solid_mechanics_model.cc
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Created: Tue, Dec 3, 14:18

solid_mechanics_model.cc
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	/**
	* @file solid_mechanics_model.cc
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Jul 27 2010
	* @date last modification: Fri Sep 19 2014
	*
	* @brief Implementation of the SolidMechanicsModel class
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_math.hh"
	#include "aka_common.hh"
	#include "solid_mechanics_model.hh"
	#include "group_manager_inline_impl.cc"
	#include "dumpable_inline_impl.hh"
	#include "integration_scheme_2nd_order.hh"
	#include "element_group.hh"

	#include "static_communicator.hh"

	#include "dof_synchronizer.hh"
	#include "element_group.hh"

	#include <cmath>

	#ifdef AKANTU_USE_MUMPS
	#include "solver_mumps.hh"
	#endif

	#ifdef AKANTU_USE_PETSC
	#include "solver_petsc.hh"
	#include "petsc_matrix.hh"
	#endif

	#ifdef AKANTU_USE_IOHELPER
	# include "dumper_field.hh"
	# include "dumper_paraview.hh"
	# include "dumper_homogenizing_field.hh"
	# include "dumper_internal_material_field.hh"
	# include "dumper_elemental_field.hh"
	# include "dumper_material_padders.hh"
	# include "dumper_element_partition.hh"
	# include "dumper_iohelper.hh"
	#endif

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	# include "non_local_manager.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	__BEGIN_AKANTU__

	const SolidMechanicsModelOptions default_solid_mechanics_model_options(_explicit_lumped_mass, false);

	/* -------------------------------------------------------------------------- */
	/**
	* A solid mechanics model need a mesh and a dimension to be created. the model
	* by it self can not do a lot, the good init functions should be called in
	* order to configure the model depending on what we want to do.
	*
	* @param mesh mesh representing the model we want to simulate
	* @param dim spatial dimension of the problem, if dim = 0 (default value) the
	* dimension of the problem is assumed to be the on of the mesh
	* @param id an id to identify the model
	*/
	SolidMechanicsModel::SolidMechanicsModel(Mesh & mesh,
	UInt dim,
	const ID & id,
	const MemoryID & memory_id) :
	Model(mesh, dim, id, memory_id),
	BoundaryCondition<SolidMechanicsModel>(),
	time_step(NAN), f_m2a(1.0),
	mass_matrix(NULL),
	velocity_damping_matrix(NULL),
	stiffness_matrix(NULL),
	jacobian_matrix(NULL),
	material_index("material index", id),
	material_local_numbering("material local numbering", id),
	material_selector(new DefaultMaterialSelector(material_index)),
	is_default_material_selector(true),
	integrator(NULL),
	increment_flag(false), solver(NULL),
	synch_parallel(NULL),
	are_materials_instantiated(false),
	non_local_manager(NULL),
	pbc_synch(NULL) {

	AKANTU_DEBUG_IN();

	createSynchronizerRegistry(this);

	registerFEEngineObject<MyFEEngineType>("SolidMechanicsFEEngine", mesh, spatial_dimension);

	this->displacement = NULL;
	this->mass = NULL;
	this->velocity = NULL;
	this->acceleration = NULL;
	this->force = NULL;
	this->residual = NULL;
	this->blocked_dofs = NULL;

	this->increment = NULL;
	this->increment_acceleration = NULL;

	this->dof_synchronizer = NULL;

	this->previous_displacement = NULL;

	materials.clear();

	mesh.registerEventHandler(*this);

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.registerDumper<DumperParaview>("paraview_all", id, true);
	this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_regular);
	#endif
	AKANTU_DEBUG_OUT();
	}



	/* -------------------------------------------------------------------------- */
	SolidMechanicsModel::~SolidMechanicsModel() {
	AKANTU_DEBUG_IN();

	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	delete *mat_it;
	}

	materials.clear();

	delete integrator;

	delete solver;
	delete mass_matrix;
	delete velocity_damping_matrix;

	if(stiffness_matrix && stiffness_matrix != jacobian_matrix)
	delete stiffness_matrix;

	delete jacobian_matrix;

	delete synch_parallel;

	if(is_default_material_selector) {
	delete material_selector;
	material_selector = NULL;
	}

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	delete non_local_manager;
	non_local_manager = NULL;
	#endif

	delete pbc_synch;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::setTimeStep(Real time_step) {
	this->time_step = time_step;

	#if defined(AKANTU_USE_IOHELPER)
	this->mesh.getDumper().setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	/* Initialisation */
	/* -------------------------------------------------------------------------- */
	/**
	* This function groups many of the initialization in on function. For most of
	* basics case the function should be enough. The functions initialize the
	* model, the internal vectors, set them to 0, and depending on the parameters
	* it also initialize the explicit or implicit solver.
	*
	* @param material_file the file containing the materials to use
	* @param method the analysis method wanted. See the akantu::AnalysisMethod for
	* the different possibilities
	*/
	void SolidMechanicsModel::initFull(const ModelOptions & options) {
	Model::initFull(options);

	const SolidMechanicsModelOptions & smm_options =
	dynamic_cast<const SolidMechanicsModelOptions &>(options);

	this->method = smm_options.analysis_method;

	// initialize the vectors
	this->initArrays();

	// set the initial condition to 0
	this->force->clear();
	this->velocity->clear();
	this->acceleration->clear();
	this->displacement->clear();

	// initialize pbc
	if(this->pbc_pair.size()!=0)
	this->initPBC();

	// initialize the time integration schemes
	switch(this->method) {
	case _explicit_lumped_mass:
	this->initExplicit();
	break;
	case _explicit_consistent_mass:
	this->initSolver();
	this->initExplicit();
	break;
	case _implicit_dynamic:
	this->initImplicit(true);
	break;
	case _static:
	this->initImplicit(false);
	this->initArraysPreviousDisplacment();
	break;
	default:
	AKANTU_EXCEPTION("analysis method not recognised by SolidMechanicsModel");
	break;
	}

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	/// create the non-local manager object for non-local damage computations
	this->non_local_manager = new NonLocalManager(*this);
	#endif

