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dof_manager.cc
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			/**
			* @file dof_manager.cc
			*
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Tue Aug 18 2015
			* @date last modification: Sat Mar 06 2021
			*
			* @brief Implementation of the common parts of the DOFManagers
			*
			*
			* @section LICENSE
			*
			* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "dof_manager.hh"
			#include "communicator.hh"
			#include "mesh.hh"
			#include "mesh_utils.hh"
			#include "node_group.hh"
			#include "node_synchronizer.hh"
			#include "non_linear_solver.hh"
			#include "periodic_node_synchronizer.hh"
			#include "time_step_solver.hh"
			/* -------------------------------------------------------------------------- */
			#include <memory>
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			DOFManager::DOFManager(const ID & id)
			: id(id), dofs_flag(0, 1, std::string(id + ":dofs_type")),
			global_equation_number(0, 1, "global_equation_number"),
			communicator(Communicator::getStaticCommunicator()) {}

			/* -------------------------------------------------------------------------- */
			DOFManager::DOFManager(Mesh & mesh, const ID & id)
			: id(id), mesh(&mesh), dofs_flag(0, 1, std::string(id + ":dofs_type")),
			global_equation_number(0, 1, "global_equation_number"),
			communicator(mesh.getCommunicator()) {
			this->mesh->registerEventHandler(*this, _ehp_dof_manager);
			}

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

			/* -------------------------------------------------------------------------- */
			std::vector<ID> DOFManager::getDOFIDs() const {
			std::vector<ID> keys;
			for (const auto & dof_data : this->dofs) {
			keys.push_back(dof_data.first);
			}

			return keys;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleElementalArrayLocalArray(
			const Array<Real> & elementary_vect, Array<Real> & array_assembeled,
			ElementType type, GhostType ghost_type, Real scale_factor,
			const Array<UInt> & filter_elements) {
			AKANTU_DEBUG_IN();

			UInt nb_element;
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_degree_of_freedom =
			elementary_vect.getNbComponent() / nb_nodes_per_element;

			UInt * filter_it = nullptr;
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			filter_it = filter_elements.storage();
			} else {
			nb_element = this->mesh->getNbElement(type, ghost_type);
			}

			AKANTU_DEBUG_ASSERT(elementary_vect.size() == nb_element,
			"The vector elementary_vect("
			<< elementary_vect.getID()
			<< ") has not the good size.");

			const Array<UInt> & connectivity =
			this->mesh->getConnectivity(type, ghost_type);

			Array<Real>::const_matrix_iterator elem_it =
			elementary_vect.begin(nb_degree_of_freedom, nb_nodes_per_element);

			for (UInt el = 0; el < nb_element; ++el, ++elem_it) {
			UInt element = el;
			if (filter_it != nullptr) {
			// conn_it = conn_begin + *filter_it;
			element = *filter_it;
			}

			// const Vector<UInt> & conn = *conn_it;
			const Matrix<Real> & elemental_val = *elem_it;
			for (UInt n = 0; n < nb_nodes_per_element; ++n) {
			UInt offset_node = connectivity(element, n) * nb_degree_of_freedom;
			Vector<Real> assemble(array_assembeled.storage() + offset_node,
			nb_degree_of_freedom);
			Vector<Real> elem_val = elemental_val(n);
			assemble.aXplusY(elem_val, scale_factor);
			}

			if (filter_it != nullptr) {
			++filter_it;
			}
			// else
			// ++conn_it;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleElementalArrayToResidual(
			const ID & dof_id, const Array<Real> & elementary_vect, ElementType type,
			GhostType ghost_type, Real scale_factor,
			const Array<UInt> & filter_elements) {
			AKANTU_DEBUG_IN();

			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_degree_of_freedom =
			elementary_vect.getNbComponent() / nb_nodes_per_element;
			Array<Real> array_localy_assembeled(this->mesh->getNbNodes(),
			nb_degree_of_freedom);

			array_localy_assembeled.zero();

			this->assembleElementalArrayLocalArray(
			elementary_vect, array_localy_assembeled, type, ghost_type, scale_factor,
			filter_elements);

			this->assembleToResidual(dof_id, array_localy_assembeled, 1);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleElementalArrayToLumpedMatrix(
			const ID & dof_id, const Array<Real> & elementary_vect,
			const ID & lumped_mtx, ElementType type, GhostType ghost_type,
			Real scale_factor, const Array<UInt> & filter_elements) {
			AKANTU_DEBUG_IN();

