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mesh_utils.cc
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			/**
			* @file mesh_utils.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>
			* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Fri Aug 20 2010
			* @date last modification: Fri Jan 22 2016
			*
			* @brief All mesh utils necessary for various tasks
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2012, 2014, 2015 EPFL (Ecole Polytechnique Fédérale de
			* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
			* Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You 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 <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();

			AKANTU_DEBUG_ASSERT(
			mesh.firstType(spatial_dimension) != mesh.lastType(spatial_dimension),
			"Some elements must be found in right dimension to compute facets!");

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			Mesh::type_iterator first =
			mesh.firstType(spatial_dimension, *gt, _ek_not_defined);
			Mesh::type_iterator last =
			mesh.lastType(spatial_dimension, *gt, _ek_not_defined);

			for (; first != last; ++first) {
			ElementType type = *first;
			UInt nb_element = mesh.getNbElement(type, *gt);
			Array<UInt>::const_iterator<Vector<UInt>> conn_it =
			mesh.getConnectivity(type, *gt).begin(
			Mesh::getNbNodesPerElement(type));

			for (UInt el = 0; el < nb_element; ++el, ++conn_it)
			for (UInt n = 0; n < conn_it->size(); ++n)
			++node_to_elem.rowOffset((*conn_it)(n));
			}
			}

			node_to_elem.countToCSR();
			node_to_elem.resizeCols();

			/// rearrange element to get the node-element list
			Element e;
			node_to_elem.beginInsertions();

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			Mesh::type_iterator first =
			mesh.firstType(spatial_dimension, *gt, _ek_not_defined);
			Mesh::type_iterator last =
			mesh.lastType(spatial_dimension, *gt, _ek_not_defined);
			e.ghost_type = *gt;
			for (; first != last; ++first) {
			ElementType type = *first;
			e.type = type;
			e.kind = Mesh::getKind(type);
			UInt nb_element = mesh.getNbElement(type, *gt);
			Array<UInt>::const_iterator<Vector<UInt>> conn_it =
			mesh.getConnectivity(type, *gt).begin(
			Mesh::getNbNodesPerElement(type));

			for (UInt el = 0; el < nb_element; ++el, ++conn_it) {
			e.element = el;
			for (UInt n = 0; n < conn_it->size(); ++n)
			node_to_elem.insertInRow((*conn_it)(n), e);
			}
			}
			}

			node_to_elem.endInsertions();

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* This function should disappear in the future (used in mesh partitioning)
			*/
			void MeshUtils::buildNode2Elements(const Mesh & mesh, CSR<UInt> & node_to_elem,
			UInt spatial_dimension) {
			AKANTU_DEBUG_IN();
			if (spatial_dimension == _all_dimensions)
			spatial_dimension = mesh.getSpatialDimension();
			UInt nb_nodes = mesh.getNbNodes();

			const Mesh::ConnectivityTypeList & type_list = mesh.getConnectivityTypeList();
			Mesh::ConnectivityTypeList::const_iterator it;

			UInt nb_types = type_list.size();
			UInt nb_good_types = 0;

			Vector<UInt> nb_nodes_per_element(nb_types);
			UInt ** conn_val = new UInt *[nb_types];
			Vector<UInt> nb_element(nb_types);

			for (it = type_list.begin(); it != type_list.end(); ++it) {
			ElementType type = *it;
			if (Mesh::getSpatialDimension(type) != spatial_dimension)
			continue;

			nb_nodes_per_element[nb_good_types] = Mesh::getNbNodesPerElement(type);
			conn_val[nb_good_types] = mesh.getConnectivity(type, _not_ghost).storage();
			nb_element[nb_good_types] =
			mesh.getConnectivity(type, _not_ghost).getSize();
			nb_good_types++;
			}

			AKANTU_DEBUG_ASSERT(
			nb_good_types != 0,
			"Some elements must be found in right dimension to compute facets!");

			/// 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 t = 0; t < nb_good_types; ++t) {
			for (UInt el = 0; el < nb_element[t]; ++el) {
			UInt el_offset = el * nb_nodes_per_element[t];
			for (UInt n = 0; n < nb_nodes_per_element[t]; ++n) {
			++node_to_elem.rowOffset(conn_val[t][el_offset + n]);
			}
			}
			}

			node_to_elem.countToCSR();
			node_to_elem.resizeCols();
			node_to_elem.beginInsertions();

			/// rearrange element to get the node-element list
			for (UInt t = 0, linearized_el = 0; t < nb_good_types; ++t)
			for (UInt el = 0; el < nb_element[t]; ++el, ++linearized_el) {
			UInt el_offset = el * nb_nodes_per_element[t];
			for (UInt n = 0; n < nb_nodes_per_element[t]; ++n)
			node_to_elem.insertInRow(conn_val[t][el_offset + n], linearized_el);
			}

			node_to_elem.endInsertions();
			delete[] conn_val;
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::buildNode2ElementsElementTypeMap(const Mesh & mesh,
			CSR<UInt> & node_to_elem,
			const ElementType & type,
			const 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).getSize();

			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 (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			GhostType gt_facet = *gt;
			Mesh::type_iterator it = mesh.firstType(spatial_dimension - 1, gt_facet);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension - 1, gt_facet);
			for (; it != end; ++it) {
			mesh.getConnectivity(it, gt).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();

			AKANTU_DEBUG_ASSERT(
			mesh_facets.isMeshFacets(),
			"The mesh_facets should be initialized with initMeshFacets");

			const ElementTypeMapArray<UInt> * prank_to_element = nullptr;

			if (mesh.isDistributed()) {
			prank_to_element = &(mesh.getElementSynchronizer().getPrankToElement());
			}

			/// generate facets
			buildFacetsDimension(mesh, mesh_facets, false, from_dimension,
			prank_to_element);

			/// copy nodes type
			MeshAccessor mesh_accessor_facets(mesh_facets);
			mesh_accessor_facets.getNodesType().copy(mesh.getNodesType());

			/// sort facets and generate sub-facets
			for (UInt i = from_dimension - 1; i > to_dimension; --i) {
			buildFacetsDimension(mesh_facets, mesh_facets, false, i, prank_to_element);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::buildFacetsDimension(
			const Mesh & mesh, Mesh & mesh_facets, bool boundary_only, UInt dimension,
			const ElementTypeMapArray<UInt> * prank_to_element) {
			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 Array<Real>::const_vector_iterator 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;

			// init the SubelementToElement data to improve performance
			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			GhostType ghost_type = *gt;
			Mesh::type_iterator first = mesh.firstType(dimension, ghost_type);
			Mesh::type_iterator last = mesh.lastType(dimension, ghost_type);

			for (; first != last; ++first) {
			ElementType type = *first;

			mesh_accessor.getSubelementToElement(type, ghost_type);

			Vector<ElementType> facet_types = mesh.getAllFacetTypes(type);

			for (UInt ft = 0; ft < facet_types.size(); ++ft) {
			ElementType facet_type = facet_types(ft);
			mesh_accessor.getElementToSubelement(facet_type, ghost_type);
			mesh_accessor.getConnectivity(facet_type, ghost_type);
			}
			}
			}

			Element current_element;
			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			GhostType ghost_type = *gt;
			GhostType facet_ghost_type = ghost_type;

			current_element.ghost_type = ghost_type;
			Mesh::type_iterator first = mesh.firstType(dimension, ghost_type);
			Mesh::type_iterator last = mesh.lastType(dimension, ghost_type);

			for (; first != last; ++first) {
			ElementType type = *first;
			Vector<ElementType> facet_types = mesh.getAllFacetTypes(type);

			current_element.type = type;

			for (UInt ft = 0; ft < facet_types.size(); ++ft) {
			ElementType facet_type = facet_types(ft);
			UInt nb_element = mesh.getNbElement(type, ghost_type);

			Array<std::vector<Element>> * element_to_subelement =
			&mesh_facets.getElementToSubelement(facet_type, ghost_type);
			Array<UInt> * connectivity_facets =
			&mesh_facets.getConnectivity(facet_type, ghost_type);

			UInt nb_facet_per_element = mesh.getNbFacetsPerElement(type, ft);
			const Array<UInt> & element_connectivity =
			mesh.getConnectivity(type, ghost_type);

			const Matrix<UInt> facet_local_connectivity =
			mesh.getFacetLocalConnectivity(type, ft);
			UInt 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;

			for (UInt f = 0; f < nb_facet_per_element; ++f) {
			for (UInt n = 0; n < nb_nodes_per_facet; ++n)
			facet(n) =
			element_connectivity(el, facet_local_connectivity(f, n));

			UInt first_node_nb_elements = node_to_elem.getNbCols(facet(0));
			counter.resize(first_node_nb_elements);
			counter.clear();

