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shape_lagrange_inline_impl.hh
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/**
* @file shape_lagrange_inline_impl.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Mohit Pundir <mohit.pundir@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Oct 27 2010
* @date last modification: Fri May 14 2021
*
* @brief ShapeLagrange inline implementation
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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_iterators.hh"
#include "aka_voigthelper.hh"
#include "fe_engine.hh"
//#include "shape_lagrange.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_
#define AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <typename D>
inline void ShapeLagrange<kind>::initShapeFunctions(
const Array<Real> & /*nodes*/,
const Eigen::MatrixBase<D> & /*integration_points*/, ElementType /*type*/,
GhostType /*ghost_type*/) {}
/* -------------------------------------------------------------------------- */
template <>
template <typename D>
inline void ShapeLagrange<_ek_regular>::initShapeFunctions(
const Array<Real> & nodes, const Eigen::MatrixBase<D> & integration_points,
ElementType type, GhostType ghost_type) {
tuple_dispatch<ElementTypes_t<_ek_regular>>(
[&](auto && enum_type) {
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value;
this->setIntegrationPointsByType<type>(integration_points, ghost_type);
this->precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type);
if (ElementClass<type>::getNaturalSpaceDimension() ==
mesh.getSpatialDimension()) {
this->precomputeShapeDerivativesOnIntegrationPoints<type>(nodes,
ghost_type);
}
},
type);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D1, typename D2>
inline void ShapeLagrange<kind>::computeShapeDerivativesOnCPointsByElement(
const Eigen::MatrixBase<D1> & node_coords,
const Eigen::MatrixBase<D2> & natural_coords,
Tensor3Base<Real> & shapesd) const {
AKANTU_DEBUG_IN();
// compute dnds
Tensor3<Real> dnds(node_coords.rows(), node_coords.cols(),
natural_coords.cols());
ElementClass<type>::computeDNDS(natural_coords, dnds);
// compute jacobian
Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
natural_coords.cols());
ElementClass<type>::computeJMat(dnds, node_coords, J);
// compute dndx
ElementClass<type>::computeShapeDerivatives(J, dnds, shapesd);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D1, typename D2>
void ShapeLagrange<kind>::inverseMap(
const Eigen::MatrixBase<D1> & real_coords, Int elem,
const Eigen::MatrixBase<D2> & natural_coords_, GhostType ghost_type) const {
AKANTU_DEBUG_IN();
// as advised by the Eigen developers even though this is a UB
auto & natural_coords = const_cast<Eigen::MatrixBase<D2> &>(natural_coords_);
auto nodes_coord = mesh.extractNodalValuesFromElement(
mesh.getNodes(), Element{type, elem, ghost_type});
ElementClass<type>::inverseMap(real_coords, nodes_coord, natural_coords);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D, std::enable_if_t<aka::is_vector_v<D>> *>
bool ShapeLagrange<kind>::contains(const Eigen::MatrixBase<D> & real_coords,
Idx elem, GhostType ghost_type) const {
auto spatial_dimension = mesh.getSpatialDimension();
Vector<Real> natural_coords(spatial_dimension);
inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
return ElementClass<type>::contains(natural_coords);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D1, typename D2, typename D3,
std::enable_if_t<aka::are_vectors<D1, D3>::value> *>
void ShapeLagrange<kind>::interpolate(
const Eigen::MatrixBase<D1> & real_coords, Idx elem,
const Eigen::MatrixBase<D2> & nodal_values,
Eigen::MatrixBase<D3> & interpolated, GhostType ghost_type) const {
constexpr auto nb_shapes = ElementClass<type>::getShapeSize();
Vector<Real, nb_shapes> shapes;
computeShapes<type>(real_coords, elem, shapes, ghost_type);
ElementClass<type>::interpolate(nodal_values, shapes, interpolated);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D1, typename D2>
void ShapeLagrange<kind>::computeShapes(
const Eigen::MatrixBase<D1> & real_coords, Idx elem,
Eigen::MatrixBase<D2> & shapes, GhostType ghost_type) const {
AKANTU_DEBUG_IN();
auto spatial_dimension = mesh.getSpatialDimension();
Vector<Real> natural_coords(spatial_dimension);
inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
ElementClass<type>::computeShapes(natural_coords, shapes);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D>
void ShapeLagrange<kind>::computeShapeDerivatives(
const Eigen::MatrixBase<D> & real_coords, Idx elem,
Tensor3Base<Real> & shapesd, GhostType ghost_type) const {
AKANTU_DEBUG_IN();
auto spatial_dimension = mesh.getSpatialDimension();
auto nb_points = real_coords.cols();
#if !defined(AKANTU_NDEBUG)
const auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == shapesd.size(0) &&
nb_nodes_per_element == shapesd.size(1),
"Shape size doesn't match");
AKANTU_DEBUG_ASSERT(nb_points == shapesd.size(2),
"Number of points doesn't match shapes size");
#endif
Matrix<Real> natural_coords(spatial_dimension, nb_points);
// Creates the matrix of natural coordinates
for (Int i = 0; i < nb_points; i++) {
