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shape_functions_inline_impl.cc
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			/**
			* @file shape_functions_inline_impl.cc
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Fabian Barras <fabian.barras@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Wed Oct 27 2010
			* @date last modification: Thu Oct 15 2015
			*
			* @brief ShapeFunctions inline implementation
			*
			* @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/>.
			*
			*/

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

			__END_AKANTU__
			#include "fe_engine.hh"
			__BEGIN_AKANTU__

			/* -------------------------------------------------------------------------- */
			inline UInt ShapeFunctions::getShapeSize(const ElementType & type) {
			AKANTU_DEBUG_IN();

			UInt shape_size = 0;
			#define GET_SHAPE_SIZE(type) \
			shape_size = ElementClass<type>::getShapeSize()

			AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_SIZE);// ,

			#undef GET_SHAPE_SIZE

			AKANTU_DEBUG_OUT();
			return shape_size;
			}

			/* -------------------------------------------------------------------------- */
			inline UInt ShapeFunctions::getShapeDerivativesSize(const ElementType & type) {
			AKANTU_DEBUG_IN();

			UInt shape_derivatives_size = 0;
			#define GET_SHAPE_DERIVATIVES_SIZE(type) \
			shape_derivatives_size = ElementClass<type>::getShapeDerivativesSize()

			AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_DERIVATIVES_SIZE);// ,

			#undef GET_SHAPE_DERIVATIVES_SIZE

			AKANTU_DEBUG_OUT();
			return shape_derivatives_size;
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void ShapeFunctions::setIntegrationPointsByType(const Matrix<Real> & points,
			const GhostType & ghost_type) {
			integration_points(type, ghost_type).shallowCopy(points);
			}

			/* -------------------------------------------------------------------------- */
			inline void ShapeFunctions::initElementalFieldInterpolationFromIntegrationPoints(const ElementTypeMapArray<Real> & interpolation_points_coordinates,
			ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
			ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
			const ElementTypeMapArray<Real> & quadrature_points_coordinates,
			const ElementTypeMapArray<UInt> * element_filter) const {

			AKANTU_DEBUG_IN();

			UInt spatial_dimension = this->mesh.getSpatialDimension();

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

			GhostType ghost_type = *gt;

			Mesh::type_iterator it, last;

			if(element_filter) {
			it = element_filter->firstType(spatial_dimension, ghost_type);
			last = element_filter->lastType(spatial_dimension, ghost_type);
			}
			else {
			it = mesh.firstType(spatial_dimension, ghost_type);
			last = mesh.lastType(spatial_dimension, ghost_type);
			}
			for (; it != last; ++it) {

			ElementType type = *it;
			UInt nb_element = mesh.getNbElement(type, ghost_type);
			if (nb_element == 0) continue;

			const Array<UInt> * elem_filter;
			if(element_filter) elem_filter = &((*element_filter)(type, ghost_type));
			else elem_filter = &(empty_filter);

			#define AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS(type) \
			initElementalFieldInterpolationFromIntegrationPoints<type>(interpolation_points_coordinates(type, ghost_type), \
			interpolation_points_coordinates_matrices, \
			quad_points_coordinates_inv_matrices, \
			quadrature_points_coordinates(type, ghost_type), \
			ghost_type, \
			*elem_filter) \


			AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS);
			#undef AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			inline void ShapeFunctions::initElementalFieldInterpolationFromIntegrationPoints(const Array<Real> & interpolation_points_coordinates,
			ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
			ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
			const Array<Real> & quadrature_points_coordinates,
			GhostType & ghost_type,
			const Array<UInt> & element_filter) const {

			AKANTU_DEBUG_IN();

			UInt spatial_dimension = this->mesh.getSpatialDimension();
			UInt nb_element = this->mesh.getNbElement(type, ghost_type);
			UInt nb_element_filter;

			if(element_filter == empty_filter)
			nb_element_filter = nb_element;
			else nb_element_filter = element_filter.getSize();

			UInt nb_quad_per_element = GaussIntegrationElement<type>::getNbQuadraturePoints();
			UInt nb_interpolation_points_per_elem = interpolation_points_coordinates.getSize() / nb_element;

