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			/**
			* Copyright (©) 2017-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* This file is part of Akantu
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*/

			/* -------------------------------------------------------------------------- */
			#include "mesh_iterators.hh"
			#include "shape_structural.hh"
			/* -------------------------------------------------------------------------- */

			//#ifndef AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_
			//#define AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_

			namespace akantu {

			namespace {
			/// Extract nodal coordinates per elements
			template <ElementType type>
			std::unique_ptr<Array<Real>> getNodesPerElement(const Mesh & mesh,
			const Array<Real> & nodes,
			GhostType ghost_type) {
			const auto dim = ElementClass<type>::getSpatialDimension();
			const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

			auto nodes_per_element =
			std::make_unique<Array<Real>>(0, dim * nb_nodes_per_element);
			FEEngine::extractNodalToElementField(mesh, nodes, *nodes_per_element, type,
			ghost_type);
			return nodes_per_element;
			}
			} // namespace

			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::computeShapesOnIntegrationPointsInternal(
			const Array<Real> & nodes, const Matrix<Real> & integration_points,
			Array<Real> & shapes, GhostType ghost_type,
			const Array<Idx> & filter_elements, bool mass) const {

			auto nb_points = integration_points.cols();
			auto nb_element = mesh.getConnectivity(type, ghost_type).size();
			const auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();

			shapes.resize(nb_element * nb_points);

			const auto nb_dofs = ElementClass<type>::getNbDegreeOfFreedom();
			auto nb_rows = nb_dofs;

			if (mass) {
			nb_rows = ElementClass<type>::getNbStressComponents();
			}

			#if !defined(AKANTU_NDEBUG)
			Int size_of_shapes = nb_rows * nb_dofs * nb_nodes_per_element;
			AKANTU_DEBUG_ASSERT(shapes.getNbComponent() == size_of_shapes,
			"The shapes array does not have the correct "
			<< "number of component");
			#endif

			const auto nb_cols_shapes =
			ElementClass<type>::getNbNodesPerInterpolationElement() * nb_dofs;
			auto nodes_per_element = getNodesPerElement<type>(mesh, nodes, ghost_type);

			auto shapes_view = make_view(shapes, nb_rows, nb_cols_shapes, nb_points);
			auto nodes_view = make_view<Eigen::Dynamic, nb_nodes_per_element>(
			*nodes_per_element, mesh.getSpatialDimension(), nb_nodes_per_element);
			auto R_view =
			make_view<nb_dofs, nb_dofs>(rotation_matrices(type, ghost_type));

			auto loop_core = [&](auto && data) {
			auto & N = std::get<0>(data);
			auto & X = std::get<1>(data);
			auto & R = std::get<2>(data);

			Matrix<Real, nb_cols_shapes, nb_cols_shapes> T;
			T.zero();

			for (Int i = 0; i < nb_nodes_per_element; ++i) {
			T.template block<nb_dofs, nb_dofs>(i * nb_dofs, i * nb_dofs) = R;
			}

			if (not mass) {
			ElementClass<type>::computeShapes(integration_points, X, T, N);
			} else {
			ElementClass<type>::computeShapesMass(integration_points, X, T, N);
			}
			};

			if (filter_elements == empty_filter) {
			for (auto && data : zip(shapes_view, nodes_view, R_view)) {
			loop_core(data);
			}

			} else {
			for (auto && data :
			filter(filter_elements, zip(shapes_view, nodes_view, R_view))) {
			loop_core(data);
			}
			}
			}

			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::precomputeRotationMatrices(
			const Array<Real> & nodes, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const auto spatial_dimension = mesh.getSpatialDimension();
			const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			const auto nb_element = mesh.getNbElement(type, ghost_type);
			const auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();

			if (not this->rotation_matrices.exists(type, ghost_type)) {
			this->rotation_matrices.alloc(0, nb_dof * nb_dof, type, ghost_type);
			}

			auto & rot_matrices = this->rotation_matrices(type, ghost_type);
			rot_matrices.resize(nb_element);

			Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
			FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

			bool has_extra_normal = mesh.hasData<Real>("extra_normal", type, ghost_type);
			Array<Real>::const_vector_iterator extra_normal;
			if (has_extra_normal) {
			extra_normal = mesh.getData<Real>("extra_normal", type, ghost_type)
			.begin(spatial_dimension);
			}

			for (auto && tuple :
			zip(make_view(x_el, spatial_dimension, nb_nodes_per_element),
			make_view(rot_matrices, nb_dof, nb_dof))) {
			// compute shape derivatives
			auto & X = std::get<0>(tuple);
			auto & R = std::get<1>(tuple);

			if (has_extra_normal) {
			ElementClass<type>::computeRotationMatrix(R, X, *extra_normal);
			++extra_normal;
			} else {
			ElementClass<type>::computeRotationMatrix(
			R, X, Vector<Real>(spatial_dimension));
			}
			}

			AKANTU_DEBUG_OUT();
			}

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

			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::precomputeShapesOnIntegrationPoints(
			const Array<Real> & nodes, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const auto & natural_coords = integration_points(type, ghost_type);
			auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto nb_points = integration_points(type, ghost_type).cols();
			auto nb_element = mesh.getNbElement(type, ghost_type);
			auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
			const auto dim = ElementClass<type>::getSpatialDimension();
			const auto spatial_dimension = mesh.getSpatialDimension();
			const auto natural_spatial_dimension =
			ElementClass<type>::getNaturalSpaceDimension();

			auto itp_type = FEEngine::getInterpolationType(type);
			if (not shapes.exists(itp_type, ghost_type)) {
			auto size_of_shapes = this->getShapeSize(type);
			this->shapes.alloc(0, size_of_shapes, itp_type, ghost_type);
			}

			auto & rot_matrices = this->rotation_matrices(type, ghost_type);
			auto & shapes_ = this->shapes(itp_type, ghost_type);
			shapes_.resize(nb_element * nb_points);

			auto nodes_per_element = getNodesPerElement<type>(mesh, nodes, ghost_type);

			for (auto && tuple :
			zip(make_view(shapes_, nb_dof, nb_dof * nb_nodes_per_element, nb_points),
			make_view(*nodes_per_element, dim, nb_nodes_per_element),
			make_view(rot_matrices, nb_dof, nb_dof))) {
			auto && N = std::get<0>(tuple);
			auto && X = std::get<1>(tuple);
			auto && RDOFs = std::get<2>(tuple);

			Matrix<Real> T(N.size(1), N.size(1));
			T.zero();

			for (Idx i = 0; i < nb_nodes_per_element; ++i) {
			T.block(i * RDOFs.rows(), i * RDOFs.cols(), RDOFs.rows(), RDOFs.cols()) =
			RDOFs;
			}

			auto R = RDOFs.block(0, 0, spatial_dimension, spatial_dimension);
			// Rotate to local basis
			auto x =
			(R * X).block(0, 0, natural_spatial_dimension, nb_nodes_per_element);

			ElementClass<type>::computeShapes(natural_coords, x, T, N);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::precomputeShapeDerivativesOnIntegrationPoints(
			const Array<Real> & nodes, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			const auto & natural_coords = integration_points(type, ghost_type);
			const auto spatial_dimension = mesh.getSpatialDimension();
			const auto natural_spatial_dimension =
			ElementClass<type>::getNaturalSpaceDimension();
			const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			const auto nb_points = natural_coords.cols();
			const auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
			const auto nb_element = mesh.getNbElement(type, ghost_type);
			const auto nb_stress_components = ElementClass<type>::getNbStressComponents();
			const auto nb_cols_shaped = nb_dof * nb_nodes_per_element;

			auto itp_type = FEEngine::getInterpolationType(type);
			if (not this->shapes_derivatives.exists(itp_type, ghost_type)) {
			auto size_of_shapesd = this->getShapeDerivativesSize(type);
			this->shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);
			}

			auto & rot_matrices = this->rotation_matrices(type, ghost_type);

			Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
			FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

			auto & shapesd = this->shapes_derivatives(itp_type, ghost_type);
			shapesd.resize(nb_element * nb_points);

			for (auto && tuple :
			zip(make_view(x_el, spatial_dimension, nb_nodes_per_element),
			make_view(shapesd, nb_stress_components, nb_cols_shaped, nb_points),
			make_view<nb_dof, nb_dof>(rot_matrices))) {
			// compute shape derivatives
			auto & X = std::get<0>(tuple);
			auto & B = std::get<1>(tuple);
			auto & RDOFs = std::get<2>(tuple);