			// loop over the other nodes to search intersecting elements,
			// which are the elements that share another node with the
			// starting element after first_node
			CSR<Element>::iterator first_node_elements =
			node_to_elem.begin(facet(0));
			CSR<Element>::iterator first_node_elements_end =
			node_to_elem.end(facet(0));
			UInt local_el = 0;
			for (; first_node_elements != first_node_elements_end;
			++first_node_elements, ++local_el) {
			for (UInt n = 1; n < nb_nodes_per_facet; ++n) {
			CSR<Element>::iterator node_elements_begin =
			node_to_elem.begin(facet(n));
			CSR<Element>::iterator node_elements_end =
			node_to_elem.end(facet(n));
			counter(local_el) +=
			std::count(node_elements_begin, node_elements_end,
			*first_node_elements);
			}
			}

			// 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 (UInt el_f = 0; el_f < first_node_nb_elements; el_f++) {
			Element real_el = node_to_elem(facet(0), el_f);
			if (counter(el_f) == nb_nodes_per_facet - 1) {
			++nb_element_connected_to_facet;
			minimum_el = std::min(minimum_el, real_el);
			connected_elements.push_back(real_el);
			}
			}

			if (minimum_el == current_element) {
			bool full_ghost_facet = false;

			UInt n = 0;
			while (n < nb_nodes_per_facet && mesh.isPureGhostNode(facet(n)))
			++n;
			if (n == nb_nodes_per_facet)
			full_ghost_facet = true;

			if (!full_ghost_facet) {
			if (!boundary_only \|\|
			(boundary_only && nb_element_connected_to_facet == 1)) {

			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.push_back(current_element);

			/// boundary facet
			if (nb_element_connected_to_facet == 1)
			elements.push_back(ElementNull);
			/// internal facet
			else if (nb_element_connected_to_facet == 2) {
			elements.push_back(connected_elements[1]);

			/// 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] + gt[1] == 1) {
			if (prank_to_element) {
			UInt prank[2];
			for (UInt el = 0; el < 2; ++el) {
			UInt current_el = connected_elements[el].element;
			ElementType current_type =
			connected_elements[el].type;
			GhostType current_gt =
			connected_elements[el].ghost_type;

			const Array<UInt> & prank_to_el =
			(*prank_to_element)(current_type, current_gt);

			prank[el] = prank_to_el(current_el);
			}

			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_facets.getConnectivity(
			facet_type, facet_ghost_type);
			element_to_subelement =
			&mesh_facets.getElementToSubelement(
			facet_type, facet_ghost_type);
			}
			}
			}
			/// facet of facet
			else {
			for (UInt i = 1; i < nb_element_connected_to_facet; ++i) {
			elements.push_back(connected_elements[i]);
			}
			}

			element_to_subelement->push_back(elements);
			connectivity_facets->push_back(facet);

			/// current facet index
			UInt current_facet = connectivity_facets->getSize() - 1;

			/// loop on every element connected to current facet and
			/// insert current facet in the first free spot of the
			/// subelement_to_element vector
			for (UInt elem = 0; elem < elements.size(); ++elem) {
			Element loc_el = elements[elem];

			if (loc_el.type != _not_defined) {

			Array<Element> & subelement_to_element =
			mesh_facets.getSubelementToElement(loc_el.type,
			loc_el.ghost_type);

			UInt nb_facet_per_loc_element =
			subelement_to_element.getNbComponent();

			for (UInt f_in = 0; f_in < nb_facet_per_loc_element;
			++f_in) {
			if (subelement_to_element(loc_el.element, f_in).type ==
			_not_defined) {
			subelement_to_element(loc_el.element, f_in).type =
			facet_type;
			subelement_to_element(loc_el.element, f_in).element =
			current_facet;
			subelement_to_element(loc_el.element, f_in)
			.ghost_type = facet_ghost_type;
			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);
			}
			}
			}
			}
			}
			}
			}
			}
			}

			// restore the parent of mesh_facet
			if (mesh_facets_parent)
			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.getSize(); ++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);

			std::map<UInt, UInt>::iterator it = renumbering_map.begin();
			std::map<UInt, UInt>::iterator end = renumbering_map.end();
			old_nodes_numbers.resize(renumbering_map.size());
			for (; it != end; ++it) {
			old_nodes_numbers(it->second) = it->first;
			}
			renumbering_map.clear();

			MeshAccessor mesh_accessor(mesh);

			/// copy the renumbered connectivity to the right place
			Array<UInt> & local_conn = mesh_accessor.getConnectivity(type);
			local_conn.resize(nb_local_element);
			memcpy(local_conn.storage(), local_connectivities.storage(),
			nb_local_element * nb_nodes_per_element * sizeof(UInt));

			Array<UInt> & ghost_conn = mesh_accessor.getConnectivity(type, _ghost);
			ghost_conn.resize(nb_ghost_element);
			memcpy(ghost_conn.storage(),
			local_connectivities.storage() +
			nb_local_element * nb_nodes_per_element,
			nb_ghost_element * nb_nodes_per_element * sizeof(UInt));

			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;
			std::map<UInt, UInt>::iterator 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);
			Array<UInt> & nodes_removed = remove_nodes.getList();

			for (UInt gt = _not_ghost; gt <= _ghost; ++gt) {
			GhostType ghost_type = (GhostType)gt;

			Mesh::type_iterator it =
			mesh.firstType(_all_dimensions, ghost_type, _ek_not_defined);
			Mesh::type_iterator end =
			mesh.lastType(_all_dimensions, ghost_type, _ek_not_defined);
			for (; it != end; ++it) {

			ElementType type(*it);
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

			Array<UInt> & connectivity = mesh.getConnectivity(type, ghost_type);
			UInt nb_element(connectivity.getSize());

			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));

			std::map<UInt, UInt>::iterator it = renumbering_map.begin();
			std::map<UInt, UInt>::iterator end = renumbering_map.end();
			for (; it != end; ++it) {
			new_numbering(it->first) = it->second;
			}

			for (UInt i = 0; i < new_numbering.getSize(); ++i) {
			if (new_numbering(i) == UInt(-1))
			nodes_removed.push_back(i);
			}

			mesh.sendEvent(remove_nodes);

			AKANTU_DEBUG_OUT();
			}

			#if defined(AKANTU_COHESIVE_ELEMENT)
			/* -------------------------------------------------------------------------- */
			UInt MeshUtils::insertCohesiveElements(
			Mesh & mesh, Mesh & mesh_facets,
			const ElementTypeMapArray<bool> & facet_insertion,
			Array<UInt> & doubled_nodes, Array<Element> & new_elements,
			bool only_double_facets) {
			UInt spatial_dimension = mesh.getSpatialDimension();
			UInt elements_to_insert = updateFacetToDouble(mesh_facets, facet_insertion);

			if (elements_to_insert > 0) {

			if (spatial_dimension == 1) {
			doublePointFacet(mesh, mesh_facets, doubled_nodes);
			} else {
			doubleFacet(mesh, mesh_facets, spatial_dimension - 1, doubled_nodes,
			true);
			findSubfacetToDouble<false>(mesh, mesh_facets);

			if (spatial_dimension == 2) {
			doubleSubfacet<2>(mesh, mesh_facets, doubled_nodes);
			} else if (spatial_dimension == 3) {
			doubleFacet(mesh, mesh_facets, 1, doubled_nodes, false);
			findSubfacetToDouble<true>(mesh, mesh_facets);
			doubleSubfacet<3>(mesh, mesh_facets, doubled_nodes);
			}
			}

			if (!only_double_facets)
			updateCohesiveData(mesh, mesh_facets, new_elements);
			}

			return elements_to_insert;
			}
			#endif

			/* -------------------------------------------------------------------------- */
			void MeshUtils::doubleNodes(Mesh & mesh, const std::vector<UInt> & old_nodes,
			Array<UInt> & doubled_nodes) {
			AKANTU_DEBUG_IN();

			Array<Real> & position = mesh.getNodes();
			UInt spatial_dimension = mesh.getSpatialDimension();

			UInt old_nb_nodes = position.getSize();
			UInt new_nb_nodes = old_nb_nodes + old_nodes.size();

			UInt old_nb_doubled_nodes = doubled_nodes.getSize();
			UInt new_nb_doubled_nodes = old_nb_doubled_nodes + old_nodes.size();

			position.resize(new_nb_nodes);
			doubled_nodes.resize(new_nb_doubled_nodes);

			Array<Real>::iterator<Vector<Real>> position_begin =
			position.begin(spatial_dimension);

			for (UInt n = 0; n < old_nodes.size(); ++n) {
			UInt new_node = old_nb_nodes + n;

			/// store doubled nodes
			doubled_nodes(old_nb_doubled_nodes + n, 0) = old_nodes[n];
			doubled_nodes(old_nb_doubled_nodes + n, 1) = new_node;

			/// update position
			std::copy(position_begin + old_nodes[n], position_begin + old_nodes[n] + 1,
			position_begin + new_node);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::doubleFacet(Mesh & mesh, Mesh & mesh_facets,
			UInt facet_dimension, Array<UInt> & doubled_nodes,
			bool facet_mode) {
			AKANTU_DEBUG_IN();

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType gt_facet = *gt;

			Mesh::type_iterator it = mesh_facets.firstType(facet_dimension, gt_facet);
			Mesh::type_iterator end = mesh_facets.lastType(facet_dimension, gt_facet);

			for (; it != end; ++it) {

			ElementType type_facet = *it;

			Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);
			UInt nb_facet_to_double = f_to_double.getSize();

			if (nb_facet_to_double == 0)
			continue;

			ElementType type_subfacet = Mesh::getFacetType(type_facet);
			const UInt nb_subfacet_per_facet =
			Mesh::getNbFacetsPerElement(type_facet);
			GhostType gt_subfacet = _casper;
			Array<std::vector<Element>> * f_to_subfacet = NULL;

			Array<Element> & subfacet_to_facet =
			mesh_facets.getSubelementToElement(type_facet, gt_facet);

			Array<UInt> & conn_facet =
			mesh_facets.getConnectivity(type_facet, gt_facet);
			UInt nb_nodes_per_facet = conn_facet.getNbComponent();

			UInt old_nb_facet = conn_facet.getSize();
			UInt new_nb_facet = old_nb_facet + nb_facet_to_double;

			conn_facet.resize(new_nb_facet);
			subfacet_to_facet.resize(new_nb_facet);

			UInt new_facet = old_nb_facet - 1;
			Element new_facet_el(type_facet, 0, gt_facet);

			Array<Element>::iterator<Vector<Element>> subfacet_to_facet_begin =
			subfacet_to_facet.begin(nb_subfacet_per_facet);
			Array<UInt>::iterator<Vector<UInt>> conn_facet_begin =
			conn_facet.begin(nb_nodes_per_facet);

			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {
			UInt old_facet = f_to_double(facet);
			++new_facet;

			/// adding a new facet by copying original one

			/// copy connectivity in new facet
			std::copy(conn_facet_begin + old_facet,
			conn_facet_begin + old_facet + 1,
			conn_facet_begin + new_facet);

			/// update subfacet_to_facet
			std::copy(subfacet_to_facet_begin + old_facet,
			subfacet_to_facet_begin + old_facet + 1,
			subfacet_to_facet_begin + new_facet);

			new_facet_el.element = new_facet;

			/// loop on every subfacet
			for (UInt sf = 0; sf < nb_subfacet_per_facet; ++sf) {
			Element & subfacet = subfacet_to_facet(old_facet, sf);
			if (subfacet == ElementNull)
			continue;

			if (gt_subfacet != subfacet.ghost_type) {
			gt_subfacet = subfacet.ghost_type;
			f_to_subfacet = &mesh_facets.getElementToSubelement(
			type_subfacet, subfacet.ghost_type);
			}

			/// update facet_to_subfacet array
			(*f_to_subfacet)(subfacet.element).push_back(new_facet_el);
			}
			}

			/// update facet_to_subfacet and _segment_3 facets if any
			if (!facet_mode) {
			updateSubfacetToFacet(mesh_facets, type_facet, gt_facet, true);
			updateFacetToSubfacet(mesh_facets, type_facet, gt_facet, true);
			updateQuadraticSegments<true>(mesh, mesh_facets, type_facet, gt_facet,
			doubled_nodes);
			} else
			updateQuadraticSegments<false>(mesh, mesh_facets, type_facet, gt_facet,
			doubled_nodes);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			UInt MeshUtils::updateFacetToDouble(
			Mesh & mesh_facets, const ElementTypeMapArray<bool> & facet_insertion) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = mesh_facets.getSpatialDimension();
			UInt nb_facets_to_double = 0.;

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType gt_facet = *gt;

			Mesh::type_iterator it =
			mesh_facets.firstType(spatial_dimension - 1, gt_facet);
			Mesh::type_iterator end =
			mesh_facets.lastType(spatial_dimension - 1, gt_facet);

			for (; it != end; ++it) {

			ElementType type_facet = *it;

			const Array<bool> & f_insertion = facet_insertion(type_facet, gt_facet);
			Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);

			Array<std::vector<Element>> & element_to_facet =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);

			ElementType el_type = _not_defined;
			GhostType el_gt = _casper;
			UInt nb_facet_per_element = 0;
			Element old_facet_el(type_facet, 0, gt_facet);

			Array<Element> * facet_to_element = NULL;

			for (UInt f = 0; f < f_insertion.getSize(); ++f) {

			if (f_insertion(f) == false)
			continue;

			++nb_facets_to_double;

			if (element_to_facet(f)[1].type == _not_defined
			#if defined(AKANTU_COHESIVE_ELEMENT)
			\|\| element_to_facet(f)[1].kind == _ek_cohesive
			#endif
			) {
			AKANTU_DEBUG_WARNING("attempt to double a facet on the boundary");
			continue;
			}

			f_to_double.push_back(f);

			UInt new_facet = mesh_facets.getNbElement(type_facet, gt_facet) +
			f_to_double.getSize() - 1;
			old_facet_el.element = f;

			/// update facet_to_element vector
			Element & elem_to_update = element_to_facet(f)[1];
			UInt el = elem_to_update.element;

			if (elem_to_update.ghost_type != el_gt \|\|
			elem_to_update.type != el_type) {
			el_type = elem_to_update.type;
			el_gt = elem_to_update.ghost_type;
			facet_to_element =
			&mesh_facets.getSubelementToElement(el_type, el_gt);
			nb_facet_per_element = facet_to_element->getNbComponent();
			}

			Element * f_update =
			std::find(facet_to_element->storage() + el * nb_facet_per_element,
			facet_to_element->storage() + el * nb_facet_per_element +
			nb_facet_per_element,
			old_facet_el);

			AKANTU_DEBUG_ASSERT(
			facet_to_element->storage() + el * nb_facet_per_element !=
			facet_to_element->storage() + el * nb_facet_per_element +
			nb_facet_per_element,
			"Facet not found");

			f_update->element = new_facet;

			/// update elements connected to facet
			std::vector<Element> first_facet_list = element_to_facet(f);
			element_to_facet.push_back(first_facet_list);

			/// set new and original facets as boundary facets
			element_to_facet(new_facet)[0] = element_to_facet(new_facet)[1];

			element_to_facet(f)[1] = ElementNull;
			element_to_facet(new_facet)[1] = ElementNull;
			}
			}
			}

			AKANTU_DEBUG_OUT();
			return nb_facets_to_double;
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::resetFacetToDouble(Mesh & mesh_facets) {
			AKANTU_DEBUG_IN();

			for (UInt g = _not_ghost; g <= _ghost; ++g) {
			GhostType gt = (GhostType)g;

			Mesh::type_iterator it = mesh_facets.firstType(_all_dimensions, gt);
			Mesh::type_iterator end = mesh_facets.lastType(_all_dimensions, gt);
			for (; it != end; ++it) {
			ElementType type = *it;
			mesh_facets.getDataPointer<UInt>("facet_to_double", type, gt, 1, false);

			mesh_facets.getDataPointer<std::vector<Element>>(
			"facets_to_subfacet_double", type, gt, 1, false);

			mesh_facets.getDataPointer<std::vector<Element>>(
			"elements_to_subfacet_double", type, gt, 1, false);

			mesh_facets.getDataPointer<std::vector<Element>>(
			"subfacets_to_subsubfacet_double", type, gt, 1, false);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <bool subsubfacet_mode>
			void MeshUtils::findSubfacetToDouble(Mesh & mesh, Mesh & mesh_facets) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = mesh_facets.getSpatialDimension();
			if (spatial_dimension == 1)
			return;

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType gt_facet = *gt;

			Mesh::type_iterator it =
			mesh_facets.firstType(spatial_dimension - 1, gt_facet);
			Mesh::type_iterator end =
			mesh_facets.lastType(spatial_dimension - 1, gt_facet);

			for (; it != end; ++it) {

			ElementType type_facet = *it;

			Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);
			UInt nb_facet_to_double = f_to_double.getSize();
			if (nb_facet_to_double == 0)
			continue;

			ElementType type_subfacet = Mesh::getFacetType(type_facet);
			GhostType gt_subfacet = _casper;

			ElementType type_subsubfacet = Mesh::getFacetType(type_subfacet);
			GhostType gt_subsubfacet = _casper;

			Array<UInt> * conn_subfacet = NULL;
			Array<UInt> * sf_to_double = NULL;
			Array<std::vector<Element>> * sf_to_subfacet_double = NULL;
			Array<std::vector<Element>> * f_to_subfacet_double = NULL;
			Array<std::vector<Element>> * el_to_subfacet_double = NULL;

			UInt nb_subfacet = Mesh::getNbFacetsPerElement(type_facet);

			UInt nb_subsubfacet;
			UInt nb_nodes_per_sf_el;

			if (subsubfacet_mode) {
			nb_nodes_per_sf_el = Mesh::getNbNodesPerElement(type_subsubfacet);
			nb_subsubfacet = Mesh::getNbFacetsPerElement(type_subfacet);
			} else
			nb_nodes_per_sf_el = Mesh::getNbNodesPerElement(type_subfacet);

			Array<Element> & subfacet_to_facet =
			mesh_facets.getSubelementToElement(type_facet, gt_facet);

			Array<std::vector<Element>> & element_to_facet =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);

			Array<Element> * subsubfacet_to_subfacet = NULL;