			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_degree_of_freedom =
			elementary_vect.getNbComponent() / nb_nodes_per_element;
			Array<Real> array_localy_assembeled(this->mesh->getNbNodes(),
			nb_degree_of_freedom);

			array_localy_assembeled.zero();

			this->assembleElementalArrayLocalArray(
			elementary_vect, array_localy_assembeled, type, ghost_type, scale_factor,
			filter_elements);

			this->assembleToLumpedMatrix(dof_id, array_localy_assembeled, lumped_mtx, 1);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleMatMulDOFsToResidual(const ID & A_id,
			Real scale_factor) {
			for (auto & pair : this->dofs) {
			const auto & dof_id = pair.first;
			auto & dof_data = *pair.second;

			this->assembleMatMulVectToResidual(dof_id, A_id, *dof_data.dof,
			scale_factor);
			}
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::splitSolutionPerDOFs() {
			for (auto && data : this->dofs) {
			auto & dof_data = *data.second;
			dof_data.solution.resize(dof_data.dof->size() *
			dof_data.dof->getNbComponent());
			this->getSolutionPerDOFs(data.first, dof_data.solution);
			}
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::getSolutionPerDOFs(const ID & dof_id,
			Array<Real> & solution_array) {
			AKANTU_DEBUG_IN();
			this->getArrayPerDOFs(dof_id, this->getSolution(), solution_array);
			AKANTU_DEBUG_OUT();
			}
			/* -------------------------------------------------------------------------- */
			void DOFManager::getLumpedMatrixPerDOFs(const ID & dof_id,
			const ID & lumped_mtx,
			Array<Real> & lumped) {
			AKANTU_DEBUG_IN();
			this->getArrayPerDOFs(dof_id, this->getLumpedMatrix(lumped_mtx), lumped);
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleToResidual(const ID & dof_id,
			Array<Real> & array_to_assemble,
			Real scale_factor) {
			AKANTU_DEBUG_IN();

			// this->makeConsistentForPeriodicity(dof_id, array_to_assemble);
			this->assembleToGlobalArray(dof_id, array_to_assemble, this->getResidual(),
			scale_factor);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleToLumpedMatrix(const ID & dof_id,
			Array<Real> & array_to_assemble,
			const ID & lumped_mtx,
			Real scale_factor) {
			AKANTU_DEBUG_IN();

			// this->makeConsistentForPeriodicity(dof_id, array_to_assemble);
			auto & lumped = this->getLumpedMatrix(lumped_mtx);
			this->assembleToGlobalArray(dof_id, array_to_assemble, lumped, scale_factor);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/* -------------------------------------------------------------------------- */
			DOFManager::DOFData::DOFData(const ID & dof_id)
			: support_type(_dst_generic), group_support("__mesh__"),
			solution(0, 1, dof_id + ":solution"),
			local_equation_number(0, 1, dof_id + ":local_equation_number"),
			associated_nodes(0, 1, dof_id + "associated_nodes") {}

			/* -------------------------------------------------------------------------- */
			DOFManager::DOFData::~DOFData() = default;

			/* -------------------------------------------------------------------------- */
			template <typename Func>
			auto DOFManager::countDOFsForNodes(const DOFData & dof_data, UInt nb_nodes,
			Func && getNode) {
			auto nb_local_dofs = nb_nodes;
			decltype(nb_local_dofs) nb_pure_local = 0;
			for (auto n : arange(nb_nodes)) {
			UInt node = getNode(n);

			// http://www.open-std.org/jtc1/sc22/open/n2356/conv.html
			// bool are by convention casted to 0 and 1 when promoted to int
			nb_pure_local += this->mesh->isLocalOrMasterNode(node);
			nb_local_dofs -= this->mesh->isPeriodicSlave(node);
			}

			const auto & dofs_array = *dof_data.dof;
			nb_pure_local *= dofs_array.getNbComponent();
			nb_local_dofs *= dofs_array.getNbComponent();
			return std::make_pair(nb_local_dofs, nb_pure_local);
			}

