDOFs().set(true);
	auto center_node = this->model->getBlockedDOFs().end(parent::ndof) - 1;
	*center_node = {false, false, false, false, false, true};

	this->model->getDisplacement().zero();
	auto disp = ++this->model->getDisplacement().begin(parent::ndof);

	// Displacement field from Batoz Vol. 2 p. 392
	// with theta to beta correction from discrete Kirchhoff condition
	// see also the master thesis of Michael Lozano

	// clang-format off

	// This displacement field tests membrane and bending modes
	*disp = {40, 20, -800 , -20, 40, 0}; ++disp;
	*disp = {50, 40, -1400, -40, 50, 0}; ++disp;
	*disp = {10, 20, -200 , -20, 10, 0}; ++disp;

	// This displacement tests the bending mode
	// *disp = {0, 0, -800 , -20, 40, 0}; ++disp;
	// *disp = {0, 0, -1400, -40, 50, 0}; ++disp;
	// *disp = {0, 0, -200 , -20, 10, 0}; ++disp;

	// This displacement tests the membrane mode
	// *disp = {40, 20, 0, 0, 0, 0}; ++disp;
	// *disp = {50, 40, 0, 0, 0, 0}; ++disp;
	// *disp = {10, 20, 0, 0, 0, 0}; ++disp;

	// clang-format on
	}

	void setNeumannBCs() override {}

	protected:
	StructuralMaterial mat;
	};

	/* -------------------------------------------------------------------------- */

	// Batoz Vol 2. patch test, ISBN 2-86601-259-3
	TEST_F(TestStructDKT18, TestDisplacements) {
	model->solveStep();
	Vector<Real> solution = {22.5, 22.5, -337.5, -22.5, 22.5, 0};
	auto nb_nodes = this->model->getDisplacement().size();

	Vector<Real> center_node_disp =
	model->getDisplacement().begin(solution.size())[nb_nodes - 1];

	auto error = solution - center_node_disp;

	EXPECT_NEAR(error.norm<L_2>(), 0., 1e-12);
	}
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_fixture.hh b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_fixture.hh
	index 427bce303..86ccef582 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_fixture.hh
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_fixture.hh
	@@ -1,118 +1,117 @@
	/**
	* @file test_structural_mechanics_model_fixture.hh
	*
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Nov 14 2017
	* @date last modification: Thu Feb 25 2021
	*
	* @brief Main test for structural model
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "element_class_structural.hh"
	#include "structural_mechanics_model.hh"
	#include "test_gtest_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <vector>
	/* -------------------------------------------------------------------------- */

	#ifndef AKANTU_TEST_STRUCTURAL_MECHANICS_MODEL_FIXTURE_HH_
	#define AKANTU_TEST_STRUCTURAL_MECHANICS_MODEL_FIXTURE_HH_

	using namespace akantu;

	template <typename type_> class TestStructuralFixture : public ::testing::Test {
	public:
	static constexpr const ElementType type = type_::value;
	static constexpr const size_t spatial_dimension =
	ElementClass<type>::getSpatialDimension();
	static const UInt ndof = ElementClass<type>::getNbDegreeOfFreedom();

	void SetUp() override {
	const auto spatial_dimension = this->spatial_dimension;
	mesh = std::make_unique<Mesh>(spatial_dimension);
	readMesh(makeMeshName());

	std::stringstream element_type;
	element_type << this->type;
	model = std::make_unique<StructuralMechanicsModel>(*mesh, _all_dimensions,
	element_type.str());

	setNormals();
	initModel();
	}

	virtual void initModel() {
	this->addMaterials();
	auto method = getAnalysisMethod();

	this->model->initFull(_analysis_method = method);

	this->assignMaterials();

	this->setDirichletBCs();
	this->setNeumannBCs();
	}

	virtual AnalysisMethod getAnalysisMethod() const { return _static; }

	virtual void readMesh(std::string filename) {
	mesh->read(filename, _miot_gmsh_struct);
	}

	virtual std::string makeMeshName() {
	std::stringstream element_type;
	element_type << type;
	SCOPED_TRACE(element_type.str().c_str());
	return element_type.str() + ".msh";
	}

	void TearDown() override {
	model.reset(nullptr);
	mesh.reset(nullptr);
	}

	virtual void addMaterials() = 0;
	virtual void assignMaterials() = 0;
	virtual void setDirichletBCs() = 0;
	virtual void setNeumannBCs() = 0;
	virtual void setNormals() {}

	protected:
	std::unique_ptr<Mesh> mesh;
	std::unique_ptr<StructuralMechanicsModel> model;
	};

	template <typename type_>
	constexpr ElementType TestStructuralFixture<type_>::type;
	template <typename type_>
	constexpr size_t TestStructuralFixture<type_>::spatial_dimension;
	template <typename type_> const UInt TestStructuralFixture<type_>::ndof;

	using structural_types = gtest_list_t<StructuralTestElementTypes>;

	-
	#endif /* AKANTU_TEST_STRUCTURAL_MECHANICS_MODEL_FIXTURE_HH_ */
	diff --git a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_kirchhoff_shell_patch_test_4_5_5.cc b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_kirchhoff_shell_patch_test_4_5_5.cc
	index 7cb3a5ae2..de68ade0a 100644
	--- a/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_kirchhoff_shell_patch_test_4_5_5.cc
	+++ b/test/test_model/test_structural_mechanics_model/test_structural_mechanics_model_kirchhoff_shell_patch_test_4_5_5.cc
	@@ -1,250 +1,250 @@
	/**
	* @file test_structural_mechanics_model_kirchhoff_shell_patch_test_4_5_5.cc
	*
	* @author Damien Spielmann <damien.spielmann@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 22 2017
	*
	* @brief patch test exemple 4.5.5 c.f. modelisation des structures par
	* éléments finis J.-L. Batoz/G Dhatt
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include <fstream>
	#include <limits>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "material.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_io_msh.hh"
	#include "structural_mechanics_model.hh"
	/* -------------------------------------------------------------------------- */

	#define TYPE _discrete_kirchhoff_triangle_18

	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);
	Mesh shell(3);
	debug::setDebugLevel(dblWarning);
	std::cout << "Initialisation" << std::endl;
	/* --------------------------------------------------------------------------
	*/
	// Defining the mesh

	UInt nb_nodes = 5;
	UInt nb_element = 4;

	Array<Real> & nodes = const_cast<Array<Real> &>(shell.getNodes());
	nodes.resize(nb_nodes);

	Real a = 20.;
	Real b = 10.;

	nodes(0, 0) = 0.;
	nodes(0, 1) = 0.;
	nodes(0, 2) = 0.;

	nodes(1, 0) = 2 * a;
	nodes(1, 1) = 0.;
	nodes(1, 2) = 0.;

	nodes(2, 0) = 0.;
	nodes(2, 1) = 2 * b;
	nodes(2, 2) = 0.;

	nodes(3, 0) = 2 * a;
	nodes(3, 1) = 2 * b;
	nodes(3, 2) = 0.;

	nodes(4, 0) = 15.;
	nodes(4, 1) = 15.;
	nodes(4, 2) = 0.;

	shell.addConnectivityType(TYPE);
	Array<UInt> & connectivity =
	const_cast<Array<UInt> &>(shell.getConnectivity(TYPE));

	connectivity.resize(nb_element);

	connectivity(0, 0) = 1;
	connectivity(0, 1) = 3;
	connectivity(0, 2) = 4;

	connectivity(1, 0) = 3;
	connectivity(1, 1) = 2;
	connectivity(1, 2) = 4;

	connectivity(2, 0) = 2;
	connectivity(2, 1) = 4;
	connectivity(2, 2) = 0;

	connectivity(3, 0) = 0;
	connectivity(3, 1) = 1;
	connectivity(3, 2) = 4;

	akantu::MeshIOMSH mesh_io;
	mesh_io.write("b_beam_3_12_10_13.msh", shell);
	std::cout << "Mesh definition" << std::endl;
	/* --------------------------------------------------------------------------
	*/
	// Defining the materials

	akantu::StructuralMechanicsModel model(shell); // ä döfinir

	StructuralMaterial mat1;
	mat1.E = 1000;
	mat1.nu = 0.3;
	mat1.t = 1;

	model.addMaterial(mat1);

	std::cout << "Material Definition" << std::endl;
	/* --------------------------------------------------------------------------
	*/
	// Defining the deplacement

	model.initFull();

	// Array<Real> & forces = model.getForce();
	Array<Real> & displacement = model.getDisplacement();
	Array<bool> & boundary = model.getBlockedDOFs();

	displacement(0, 0) = 0;
	displacement(0, 1) = 0;
	displacement(0, 2) = 0;
	displacement(0, 3) = 0;
	displacement(0, 4) = 0;

	displacement(1, 0) = 0;
	displacement(1, 1) = 0;
	displacement(1, 2) = -800;
	displacement(1, 3) = -40;
	displacement(1, 4) = -20;

	displacement(2, 0) = 0;
	displacement(2, 1) = 0;
	displacement(2, 2) = -200;
	displacement(2, 3) = -10;
	displacement(2, 4) = -20;

	displacement(3, 0) = 0;
	displacement(3, 1) = 0;
	displacement(3, 2) = -1400;
	displacement(3, 3) = -50;
	displacement(3, 4) = -40;

	/*displacement(4,0)=0;
	displacement(4,1)=0;*/
	/* displacement(4,2)=;
	displacement(4,3)=;
	displacement(4,4)=;*/

	/* --------------------------------------------------------------------------
	*/
	// Defining the boundary conditions

	boundary(0, 0) = true;
	boundary(0, 1) = true;
	boundary(0, 2) = true;
	boundary(0, 3) = true;
	boundary(0, 4) = true;
	boundary(0, 5) = true;

	boundary(1, 0) = true;
	boundary(1, 1) = true;
	boundary(1, 2) = true;
	boundary(1, 3) = true;
	boundary(1, 4) = true;
	boundary(1, 5) = true;

	boundary(2, 0) = true;
	boundary(2, 1) = true;
	boundary(2, 2) = true;
	boundary(2, 3) = true;
	boundary(2, 4) = true;
	boundary(2, 5) = true;

	boundary(3, 0) = true;
	boundary(3, 1) = true;
	boundary(3, 2) = true;
	boundary(3, 3) = true;
	boundary(3, 4) = true;
	boundary(3, 5) = true;

	// boundary(4,0) = true;
	// boundary(4,1) = true;
	// boundary(4,2) = true;
	// boundary(4,3) = true;
	// boundary(4,4) = true;
	boundary(4, 5) = true;

	std::cout << "BC Definition" << std::endl;
	/* --------------------------------------------------------------------------
	*/
	// Solve

	Real error;

	model.assembleStiffnessMatrix();
	std::cout << "Assemble Done" << std::endl;
	model.getStiffnessMatrix().saveMatrix("K_4_5_5.mtx");

	UInt count = 0;
	std::cout << "Matrix saved" << std::endl;

	model.addDumpField("displacement");
	model.addDumpField("rotation");
	model.addDumpField("force");
	model.addDumpField("momentum");

	do {
	model.updateResidual();
	model.solve();
	count++;
	} while (!model.testConvergenceIncrement(1e-10, error) && count < 10);

	/* --------------------------------------------------------------------------
	*/
	// Post-Processing

	model.computeStresses();

	// const SparseMatrix = model.getStiffnessMatrix();
	std::cout << "u = " << displacement(4, 0) << std::endl;
	std::cout << "v = " << displacement(4, 1) << std::endl;
	std::cout << "w5 = " << displacement(4, 2) << std::endl;
	std::cout << "betax = " << displacement(4, 3) << std::endl;
	std::cout << "betay = " << displacement(4, 4) << std::endl;
	std::cout << "betaz = " << displacement(4, 5) << std::endl;

	// model.dump();
	}
	diff --git a/test/test_python_interface/test_common.cc b/test/test_python_interface/test_common.cc
	index 72ab54d28..3fc70fd9e 100644
	--- a/test/test_python_interface/test_common.cc
	+++ b/test/test_python_interface/test_common.cc
	@@ -1,153 +1,156 @@
	/**
	* @file test_common.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 31 2018
	* @date last modification: Tue Jun 30 2020
	*
	* @brief pybind11 interface for test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "py_akantu.hh"
	/* -------------------------------------------------------------------------- */
	#include <pybind11/pybind11.h>
	/* -------------------------------------------------------------------------- */
	#include <map>
	/* -------------------------------------------------------------------------- */

	namespace py = pybind11;
	namespace _aka = akantu;

	std::map<long, std::shared_ptr<_aka::Array<_aka::Real>>> arrays;
	std::map<long, std::shared_ptr<_aka::Vector<_aka::Real>>> vectors;
	std::map<long, std::shared_ptr<_aka::Matrix<_aka::Real>>> matrices;

	PYBIND11_MODULE(py11_akantu_test_common, mod) {
	mod.doc() = "Akantu Test function for common ";