			UInt old_nb_facet = subfacet_to_facet.getSize() - nb_facet_to_double;

			Element current_facet(type_facet, 0, gt_facet);
			std::vector<Element> element_list;
			std::vector<Element> facet_list;
			std::vector<Element> * subfacet_list;
			if (subsubfacet_mode)
			subfacet_list = new std::vector<Element>;

			/// map to filter subfacets
			Array<std::vector<Element>> * facet_to_subfacet = NULL;

			/// this is used to make sure that both new and old facets are
			/// checked
			UInt facets[2];

			/// loop on every facet
			for (UInt f_index = 0; f_index < 2; ++f_index) {
			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {
			facets[bool(f_index)] = f_to_double(facet);
			facets[!bool(f_index)] = old_nb_facet + facet;

			UInt old_facet = facets[0];
			UInt new_facet = facets[1];

			Element & starting_element = element_to_facet(new_facet)[0];
			current_facet.element = old_facet;

			/// loop on every subfacet
			for (UInt sf = 0; sf < nb_subfacet; ++sf) {

			Element & subfacet = subfacet_to_facet(old_facet, sf);
			if (subfacet == ElementNull)
			continue;

			if (gt_subfacet != subfacet.ghost_type) {
			gt_subfacet = subfacet.ghost_type;

			if (subsubfacet_mode) {
			subsubfacet_to_subfacet = &mesh_facets.getSubelementToElement(
			type_subfacet, gt_subfacet);
			} else {
			conn_subfacet =
			&mesh_facets.getConnectivity(type_subfacet, gt_subfacet);
			sf_to_double = &mesh_facets.getData<UInt>(
			"facet_to_double", type_subfacet, gt_subfacet);

			f_to_subfacet_double =
			&mesh_facets.getData<std::vector<Element>>(
			"facets_to_subfacet_double", type_subfacet,
			gt_subfacet);

			el_to_subfacet_double =
			&mesh_facets.getData<std::vector<Element>>(
			"elements_to_subfacet_double", type_subfacet,
			gt_subfacet);

			facet_to_subfacet = &mesh_facets.getElementToSubelement(
			type_subfacet, gt_subfacet);
			}
			}

			if (subsubfacet_mode) {
			/// loop on every subsubfacet
			for (UInt ssf = 0; ssf < nb_subsubfacet; ++ssf) {
			Element & subsubfacet =
			(*subsubfacet_to_subfacet)(subfacet.element, ssf);

			if (subsubfacet == ElementNull)
			continue;

			if (gt_subsubfacet != subsubfacet.ghost_type) {
			gt_subsubfacet = subsubfacet.ghost_type;
			conn_subfacet = &mesh_facets.getConnectivity(type_subsubfacet,
			gt_subsubfacet);
			sf_to_double = &mesh_facets.getData<UInt>(
			"facet_to_double", type_subsubfacet, gt_subsubfacet);

			sf_to_subfacet_double =
			&mesh_facets.getData<std::vector<Element>>(
			"subfacets_to_subsubfacet_double", type_subsubfacet,
			gt_subsubfacet);

			f_to_subfacet_double =
			&mesh_facets.getData<std::vector<Element>>(
			"facets_to_subfacet_double", type_subsubfacet,
			gt_subsubfacet);

			el_to_subfacet_double =
			&mesh_facets.getData<std::vector<Element>>(
			"elements_to_subfacet_double", type_subsubfacet,
			gt_subsubfacet);

			facet_to_subfacet = &mesh_facets.getElementToSubelement(
			type_subsubfacet, gt_subsubfacet);
			}

			UInt global_ssf = subsubfacet.element;

			Vector<UInt> subsubfacet_connectivity(
			conn_subfacet->storage() + global_ssf * nb_nodes_per_sf_el,
			nb_nodes_per_sf_el);

			/// check if subsubfacet is to be doubled
			if (findElementsAroundSubfacet<true>(
			mesh, mesh_facets, starting_element, current_facet,
			subsubfacet_connectivity, element_list, facet_list,
			subfacet_list) == false &&
			removeElementsInVector(*subfacet_list,
			(*facet_to_subfacet)(global_ssf)) ==
			false) {

			sf_to_double->push_back(global_ssf);
			sf_to_subfacet_double->push_back(*subfacet_list);
			f_to_subfacet_double->push_back(facet_list);
			el_to_subfacet_double->push_back(element_list);
			}
			}
			} else {
			const UInt global_sf = subfacet.element;

			Vector<UInt> subfacet_connectivity(
			conn_subfacet->storage() + global_sf * nb_nodes_per_sf_el,
			nb_nodes_per_sf_el);

			/// check if subfacet is to be doubled
			if (findElementsAroundSubfacet<false>(
			mesh, mesh_facets, starting_element, current_facet,
			subfacet_connectivity, element_list,
			facet_list) == false &&
			removeElementsInVector(
			facet_list, (*facet_to_subfacet)(global_sf)) == false) {

			sf_to_double->push_back(global_sf);
			f_to_subfacet_double->push_back(facet_list);
			el_to_subfacet_double->push_back(element_list);
			}
			}
			}
			}
			}

			if (subsubfacet_mode)
			delete subfacet_list;
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			#if defined(AKANTU_COHESIVE_ELEMENT)
			void MeshUtils::updateCohesiveData(Mesh & mesh, Mesh & mesh_facets,
			Array<Element> & new_elements) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = mesh.getSpatialDimension();
			bool third_dimension = spatial_dimension == 3;

			MeshAccessor mesh_facets_accessor(mesh_facets);

			for (auto gt_facet : ghost_types) {
			for (auto type_facet :
			mesh_facets.elementTypes(spatial_dimension - 1, gt_facet)) {

			Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);

			UInt nb_facet_to_double = f_to_double.getSize();
			if (nb_facet_to_double == 0)
			continue;

			ElementType type_cohesive = FEEngine::getCohesiveElementType(type_facet);

			auto & facet_to_coh_element =
			mesh_facets_accessor.getSubelementToElement(type_cohesive, gt_facet);

			auto & conn_facet =
			mesh_facets.getConnectivity(type_facet, gt_facet);
			auto & conn_cohesive =
			mesh.getConnectivity(type_cohesive, gt_facet);
			UInt nb_nodes_per_facet = Mesh::getNbNodesPerElement(type_facet);

			Array<std::vector<Element>> & element_to_facet =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);

			UInt old_nb_cohesive_elements = conn_cohesive.getSize();
			UInt new_nb_cohesive_elements =
			conn_cohesive.getSize() + nb_facet_to_double;

			UInt old_nb_facet = element_to_facet.getSize() - nb_facet_to_double;
			facet_to_coh_element.resize(new_nb_cohesive_elements);
			conn_cohesive.resize(new_nb_cohesive_elements);

			UInt new_elements_old_size = new_elements.getSize();
			new_elements.resize(new_elements_old_size + nb_facet_to_double);

			Element c_element(type_cohesive, 0, gt_facet, _ek_cohesive);
			Element f_element(type_facet, 0, gt_facet);

			UInt facets[2];

			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {

			/// (in 3D cohesive elements connectivity is inverted)
			facets[third_dimension] = f_to_double(facet);
			facets[!third_dimension] = old_nb_facet + facet;

			UInt cohesive_element = old_nb_cohesive_elements + facet;

			/// store doubled facets
			f_element.element = facets[0];
			facet_to_coh_element(cohesive_element, 0) = f_element;
			f_element.element = facets[1];
			facet_to_coh_element(cohesive_element, 1) = f_element;

			/// modify cohesive elements' connectivity
			for (UInt n = 0; n < nb_nodes_per_facet; ++n) {
			conn_cohesive(cohesive_element, n) = conn_facet(facets[0], n);
			conn_cohesive(cohesive_element, n + nb_nodes_per_facet) =
			conn_facet(facets[1], n);
			}

			/// update element_to_facet vectors
			c_element.element = cohesive_element;
			element_to_facet(facets[0])[1] = c_element;
			element_to_facet(facets[1])[1] = c_element;

			/// add cohesive element to the element event list
			new_elements(new_elements_old_size + facet) = c_element;
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}
			#endif

			/* -------------------------------------------------------------------------- */
			void MeshUtils::doublePointFacet(Mesh & mesh, Mesh & mesh_facets,
			Array<UInt> & doubled_nodes) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = mesh.getSpatialDimension();
			if (spatial_dimension != 1)
			return;

			Array<Real> & position = mesh.getNodes();

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType gt_facet = *gt;

			Mesh::type_iterator it =
			mesh_facets.firstType(spatial_dimension - 1, gt_facet);
			Mesh::type_iterator end =
			mesh_facets.lastType(spatial_dimension - 1, gt_facet);

			for (; it != end; ++it) {

			ElementType type_facet = *it;

			Array<UInt> & conn_facet =
			mesh_facets.getConnectivity(type_facet, gt_facet);
			Array<std::vector<Element>> & element_to_facet =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);

			const Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);

			UInt nb_facet_to_double = f_to_double.getSize();

