shape_structural_inline_impl.hh
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shape_structural_inline_impl.hh
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	/**
	* @file shape_structural_inline_impl.hh
	*
	* @author Fabian Barras <fabian.barras@epfl.ch>
	* @author Lucas Frerot <lucas.frerot@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Wed Oct 11 2017
	* @date last modification: Wed Feb 21 2018
	*
	* @brief ShapeStructural inline implementation
	*
	*
	* Copyright (©) 2016-2018 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 "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>
	inline void ShapeStructural<kind>::initShapeFunctions(
	const Array<Real> & /* unused /, const Matrix<Real> & / unused */,
	ElementType /* unused /, GhostType / unused */) {
	AKANTU_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	precomputeRotationMatrices<type>(nodes, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type);

	template <>
	inline void ShapeStructural<_ek_structural>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	ElementType type, GhostType ghost_type) {
	AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}

	#undef INIT_SHAPE_FUNCTIONS

	/* -------------------------------------------------------------------------- */
	template <>
	template <ElementType type>
	void ShapeStructural<_ek_structural>::computeShapesOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	Array<Real> & shapes, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {

	UInt nb_points = integration_points.cols();
	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	shapes.resize(nb_element * nb_points);

	UInt ndof = ElementClass<type>::getNbDegreeOfFreedom();

	#if !defined(AKANTU_NDEBUG)
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	AKANTU_DEBUG_ASSERT(shapes.getNbComponent() == size_of_shapes,
	"The shapes array does not have the correct "
	<< "number of component");
	#endif

	auto shapes_it = shapes.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(), ndof, nb_points,
	nb_element);

	auto shapes_begin = shapes_it;
	if (filter_elements != empty_filter) {
	nb_element = filter_elements.size();
	}

	auto nodes_per_element = getNodesPerElement<type>(mesh, nodes, ghost_type);
	auto nodes_it = nodes_per_element->begin(mesh.getSpatialDimension(),
	Mesh::getNbNodesPerElement(type));
	auto nodes_begin = nodes_it;

	for (UInt elem = 0; elem < nb_element; ++elem) {
	if (filter_elements != empty_filter) {
	shapes_it = shapes_begin + filter_elements(elem);
	nodes_it = nodes_begin + filter_elements(elem);
	}

	Tensor3<Real> & N = *shapes_it;
	auto & real_coord = *nodes_it;
	ElementClass<type>::computeShapes(integration_points, real_coord, N);

	if (filter_elements == empty_filter) {
	++shapes_it;
	++nodes_it;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	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();

	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 & 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))) {
	auto & N = std::get<0>(tuple);
	auto & real_coord = std::get<1>(tuple);
	ElementClass<type>::computeShapes(natural_coords, real_coord, 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();

	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_nodes_per_element * nb_dof, nb_points),
	make_view(rot_matrices, nb_dof, nb_dof))) {
	// 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
	auto R = RDOFs.block(0, 0, spatial_dimension, spatial_dimension);
	Matrix<Real> T(B.size(1), B.size(1), 0);

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

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

	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, UInt nb_dof,
	GhostType ghost_type, const Array<UInt> & 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 = out_uq.begin_reinterpret(nb_dof, 1, nb_quad_points_per_element,
	u_el.size());
	auto shapes_it =
	shapes_.begin_reinterpret(nb_dof, nb_dof * nb_nodes_per_element,
	nb_quad_points_per_element, nb_element);
	auto u_it = u_el.begin_reinterpret(nb_dof * nb_nodes_per_element, 1,
	nb_quad_points_per_element, u_el.size());

	for_each_element(nb_element, filter_elements, [&](auto && el) {
	auto & uq = *out_it;
	const auto & u = *u_it;
	auto N = Tensor3<Real>(shapes_it[el]);

	for (auto && q : arange(uq.size(2))) {
	auto uq_q = Matrix<Real>(uq(q));
	auto u_q = Matrix<Real>(u(q));
	auto N_q = Matrix<Real>(N(q));

	uq_q.mul<false, false>(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, UInt nb_dof,
	GhostType ghost_type, const Array<UInt> & 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 = out_nablauq.begin_reinterpret(
	element_dimension, 1, nb_quad_points_per_element, u_el.size());
	auto shapesd_it = shapesd.begin_reinterpret(
	element_dimension, nb_dof * nb_nodes_per_element,
	nb_quad_points_per_element, nb_element);
	auto u_it = u_el.begin_reinterpret(nb_dof * nb_nodes_per_element, 1,
	nb_quad_points_per_element, u_el.size());

	for_each_element(nb_element, filter_elements, [&](auto && el) {
	auto & nablau = *out_it;
	const auto & u = *u_it;
	auto B = Tensor3<Real>(shapesd_it[el]);

	for (auto && q : arange(nablau.size(2))) {
	auto nablau_q = Matrix<Real>(nablau(q));
	auto u_q = Matrix<Real>(u(q));
	auto B_q = Matrix<Real>(B(q));

	nablau_q.mul<false, false>(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<UInt> & 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.template mul<true>(B, D);
	}
	}

	} // namespace akantu

	#endif /* AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_HH_ */

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