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heat_transfer_model.cc
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			/**
			* @file heat_transfer_model.cc
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Lucas Frerot <lucas.frerot@epfl.ch>
			* @author David Simon Kammer <david.kammer@epfl.ch>
			* @author Srinivasa Babu Ramisetti <srinivasa.ramisetti@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Rui Wang <rui.wang@epfl.ch>
			*
			* @date creation: Sun May 01 2011
			* @date last modification: Mon Nov 30 2015
			*
			* @brief Implementation of HeatTransferModel class
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2012, 2014, 2015 EPFL (Ecole Polytechnique Fédérale de
			* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
			* Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "aka_common.hh"
			#include "heat_transfer_model.hh"
			#include "group_manager_inline_impl.cc"
			#include "dumpable_inline_impl.hh"
			#include "aka_math.hh"
			#include "aka_common.hh"
			#include "fe_engine_template.hh"
			#include "mesh.hh"
			#include "static_communicator.hh"
			#include "parser.hh"
			#include "generalized_trapezoidal.hh"

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

			#ifdef AKANTU_USE_IOHELPER
			#include "dumper_paraview.hh"
			#include "dumper_elemental_field.hh"
			#include "dumper_element_partition.hh"
			#include "dumper_internal_material_field.hh"
			#endif

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

			const HeatTransferModelOptions
			default_heat_transfer_model_options(_explicit_lumped_capacity);

			/* -------------------------------------------------------------------------- */
			HeatTransferModel::HeatTransferModel(Mesh & mesh, UInt dim, const ID & id,
			const MemoryID & memory_id)
			: Model(mesh, dim, id, memory_id), Parsable(_st_heat, id), integrator(NULL),
			conductivity_matrix(NULL), capacity_matrix(NULL), jacobian_matrix(NULL),
			temperature_gradient("temperature_gradient", id),
			temperature_on_qpoints("temperature_on_qpoints", id),
			conductivity_on_qpoints("conductivity_on_qpoints", id),
			k_gradt_on_qpoints("k_gradt_on_qpoints", id),
			int_bt_k_gT("int_bt_k_gT", id), bt_k_gT("bt_k_gT", id),
			conductivity(spatial_dimension, spatial_dimension),
			thermal_energy("thermal_energy", id), solver(NULL), pbc_synch(NULL) {
			AKANTU_DEBUG_IN();

			createSynchronizerRegistry(this);

			std::stringstream sstr;
			sstr << id << ":fem";
			registerFEEngineObject<MyFEEngineType>(sstr.str(), mesh, spatial_dimension);

			this->temperature = NULL;
			this->residual = NULL;
			this->blocked_dofs = NULL;

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

			this->registerParam("conductivity", conductivity, _pat_parsmod);
			this->registerParam("conductivity_variation", conductivity_variation, 0.,
			_pat_parsmod);
			this->registerParam("temperature_reference", T_ref, 0., _pat_parsmod);
			this->registerParam("capacity", capacity, _pat_parsmod);
			this->registerParam("density", density, _pat_parsmod);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::initModel() {
			getFEEngine().initShapeFunctions(_not_ghost);
			getFEEngine().initShapeFunctions(_ghost);
			}

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

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

			synch_registry->registerSynchronizer(synch_parallel, _gst_htm_capacity);
			synch_registry->registerSynchronizer(synch_parallel, _gst_htm_temperature);
			synch_registry->registerSynchronizer(synch_parallel,
			_gst_htm_gradient_temperature);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::initPBC() {
			AKANTU_DEBUG_IN();

			Model::initPBC();
			pbc_synch = new PBCSynchronizer(pbc_pair);

			synch_registry->registerSynchronizer(*pbc_synch, _gst_htm_capacity);
			synch_registry->registerSynchronizer(*pbc_synch, _gst_htm_temperature);
			changeLocalEquationNumberForPBC(pbc_pair, 1);

			// 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();
			while (it != end) {
			(blocked_dofs)((it).first, 0) = true;
			++it;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::initArrays() {
			AKANTU_DEBUG_IN();