	- mod.def("createArray",
	- [&](_aka::UInt size, _aka::UInt nb_components) {
	- auto ptr =
	- std::make_shared<_aka::Array<_aka::Real>>(size, nb_components);
	- ptr->zero();
	- long addr = (long)ptr->storage();
	- py::print("initial pointer: " + std::to_string(addr));
	- arrays[addr] = ptr;
	- return std::tuple<long, _aka::Array<_aka::Real> &>(addr, *ptr);
	- },
	- py::return_value_policy::reference);
	- mod.def("getArray",
	- [&](long addr) -> _aka::Array<_aka::Real> & {
	- auto & array = *arrays[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)array.storage()));
	- return array;
	- },
	- py::return_value_policy::reference);
	+ mod.def(
	+ "createArray",
	+ [&](_aka::UInt size, _aka::UInt nb_components) {
	+ auto ptr =
	+ std::make_shared<_aka::Array<_aka::Real>>(size, nb_components);
	+ ptr->zero();
	+ long addr = (long)ptr->storage();
	+ py::print("initial pointer: " + std::to_string(addr));
	+ arrays[addr] = ptr;
	+ return std::tuple<long, _aka::Array<_aka::Real> &>(addr, *ptr);
	+ },
	+ py::return_value_policy::reference);
	+ mod.def(
	+ "getArray",
	+ [&](long addr) -> _aka::Array<_aka::Real> & {
	+ auto & array = *arrays[addr];
	+ py::print("gotten pointer: " + std::to_string((long)array.storage()));
	+ return array;
	+ },
	+ py::return_value_policy::reference);

	- mod.def("copyArray",
	- [&](long addr) -> _aka::Array<_aka::Real> {
	- auto & array = *arrays[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)array.storage()));
	- return array;
	- },
	- py::return_value_policy::copy);
	+ mod.def(
	+ "copyArray",
	+ [&](long addr) -> _aka::Array<_aka::Real> {
	+ auto & array = *arrays[addr];
	+ py::print("gotten pointer: " + std::to_string((long)array.storage()));
	+ return array;
	+ },
	+ py::return_value_policy::copy);

	mod.def("getRawPointerArray", [](_aka::Array<_aka::Real> & _data) {
	py::print("received proxy: " + std::to_string((long)&_data));
	py::print("raw pointer: " + std::to_string((long)_data.storage()));
	return (long)_data.storage();
	});

	- mod.def("createVector",
	- [&](_aka::UInt size) {
	- auto ptr = std::make_shared<_aka::Vector<_aka::Real>>(size);
	- ptr->zero();
	- long addr = (long)ptr->storage();
	- py::print("initial pointer: " + std::to_string(addr));
	- vectors[addr] = ptr;
	- return std::tuple<long, _aka::Vector<_aka::Real> &>(addr, *ptr);
	- },
	- py::return_value_policy::reference);
	- mod.def("getVector",
	- [&](long addr) -> _aka::Vector<_aka::Real> & {
	- auto & vector = *vectors[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)vector.storage()));
	- return vector;
	- },
	- py::return_value_policy::reference);
	+ mod.def(
	+ "createVector",
	+ [&](_aka::UInt size) {
	+ auto ptr = std::make_shared<_aka::Vector<_aka::Real>>(size);
	+ ptr->zero();
	+ long addr = (long)ptr->storage();
	+ py::print("initial pointer: " + std::to_string(addr));
	+ vectors[addr] = ptr;
	+ return std::tuple<long, _aka::Vector<_aka::Real> &>(addr, *ptr);
	+ },
	+ py::return_value_policy::reference);
	+ mod.def(
	+ "getVector",
	+ [&](long addr) -> _aka::Vector<_aka::Real> & {
	+ auto & vector = *vectors[addr];
	+ py::print("gotten pointer: " + std::to_string((long)vector.storage()));
	+ return vector;
	+ },
	+ py::return_value_policy::reference);

	- mod.def("copyVector",
	- [&](long addr) -> _aka::Vector<_aka::Real> {
	- auto & vector = *vectors[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)vector.storage()));
	- return vector;
	- },
	- py::return_value_policy::copy);
	+ mod.def(
	+ "copyVector",
	+ [&](long addr) -> _aka::Vector<_aka::Real> {
	+ auto & vector = *vectors[addr];
	+ py::print("gotten pointer: " + std::to_string((long)vector.storage()));
	+ return vector;
	+ },
	+ py::return_value_policy::copy);

	mod.def("getRawPointerVector", [](_aka::Vector<_aka::Real> & _data) {
	py::print("received proxy: " + std::to_string((long)&_data));
	py::print("raw pointer: " + std::to_string((long)_data.storage()));
	return (long)_data.storage();
	});

	- mod.def("createMatrix",
	- [&](_aka::UInt size1, _aka::UInt size2) {
	- auto ptr = std::make_shared<_aka::Matrix<_aka::Real>>(size1, size2);
	- ptr->zero();
	- long addr = (long)ptr->storage();
	- py::print("initial pointer: " + std::to_string(addr));
	- matrices[addr] = ptr;
	- return std::tuple<long, _aka::Matrix<_aka::Real> &>(addr, *ptr);
	- },
	- py::return_value_policy::reference);
	- mod.def("getMatrix",
	- [&](long addr) -> _aka::Matrix<_aka::Real> & {
	- auto & matrix = *matrices[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)matrix.storage()));
	- return matrix;
	- },
	- py::return_value_policy::reference);
	+ mod.def(
	+ "createMatrix",
	+ [&](_aka::UInt size1, _aka::UInt size2) {
	+ auto ptr = std::make_shared<_aka::Matrix<_aka::Real>>(size1, size2);
	+ ptr->zero();
	+ long addr = (long)ptr->storage();
	+ py::print("initial pointer: " + std::to_string(addr));
	+ matrices[addr] = ptr;
	+ return std::tuple<long, _aka::Matrix<_aka::Real> &>(addr, *ptr);
	+ },
	+ py::return_value_policy::reference);
	+ mod.def(
	+ "getMatrix",
	+ [&](long addr) -> _aka::Matrix<_aka::Real> & {
	+ auto & matrix = *matrices[addr];
	+ py::print("gotten pointer: " + std::to_string((long)matrix.storage()));
	+ return matrix;
	+ },
	+ py::return_value_policy::reference);

	- mod.def("copyMatrix",
	- [&](long addr) -> _aka::Matrix<_aka::Real> {
	- auto & matrix = *matrices[addr];
	- py::print("gotten pointer: " +
	- std::to_string((long)matrix.storage()));
	- return matrix;
	- },
	- py::return_value_policy::copy);
	+ mod.def(
	+ "copyMatrix",
	+ [&](long addr) -> _aka::Matrix<_aka::Real> {
	+ auto & matrix = *matrices[addr];
	+ py::print("gotten pointer: " + std::to_string((long)matrix.storage()));
	+ return matrix;
	+ },
	+ py::return_value_policy::copy);

	mod.def("getRawPointerMatrix", [](_aka::Matrix<_aka::Real> & _data) {
	py::print("received proxy: " + std::to_string((long)&_data));
	py::print("raw pointer: " + std::to_string((long)_data.storage()));
	return (long)_data.storage();
	});
	} // Module akantu_test_common
	diff --git a/test/test_solver/test_petsc_matrix_apply_boundary.cc b/test/test_solver/test_petsc_matrix_apply_boundary.cc
	index b5ce50cf8..3a2682a97 100644
	--- a/test/test_solver/test_petsc_matrix_apply_boundary.cc
	+++ b/test/test_solver/test_petsc_matrix_apply_boundary.cc
	@@ -1,150 +1,150 @@
	/**
	* @file test_petsc_matrix_apply_boundary.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 08 2017
	*
	* @brief test the applyBoundary method of the PETScMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"
	#include "petsc_matrix.hh"

	#include "mesh_partition_scotch.hh"

	using namespace akantu;
	int main(int argc, char * argv[]) {

	initialize(argc, argv);
	const ElementType element_type = _triangle_3;
	const GhostType ghost_type = _not_ghost;
	UInt spatial_dimension = 2;

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	/// read the mesh and partition it
	Mesh mesh(spatial_dimension);

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	/// creation mesh
	mesh.read("triangle.msh");
	MeshPartitionScotch * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	FEEngine * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
	mesh, spatial_dimension, "my_fem");

	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	dof_synchronizer.initGlobalDOFEquationNumbers();

	// fill the matrix with
	UInt nb_element = mesh.getNbElement(element_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
	UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
	SparseMatrix K(nb_global_nodes * spatial_dimension, _symmetric);
	K.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 1);
	Array<Real> K_e =
	Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
	Array<Real>::matrix_iterator K_e_it =
	K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
	Array<Real>::matrix_iterator K_e_end =
	K_e.end(nb_dofs_per_element, nb_dofs_per_element);

	for (; K_e_it != K_e_end; ++K_e_it)
	*K_e_it = element_input;

	// assemble the test matrix
	fem->assembleMatrix(K_e, K, spatial_dimension, element_type, ghost_type);

	// create petsc matrix
	PETScMatrix petsc_matrix(nb_global_nodes * spatial_dimension, _symmetric);

	petsc_matrix.buildProfile(mesh, dof_synchronizer, spatial_dimension);

	// add stiffness matrix to petsc matrix
	petsc_matrix.add(K, 1);

	// create boundary array: block all dofs
	UInt nb_nodes = mesh.getNbNodes();
	Array<bool> boundary = Array<bool>(nb_nodes, spatial_dimension, true);

	// apply boundary
	petsc_matrix.applyBoundary(boundary);

	// test if all entries except the diagonal ones have been zeroed
	Real test_passed = 0;

	for (UInt i = 0; i < nb_nodes * spatial_dimension; ++i) {
	if (dof_synchronizer.isLocalOrMasterDOF(i)) {
	for (UInt j = 0; j < nb_nodes * spatial_dimension; ++j) {
	if (dof_synchronizer.isLocalOrMasterDOF(j)) {
	if (i == j)
	test_passed += petsc_matrix(i, j) - 1;
	else
	test_passed += petsc_matrix(i, j) - 0;
	}
	}
	}
	}

	if (std::abs(test_passed) > Math::getTolerance()) {
	finalize();
	return EXIT_FAILURE;
	}
	delete communicator;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_petsc_matrix_diagonal.cc b/test/test_solver/test_petsc_matrix_diagonal.cc
	index f2cd757fb..52b6cabf6 100644
	--- a/test/test_solver/test_petsc_matrix_diagonal.cc
	+++ b/test/test_solver/test_petsc_matrix_diagonal.cc
	@@ -1,163 +1,163 @@
	/**
	* @file test_petsc_matrix_diagonal.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 08 2017
	*
	* @brief test the connectivity is correctly represented in the PETScMatrix
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "dumper_paraview.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_partition_scotch.hh"
	#include "mesh_utils.hh"
	#include "petsc_matrix.hh"

	using namespace akantu;
	int main(int argc, char * argv[]) {

	initialize(argc, argv);
	const ElementType element_type = _triangle_3;
	const GhostType ghost_type = _not_ghost;
	UInt spatial_dimension = 2;

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	/// read the mesh and partition it
	Mesh mesh(spatial_dimension);

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	/// creation mesh
	mesh.read("triangle.msh");
	MeshPartitionScotch * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	// DumperParaview mesh_dumper("mesh_dumper");
	// mesh_dumper.registerMesh(mesh, spatial_dimension, _not_ghost);
	// mesh_dumper.dump();

	/// initialize the FEEngine and the dof_synchronizer
	FEEngine * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
	mesh, spatial_dimension, "my_fem");

	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	dof_synchronizer.initGlobalDOFEquationNumbers();

	// construct an Akantu sparse matrix, build the profile and fill the matrix
	// for the given mesh
	UInt nb_element = mesh.getNbElement(element_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
	UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
	SparseMatrix K_akantu(nb_global_nodes * spatial_dimension, _unsymmetric);
	K_akantu.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// use as elemental matrices a matrix with values equal to 1 every where
	Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 1.);
	Array<Real> K_e =
	Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
	Array<Real>::matrix_iterator K_e_it =
	K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
	Array<Real>::matrix_iterator K_e_end =
	K_e.end(nb_dofs_per_element, nb_dofs_per_element);

	for (; K_e_it != K_e_end; ++K_e_it)
	*K_e_it = element_input;

	// assemble the test matrix
	fem->assembleMatrix(K_e, K_akantu, spatial_dimension, element_type,
	ghost_type);

	/// construct a PETSc matrix
	PETScMatrix K_petsc(nb_global_nodes * spatial_dimension, _unsymmetric);
	/// build the profile of the PETSc matrix for the mesh of this example
	K_petsc.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// add an Akantu sparse matrix to a PETSc sparse matrix
	K_petsc.add(K_akantu, 1);

	/// check to how many elements each node is connected
	CSR<Element> node_to_elem;

