dof_manager_default.cc
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dof_manager_default.cc
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	/**
	* @file dof_manager_default.cc
	*
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 18 2015
	* @date last modification: Thu Feb 08 2018
	*
	* @brief Implementation of the default DOFManager
	*
	* @section LICENSE
	*
	* Copyright (©) 2015-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You 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 "node_synchronizer.hh"
	#include "non_linear_solver_default.hh"
	#include "periodic_node_synchronizer.hh"
	#include "sparse_matrix_aij.hh"
	#include "terms_to_assemble.hh"
	#include "time_step_solver_default.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <memory>
	#include <numeric>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline void DOFManagerDefault::addSymmetricElementalMatrixToSymmetric(
	SparseMatrixAIJ & matrix, const Matrix<Real> & elementary_mat,
	const Vector<UInt> & equation_numbers, UInt max_size) {
	for (UInt i = 0; i < elementary_mat.rows(); ++i) {
	UInt c_irn = equation_numbers(i);
	if (c_irn < max_size) {
	for (UInt j = i; j < elementary_mat.cols(); ++j) {
	UInt c_jcn = equation_numbers(j);
	if (c_jcn < max_size) {
	matrix(c_irn, c_jcn) += elementary_mat(i, j);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void DOFManagerDefault::addUnsymmetricElementalMatrixToSymmetric(
	SparseMatrixAIJ & matrix, const Matrix<Real> & elementary_mat,
	const Vector<UInt> & equation_numbers, UInt max_size) {
	for (UInt i = 0; i < elementary_mat.rows(); ++i) {
	UInt c_irn = equation_numbers(i);
	if (c_irn < max_size) {
	for (UInt j = 0; j < elementary_mat.cols(); ++j) {
	UInt c_jcn = equation_numbers(j);
	if (c_jcn < max_size) {
	if (c_jcn >= c_irn) {
	matrix(c_irn, c_jcn) += elementary_mat(i, j);
	}
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void DOFManagerDefault::addElementalMatrixToUnsymmetric(
	SparseMatrixAIJ & matrix, const Matrix<Real> & elementary_mat,
	const Vector<UInt> & equation_numbers, UInt max_size) {
	for (UInt i = 0; i < elementary_mat.rows(); ++i) {
	UInt c_irn = equation_numbers(i);
	if (c_irn < max_size) {
	for (UInt j = 0; j < elementary_mat.cols(); ++j) {
	UInt c_jcn = equation_numbers(j);
	if (c_jcn < max_size) {
	matrix(c_irn, c_jcn) += elementary_mat(i, j);
	}
	}
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFManagerDefault(const ID & id, const MemoryID & memory_id)
	: DOFManager(id, memory_id), residual(0, 1, std::string(id + ":residual")),
	global_residual(nullptr),
	global_solution(0, 1, std::string(id + ":global_solution")),
	global_blocked_dofs(0, 1, std::string(id + ":global_blocked_dofs")),
	previous_global_blocked_dofs(
	0, 1, std::string(id + ":previous_global_blocked_dofs")),
	dofs_flag(0, 1, std::string(id + ":dofs_type")),
	data_cache(0, 1, std::string(id + ":data_cache_array")),
	global_equation_number(0, 1, "global_equation_number"),
	synchronizer(nullptr) {}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFManagerDefault(Mesh & mesh, const ID & id,
	const MemoryID & memory_id)
	: DOFManager(mesh, id, memory_id),
	residual(0, 1, std::string(id + ":residual")), global_residual(nullptr),
	global_solution(0, 1, std::string(id + ":global_solution")),
	global_blocked_dofs(0, 1, std::string(id + ":global_blocked_dofs")),
	previous_global_blocked_dofs(
	0, 1, std::string(id + ":previous_global_blocked_dofs")),
	dofs_flag(0, 1, std::string(id + ":dofs_type")),
	data_cache(0, 1, std::string(id + ":data_cache_array")),
	global_equation_number(0, 1, "global_equation_number"),
	first_global_dof_id(0), synchronizer(nullptr) {
	if (this->mesh->isDistributed())
	this->synchronizer = std::make_unique<DOFSynchronizer>(
	*this, this->id + ":dof_synchronizer", this->memory_id);
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::~DOFManagerDefault() = default;