	// initialize the materials
	if(this->parser->getLastParsedFile() != "") {
	this->instantiateMaterials();
	}

	if(!smm_options.no_init_materials) {
	this->initMaterials();
	}

	if(this->increment_flag)
	this->initBC(this, this->displacement, this->increment, this->force);
	else
	this->initBC(this, this->displacement, *this->force);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initParallel(MeshPartition * partition,
	DataAccessor * data_accessor) {
	AKANTU_DEBUG_IN();

	if (data_accessor == NULL) data_accessor = this;
	synch_parallel = &createParallelSynch(partition,data_accessor);

	synch_registry->registerSynchronizer(*synch_parallel, _gst_material_id);
	synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_mass);
	synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_stress);
	synch_registry->registerSynchronizer(*synch_parallel, _gst_smm_boundary);
	synch_registry->registerSynchronizer(*synch_parallel, _gst_for_dump);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initFEEngineBoundary() {
	FEEngine & fem_boundary = getFEEngineBoundary();
	fem_boundary.initShapeFunctions(_not_ghost);
	fem_boundary.initShapeFunctions(_ghost);

	fem_boundary.computeNormalsOnIntegrationPoints(_not_ghost);
	fem_boundary.computeNormalsOnIntegrationPoints(_ghost);
	}


	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initExplicit(AnalysisMethod analysis_method) {
	AKANTU_DEBUG_IN();

	//in case of switch from implicit to explicit
	if(!this->isExplicit())
	method = analysis_method;

	if (integrator) delete integrator;
	integrator = new CentralDifference();

	UInt nb_nodes = acceleration->getSize();
	UInt nb_degree_of_freedom = acceleration->getNbComponent();

	std::stringstream sstr; sstr << id << ":increment_acceleration";
	increment_acceleration = &(alloc<Real>(sstr.str(), nb_nodes, nb_degree_of_freedom, Real()));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initArraysPreviousDisplacment() {
	AKANTU_DEBUG_IN();

	this->setIncrementFlagOn();
	if(not this->previous_displacement) {
	UInt nb_nodes = this->mesh.getNbNodes();
	std::stringstream sstr_disp_t;
	sstr_disp_t << this->id << ":previous_displacement";

	this->previous_displacement = &(this->alloc<Real > (sstr_disp_t.str(), nb_nodes, this->spatial_dimension, 0.));
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Allocate all the needed vectors. By default their are not necessarily set to
	* 0
	*
	*/
	void SolidMechanicsModel::initArrays() {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = mesh.getNbNodes();
	std::stringstream sstr_disp; sstr_disp << id << ":displacement";
	// std::stringstream sstr_mass; sstr_mass << id << ":mass";
	std::stringstream sstr_velo; sstr_velo << id << ":velocity";
	std::stringstream sstr_acce; sstr_acce << id << ":acceleration";
	std::stringstream sstr_forc; sstr_forc << id << ":force";
	std::stringstream sstr_resi; sstr_resi << id << ":residual";
	std::stringstream sstr_boun; sstr_boun << id << ":blocked_dofs";

	displacement = &(alloc<Real>(sstr_disp.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
	// mass = &(alloc<Real>(sstr_mass.str(), nb_nodes, spatial_dimension, 0));
	velocity = &(alloc<Real>(sstr_velo.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
	acceleration = &(alloc<Real>(sstr_acce.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
	force = &(alloc<Real>(sstr_forc.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
	residual = &(alloc<Real>(sstr_resi.str(), nb_nodes, spatial_dimension, REAL_INIT_VALUE));
	blocked_dofs = &(alloc<bool>(sstr_boun.str(), nb_nodes, spatial_dimension, false));

	std::stringstream sstr_curp; sstr_curp << id << ":current_position";
	current_position = &(alloc<Real>(sstr_curp.str(), 0, spatial_dimension, REAL_INIT_VALUE));

	for(UInt g = _not_ghost; g <= _ghost; ++g) {
	GhostType gt = (GhostType) g;
	Mesh::type_iterator it = mesh.firstType(spatial_dimension, gt, _ek_not_defined);
	Mesh::type_iterator end = mesh.lastType(spatial_dimension, gt, _ek_not_defined);
	for(; it != end; ++it) {
	UInt nb_element = mesh.getNbElement(*it, gt);
	material_index.alloc(nb_element, 1, *it, gt);
	material_local_numbering.alloc(nb_element, 1, *it, gt);
	}
	}

	dof_synchronizer = new DOFSynchronizer(mesh, spatial_dimension);
	dof_synchronizer->initLocalDOFEquationNumbers();
	dof_synchronizer->initGlobalDOFEquationNumbers();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the model,basically it pre-compute the shapes, shapes derivatives
	* and jacobian
	*
	*/
	void SolidMechanicsModel::initModel() {
	/// \todo add the current position as a parameter to initShapeFunctions for
	/// large deformation
	getFEEngine().initShapeFunctions(_not_ghost);
	getFEEngine().initShapeFunctions(_ghost);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initPBC() {
	Model::initPBC();
	registerPBCSynchronizer();

	// as long as there are ones on the diagonal of the matrix, we can put boudandary true for slaves
	std::map<UInt, UInt>::iterator it = pbc_pair.begin();
	std::map<UInt, UInt>::iterator end = pbc_pair.end();
	UInt dim = mesh.getSpatialDimension();
	while(it != end) {
	for (UInt i=0; i<dim; ++i)
	(blocked_dofs)((it).first,i) = true;
	++it;
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::registerPBCSynchronizer(){
	pbc_synch = new PBCSynchronizer(pbc_pair);
	synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_uv);
	synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_mass);
	synch_registry->registerSynchronizer(*pbc_synch, _gst_smm_res);
	synch_registry->registerSynchronizer(*pbc_synch, _gst_for_dump);
	changeLocalEquationNumberForPBC(pbc_pair, mesh.getSpatialDimension());
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateCurrentPosition() {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();

	current_position->resize(nb_nodes);
	Real * current_position_val = current_position->storage();
	Real * position_val = mesh.getNodes().storage();
	Real * displacement_val = displacement->storage();

	/// compute current_position = initial_position + displacement
	memcpy(current_position_val, position_val, nb_nodesspatial_dimensionsizeof(Real));
	for (UInt n = 0; n < nb_nodes*spatial_dimension; ++n) {
	current_position_val++ += displacement_val++;
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initializeUpdateResidualData() {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();
	residual->resize(nb_nodes);

	/// copy the forces in residual for boundary conditions
	memcpy(residual->storage(), force->storage(), nb_nodesspatial_dimensionsizeof(Real));

	// start synchronization
	synch_registry->asynchronousSynchronize(_gst_smm_uv);
	synch_registry->waitEndSynchronize(_gst_smm_uv);

	updateCurrentPosition();

	AKANTU_DEBUG_OUT();
	}

	/----------------------------------------------------------------------------/
	void SolidMechanicsModel::reInitialize()
	{

