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shape_functions_inline_impl.hh
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/**
* @file shape_functions_inline_impl.hh
*
* @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: Sat Dec 19 2020
*
* @brief ShapeFunctions 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 "fe_engine.hh"
#include "shape_functions.hh"
/* -------------------------------------------------------------------------- */
//#ifndef AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_
//#define AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
inline const Array<Real> &
ShapeFunctions::getShapes(ElementType el_type, GhostType ghost_type) const {
return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
}
/* -------------------------------------------------------------------------- */
inline const Array<Real> &
ShapeFunctions::getShapesDerivatives(ElementType el_type,
GhostType ghost_type) const {
return shapes_derivatives(FEEngine::getInterpolationType(el_type),
ghost_type);
}
/* -------------------------------------------------------------------------- */
inline Int ShapeFunctions::getShapeSize(ElementType type) {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value;
return ElementClass<type>::getShapeSize();
},
type);
}
/* -------------------------------------------------------------------------- */
inline Int ShapeFunctions::getShapeDerivativesSize(ElementType type) {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value;
return ElementClass<type>::getShapeDerivativesSize();
},
type);
}
/* -------------------------------------------------------------------------- */
template <ElementType type, class D1>
void ShapeFunctions::setIntegrationPointsByType(
const Eigen::MatrixBase<D1> & points, GhostType ghost_type) {
this->integration_points(type, ghost_type) = points;
}
/* -------------------------------------------------------------------------- */
template <typename D1, typename D2>
inline void ShapeFunctions::buildInterpolationMatrix(
const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coordMatrix, Int integration_order) const {
switch (integration_order) {
case 1: {
for (Int i = 0; i < coordinates.cols(); ++i) {
coordMatrix(i, 0) = 1;
}
break;
}
case 2: {
auto nb_quadrature_points = coordMatrix.cols();
for (Int i = 0; i < coordinates.cols(); ++i) {
coordMatrix(i, 0) = 1;
for (Int j = 1; j < nb_quadrature_points; ++j) {
coordMatrix(i, j) = coordinates(j - 1, i);
}
}
break;
}
default: {
AKANTU_TO_IMPLEMENT();
break;
}
}
}
/* -------------------------------------------------------------------------- */
template <ElementType type> struct BuildElementalFieldInterpolationMatrix {
template <typename ShapeFunction, typename D1, typename D2>
static inline void
call(ShapeFunction && func, const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coord_matrix, Int integration_order) {
func.buildInterpolationMatrix(coordinates, coord_matrix, integration_order);
}
};
/**
* @todo Write a more efficient interpolation for quadrangles by
* dropping unnecessary quadrature points
*
*/
/* -------------------------------------------------------------------------- */
template <> struct BuildElementalFieldInterpolationMatrix<_quadrangle_4> {
template <typename ShapeFunction, typename D1, typename D2>
static inline void
call(ShapeFunction && /*func*/, const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coord_matrix, Int integration_order) {
if (integration_order !=
ElementClassProperty<_quadrangle_4>::polynomial_degree) {
AKANTU_TO_IMPLEMENT();
} else {
for (Int i = 0; i < coordinates.cols(); ++i) {
auto x = coordinates(0, i);
auto y = coordinates(1, i);
coord_matrix(i, 0) = 1;
coord_matrix(i, 1) = x;
coord_matrix(i, 2) = y;
coord_matrix(i, 3) = x * y;
}
}
}
};
/* -------------------------------------------------------------------------- */
template <> struct BuildElementalFieldInterpolationMatrix<_quadrangle_8> {
template <typename ShapeFunction, typename D1, typename D2>
static inline void
call(ShapeFunction && /*func*/, const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coordMatrix, Int integration_order) {
if (integration_order !=
ElementClassProperty<_quadrangle_8>::polynomial_degree) {
AKANTU_TO_IMPLEMENT();
} else {
for (Int i = 0; i < coordinates.cols(); ++i) {
// Int j = 0;
auto x = coordinates(0, i);
auto y = coordinates(1, i);
coordMatrix(i, 0) = 1;
coordMatrix(i, 1) = x;
coordMatrix(i, 2) = y;
coordMatrix(i, 3) = x * y;
}
}
}
};
/* -------------------------------------------------------------------------- */
template <ElementType type, typename D1, typename D2>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix(