	MeshUtils::buildNode2Elements(mesh, node_to_elem, spatial_dimension);

	/// test the diagonal of the PETSc matrix: the diagonal entries
	/// of the PETSc matrix correspond to the number of elements
	/// connected to the node of the dof. Note: for an Akantu matrix this is only
	/// true for the serial case
	Real error = 0.;
	/// loop over all diagonal values of the matrix
	for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
	for (UInt j = 0; j < spatial_dimension; ++j) {
	UInt dof = i * spatial_dimension + j;
	/// for PETSc matrix only DOFs on the processor and be accessed
	if (dof_synchronizer.isLocalOrMasterDOF(dof)) {
	UInt global_dof = dof_synchronizer.getDOFGlobalID(dof);
	std::cout << "Number of elements connected: "
	<< node_to_elem.getNbCols(i) << std::endl;
	std::cout << "K_petsc(" << global_dof << "," << global_dof
	<< ")=" << K_petsc(dof, dof) << std::endl;
	error += std::abs(K_petsc(dof, dof) - node_to_elem.getNbCols(i));
	}
	}
	}

	if (error > Math::getTolerance()) {
	std::cout << "error in the stiffness matrix!!!" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}

	delete communicator;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_petsc_matrix_profile.cc b/test/test_solver/test_petsc_matrix_profile.cc
	index fc218c3bb..9ba395d83 100644
	--- a/test/test_solver/test_petsc_matrix_profile.cc
	+++ b/test/test_solver/test_petsc_matrix_profile.cc
	@@ -1,144 +1,144 @@
	/**
	* @file test_petsc_matrix_profile.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Jan 01 2019
	*
	* @brief test the profile generation of the PETScMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"
	#include "sparse_matrix_petsc.hh"
	/// #include "dumper_paraview.hh"
	#include "mesh_partition_scotch.hh"

	using namespace akantu;
	int main(int argc, char * argv[]) {

	initialize(argc, argv);
	const ElementType element_type = _triangle_3;
	const GhostType ghost_type = _not_ghost;
	UInt spatial_dimension = 2;

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	/// read the mesh and partition it
	Mesh mesh(spatial_dimension);

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	/// creation mesh
	mesh.read("square.msh");
	MeshPartitionScotch * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	// dump mesh in paraview
	// DumperParaview mesh_dumper("mesh_dumper");
	// mesh_dumper.registerMesh(mesh, spatial_dimension, _not_ghost);
	// mesh_dumper.dump();

	/// initialize the FEEngine and the dof_synchronizer
	FEEngine * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
	mesh, spatial_dimension, "my_fem");

	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	dof_synchronizer.initGlobalDOFEquationNumbers();

	// construct an Akantu sparse matrix, build the profile and fill the matrix
	// for the given mesh
	UInt nb_element = mesh.getNbElement(element_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
	UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
	SparseMatrix K_akantu(nb_global_nodes * spatial_dimension, _unsymmetric);
	K_akantu.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// use as elemental matrices a matrix with values equal to 1 every where
	Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 1.);
	Array<Real> K_e =
	Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
	Array<Real>::matrix_iterator K_e_it =
	K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
	Array<Real>::matrix_iterator K_e_end =
	K_e.end(nb_dofs_per_element, nb_dofs_per_element);

	for (; K_e_it != K_e_end; ++K_e_it)
	*K_e_it = element_input;

	// assemble the test matrix
	fem->assembleMatrix(K_e, K_akantu, spatial_dimension, element_type,
	ghost_type);

	/// construct a PETSc matrix
	PETScMatrix K_petsc(nb_global_nodes * spatial_dimension, _unsymmetric);
	/// build the profile of the PETSc matrix for the mesh of this example
	K_petsc.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// add an Akantu sparse matrix to a PETSc sparse matrix
	K_petsc.add(K_akantu, 1);

	/// save the profile
	K_petsc.saveMatrix("profile.txt");

	/// print the matrix to screen
	std::ifstream profile;
	profile.open("profile.txt");
	std::string current_line;
	while (getline(profile, current_line))
	std::cout << current_line << std::endl;
	profile.close();

	delete communicator;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_petsc_matrix_profile_parallel.cc b/test/test_solver/test_petsc_matrix_profile_parallel.cc
	index f2a0577f7..164783a19 100644
	--- a/test/test_solver/test_petsc_matrix_profile_parallel.cc
	+++ b/test/test_solver/test_petsc_matrix_profile_parallel.cc
	@@ -1,144 +1,144 @@
	/**
	* @file test_petsc_matrix_profile_parallel.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Jan 01 2019
	*
	* @brief test the profile generation of the PETScMatrix class in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	#include <fstream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"
	#include "sparse_matrix_petsc.hh"
	/// #include "dumper_paraview.hh"
	#include "mesh_partition_scotch.hh"

	using namespace akantu;
	int main(int argc, char * argv[]) {

	initialize(argc, argv);
	const ElementType element_type = _triangle_3;
	const GhostType ghost_type = _not_ghost;
	UInt spatial_dimension = 2;

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	/// read the mesh and partition it
	Mesh mesh(spatial_dimension);

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	/// creation mesh
	mesh.read("square.msh");
	MeshPartitionScotch * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	// dump mesh in paraview
	// DumperParaview mesh_dumper("mesh_dumper");
	// mesh_dumper.registerMesh(mesh, spatial_dimension, _not_ghost);
	// mesh_dumper.dump();

	/// initialize the FEEngine and the dof_synchronizer
	FEEngine * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
	mesh, spatial_dimension, "my_fem");

	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	dof_synchronizer.initGlobalDOFEquationNumbers();

	// construct an Akantu sparse matrix, build the profile and fill the matrix
	// for the given mesh
	UInt nb_element = mesh.getNbElement(element_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
	UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
	SparseMatrix K_akantu(nb_global_nodes * spatial_dimension, _unsymmetric);
	K_akantu.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// use as elemental matrices a matrix with values equal to 1 every where
	Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 1.);
	Array<Real> K_e =
	Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
	Array<Real>::matrix_iterator K_e_it =
	K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
	Array<Real>::matrix_iterator K_e_end =
	K_e.end(nb_dofs_per_element, nb_dofs_per_element);

	for (; K_e_it != K_e_end; ++K_e_it)
	*K_e_it = element_input;

	// assemble the test matrix
	fem->assembleMatrix(K_e, K_akantu, spatial_dimension, element_type,
	ghost_type);

	/// construct a PETSc matrix
	PETScMatrix K_petsc(nb_global_nodes * spatial_dimension, _unsymmetric);
	/// build the profile of the PETSc matrix for the mesh of this example
	K_petsc.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	/// add an Akantu sparse matrix to a PETSc sparse matrix
	K_petsc.add(K_akantu, 1);

	/// save the profile
	K_petsc.saveMatrix("profile_parallel.txt");
	/// print the matrix to screen
	if (prank == 0) {
	std::ifstream profile;
	profile.open("profile_parallel.txt");
	std::string current_line;
	while (getline(profile, current_line))
	std::cout << current_line << std::endl;
	profile.close();
	}

	delete communicator;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_solver_petsc.cc b/test/test_solver/test_solver_petsc.cc
	index 4fc6ab5fc..0972c9bc2 100644
	--- a/test/test_solver/test_solver_petsc.cc
	+++ b/test/test_solver/test_solver_petsc.cc
	@@ -1,173 +1,173 @@
	/**
	* @file test_solver_petsc.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Jan 01 2019
	*
	* @brief test the PETSc solver interface
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_csr.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"
	#include "mesh_utils.hh"
	#include "solver_petsc.hh"
	#include "sparse_matrix_petsc.hh"

	#include "mesh_partition_scotch.hh"

	using namespace akantu;
	int main(int argc, char * argv[]) {

	initialize(argc, argv);
	const ElementType element_type = _segment_2;
	const GhostType ghost_type = _not_ghost;
	UInt spatial_dimension = 1;

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	/// read the mesh and partition it
	Mesh mesh(spatial_dimension);

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	/// creation mesh
	mesh.read("1D_bar.msh");
	MeshPartitionScotch * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	FEEngine * fem =
	new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
	mesh, spatial_dimension, "my_fem");

	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	dof_synchronizer.initGlobalDOFEquationNumbers();

	// fill the matrix with
	UInt nb_element = mesh.getNbElement(element_type);
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
	UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
	SparseMatrix K(nb_global_nodes * spatial_dimension, _symmetric);
	K.buildProfile(mesh, dof_synchronizer, spatial_dimension);
	Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 0);
	for (UInt i = 0; i < nb_dofs_per_element; ++i) {
	for (UInt j = 0; j < nb_dofs_per_element; ++j) {
	element_input(i, j) = ((i == j) ? 1 : -1);
	}
	}
	Array<Real> K_e =
	Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
	Array<Real>::matrix_iterator K_e_it =
	K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
	Array<Real>::matrix_iterator K_e_end =
	K_e.end(nb_dofs_per_element, nb_dofs_per_element);

	for (; K_e_it != K_e_end; ++K_e_it)
	*K_e_it = element_input;

	// assemble the test matrix
	fem->assembleMatrix(K_e, K, spatial_dimension, element_type, ghost_type);

	// apply boundary: block first node
	const Array<Real> & position = mesh.getNodes();
	UInt nb_nodes = mesh.getNbNodes();
	Array<bool> boundary = Array<bool>(nb_nodes, spatial_dimension, false);
	for (UInt i = 0; i < nb_nodes; ++i) {
	if (std::abs(position(i, 0)) < Math::getTolerance())
	boundary(i, 0) = true;
	}

	K.applyBoundary(boundary);

	/// create the PETSc matrix for the solve step
	PETScMatrix petsc_matrix(nb_global_nodes * spatial_dimension, _symmetric);
	petsc_matrix.buildProfile(mesh, dof_synchronizer, spatial_dimension);

	/// copy the stiffness matrix into the petsc matrix
	petsc_matrix.add(K, 1);

	// initialize internal forces: they are zero because imposed displacement is
	// zero
	Array<Real> internal_forces(nb_nodes, spatial_dimension, 0.);

	// compute residual: apply nodal force on last node
	Array<Real> residual(nb_nodes, spatial_dimension, 0.);

	for (UInt i = 0; i < nb_nodes; ++i) {
	if (std::abs(position(i, 0) - 10) < Math::getTolerance())
	residual(i, 0) += 2;
	}

	residual -= internal_forces;

	/// initialize solver and solution
	Array<Real> solution(nb_nodes, spatial_dimension, 0.);
	SolverPETSc solver(petsc_matrix);
	solver.initialize();
	solver.setOperators();
	solver.setRHS(residual);
	solver.solve(solution);

	/// verify solution
	Math::setTolerance(1e-11);
	for (UInt i = 0; i < nb_nodes; ++i) {
	if (!dof_synchronizer.isPureGhostDOF(i) &&
	!Math::are_float_equal(2 * position(i, 0), solution(i, 0))) {
	std::cout << "The solution is not correct!!!!" << std::endl;
	finalize();
	return EXIT_FAILURE;
	}
	}

	delete communicator;

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_sparse_matrix_assemble.cc b/test/test_solver/test_sparse_matrix_assemble.cc
	index 5cd429f3e..130128358 100644
	--- a/test/test_solver/test_sparse_matrix_assemble.cc
	+++ b/test/test_solver/test_sparse_matrix_assemble.cc
	@@ -1,86 +1,86 @@
	/**
	* @file test_sparse_matrix_assemble.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri May 19 2017
	*
	* @brief test the assembling method of the SparseMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "mesh.hh"
	#include "mesh_io.hh"

	#include "dof_synchronizer.hh"
	#include "sparse_matrix.hh"

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	UInt nb_nodes = mesh.getNbNodes();

	DOFManagerDefault dof_manager(mesh, "test_dof_manager");

	Array<Real> test_synchronize(nb_nodes, spatial_dimension, "Test vector");
	dof_manager.registerDOFs("test_synchronize", test_synchronize, _dst_nodal);

	auto & A = dof_manager.getNewMatrix("A", _symmetric);

	// const akantu::Mesh::ConnectivityTypeList & type_list =
	// mesh.getConnectivityTypeList();
	// akantu::Mesh::ConnectivityTypeList::const_iterator it;

	// for(it = type_list.begin(); it != type_list.end(); ++it) {
	// if(mesh.getSpatialDimension(*it) != spatial_dimension) continue;
	// akantu::UInt nb_element = mesh.getNbElement(*it);
	// akantu::UInt nb_nodes_per_element = mesh.getNbNodesPerElement(*it);
	// akantu::Element element(*it);

	// akantu::UInt m = nb_nodes_per_element * spatial_dimension;
	// akantu::Array<akantu::Real> local_mat(m, m, 1, "local_mat");

	// for(akantu::UInt e = 0; e < nb_element; ++e) {
	// element.element = e;
	// sparse_matrix.addToMatrix(local_mat.storage(), element,
	// nb_nodes_per_element);
	// }
	// }