			UInt nb_nodes = getFEEngine().getMesh().getNbNodes();

			std::stringstream sstr_temp;
			sstr_temp << Model::id << ":temperature";
			std::stringstream sstr_temp_rate;
			sstr_temp_rate << Model::id << ":temperature_rate";
			std::stringstream sstr_inc;
			sstr_inc << Model::id << ":increment";
			std::stringstream sstr_ext_flx;
			sstr_ext_flx << Model::id << ":external_flux";
			std::stringstream sstr_residual;
			sstr_residual << Model::id << ":residual";
			std::stringstream sstr_lump;
			sstr_lump << Model::id << ":lumped";
			std::stringstream sstr_boun;
			sstr_boun << Model::id << ":blocked_dofs";

			temperature = &(alloc<Real>(sstr_temp.str(), nb_nodes, 1, REAL_INIT_VALUE));
			temperature_rate =
			&(alloc<Real>(sstr_temp_rate.str(), nb_nodes, 1, REAL_INIT_VALUE));
			increment = &(alloc<Real>(sstr_inc.str(), nb_nodes, 1, REAL_INIT_VALUE));
			external_heat_rate =
			&(alloc<Real>(sstr_ext_flx.str(), nb_nodes, 1, REAL_INIT_VALUE));
			residual = &(alloc<Real>(sstr_residual.str(), nb_nodes, 1, REAL_INIT_VALUE));
			capacity_lumped =
			&(alloc<Real>(sstr_lump.str(), nb_nodes, 1, REAL_INIT_VALUE));
			blocked_dofs = &(alloc<bool>(sstr_boun.str(), nb_nodes, 1, false));

			Mesh::ConnectivityTypeList::const_iterator it;

			/* --------------------------------------------------------------------------
			*/
			// byelementtype vectors
			getFEEngine().getMesh().initElementTypeMapArray(temperature_on_qpoints, 1,
			spatial_dimension);

			getFEEngine().getMesh().initElementTypeMapArray(
			temperature_gradient, spatial_dimension, spatial_dimension);

			getFEEngine().getMesh().initElementTypeMapArray(
			conductivity_on_qpoints, spatial_dimension * spatial_dimension,
			spatial_dimension);

			getFEEngine().getMesh().initElementTypeMapArray(
			k_gradt_on_qpoints, spatial_dimension, spatial_dimension);

			getFEEngine().getMesh().initElementTypeMapArray(bt_k_gT, 1, spatial_dimension,
			true);

			getFEEngine().getMesh().initElementTypeMapArray(int_bt_k_gT, 1,
			spatial_dimension, true);

			getFEEngine().getMesh().initElementTypeMapArray(thermal_energy, 1,
			spatial_dimension);

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

			const Mesh::ConnectivityTypeList & type_list =
			getFEEngine().getMesh().getConnectivityTypeList(gt);

			for (it = type_list.begin(); it != type_list.end(); ++it) {
			if (Mesh::getSpatialDimension(*it) != spatial_dimension)
			continue;
			UInt nb_element = getFEEngine().getMesh().getNbElement(*it, gt);
			UInt nb_quad_points =
			this->getFEEngine().getNbIntegrationPoints(it, gt) nb_element;

			temperature_on_qpoints(*it, gt).resize(nb_quad_points);
			temperature_on_qpoints(*it, gt).clear();

			temperature_gradient(*it, gt).resize(nb_quad_points);
			temperature_gradient(*it, gt).clear();

			conductivity_on_qpoints(*it, gt).resize(nb_quad_points);
			conductivity_on_qpoints(*it, gt).clear();

			k_gradt_on_qpoints(*it, gt).resize(nb_quad_points);
			k_gradt_on_qpoints(*it, gt).clear();

			bt_k_gT(*it, gt).resize(nb_quad_points);
			bt_k_gT(*it, gt).clear();

			int_bt_k_gT(*it, gt).resize(nb_element);
			int_bt_k_gT(*it, gt).clear();

			thermal_energy(*it, gt).resize(nb_element);
			thermal_energy(*it, gt).clear();
			}
			}

			/* --------------------------------------------------------------------------
			*/
			dof_synchronizer = new DOFSynchronizer(getFEEngine().getMesh(), 1);
			dof_synchronizer->initLocalDOFEquationNumbers();
			dof_synchronizer->initGlobalDOFEquationNumbers();

			AKANTU_DEBUG_OUT();
			}

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

			void HeatTransferModel::initSolver(__attribute__((unused))
			SolverOptions & options) {
			#if !defined(AKANTU_USE_MUMPS) // 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 << Memory::id << ":jacobian_matrix";
			jacobian_matrix =
			new SparseMatrix(nb_global_nodes, _symmetric, sstr.str(), memory_id);

			jacobian_matrix->buildProfile(mesh, *dof_synchronizer, 1);

			delete conductivity_matrix;
			std::stringstream sstr_sti;
			sstr_sti << Memory::id << ":conductivity_matrix";
			conductivity_matrix =
			new SparseMatrix(*jacobian_matrix, sstr_sti.str(), memory_id);