			AKANTU_DEBUG_ASSERT(interpolation_points_coordinates.getSize() % nb_element == 0,
			"Number of interpolation points should be a multiple of total number of elements");


			if(!quad_points_coordinates_inv_matrices.exists(type, ghost_type))
			quad_points_coordinates_inv_matrices.alloc(nb_element_filter,
			nb_quad_per_element*nb_quad_per_element,
			type, ghost_type);
			else
			quad_points_coordinates_inv_matrices(type, ghost_type).resize(nb_element_filter);

			if(!interpolation_points_coordinates_matrices.exists(type, ghost_type))
			interpolation_points_coordinates_matrices.alloc(nb_element_filter,
			nb_interpolation_points_per_elem * nb_quad_per_element,
			type, ghost_type);
			else
			interpolation_points_coordinates_matrices(type, ghost_type).resize(nb_element_filter);

			Array<Real> & quad_inv_mat = quad_points_coordinates_inv_matrices(type, ghost_type);
			Array<Real> & interp_points_mat = interpolation_points_coordinates_matrices(type, ghost_type);

			Matrix<Real> quad_coord_matrix(nb_quad_per_element, nb_quad_per_element);

			Array<Real>::const_matrix_iterator quad_coords_it =
			quadrature_points_coordinates.begin_reinterpret(spatial_dimension,
			nb_quad_per_element,
			nb_element_filter);

			Array<Real>::const_matrix_iterator points_coords_begin =
			interpolation_points_coordinates.begin_reinterpret(spatial_dimension,
			nb_interpolation_points_per_elem,
			nb_element);

			Array<Real>::matrix_iterator inv_quad_coord_it =
			quad_inv_mat.begin(nb_quad_per_element, nb_quad_per_element);

			Array<Real>::matrix_iterator int_points_mat_it =
			interp_points_mat.begin(nb_interpolation_points_per_elem, nb_quad_per_element);

			/// loop over the elements of the current material and element type
			for (UInt el = 0; el < nb_element_filter; ++el, ++inv_quad_coord_it,
			++int_points_mat_it, ++quad_coords_it) {
			/// matrix containing the quadrature points coordinates
			const Matrix<Real> & quad_coords = *quad_coords_it;
			/// matrix to store the matrix inversion result
			Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

			/// insert the quad coordinates in a matrix compatible with the interpolation
			buildElementalFieldInterpolationMatrix<type>(quad_coords,
			quad_coord_matrix);

			/// invert the interpolation matrix
			inv_quad_coord_matrix.inverse(quad_coord_matrix);


			/// matrix containing the interpolation points coordinates
			const Matrix<Real> & points_coords = points_coords_begin[element_filter(el)];
			/// matrix to store the interpolation points coordinates
			/// compatible with these functions
			Matrix<Real> & inv_points_coord_matrix = *int_points_mat_it;

			/// insert the quad coordinates in a matrix compatible with the interpolation
			buildElementalFieldInterpolationMatrix<type>(points_coords,
			inv_points_coord_matrix);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			inline void ShapeFunctions::buildInterpolationMatrix(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {
			switch (integration_order) {

			case 1:{
			for (UInt i = 0; i < coordinates.cols(); ++i)
			coordMatrix(i, 0) = 1;
			break;
			}

			case 2:{
			UInt nb_quadrature_points = coordMatrix.cols();

			for (UInt i = 0; i < coordinates.cols(); ++i) {
			coordMatrix(i, 0) = 1;
			for (UInt j = 1; j < nb_quadrature_points; ++j)
			coordMatrix(i, j) = coordinates(j-1, i);
			}
			break;
			}

			default:{

			AKANTU_DEBUG_TO_IMPLEMENT();
			break;
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			template<ElementType type>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix(__attribute__((unused)) const Matrix<Real> & coordinates,
			__attribute__((unused)) Matrix<Real> & coordMatrix,
			__attribute__((unused)) UInt integration_order) const {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_2>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {
			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_3>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {

			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_3>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {
			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_6>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {

			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}


			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_4>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {
			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_10>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {

			buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
			}

			/**
			* @todo Write a more efficient interpolation for quadrangles by
			* dropping unnecessary quadrature points
			*
			*/

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_4>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {

			if(integration_order!=ElementClassProperty<_quadrangle_4>::minimal_integration_order){