	A.saveMatrix("matrix.mtx");

	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_sparse_matrix_product.cc b/test/test_solver/test_sparse_matrix_product.cc
	index afec8d909..9bda5fc60 100644
	--- a/test/test_solver/test_sparse_matrix_product.cc
	+++ b/test/test_solver/test_sparse_matrix_product.cc
	@@ -1,123 +1,123 @@
	/**
	* @file test_sparse_matrix_product.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Jan 01 2019
	*
	* @brief test the matrix vector product in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_partition_scotch.hh"
	#include "sparse_matrix_aij.hh"
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);
	const UInt spatial_dimension = 2;
	const UInt nb_dof = 2;

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	Mesh mesh(spatial_dimension);
	mesh.read("bar.msh");
	mesh.distribute();

	UInt nb_nodes = mesh.getNbNodes();
	DOFManagerDefault dof_manager(mesh, "test_dof_manager");

	Array<Real> test_synchronize(nb_nodes, nb_dof, "Test vector");
	dof_manager.registerDOFs("test_synchronize", test_synchronize, _dst_nodal);

	if (prank == 0)
	std::cout << "Creating a SparseMatrix" << std::endl;

	auto & A = dynamic_cast<SparseMatrixAIJ &>(
	dof_manager.getNewMatrix("A", _symmetric));

	Array<Real> dof_vector(nb_nodes, nb_dof, "vector");

	if (prank == 0)
	std::cout << "Filling the matrix" << std::endl;

	for (UInt i = 0; i < nb_nodes * nb_dof; ++i) {
	if (dof_manager.isLocalOrMasterDOF(i))
	A.add(i, i, 2.);
	}

	std::stringstream str;
	str << "Matrix_" << prank << ".mtx";
	A.saveMatrix(str.str());

	for (UInt n = 0; n < nb_nodes; ++n) {
	for (UInt d = 0; d < nb_dof; ++d) {
	dof_vector(n, d) = 1.;
	}
	}

	Array<Real> dof_vector_tmp(dof_vector);

	if (prank == 0)
	std::cout << "Computing x = A * x" << std::endl;
	A.matVecMul(dof_vector, dof_vector_tmp);
	dof_vector.copy(dof_vector_tmp);

	auto & sync =
	dynamic_cast<DOFManagerDefault &>(dof_manager).getSynchronizer();

	if (prank == 0)
	std::cout << "Gathering the results on proc 0" << std::endl;
	if (psize > 1) {
	if (prank == 0) {
	Array<Real> gathered;
	sync.gather(dof_vector, gathered);

	debug::setDebugLevel(dblTest);
	std::cout << gathered << std::endl;
	debug::setDebugLevel(dblWarning);
	} else {
	sync.gather(dof_vector);
	}
	} else {
	debug::setDebugLevel(dblTest);
	std::cout << dof_vector << std::endl;
	debug::setDebugLevel(dblWarning);
	}

	finalize();

	return 0;
	}
	diff --git a/test/test_solver/test_sparse_matrix_profile.cc b/test/test_solver/test_sparse_matrix_profile.cc
	index 9df8c129e..facf232c1 100644
	--- a/test/test_solver/test_sparse_matrix_profile.cc
	+++ b/test/test_solver/test_sparse_matrix_profile.cc
	@@ -1,76 +1,76 @@
	/**
	* @file test_sparse_matrix_profile.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Aug 29 2017
	*
	* @brief test the profile generation of the SparseMatrix class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "dof_manager_default.hh"
	#include "mesh.hh"
	#include "sparse_matrix.hh"
	/* -------------------------------------------------------------------------- */
	#include <cstdlib>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt spatial_dimension = 2;
	Mesh mesh(spatial_dimension);
	mesh.read("triangle.msh");

	UInt nb_nodes = mesh.getNbNodes();

	DOFManagerDefault dof_manager(mesh, "test_dof_manager");
	Array<Real> test_synchronize(nb_nodes, spatial_dimension, "Test vector");
	dof_manager.registerDOFs("test_synchronize", test_synchronize, _dst_nodal);

	auto & A = dof_manager.getNewMatrix("A", _symmetric);

	for (UInt i = 0; i < 10; ++i) {
	A.add(i, i);
	}

	A.add(0, 9);
	A.saveProfile("profile_hand.mtx");

	for (UInt i = 0; i < 10; ++i) {
	A.add(i, i, i * 10);
	}
	A.add(0, 9, 100);

	A.saveMatrix("matrix_hand.mtx");

	/* ------------------------------------------------------------------------ */
	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_sparse_matrix_profile_parallel.cc b/test/test_solver/test_sparse_matrix_profile_parallel.cc
	index 77052e4b1..ff9cd2370 100644
	--- a/test/test_solver/test_sparse_matrix_profile_parallel.cc
	+++ b/test/test_solver/test_sparse_matrix_profile_parallel.cc
	@@ -1,114 +1,114 @@
	/**
	* @file test_sparse_matrix_profile_parallel.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Nov 08 2017
	*
	* @brief test the sparse matrix class in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "communicator.hh"
	#include "mesh.hh"
	#include "mesh_io_msh.hh"
	#include "mesh_partition_scotch.hh"
	#include "solver_mumps.hh"
	#include "sparse_matrix.hh"

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);

	int dim = 2;
	//#ifdef AKANTU_USE_IOHELPER
	// akantu::ElementType type = akantu::_triangle_6;
	//#endif //AKANTU_USE_IOHELPER
	akantu::Mesh mesh(dim);

	// akantu::debug::setDebugLevel(akantu::dblDump);

	akantu::StaticCommunicator * comm =
	akantu::Communicator::getStaticCommunicator();
	akantu::Int psize = comm->getNbProc();
	akantu::Int prank = comm->whoAmI();

	akantu::UInt n = 0;

	/* ------------------------------------------------------------------------ */
	/* Parallel initialization */
	/* ------------------------------------------------------------------------ */
	akantu::Communicator * communicator;
	if (prank == 0) {
	akantu::MeshIOMSH mesh_io;
	mesh_io.read("triangle.msh", mesh);
	akantu::MeshPartition * partition =
	new akantu::MeshPartitionScotch(mesh, dim);

	// partition->reorder();
	mesh_io.write("triangle_reorder.msh", mesh);

	n = mesh.getNbNodes();

	partition->partitionate(psize);
	communicator =
	akantu::Communicator::createCommunicatorDistributeMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	akantu::Communicator::createCommunicatorDistributeMesh(mesh, NULL);
	}

	std::cout << "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA "
	<< mesh.getNbGlobalNodes() << std::endl;

	akantu::SparseMatrix sparse_matrix(mesh, akantu::_symmetric, 2, "mesh");
	sparse_matrix.buildProfile();

	akantu::Solver * solver = new akantu::SolverMumps(sparse_matrix);

	if (prank == 0) {
	for (akantu::UInt i = 0; i < n; ++i) {
	solver->getRHS().storage()[i] = 1.;
	}
	}

	akantu::debug::setDebugLevel(akantu::dblDump);
	solver->initialize();

	std::stringstream sstr;
	sstr << "profile_" << prank << ".mtx";
	sparse_matrix.saveProfile(sstr.str());

	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_solver/test_sparse_solver_mumps.cc b/test/test_solver/test_sparse_solver_mumps.cc
	index 3ab355a0d..a96055b2b 100644
	--- a/test/test_solver/test_sparse_solver_mumps.cc
	+++ b/test/test_solver/test_sparse_solver_mumps.cc
	@@ -1,169 +1,169 @@
	/**
	* @file test_sparse_solver_mumps.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri May 19 2017
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test the matrix vector product in parallel
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_accessor.hh"
	#include "mesh_partition_scotch.hh"
	#include "sparse_matrix_aij.hh"
	#include "sparse_solver_mumps.hh"
	#include "terms_to_assemble.hh"
	/* -------------------------------------------------------------------------- */
	#include <iostream>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	void genMesh(Mesh & mesh, UInt nb_nodes);
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);
	const UInt spatial_dimension = 1;
	const UInt nb_global_dof = 11;
	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	Mesh mesh(spatial_dimension);

	if (prank == 0) {
	genMesh(mesh, nb_global_dof);
	RandomGenerator<UInt>::seed(1496137735);
	} else {
	RandomGenerator<UInt>::seed(2992275470);
	}

	mesh.distribute();
	UInt node = 0;
	for (auto pos : mesh.getNodes()) {
	std::cout << prank << " " << node << " pos: " << pos << " ["
	<< mesh.getNodeGlobalId(node) << "] " << mesh.getNodeFlag(node)
	<< std::endl;
	++node;
	}
	UInt nb_nodes = mesh.getNbNodes();

	DOFManagerDefault dof_manager(mesh, "test_dof_manager");

	Array<Real> x(nb_nodes);
	dof_manager.registerDOFs("x", x, _dst_nodal);

	const auto & local_equation_number =
	dof_manager.getLocalEquationsNumbers("x");

	auto & A = dof_manager.getNewMatrix("A", _symmetric);

	Array<Real> b(nb_nodes);
	TermsToAssemble terms;

	for (UInt i = 0; i < nb_nodes; ++i) {
	if (dof_manager.isLocalOrMasterDOF(i)) {
	auto li = local_equation_number(i);
	auto gi = dof_manager.localToGlobalEquationNumber(li);
	terms(i, i) = 1. / (1. + gi);
	}
	}

	dof_manager.assemblePreassembledMatrix("x", "x", "A", terms);

	std::stringstream str;
	str << "Matrix_" << prank << ".mtx";
	A.saveMatrix(str.str());

	for (UInt n = 0; n < nb_nodes; ++n) {
	b(n) = 1.;
	}

	SparseSolverMumps solver(dof_manager, "A");

	solver.solve(x, b);

	auto && check = [&](auto && xs) {
	debug::setDebugLevel(dblTest);
	std::cout << xs << std::endl;
	debug::setDebugLevel(dblWarning);

	UInt d = 1.;
	for (auto x : xs) {
	if (std::abs(x - d) / d > 1e-15)
	AKANTU_EXCEPTION("Error in the solution: " << x << " != " << d << " ["
	<< (std::abs(x - d) / d)
	<< "].");
	++d;
	}
	};

	if (psize > 1) {
	auto & sync =
	dynamic_cast<DOFManagerDefault &>(dof_manager).getSynchronizer();

	if (prank == 0) {
	Array<Real> x_gathered(dof_manager.getSystemSize());
	sync.gather(x, x_gathered);
	check(x_gathered);
	} else {
	sync.gather(x);
	}
	} else {
	check(x);
	}

	finalize();

	return 0;
	}

	/* -------------------------------------------------------------------------- */
	void genMesh(Mesh & mesh, UInt nb_nodes) {
	MeshAccessor mesh_accessor(mesh);
	Array<Real> & nodes = mesh_accessor.getNodes();
	Array<UInt> & conn = mesh_accessor.getConnectivity(_segment_2);

	nodes.resize(nb_nodes);

	for (UInt n = 0; n < nb_nodes; ++n) {
	nodes(n, _x) = n * (1. / (nb_nodes - 1));
	}

	conn.resize(nb_nodes - 1);
	for (UInt n = 0; n < nb_nodes - 1; ++n) {
	conn(n, 0) = n;
	conn(n, 1) = n + 1;
	}

	mesh_accessor.makeReady();
	}
	diff --git a/test/test_synchronizer/test_communicator.cc b/test/test_synchronizer/test_communicator.cc
	index 3ce704aa8..fed5c0db9 100644
	--- a/test/test_synchronizer/test_communicator.cc
	+++ b/test/test_synchronizer/test_communicator.cc
	@@ -1,141 +1,143 @@
	/**
	* @file test_communicator.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 26 2019
	* @date last modification: Tue Nov 17 2020
	*
	* @brief Test the communicators
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <aka_iterators.hh>
	#include <communication_tag.hh>
	#include <communicator.hh>
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	#include <random>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	TEST(Communicator, Bcast) {
	auto r = 0xdeadbeef;

	auto & c = Communicator::getStaticCommunicator();
	c.broadcast(r);