			#ifdef AKANTU_USE_MUMPS
			std::stringstream sstr_solv;
			sstr_solv << Memory::id << ":solver";
			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 HeatTransferModel::initImplicit(bool dynamic,
			SolverOptions & solver_options) {
			AKANTU_DEBUG_IN();

			method = dynamic ? _implicit_dynamic : _static;
			initSolver(solver_options);

			if (method == _implicit_dynamic) {
			if (integrator)
			delete integrator;
			integrator = new TrapezoidalRule1();
			}

			AKANTU_DEBUG_OUT();
			}

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

			HeatTransferModel::~HeatTransferModel() {
			AKANTU_DEBUG_IN();
			if (integrator)
			delete integrator;
			if (conductivity_matrix)
			delete conductivity_matrix;
			if (capacity_matrix)
			delete capacity_matrix;
			if (jacobian_matrix)
			delete jacobian_matrix;
			if (solver)
			delete solver;

			delete pbc_synch;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::assembleCapacityLumped(const GhostType & ghost_type) {
			AKANTU_DEBUG_IN();

			FEEngine & fem = getFEEngine();

			const Mesh::ConnectivityTypeList & type_list =
			fem.getMesh().getConnectivityTypeList(ghost_type);

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

			UInt nb_element = getFEEngine().getMesh().getNbElement(*it, ghost_type);
			UInt nb_quadrature_points =
			getFEEngine().getNbIntegrationPoints(*it, ghost_type);

			Array<Real> rho_1(nb_element * nb_quadrature_points, 1, capacity * density);
			fem.assembleFieldLumped(rho_1, 1, *capacity_lumped,
			dof_synchronizer->getLocalDOFEquationNumbers(), *it,
			ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::assembleCapacityLumped() {
			AKANTU_DEBUG_IN();

			capacity_lumped->clear();

			assembleCapacityLumped(_not_ghost);
			assembleCapacityLumped(_ghost);

			getSynchronizerRegistry().synchronize(_gst_htm_capacity);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::updateResidual(
			__attribute__((unused)) bool compute_conductivity) {
			AKANTU_DEBUG_IN();
			/// @f$ r = q_{ext} - q_{int} - C \dot T @f$

			// start synchronization
			synch_registry->asynchronousSynchronize(_gst_htm_temperature);
			// finalize communications
			synch_registry->waitEndSynchronize(_gst_htm_temperature);

			// clear the array
			/// first @f$ r = q_{ext} @f$
			// residual->clear();
			residual->copy(*external_heat_rate);

			/// then @f$ r -= q_{int} @f$
			// update the not ghost ones

			updateResidual(_not_ghost);
			// update for the received ghosts
			updateResidual(_ghost);

			/* if (method == _explicit_lumped_capacity) {
			this->solveExplicitLumped();
			}*/

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::assembleConductivityMatrix(bool compute_conductivity) {
			AKANTU_DEBUG_IN();

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

			conductivity_matrix->clear();

			switch (mesh.getSpatialDimension()) {
			case 1:
			this->assembleConductivityMatrix<1>(_not_ghost, compute_conductivity);
			break;
			case 2:
			this->assembleConductivityMatrix<2>(_not_ghost, compute_conductivity);
			break;
			case 3:
			this->assembleConductivityMatrix<3>(_not_ghost, compute_conductivity);
			break;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void HeatTransferModel::assembleConductivityMatrix(const GhostType & ghost_type,
			bool compute_conductivity) {
			AKANTU_DEBUG_IN();

			Mesh & mesh = this->getFEEngine().getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, ghost_type);
			for (; it != last_type; ++it) {
			this->assembleConductivityMatrix<dim>(*it, ghost_type,
			compute_conductivity);
			}

			AKANTU_DEBUG_OUT();
			}

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

			/* -------------------------------------------------------------------------- */
			template <UInt dim>
			void HeatTransferModel::assembleConductivityMatrix(const ElementType & type,
			const GhostType & ghost_type,
			bool compute_conductivity) {
			AKANTU_DEBUG_IN();

			SparseMatrix & K = *conductivity_matrix;
			const Array<Real> & shapes_derivatives =
			this->getFEEngine().getShapesDerivatives(type, ghost_type);

			UInt nb_element = mesh.getNbElement(type, ghost_type);
			UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			UInt nb_quadrature_points =
			getFEEngine().getNbIntegrationPoints(type, ghost_type);

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			UInt bt_d_b_size = nb_nodes_per_element;