			/* -------------------------------------------------------------------------- */
			auto DOFManager::getNewDOFDataInternal(const ID & dof_id) -> DOFData & {
			auto it = this->dofs.find(dof_id);
			if (it != this->dofs.end()) {
			AKANTU_EXCEPTION("This dof array has already been registered");
			}

			std::unique_ptr<DOFData> dof_data_ptr = this->getNewDOFData(dof_id);
			DOFData & dof_data = *dof_data_ptr;

			this->dofs[dof_id] = std::move(dof_data_ptr);
			return dof_data;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
			const DOFSupportType & support_type) {
			auto & dofs_storage = this->getNewDOFDataInternal(dof_id);
			dofs_storage.support_type = support_type;

			this->registerDOFsInternal(dof_id, dofs_array);

			resizeGlobalArrays();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerDOFs(const ID & dof_id, Array<Real> & dofs_array,
			const ID & support_group) {
			auto & dofs_storage = this->getNewDOFDataInternal(dof_id);
			dofs_storage.support_type = _dst_nodal;
			dofs_storage.group_support = support_group;

			this->registerDOFsInternal(dof_id, dofs_array);

			resizeGlobalArrays();
			}

			/* -------------------------------------------------------------------------- */
			std::tuple<UInt, UInt, UInt>
			DOFManager::registerDOFsInternal(const ID & dof_id, Array<Real> & dofs_array) {
			DOFData & dof_data = this->getDOFData(dof_id);
			dof_data.dof = &dofs_array;

			UInt nb_local_dofs = 0;
			UInt nb_pure_local = 0;

			const auto & support_type = dof_data.support_type;

			switch (support_type) {
			case _dst_nodal: {
			const auto & group = dof_data.group_support;

			std::function<UInt(UInt)> getNode;
			if (group == "__mesh__") {
			AKANTU_DEBUG_ASSERT(
			dofs_array.size() == this->mesh->getNbNodes(),
			"The array of dof is too short to be associated to nodes.");

			std::tie(nb_local_dofs, nb_pure_local) = countDOFsForNodes(
			dof_data, this->mesh->getNbNodes(), [](auto && n) { return n; });
			} else {
			const auto & node_group =
			this->mesh->getElementGroup(group).getNodeGroup().getNodes();

			AKANTU_DEBUG_ASSERT(
			dofs_array.size() == node_group.size(),
			"The array of dof is too shot to be associated to nodes.");

			std::tie(nb_local_dofs, nb_pure_local) =
			countDOFsForNodes(dof_data, node_group.size(),
			[&node_group](auto && n) { return node_group(n); });
			}

			break;
			}
			case _dst_generic: {
			nb_local_dofs = nb_pure_local =
			dofs_array.size() * dofs_array.getNbComponent();
			break;
			}
			default: {
			AKANTU_EXCEPTION("This type of dofs is not handled yet.");
			}
			}

			dof_data.local_nb_dofs = nb_local_dofs;
			dof_data.pure_local_nb_dofs = nb_pure_local;
			dof_data.ghosts_nb_dofs = nb_local_dofs - nb_pure_local;

			this->pure_local_system_size += nb_pure_local;
			this->local_system_size += nb_local_dofs;

			auto nb_total_pure_local = nb_pure_local;
			communicator.allReduce(nb_total_pure_local, SynchronizerOperation::_sum);

			this->system_size += nb_total_pure_local;

			// updating the dofs data after counting is finished
			switch (support_type) {
			case _dst_nodal: {
			const auto & group = dof_data.group_support;
			if (group != "__mesh__") {
			auto & support_nodes =
			this->mesh->getElementGroup(group).getNodeGroup().getNodes();
			this->updateDOFsData(
			dof_data, nb_local_dofs, nb_pure_local, support_nodes.size(),
			[&support_nodes](UInt node) -> UInt { return support_nodes[node]; });
			} else {
			this->updateDOFsData(dof_data, nb_local_dofs, nb_pure_local,
			mesh->getNbNodes(),
			[](UInt node) -> UInt { return node; });
			}
			break;
			}
			case _dst_generic: {
			this->updateDOFsData(dof_data, nb_local_dofs, nb_pure_local);
			break;
			}
			}