	EXPECT_EQ(r, 0xdeadbeef);
	}

	TEST(Communicator, ReceiveAny) {
	std::random_device rd;
	std::mt19937 gen(rd());
	std::uniform_int_distribution<> dis(1, 10);
	std::vector<CommunicationRequest> reqs;

	auto & c = Communicator::getStaticCommunicator();
	auto && rank = c.whoAmI();
	auto && size = c.getNbProc();

	for (auto n [[gnu::unused]] : arange(100)) {
	AKANTU_DEBUG_INFO("ROUND " << n);
	auto tag = Tag::genTag(0, 1, 0);

	if (rank == 0) {
	std::vector<int> sends(size - 1);
	for (auto & s : sends) {
	s = dis(gen);
	}

	c.broadcast(sends);
	AKANTU_DEBUG_INFO("Messages " << [&]() {
	std::string msgs;
	for (auto s : enumerate(sends)) {
	if (std::get<0>(s) != 0)
	msgs += ", ";
	msgs += std::to_string(std::get<0>(s) + 1) + ": " +
	std::to_string(std::get<1>(s));
	}
	return msgs;
	}());

	int nb_recvs = 0;
	for (auto && data : enumerate(sends)) {
	auto & send = std::get<1>(data);
	int p = std::get<0>(data) + 1;

	if (send > 5) {
	reqs.push_back(
	c.asyncSend(send, p, tag, CommunicationMode::_synchronous));
	}

	if (p <= send) {
	++nb_recvs;
	}
	}

	- c.receiveAnyNumber<int>(reqs,
	- [&](auto && proc, auto && msg) {
	- EXPECT_EQ(msg[0], sends[proc - 1] + 100 * proc);
	- EXPECT_LE(proc, sends[proc - 1]);
	- --nb_recvs;
	- },
	- tag);
	+ c.receiveAnyNumber<int>(
	+ reqs,
	+ [&](auto && proc, auto && msg) {
	+ EXPECT_EQ(msg[0], sends[proc - 1] + 100 * proc);
	+ EXPECT_LE(proc, sends[proc - 1]);
	+ --nb_recvs;
	+ },
	+ tag);
	EXPECT_EQ(nb_recvs, 0);
	} else {
	std::vector<int> recv(size - 1);
	c.broadcast(recv);

	AKANTU_DEBUG_INFO("Messages " << [&]() {
	std::string msgs;
	for (auto s : enumerate(recv)) {
	if (std::get<0>(s) != 0)
	msgs += ", ";
	msgs += std::to_string(std::get<0>(s) + 1) + ": " +
	std::to_string(std::get<1>(s));
	}
	return msgs;
	}());
	auto send = recv[rank - 1] + 100 * rank;
	if (rank <= recv[rank - 1]) {
	reqs.push_back(
	c.asyncSend(send, 0, tag, CommunicationMode::_synchronous));
	}

	bool has_recv = false;
	- c.receiveAnyNumber<int>(reqs,
	- [&](auto && proc, auto && msg) {
	- EXPECT_EQ(msg[0], recv[rank - 1]);
	- EXPECT_EQ(proc, 0);
	- has_recv = true;
	- },
	- tag);
	+ c.receiveAnyNumber<int>(
	+ reqs,
	+ [&](auto && proc, auto && msg) {
	+ EXPECT_EQ(msg[0], recv[rank - 1]);
	+ EXPECT_EQ(proc, 0);
	+ has_recv = true;
	+ },
	+ tag);

	bool should_recv = (recv[rank - 1] > 5);
	EXPECT_EQ(has_recv, should_recv);
	}
	reqs.clear();
	}
	}
	diff --git a/test/test_synchronizer/test_data_accessor.hh b/test/test_synchronizer/test_data_accessor.hh
	index 7a0b0fc00..839124539 100644
	--- a/test/test_synchronizer/test_data_accessor.hh
	+++ b/test/test_synchronizer/test_data_accessor.hh
	@@ -1,125 +1,125 @@
	/**
	* @file test_data_accessor.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Jan 26 2018
	*
	* @brief Data Accessor class for testing
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "data_accessor.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;
	/* -------------------------------------------------------------------------- */

	class TestAccessor : public DataAccessor<Element> {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	inline TestAccessor(const Mesh & mesh,
	const ElementTypeMapArray<Real> & barycenters);

	AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Barycenter, barycenters, Real);

	/* ------------------------------------------------------------------------ */
	/* Ghost Synchronizer inherited members */
	/* ------------------------------------------------------------------------ */
	protected:
	inline UInt getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const;
	inline void packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const;
	inline void unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	const ElementTypeMapArray<Real> & barycenters;
	const Mesh & mesh;
	};

	/* -------------------------------------------------------------------------- */
	/* TestSynchronizer implementation */
	/* -------------------------------------------------------------------------- */
	inline TestAccessor::TestAccessor(const Mesh & mesh,
	const ElementTypeMapArray<Real> & barycenters)
	: barycenters(barycenters), mesh(mesh) {}

	inline UInt TestAccessor::getNbData(const Array<Element> & elements,
	const SynchronizationTag &) const {
	if (elements.size())
	// return Mesh::getSpatialDimension(elements(0).type) * sizeof(Real) *
	// elements.size();
	return mesh.getSpatialDimension() * sizeof(Real) * elements.size();
	else
	return 0;
	}

	inline void TestAccessor::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag &) const {
	UInt spatial_dimension = mesh.getSpatialDimension();
	Array<Element>::const_iterator<Element> bit = elements.begin();
	Array<Element>::const_iterator<Element> bend = elements.end();
	for (; bit != bend; ++bit) {
	const Element & element = *bit;

	Vector<Real> bary(
	this->barycenters(element.type, element.ghost_type).storage() +
	element.element * spatial_dimension,
	spatial_dimension);
	buffer << bary;
	}
	}

	inline void TestAccessor::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag &) {
	UInt spatial_dimension = mesh.getSpatialDimension();

	for (const auto & element : elements) {
	Vector<Real> barycenter_loc(
	this->barycenters(element.type, element.ghost_type).storage() +
	element.element * spatial_dimension,
	spatial_dimension);

	Vector<Real> bary(spatial_dimension);
	buffer >> bary;

	auto dist = (barycenter_loc - bary).template norm<L_inf>();
	EXPECT_NEAR(0, dist, 1e-15);
	}
	}
	diff --git a/test/test_synchronizer/test_data_distribution.cc b/test/test_synchronizer/test_data_distribution.cc
	index f1082a2ec..02b94ff20 100644
	--- a/test/test_synchronizer/test_data_distribution.cc
	+++ b/test/test_synchronizer/test_data_distribution.cc
	@@ -1,89 +1,89 @@
	/**
	* @file test_data_distribution.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Dec 28 2018
	*
	* @brief Test the mesh distribution on creation of a distributed synchonizer
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_synchronizers_fixture.hh"
	/* -------------------------------------------------------------------------- */

	TEST_F(TestSynchronizerFixture, DataDistribution) {
	auto & barycenters = this->mesh->getElementalData<Real>("barycenters");
	auto spatial_dimension = this->mesh->getSpatialDimension();
	barycenters.initialize(*this->mesh, _spatial_dimension = _all_dimensions,
	_nb_component = spatial_dimension);

	this->initBarycenters(barycenters, *this->mesh);

	auto & gids = this->mesh->getNodalData<UInt>("gid");
	gids.resize(this->mesh->getNbNodes());

	for (auto && data : enumerate(gids)) {
	std::get<1>(data) = std::get<0>(data);
	}

	this->distribute();

	for (auto && ghost_type : ghost_types) {
	for (const auto & type :
	this->mesh->elementTypes(_all_dimensions, ghost_type)) {
	auto & barycenters =
	this->mesh->getData<Real>("barycenters", type, ghost_type);

	for (auto && data :
	enumerate(make_view(barycenters, spatial_dimension))) {
	Element element{type, UInt(std::get<0>(data)), ghost_type};
	Vector<Real> barycenter(spatial_dimension);
	this->mesh->getBarycenter(element, barycenter);

	auto dist = (std::get<1>(data) - barycenter).template norm<L_inf>();
	EXPECT_NEAR(dist, 0, 1e-7);
	}
	}
	}

	if (psize > 1) {
	for (auto && data : zip(gids, this->mesh->getGlobalNodesIds())) {
	EXPECT_EQ(std::get<0>(data), std::get<1>(data));
	}
	}
	}

	TEST_F(TestSynchronizerFixture, DataDistributionTags) {
	this->distribute();

	for (const auto & type : this->mesh->elementTypes(_all_dimensions)) {
	auto & tags = this->mesh->getData<UInt>("tag_0", type);
	Array<UInt>::const_vector_iterator tags_it = tags.begin(1);
	Array<UInt>::const_vector_iterator tags_end = tags.end(1);

	// The number of tags should match the number of elements on rank"
	EXPECT_EQ(this->mesh->getNbElement(type), tags.size());
	}
	}
	diff --git a/test/test_synchronizer/test_dof_data_accessor.hh b/test/test_synchronizer/test_dof_data_accessor.hh
	index a8219d7fb..ba564b179 100644
	--- a/test/test_synchronizer/test_dof_data_accessor.hh
	+++ b/test/test_synchronizer/test_dof_data_accessor.hh
	@@ -1,119 +1,119 @@
	/**
	* @file test_dof_data_accessor.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Dec 09 2014
	* @date last modification: Tue Feb 20 2018
	*
	* @brief data accessor class for testing the
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */

	#include "aka_common.hh"
	#include "data_accessor.hh"

	/* -------------------------------------------------------------------------- */

	namespace akantu {

	class TestDOFAccessor : public DataAccessor {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	inline TestDOFAccessor(const Array<Int> & global_dof_equation_numbers);

	/* ------------------------------------------------------------------------ */
	/* Ghost Synchronizer inherited members */
	/* ------------------------------------------------------------------------ */
	protected:
	inline UInt getNbDataForDOFs(const Array<UInt> & dofs,
	SynchronizationTag tag) const;
	inline void packDOFData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs,
	SynchronizationTag tag) const;
	inline void unpackDOFData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs, SynchronizationTag tag);

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	protected:
	const Array<Int> & global_dof_equation_numbers;
	};

	/* -------------------------------------------------------------------------- */
	/* TestDOFSynchronizer implementation */
	/* -------------------------------------------------------------------------- */
	inline TestDOFAccessor::TestDOFAccessor(
	const Array<Int> & global_dof_equation_numbers)
	: global_dof_equation_numbers(global_dof_equation_numbers) {}

	inline UInt TestDOFAccessor::getNbDataForDOFs(const Array<UInt> & dofs,
	__attribute__((unused))
	SynchronizationTag tag) const {
	if (dofs.size())
	// return Mesh::getSpatialDimension(elements(0).type) * sizeof(Real) *
	// elements.size();
	return sizeof(Int) * dofs.size();
	else
	return 0;
	}

	inline void TestDOFAccessor::packDOFData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs,
	__attribute__((unused))
	SynchronizationTag tag) const {
	Array<UInt>::const_scalar_iterator bit = dofs.begin();
	Array<UInt>::const_scalar_iterator bend = dofs.end();
	for (; bit != bend; ++bit) {
	buffer << this->global_dof_equation_numbers[*bit];
	}
	}

	inline void TestDOFAccessor::unpackDOFData(CommunicationBuffer & buffer,
	const Array<UInt> & dofs,
	__attribute__((unused))
	SynchronizationTag tag) {
	Array<UInt>::const_scalar_iterator bit = dofs.begin();
	Array<UInt>::const_scalar_iterator bend = dofs.end();
	for (; bit != bend; ++bit) {
	Int global_dof_eq_nb_local = global_dof_equation_numbers[*bit];
	Int global_dof_eq_nb = 0;
	buffer >> global_dof_eq_nb;
	std::cout << *bit << global_dof_eq_nb_local << std::endl;
	Real tolerance = Math::getTolerance();
	if (!(std::abs(global_dof_eq_nb - global_dof_eq_nb_local) <= tolerance))
	AKANTU_ERROR(
	"Unpacking an unknown value for the dof: "
	<< *bit << "(global_dof_equation_number = " << global_dof_eq_nb_local
	<< " and buffer = " << global_dof_eq_nb << ") - tag: " << tag);
	}
	}

	} // namespace akantu
	diff --git a/test/test_synchronizer/test_dof_synchronizer.cc b/test/test_synchronizer/test_dof_synchronizer.cc
	index bfd711c23..773683e93 100644
	--- a/test/test_synchronizer/test_dof_synchronizer.cc
	+++ b/test/test_synchronizer/test_dof_synchronizer.cc
	@@ -1,148 +1,148 @@
	/**
	* @file test_dof_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Wed Jan 15 2020
	*
	* @brief Test the functionality of the DOFSynchronizer class
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "communicator.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "mesh_io.hh"
	#include "mesh_partition_scotch.hh"

	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "io_helper.hh"
	#endif // AKANTU_USE_IOHELPER

	/* -------------------------------------------------------------------------- */
	using namespace akantu;

	int main(int argc, char * argv[]) {
	const UInt spatial_dimension = 2;

	initialize(argc, argv);

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	Mesh mesh(spatial_dimension);

	if (prank == 0)
	mesh.read("bar.msh");
	mesh.distribute();

	DOFManagerDefault dof_manager(mesh, "test_dof_manager");

	UInt nb_nodes = mesh.getNbNodes();

	/* ------------------------------------------------------------------------ */
	/* test the synchronization */
	/* ------------------------------------------------------------------------ */
	Array<Real> test_synchronize(nb_nodes, spatial_dimension, "Test vector");
	dof_manager.registerDOFs("test_synchronize", test_synchronize, _dst_nodal);

	auto & equation_number =
	dof_manager.getLocalEquationsNumbers("test_synchronize");