			AKANTU_DEBUG_TO_IMPLEMENT();
			} else {

			for (UInt i = 0; i < coordinates.cols(); ++i) {
			Real x = coordinates(0, i);
			Real y = coordinates(1, i);

			coordMatrix(i, 0) = 1;
			coordMatrix(i, 1) = x;
			coordMatrix(i, 2) = y;
			coordMatrix(i, 3) = x * y;
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			template<>
			inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_8>(const Matrix<Real> & coordinates,
			Matrix<Real> & coordMatrix,
			UInt integration_order) const {

			if(integration_order!=ElementClassProperty<_quadrangle_8>::minimal_integration_order){

			AKANTU_DEBUG_TO_IMPLEMENT();
			} else {

			for (UInt i = 0; i < coordinates.cols(); ++i) {

			UInt j = 0;
			Real x = coordinates(0, i);
			Real y = coordinates(1, i);

			for (UInt e = 0; e <= 2; ++e) {
			for (UInt n = 0; n <= 2; ++n) {
			coordMatrix(i, j) = std::pow(x, e) * std::pow(y, n);
			++j;
			}
			}
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			void ShapeFunctions::interpolateElementalFieldFromIntegrationPoints(const ElementTypeMapArray<Real> & field,
			const ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
			const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
			ElementTypeMapArray<Real> & result,
			const GhostType ghost_type,
			const ElementTypeMapArray<UInt> * element_filter) const {

			AKANTU_DEBUG_IN();

			UInt spatial_dimension = this->mesh.getSpatialDimension();

			Mesh::type_iterator it, last;

			if(element_filter) {
			it = element_filter->firstType(spatial_dimension, ghost_type);
			last = element_filter->lastType(spatial_dimension, ghost_type);
			}
			else {
			it = mesh.firstType(spatial_dimension, ghost_type);
			last = mesh.lastType(spatial_dimension, ghost_type);
			}

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

			ElementType type = *it;
			UInt nb_element = mesh.getNbElement(type, ghost_type);
			if (nb_element == 0) continue;

			const Array<UInt> * elem_filter;
			if(element_filter) elem_filter = &((*element_filter)(type, ghost_type));
			else elem_filter = &(empty_filter);

			#define AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS(type) \
			interpolateElementalFieldFromIntegrationPoints<type>(field(type, ghost_type), \
			interpolation_points_coordinates_matrices(type, ghost_type), \
			quad_points_coordinates_inv_matrices(type, ghost_type), \
			result, \
			ghost_type, \
			*elem_filter) \


			AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS);
			#undef AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			inline void ShapeFunctions::interpolateElementalFieldFromIntegrationPoints(const Array<Real> & field,
			const Array<Real> & interpolation_points_coordinates_matrices,
			const Array<Real> & quad_points_coordinates_inv_matrices,
			ElementTypeMapArray<Real> & result,
			const GhostType ghost_type,
			const Array<UInt> & element_filter) const {
			AKANTU_DEBUG_IN();

			UInt nb_element = this->mesh.getNbElement(type, ghost_type);

			UInt nb_quad_per_element = GaussIntegrationElement<type>::getNbQuadraturePoints();
			UInt nb_interpolation_points_per_elem
			= interpolation_points_coordinates_matrices.getNbComponent() / nb_quad_per_element;

			if(!result.exists(type, ghost_type))
			result.alloc(nb_element*nb_interpolation_points_per_elem,
			field.getNbComponent(),
			type, ghost_type);

			if(element_filter != empty_filter)
			nb_element = element_filter.getSize();

			Matrix<Real> coefficients(nb_quad_per_element, field.getNbComponent());

			Array<Real> & result_vec = result(type, ghost_type);


			Array<Real>::const_matrix_iterator field_it
			= field.begin_reinterpret(field.getNbComponent(),
			nb_quad_per_element,
			nb_element);

			Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
			interpolation_points_coordinates_matrices.begin(nb_interpolation_points_per_elem, nb_quad_per_element);

			Array<Real>::matrix_iterator result_begin
			= result_vec.begin_reinterpret(field.getNbComponent(),
			nb_interpolation_points_per_elem,
			result_vec.getSize() / nb_interpolation_points_per_elem);

			Array<Real>::const_matrix_iterator inv_quad_coord_it =
			quad_points_coordinates_inv_matrices.begin(nb_quad_per_element, nb_quad_per_element);

			/// loop over the elements of the current filter and element type
			for (UInt el = 0; el < nb_element;
			++el, ++field_it, ++inv_quad_coord_it, ++interpolation_points_coordinates_it) {
			/**
			* matrix containing the inversion of the quadrature points'
			* coordinates
			*/
			const Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;