inverseMap<type>(real_coords(i), elem, natural_coords(i), ghost_type);
}
auto nodes_coord = mesh.extractNodalValuesFromElement(
mesh.getNodes(), Element{type, elem, ghost_type});
computeShapeDerivativesOnCPointsByElement<type>(nodes_coord, natural_coords,
shapesd);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
ShapeLagrange<kind>::ShapeLagrange(const Mesh & mesh, Int spatial_dimension,
const ID & id)
: ShapeLagrangeBase(mesh, spatial_dimension, kind, id) {}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type, typename D>
void ShapeLagrange<kind>::computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Eigen::MatrixBase<D> & integration_points,
Array<Real> & shape_derivatives, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
AKANTU_DEBUG_IN();
auto spatial_dimension = mesh.getSpatialDimension();
auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
auto nb_points = integration_points.cols();
auto nb_element = mesh.getConnectivity(type, ghost_type).size();
auto size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();
AKANTU_DEBUG_ASSERT(shape_derivatives.getNbComponent() == size_of_shapesd,
"The shapes_derivatives array does not have the correct "
<< "number of component");
shape_derivatives.resize(nb_element * nb_points);
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
filter_elements);
auto * shapesd_val = shape_derivatives.data();
auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);
if (filter_elements != empty_filter) {
nb_element = filter_elements.size();
}
for (Int elem = 0; elem < nb_element; ++elem, ++x_it) {
if (filter_elements != empty_filter) {
shapesd_val = shape_derivatives.data() +
filter_elements(elem) * size_of_shapesd * nb_points;
}
auto & X = *x_it;
Tensor3Proxy<Real> B(shapesd_val, spatial_dimension, nb_nodes_per_element,
nb_points);
computeShapeDerivativesOnCPointsByElement<type>(X, integration_points, B);
if (filter_elements == empty_filter) {
shapesd_val += size_of_shapesd * nb_points;
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
void ShapeLagrange<kind>::computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Ref<const MatrixXr> integration_points,
Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
tuple_dispatch<ElementTypes_t<_ek_regular>>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
this->computeShapeDerivativesOnIntegrationPoints<type>(
nodes, integration_points, shape_derivatives, ghost_type,
filter_elements);
},
type);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::precomputeShapesOnIntegrationPoints(
const Array<Real> & nodes, GhostType ghost_type) {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
Matrix<Real> & natural_coords = integration_points(type, ghost_type);
auto size_of_shapes = ElementClass<type>::getShapeSize();
Array<Real> & shapes_tmp =
shapes.alloc(0, size_of_shapes, itp_type, ghost_type);
this->computeShapesOnIntegrationPoints<type>(nodes, natural_coords,
shapes_tmp, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::precomputeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, GhostType ghost_type) {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
Matrix<Real> & natural_coords = integration_points(type, ghost_type);
auto size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();
Array<Real> & shapes_derivatives_tmp =
shapes_derivatives.alloc(0, size_of_shapesd, itp_type, ghost_type);
this->computeShapeDerivativesOnIntegrationPoints<type>(
nodes, natural_coords, shapes_derivatives_tmp, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::interpolateOnIntegrationPoints(
const Array<Real> & in_u, Array<Real> & out_uq, Int nb_degree_of_freedom,
const Array<Real> & shapes, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
AKANTU_DEBUG_IN();
auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
filter_elements);
this->interpolateElementalFieldOnIntegrationPoints<type>(
u_el, out_uq, ghost_type, shapes, filter_elements);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::interpolateOnIntegrationPoints(
const Array<Real> & in_u, Array<Real> & out_uq, Int nb_degree_of_freedom,
GhostType ghost_type, const Array<Idx> & filter_elements) const {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
AKANTU_DEBUG_ASSERT(shapes.exists(itp_type, ghost_type),
"No shapes for the type "
<< shapes.printType(itp_type, ghost_type));
this->interpolateOnIntegrationPoints<type>(in_u, out_uq, nb_degree_of_freedom,
shapes(itp_type, ghost_type),
ghost_type, filter_elements);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::gradientOnIntegrationPoints(
const Array<Real> & in_u, Array<Real> & out_nablauq,
Int nb_degree_of_freedom, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
AKANTU_DEBUG_ASSERT(
shapes_derivatives.exists(itp_type, ghost_type),
"No shapes derivatives for the type "
<< shapes_derivatives.printType(itp_type, ghost_type));
auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
filter_elements);
this->gradientElementalFieldOnIntegrationPoints<type>(
u_el, out_nablauq, ghost_type, shapes_derivatives(itp_type, ghost_type),
filter_elements);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