			return std::make_tuple(nb_local_dofs, nb_pure_local, nb_total_pure_local);
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerDOFsPrevious(const ID & dof_id, Array<Real> & array) {
			DOFData & dof = this->getDOFData(dof_id);

			if (dof.previous != nullptr) {
			AKANTU_EXCEPTION("The previous dofs array for "
			<< dof_id << " has already been registered");
			}

			dof.previous = &array;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerDOFsIncrement(const ID & dof_id, Array<Real> & array) {
			DOFData & dof = this->getDOFData(dof_id);

			if (dof.increment != nullptr) {
			AKANTU_EXCEPTION("The dofs increment array for "
			<< dof_id << " has already been registered");
			}

			dof.increment = &array;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerDOFsDerivative(const ID & dof_id, UInt order,
			Array<Real> & dofs_derivative) {
			DOFData & dof = this->getDOFData(dof_id);
			std::vector<Array<Real> *> & derivatives = dof.dof_derivatives;

			if (derivatives.size() < order) {
			derivatives.resize(order, nullptr);
			} else {
			if (derivatives[order - 1] != nullptr) {
			AKANTU_EXCEPTION("The dof derivatives of order "
			<< order << " already been registered for this dof ("
			<< dof_id << ")");
			}
			}

			derivatives[order - 1] = &dofs_derivative;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::registerBlockedDOFs(const ID & dof_id,
			Array<bool> & blocked_dofs) {
			DOFData & dof = this->getDOFData(dof_id);

			if (dof.blocked_dofs != nullptr) {
			AKANTU_EXCEPTION("The blocked dofs array for "
			<< dof_id << " has already been registered");
			}

			dof.blocked_dofs = &blocked_dofs;
			}

			/* -------------------------------------------------------------------------- */
			SparseMatrix &
			DOFManager::registerSparseMatrix(const ID & matrix_id,
			std::unique_ptr<SparseMatrix> & matrix) {
			auto it = this->matrices.find(matrix_id);
			if (it != this->matrices.end()) {
			AKANTU_EXCEPTION("The matrix " << matrix_id << " already exists in "
			<< this->id);
			}

			auto & ret = *matrix;
			this->matrices[matrix_id] = std::move(matrix);
			return ret;
			}

			/* -------------------------------------------------------------------------- */
			/// Get an instance of a new SparseMatrix
			SolverVector &
			DOFManager::registerLumpedMatrix(const ID & matrix_id,
			std::unique_ptr<SolverVector> & matrix) {
			auto it = this->lumped_matrices.find(matrix_id);
			if (it != this->lumped_matrices.end()) {
			AKANTU_EXCEPTION("The lumped matrix " << matrix_id << " already exists in "
			<< this->id);
			}

			auto & ret = *matrix;
			this->lumped_matrices[matrix_id] = std::move(matrix);
			ret.resize();
			return ret;
			}

			/* -------------------------------------------------------------------------- */
			NonLinearSolver & DOFManager::registerNonLinearSolver(
			const ID & non_linear_solver_id,
			std::unique_ptr<NonLinearSolver> & non_linear_solver) {
			NonLinearSolversMap::const_iterator it =
			this->non_linear_solvers.find(non_linear_solver_id);
			if (it != this->non_linear_solvers.end()) {
			AKANTU_EXCEPTION("The non linear solver " << non_linear_solver_id
			<< " already exists in "
			<< this->id);
			}

			NonLinearSolver & ret = *non_linear_solver;
			this->non_linear_solvers[non_linear_solver_id] = std::move(non_linear_solver);

			return ret;
			}

			/* -------------------------------------------------------------------------- */
			TimeStepSolver & DOFManager::registerTimeStepSolver(
			const ID & time_step_solver_id,
			std::unique_ptr<TimeStepSolver> & time_step_solver) {
			TimeStepSolversMap::const_iterator it =
			this->time_step_solvers.find(time_step_solver_id);
			if (it != this->time_step_solvers.end()) {
			AKANTU_EXCEPTION("The non linear solver " << time_step_solver_id
			<< " already exists in "
			<< this->id);
			}

			TimeStepSolver & ret = *time_step_solver;
			this->time_step_solvers[time_step_solver_id] = std::move(time_step_solver);
			return ret;
			}