			UInt old_nb_facet = element_to_facet.getSize() - nb_facet_to_double;
			UInt new_nb_facet = element_to_facet.getSize();

			UInt old_nb_nodes = position.getSize();
			UInt new_nb_nodes = old_nb_nodes + nb_facet_to_double;

			position.resize(new_nb_nodes);
			conn_facet.resize(new_nb_facet);

			UInt old_nb_doubled_nodes = doubled_nodes.getSize();
			doubled_nodes.resize(old_nb_doubled_nodes + nb_facet_to_double);

			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {
			UInt old_facet = f_to_double(facet);
			UInt new_facet = old_nb_facet + facet;

			ElementType type = element_to_facet(new_facet)[0].type;
			UInt el = element_to_facet(new_facet)[0].element;
			GhostType gt = element_to_facet(new_facet)[0].ghost_type;

			UInt old_node = conn_facet(old_facet);
			UInt new_node = old_nb_nodes + facet;

			/// update position
			position(new_node) = position(old_node);

			conn_facet(new_facet) = new_node;
			Array<UInt> & conn_segment = mesh.getConnectivity(type, gt);
			UInt nb_nodes_per_segment = conn_segment.getNbComponent();

			/// update facet connectivity
			UInt i;
			for (i = 0;
			conn_segment(el, i) != old_node && i <= nb_nodes_per_segment; ++i)
			;
			conn_segment(el, i) = new_node;

			doubled_nodes(old_nb_doubled_nodes + facet, 0) = old_node;
			doubled_nodes(old_nb_doubled_nodes + facet, 1) = new_node;
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <bool third_dim_segments>
			void MeshUtils::updateQuadraticSegments(Mesh & mesh, Mesh & mesh_facets,
			ElementType type_facet,
			GhostType gt_facet,
			Array<UInt> & doubled_nodes) {
			AKANTU_DEBUG_IN();

			if (type_facet != _segment_3)
			return;

			Array<UInt> & f_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_facet, gt_facet);
			UInt nb_facet_to_double = f_to_double.getSize();

			UInt old_nb_facet =
			mesh_facets.getNbElement(type_facet, gt_facet) - nb_facet_to_double;

			Array<UInt> & conn_facet = mesh_facets.getConnectivity(type_facet, gt_facet);

			Array<std::vector<Element>> & element_to_facet =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);

			/// this ones matter only for segments in 3D
			Array<std::vector<Element>> * el_to_subfacet_double = NULL;
			Array<std::vector<Element>> * f_to_subfacet_double = NULL;

			if (third_dim_segments) {
			el_to_subfacet_double = &mesh_facets.getData<std::vector<Element>>(
			"elements_to_subfacet_double", type_facet, gt_facet);

			f_to_subfacet_double = &mesh_facets.getData<std::vector<Element>>(
			"facets_to_subfacet_double", type_facet, gt_facet);
			}

			std::vector<UInt> middle_nodes;

			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {
			UInt old_facet = f_to_double(facet);
			UInt node = conn_facet(old_facet, 2);
			if (!mesh.isPureGhostNode(node))
			middle_nodes.push_back(node);
			}

			UInt n = doubled_nodes.getSize();

			doubleNodes(mesh, middle_nodes, doubled_nodes);

			for (UInt facet = 0; facet < nb_facet_to_double; ++facet) {
			UInt old_facet = f_to_double(facet);
			UInt old_node = conn_facet(old_facet, 2);
			if (mesh.isPureGhostNode(old_node))
			continue;

			UInt new_node = doubled_nodes(n, 1);
			UInt new_facet = old_nb_facet + facet;

			conn_facet(new_facet, 2) = new_node;

			if (third_dim_segments) {
			updateElementalConnectivity(mesh_facets, old_node, new_node,
			element_to_facet(new_facet));

			updateElementalConnectivity(mesh, old_node, new_node,
			(*el_to_subfacet_double)(facet),
			&(*f_to_subfacet_double)(facet));
			} else {
			updateElementalConnectivity(mesh, old_node, new_node,
			element_to_facet(new_facet));
			}
			++n;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::updateSubfacetToFacet(Mesh & mesh_facets,
			ElementType type_subfacet,
			GhostType gt_subfacet, bool facet_mode) {
			AKANTU_DEBUG_IN();

			Array<UInt> & sf_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_subfacet, gt_subfacet);
			UInt nb_subfacet_to_double = sf_to_double.getSize();

			/// update subfacet_to_facet vector
			ElementType type_facet = _not_defined;
			GhostType gt_facet = _casper;
			Array<Element> * subfacet_to_facet = NULL;
			UInt nb_subfacet_per_facet = 0;
			UInt old_nb_subfacet = mesh_facets.getNbElement(type_subfacet, gt_subfacet) -
			nb_subfacet_to_double;

			Array<std::vector<Element>> * facet_list = NULL;
			if (facet_mode)
			facet_list = &mesh_facets.getData<std::vector<Element>>(
			"facets_to_subfacet_double", type_subfacet, gt_subfacet);
			else
			facet_list = &mesh_facets.getData<std::vector<Element>>(
			"subfacets_to_subsubfacet_double", type_subfacet, gt_subfacet);

			Element old_subfacet_el(type_subfacet, 0, gt_subfacet);
			Element new_subfacet_el(type_subfacet, 0, gt_subfacet);

			for (UInt sf = 0; sf < nb_subfacet_to_double; ++sf) {
			old_subfacet_el.element = sf_to_double(sf);
			new_subfacet_el.element = old_nb_subfacet + sf;

			for (UInt f = 0; f < (*facet_list)(sf).size(); ++f) {
			Element & facet = (*facet_list)(sf)[f];

			if (facet.type != type_facet \|\| facet.ghost_type != gt_facet) {
			type_facet = facet.type;
			gt_facet = facet.ghost_type;

			subfacet_to_facet =
			&mesh_facets.getSubelementToElement(type_facet, gt_facet);
			nb_subfacet_per_facet = subfacet_to_facet->getNbComponent();
			}

			Element * sf_update = std::find(
			subfacet_to_facet->storage() + facet.element * nb_subfacet_per_facet,
			subfacet_to_facet->storage() + facet.element * nb_subfacet_per_facet +
			nb_subfacet_per_facet,
			old_subfacet_el);

			AKANTU_DEBUG_ASSERT(subfacet_to_facet->storage() +
			facet.element * nb_subfacet_per_facet !=
			subfacet_to_facet->storage() +
			facet.element * nb_subfacet_per_facet +
			nb_subfacet_per_facet,
			"Subfacet not found");

			*sf_update = new_subfacet_el;
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::updateFacetToSubfacet(Mesh & mesh_facets,
			ElementType type_subfacet,
			GhostType gt_subfacet, bool facet_mode) {
			AKANTU_DEBUG_IN();

			Array<UInt> & sf_to_double =
			mesh_facets.getData<UInt>("facet_to_double", type_subfacet, gt_subfacet);
			UInt nb_subfacet_to_double = sf_to_double.getSize();

			Array<std::vector<Element>> & facet_to_subfacet =
			mesh_facets.getElementToSubelement(type_subfacet, gt_subfacet);

			Array<std::vector<Element>> * facet_to_subfacet_double = NULL;

			if (facet_mode) {
			facet_to_subfacet_double = &mesh_facets.getData<std::vector<Element>>(
			"facets_to_subfacet_double", type_subfacet, gt_subfacet);
			} else {
			facet_to_subfacet_double = &mesh_facets.getData<std::vector<Element>>(
			"subfacets_to_subsubfacet_double", type_subfacet, gt_subfacet);
			}

			UInt old_nb_subfacet = facet_to_subfacet.getSize();
			facet_to_subfacet.resize(old_nb_subfacet + nb_subfacet_to_double);

			for (UInt sf = 0; sf < nb_subfacet_to_double; ++sf)
			facet_to_subfacet(old_nb_subfacet + sf) = (*facet_to_subfacet_double)(sf);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt spatial_dimension>
			void MeshUtils::doubleSubfacet(Mesh & mesh, Mesh & mesh_facets,
			Array<UInt> & doubled_nodes) {
			AKANTU_DEBUG_IN();

			if (spatial_dimension == 1)
			return;

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {

			GhostType gt_subfacet = *gt;

			Mesh::type_iterator it = mesh_facets.firstType(0, gt_subfacet);
			Mesh::type_iterator end = mesh_facets.lastType(0, gt_subfacet);

			for (; it != end; ++it) {

			ElementType type_subfacet = *it;

			Array<UInt> & sf_to_double = mesh_facets.getData<UInt>(
			"facet_to_double", type_subfacet, gt_subfacet);
			UInt nb_subfacet_to_double = sf_to_double.getSize();

			if (nb_subfacet_to_double == 0)
			continue;

			AKANTU_DEBUG_ASSERT(
			type_subfacet == _point_1,
			"Only _point_1 subfacet doubling is supported at the moment");

			Array<UInt> & conn_subfacet =
			mesh_facets.getConnectivity(type_subfacet, gt_subfacet);