	}


	/* -------------------------------------------------------------------------- */
	/* Explicit scheme */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/**
	* This function compute the second member of the motion equation. That is to
	* say the sum of forces @f$ r = F_{ext} - F_{int} @f$. @f$ F_{ext} @f$ is given
	* by the user in the force vector, and @f$ F_{int} @f$ is computed as @f$
	* F_{int} = \int_{\Omega} N \sigma d\Omega@f$
	*
	*/
	void SolidMechanicsModel::updateResidual(bool need_initialize) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the internal forces");
	// f = f_ext - f_int

	// f = f_ext
	if(need_initialize) initializeUpdateResidualData();

	AKANTU_DEBUG_INFO("Compute local stresses");

	std::vector<Material *>::iterator mat_it;
	for (mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	mat.computeAllStresses(_not_ghost);
	}

	#ifdef AKANTU_DAMAGE_NON_LOCAL
	/* ------------------------------------------------------------------------ */
	/* Computation of the non local part */
	this->non_local_manager->computeAllNonLocalStresses();
	#endif

	/* ------------------------------------------------------------------------ */
	/* assembling the forces internal */
	// communicate the stress
	AKANTU_DEBUG_INFO("Send data for residual assembly");
	synch_registry->asynchronousSynchronize(_gst_smm_stress);

	AKANTU_DEBUG_INFO("Assemble residual for local elements");
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	mat.assembleResidual(_not_ghost);
	}


	AKANTU_DEBUG_INFO("Wait distant stresses");
	// finalize communications
	synch_registry->waitEndSynchronize(_gst_smm_stress);

	AKANTU_DEBUG_INFO("Assemble residual for ghost elements");
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	mat.assembleResidual(_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::computeStresses() {
	if (isExplicit()) {
	// start synchronization
	synch_registry->asynchronousSynchronize(_gst_smm_uv);
	synch_registry->waitEndSynchronize(_gst_smm_uv);

	// compute stresses on all local elements for each materials
	std::vector<Material *>::iterator mat_it;
	for (mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	mat.computeAllStresses(_not_ghost);
	}

	/* ------------------------------------------------------------------------ */
	#ifdef AKANTU_DAMAGE_NON_LOCAL
	/* Computation of the non local part */
	this->non_local_manager->computeAllNonLocalStresses();
	#endif
	} else {
	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	mat.computeAllStressesFromTangentModuli(_not_ghost);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateResidualInternal() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Update the residual");
	// f = f_ext - f_int - Ma - Cv = r - Ma - Cv;

	if(method != _static) {
	// f -= Ma
	if(mass_matrix) {
	// if full mass_matrix
	Array<Real> * Ma = new Array<Real>(*acceleration, true, "Ma");
	Ma = *mass_matrix;
	/// \todo check unit conversion for implicit dynamics
	// *Ma /= f_m2a
	residual -= Ma;
	delete Ma;
	} else if (mass) {

	// else lumped mass
	UInt nb_nodes = acceleration->getSize();
	UInt nb_degree_of_freedom = acceleration->getNbComponent();

	Real * mass_val = mass->storage();
	Real * accel_val = acceleration->storage();
	Real * res_val = residual->storage();
	bool * blocked_dofs_val = blocked_dofs->storage();

	for (UInt n = 0; n < nb_nodes * nb_degree_of_freedom; ++n) {
	if(!(*blocked_dofs_val)) {
	res_val -= accel_val * *mass_val /f_m2a;
	}
	blocked_dofs_val++;
	res_val++;
	mass_val++;
	accel_val++;
	}
	} else {
	AKANTU_DEBUG_ERROR("No function called to assemble the mass matrix.");
	}

	// f -= Cv
	if(velocity_damping_matrix) {
	Array<Real> * Cv = new Array<Real>(*velocity);
	Cv = *velocity_damping_matrix;
	residual -= Cv;
	delete Cv;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateAcceleration() {
	AKANTU_DEBUG_IN();

	updateResidualInternal();

	if(method == _explicit_lumped_mass) {
	/* residual = residual_{n+1} - M * acceleration_n therefore
	solution = increment acceleration not acceleration */
	solveLumped(*increment_acceleration,
	*mass,
	*residual,
	*blocked_dofs,
	f_m2a);
	} else if (method == _explicit_consistent_mass) {
	solve<NewmarkBeta::_acceleration_corrector>(*increment_acceleration);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::solveLumped(Array<Real> & x,
	const Array<Real> & A,
	const Array<Real> & b,
	const Array<bool> & blocked_dofs,
	Real alpha) {

	Real * A_val = A.storage();
	Real * b_val = b.storage();
	Real * x_val = x.storage();
	bool * blocked_dofs_val = blocked_dofs.storage();

	UInt nb_degrees_of_freedom = x.getSize() * x.getNbComponent();

	for (UInt n = 0; n < nb_degrees_of_freedom; ++n) {
	if(!(*blocked_dofs_val)) {
	x_val = alpha (b_val / A_val);
	}
	x_val++;
	A_val++;
	b_val++;
	blocked_dofs_val++;
	}
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::explicitPred() {
	AKANTU_DEBUG_IN();

	if(increment_flag) {
	if(previous_displacement) increment->copy(*previous_displacement);
	else increment->copy(*displacement);
	}

	AKANTU_DEBUG_ASSERT(integrator,"itegrator should have been allocated: "
	<< "have called initExplicit ? "
	<< "or initImplicit ?");

	integrator->integrationSchemePred(time_step,
	*displacement,
	*velocity,
	*acceleration,
	*blocked_dofs);

	if(increment_flag) {
	Real * inc_val = increment->storage();
	Real * dis_val = displacement->storage();
	UInt nb_degree_of_freedom = displacement->getSize() * displacement->getNbComponent();

	for (UInt n = 0; n < nb_degree_of_freedom; ++n) {
	inc_val = dis_val - *inc_val;
	inc_val++;
	dis_val++;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::explicitCorr() {
	AKANTU_DEBUG_IN();

	integrator->integrationSchemeCorrAccel(time_step,
	*displacement,
	*velocity,
	*acceleration,
	*blocked_dofs,
	*increment_acceleration);

	if(previous_displacement) previous_displacement->copy(*displacement);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::solveStep() {
	AKANTU_DEBUG_IN();

	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeSolveStepEvent(method));

	this->explicitPred();
	this->updateResidual();
	this->updateAcceleration();
	this->explicitCorr();

	EventManager::sendEvent(SolidMechanicsModelEvent::AfterSolveStepEvent(method));