			/* -------------------------------------------------------------------------- */
			SparseMatrix & DOFManager::getMatrix(const ID & id) {
			ID matrix_id = this->id + ":mtx:" + id;
			SparseMatricesMap::const_iterator it = this->matrices.find(matrix_id);
			if (it == this->matrices.end()) {
			AKANTU_SILENT_EXCEPTION("The matrix " << matrix_id << " does not exists in "
			<< this->id);
			}

			return *(it->second);
			}

			/* -------------------------------------------------------------------------- */
			bool DOFManager::hasMatrix(const ID & id) const {
			ID mtx_id = this->id + ":mtx:" + id;
			auto it = this->matrices.find(mtx_id);
			return it != this->matrices.end();
			}

			/* -------------------------------------------------------------------------- */
			SolverVector & DOFManager::getLumpedMatrix(const ID & id) {
			ID matrix_id = this->id + ":lumped_mtx:" + id;
			LumpedMatricesMap::const_iterator it = this->lumped_matrices.find(matrix_id);
			if (it == this->lumped_matrices.end()) {
			AKANTU_SILENT_EXCEPTION("The lumped matrix "
			<< matrix_id << " does not exists in " << this->id);
			}

			return *(it->second);
			}

			/* -------------------------------------------------------------------------- */
			const SolverVector & DOFManager::getLumpedMatrix(const ID & id) const {
			ID matrix_id = this->id + ":lumped_mtx:" + id;
			auto it = this->lumped_matrices.find(matrix_id);
			if (it == this->lumped_matrices.end()) {
			AKANTU_SILENT_EXCEPTION("The lumped matrix "
			<< matrix_id << " does not exists in " << this->id);
			}

			return *(it->second);
			}

			/* -------------------------------------------------------------------------- */
			bool DOFManager::hasLumpedMatrix(const ID & id) const {
			ID mtx_id = this->id + ":lumped_mtx:" + id;
			auto it = this->lumped_matrices.find(mtx_id);
			return it != this->lumped_matrices.end();
			}

			/* -------------------------------------------------------------------------- */
			NonLinearSolver & DOFManager::getNonLinearSolver(const ID & id) {
			ID non_linear_solver_id = this->id + ":nls:" + id;
			NonLinearSolversMap::const_iterator it =
			this->non_linear_solvers.find(non_linear_solver_id);
			if (it == this->non_linear_solvers.end()) {
			AKANTU_EXCEPTION("The non linear solver " << non_linear_solver_id
			<< " does not exists in "
			<< this->id);
			}

			return *(it->second);
			}

			/* -------------------------------------------------------------------------- */
			bool DOFManager::hasNonLinearSolver(const ID & id) const {
			ID solver_id = this->id + ":nls:" + id;
			auto it = this->non_linear_solvers.find(solver_id);
			return it != this->non_linear_solvers.end();
			}

			/* -------------------------------------------------------------------------- */
			TimeStepSolver & DOFManager::getTimeStepSolver(const ID & id) {
			ID time_step_solver_id = this->id + ":tss:" + id;
			TimeStepSolversMap::const_iterator it =
			this->time_step_solvers.find(time_step_solver_id);
			if (it == this->time_step_solvers.end()) {
			AKANTU_EXCEPTION("The non linear solver " << time_step_solver_id
			<< " does not exists in "
			<< this->id);
			}

			return *(it->second);
			}

			/* -------------------------------------------------------------------------- */
			bool DOFManager::hasTimeStepSolver(const ID & solver_id) const {
			ID time_step_solver_id = this->id + ":tss:" + solver_id;
			auto it = this->time_step_solvers.find(time_step_solver_id);
			return it != this->time_step_solvers.end();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::savePreviousDOFs(const ID & dofs_id) {
			this->getPreviousDOFs(dofs_id).copy(this->getDOFs(dofs_id));
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::zeroResidual() { this->residual->zero(); }

			/* -------------------------------------------------------------------------- */
			void DOFManager::zeroMatrix(const ID & mtx) { this->getMatrix(mtx).zero(); }

			/* -------------------------------------------------------------------------- */
			void DOFManager::zeroLumpedMatrix(const ID & mtx) {
			this->getLumpedMatrix(mtx).zero();
			}