			UInt old_nb_subfacet = conn_subfacet.getSize();
			UInt new_nb_subfacet = old_nb_subfacet + nb_subfacet_to_double;

			conn_subfacet.resize(new_nb_subfacet);

			std::vector<UInt> nodes_to_double;
			UInt old_nb_doubled_nodes = doubled_nodes.getSize();

			/// double nodes
			for (UInt sf = 0; sf < nb_subfacet_to_double; ++sf) {
			UInt old_subfacet = sf_to_double(sf);
			nodes_to_double.push_back(conn_subfacet(old_subfacet));
			}

			doubleNodes(mesh, nodes_to_double, doubled_nodes);

			/// add new nodes in connectivity
			for (UInt sf = 0; sf < nb_subfacet_to_double; ++sf) {
			UInt new_subfacet = old_nb_subfacet + sf;
			UInt new_node = doubled_nodes(old_nb_doubled_nodes + sf, 1);

			conn_subfacet(new_subfacet) = new_node;
			}

			/// update facet and element connectivity
			Array<std::vector<Element>> & f_to_subfacet_double =
			mesh_facets.getData<std::vector<Element>>("facets_to_subfacet_double",
			type_subfacet, gt_subfacet);

			Array<std::vector<Element>> & el_to_subfacet_double =
			mesh_facets.getData<std::vector<Element>>(
			"elements_to_subfacet_double", type_subfacet, gt_subfacet);

			Array<std::vector<Element>> * sf_to_subfacet_double = NULL;

			if (spatial_dimension == 3)
			sf_to_subfacet_double = &mesh_facets.getData<std::vector<Element>>(
			"subfacets_to_subsubfacet_double", type_subfacet, gt_subfacet);

			for (UInt sf = 0; sf < nb_subfacet_to_double; ++sf) {
			UInt old_node = doubled_nodes(old_nb_doubled_nodes + sf, 0);
			UInt new_node = doubled_nodes(old_nb_doubled_nodes + sf, 1);

			updateElementalConnectivity(mesh, old_node, new_node,
			el_to_subfacet_double(sf),
			&f_to_subfacet_double(sf));

			updateElementalConnectivity(mesh_facets, old_node, new_node,
			f_to_subfacet_double(sf));

			if (spatial_dimension == 3)
			updateElementalConnectivity(mesh_facets, old_node, new_node,
			(*sf_to_subfacet_double)(sf));
			}

			if (spatial_dimension == 2) {
			updateSubfacetToFacet(mesh_facets, type_subfacet, gt_subfacet, true);
			updateFacetToSubfacet(mesh_facets, type_subfacet, gt_subfacet, true);
			} else if (spatial_dimension == 3) {
			updateSubfacetToFacet(mesh_facets, type_subfacet, gt_subfacet, false);
			updateFacetToSubfacet(mesh_facets, type_subfacet, gt_subfacet, false);
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::flipFacets(
			Mesh & mesh_facets, const ElementTypeMapArray<UInt> & global_connectivity,
			GhostType gt_facet) {
			AKANTU_DEBUG_IN();

			UInt spatial_dimension = mesh_facets.getSpatialDimension();

			/// get global connectivity for local mesh
			ElementTypeMapArray<UInt> global_connectivity_tmp("global_connectivity_tmp",
			mesh_facets.getID(),
			mesh_facets.getMemoryID());

			mesh_facets.initElementTypeMapArray(global_connectivity_tmp, 1,
			spatial_dimension - 1, gt_facet, true,
			_ek_regular, true);

			mesh_facets.getGlobalConnectivity(global_connectivity_tmp,
			spatial_dimension - 1, gt_facet);

			Mesh::type_iterator it =
			mesh_facets.firstType(spatial_dimension - 1, gt_facet);
			Mesh::type_iterator end =
			mesh_facets.lastType(spatial_dimension - 1, gt_facet);

			/// loop on every facet
			for (; it != end; ++it) {
			ElementType type_facet = *it;

			Array<UInt> & connectivity =
			mesh_facets.getConnectivity(type_facet, gt_facet);
			const Array<UInt> & g_connectivity =
			global_connectivity(type_facet, gt_facet);

			Array<std::vector<Element>> & el_to_f =
			mesh_facets.getElementToSubelement(type_facet, gt_facet);
			Array<Element> & subfacet_to_facet =
			mesh_facets.getSubelementToElement(type_facet, gt_facet);

			UInt nb_subfacet_per_facet = subfacet_to_facet.getNbComponent();
			UInt nb_nodes_per_facet = connectivity.getNbComponent();
			UInt nb_facet = connectivity.getSize();

			UInt nb_nodes_per_P1_facet =
			Mesh::getNbNodesPerElement(Mesh::getP1ElementType(type_facet));

			Array<UInt> & global_conn_tmp =
			global_connectivity_tmp(type_facet, gt_facet);

			Array<UInt>::iterator<Vector<UInt>> conn_it =
			connectivity.begin(nb_nodes_per_facet);
			Array<UInt>::iterator<Vector<UInt>> gconn_tmp_it =
			global_conn_tmp.begin(nb_nodes_per_facet);
			Array<UInt>::const_iterator<Vector<UInt>> conn_glob_it =
			g_connectivity.begin(nb_nodes_per_facet);
			Array<Element>::iterator<Vector<Element>> subf_to_f =
			subfacet_to_facet.begin(nb_subfacet_per_facet);

			UInt * conn_tmp_pointer = new UInt[nb_nodes_per_facet];
			Vector<UInt> conn_tmp(conn_tmp_pointer, nb_nodes_per_facet);

			Element el_tmp;
			Element * subf_tmp_pointer = new Element[nb_subfacet_per_facet];
			Vector<Element> subf_tmp(subf_tmp_pointer, nb_subfacet_per_facet);

			for (UInt f = 0; f < nb_facet;
			++f, ++conn_it, ++gconn_tmp_it, ++subf_to_f, ++conn_glob_it) {

			Vector<UInt> & gconn_tmp = *gconn_tmp_it;
			const Vector<UInt> & conn_glob = *conn_glob_it;
			Vector<UInt> & conn_local = *conn_it;

			/// skip facet if connectivities are the same
			if (gconn_tmp == conn_glob)
			continue;

			/// re-arrange connectivity
			conn_tmp = conn_local;

			UInt * begin = conn_glob.storage();
			UInt * end = conn_glob.storage() + nb_nodes_per_facet;

			for (UInt n = 0; n < nb_nodes_per_facet; ++n) {

			UInt * new_node = std::find(begin, end, gconn_tmp(n));
			AKANTU_DEBUG_ASSERT(new_node != end, "Node not found");

			UInt new_position = new_node - begin;

			conn_local(new_position) = conn_tmp(n);
			}

			/// if 3D, check if facets are just rotated
			if (spatial_dimension == 3) {
			/// find first node
			UInt * new_node = std::find(begin, end, gconn_tmp(0));
			AKANTU_DEBUG_ASSERT(new_node != end, "Node not found");

			UInt new_position = new_node - begin;
			UInt n = 1;

			/// count how many nodes in the received connectivity follow
			/// the same order of those in the local connectivity
			for (; n < nb_nodes_per_P1_facet &&
			gconn_tmp(n) ==
			conn_glob((new_position + 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
			el_tmp = el_to_f(f)[0];
			el_to_f(f)[0] = el_to_f(f)[1];
			el_to_f(f)[1] = el_tmp;

			subf_tmp = (*subf_to_f);
			(*subf_to_f)(0) = subf_tmp(1);
			(*subf_to_f)(1) = subf_tmp(0);
			}

			delete[] subf_tmp_pointer;
			delete[] conn_tmp_pointer;
			}

			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(),
			mesh.getMemoryID());
			mesh.initElementTypeMapArray(barycenters, spatial_dimension, _all_dimensions);

			for (ghost_type_t::iterator gt = ghost_type_t::begin();
			gt != ghost_type_t::end(); ++gt) {
			Mesh::type_iterator it = mesh.firstType(_all_dimensions, *gt);
			Mesh::type_iterator end = mesh.lastType(_all_dimensions, *gt);
			for (; it != end; ++it) {
			UInt nb_element = mesh.getNbElement(it, gt);
			Array<Real> & barycenters_arr = barycenters(it, gt);
			barycenters_arr.resize(nb_element);
			Array<Real>::vector_iterator bary =
			barycenters_arr.begin(spatial_dimension);
			Array<Real>::vector_iterator bary_end =
			barycenters_arr.end(spatial_dimension);

			for (UInt el = 0; bary != bary_end; ++bary, ++el) {
			mesh.getBarycenter(el, it, bary->storage(), gt);
			}
			}
			}