			Tensor3<Real> dnds(natural_spatial_dimension,
			ElementClass<type>::interpolation_property::dnds_columns,
			B.size(2));
			ElementClass<type>::computeDNDS(natural_coords, X, dnds);

			Tensor3<Real> J(natural_spatial_dimension, natural_spatial_dimension,
			natural_coords.cols());

			// Computing the coordinates of the element in the natural space
			Matrix<Real, nb_cols_shaped, nb_cols_shaped> T;
			T.zero();

			for (Int i = 0; i < nb_nodes_per_element; ++i) {
			T.template block<nb_dof, nb_dof>(i * nb_dof, i * nb_dof) = RDOFs;
			}

			auto && R = RDOFs.block(0, 0, spatial_dimension, spatial_dimension);
			// Rotate to local basis
			auto x =
			(R * X).template block<natural_spatial_dimension, nb_nodes_per_element>(
			0, 0);

			ElementClass<type>::computeJMat(natural_coords, x, J);
			ElementClass<type>::computeShapeDerivatives(J, dnds, T, B);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::interpolateOnIntegrationPoints(
			const Array<Real> & in_u, Array<Real> & out_uq, Int nb_dof,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			AKANTU_DEBUG_IN();

			AKANTU_DEBUG_ASSERT(out_uq.getNbComponent() == nb_dof,
			"The output array shape is not correct");

			auto itp_type = FEEngine::getInterpolationType(type);
			const auto & shapes_ = shapes(itp_type, ghost_type);

			auto nb_element = mesh.getNbElement(type, ghost_type);
			auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();
			auto nb_quad_points_per_element = integration_points(type, ghost_type).cols();

			Array<Real> u_el(0, nb_nodes_per_element * nb_dof);
			FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
			filter_elements);

			auto nb_quad_points = nb_quad_points_per_element * u_el.size();
			out_uq.resize(nb_quad_points);

			auto out_it =
			make_view(out_uq, nb_dof, 1, nb_quad_points_per_element).begin();
			auto shapes_it = make_view(shapes_, nb_dof, nb_dof * nb_nodes_per_element,
			nb_quad_points_per_element)
			.begin();
			auto u_it = make_view(u_el, nb_dof * nb_nodes_per_element, 1,
			nb_quad_points_per_element)
			.begin();

			for_each_element(nb_element, filter_elements, [&](auto && el) {
			auto & uq = *out_it;
			const auto & u = *u_it;
			auto && N = shapes_it[el];

			for (auto && q : arange(uq.size(2))) {
			uq(q) = N(q) * u(q);
			}

			++out_it;
			++u_it;
			});
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			template <ElementType type>
			void ShapeStructural<kind>::gradientOnIntegrationPoints(
			const Array<Real> & in_u, Array<Real> & out_nablauq, Int nb_dof,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			AKANTU_DEBUG_IN();

			auto itp_type = FEEngine::getInterpolationType(type);
			const auto & shapesd = shapes_derivatives(itp_type, ghost_type);

			auto nb_element = mesh.getNbElement(type, ghost_type);
			auto element_dimension = ElementClass<type>::getSpatialDimension();
			auto nb_quad_points_per_element = integration_points(type, ghost_type).cols();
			auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();

			Array<Real> u_el(0, nb_nodes_per_element * nb_dof);
			FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
			filter_elements);

			auto nb_quad_points = nb_quad_points_per_element * u_el.size();
			out_nablauq.resize(nb_quad_points);

			auto out_it =
			make_view(out_nablauq, element_dimension, 1, nb_quad_points_per_element)
			.begin();
			auto shapesd_it =
			make_view(shapesd, element_dimension, nb_dof * nb_nodes_per_element,
			nb_quad_points_per_element)
			.begin();
			auto u_it = make_view(u_el, nb_dof * nb_nodes_per_element, 1,
			nb_quad_points_per_element)
			.begin();

			for_each_element(nb_element, filter_elements, [&](auto && el) {
			auto & nablau = *out_it;
			const auto & u = *u_it;
			auto B = shapesd_it[el];

			for (auto && q : arange(nablau.size(2))) {
			nablau(q) = B(q) * u(q);
			}

			++out_it;
			++u_it;
			});