GhostType ghost_type,
const Array<Idx> & filter_elements) const {
auto itp_type = ElementClassProperty<type>::interpolation_type;
const auto & shapes_derivatives =
this->shapes_derivatives(itp_type, ghost_type);
auto spatial_dimension = mesh.getSpatialDimension();
auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
Array<Real> shapes_derivatives_filtered(0,
shapes_derivatives.getNbComponent());
auto view = make_const_view(shapes_derivatives, spatial_dimension,
nb_nodes_per_element);
if (filter_elements != empty_filter) {
FEEngine::filterElementalData(this->mesh, shapes_derivatives,
shapes_derivatives_filtered, type, ghost_type,
filter_elements);
view = make_const_view(shapes_derivatives_filtered, spatial_dimension,
nb_nodes_per_element);
}
for (auto && values :
zip(view,
make_view(Ds, Ds.getNbComponent() / spatial_dimension,
spatial_dimension),
make_view(BtDs, BtDs.getNbComponent() / nb_nodes_per_element,
nb_nodes_per_element))) {
const auto & B = std::get<0>(values);
const auto & D = std::get<1>(values);
auto & Bt_D = std::get<2>(values);
// transposed due to the storage layout of B
Bt_D.noalias() = D * B;
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <
ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() != 0> *>
void ShapeLagrange<kind>::computeBtDB(
const Array<Real> & Ds, Array<Real> & BtDBs, Int order_d,
GhostType ghost_type, const Array<Idx> & filter_elements) const {
auto itp_type = ElementClassProperty<type>::interpolation_type;
const auto & shapes_derivatives =
this->shapes_derivatives(itp_type, ghost_type);
constexpr auto dim = ElementClass<type>::getSpatialDimension();
auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
Array<Real> shapes_derivatives_filtered(0,
shapes_derivatives.getNbComponent());
auto && view = make_const_view(shapes_derivatives, dim, nb_nodes_per_element);
if (filter_elements != empty_filter) {
FEEngine::filterElementalData(this->mesh, shapes_derivatives,
shapes_derivatives_filtered, type, ghost_type,
filter_elements);
view =
make_const_view(shapes_derivatives_filtered, dim, nb_nodes_per_element);
}
if (order_d == 4) {
auto tangent_size = VoigtHelper<dim>::size;
Matrix<Real> B(tangent_size, dim * nb_nodes_per_element);
for (auto && values : zip(view, make_view(Ds, tangent_size, tangent_size),
make_view(BtDBs, dim * nb_nodes_per_element,
dim * nb_nodes_per_element))) {
const auto & Bfull = std::get<0>(values);
const auto & D = std::get<1>(values);
auto & Bt_D_B = std::get<2>(values);
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(Bfull, B,
nb_nodes_per_element);
Bt_D_B.noalias() = B.transpose() * D * B;
}
} else if (order_d == 2) {
for (auto && values :
zip(view, make_view(Ds, dim, dim),
make_view(BtDBs, nb_nodes_per_element, nb_nodes_per_element))) {
const auto & B = std::get<0>(values);
const auto & D = std::get<1>(values);
auto & Bt_D_B = std::get<2>(values);
Bt_D_B.noalias() = B.transpose() * D * B;
}
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::computeNtbN(
const Array<Real> & bs, Array<Real> & NtbNs, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
auto itp_type = ElementClassProperty<type>::interpolation_type;
auto size_of_shapes = ElementClass<type>::getShapeSize();
auto nb_degree_of_freedom = bs.getNbComponent();
auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
Array<Real> shapes_filtered(0, size_of_shapes);
auto && view =
make_const_view(shapes(itp_type, ghost_type), 1, size_of_shapes);
if (filter_elements != empty_filter) {
FEEngine::filterElementalData(this->mesh, shapes(itp_type, ghost_type),
shapes_filtered, type, ghost_type,
filter_elements);
view = make_const_view(shapes_filtered, 1, size_of_shapes);
}
Matrix<Real> Nt_b(nb_nodes_per_element, nb_degree_of_freedom);
for (auto && values :
zip(view, make_view(bs, nb_degree_of_freedom, 1),
make_view(NtbNs, nb_nodes_per_element, nb_nodes_per_element))) {
const auto & N = std::get<0>(values);
const auto & b = std::get<1>(values);
auto & Nt_b_N = std::get<2>(values);
Nt_b_N.noalias() = N.transpose() * b * N;
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
GhostType ghost_type,
const Array<Idx> & filter_elements) const {
AKANTU_DEBUG_IN();
Ntbs.resize(bs.size());
auto size_of_shapes = ElementClass<type>::getShapeSize();
auto itp_type = ElementClassProperty<type>::interpolation_type;
auto nb_degree_of_freedom = bs.getNbComponent();
Array<Real> shapes_filtered(0, size_of_shapes);
auto && view =
make_const_view(shapes(itp_type, ghost_type), 1, size_of_shapes);
if (filter_elements != empty_filter) {
FEEngine::filterElementalData(this->mesh, shapes(itp_type, ghost_type),
shapes_filtered, type, ghost_type,
filter_elements);
view = make_const_view(shapes_filtered, 1, size_of_shapes);
}
for (auto && values :
zip(make_view(bs, nb_degree_of_freedom, 1), view,
make_view(Ntbs, nb_degree_of_freedom, size_of_shapes))) {
const auto & b = std::get<0>(values);
const auto & N = std::get<1>(values);
auto & Ntb = std::get<2>(values);
Ntb.noalias() = b * N;
}
AKANTU_DEBUG_OUT();
}
} // namespace akantu
#endif /* AKANTU_SHAPE_LAGRANGE_INLINE_IMPL_HH_ */

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