			Array<Real> * bt_d_b = new Array<Real>(nb_element * nb_quadrature_points,
			bt_d_b_size * bt_d_b_size, "B^tDB");

			Matrix<Real> Bt_D(nb_nodes_per_element, dim);

			Array<Real>::const_iterator<Matrix<Real> > shapes_derivatives_it =
			shapes_derivatives.begin(dim, nb_nodes_per_element);

			Array<Real>::iterator<Matrix<Real> > Bt_D_B_it =
			bt_d_b->begin(bt_d_b_size, bt_d_b_size);

			if (compute_conductivity)
			this->computeConductivityOnQuadPoints(ghost_type);
			Array<Real>::iterator<Matrix<Real> > D_it =
			conductivity_on_qpoints(type, ghost_type).begin(dim, dim);
			Array<Real>::iterator<Matrix<Real> > D_end =
			conductivity_on_qpoints(type, ghost_type).end(dim, dim);

			for (; D_it != D_end; ++D_it, ++Bt_D_B_it, ++shapes_derivatives_it) {
			Matrix<Real> & D = *D_it;
			const Matrix<Real> & B = *shapes_derivatives_it;
			Matrix<Real> & Bt_D_B = *Bt_D_B_it;

			Bt_D.mul<true, false>(B, D);
			Bt_D_B.mul<false, false>(Bt_D, B);
			}

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			Array<Real> * K_e =
			new Array<Real>(nb_element, bt_d_b_size * bt_d_b_size, "K_e");

			this->getFEEngine().integrate(bt_d_b, K_e, bt_d_b_size * bt_d_b_size, type,
			ghost_type);

			delete bt_d_b;

			this->getFEEngine().assembleMatrix(*K_e, K, 1, type, ghost_type);
			delete K_e;

			AKANTU_DEBUG_OUT();
			}

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

			void HeatTransferModel::updateResidualInternal() {

			AKANTU_DEBUG_IN();

			AKANTU_DEBUG_INFO("Update the residual");
			// f = q_ext - q_int - Mddot = q - Mddot;

			if (method != _static) {
			// f -= Mddot
			if (capacity_matrix) {
			// if full mass_matrix
			Array<Real> * Mddot = new Array<Real>(*temperature_rate, true, "Mddot");
			Mddot = *capacity_matrix;
			residual -= Mddot;
			delete Mddot;
			} else if (capacity_lumped) {

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

			Real * capacity_val = capacity_lumped->storage();
			Real * temp_rate_val = temperature_rate->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 -= temp_rate_val ** capacity_val;
			}
			blocked_dofs_val++;
			res_val++;
			capacity_val++;
			temp_rate_val++;
			}
			} else {
			AKANTU_DEBUG_ERROR("No function called to assemble the mass matrix.");
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::solveStatic() {
			AKANTU_DEBUG_IN();

			AKANTU_DEBUG_INFO("Solving Ku = f");
			AKANTU_DEBUG_ASSERT(conductivity_matrix != NULL,
			"You should first initialize the implicit solver and "
			"assemble the stiffness matrix");

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

			jacobian_matrix->copyContent(*conductivity_matrix);
			jacobian_matrix->applyBoundary(*blocked_dofs);

			increment->clear();

			solver->setRHS(*residual);
			solver->factorize();
			solver->solve(*increment);

			Real * increment_val = increment->storage();
			Real * temperature_val = temperature->storage();
			bool * blocked_dofs_val = blocked_dofs->storage();

			for (UInt j = 0; j < nb_degree_of_freedom;
			++j, ++temperature_val, ++increment_val, ++blocked_dofs_val) {
			if (!(*blocked_dofs_val)) {
			temperature_val += increment_val;
			} else {
			*increment_val = 0.0;
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::computeConductivityOnQuadPoints(
			const GhostType & ghost_type) {
			const Mesh::ConnectivityTypeList & type_list =
			this->getFEEngine().getMesh().getConnectivityTypeList(ghost_type);
			Mesh::ConnectivityTypeList::const_iterator it;

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

			Array<Real> & temperature_interpolated =
			temperature_on_qpoints(*it, ghost_type);

			// compute the temperature on quadrature points
			this->getFEEngine().interpolateOnIntegrationPoints(
			temperature, temperature_interpolated, 1, it, ghost_type);

			Array<Real>::matrix_iterator C_it =
			conductivity_on_qpoints(*it, ghost_type)
			.begin(spatial_dimension, spatial_dimension);
			Array<Real>::matrix_iterator C_end =
			conductivity_on_qpoints(*it, ghost_type)
			.end(spatial_dimension, spatial_dimension);