	AKANTU_DEBUG_OUT();
	}


	/* -------------------------------------------------------------------------- */
	/* Implicit scheme */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the solver and create the sparse matrices needed.
	*
	*/
	void SolidMechanicsModel::initSolver(__attribute__((unused)) SolverOptions & options) {
	#if !defined(AKANTU_USE_MUMPS) && !defined(AKANTU_USE_PETSC)// or other solver in the future \todo add AKANTU_HAS_SOLVER in CMake
	AKANTU_DEBUG_ERROR("You should at least activate one solver.");
	#else
	UInt nb_global_nodes = mesh.getNbGlobalNodes();

	delete jacobian_matrix;
	std::stringstream sstr; sstr << id << ":jacobian_matrix";

	#ifdef AKANTU_USE_PETSC
	jacobian_matrix = new PETScMatrix(nb_global_nodes * spatial_dimension, _symmetric, sstr.str(), memory_id);
	#else
	jacobian_matrix = new SparseMatrix(nb_global_nodes * spatial_dimension, _unsymmetric, sstr.str(), memory_id);
	#endif //AKANTU_USE PETSC
	jacobian_matrix->buildProfile(mesh, *dof_synchronizer, spatial_dimension);

	if (!isExplicit()) {
	delete stiffness_matrix;
	std::stringstream sstr_sti; sstr_sti << id << ":stiffness_matrix";
	#ifdef AKANTU_USE_PETSC
	stiffness_matrix = new SparseMatrix(nb_global_nodes * spatial_dimension, _symmetric, sstr.str(), memory_id);
	stiffness_matrix->buildProfile(mesh, *dof_synchronizer, spatial_dimension);
	#else
	stiffness_matrix = new SparseMatrix(*jacobian_matrix, sstr_sti.str(), memory_id);
	#endif //AKANTU_USE_PETSC
	}

	delete solver;
	std::stringstream sstr_solv; sstr_solv << id << ":solver";
	#ifdef AKANTU_USE_PETSC
	solver = new SolverPETSc(*jacobian_matrix, sstr_solv.str());
	#elif defined(AKANTU_USE_MUMPS)
	solver = new SolverMumps(*jacobian_matrix, sstr_solv.str());
	dof_synchronizer->initScatterGatherCommunicationScheme();
	#else
	AKANTU_DEBUG_ERROR("You should at least activate one solver.");
	#endif //AKANTU_USE_MUMPS

	if(solver)
	solver->initialize(options);
	#endif //AKANTU_HAS_SOLVER
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initJacobianMatrix() {
	#if defined(AKANTU_USE_MUMPS) && !defined(AKANTU_USE_PETSC)

	// @todo make it more flexible: this is an ugly patch to treat the case of non
	// fix profile of the K matrix
	delete jacobian_matrix;
	std::stringstream sstr_sti; sstr_sti << id << ":jacobian_matrix";
	jacobian_matrix = new SparseMatrix(*stiffness_matrix, sstr_sti.str(), memory_id);

	std::stringstream sstr_solv; sstr_solv << id << ":solver";
	delete solver;
	solver = new SolverMumps(*jacobian_matrix, sstr_solv.str());
	if(solver)
	solver->initialize(_solver_no_options);
	#else
	AKANTU_DEBUG_ERROR("You need to activate the solver mumps.");
	#endif
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Initialize the implicit solver, either for dynamic or static cases,
	*
	* @param dynamic
	*/
	void SolidMechanicsModel::initImplicit(bool dynamic, SolverOptions & solver_options) {
	AKANTU_DEBUG_IN();

	method = dynamic ? _implicit_dynamic : _static;

	if (!increment) setIncrementFlagOn();

	initSolver(solver_options);

	if(method == _implicit_dynamic) {
	if(integrator) delete integrator;
	integrator = new TrapezoidalRule2();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::initialAcceleration() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Solving Ma = f");

	Solver * acc_solver = NULL;

	std::stringstream sstr; sstr << id << ":tmp_mass_matrix";
	SparseMatrix * tmp_mass = new SparseMatrix(*mass_matrix, sstr.str(), memory_id);

	#ifdef AKANTU_USE_MUMPS
	std::stringstream sstr_solver; sstr << id << ":solver_mass_matrix";
	acc_solver = new SolverMumps(*mass_matrix, sstr_solver.str());

	dof_synchronizer->initScatterGatherCommunicationScheme();
	#else
	AKANTU_DEBUG_ERROR("You should at least activate one solver.");
	#endif //AKANTU_USE_MUMPS

	acc_solver->initialize();

	tmp_mass->applyBoundary(*blocked_dofs);

	acc_solver->setRHS(*residual);
	acc_solver->solve(*acceleration);

	delete acc_solver;
	delete tmp_mass;

	AKANTU_DEBUG_OUT();
	}


	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::assembleStiffnessMatrix() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_INFO("Assemble the new stiffness matrix.");

	stiffness_matrix->clear();

	// call compute stiffness matrix on each local elements
	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	(*mat_it)->assembleStiffnessMatrix(_not_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	SparseMatrix & SolidMechanicsModel::initVelocityDampingMatrix() {
	if(!velocity_damping_matrix)
	velocity_damping_matrix =
	new SparseMatrix(*jacobian_matrix, id + ":velocity_damping_matrix", memory_id);

	return *velocity_damping_matrix;
	}

	/* -------------------------------------------------------------------------- */
	template<>
	bool SolidMechanicsModel::testConvergence<_scc_increment>(Real tolerance, Real & error){
	AKANTU_DEBUG_IN();

	UInt nb_nodes = displacement->getSize();
	UInt nb_degree_of_freedom = displacement->getNbComponent();

	error = 0;
	Real norm[2] = {0., 0.};
	Real * increment_val = increment->storage();
	bool * blocked_dofs_val = blocked_dofs->storage();
	Real * displacement_val = displacement->storage();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
	if(!(*blocked_dofs_val) && is_local_node) {
	norm[0] += increment_val *increment_val;
	norm[1] += displacement_val *displacement_val;
	}
	blocked_dofs_val++;
	increment_val++;
	displacement_val++;
	}
	}

	StaticCommunicator::getStaticCommunicator().allReduce(norm, 2, _so_sum);

	norm[0] = sqrt(norm[0]);
	norm[1] = sqrt(norm[1]);

	AKANTU_DEBUG_ASSERT(!Math::isnan(norm[0]), "Something goes wrong in the solve phase");

	if (norm[1] < Math::getTolerance()) {
	error = norm[0];
	AKANTU_DEBUG_OUT();
	// cout<<"Error 1: "<<error<<endl;
	return error < tolerance;
	}


	AKANTU_DEBUG_OUT();
	if(norm[1] > Math::getTolerance())
	error = norm[0] / norm[1];
	else
	error = norm[0]; //In case the total displacement is zero!

