shape_structural_inline_impl.hh
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shape_structural_inline_impl.hh
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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_ */

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