	/* -------------------------------------------------------------------------- */
	template <typename T>
	void DOFManagerDefault::makeConsistentForPeriodicity(const ID & dof_id,
	Array<T> & 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>(array);
	}

	/* -------------------------------------------------------------------------- */
	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);
	global_array(equ_num) +=
	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();
	}

	/* -------------------------------------------------------------------------- */
	DOFManagerDefault::DOFDataDefault::DOFDataDefault(const ID & dof_id)
	: DOFData(dof_id), associated_nodes(0, 1, dof_id + "associated_nodes") {}

	/* -------------------------------------------------------------------------- */
	DOFManager::DOFData & DOFManagerDefault::getNewDOFData(const ID & dof_id) {
	this->dofs[dof_id] = std::make_unique<DOFDataDefault>(dof_id);
	return *this->dofs[dof_id];
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::registerDOFsInternal(const ID & dof_id, UInt nb_dofs,
	UInt nb_pure_local_dofs) {
	// auto prank = this->communicator.whoAmI();
	// auto psize = this->communicator.getNbProc();

	// access the relevant data to update
	auto & dof_data = this->getDOFDataTyped<DOFDataDefault>(dof_id);
	const auto & support_type = dof_data.support_type;

	const auto & group = dof_data.group_support;

	switch (support_type) {
	case _dst_nodal:
	if (group != "__mesh__") {
	auto & support_nodes =
	this->mesh->getElementGroup(group).getNodeGroup().getNodes();
	this->updateDOFsData(
	dof_data, nb_dofs, nb_pure_local_dofs, support_nodes.size(),
	[&support_nodes](UInt node) -> UInt { return support_nodes[node]; });
	} else {
	this->updateDOFsData(dof_data, nb_dofs, nb_pure_local_dofs,
	mesh->getNbNodes(),
	[](UInt node) -> UInt { return node; });
	}
	break;
	case _dst_generic:
	this->updateDOFsData(dof_data, nb_dofs, nb_pure_local_dofs);
	break;
	}

	// update the synchronizer if needed
	if (this->synchronizer)
	this->synchronizer->registerDOFs(dof_id);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::registerDOFs(const ID & dof_id,
	Array<Real> & dofs_array,
	const DOFSupportType & support_type) {
	// stores the current numbers of dofs
	UInt nb_dofs_old = this->local_system_size;
	UInt nb_pure_local_dofs_old = this->pure_local_system_size;

	// update or create the dof_data
	DOFManager::registerDOFs(dof_id, dofs_array, support_type);

	UInt nb_dofs = this->local_system_size - nb_dofs_old;
	UInt nb_pure_local_dofs =
	this->pure_local_system_size - nb_pure_local_dofs_old;

	this->registerDOFsInternal(dof_id, nb_dofs, nb_pure_local_dofs);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::registerDOFs(const ID & dof_id,
	Array<Real> & dofs_array,
	const ID & group_support) {
	// stores the current numbers of dofs
	UInt nb_dofs_old = this->local_system_size;
	UInt nb_pure_local_dofs_old = this->pure_local_system_size;

	// update or create the dof_data
	DOFManager::registerDOFs(dof_id, dofs_array, group_support);

	UInt nb_dofs = this->local_system_size - nb_dofs_old;
	UInt nb_pure_local_dofs =
	this->pure_local_system_size - nb_pure_local_dofs_old;

	this->registerDOFsInternal(dof_id, nb_dofs, nb_pure_local_dofs);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerDefault::getNewMatrix(const ID & id,
	const MatrixType & matrix_type) {
	ID matrix_id = this->id + ":mtx:" + id;
	std::unique_ptr<SparseMatrix> sm =
	std::make_unique<SparseMatrixAIJ>(*this, matrix_type, matrix_id);
	return this->registerSparseMatrix(matrix_id, sm);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & DOFManagerDefault::getNewMatrix(const ID & id,
	const ID & matrix_to_copy_id) {