	// cout<<"Error 2: "<<error<<endl;

	return (error < tolerance);
	}


	/* -------------------------------------------------------------------------- */
	template<>
	bool SolidMechanicsModel::testConvergence<_scc_residual>(Real tolerance, Real & norm) {
	AKANTU_DEBUG_IN();

	UInt nb_nodes = residual->getSize();
	UInt nb_degree_of_freedom = displacement->getNbComponent();

	norm = 0;
	Real * residual_val = residual->storage();
	bool * blocked_dofs_val = blocked_dofs->storage();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	if(is_local_node) {
	for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
	if(!(*blocked_dofs_val)) {
	norm += residual_val *residual_val;
	}
	blocked_dofs_val++;
	residual_val++;
	}
	} else {
	blocked_dofs_val += spatial_dimension;
	residual_val += spatial_dimension;
	}
	}

	StaticCommunicator::getStaticCommunicator().allReduce(&norm, 1, _so_sum);

	norm = sqrt(norm);

	AKANTU_DEBUG_ASSERT(!Math::isnan(norm), "Something goes wrong in the solve phase");

	AKANTU_DEBUG_OUT();
	return (norm < tolerance);
	}

	/* -------------------------------------------------------------------------- */
	template<>
	bool SolidMechanicsModel::testConvergence<_scc_residual_mass_wgh>(Real tolerance,
	Real & norm) {
	AKANTU_DEBUG_IN();



	UInt nb_nodes = residual->getSize();

	norm = 0;
	Real * residual_val = residual->storage();
	Real * mass_val = this->mass->storage();
	bool * blocked_dofs_val = blocked_dofs->storage();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	if(is_local_node) {
	for (UInt d = 0; d < spatial_dimension; ++d) {
	if(!(*blocked_dofs_val)) {
	norm += residual_val residual_val/(mass_val * *mass_val);
	}
	blocked_dofs_val++;
	residual_val++;
	mass_val++;
	}
	} else {
	blocked_dofs_val += spatial_dimension;
	residual_val += spatial_dimension;
	mass_val += spatial_dimension;
	}
	}

	StaticCommunicator::getStaticCommunicator().allReduce(&norm, 1, _so_sum);

	norm = sqrt(norm);

	AKANTU_DEBUG_ASSERT(!Math::isnan(norm), "Something goes wrong in the solve phase");

	AKANTU_DEBUG_OUT();
	return (norm < tolerance);
	}

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::testConvergenceResidual(Real tolerance){
	AKANTU_DEBUG_IN();

	Real error=0;
	bool res = this->testConvergence<_scc_residual>(tolerance, error);
	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::testConvergenceResidual(Real tolerance, Real & error){
	AKANTU_DEBUG_IN();

	bool res = this->testConvergence<_scc_residual>(tolerance, error);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::testConvergenceIncrement(Real tolerance){
	AKANTU_DEBUG_IN();

	Real error=0;
	bool res = this->testConvergence<_scc_increment>(tolerance, error);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::testConvergenceIncrement(Real tolerance, Real & error){
	AKANTU_DEBUG_IN();

	bool res = this->testConvergence<_scc_increment>(tolerance, error);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::implicitPred() {
	AKANTU_DEBUG_IN();

	if(method == _implicit_dynamic)
	integrator->integrationSchemePred(time_step,
	*displacement,
	*velocity,
	*acceleration,
	*blocked_dofs);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::implicitCorr() {
	AKANTU_DEBUG_IN();

	if(method == _implicit_dynamic) {
	integrator->integrationSchemeCorrDispl(time_step,
	*displacement,
	*velocity,
	*acceleration,
	*blocked_dofs,
	*increment);
	} else {
	UInt nb_nodes = displacement->getSize();
	UInt nb_degree_of_freedom = displacement->getNbComponent() * nb_nodes;

	Real * incr_val = increment->storage();
	Real * disp_val = displacement->storage();
	bool * boun_val = blocked_dofs->storage();

	for (UInt j = 0; j < nb_degree_of_freedom; ++j, ++disp_val, ++incr_val, ++boun_val){
	incr_val = (1. - *boun_val);
	disp_val += incr_val;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateIncrement() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(previous_displacement,"The previous displacement has to be initialized."
	<< " Are you working with Finite or Ineslactic deformations?");

	UInt nb_nodes = displacement->getSize();
	UInt nb_degree_of_freedom = displacement->getNbComponent() * nb_nodes;

	Real * incr_val = increment->storage();
	Real * disp_val = displacement->storage();
	Real * prev_disp_val = previous_displacement->storage();

	for (UInt j = 0; j < nb_degree_of_freedom; ++j, ++disp_val, ++incr_val, ++prev_disp_val)
	incr_val = (disp_val - *prev_disp_val);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updatePreviousDisplacement() {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(previous_displacement,"The previous displacement has to be initialized."
	<< " Are you working with Finite or Ineslactic deformations?");

	previous_displacement->copy(*displacement);

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	/* Information */
	/* -------------------------------------------------------------------------- */

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::synchronizeBoundaries() {
	AKANTU_DEBUG_IN();
	AKANTU_DEBUG_ASSERT(synch_registry,"Synchronizer registry was not initialized."
	<< " Did you call initParallel?");
	synch_registry->synchronize(_gst_smm_boundary);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::synchronizeResidual() {
	AKANTU_DEBUG_IN();
	AKANTU_DEBUG_ASSERT(synch_registry,"Synchronizer registry was not initialized."
	<< " Did you call initPBC?");
	synch_registry->synchronize(_gst_smm_res);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::setIncrementFlagOn() {
	AKANTU_DEBUG_IN();

	if(!increment) {
	UInt nb_nodes = mesh.getNbNodes();
	std::stringstream sstr_inc; sstr_inc << id << ":increment";
	increment = &(alloc<Real>(sstr_inc.str(), nb_nodes, spatial_dimension, 0.));
	}

	increment_flag = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep() {
	AKANTU_DEBUG_IN();

	Real min_dt = getStableTimeStep(_not_ghost);

	/// reduction min over all processors
	StaticCommunicator::getStaticCommunicator().allReduce(&min_dt, 1, _so_min);

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getStableTimeStep(const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	Material ** mat_val = &(materials.at(0));
	Real min_dt = std::numeric_limits<Real>::max();

	updateCurrentPosition();

	Element elem;
	elem.ghost_type = ghost_type;
	elem.kind = _ek_regular;

	Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type, _ek_regular);
	Mesh::type_iterator end = mesh.lastType(spatial_dimension, ghost_type, _ek_regular);
	for(; it != end; ++it) {
	elem.type = *it;
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(*it);
	UInt nb_element = mesh.getNbElement(*it);

	Array<UInt>::const_scalar_iterator mat_indexes = material_index(*it, ghost_type).begin();
	Array<UInt>::const_scalar_iterator mat_loc_num = material_local_numbering(*it, ghost_type).begin();

	Array<Real> X(0, nb_nodes_per_element*spatial_dimension);
	FEEngine::extractNodalToElementField(mesh, *current_position,
	X, *it, _not_ghost);

	Array<Real>::matrix_iterator X_el =
	X.begin(spatial_dimension, nb_nodes_per_element);

	for (UInt el = 0; el < nb_element; ++el, ++X_el, ++mat_indexes, ++mat_loc_num) {
	elem.element = *mat_loc_num;
	Real el_h = getFEEngine().getElementInradius(X_el, it);
	Real el_c = mat_val[*mat_indexes]->getCelerity(elem);
	Real el_dt = el_h / el_c;

	min_dt = std::min(min_dt, el_dt);
	}
	}

	AKANTU_DEBUG_OUT();
	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy() {
	AKANTU_DEBUG_IN();

	if (!mass && !mass_matrix)
	AKANTU_DEBUG_ERROR("No function called to assemble the mass matrix.");


	Real ekin = 0.;

	UInt nb_nodes = mesh.getNbNodes();

	Real * vel_val = velocity->storage();
	Real * mass_val = mass->storage();

	for (UInt n = 0; n < nb_nodes; ++n) {
	Real mv2 = 0;
	bool is_local_node = mesh.isLocalOrMasterNode(n);
	bool is_not_pbc_slave_node = !isPBCSlaveNode(n);
	bool count_node = is_local_node && is_not_pbc_slave_node;
	for (UInt i = 0; i < spatial_dimension; ++i) {
	if (count_node)
	mv2 += vel_val vel_val *mass_val;

	vel_val++;
	mass_val++;
	}
	ekin += mv2;
	}

	StaticCommunicator::getStaticCommunicator().allReduce(&ekin, 1, _so_sum);

	AKANTU_DEBUG_OUT();
	return ekin * .5;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getKineticEnergy(const ElementType & type, UInt index) {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);

	Array<Real> vel_on_quad(nb_quadrature_points, spatial_dimension);
	Array<UInt> filter_element(1, 1, index);

	getFEEngine().interpolateOnIntegrationPoints(*velocity, vel_on_quad,
	spatial_dimension,
	type, _not_ghost,
	filter_element);

	Array<Real>::vector_iterator vit = vel_on_quad.begin(spatial_dimension);
	Array<Real>::vector_iterator vend = vel_on_quad.end(spatial_dimension);

	Vector<Real> rho_v2(nb_quadrature_points);

	Real rho = materials[material_index(type)(index)]->getRho();

	for (UInt q = 0; vit != vend; ++vit, ++q) {
	rho_v2(q) = rho * vit->dot(*vit);
	}

	AKANTU_DEBUG_OUT();

	return .5*getFEEngine().integrate(rho_v2, type, index);
	}


	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getExternalWork() {
	AKANTU_DEBUG_IN();

	Real * incr_or_velo = NULL;
	if(this->method == _static){
	incr_or_velo = this->increment->storage();
	}
	else
	incr_or_velo = this->velocity->storage();
	Real * forc = this->force->storage();
	Real * resi = this->residual->storage();
	bool * boun = this->blocked_dofs->storage();

	Real work = 0.;

	UInt nb_nodes = this->mesh.getNbNodes();

	for (UInt n = 0; n < nb_nodes; ++n) {
	bool is_local_node = this->mesh.isLocalOrMasterNode(n);
	bool is_not_pbc_slave_node = !this->isPBCSlaveNode(n);
	bool count_node = is_local_node && is_not_pbc_slave_node;

	for (UInt i = 0; i < this->spatial_dimension; ++i) {
	if (count_node) {
	if(*boun)
	work -= resi *incr_or_velo;
	else
	work += forc *incr_or_velo;
	}

	++incr_or_velo;
	++forc;
	++resi;
	++boun;
	}
	}

	StaticCommunicator::getStaticCommunicator().allReduce(&work, 1, _so_sum);

	if(this->method != _static)
	work *= this->time_step;
	AKANTU_DEBUG_OUT();
	return work;
	}

	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy();
	} else if (energy_id == "external work"){
	return getExternalWork();
	}

	Real energy = 0.;
	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	energy += (*mat_it)->getEnergy(energy_id);
	}

	/// reduction sum over all processors
	StaticCommunicator::getStaticCommunicator().allReduce(&energy, 1, _so_sum);

	AKANTU_DEBUG_OUT();
	return energy;
	}
	/* -------------------------------------------------------------------------- */
	Real SolidMechanicsModel::getEnergy(const std::string & energy_id,
	const ElementType & type,
	UInt index) {
	AKANTU_DEBUG_IN();

	if (energy_id == "kinetic") {
	return getKineticEnergy(type, index);
	}

	std::vector<Material *>::iterator mat_it;
	UInt mat_index = this->material_index(type, _not_ghost)(index);
	UInt mat_loc_num = this->material_local_numbering(type, _not_ghost)(index);
	Real energy = this->materials[mat_index]->getEnergy(energy_id, type, mat_loc_num);

	AKANTU_DEBUG_OUT();
	return energy;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & event) {
	AKANTU_DEBUG_IN();

	this->getFEEngine().initShapeFunctions(_not_ghost);
	this->getFEEngine().initShapeFunctions(_ghost);

	for(UInt g = _not_ghost; g <= _ghost; ++g) {
	GhostType gt = (GhostType) g;
	Mesh::type_iterator it = this->mesh.firstType(spatial_dimension, gt, _ek_not_defined);
	Mesh::type_iterator end = this->mesh.lastType(spatial_dimension, gt, _ek_not_defined);
	for(; it != end; ++it) {
	UInt nb_element = this->mesh.getNbElement(*it, gt);
	if(!material_index.exists(*it, gt)) {
	this->material_index .alloc(nb_element, 1, *it, gt);
	this->material_local_numbering.alloc(nb_element, 1, *it, gt);
	} else {
	this->material_index (*it, gt).resize(nb_element);
	this->material_local_numbering(*it, gt).resize(nb_element);
	}
	}
	}

	Array<Element>::const_iterator<Element> it = element_list.begin();
	Array<Element>::const_iterator<Element> end = element_list.end();