			/* -------------------------------------------------------------------------- */
			/* Mesh Events */
			/* -------------------------------------------------------------------------- */
			std::pair<UInt, UInt>
			DOFManager::updateNodalDOFs(const ID & dof_id, const Array<UInt> & nodes_list) {
			auto & dof_data = this->getDOFData(dof_id);
			UInt nb_new_local_dofs;
			UInt nb_new_pure_local;

			std::tie(nb_new_local_dofs, nb_new_pure_local) =
			countDOFsForNodes(dof_data, nodes_list.size(),
			[&nodes_list](auto && n) { return nodes_list(n); });

			this->pure_local_system_size += nb_new_pure_local;
			this->local_system_size += nb_new_local_dofs;

			UInt nb_new_global = nb_new_pure_local;
			communicator.allReduce(nb_new_global, SynchronizerOperation::_sum);

			this->system_size += nb_new_global;

			dof_data.solution.resize(local_system_size);

			updateDOFsData(dof_data, nb_new_local_dofs, nb_new_pure_local,
			nodes_list.size(),
			[&nodes_list](UInt pos) -> UInt { return nodes_list[pos]; });

			return std::make_pair(nb_new_local_dofs, nb_new_pure_local);
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::resizeGlobalArrays() {
			// resize all relevant arrays
			this->residual->resize();
			this->solution->resize();
			this->data_cache->resize();

			for (auto & lumped_matrix : lumped_matrices) {
			lumped_matrix.second->resize();
			}

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

			/* -------------------------------------------------------------------------- */
			void DOFManager::onNodesAdded(const Array<UInt> & nodes_list,
			const NewNodesEvent & /unused/) {
			for (auto & pair : this->dofs) {
			const auto & dof_id = pair.first;
			auto & dof_data = this->getDOFData(dof_id);
			if (dof_data.support_type != _dst_nodal) {
			continue;
			}

			const auto & group = dof_data.group_support;

			if (group == "__mesh__") {
			this->updateNodalDOFs(dof_id, nodes_list);
			} else {
			const auto & node_group =
			this->mesh->getElementGroup(group).getNodeGroup();
			Array<UInt> new_nodes_list;
			for (const auto & node : nodes_list) {
			if (node_group.find(node) != UInt(-1)) {
			new_nodes_list.push_back(node);
			}
			}

			this->updateNodalDOFs(dof_id, new_nodes_list);
			}
			}

			this->resizeGlobalArrays();
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::onMeshIsDistributed(const Mesh & mesh_,
			const MeshIsDistributedEvent & event) {
			if (this->mesh == nullptr) {
			AKANTU_EXCEPTION("The `Mesh` pointer is not set.");
			}

			// check if the distributed state of the residual and the mesh are the same.
			if (this->mesh->isDistributed() != this->residual->isDistributed()) {
			// TODO: Allow to reallocate the internals, in that case one could actually
			// react on that event.
			#define YN(q) ((q) ? std::string("is") : std::string("is not"))
			AKANTU_EXCEPTION("There is an inconsistency about the distribution state "
			"of the `DOFManager`."
			" It seams that the `Mesh` "
			<< YN(this->mesh->isDistributed())
			<< " distributed, but the `DOFManager`'s residual "
			<< YN(this->residual->isDistributed())
			<< ", which is of type "
			<< debug::demangle(typeid(*this->residual).name()) << ".");
			#undef YN
			};

			return;
			}

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

			GlobalDOFInfoDataAccessor(DOFManager::DOFData & dof_data,
			DOFManager & dof_manager)
			: dof_data(dof_data), dof_manager(dof_manager) {
			for (auto && pair :
			zip(dof_data.local_equation_number, dof_data.associated_nodes)) {
			UInt node;
			Int dof;
			std::tie(dof, node) = pair;

			dofs_per_node[node].push_back(dof);
			}
			}

			UInt getNbData(const Array<UInt> & nodes,
			const SynchronizationTag & tag) const override {
			if (tag == SynchronizationTag::_ask_nodes or
			tag == SynchronizationTag::_giu_global_conn) {
			return nodes.size() * dof_data.dof->getNbComponent() * sizeof(Int);
			}