	ID matrix_id = this->id + ":mtx:" + id;
	SparseMatrixAIJ & sm_to_copy = this->getMatrix(matrix_to_copy_id);
	std::unique_ptr<SparseMatrix> sm =
	std::make_unique<SparseMatrixAIJ>(sm_to_copy, matrix_id);
	return this->registerSparseMatrix(matrix_id, sm);
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrixAIJ & DOFManagerDefault::getMatrix(const ID & id) {
	SparseMatrix & matrix = DOFManager::getMatrix(id);

	return dynamic_cast<SparseMatrixAIJ &>(matrix);
	}

	/* -------------------------------------------------------------------------- */
	NonLinearSolver &
	DOFManagerDefault::getNewNonLinearSolver(const ID & id,
	const NonLinearSolverType & type) {
	ID non_linear_solver_id = this->id + ":nls:" + id;
	std::unique_ptr<NonLinearSolver> nls;
	switch (type) {
	#if defined(AKANTU_IMPLICIT)
	case _nls_newton_raphson:
	case _nls_newton_raphson_modified: {
	nls = std::make_unique<NonLinearSolverNewtonRaphson>(
	*this, type, non_linear_solver_id, this->memory_id);
	break;
	}
	case _nls_linear: {
	nls = std::make_unique<NonLinearSolverLinear>(
	*this, type, non_linear_solver_id, this->memory_id);
	break;
	}
	#endif
	case _nls_lumped: {
	nls = std::make_unique<NonLinearSolverLumped>(
	*this, type, non_linear_solver_id, this->memory_id);
	break;
	}
	default:
	AKANTU_EXCEPTION("The asked type of non linear solver is not supported by "
	"this dof manager");
	}

	return this->registerNonLinearSolver(non_linear_solver_id, nls);
	}

	/* -------------------------------------------------------------------------- */
	TimeStepSolver & DOFManagerDefault::getNewTimeStepSolver(
	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<TimeStepSolverDefault>(
	*this, type, non_linear_solver, solver_callback, time_step_solver_id,
	this->memory_id);

	return this->registerTimeStepSolver(time_step_solver_id, tss);
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::clearResidual() {
	this->residual.resize(this->local_system_size);
	this->residual.clear();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::clearMatrix(const ID & mtx) {
	this->getMatrix(mtx).clear();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::clearLumpedMatrix(const ID & mtx) {
	this->getLumpedMatrix(mtx).clear();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::updateGlobalBlockedDofs() {
	auto it = this->dofs.begin();
	auto end = this->dofs.end();

	this->previous_global_blocked_dofs.copy(this->global_blocked_dofs);
	this->global_blocked_dofs.resize(this->local_system_size);
	this->global_blocked_dofs.clear();

	for (; it != end; ++it) {
	if (!this->hasBlockedDOFs(it->first))
	continue;

	DOFData & dof_data = *it->second;
	this->assembleToGlobalArray(it->first, *dof_data.blocked_dofs,
	this->global_blocked_dofs, true);
	}
	}

	/* -------------------------------------------------------------------------- */
	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<UInt> & equation_number = this->getLocalEquationNumbers(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::getSolutionPerDOFs(const ID & dof_id,
	Array<Real> & solution_array) {
	AKANTU_DEBUG_IN();
	this->getArrayPerDOFs(dof_id, this->global_solution, solution_array);
	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::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 DOFManagerDefault::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->residual,
	scale_factor);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::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);