			/**
			* multiply it by the field values over quadrature points to get
			* the interpolation coefficients
			*/
			coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);

			/// matrix containing the points' coordinates
			const Matrix<Real> & coord = *interpolation_points_coordinates_it;

			/// multiply the coordinates matrix by the coefficients matrix and store the result
			Matrix<Real> res(result_begin[element_filter(el)]);
			res.mul<true, true>(coefficients, coord);
			}

			AKANTU_DEBUG_OUT();

			}
			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			inline void ShapeFunctions::interpolateElementalFieldOnIntegrationPoints(const Array<Real> &u_el,
			Array<Real> &uq,
			GhostType ghost_type,
			const Array<Real> & shapes,
			const Array<UInt> & filter_elements) const {
			UInt nb_element;
			UInt nb_points = integration_points(type, ghost_type).cols();
			UInt nb_nodes_per_element = ElementClass<type>::getShapeSize();
			UInt nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;

			Array<Real>::const_matrix_iterator N_it;
			Array<Real>::const_matrix_iterator u_it;
			Array<Real>::matrix_iterator inter_u_it;

			Array<Real> * filtered_N = NULL;
			if(filter_elements != empty_filter) {
			nb_element = filter_elements.getSize();
			filtered_N = new Array<Real>(0, shapes.getNbComponent());
			FEEngine::filterElementalData(mesh, shapes, *filtered_N, type, ghost_type, filter_elements);
			N_it = filtered_N->begin_reinterpret(nb_nodes_per_element, nb_points, nb_element);
			} else {
			nb_element = mesh.getNbElement(type,ghost_type);
			N_it = shapes.begin_reinterpret(nb_nodes_per_element, nb_points, nb_element);
			}

			uq.resize(nb_element*nb_points);

			u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
			inter_u_it = uq.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);

			for (UInt el = 0; el < nb_element; ++el, ++N_it, ++u_it, ++inter_u_it) {
			const Matrix<Real> & u = *u_it;
			const Matrix<Real> & N = *N_it;
			Matrix<Real> & inter_u = *inter_u_it;

			inter_u.mul<false, false>(u, N);
			}

			delete filtered_N;
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void ShapeFunctions::gradientElementalFieldOnIntegrationPoints(const Array<Real> &u_el,
			Array<Real> &out_nablauq,
			GhostType ghost_type,
			const Array<Real> & shapes_derivatives,
			const Array<UInt> & filter_elements) const {
			AKANTU_DEBUG_IN();

			UInt nb_nodes_per_element = ElementClass<type>::getNbNodesPerInterpolationElement();
			UInt nb_points = integration_points(type, ghost_type).cols();
			UInt element_dimension = ElementClass<type>::getNaturalSpaceDimension();
			UInt nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;

			Array<Real>::const_matrix_iterator B_it;
			Array<Real>::const_matrix_iterator u_it;
			Array<Real>::matrix_iterator nabla_u_it;

			UInt nb_element;
			Array<Real> * filtered_B = NULL;
			if(filter_elements != empty_filter) {
			nb_element = filter_elements.getSize();
			filtered_B = new Array<Real>(0, shapes_derivatives.getNbComponent());
			FEEngine::filterElementalData(mesh, shapes_derivatives, *filtered_B, type, ghost_type, filter_elements);
			B_it = filtered_B->begin(element_dimension, nb_nodes_per_element);
			} else {
			B_it = shapes_derivatives.begin(element_dimension, nb_nodes_per_element);
			nb_element = mesh.getNbElement(type, ghost_type);
			}

			out_nablauq.resize(nb_element*nb_points);

			u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
			nabla_u_it = out_nablauq.begin(nb_degree_of_freedom, element_dimension);

			for (UInt el = 0; el < nb_element; ++el, ++u_it) {
			const Matrix<Real> & u = *u_it;
			for (UInt q = 0; q < nb_points; ++q, ++B_it, ++nabla_u_it) {
			const Matrix<Real> & B = *B_it;
			Matrix<Real> & nabla_u = *nabla_u_it;

			nabla_u.mul<false, true>(u, B);
			}
			}

			delete filtered_B;

			AKANTU_DEBUG_OUT();
			}

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

rAKA/src/fe_engine/shape_functions_inline_impl.cc123b4134e86bfeatures/doc_material_p…

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rAKA/src/fe_engine/shape_functions_inline_impl.cc
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shape_functions_inline_impl.cc
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