			Array<Real>::iterator<Real> T_it = temperature_interpolated.begin();

			for (; C_it != C_end; ++C_it, ++T_it) {
			Matrix<Real> & C = *C_it;
			Real & T = *T_it;
			C = conductivity;

			Matrix<Real> variation(spatial_dimension, spatial_dimension,
			conductivity_variation * (T - T_ref));
			C += conductivity_variation;
			}
			}
			AKANTU_DEBUG_OUT();
			}
			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::computeKgradT(const GhostType & ghost_type,
			bool compute_conductivity) {

			if (compute_conductivity)
			computeConductivityOnQuadPoints(ghost_type);

			const Mesh::ConnectivityTypeList & type_list =
			this->getFEEngine().getMesh().getConnectivityTypeList(ghost_type);
			Mesh::ConnectivityTypeList::const_iterator it;

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

			Array<Real> & gradient = temperature_gradient(*it, ghost_type);
			this->getFEEngine().gradientOnIntegrationPoints(*temperature, gradient, 1,
			*it, ghost_type);

			Array<Real>::matrix_iterator C_it =
			conductivity_on_qpoints(*it, ghost_type)
			.begin(spatial_dimension, spatial_dimension);

			Array<Real>::vector_iterator BT_it = gradient.begin(spatial_dimension);

			Array<Real>::vector_iterator k_BT_it =
			k_gradt_on_qpoints(type, ghost_type).begin(spatial_dimension);
			Array<Real>::vector_iterator k_BT_end =
			k_gradt_on_qpoints(type, ghost_type).end(spatial_dimension);

			for (; k_BT_it != k_BT_end; ++k_BT_it, ++BT_it, ++C_it) {
			Vector<Real> & k_BT = *k_BT_it;
			Vector<Real> & BT = *BT_it;
			Matrix<Real> & C = *C_it;

			k_BT.mul<false>(C, BT);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::updateResidual(const GhostType & ghost_type,
			bool compute_conductivity) {
			AKANTU_DEBUG_IN();

			const Mesh::ConnectivityTypeList & type_list =
			this->getFEEngine().getMesh().getConnectivityTypeList(ghost_type);
			Mesh::ConnectivityTypeList::const_iterator it;

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

			Array<Real> & shapes_derivatives = const_cast<Array<Real> &>(
			getFEEngine().getShapesDerivatives(*it, ghost_type));

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

			// compute k \grad T
			computeKgradT(ghost_type, compute_conductivity);

			Array<Real>::vector_iterator k_BT_it =
			k_gradt_on_qpoints(*it, ghost_type).begin(spatial_dimension);

			Array<Real>::matrix_iterator B_it =
			shapes_derivatives.begin(spatial_dimension, nb_nodes_per_element);

			Array<Real>::vector_iterator Bt_k_BT_it =
			bt_k_gT(*it, ghost_type).begin(nb_nodes_per_element);

			Array<Real>::vector_iterator Bt_k_BT_end =
			bt_k_gT(*it, ghost_type).end(nb_nodes_per_element);

			for (; Bt_k_BT_it != Bt_k_BT_end; ++Bt_k_BT_it, ++B_it, ++k_BT_it) {
			Vector<Real> & k_BT = *k_BT_it;
			Vector<Real> & Bt_k_BT = *Bt_k_BT_it;
			Matrix<Real> & B = *B_it;

			Bt_k_BT.mul<true>(B, k_BT);
			}

			this->getFEEngine().integrate(bt_k_gT(*it, ghost_type),
			int_bt_k_gT(*it, ghost_type),
			nb_nodes_per_element, *it, ghost_type);

			this->getFEEngine().assembleArray(
			int_bt_k_gT(it, ghost_type), residual,
			dof_synchronizer->getLocalDOFEquationNumbers(), 1, *it, ghost_type,
			empty_filter, -1);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::solveExplicitLumped() {
			AKANTU_DEBUG_IN();

			/// finally @f$ r -= C \dot T @f$
			// lumped C
			UInt nb_nodes = temperature_rate->getSize();
			UInt nb_degree_of_freedom = temperature_rate->getNbComponent();

			Real * capacity_val = capacity_lumped->storage();
			Real * temp_rate_val = temperature_rate->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 -= capacity_val ** temp_rate_val;
			}
			blocked_dofs_val++;
			res_val++;
			capacity_val++;
			temp_rate_val++;
			}