	Array<Real> & lumped = this->getLumpedMatrix(lumped_mtx);
	this->assembleToGlobalArray(dof_id, array_to_assemble, lumped, scale_factor);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleMatMulVectToResidual(const ID & dof_id,
	const ID & A_id,
	const Array<Real> & x,
	Real scale_factor) {
	SparseMatrixAIJ & A = this->getMatrix(A_id);

	// Array<Real> data_cache(this->local_system_size, 1, 0.);
	this->data_cache.resize(this->local_system_size);
	this->data_cache.clear();

	this->assembleToGlobalArray(dof_id, x, data_cache, 1.);

	Array<Real> tmp_residual(this->residual.size(), 1, 0.);

	A.matVecMul(data_cache, tmp_residual, scale_factor, 1.);
	this->residual += tmp_residual;
	}

	/* -------------------------------------------------------------------------- */
	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);

	// Array<Real> data_cache(this->local_system_size, 1, 0.);
	this->data_cache.resize(this->local_system_size);
	this->data_cache.clear();

	this->assembleToGlobalArray(dof_id, x, data_cache, scale_factor);

	auto A_it = A.begin();
	auto A_end = A.end();
	auto x_it = data_cache.begin();
	auto r_it = this->residual.begin();

	for (; A_it != A_end; ++A_it, ++x_it, ++r_it) {
	r_it += A_it * *x_it;
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assembleElementalMatricesToMatrix(
	const ID & matrix_id, const ID & dof_id, const Array<Real> & elementary_mat,
	const ElementType & type, const 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");

	this->addToProfile(matrix_id, dof_id, type, ghost_type);

	const auto & equation_number = this->getLocalEquationNumbers(dof_id);
	auto & A = this->getMatrix(matrix_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;

	UInt size_mat = nb_nodes_per_element * nb_degree_of_freedom;

	Vector<UInt> element_eq_nb(nb_degree_of_freedom * nb_nodes_per_element);
	Array<Real>::const_matrix_iterator 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(), [&](UInt & local) -> UInt {
	return this->localToGlobalEquationNumber(local);
	});

	if (filter_it)
	++filter_it;
	else
	++conn_it;

	if (A.getMatrixType() == _symmetric)
	if (elemental_matrix_type == _symmetric)
	this->addSymmetricElementalMatrixToSymmetric(A, *el_mat_it,
	element_eq_nb, A.size());
	else
	this->addUnsymmetricElementalMatrixToSymmetric(A, *el_mat_it,
	element_eq_nb, A.size());
	else
	this->addElementalMatrixToUnsymmetric(A, *el_mat_it, element_eq_nb,
	A.size());
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::assemblePreassembledMatrix(
	const ID & dof_id_m, const ID & dof_id_n, const ID & matrix_id,
	const TermsToAssemble & terms) {
	const Array<UInt> & equation_number_m =
	this->getLocalEquationNumbers(dof_id_m);
	const Array<UInt> & equation_number_n =
	this->getLocalEquationNumbers(dof_id_n);
	SparseMatrixAIJ & A = this->getMatrix(matrix_id);

	for (const auto & term : terms) {
	UInt gi = this->localToGlobalEquationNumber(equation_number_m(term.i()));
	UInt gj = this->localToGlobalEquationNumber(equation_number_n(term.j()));
	A.add(gi, gj, term);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::addToProfile(const ID & matrix_id, const ID & dof_id,
	const ElementType & type,
	const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	const DOFData & 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;

	UInt nb_degree_of_freedom_per_node = dof_data.dof->getNbComponent();

	const auto & equation_number = this->getLocalEquationNumbers(dof_id);

	auto & A = this->getMatrix(matrix_id);

	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;