	DOFSynchronizer & dof_synchronizer = dof_manager.getSynchronizer();

	std::cout << "Synchronizing a dof vector" << std::endl;

	Array<Int> local_data_array(dof_manager.getLocalSystemSize(), 2);
	auto it_data = local_data_array.begin(2);

	for (UInt local_dof = 0; local_dof < dof_manager.getLocalSystemSize();
	++local_dof) {
	UInt equ_number = equation_number(local_dof);
	Vector<Int> val;
	if (dof_manager.isLocalOrMasterDOF(equ_number)) {
	UInt global_dof = dof_manager.localToGlobalEquationNumber(local_dof);
	val = {0, 1};
	val += global_dof * 2;
	} else {
	val = {-1, -1};
	}

	Vector<Int> data = it_data[local_dof];
	data = val;
	}

	dof_synchronizer.synchronizeArray(local_data_array);

	auto test_data = [&]() -> void {
	auto it_data = local_data_array.begin(2);
	for (UInt local_dof = 0; local_dof < dof_manager.getLocalSystemSize();
	++local_dof) {
	UInt equ_number = equation_number(local_dof);

	Vector<Int> exp_val;

	UInt global_dof = dof_manager.localToGlobalEquationNumber(local_dof);

	if (dof_manager.isLocalOrMasterDOF(equ_number) \|\|
	dof_manager.isSlaveDOF(equ_number)) {
	exp_val = {0, 1};
	exp_val += global_dof * 2;
	} else {
	exp_val = {-1, -1};
	}

	Vector<Int> val = it_data[local_dof];
	if (exp_val != val) {
	std::cerr << "Failed !" << prank << " DOF: " << global_dof << " - l"
	<< local_dof << " value:" << val << " expected: " << exp_val
	<< std::endl;
	exit(1);
	}
	}
	};

	test_data();

	if (prank == 0) {
	Array<Int> test_gathered(dof_manager.getSystemSize(), 2);
	dof_synchronizer.gather(local_data_array, test_gathered);

	local_data_array.set(-1);
	dof_synchronizer.scatter(local_data_array, test_gathered);
	} else {
	dof_synchronizer.gather(local_data_array);

	local_data_array.set(-1);
	dof_synchronizer.scatter(local_data_array);
	}

	test_data();

	finalize();

	return 0;
	}
	diff --git a/test/test_synchronizer/test_dof_synchronizer_communication.cc b/test/test_synchronizer/test_dof_synchronizer_communication.cc
	index 5cfa8bb89..7e6a3e0a5 100644
	--- a/test/test_synchronizer/test_dof_synchronizer_communication.cc
	+++ b/test/test_synchronizer/test_dof_synchronizer_communication.cc
	@@ -1,110 +1,110 @@
	/**
	* @file test_dof_synchronizer_communication.cc
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Dec 09 2014
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test to synchronize global equation numbers
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "dof_synchronizer.hh"
	#include "element_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_partition_scotch.hh"
	#include "synchronizer_registry.hh"
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_paraview.hh"
	#endif // AKANTU_USE_IOHELPER

	#include "test_dof_data_accessor.hh"

	using namespace akantu;

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	UInt spatial_dimension = 3;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();
	bool wait = true;
	if (argc > 1) {
	if (prank == 0)
	while (wait)
	;
	}

	ElementSynchronizer * communicator = NULL;
	if (prank == 0) {
	mesh.read("cube.msh");

	MeshPartition * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	communicator =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	/* --------------------------------------------------------------------------
	*/
	/* test the communications of the dof synchronizer */
	/* --------------------------------------------------------------------------
	*/

	std::cout << "Initializing the synchronizer" << std::endl;
	DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
	dof_synchronizer.initGlobalDOFEquationNumbers();

	AKANTU_DEBUG_INFO("Creating TestDOFAccessor");
	TestDOFAccessor test_dof_accessor(
	dof_synchronizer.getGlobalDOFEquationNumbers());
	SynchronizerRegistry synch_registry(test_dof_accessor);
	synch_registry.registerSynchronizer(dof_synchronizer,
	SynchronizationTag::_test);

	AKANTU_DEBUG_INFO("Synchronizing tag");
	synch_registry.synchronize(SynchronizationTag::_test);

	delete communicator;
	finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_synchronizer/test_facet_synchronizer.cc b/test/test_synchronizer/test_facet_synchronizer.cc
	index fffad2d1c..3c2256555 100644
	--- a/test/test_synchronizer/test_facet_synchronizer.cc
	+++ b/test/test_synchronizer/test_facet_synchronizer.cc
	@@ -1,98 +1,97 @@
	/**
	* @file test_facet_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	* @author Marco Vocialta <marco.vocialta@epfl.ch>
	*
	* @date creation: Fri Oct 13 2017
	* @date last modification: Sun Dec 30 2018
	*
	* @brief Facet synchronizer test
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_data_accessor.hh"
	#include "test_synchronizers_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <chrono>
	#include <random>
	#include <thread>
	/* -------------------------------------------------------------------------- */

	class TestFacetSynchronizerFixture : public TestSynchronizerFixture {
	public:
	void SetUp() override {
	TestSynchronizerFixture::SetUp();
	this->distribute();

	this->mesh->initMeshFacets();

	/// compute barycenter for each element
	- barycenters =
	- std::make_unique<ElementTypeMapArray<Real>>("barycenters");
	+ barycenters = std::make_unique<ElementTypeMapArray<Real>>("barycenters");
	this->initBarycenters(*barycenters, this->mesh->getMeshFacets());

	test_accessor =
	std::make_unique<TestAccessor>(this->mesh, this->barycenters);
	}

	void TearDown() override {
	barycenters.reset(nullptr);
	test_accessor.reset(nullptr);
	}

	protected:
	std::unique_ptr<ElementTypeMapArray<Real>> barycenters;
	std::unique_ptr<TestAccessor> test_accessor;
	};

	/* -------------------------------------------------------------------------- */
	TEST_F(TestFacetSynchronizerFixture, SynchroneOnce) {
	auto & synchronizer = this->mesh->getMeshFacets().getElementSynchronizer();
	synchronizer.synchronizeOnce(*this->test_accessor, SynchronizationTag::_test);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestFacetSynchronizerFixture, Synchrone) {
	auto & synchronizer = this->mesh->getMeshFacets().getElementSynchronizer();
	synchronizer.synchronize(*this->test_accessor, SynchronizationTag::_test);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestFacetSynchronizerFixture, Asynchrone) {
	auto & synchronizer = this->mesh->getMeshFacets().getElementSynchronizer();
	synchronizer.asynchronousSynchronize(*this->test_accessor,
	SynchronizationTag::_test);

	std::random_device r;
	std::default_random_engine engine(r());
	std::uniform_int_distribution<int> uniform_dist(10, 100);
	std::chrono::microseconds delay(uniform_dist(engine));

	std::this_thread::sleep_for(delay);

	synchronizer.waitEndSynchronize(*this->test_accessor,
	SynchronizationTag::_test);
	}
	diff --git a/test/test_synchronizer/test_grid_synchronizer.cc b/test/test_synchronizer/test_grid_synchronizer.cc
	index 4b0ae9789..465080ba0 100644
	--- a/test/test_synchronizer/test_grid_synchronizer.cc
	+++ b/test/test_synchronizer/test_grid_synchronizer.cc
	@@ -1,311 +1,311 @@
	/**
	* @file test_grid_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test the GridSynchronizer object
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	#include "aka_grid_dynamic.hh"
	#include "grid_synchronizer.hh"
	#include "mesh.hh"
	#include "mesh_partition.hh"
	#include "synchronizer_registry.hh"
	#include "test_data_accessor.hh"
	#ifdef AKANTU_USE_IOHELPER
	#include "io_helper.hh"
	#endif // AKANTU_USE_IOHELPER

	using namespace akantu;

	const UInt spatial_dimension = 2;

	typedef std::map<std::pair<Element, Element>, Real> pair_list;

	#include "test_grid_tools.hh"

	static void
	updatePairList(const ElementTypeMapArray<Real> & barycenter,
	const SpatialGrid<Element> & grid, Real radius,
	pair_list & neighbors,
	neighbors_map_t<spatial_dimension>::type & neighbors_map) {
	AKANTU_DEBUG_IN();

	GhostType ghost_type = _not_ghost;

	Element e;
	e.ghost_type = ghost_type;

	// generate the pair of neighbor depending of the cell_list
	ElementTypeMapArray<Real>::type_iterator it =
	barycenter.firstType(_all_dimensions, ghost_type);
	ElementTypeMapArray<Real>::type_iterator last_type =
	barycenter.lastType(0, ghost_type);
	for (; it != last_type; ++it) {
	// loop over quad points

	e.type = *it;
	e.element = 0;

	const Array<Real> & barycenter_vect = barycenter(*it, ghost_type);
	UInt sp = barycenter_vect.getNbComponent();

	Array<Real>::const_iterator<Vector<Real>> bary = barycenter_vect.begin(sp);
	Array<Real>::const_iterator<Vector<Real>> bary_end =
	barycenter_vect.end(sp);

	for (; bary != bary_end; ++bary, e.element++) {
	#if !defined(AKANTU_NDEBUG)
	Point<spatial_dimension> pt1(*bary);
	#endif

	SpatialGrid<Element>::CellID cell_id = grid.getCellID(*bary);
	SpatialGrid<Element>::neighbor_cells_iterator first_neigh_cell =
	grid.beginNeighborCells(cell_id);
	SpatialGrid<Element>::neighbor_cells_iterator last_neigh_cell =
	grid.endNeighborCells(cell_id);

	// loop over neighbors cells of the one containing the current element
	for (; first_neigh_cell != last_neigh_cell; ++first_neigh_cell) {
	SpatialGrid<Element>::Cell::const_iterator first_neigh_el =
	grid.beginCell(*first_neigh_cell);
	SpatialGrid<Element>::Cell::const_iterator last_neigh_el =
	grid.endCell(*first_neigh_cell);

	// loop over the quadrature point in the current cell of the cell list
	for (; first_neigh_el != last_neigh_el; ++first_neigh_el) {
	const Element & elem = *first_neigh_el;

	Array<Real>::const_iterator<Vector<Real>> neigh_it =
	barycenter(elem.type, elem.ghost_type).begin(sp);

	const Vector<Real> & neigh_bary = neigh_it[elem.element];

	Real distance = bary->distance(neigh_bary);
	if (distance <= radius) {
	#if !defined(AKANTU_NDEBUG)
	Point<spatial_dimension> pt2(neigh_bary);
	neighbors_map[pt1].push_back(pt2);
	#endif
	std::pair<Element, Element> pair = std::make_pair(e, elem);
	pair_list::iterator p = neighbors.find(pair);
	if (p != neighbors.end()) {
	AKANTU_ERROR("Pair already registered ["
	<< e << " " << elem << "] -> " << p->second << " "
	<< distance);
	} else {
	neighbors[pair] = distance;
	}
	}
	}
	}
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/* Main */
	/* -------------------------------------------------------------------------- */
	int main(int argc, char * argv[]) {
	akantu::initialize(argc, argv);

	Real radius = 0.001;

	Mesh mesh(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();
	ElementSynchronizer * dist = NULL;

	if (prank == 0) {
	mesh.read("bar.msh");
	MeshPartition * partition =
	new MeshPartitionScotch(mesh, spatial_dimension);
	partition->partitionate(psize);
	dist =
	ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
	delete partition;
	} else {
	dist = ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
	}

	mesh.computeBoundingBox();

	const Vector<Real> & lower_bounds = mesh.getLowerBounds();
	const Vector<Real> & upper_bounds = mesh.getUpperBounds();

	Vector<Real> center = 0.5 * (upper_bounds + lower_bounds);

	Vector<Real> spacing(spatial_dimension);
	for (UInt i = 0; i < spatial_dimension; ++i) {
	spacing[i] = radius * 1.2;
	}

	SpatialGrid<Element> grid(spatial_dimension, spacing, center);

	GhostType ghost_type = _not_ghost;

	Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
	Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, ghost_type);

	ElementTypeMapArray<Real> barycenters("", "");
	mesh.initElementTypeMapArray(barycenters, spatial_dimension,
	spatial_dimension);

	Element e;
	e.ghost_type = ghost_type;

	for (; it != last_type; ++it) {
	UInt nb_element = mesh.getNbElement(*it, ghost_type);
	e.type = *it;
	Array<Real> & barycenter = barycenters(*it, ghost_type);
	barycenter.resize(nb_element);

	Array<Real>::iterator<Vector<Real>> bary_it =
	barycenter.begin(spatial_dimension);
	for (UInt elem = 0; elem < nb_element; ++elem) {
	mesh.getBarycenter(elem, *it, bary_it->storage(), ghost_type);
	e.element = elem;
	grid.insert(e, *bary_it);
	++bary_it;
	}
	}

	std::stringstream sstr;
	sstr << "mesh_" << prank << ".msh";
	mesh.write(sstr.str());