	ElementTypeMapArray<UInt> filter("new_element_filter", this->getID());

	for (UInt el = 0; it != end; ++it, ++el) {
	const Element & elem = *it;

	if(!filter.exists(elem.type, elem.ghost_type))
	filter.alloc(0, 1, elem.type, elem.ghost_type);

	filter(elem.type, elem.ghost_type).push_back(elem.element);
	}

	this->assignMaterialToElements(&filter);

	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	(*mat_it)->onElementsAdded(element_list, event);
	}

	if(method == _explicit_lumped_mass) this->assembleMassLumped();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onElementsRemoved(__attribute__((unused)) const Array<Element> & element_list,
	const ElementTypeMapArray<UInt> & new_numbering,
	const RemovedElementsEvent & event) {
	this->getFEEngine().initShapeFunctions(_not_ghost);
	this->getFEEngine().initShapeFunctions(_ghost);

	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	(*mat_it)->onElementsRemoved(element_list, new_numbering, event);
	}

	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesAdded(const Array<UInt> & nodes_list,
	__attribute__((unused)) const NewNodesEvent & event) {
	AKANTU_DEBUG_IN();
	UInt nb_nodes = mesh.getNbNodes();

	if(displacement) displacement->resize(nb_nodes);
	if(mass ) mass ->resize(nb_nodes);
	if(velocity ) velocity ->resize(nb_nodes);
	if(acceleration) acceleration->resize(nb_nodes);
	if(force ) force ->resize(nb_nodes);
	if(residual ) residual ->resize(nb_nodes);
	if(blocked_dofs) blocked_dofs->resize(nb_nodes);

	if(previous_displacement) previous_displacement->resize(nb_nodes);
	if(increment_acceleration) increment_acceleration->resize(nb_nodes);
	if(increment) increment->resize(nb_nodes);

	if(current_position) current_position->resize(nb_nodes);

	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	(*mat_it)->onNodesAdded(nodes_list, event);
	}

	delete dof_synchronizer;
	dof_synchronizer = new DOFSynchronizer(mesh, spatial_dimension);
	dof_synchronizer->initLocalDOFEquationNumbers();
	dof_synchronizer->initGlobalDOFEquationNumbers();

	if (method != _explicit_lumped_mass) {
	this->initSolver();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::onNodesRemoved(__attribute__((unused)) const Array<UInt> & element_list,
	const Array<UInt> & new_numbering,
	__attribute__((unused)) const RemovedNodesEvent & event) {
	if(displacement) mesh.removeNodesFromArray(*displacement, new_numbering);
	if(mass ) mesh.removeNodesFromArray(*mass , new_numbering);
	if(velocity ) mesh.removeNodesFromArray(*velocity , new_numbering);
	if(acceleration) mesh.removeNodesFromArray(*acceleration, new_numbering);
	if(force ) mesh.removeNodesFromArray(*force , new_numbering);
	if(residual ) mesh.removeNodesFromArray(*residual , new_numbering);
	if(blocked_dofs) mesh.removeNodesFromArray(*blocked_dofs, new_numbering);

	if(increment_acceleration) mesh.removeNodesFromArray(*increment_acceleration, new_numbering);
	if(increment) mesh.removeNodesFromArray(*increment , new_numbering);

	delete dof_synchronizer;
	dof_synchronizer = new DOFSynchronizer(mesh, spatial_dimension);
	dof_synchronizer->initLocalDOFEquationNumbers();
	dof_synchronizer->initGlobalDOFEquationNumbers();

	if (method != _explicit_lumped_mass) {
	this->initSolver();
	}

	}

	/* -------------------------------------------------------------------------- */
	bool SolidMechanicsModel::isInternal(const std::string & field_name,
	const ElementKind & element_kind) {

	bool is_internal = false;

	/// check if at least one material contains field_id as an internal
	for (UInt m = 0; m < materials.size() && !is_internal; ++m) {
	is_internal \|= materials[m]->isInternal<Real>(field_name, element_kind);
	}

	return is_internal;
	}
	/* -------------------------------------------------------------------------- */
	ElementTypeMap<UInt>
	SolidMechanicsModel::getInternalDataPerElem(const std::string & field_name,
	const ElementKind & element_kind) {

	if (!(this->isInternal(field_name, element_kind)))
	AKANTU_EXCEPTION("unknown internal " << field_name);

	for (UInt m = 0; m < materials.size(); ++m) {
	if (materials[m]->isInternal<Real>(field_name, element_kind))
	return materials[m]->getInternalDataPerElem<Real>(field_name, element_kind);
	}

	return ElementTypeMap<UInt>();
	}

	/* -------------------------------------------------------------------------- */
	ElementTypeMapArray<Real> &
	SolidMechanicsModel::flattenInternal(const std::string & field_name,
	const ElementKind & kind,
	const GhostType ghost_type) {
	std::pair<std::string, ElementKind> key(field_name, kind);
	if (this->registered_internals.count(key) == 0) {
	this->registered_internals[key] =
	new ElementTypeMapArray<Real>(field_name, this->id);
	}

	ElementTypeMapArray<Real> * internal_flat = this->registered_internals[key];

	typedef ElementTypeMapArray<Real>::type_iterator iterator;
	iterator tit = internal_flat->firstType(spatial_dimension, ghost_type, kind);
	iterator end = internal_flat->lastType(spatial_dimension, ghost_type, kind);

	for (; tit != end; ++tit) {
	ElementType type = *tit;
	(*internal_flat)(type, ghost_type).clear();
	}

	for (UInt m = 0; m < materials.size(); ++m) {
	if (materials[m]->isInternal<Real>(field_name, kind))
	materials[m]->flattenInternal(field_name, *internal_flat, ghost_type,
	kind);
	}

	return *internal_flat;
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::flattenAllRegisteredInternals(
	const ElementKind & kind) {

	typedef std::map<std::pair<std::string, ElementKind>,
	ElementTypeMapArray<Real> *>::iterator iterator;
	iterator it = this->registered_internals.begin();
	iterator end = this->registered_internals.end();

	while (it != end) {
	if (kind == it->first.second)
	this->flattenInternal(it->first.first, kind);
	++it;
	}
	}

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

	void SolidMechanicsModel::onDump(){
	this->flattenAllRegisteredInternals(_ek_regular);
	}
	/* -------------------------------------------------------------------------- */