	UInt 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<UInt> element_eq_nb(size_mat);

	for (UInt e = 0; e < nb_elements; ++e) {
	if (ge_it)
	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(), [&](UInt & local) -> UInt {
	return this->localToGlobalEquationNumber(local);
	});

	if (ge_it)
	++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();
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::applyBoundary(const ID & matrix_id) {
	SparseMatrixAIJ & J = this->getMatrix(matrix_id);

	if (this->jacobian_release == J.getValueRelease()) {
	auto are_equal =
	std::equal(global_blocked_dofs.begin(), global_blocked_dofs.end(),
	previous_global_blocked_dofs.begin());

	if (not are_equal)
	J.applyBoundary();

	previous_global_blocked_dofs.copy(global_blocked_dofs);
	} else {
	J.applyBoundary();
	}

	this->jacobian_release = J.getValueRelease();
	}

	/* -------------------------------------------------------------------------- */
	const Array<Real> & DOFManagerDefault::getGlobalResidual() {
	if (this->synchronizer) {
	if (not this->global_residual) {
	this->global_residual =
	std::make_unique<Array<Real>>(0, 1, "global_residual");
	}

	if (this->synchronizer->getCommunicator().whoAmI() == 0) {
	this->global_residual->resize(this->system_size);
	this->synchronizer->gather(this->residual, *this->global_residual);
	} else {
	this->synchronizer->gather(this->residual);
	}

	return *this->global_residual;
	} else {
	return this->residual;
	}
	}

	/* -------------------------------------------------------------------------- */
	const Array<Real> & DOFManagerDefault::getResidual() const {
	return this->residual;
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::setGlobalSolution(const Array<Real> & solution) {
	if (this->synchronizer) {
	if (this->synchronizer->getCommunicator().whoAmI() == 0) {
	this->synchronizer->scatter(this->global_solution, solution);
	} else {
	this->synchronizer->scatter(this->global_solution);
	}
	} else {
	AKANTU_DEBUG_ASSERT(solution.size() == this->global_solution.size(),
	"Sequential call to this function needs the solution "
	"to be the same size as the global_solution");
	this->global_solution.copy(solution);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::onNodesAdded(const Array<UInt> & nodes_list,
	const NewNodesEvent & event) {
	DOFManager::onNodesAdded(nodes_list, event);

	if (this->synchronizer)
	this->synchronizer->onNodesAdded(nodes_list);
	}

	/* -------------------------------------------------------------------------- */
	std::pair<UInt, UInt>
	DOFManagerDefault::updateNodalDOFs(const ID & dof_id,
	const Array<UInt> & nodes_list) {
	UInt nb_new_local_dofs, nb_new_pure_local;
	std::tie(nb_new_local_dofs, nb_new_pure_local) =
	DOFManager::updateNodalDOFs(dof_id, nodes_list);

	auto & dof_data = this->getDOFDataTyped<DOFDataDefault>(dof_id);
	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);
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	class GlobalDOFInfoDataAccessor : public DataAccessor<UInt> {
	public:
	using size_type =
	typename std::unordered_map<UInt, std::vector<UInt>>::size_type;

	GlobalDOFInfoDataAccessor(DOFManagerDefault::DOFDataDefault & dof_data,
	DOFManagerDefault & 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, 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 == _gst_ask_nodes or tag == _gst_giu_global_conn) {
	return nodes.size() * dof_data.dof->getNbComponent() * sizeof(UInt);
	}

	return 0;
	}

	void packData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag & tag) const override {
	if (tag == _gst_ask_nodes or tag == _gst_giu_global_conn) {
	for (auto & node : nodes) {
	auto & dofs = dofs_per_node.at(node);
	for (auto & dof : dofs) {
	buffer << dof_manager.global_equation_number(dof);
	}
	}
	}
	}

	void unpackData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
	const SynchronizationTag & tag) override {
	if (tag == _gst_ask_nodes or tag == _gst_giu_global_conn) {
	for (auto & node : nodes) {
	auto & dofs = dofs_per_node[node];
	for (auto dof : dofs) {
	UInt global_dof;
	buffer >> global_dof;
	AKANTU_DEBUG_ASSERT(
	(dof_manager.global_equation_number(dof) == UInt(-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<UInt>> dofs_per_node;
	DOFManagerDefault::DOFDataDefault & dof_data;
	DOFManagerDefault & dof_manager;
	};