			return 0;
			}

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

			void unpackData(CommunicationBuffer & buffer, const Array<UInt> & nodes,
			const SynchronizationTag & tag) override {
			if (tag == SynchronizationTag::_ask_nodes or
			tag == SynchronizationTag::_giu_global_conn) {
			for (const auto & node : nodes) {
			const auto & dofs = dofs_per_node[node];
			for (const auto & dof : dofs) {
			Int global_dof;
			buffer >> global_dof;
			AKANTU_DEBUG_ASSERT(
			(dof_manager.global_equation_number(dof) == -1 or
			dof_manager.global_equation_number(dof) == global_dof),
			"This dof already had a global_dof_id which is different from "
			"the received one. "
			<< dof_manager.global_equation_number(dof)
			<< " != " << global_dof);
			dof_manager.global_equation_number(dof) = global_dof;
			dof_manager.global_to_local_mapping[global_dof] = dof;
			}
			}
			}
			}

			protected:
			std::unordered_map<UInt, std::vector<Int>> dofs_per_node;
			DOFManager::DOFData & dof_data;
			DOFManager & dof_manager;
			};

			/* -------------------------------------------------------------------------- */
			auto DOFManager::computeFirstDOFIDs(UInt nb_new_local_dofs,
			UInt nb_new_pure_local) {
			// determine the first local/global dof id to use
			UInt offset = 0;

			this->communicator.exclusiveScan(nb_new_pure_local, offset);

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

			offset = nb_new_pure_local;
			this->communicator.allReduce(offset);
			this->first_global_dof_id += offset;

			return std::make_pair(first_local_dof_id, first_global_dof_id);
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
			UInt nb_new_pure_local, UInt nb_node,
			const std::function<UInt(UInt)> & getNode) {
			auto nb_local_dofs_added = nb_node * dof_data.dof->getNbComponent();

			auto first_dof_pos = dof_data.local_equation_number.size();
			dof_data.local_equation_number.reserve(dof_data.local_equation_number.size() +
			nb_local_dofs_added);
			dof_data.associated_nodes.reserve(dof_data.associated_nodes.size() +
			nb_local_dofs_added);

			this->dofs_flag.resize(this->local_system_size, NodeFlag::_normal);
			this->global_equation_number.resize(this->local_system_size, -1);

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

			// update per dof info
			UInt local_eq_num;
			UInt first_global_dof_id;
			std::tie(local_eq_num, first_global_dof_id) =
			computeFirstDOFIDs(nb_new_local_dofs, nb_new_pure_local);
			for (auto d : arange(nb_local_dofs_added)) {
			auto node = getNode(d / dof_data.dof->getNbComponent());
			auto dof_flag = this->mesh->getNodeFlag(node);

			dof_data.associated_nodes.push_back(node);
			auto is_local_dof = this->mesh->isLocalOrMasterNode(node);
			auto is_periodic_slave = this->mesh->isPeriodicSlave(node);
			auto is_periodic_master = this->mesh->isPeriodicMaster(node);

			if (is_periodic_slave) {
			dof_data.local_equation_number.push_back(-1);
			continue;
			}

			// update equation numbers
			this->dofs_flag(local_eq_num) = dof_flag;
			dof_data.local_equation_number.push_back(local_eq_num);

			if (is_local_dof) {
			this->global_equation_number(local_eq_num) = first_global_dof_id;
			this->global_to_local_mapping[first_global_dof_id] = local_eq_num;
			++first_global_dof_id;
			} else {
			this->global_equation_number(local_eq_num) = -1;
			}

			if (is_periodic_master) {
			auto node = getNode(d / dof_data.dof->getNbComponent());
			auto dof = d % dof_data.dof->getNbComponent();
			masters_dofs.insert(
			std::make_pair(std::make_pair(node, dof), local_eq_num));
			}

			++local_eq_num;
			}

			// correct periodic slave equation numbers
			if (this->mesh->isPeriodic()) {
			auto assoc_begin = dof_data.associated_nodes.begin();
			for (auto d : arange(nb_local_dofs_added)) {
			auto node = dof_data.associated_nodes(first_dof_pos + d);
			if (not this->mesh->isPeriodicSlave(node)) {
			continue;
			}

			auto master_node = this->mesh->getPeriodicMaster(node);
			auto dof = d % dof_data.dof->getNbComponent();
			dof_data.local_equation_number(first_dof_pos + d) =
			masters_dofs[std::make_pair(master_node, dof)];
			}
			}