	#ifdef AKANTU_USE_IOHELPER

	dumper::Field * SolidMechanicsModel
	::createElementalField(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag,
	const UInt & spatial_dimension,
	const ElementKind & kind) {

	dumper::Field * field = NULL;

	if(field_name == "partitions")
	field = mesh.createElementalField<UInt, dumper::ElementPartitionField>(mesh.getConnectivities(),group_name,spatial_dimension,kind);
	else if(field_name == "material_index")
	field = mesh.createElementalField<UInt, Vector, dumper::ElementalField >(material_index,group_name,spatial_dimension,kind);
	else {
	// this copy of field_name is used to compute derivated data such as
	// strain and von mises stress that are based on grad_u and stress
	std::string field_name_copy(field_name);

	if (field_name == "strain"
	\|\| field_name == "Green strain"
	\|\| field_name == "principal strain"
	\|\| field_name == "principal Green strain")
	field_name_copy = "grad_u";
	else if (field_name == "Von Mises stress")
	field_name_copy = "stress";

	bool is_internal = this->isInternal(field_name_copy,kind);

	if (is_internal) {
	ElementTypeMap<UInt> nb_data_per_elem = this->getInternalDataPerElem(field_name_copy, kind);
	ElementTypeMapArray<Real> & internal_flat = this->flattenInternal(field_name_copy,kind);
	field = mesh.createElementalField<Real, dumper::InternalMaterialField>(internal_flat,
	group_name,
	spatial_dimension,kind,nb_data_per_elem);
	if (field_name == "strain"){
	dumper::ComputeStrain<false> * foo = new dumper::ComputeStrain<false>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	} else if (field_name == "Von Mises stress") {
	dumper::ComputeVonMisesStress * foo = new dumper::ComputeVonMisesStress(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	} else if (field_name == "Green strain") {
	dumper::ComputeStrain<true> * foo = new dumper::ComputeStrain<true>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	} else if (field_name == "principal strain") {
	dumper::ComputePrincipalStrain<false> * foo = new dumper::ComputePrincipalStrain<false>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	} else if (field_name == "principal Green strain") {
	dumper::ComputePrincipalStrain<true> * foo = new dumper::ComputePrincipalStrain<true>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	}

	//treat the paddings
	if (padding_flag){
	if (field_name == "stress"){
	if (spatial_dimension == 2) {
	dumper::StressPadder<2> * foo = new dumper::StressPadder<2>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	}
	} else if (field_name == "strain" \|\| field_name == "Green strain"){
	if (spatial_dimension == 2) {
	dumper::StrainPadder<2> * foo = new dumper::StrainPadder<2>(*this);
	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);
	}
	}
	}

	// homogenize the field
	dumper::ComputeFunctorInterface * foo =
	dumper::HomogenizerProxy::createHomogenizer(*field);

	field = dumper::FieldComputeProxy::createFieldCompute(field,*foo);

	}
	}
	return field;
	}

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

	dumper::Field * SolidMechanicsModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	std::map<std::string,Array<Real>* > real_nodal_fields;
	real_nodal_fields["displacement" ] = displacement;
	real_nodal_fields["mass" ] = mass;
	real_nodal_fields["velocity" ] = velocity;
	real_nodal_fields["acceleration" ] = acceleration;
	real_nodal_fields["force" ] = force;
	real_nodal_fields["residual" ] = residual;
	real_nodal_fields["increment" ] = increment;

	dumper::Field * field = NULL;
	if (padding_flag)
	field = mesh.createNodalField(real_nodal_fields[field_name], group_name, 3);
	else
	field = mesh.createNodalField(real_nodal_fields[field_name], group_name);

	return field;
	}
	/* -------------------------------------------------------------------------- */

	dumper::Field * SolidMechanicsModel::createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {

	std::map<std::string,Array<bool>* > uint_nodal_fields;
	uint_nodal_fields["blocked_dofs" ] = blocked_dofs;

	dumper::Field * field = NULL;
	field = mesh.createNodalField(uint_nodal_fields[field_name],group_name);
	return field;

	}
	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */

	dumper::Field * SolidMechanicsModel
	::createElementalField(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag,
	const UInt & spatial_dimension,
	const ElementKind & kind){
	return NULL;
	}

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

	dumper::Field * SolidMechanicsModel::createNodalFieldReal(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {
	return NULL;
	}

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

	dumper::Field * SolidMechanicsModel::createNodalFieldBool(const std::string & field_name,
	const std::string & group_name,
	bool padding_flag) {
	return NULL;
	}

	#endif
	/* -------------------------------------------------------------------------- */

	void SolidMechanicsModel::dump(const std::string & dumper_name) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(const std::string & dumper_name, UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name, step);
	}

	/* ------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(const std::string & dumper_name, Real time, UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump() {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::dump(Real time, UInt step) {
	this->onDump();
	EventManager::sendEvent(SolidMechanicsModelEvent::BeforeDumpEvent());
	mesh.dump(time, step);
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::computeCauchyStresses() {
	AKANTU_DEBUG_IN();

	// call compute stiffness matrix on each local elements
	std::vector<Material *>::iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	Material & mat = **mat_it;
	if(mat.isFiniteDeformation())
	mat.computeAllCauchyStresses(_not_ghost);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::saveStressAndStrainBeforeDamage() {
	EventManager::sendEvent(SolidMechanicsModelEvent::BeginningOfDamageIterationEvent());
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::updateEnergiesAfterDamage() {
	EventManager::sendEvent(SolidMechanicsModelEvent::AfterDamageEvent());
	}

	/* -------------------------------------------------------------------------- */
	void SolidMechanicsModel::printself(std::ostream & stream, int indent) const {
	std::string space;
	for(Int i = 0; i < indent; i++, space += AKANTU_INDENT);

	stream << space << "Solid Mechanics Model [" << std::endl;
	stream << space << " + id : " << id << std::endl;
	stream << space << " + spatial dimension : " << spatial_dimension << std::endl;
	stream << space << " + fem [" << std::endl;
	getFEEngine().printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;
	stream << space << " + nodals information [" << std::endl;
	displacement->printself(stream, indent + 2);
	mass ->printself(stream, indent + 2);
	velocity ->printself(stream, indent + 2);
	acceleration->printself(stream, indent + 2);
	force ->printself(stream, indent + 2);
	residual ->printself(stream, indent + 2);
	blocked_dofs->printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + material information [" << std::endl;
	material_index.printself(stream, indent + 2);
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << " + materials [" << std::endl;
	std::vector<Material *>::const_iterator mat_it;
	for(mat_it = materials.begin(); mat_it != materials.end(); ++mat_it) {
	const Material & mat = (mat_it);
	mat.printself(stream, indent + 1);
	}
	stream << space << AKANTU_INDENT << "]" << std::endl;

	stream << space << "]" << std::endl;
	}

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

	__END_AKANTU__

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