			MeshAccessor mesh_accessor(mesh);
			for (Int sp(spatial_dimension); sp >= 1; --sp) {
			if (mesh.getNbElement(sp) == 0)
			continue;

			for (ghost_type_t::iterator git = ghost_type_t::begin();
			git != ghost_type_t::end(); ++git) {
			Mesh::type_iterator tit = mesh.firstType(sp, *git);
			Mesh::type_iterator tend = mesh.lastType(sp, *git);
			for (; tit != tend; ++tit) {
			mesh_accessor.getSubelementToElement(tit, git)
			.resize(mesh.getNbElement(tit, git));
			mesh_accessor.getSubelementToElement(tit, git).clear();
			}

			tit = mesh.firstType(sp - 1, *git);
			tend = mesh.lastType(sp - 1, *git);
			for (; tit != tend; ++tit) {
			mesh_accessor.getElementToSubelement(tit, git)
			.resize(mesh.getNbElement(tit, git));
			mesh.getElementToSubelement(tit, git).clear();
			}
			}

			CSR<Element> nodes_to_elements;
			buildNode2Elements(mesh, nodes_to_elements, sp);

			Element facet_element;

			for (ghost_type_t::iterator git = ghost_type_t::begin();
			git != ghost_type_t::end(); ++git) {
			Mesh::type_iterator tit = mesh.firstType(sp - 1, *git);
			Mesh::type_iterator tend = mesh.lastType(sp - 1, *git);

			facet_element.ghost_type = *git;
			for (; tit != tend; ++tit) {
			facet_element.type = *tit;

			Array<std::vector<Element>> & element_to_subelement =
			mesh.getElementToSubelement(tit, git);

			const Array<UInt> & connectivity = mesh.getConnectivity(tit, git);

			Array<UInt>::const_iterator<Vector<UInt>> fit =
			connectivity.begin(mesh.getNbNodesPerElement(*tit));
			Array<UInt>::const_iterator<Vector<UInt>> fend =
			connectivity.end(mesh.getNbNodesPerElement(*tit));

			UInt fid = 0;
			for (; fit != fend; ++fit, ++fid) {
			const Vector<UInt> & facet = *fit;
			facet_element.element = fid;
			std::map<Element, UInt> element_seen_counter;
			UInt nb_nodes_per_facet =
			mesh.getNbNodesPerElement(Mesh::getP1ElementType(*tit));
			for (UInt n(0); n < nb_nodes_per_facet; ++n) {
			CSR<Element>::iterator eit = nodes_to_elements.begin(facet(n));
			CSR<Element>::iterator eend = nodes_to_elements.end(facet(n));
			for (; eit != eend; ++eit) {
			Element & elem = *eit;
			std::map<Element, UInt>::iterator cit =
			element_seen_counter.find(elem);
			if (cit != element_seen_counter.end()) {
			cit->second++;
			} else {
			element_seen_counter[elem] = 1;
			}
			}
			}

			std::vector<Element> connected_elements;
			std::map<Element, UInt>::iterator cit = element_seen_counter.begin();
			std::map<Element, UInt>::iterator cend = element_seen_counter.end();
			for (; cit != cend; ++cit) {
			if (cit->second == nb_nodes_per_facet)
			connected_elements.push_back(cit->first);
			}

			std::vector<Element>::iterator ceit = connected_elements.begin();
			std::vector<Element>::iterator ceend = connected_elements.end();
			for (; ceit != ceend; ++ceit)
			element_to_subelement(fid).push_back(*ceit);

			for (UInt ce = 0; ce < connected_elements.size(); ++ce) {
			Element & elem = connected_elements[ce];
			Array<Element> & subelement_to_element =
			mesh_accessor.getSubelementToElement(elem.type,
			elem.ghost_type);

			UInt f(0);
			for (; f < mesh.getNbFacetsPerElement(elem.type) &&
			subelement_to_element(elem.element, f) != ElementNull;
			++f)
			;

			AKANTU_DEBUG_ASSERT(
			f < mesh.getNbFacetsPerElement(elem.type),
			"The element " << elem << " seems to have too many facets!! ("
			<< f << " < "
			<< mesh.getNbFacetsPerElement(elem.type) << ")");

			subelement_to_element(elem.element, f) = facet_element;
			}
			}
			}
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <bool third_dim_points>
			bool MeshUtils::findElementsAroundSubfacet(
			const Mesh & mesh, const Mesh & mesh_facets,
			const Element & starting_element, const Element & end_facet,
			const Vector<UInt> & subfacet_connectivity,
			std::vector<Element> & elem_list, std::vector<Element> & facet_list,
			std::vector<Element> * subfacet_list) {
			AKANTU_DEBUG_IN();

			/// preallocated stuff before starting
			bool facet_matched = false;

			elem_list.clear();
			facet_list.clear();

			if (third_dim_points)
			subfacet_list->clear();

			elem_list.push_back(starting_element);

			const Array<UInt> * facet_connectivity = NULL;
			const Array<UInt> * sf_connectivity = NULL;
			const Array<Element> * facet_to_element = NULL;
			const Array<Element> * subfacet_to_facet = NULL;

			ElementType current_type = _not_defined;
			GhostType current_ghost_type = _casper;

			ElementType current_facet_type = _not_defined;
			GhostType current_facet_ghost_type = _casper;

			ElementType current_subfacet_type = _not_defined;
			GhostType current_subfacet_ghost_type = _casper;

			const Array<std::vector<Element>> * element_to_facet = NULL;

			const Element * opposing_el = NULL;

			std::queue<Element> elements_to_check;
			elements_to_check.push(starting_element);

			/// keep going until there are elements to check
			while (!elements_to_check.empty()) {

			/// check current element
			Element & current_el = elements_to_check.front();

			if (current_el.type != current_type \|\|
			current_el.ghost_type != current_ghost_type) {

			current_type = current_el.type;
			current_ghost_type = current_el.ghost_type;

			facet_to_element =
			&mesh_facets.getSubelementToElement(current_type, current_ghost_type);
			}

			/// loop over each facet of the element
			for (UInt f = 0; f < facet_to_element->getNbComponent(); ++f) {

			const Element & current_facet =
			(*facet_to_element)(current_el.element, f);

			if (current_facet == ElementNull)
			continue;

			if (current_facet_type != current_facet.type \|\|
			current_facet_ghost_type != current_facet.ghost_type) {

			current_facet_type = current_facet.type;
			current_facet_ghost_type = current_facet.ghost_type;

			element_to_facet = &mesh_facets.getElementToSubelement(
			current_facet_type, current_facet_ghost_type);
			facet_connectivity = &mesh_facets.getConnectivity(
			current_facet_type, current_facet_ghost_type);

			if (third_dim_points)
			subfacet_to_facet = &mesh_facets.getSubelementToElement(
			current_facet_type, current_facet_ghost_type);
			}

			/// check if end facet is reached
			if (current_facet == end_facet)
			facet_matched = true;

			/// add this facet if not already passed
			if (std::find(facet_list.begin(), facet_list.end(), current_facet) ==
			facet_list.end() &&
			hasElement(*facet_connectivity, current_facet,
			subfacet_connectivity)) {
			facet_list.push_back(current_facet);

			if (third_dim_points) {
			/// check subfacets
			for (UInt sf = 0; sf < subfacet_to_facet->getNbComponent(); ++sf) {
			const Element & current_subfacet =
			(*subfacet_to_facet)(current_facet.element, sf);

			if (current_subfacet == ElementNull)
			continue;

			if (current_subfacet_type != current_subfacet.type \|\|
			current_subfacet_ghost_type != current_subfacet.ghost_type) {
			current_subfacet_type = current_subfacet.type;
			current_subfacet_ghost_type = current_subfacet.ghost_type;

			sf_connectivity = &mesh_facets.getConnectivity(
			current_subfacet_type, current_subfacet_ghost_type);
			}

			if (std::find(subfacet_list->begin(), subfacet_list->end(),
			current_subfacet) == subfacet_list->end() &&
			hasElement(*sf_connectivity, current_subfacet,
			subfacet_connectivity))
			subfacet_list->push_back(current_subfacet);
			}
			}
			} else
			continue;

			/// consider opposing element
			if ((*element_to_facet)(current_facet.element)[0] == current_el)
			opposing_el = &(*element_to_facet)(current_facet.element)[1];
			else
			opposing_el = &(*element_to_facet)(current_facet.element)[0];

			/// skip null elements since they are on a boundary
			if (*opposing_el == ElementNull)
			continue;

			/// skip this element if already added
			if (std::find(elem_list.begin(), elem_list.end(), *opposing_el) !=
			elem_list.end())
			continue;

			/// only regular elements have to be checked
			if (opposing_el->kind == _ek_regular)
			elements_to_check.push(*opposing_el);

			elem_list.push_back(*opposing_el);

			#ifndef AKANTU_NDEBUG
			const Array<UInt> & conn_elem =
			mesh.getConnectivity(opposing_el->type, opposing_el->ghost_type);

			AKANTU_DEBUG_ASSERT(
			hasElement(conn_elem, *opposing_el, subfacet_connectivity),
			"Subfacet doesn't belong to this element");
			#endif
			}

			/// erased checked element from the list
			elements_to_check.pop();
			}

			AKANTU_DEBUG_OUT();
			return facet_matched;
			}

			/* -------------------------------------------------------------------------- */
			void MeshUtils::buildSegmentToNodeType(const Mesh & mesh, Mesh & mesh_facets) {
			buildAllFacets(mesh, mesh_facets, 1);