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::resizeGlobalArrays() {
	// resize all relevant arrays
	this->residual.resize(this->local_system_size, 0.);
	this->dofs_flag.resize(this->local_system_size, NodeFlag::_normal);
	this->global_solution.resize(this->local_system_size, 0.);
	this->global_blocked_dofs.resize(this->local_system_size, true);
	this->previous_global_blocked_dofs.resize(this->local_system_size, true);
	this->global_equation_number.resize(this->local_system_size, -1);

	for (auto & lumped_matrix : lumped_matrices)
	lumped_matrix.second->resize(this->local_system_size);

	matrix_profiled_dofs.clear();
	for (auto & matrix : matrices) {
	matrix.second->clearProfile();
	}
	}

	/* -------------------------------------------------------------------------- */
	auto DOFManagerDefault::computeFirstDOFIDs(UInt nb_new_local_dofs,
	UInt nb_new_pure_local) {
	auto prank = this->communicator.whoAmI();
	auto psize = this->communicator.getNbProc();

	// determine the first local/global dof id to use
	Array<UInt> nb_dofs_per_proc(psize);
	nb_dofs_per_proc(prank) = nb_new_pure_local;
	this->communicator.allGather(nb_dofs_per_proc);

	this->first_global_dof_id += std::accumulate(
	nb_dofs_per_proc.begin(), nb_dofs_per_proc.begin() + prank, 0);

	auto first_global_dof_id = this->first_global_dof_id;
	auto first_local_dof_id = this->local_system_size - nb_new_local_dofs;

	this->first_global_dof_id += std::accumulate(nb_dofs_per_proc.begin() + prank,
	nb_dofs_per_proc.end(), 0);

	return std::make_pair(first_local_dof_id, first_global_dof_id);
	}
	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::updateDOFsData(
	DOFDataDefault & 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();

	resizeGlobalArrays();

	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);

	std::unordered_map<std::pair<UInt, UInt>, UInt> masters_dofs;

	// update per dof info
	UInt local_eq_num, 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(UInt(-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) = UInt(-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
	if (this->synchronizer) {
	GlobalDOFInfoDataAccessor data_accessor(dof_data, *this);

	if (this->mesh->isPeriodic()) {
	mesh->getPeriodicNodeSynchronizer().synchronizeOnce(data_accessor,
	_gst_giu_global_conn);
	}

	auto & node_synchronizer = this->mesh->getNodeSynchronizer();
	node_synchronizer.synchronizeOnce(data_accessor, _gst_ask_nodes);
	}
	}

	/* -------------------------------------------------------------------------- */
	void DOFManagerDefault::updateDOFsData(DOFDataDefault & dof_data,
	UInt nb_new_local_dofs,
	UInt nb_new_pure_local) {
	resizeGlobalArrays();

	dof_data.local_equation_number.reserve(dof_data.local_equation_number.size() +
	nb_new_local_dofs);

	UInt first_local_dof_id, first_global_dof_id;
	std::tie(first_local_dof_id, first_global_dof_id) =
	computeFirstDOFIDs(nb_new_local_dofs, nb_new_pure_local);

	// 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;
	}
	}

	/* -------------------------------------------------------------------------- */
	// register in factory
	static bool default_dof_manager_is_registered [[gnu::unused]] =
	DefaultDOFManagerFactory::getInstance().registerAllocator(
	"default",
	[](const ID & id,
	const MemoryID & mem_id) -> std::unique_ptr<DOFManager> {
	return std::make_unique<DOFManagerDefault>(id, mem_id);
	});

	static bool dof_manager_is_registered [[gnu::unused]] =
	DOFManagerFactory::getInstance().registerAllocator(
	"default",
	[](Mesh & mesh, const ID & id,
	const MemoryID & mem_id) -> std::unique_ptr<DOFManager> {
	return std::make_unique<DOFManagerDefault>(mesh, id, mem_id);
	});
	} // namespace akantu

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