	Mesh grid_mesh(spatial_dimension, "grid_mesh", 0);
	std::stringstream sstr_grid;
	sstr_grid << "grid_mesh_" << prank << ".msh";
	grid.saveAsMesh(grid_mesh);
	grid_mesh.write(sstr_grid.str());

	std::cout << "Pouet 1" << std::endl;

	AKANTU_DEBUG_INFO("Creating TestAccessor");
	TestAccessor test_accessor(mesh, barycenters);
	SynchronizerRegistry synch_registry(test_accessor);

	GridSynchronizer * grid_communicator =
	GridSynchronizer::createGridSynchronizer(mesh, grid);

	std::cout << "Pouet 2" << std::endl;

	ghost_type = _ghost;

	it = mesh.firstType(spatial_dimension, ghost_type);
	last_type = mesh.lastType(spatial_dimension, ghost_type);
	e.ghost_type = ghost_type;
	for (; it != last_type; ++it) {
	UInt nb_element = mesh.getNbElement(*it, ghost_type);
	e.type = *it;
	Array<Real> & barycenter = barycenters(*it, ghost_type);
	barycenter.resize(nb_element);

	Array<Real>::iterator<Vector<Real>> bary_it =
	barycenter.begin(spatial_dimension);
	for (UInt elem = 0; elem < nb_element; ++elem) {
	mesh.getBarycenter(elem, *it, bary_it->storage(), ghost_type);
	e.element = elem;
	grid.insert(e, *bary_it);
	++bary_it;
	}
	}

	Mesh grid_mesh_ghost(spatial_dimension, "grid_mesh_ghost", 0);
	std::stringstream sstr_gridg;
	sstr_gridg << "grid_mesh_ghost_" << prank << ".msh";
	grid.saveAsMesh(grid_mesh_ghost);
	grid_mesh_ghost.write(sstr_gridg.str());

	std::cout << "Pouet 3" << std::endl;

	neighbors_map_t<spatial_dimension>::type neighbors_map;
	pair_list neighbors;

	updatePairList(barycenters, grid, radius, neighbors, neighbors_map);
	pair_list::iterator nit = neighbors.begin();
	pair_list::iterator nend = neighbors.end();

	std::stringstream sstrp;
	sstrp << "pairs_" << prank;
	std::ofstream fout(sstrp.str().c_str());
	for (; nit != nend; ++nit) {
	fout << "[" << nit->first.first << "," << nit->first.second << "] -> "
	<< nit->second << std::endl;
	}

	std::string file = "neighbors_ref";
	std::stringstream sstrf;
	sstrf << file << "_" << psize << "_" << prank;

	file = sstrf.str();

	std::ofstream nout;
	nout.open(file.c_str());
	neighbors_map_t<spatial_dimension>::type::iterator it_n =
	neighbors_map.begin();
	neighbors_map_t<spatial_dimension>::type::iterator end_n =
	neighbors_map.end();
	for (; it_n != end_n; ++it_n) {
	std::sort(it_n->second.begin(), it_n->second.end());

	std::vector<Point<spatial_dimension>>::iterator it_v = it_n->second.begin();
	std::vector<Point<spatial_dimension>>::iterator end_v = it_n->second.end();

	nout << "####" << std::endl;
	nout << it_n->second.size() << std::endl;
	nout << it_n->first << std::endl;
	nout << "#" << std::endl;
	for (; it_v != end_v; ++it_v) {
	nout << *it_v << std::endl;
	}
	}

	fout.close();

	synch_registry.registerSynchronizer(*dist, SynchronizationTag::_smm_mass);

	synch_registry.registerSynchronizer(*grid_communicator,
	SynchronizationTag::_test);

	AKANTU_DEBUG_INFO("Synchronizing tag on Dist");
	synch_registry.synchronize(SynchronizationTag::_smm_mass);

	AKANTU_DEBUG_INFO("Synchronizing tag on Grid");
	synch_registry.synchronize(SynchronizationTag::_test);

	delete grid_communicator;
	delete dist;
	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_synchronizer/test_grid_synchronizer_check_neighbors.cc b/test/test_synchronizer/test_grid_synchronizer_check_neighbors.cc
	index 5cdc14aa4..8449c5936 100644
	--- a/test/test_synchronizer/test_grid_synchronizer_check_neighbors.cc
	+++ b/test/test_synchronizer/test_grid_synchronizer_check_neighbors.cc
	@@ -1,132 +1,132 @@
	/**
	* @file test_grid_synchronizer_check_neighbors.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Tue Feb 20 2018
	*
	* @brief Test the generation of neighbors list based on a akaentu::Grid
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <fstream>
	#include <iostream>
	#include <string>

	#include "aka_common.hh"
	#include "communicator.hh"

	using namespace akantu;

	const UInt spatial_dimension = 3;

	#include "test_grid_tools.hh"

	void readNeighbors(
	std::ifstream & nin,
	neighbors_map_t<spatial_dimension>::type & neighbors_map_read) {
	std::string line;
	while (std::getline(nin, line)) {
	std::getline(nin, line);
	std::istringstream iss(line);
	UInt nb_neig;
	iss >> nb_neig;
	std::getline(nin, line);
	Point<spatial_dimension> pt;
	pt.read(line);
	std::getline(nin, line);
	for (UInt i = 0; i < nb_neig; ++i) {
	std::getline(nin, line);
	Point<spatial_dimension> ne;
	ne.read(line);
	neighbors_map_read[pt].push_back(ne);
	}
	}
	}

	int main(int argc, char * argv[]) {
	initialize(argc, argv);

	const auto & comm = Communicator::getStaticCommunicator();
	Int psize = comm.getNbProc();
	Int prank = comm.whoAmI();

	std::string file_ref = "neighbors_ref_1_0";
	std::string file = "neighbors_ref";
	std::stringstream sstr;
	sstr << file << "_" << psize << "_" << prank;
	file = sstr.str();

	std::ifstream nin;

	neighbors_map_t<spatial_dimension>::type neighbors_map_read;
	nin.open(file_ref.c_str());
	readNeighbors(nin, neighbors_map_read);
	nin.close();

	neighbors_map_t<spatial_dimension>::type neighbors_map;
	nin.open(file.c_str());
	readNeighbors(nin, neighbors_map);
	nin.close();

	neighbors_map_t<spatial_dimension>::type::iterator it_n =
	neighbors_map.begin();
	neighbors_map_t<spatial_dimension>::type::iterator end_n =
	neighbors_map.end();
	for (; it_n != end_n; ++it_n) {
	std::sort(it_n->second.begin(), it_n->second.end());

	std::vector<Point<spatial_dimension>>::iterator it_v = it_n->second.begin();
	std::vector<Point<spatial_dimension>>::iterator end_v = it_n->second.end();

	neighbors_map_t<spatial_dimension>::type::iterator it_nr =
	neighbors_map_read.find(it_n->first);
	if (it_nr == neighbors_map_read.end())
	AKANTU_ERROR(
	"Argh what is this point that is not present in the ref file "
	<< it_n->first);

	std::vector<Point<spatial_dimension>>::iterator it_vr =
	it_nr->second.begin();
	std::vector<Point<spatial_dimension>>::iterator end_vr =
	it_nr->second.end();

	for (; it_v != end_v && it_vr != end_vr; ++it_v, ++it_vr) {
	if (it_vr != it_v)
	AKANTU_ERROR("Neighbors does not match " << it_v << " != " << it_vr
	<< " neighbor of "
	<< it_n->first);
	}

	if (it_v == end_v && it_vr != end_vr) {
	AKANTU_ERROR("Some neighbors of " << it_n->first << " are missing!");
	}

	if (it_v != end_v && it_vr == end_vr)
	AKANTU_ERROR("Some neighbors of " << it_n->first << " are in excess!");
	}

	akantu::finalize();

	return EXIT_SUCCESS;
	}
	diff --git a/test/test_synchronizer/test_grid_tools.hh b/test/test_synchronizer/test_grid_tools.hh
	index 4b8ecacb7..2c2fdf28d 100644
	--- a/test/test_synchronizer/test_grid_tools.hh
	+++ b/test/test_synchronizer/test_grid_tools.hh
	@@ -1,116 +1,116 @@
	/**
	* @file test_grid_tools.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Sun Oct 19 2014
	* @date last modification: Fri Jan 15 2016
	*
	* @brief Tools to help for the akantu::Grid class tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	#include <map>

	#include "aka_common.hh"
	#include "aka_types.hh"

	#define TOLERANCE 1e-7

	template <UInt dim> class Point {
	public:
	Point() : id(0), tol(TOLERANCE) {
	for (UInt i = 0; i < dim; ++i)
	pos[i] = 0.;
	}

	Point(const Point & pt) : id(pt.id), tol(pt.tol) {
	for (UInt i = 0; i < dim; ++i)
	pos[i] = pt.pos[i];
	}

	Point(const Vector<Real> & pt, UInt id = 0) : id(id), tol(TOLERANCE) {
	for (UInt i = 0; i < dim; ++i)
	pos[i] = pt(i);
	}

	bool operator==(const Point & pt) const {
	for (UInt i = 0; i < dim; ++i) {
	// std::cout << i << " " << pos[i] << " " << pt.pos[i] << " " <<
	// std::abs(pos[i] - pt.pos[i]);
	if (std::abs(pos[i] - pt.pos[i]) > tol) {
	// std::cout << " " << false << std::endl;
	return false;
	} // else
	// std::cout << " " << true << std::endl;
	}
	return true;
	}

	bool operator<(const Point & pt) const {
	UInt i = 0, j = 0;
	for (; (i < dim) && (j < dim); i++, j++) {
	if (pos[i] < pt.pos[j])
	return true;
	if (pt.pos[j] < pos[i])
	return false;
	}
	return (i == dim) && (j != dim);
	}

	bool operator!=(const Point & pt) const { return !(operator==(pt)); }

	Real & operator()(UInt d) { return pos[d]; }
	const Real & operator()(UInt d) const { return pos[d]; }

	void read(const std::string & str) {
	std::stringstream sstr(str);
	for (UInt i = 0; i < dim; ++i)
	sstr >> pos[i];
	}

	void write(std::ostream & ostr) const {
	for (UInt i = 0; i < dim; ++i) {
	if (i != 0)
	ostr << " ";
	// ostr << std::setprecision(std::numeric_limits<Real>::digits) <<
	// pos[i];
	ostr << std::setprecision(9) << pos[i];
	}
	}

	private:
	UInt id;
	Real pos[dim];
	double tol;
	};

	template <UInt dim> struct neighbors_map_t {
	typedef std::map<Point<dim>, std::vector<Point<dim>>> type;
	};

	template <UInt dim>
	inline std::ostream & operator<<(std::ostream & stream,
	const Point<dim> & _this) {
	_this.write(stream);
	return stream;
	}
	diff --git a/test/test_synchronizer/test_node_synchronizer.cc b/test/test_synchronizer/test_node_synchronizer.cc
	index f4a2cca96..4508419d4 100644
	--- a/test/test_synchronizer/test_node_synchronizer.cc
	+++ b/test/test_synchronizer/test_node_synchronizer.cc
	@@ -1,213 +1,213 @@
	/**
	* @file test_node_synchronizer.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Thu May 11 2017
	* @date last modification: Wed Jan 15 2020
	*
	* @brief test the default node synchronizer present in the mesh
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_synchronizers_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "communicator.hh"
	#include "data_accessor.hh"
	#include "mesh.hh"
	#include "node_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <chrono>
	#include <limits>
	#include <random>
	#include <thread>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class DataAccessorTest : public DataAccessor<UInt> {
	public:
	explicit DataAccessorTest(Array<int> & data) : data(data) {}

	UInt getNbData(const Array<UInt> & nodes, const SynchronizationTag &) const {
	return nodes.size() * sizeof(int);
	}

	void packData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag &) const {
	for (auto node : nodes) {
	buffer << data(node);
	}
	}

	void unpackData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag &) {
	for (auto node : nodes) {
	buffer >> data(node);
	}
	}

	protected:
	Array<int> & data;
	};

	class TestNodeSynchronizerFixture : public TestSynchronizerFixture {
	public:
	static constexpr int max_int = std::numeric_limits<int>::max();

	void SetUp() override {
	TestSynchronizerFixture::SetUp();
	this->distribute();