			UInt spatial_dimension = mesh.getSpatialDimension();

			const ElementTypeMapArray<UInt> & element_to_rank =
			mesh.getElementSynchronizer().getPrankToElement();
			Int local_rank = StaticCommunicator::getStaticCommunicator().whoAmI();

			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(1, ghost_type);
			Mesh::type_iterator end = mesh_facets.lastType(1, ghost_type);
			for (; it != end; ++it) {
			ElementType type = *it;
			UInt nb_segments = mesh_facets.getNbElement(type, ghost_type);

			// allocate the data
			Array<Int> & segment_to_nodetype = *(mesh_facets.getDataPointer<Int>(
			"segment_to_nodetype", type, ghost_type));

			std::set<Element> connected_elements;
			const Array<std::vector<Element>> & segment_to_2Delement =
			mesh_facets.getElementToSubelement(type, ghost_type);

			// loop over segments
			for (UInt s = 0; s < nb_segments; ++s) {

			// determine the elements connected to the segment
			connected_elements.clear();
			const std::vector<Element> & twoD_elements = segment_to_2Delement(s);

			if (spatial_dimension == 2) {
			// if 2D just take the elements connected to the segments
			connected_elements.insert(twoD_elements.begin(), twoD_elements.end());
			} else if (spatial_dimension == 3) {
			// if 3D a second loop is needed to get to the 3D elements
			std::vector<Element>::const_iterator facet = twoD_elements.begin();

			for (; facet != twoD_elements.end(); ++facet) {
			const std::vector<Element> & threeD_elements =
			mesh_facets.getElementToSubelement(
			facet->type, facet->ghost_type)(facet->element);
			connected_elements.insert(threeD_elements.begin(),
			threeD_elements.end());
			}
			}

			// get the minimum processor rank associated to the connected
			// elements and verify if ghost and not ghost elements are
			// found
			Int minimum_rank = std::numeric_limits<Int>::max();

			// two booleans saying if not ghost and ghost elements are found in the
			// loop
			bool ghost_found[2];
			ghost_found[0] = false;
			ghost_found[1] = false;

			std::set<Element>::iterator connected_elements_it =
			connected_elements.begin();

			for (; connected_elements_it != connected_elements.end();
			++connected_elements_it) {
			if (*connected_elements_it == ElementNull)
			continue;
			ghost_found[connected_elements_it->ghost_type] = true;
			const Array<UInt> & el_to_rank_array = element_to_rank(
			connected_elements_it->type, connected_elements_it->ghost_type);
			minimum_rank =
			std::min(minimum_rank,
			Int(el_to_rank_array(connected_elements_it->element)));
			}

			// if no ghost elements are found the segment is local
			if (!ghost_found[1])
			segment_to_nodetype(s) = -1;
			// if no not ghost elements are found the segment is pure ghost
			else if (!ghost_found[0])
			segment_to_nodetype(s) = -3;
			// if the minimum rank is equal to the local rank, the segment is master
			else if (local_rank == minimum_rank)
			segment_to_nodetype(s) = -2;
			// if the minimum rank is less than the local rank, the segment is slave
			else if (local_rank > minimum_rank)
			segment_to_nodetype(s) = minimum_rank;
			else
			AKANTU_DEBUG_ERROR("The local rank cannot be smaller than the "
			"minimum rank if both ghost and not ghost "
			"elements are found");
			}
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			UInt MeshUtils::updateLocalMasterGlobalConnectivity(Mesh & mesh,
			UInt local_nb_new_nodes) {
			StaticCommunicator & comm = StaticCommunicator::getStaticCommunicator();
			Int rank = comm.whoAmI();
			Int nb_proc = comm.getNbProc();
			if (nb_proc == 1)
			return local_nb_new_nodes;

			/// resize global ids array
			Array<UInt> & nodes_global_ids = mesh.getGlobalNodesIds();
			UInt old_nb_nodes = mesh.getNbNodes() - local_nb_new_nodes;

			nodes_global_ids.resize(mesh.getNbNodes());

			/// compute the number of global nodes based on the number of old nodes
			Vector<UInt> old_local_master_nodes(nb_proc);
			for (UInt n = 0; n < old_nb_nodes; ++n)
			if (mesh.isLocalOrMasterNode(n))
			++old_local_master_nodes(rank);
			comm.allGather(old_local_master_nodes);
			UInt old_global_nodes =
			std::accumulate(old_local_master_nodes.storage(),
			old_local_master_nodes.storage() + nb_proc, 0);

			/// compute amount of local or master doubled nodes
			Vector<UInt> local_master_nodes(nb_proc);
			for (UInt n = old_nb_nodes; n < mesh.getNbNodes(); ++n)
			if (mesh.isLocalOrMasterNode(n))
			++local_master_nodes(rank);

			comm.allGather(local_master_nodes);

			/// update global number of nodes
			UInt total_nb_new_nodes = std::accumulate(
			local_master_nodes.storage(), local_master_nodes.storage() + nb_proc, 0);

			if (total_nb_new_nodes == 0)
			return 0;

			/// set global ids of local and master nodes
			UInt starting_index =
			std::accumulate(local_master_nodes.storage(),
			local_master_nodes.storage() + rank, old_global_nodes);

			for (UInt n = old_nb_nodes; n < mesh.getNbNodes(); ++n) {
			if (mesh.isLocalOrMasterNode(n)) {
			nodes_global_ids(n) = starting_index;
			++starting_index;
			}
			}

			MeshAccessor mesh_accessor(mesh);
			mesh_accessor.setNbGlobalNodes(old_global_nodes + total_nb_new_nodes);
			return total_nb_new_nodes;
			}

			/* -------------------------------------------------------------------------- */
			// Deactivating -Wunused-parameter
			#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-parameter"
			#endif

			/* -------------------------------------------------------------------------- */
			void MeshUtils::updateElementalConnectivity(
			Mesh & mesh, UInt old_node, UInt new_node,
			const std::vector<Element> & element_list,
			__attribute__((unused)) const std::vector<Element> * facet_list) {
			AKANTU_DEBUG_IN();

			ElementType el_type = _not_defined;
			GhostType gt_type = _casper;
			Array<UInt> * conn_elem = NULL;
			#if defined(AKANTU_COHESIVE_ELEMENT)
			const Array<Element> * cohesive_facets = NULL;
			#endif
			UInt nb_nodes_per_element = 0;
			UInt * n_update = NULL;

			for (UInt el = 0; el < element_list.size(); ++el) {
			const Element & elem = element_list[el];
			if (elem.type == _not_defined)
			continue;

			if (elem.type != el_type \|\| elem.ghost_type != gt_type) {
			el_type = elem.type;
			gt_type = elem.ghost_type;
			conn_elem = &mesh.getConnectivity(el_type, gt_type);
			nb_nodes_per_element = conn_elem->getNbComponent();
			#if defined(AKANTU_COHESIVE_ELEMENT)
			if (elem.kind == _ek_cohesive)
			cohesive_facets =
			&mesh.getMeshFacets().getSubelementToElement(el_type, gt_type);
			#endif
			}

			#if defined(AKANTU_COHESIVE_ELEMENT)
			if (elem.kind == _ek_cohesive) {

			AKANTU_DEBUG_ASSERT(
			facet_list != NULL,
			"Provide a facet list in order to update cohesive elements");

			/// loop over cohesive element's facets
			for (UInt f = 0, n = 0; f < 2; ++f, n += nb_nodes_per_element / 2) {
			const Element & facet = (*cohesive_facets)(elem.element, f);

			/// skip facets if not present in the list
			if (std::find(facet_list->begin(), facet_list->end(), facet) ==
			facet_list->end())
			continue;

			n_update = std::find(
			conn_elem->storage() + elem.element * nb_nodes_per_element + n,
			conn_elem->storage() + elem.element * nb_nodes_per_element + n +
			nb_nodes_per_element / 2,
			old_node);

			AKANTU_DEBUG_ASSERT(n_update !=
			conn_elem->storage() +
			elem.element * nb_nodes_per_element + n +
			nb_nodes_per_element / 2,
			"Node not found in current element");

			/// update connectivity
			*n_update = new_node;
			}
			} else {
			#endif
			n_update =
			std::find(conn_elem->storage() + elem.element * nb_nodes_per_element,
			conn_elem->storage() + elem.element * nb_nodes_per_element +
			nb_nodes_per_element,
			old_node);

			AKANTU_DEBUG_ASSERT(n_update != conn_elem->storage() +
			elem.element * nb_nodes_per_element +
			nb_nodes_per_element,
			"Node not found in current element");

			/// update connectivity
			*n_update = new_node;
			#if defined(AKANTU_COHESIVE_ELEMENT)
			}
			#endif
			}

			AKANTU_DEBUG_OUT();
			}

			// Reactivating -Wunused-parameter
			#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-parameter"
			#endif
			#endif
			/* -------------------------------------------------------------------------- */

			} // akantu

			// LocalWords: ElementType

rAKA/src/mesh_utils/mesh_utils.cc341103fd512efeatures/17-create-an…

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rAKA/src/mesh_utils/mesh_utils.cc
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