			// synchronize the global numbering for slaves nodes
			if (this->mesh->isDistributed()) {
			GlobalDOFInfoDataAccessor data_accessor(dof_data, *this);

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

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

			/* -------------------------------------------------------------------------- */
			void DOFManager::updateDOFsData(DOFData & dof_data, UInt nb_new_local_dofs,
			UInt nb_new_pure_local) {
			dof_data.local_equation_number.reserve(dof_data.local_equation_number.size() +
			nb_new_local_dofs);

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

			this->dofs_flag.resize(this->local_system_size, NodeFlag::_normal);
			this->global_equation_number.resize(this->local_system_size, -1);

			// update per dof info
			for (auto _ [[gnu::unused]] : arange(nb_new_local_dofs)) {
			// update equation numbers
			this->dofs_flag(first_local_dof_id) = NodeFlag::_normal;

			dof_data.local_equation_number.push_back(first_local_dof_id);

			this->global_equation_number(first_local_dof_id) = first_global_dof_id;
			this->global_to_local_mapping[first_global_dof_id] = first_local_dof_id;

			++first_global_dof_id;
			++first_local_dof_id;
			}
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::onNodesRemoved(const Array<UInt> & /unused/,
			const Array<UInt> & /unused/,
			const RemovedNodesEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			void DOFManager::onElementsAdded(const Array<Element> & /unused/,
			const NewElementsEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			void DOFManager::onElementsRemoved(const Array<Element> & /unused/,
			const ElementTypeMapArray<UInt> & /unused/,
			const RemovedElementsEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			void DOFManager::onElementsChanged(const Array<Element> & /unused/,
			const Array<Element> & /unused/,
			const ElementTypeMapArray<UInt> & /unused/,
			const ChangedElementsEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			void DOFManager::updateGlobalBlockedDofs() {
			this->previous_global_blocked_dofs.copy(this->global_blocked_dofs);
			this->global_blocked_dofs.reserve(this->local_system_size, 0);
			this->previous_global_blocked_dofs_release =
			this->global_blocked_dofs_release;

			for (auto & pair : dofs) {
			if (not this->hasBlockedDOFs(pair.first)) {
			continue;
			}

			DOFData & dof_data = *pair.second;
			for (auto && data : zip(dof_data.getLocalEquationsNumbers(),
			make_view(*dof_data.blocked_dofs))) {
			const auto & dof = std::get<0>(data);
			const auto & is_blocked = std::get<1>(data);
			if (is_blocked) {
			this->global_blocked_dofs.push_back(dof);
			}
			}
			}

			std::sort(this->global_blocked_dofs.begin(), this->global_blocked_dofs.end());
			auto last = std::unique(this->global_blocked_dofs.begin(),
			this->global_blocked_dofs.end());
			this->global_blocked_dofs.resize(last - this->global_blocked_dofs.begin());

			auto are_equal =
			global_blocked_dofs.size() == previous_global_blocked_dofs.size() and
			std::equal(global_blocked_dofs.begin(), global_blocked_dofs.end(),
			previous_global_blocked_dofs.begin());

			if (not are_equal) {
			++this->global_blocked_dofs_release;
			}
			}

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

			if (this->jacobian_release == J.getRelease()) {
			if (this->hasBlockedDOFsChanged()) {
			J.applyBoundary();
			}

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

			this->jacobian_release = J.getRelease();
			this->previous_global_blocked_dofs_release =
			this->global_blocked_dofs_release;
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleMatMulVectToGlobalArray(const ID & dof_id,
			const ID & A_id,
			const Array<Real> & x,
			SolverVector & array,
			Real scale_factor) {
			auto & A = this->getMatrix(A_id);

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

			A.matVecMul(*data_cache, array, scale_factor, 1.);
			}

			/* -------------------------------------------------------------------------- */
			void DOFManager::assembleMatMulVectToResidual(const ID & dof_id,
			const ID & A_id,
			const Array<Real> & x,
			Real scale_factor) {
			assembleMatMulVectToGlobalArray(dof_id, A_id, x, *residual, scale_factor);
			}

			} // namespace akantu

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