			#ifndef AKANTU_NDEBUG
			getSynchronizerRegistry().synchronize(akantu::_gst_htm_gradient_temperature);
			#endif

			capacity_val = capacity_lumped->storage();
			res_val = residual->storage();
			blocked_dofs_val = blocked_dofs->storage();
			Real * inc = increment->storage();

			for (UInt n = 0; n < nb_nodes * nb_degree_of_freedom; ++n) {
			if (!(*blocked_dofs_val)) {
			inc = (res_val / *capacity_val);
			}
			res_val++;
			blocked_dofs_val++;
			inc++;
			capacity_val++;
			}

			AKANTU_DEBUG_OUT();
			}

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

			AKANTU_DEBUG_ASSERT(integrator, "integrator was not instanciated");
			integrator->integrationSchemePred(time_step, temperature, temperature_rate,
			*blocked_dofs);

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

			Real * temp = temperature->storage();
			for (UInt n = 0; n < nb_nodes * nb_degree_of_freedom; ++n, ++temp)
			if (*temp < 0.)
			*temp = 0.;

			AKANTU_DEBUG_OUT();
			}

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

			integrator->integrationSchemeCorrTempRate(
			time_step, temperature, temperature_rate, blocked_dofs, increment);

			AKANTU_DEBUG_OUT();
			}

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

			if (method == _implicit_dynamic)
			integrator->integrationSchemePred(time_step, *temperature,
			temperature_rate, blocked_dofs);

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

			void HeatTransferModel::implicitCorr() {

			AKANTU_DEBUG_IN();

			if (method == _implicit_dynamic) {
			integrator->integrationSchemeCorrTemp(
			time_step, temperature, temperature_rate, blocked_dofs, increment);
			} else {
			UInt nb_nodes = temperature->getSize();
			UInt nb_degree_of_freedom = temperature->getNbComponent() * nb_nodes;

			Real * incr_val = increment->storage();
			Real * temp_val = temperature->storage();
			bool * boun_val = blocked_dofs->storage();

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

			AKANTU_DEBUG_OUT();
			}

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

			Real el_size;
			Real min_el_size = std::numeric_limits<Real>::max();
			Real conductivitymax = conductivity(0, 0);

			// get the biggest parameter from k11 until k33//
			for (UInt i = 0; i < spatial_dimension; i++)
			for (UInt j = 0; j < spatial_dimension; j++)
			conductivitymax = std::max(conductivity(i, j), conductivitymax);

			const Mesh::ConnectivityTypeList & type_list =
			getFEEngine().getMesh().getConnectivityTypeList();
			Mesh::ConnectivityTypeList::const_iterator it;
			for (it = type_list.begin(); it != type_list.end(); ++it) {
			if (getFEEngine().getMesh().getSpatialDimension(*it) != spatial_dimension)
			continue;

			UInt nb_nodes_per_element =
			getFEEngine().getMesh().getNbNodesPerElement(*it);

			Array<Real> coord(0, nb_nodes_per_element * spatial_dimension);
			FEEngine::extractNodalToElementField(getFEEngine().getMesh(),
			getFEEngine().getMesh().getNodes(),
			coord, *it, _not_ghost);

			Array<Real>::matrix_iterator el_coord =
			coord.begin(spatial_dimension, nb_nodes_per_element);
			UInt nb_element = getFEEngine().getMesh().getNbElement(*it);

			for (UInt el = 0; el < nb_element; ++el, ++el_coord) {
			el_size = getFEEngine().getElementInradius(el_coord, it);
			min_el_size = std::min(min_el_size, el_size);
			}

			AKANTU_DEBUG_INFO("The minimum element size : "
			<< min_el_size
			<< " and the max conductivity is : " << conductivitymax);
			}

			Real min_dt =
			2 * min_el_size * min_el_size * density * capacity / conductivitymax;

			StaticCommunicator::getStaticCommunicator().allReduce(&min_dt, 1, _so_min);

			AKANTU_DEBUG_OUT();

			return min_dt;
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::readMaterials() {
			std::pair<Parser::const_section_iterator, Parser::const_section_iterator>
			sub_sect = this->parser->getSubSections(_st_heat);

			Parser::const_section_iterator it = sub_sect.first;
			const ParserSection & section = *it;

			this->parseSection(section);
			}

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

			void HeatTransferModel::initFull(const ModelOptions & options) {
			Model::initFull(options);

			readMaterials();

			const HeatTransferModelOptions & my_options =
			dynamic_cast<const HeatTransferModelOptions &>(options);

			method = my_options.analysis_method;