	UInt nb_nodes = this->mesh->getNbNodes();

	node_data = std::make_unique<Array<int>>(nb_nodes);
	for (auto && data : enumerate(*node_data)) {
	auto n = std::get<0>(data);
	auto & d = std::get<1>(data);
	UInt gn = this->mesh->getNodeGlobalId(n);

	if (this->mesh->isMasterNode(n))
	d = gn;
	else if (this->mesh->isLocalNode(n))
	d = -gn;
	else if (this->mesh->isSlaveNode(n))
	d = max_int;
	else
	d = -max_int;
	}

	data_accessor = std::make_unique<DataAccessorTest>(*node_data);
	}

	void TearDown() override {
	data_accessor.reset(nullptr);
	node_data.reset(nullptr);
	}

	void checkData() {
	for (auto && data : enumerate(*this->node_data)) {
	auto n = std::get<0>(data);
	auto & d = std::get<1>(data);
	UInt gn = this->mesh->getNodeGlobalId(n);

	if (this->mesh->isMasterNode(n))
	EXPECT_EQ(d, gn);

	else if (this->mesh->isLocalNode(n))
	EXPECT_EQ(d, -gn);

	else if (this->mesh->isSlaveNode(n))
	EXPECT_EQ(d, gn);

	else

	EXPECT_EQ(d, -max_int);
	}
	}

	protected:
	std::unique_ptr<Array<int>> node_data;
	std::unique_ptr<DataAccessorTest> data_accessor;
	};

	/* -------------------------------------------------------------------------- */
	constexpr int TestNodeSynchronizerFixture::max_int;

	/* -------------------------------------------------------------------------- */
	TEST_F(TestNodeSynchronizerFixture, SynchroneOnce) {
	auto & synchronizer = this->mesh->getNodeSynchronizer();
	synchronizer.synchronizeOnce(*this->data_accessor, SynchronizationTag::_test);
	this->checkData();
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestNodeSynchronizerFixture, Synchrone) {
	auto & node_synchronizer = this->mesh->getNodeSynchronizer();
	node_synchronizer.synchronize(*this->data_accessor,
	SynchronizationTag::_test);
	this->checkData();
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestNodeSynchronizerFixture, Asynchrone) {
	auto & synchronizer = this->mesh->getNodeSynchronizer();
	synchronizer.asynchronousSynchronize(*this->data_accessor,
	SynchronizationTag::_test);

	std::random_device r;
	std::default_random_engine engine(r());
	std::uniform_int_distribution<int> uniform_dist(10, 100);
	std::chrono::microseconds delay(uniform_dist(engine));

	std::this_thread::sleep_for(delay);

	synchronizer.waitEndSynchronize(*this->data_accessor,
	SynchronizationTag::_test);
	this->checkData();
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestNodeSynchronizerFixture, Gather) {
	auto & synchronizer = this->mesh->getNodeSynchronizer();

	const auto & comm = akantu::Communicator::getStaticCommunicator();
	Int prank = comm.whoAmI();

	if (prank == 0) {
	Array<int> all_data(this->mesh->getNbGlobalNodes());
	synchronizer.gather(*(this->node_data), all_data);
	for (auto && data : enumerate(all_data)) {
	EXPECT_EQ(std::get<0>(data), std::abs(std::get<1>(data)));
	}
	} else {
	synchronizer.gather(*(this->node_data));
	}
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestNodeSynchronizerFixture, Scatter) {
	Array<int> local_data(this->mesh->getNbNodes(), 1, this->max_int);
	auto & synchronizer = this->mesh->getNodeSynchronizer();
	-
	+
	if (prank == 0) {
	Array<int> all_data(this->mesh->getNbGlobalNodes());
	for (auto && data : enumerate(all_data)) {
	std::get<1>(data) = std::get<0>(data);
	}
	synchronizer.scatter(local_data, all_data);
	} else {
	synchronizer.scatter(local_data);
	}

	for (auto && data : enumerate(local_data)) {
	auto && n = std::get<0>(data);
	auto && d = std::get<1>(data);
	UInt gn = this->mesh->getNodeGlobalId(n);
	- if(this->mesh->isPureGhostNode(n)) {
	+ if (this->mesh->isPureGhostNode(n)) {
	EXPECT_EQ(d, this->max_int);
	} else {
	EXPECT_EQ(d, gn);
	}
	}
	}
	diff --git a/test/test_synchronizer/test_synchronizer_communication.cc b/test/test_synchronizer/test_synchronizer_communication.cc
	index 2593c2d0d..975b924c8 100644
	--- a/test/test_synchronizer/test_synchronizer_communication.cc
	+++ b/test/test_synchronizer/test_synchronizer_communication.cc
	@@ -1,96 +1,95 @@
	/**
	* @file test_synchronizer_communication.cc
	*
	* @author Dana Christen <dana.christen@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Sep 01 2010
	* @date last modification: Sun Dec 30 2018
	*
	* @brief test to synchronize barycenters
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "test_data_accessor.hh"
	#include "test_synchronizers_fixture.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_synchronizer.hh"
	/* -------------------------------------------------------------------------- */
	#include <chrono>
	#include <random>
	#include <thread>
	/* -------------------------------------------------------------------------- */

	class TestElementSynchronizerFixture : public TestSynchronizerFixture {
	public:
	void SetUp() override {
	TestSynchronizerFixture::SetUp();
	this->distribute();

	/// compute barycenter for each element
	- barycenters =
	- std::make_unique<ElementTypeMapArray<Real>>("barycenters");
	+ barycenters = std::make_unique<ElementTypeMapArray<Real>>("barycenters");
	this->initBarycenters(barycenters, mesh);

	test_accessor =
	std::make_unique<TestAccessor>(this->mesh, this->barycenters);
	}

	void TearDown() override {
	barycenters.reset(nullptr);
	test_accessor.reset(nullptr);
	}

	protected:
	std::unique_ptr<ElementTypeMapArray<Real>> barycenters;
	std::unique_ptr<TestAccessor> test_accessor;
	};

	/* -------------------------------------------------------------------------- */
	TEST_F(TestElementSynchronizerFixture, SynchroneOnce) {
	auto & synchronizer = this->mesh->getElementSynchronizer();
	synchronizer.synchronizeOnce(*this->test_accessor, SynchronizationTag::_test);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestElementSynchronizerFixture, Synchrone) {
	auto & synchronizer = this->mesh->getElementSynchronizer();
	synchronizer.synchronize(*this->test_accessor, SynchronizationTag::_test);
	}

	/* -------------------------------------------------------------------------- */
	TEST_F(TestElementSynchronizerFixture, Asynchrone) {
	auto & synchronizer = this->mesh->getElementSynchronizer();
	synchronizer.asynchronousSynchronize(*this->test_accessor,
	SynchronizationTag::_test);

	std::random_device r;
	std::default_random_engine engine(r());
	std::uniform_int_distribution<int> uniform_dist(10, 100);
	std::chrono::microseconds delay(uniform_dist(engine));

	std::this_thread::sleep_for(delay);

	synchronizer.waitEndSynchronize(*this->test_accessor,
	SynchronizationTag::_test);
	}
	diff --git a/test/test_synchronizer/test_synchronizers_fixture.hh b/test/test_synchronizer/test_synchronizers_fixture.hh
	index b507d2e3b..08daef52f 100644
	--- a/test/test_synchronizer/test_synchronizers_fixture.hh
	+++ b/test/test_synchronizer/test_synchronizers_fixture.hh
	@@ -1,83 +1,83 @@
	/**
	* @file test_synchronizers_fixture.hh
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Fri Jan 26 2018
	* @date last modification: Wed Feb 28 2018
	*
	* @brief Fixture for synchronizer tests
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	- *
	+ *
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	- *
	+ *
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_iterators.hh"
	#include "communicator.hh"
	#include "mesh.hh"
	/* -------------------------------------------------------------------------- */
	#include <gtest/gtest.h>
	/* -------------------------------------------------------------------------- */

	using namespace akantu;

	class TestSynchronizerFixture : public ::testing::Test {
	public:
	virtual void SetUp() {
	const UInt spatial_dimension = 3;

	mesh = std::make_unique<Mesh>(spatial_dimension);

	const auto & comm = Communicator::getStaticCommunicator();
	prank = comm.whoAmI();
	psize = comm.getNbProc();

	if (prank == 0) {
	this->mesh->read("cube.msh");
	}
	}

	virtual void TearDown() { this->mesh.reset(nullptr); }

	void initBarycenters(ElementTypeMapArray<Real> & barycenters, Mesh & mesh) {
	auto spatial_dimension = mesh.getSpatialDimension();
	barycenters.initialize(mesh, _spatial_dimension = _all_dimensions,
	_nb_component = spatial_dimension,
	_with_nb_element = true);

	for (auto && ghost_type : ghost_types) {
	for (const auto & type : mesh.elementTypes(_all_dimensions, ghost_type)) {
	for (auto && data : enumerate(
	make_view(barycenters(type, ghost_type), spatial_dimension))) {
	Element element{type, UInt(std::get<0>(data)), ghost_type};
	mesh.getBarycenter(element, std::get<1>(data));
	}
	}
	}
	}

	void distribute() { this->mesh->distribute(); }

	protected:
	std::unique_ptr<Mesh> mesh;
	Int prank;
	Int psize;
	};
	diff --git a/third-party/iohelper/src/dumper_lammps.hh b/third-party/iohelper/src/dumper_lammps.hh
	index 22d7243ee..21a97f08f 100644
	--- a/third-party/iohelper/src/dumper_lammps.hh
	+++ b/third-party/iohelper/src/dumper_lammps.hh
	@@ -1,143 +1,143 @@
	/**
	* @file dumper_lammps.hh
	*
	* @author Till Junge <till.junge@epfl.ch>
	*
	* @date creation: Thu Nov 25 2010
	* @date last modification: Tue Jun 04 2013
	*
	* @brief header for lammps dumper
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* IOHelper is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* IOHelper is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with IOHelper. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef IOHELPER_DUMPER_LAMMPS_H_
	#define IOHELPER_DUMPER_LAMMPS_H_
	/* -------------------------------------------------------------------------- */
	#include "dumper.hh"
	#include <fstream>
	/* -------------------------------------------------------------------------- */


	namespace iohelper {

	enum LammpsAtomStyle {atomic, bond}; //please extend ad libidum

	template<LammpsAtomStyle style>
	class DumperLammps: public Dumper, public Visitor {
	/* ------------------------------------------------------------------------ */
	/* Constructors/Destructors */
	/* ------------------------------------------------------------------------ */
	public:
	DumperLammps(Real * bounds = nullptr, const std::string & prefix = "./");

	~DumperLammps() override = default;

	/* ------------------------------------------------------------------------ */
	/* Methods */
	/* ------------------------------------------------------------------------ */
	public:
	//! dump to file
	void dump(const std::string & current_name = std::string(),
	UInt count = UInt(-1)) override;
	void dumpHead(Real * bounds = nullptr);
	template<typename T>
	void visitField(T & visited);

	void dumpFinalize();
	//! set mode for file creation : TEXT, BASE64, COMPRESSED
	void setMode(int mode) override { Dumper::setMode(mode); }
	void dumpAdd(int grain_id = 1);
	- void setEmbeddedValue(__attribute__((unused)) const std::string & name,
	- __attribute__((unused)) int value){}
	+ void setEmbeddedValue(const std::string & /name/, int /value/
	+){}

	/* ------------------------------------------------------------------------ */
	/* Accessors */
	/* ------------------------------------------------------------------------ */
	public:

	/* ------------------------------------------------------------------------ */
	/* Class Members */
	/* ------------------------------------------------------------------------ */
	private:
	//position of where the number of atoms is printed;
	std::streampos nb_atom_position;
	//current number of atoms printed to the file
	unsigned long int curr_nb_atom;
	std::fstream lammps_dump_file;
	Real * bounds;

	//! flag to produce zipped files
	bool flag_compressed;
	//! current values
	int grain_id;
	};

	/* -------------------------------------------------------------------------- */
	template<>
	template <typename T>
	void DumperLammps<bond>::visitField(T & visited) {

	typename T::iterator it = visited.begin();
	typename T::iterator end = visited.end();

	UInt dim = visited.getDim();

	for (; it != end ; ++it) {
	this->lammps_dump_file << this->curr_nb_atom + 1 << " "
	<< this->grain_id + 2 << " 1 ";
	for (UInt i = 0 ; i < dim ; ++i) {
	this->lammps_dump_file << (*it)[i] << " ";
	}
	this->lammps_dump_file << std::endl;
	++this->curr_nb_atom;
	}
	}

	/* -------------------------------------------------------------------------- */
	template<>
	template <typename T>
	void DumperLammps<atomic>::visitField(T & visited) {

	typename T::iterator it = visited.begin();
	typename T::iterator end = visited.end();

	UInt dim = visited.getDim();

	for (; it != end ; ++it) {
	this->lammps_dump_file << this->curr_nb_atom + 1 << " 1 ";
	for (UInt i = 0 ; i < dim ; ++i) {
	this->lammps_dump_file << (*it)[i] << " ";
	}
	this->lammps_dump_file << std::endl;
	++this->curr_nb_atom;
	}
	}

	/* -------------------------------------------------------------------------- */
	}

	/* -------------------------------------------------------------------------- */
	#include "field_inline_impl.hh"
	/* -------------------------------------------------------------------------- */



	#endif /* IOHELPER_DUMPER_LAMMPS_H_ */

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