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <>
			template <ElementType type>
			void ShapeStructural<_ek_structural>::computeBtD(
			const Array<Real> & Ds, Array<Real> & BtDs, GhostType ghost_type,
			const Array<Idx> & filter_elements) const {
			auto itp_type = ElementClassProperty<type>::interpolation_type;

			auto nb_stress = ElementClass<type>::getNbStressComponents();
			auto nb_dof_per_element = ElementClass<type>::getNbDegreeOfFreedom() *
			mesh.getNbNodesPerElement(type);

			const auto & shapes_derivatives =
			this->shapes_derivatives(itp_type, ghost_type);

			Array<Real> shapes_derivatives_filtered(0,
			shapes_derivatives.getNbComponent());
			auto && view = make_view(shapes_derivatives, nb_stress, nb_dof_per_element);
			auto B_it = view.begin();
			auto B_end = view.end();

			if (filter_elements != empty_filter) {
			FEEngine::filterElementalData(this->mesh, shapes_derivatives,
			shapes_derivatives_filtered, type, ghost_type,
			filter_elements);
			auto && view =
			make_view(shapes_derivatives_filtered, nb_stress, nb_dof_per_element);
			B_it = view.begin();
			B_end = view.end();
			}

			for (auto && values : zip(range(B_it, B_end), make_view(Ds, nb_stress),
			make_view(BtDs, BtDs.getNbComponent()))) {
			const auto & B = std::get<0>(values);
			const auto & D = std::get<1>(values);
			auto & Bt_D = std::get<2>(values);
			Bt_D = B.transpose() * D;
			}
			}

			/* -------------------------------------------------------------------------- */
			template <>
			template <ElementType type>
			void ShapeStructural<_ek_structural>::computeNtb(
			const Array<Real> & bs, Array<Real> & Ntbs, GhostType ghost_type,
			const Array<Idx> & filter_elements) const {
			constexpr auto itp_type = ElementClassProperty<type>::interpolation_type;
			constexpr auto nb_dof = ElementClass<type>::getNbDegreeOfFreedom();
			constexpr auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

			const auto & shapes = this->shapes(itp_type, ghost_type);

			Array<Real> shapes_filtered(0, shapes.getNbComponent());
			auto && view = make_view<nb_dof, nb_dof * nb_nodes_per_element>(shapes);
			auto N_it = view.begin();
			auto N_end = view.end();

			if (filter_elements != empty_filter) {
			FEEngine::filterElementalData(this->mesh, shapes, shapes_filtered, type,
			ghost_type, filter_elements);
			auto && view =
			make_const_view<nb_dof, nb_dof * nb_nodes_per_element>(shapes_filtered);
			N_it = view.begin();
			N_end = view.end();
			}

			for (auto && [N, b, Nt_b] :
			zip(range(N_it, N_end), make_view<nb_dof>(bs),
			make_view<nb_dof * nb_nodes_per_element>(Ntbs))) {
			Nt_b = N.transpose() * b;
			}
			}
			/* -------------------------------------------------------------------------- */
			template <ElementKind kind>
			inline void ShapeStructural<kind>::initShapeFunctions(
			const Array<Real> & /* unused /, const Matrix<Real> & / unused */,
			ElementType /* unused /, GhostType / unused */) {
			AKANTU_TO_IMPLEMENT();
			}

			template <>
			inline void ShapeStructural<_ek_structural>::initShapeFunctions(
			const Array<Real> & nodes, const Matrix<Real> & integration_points,
			ElementType type, GhostType ghost_type) {
			tuple_dispatch<ElementTypes_t<_ek_structural>>(
			[&](auto && enum_type) {
			constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
			this->setIntegrationPointsByType<type>(integration_points, ghost_type);
			this->precomputeRotationMatrices<type>(nodes, ghost_type);
			this->precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type);
			this->precomputeShapeDerivativesOnIntegrationPoints<type>(nodes,
			ghost_type);
			},
			type);
			}
			/* -------------------------------------------------------------------------- */

			} // namespace akantu

			//#endif /* AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_ */

rAKA/src/fe_engine/shape_structural_inline_impl.hh1f632f71ba75bugfixes/documentation

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shape_structural_inline_impl.hh
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