			// initialize the vectors
			initArrays();
			temperature->clear();
			temperature_rate->clear();
			external_heat_rate->clear();

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

			if (method == _explicit_lumped_capacity) {
			integrator = new ForwardEuler();
			}
			if (method == _implicit_dynamic) {
			initImplicit(true);
			}
			if (method == _static) {
			initImplicit(false);
			}
			}
			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::assembleCapacity() {
			AKANTU_DEBUG_IN();

			if (!capacity_matrix) {
			std::stringstream sstr;
			sstr << id << ":capacity_matrix";
			capacity_matrix = new SparseMatrix(*jacobian_matrix, sstr.str(), memory_id);
			}

			assembleCapacity(_not_ghost);
			// assembleMass(_ghost);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::assembleCapacity(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();

			Array<Real> rho_1(0, 1);
			// UInt nb_element;
			capacity_matrix->clear();

			Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type);
			Mesh::type_iterator end = mesh.lastType(spatial_dimension, ghost_type);
			for (; it != end; ++it) {
			ElementType type = *it;

			computeRho(rho_1, type, ghost_type);
			fem.assembleFieldMatrix(rho_1, 1, *capacity_matrix, type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

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

			void HeatTransferModel::computeRho(Array<Real> & rho, ElementType type,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			FEEngine & fem = this->getFEEngine();
			UInt nb_element = fem.getMesh().getNbElement(type, ghost_type);
			UInt nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

			rho.resize(nb_element * nb_quadrature_points);
			Real * rho_1_val = rho.storage();

			/// compute @f$ rho @f$ for each nodes of each element
			for (UInt el = 0; el < nb_element; ++el) {

			for (UInt n = 0; n < nb_quadrature_points; ++n) {
			*rho_1_val++ = this->capacity;
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			template <>
			bool HeatTransferModel::testConvergence<_scc_increment>(Real tolerance,
			Real & error) {
			AKANTU_DEBUG_IN();

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

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

			/* -------------------------------------------------------------------------- */
			void HeatTransferModel::initFEEngineBoundary(bool create_surface) {

			if (create_surface)
			MeshUtils::buildFacets(getFEEngine().getMesh());

			FEEngine & fem_boundary = getFEEngineBoundary();
			fem_boundary.initShapeFunctions();
			fem_boundary.computeNormalsOnIntegrationPoints();
			}

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

			Real HeatTransferModel::computeThermalEnergyByNode() {
			AKANTU_DEBUG_IN();

			Real ethermal = 0.;

			Array<Real>::vector_iterator heat_rate_it =
			residual->begin(residual->getNbComponent());

			Array<Real>::vector_iterator heat_rate_end =
			residual->end(residual->getNbComponent());

			UInt n = 0;
			for (; heat_rate_it != heat_rate_end; ++heat_rate_it, ++n) {
			Real heat = 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;

			Vector<Real> & heat_rate = *heat_rate_it;
			for (UInt i = 0; i < heat_rate.size(); ++i) {
			if (count_node)
			heat += heat_rate[i] * time_step;
			}
			ethermal += heat;
			}

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

			AKANTU_DEBUG_OUT();
			return ethermal;
			}

			/* -------------------------------------------------------------------------- */
			template <class iterator>
			void HeatTransferModel::getThermalEnergy(
			iterator Eth, Array<Real>::const_iterator<Real> T_it,
			Array<Real>::const_iterator<Real> T_end) const {
			for (; T_it != T_end; ++T_it, ++Eth) {
			Eth = capacity density ** T_it;
			}
			}

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

			UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
			Vector<Real> Eth_on_quarature_points(nb_quadrature_points);

			Array<Real>::iterator<Real> T_it = this->temperature_on_qpoints(type).begin();
			T_it += index * nb_quadrature_points;

			Array<Real>::iterator<Real> T_end = T_it + nb_quadrature_points;

			getThermalEnergy(Eth_on_quarature_points.storage(), T_it, T_end);

			return getFEEngine().integrate(Eth_on_quarature_points, type, index);
			}

			/* -------------------------------------------------------------------------- */
			Real HeatTransferModel::getThermalEnergy() {
			Real Eth = 0;

			Mesh & mesh = getFEEngine().getMesh();
			Mesh::type_iterator it = mesh.firstType(spatial_dimension);
			Mesh::type_iterator last_type = mesh.lastType(spatial_dimension);
			for (; it != last_type; ++it) {
			UInt nb_element = getFEEngine().getMesh().getNbElement(*it, _not_ghost);
			UInt nb_quadrature_points =
			getFEEngine().getNbIntegrationPoints(*it, _not_ghost);
			Array<Real> Eth_per_quad(nb_element * nb_quadrature_points, 1);

			Array<Real>::iterator<Real> T_it =
			this->temperature_on_qpoints(*it).begin();
			Array<Real>::iterator<Real> T_end = this->temperature_on_qpoints(*it).end();
			getThermalEnergy(Eth_per_quad.begin(), T_it, T_end);

			Eth += getFEEngine().integrate(Eth_per_quad, *it);
			}

			return Eth;
			}

			/* -------------------------------------------------------------------------- */
			Real HeatTransferModel::getEnergy(const std::string & id) {
			AKANTU_DEBUG_IN();
			Real energy = 0;

			if (id == "thermal")
			energy = getThermalEnergy();

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

			AKANTU_DEBUG_OUT();
			return energy;
			}

			/* -------------------------------------------------------------------------- */
			Real HeatTransferModel::getEnergy(const std::string & id,
			const ElementType & type, UInt index) {
			AKANTU_DEBUG_IN();

			Real energy = 0.;

			if (id == "thermal")
			energy = getThermalEnergy(type, index);

			AKANTU_DEBUG_OUT();
			return energy;
			}

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

			/* -------------------------------------------------------------------------- */
			#ifdef AKANTU_USE_IOHELPER

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

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

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

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

			std::map<std::string, Array<Real> *> real_nodal_fields;
			real_nodal_fields["temperature"] = temperature;
			real_nodal_fields["temperature_rate"] = temperature_rate;
			real_nodal_fields["external_heat_rate"] = external_heat_rate;
			real_nodal_fields["residual"] = residual;
			real_nodal_fields["capacity_lumped"] = capacity_lumped;
			real_nodal_fields["increment"] = increment;

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

			return field;
			}

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

			dumper::Field * HeatTransferModel::createElementalField(
			const std::string & field_name, const std::string & group_name,
			__attribute__((unused)) bool padding_flag,
			__attribute__((unused)) const UInt & spatial_dimension,
			const ElementKind & element_kind) {

			dumper::Field * field = NULL;

			if (field_name == "partitions")
			field = mesh.createElementalField<UInt, dumper::ElementPartitionField>(
			mesh.getConnectivities(), group_name, this->spatial_dimension,
			element_kind);
			else if (field_name == "temperature_gradient") {
			ElementTypeMap<UInt> nb_data_per_elem =
			this->mesh.getNbDataPerElem(temperature_gradient, element_kind);

			field = mesh.createElementalField<Real, dumper::InternalMaterialField>(
			temperature_gradient, group_name, this->spatial_dimension, element_kind,
			nb_data_per_elem);
			} else if (field_name == "conductivity") {
			ElementTypeMap<UInt> nb_data_per_elem =
			this->mesh.getNbDataPerElem(conductivity_on_qpoints, element_kind);

			field = mesh.createElementalField<Real, dumper::InternalMaterialField>(
			conductivity_on_qpoints, group_name, this->spatial_dimension,
			element_kind, nb_data_per_elem);
			}

			return field;
			}
			/* -------------------------------------------------------------------------- */
			#else
			/* -------------------------------------------------------------------------- */
			dumper::Field * HeatTransferModel::createElementalField(
			__attribute__((unused)) const std::string & field_name,
			__attribute__((unused)) const std::string & group_name,
			__attribute__((unused)) bool padding_flag,
			__attribute__((unused)) const ElementKind & element_kind) {
			return NULL;
			}

			/* -------------------------------------------------------------------------- */
			dumper::Field * HeatTransferModel::createNodalFieldBool(
			__attribute__((unused)) const std::string & field_name,
			__attribute__((unused)) const std::string & group_name,
			__attribute__((unused)) bool padding_flag) {
			return NULL;
			}

			/* -------------------------------------------------------------------------- */
			dumper::Field * HeatTransferModel::createNodalFieldReal(
			__attribute__((unused)) const std::string & field_name,
			__attribute__((unused)) const std::string & group_name,
			__attribute__((unused)) bool padding_flag) {
			return NULL;
			}

			#endif

			__END_AKANTU__

rAKA/src/model/heat_transfer/heat_transfer_model.cca1b3497b1275features/fe_engine_pyth…

heat_transfer_model.ccView Options

rAKA/src/model/heat_transfer/heat_transfer_model.cc
a1b3497b1275features/fe_engine_pyth…

heat_transfer_model.cc
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