const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coordMatrix, Int integration_order) const {
BuildElementalFieldInterpolationMatrix<type>::call(
*this, coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
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, GhostType ghost_type,
const Array<Int> & element_filter) const {
AKANTU_DEBUG_IN();
constexpr auto nb_quad_per_element =
GaussIntegrationElement<type>::getNbQuadraturePoints();
auto nb_interpolation_points_per_elem =
interpolation_points_coordinates_matrices.getNbComponent() /
nb_quad_per_element;
if (not result.exists(type, ghost_type)) {
auto nb_element = this->mesh.getNbElement(type, ghost_type);
result.alloc(nb_element * nb_interpolation_points_per_elem,
field.getNbComponent(), type, ghost_type);
}
AKANTU_DEBUG_ASSERT(element_filter != empty_filter,
"This function does not work without an element_filter");
// auto nb_element = element_filter.size();
Matrix<Real> coefficients(nb_quad_per_element, field.getNbComponent());
auto result_begin =
make_view(result(type, ghost_type), field.getNbComponent(),
nb_interpolation_points_per_elem)
.begin();
/// loop over the elements of the current filter and element type
for (auto && data :
zip(element_filter,
make_view(field, field.getNbComponent(), nb_quad_per_element),
make_view(interpolation_points_coordinates_matrices,
nb_interpolation_points_per_elem, nb_quad_per_element),
make_view(quad_points_coordinates_inv_matrices, nb_quad_per_element,
nb_quad_per_element))) {
/**
* matrix containing the inversion of the quadrature points'
* coordinates
*/
auto && inv_quad_coord_matrix = std::get<3>(data);
/**
* multiply it by the field values over quadrature points to get
* the interpolation coefficients
*/
coefficients = inv_quad_coord_matrix * std::get<1>(data).transpose();
/// matrix containing the points' coordinates
auto && coord = std::get<2>(data);
auto el = std::get<0>(data);
/// multiply the coordinates matrix by the coefficients matrix and store the
/// result
result_begin[el] = coefficients.transpose() * coord.transpose();
}
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<Int> & filter_elements) const {
auto nb_element = mesh.getNbElement(type, ghost_type);
if (nb_element == 0) {
return;
}
auto nb_nodes_per_element = ElementClass<type>::getShapeSize();
auto nb_points = shapes.size() / nb_element;
auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
auto N_view = make_view(shapes, nb_nodes_per_element, nb_points);
std::unique_ptr<Array<Real>> filtered_N;
if (filter_elements != empty_filter) {
nb_element = filter_elements.size();
filtered_N = std::make_unique<Array<Real>>(0, shapes.getNbComponent());
FEEngine::filterElementalData(mesh, shapes, *filtered_N, type, ghost_type,
filter_elements);
N_view = make_const_view(*filtered_N, nb_nodes_per_element, nb_points);
}
uq.resize(nb_element * nb_points);
for (auto && data :
zip(N_view, make_view(uq, nb_degree_of_freedom, nb_points),
make_view(u_el, nb_degree_of_freedom, nb_nodes_per_element))) {
const auto & u = std::get<2>(data);
const auto & N = std::get<0>(data);
auto & uq = std::get<1>(data);
uq.noalias() = u * N;
}
}
/* -------------------------------------------------------------------------- */
template <
ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() != 0> *>
void ShapeFunctions::gradientElementalFieldOnIntegrationPoints(
const Array<Real> & u_el, Array<Real> & out_nablauq, GhostType ghost_type,
const Array<Real> & shapes_derivatives,
const Array<Int> & filter_elements) const {
AKANTU_DEBUG_IN();
constexpr auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
constexpr auto element_dimension =
ElementClass<type>::getNaturalSpaceDimension();
auto nb_points = integration_points(type, ghost_type).cols();
auto nb_element = mesh.getNbElement(type, ghost_type);
auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
auto B_it =
make_view<element_dimension, nb_nodes_per_element>(shapes_derivatives)
.begin();
Array<Real> * filtered_B = nullptr;
if (filter_elements != empty_filter) {
nb_element = filter_elements.size();
filtered_B = new Array<Real>(0, shapes_derivatives.getNbComponent());
FEEngine::filterElementalData(mesh, shapes_derivatives, *filtered_B, type,
ghost_type, filter_elements);
B_it =
make_view<element_dimension, nb_nodes_per_element>(*filtered_B).begin();
}
out_nablauq.resize(nb_element * nb_points);
auto u_it = make_view<Eigen::Dynamic, nb_nodes_per_element>(
u_el, nb_degree_of_freedom, nb_nodes_per_element)
.begin();
auto nabla_u_it = make_view<Eigen::Dynamic, element_dimension>(
out_nablauq, nb_degree_of_freedom, element_dimension)
.begin();
for (Int el = 0; el < nb_element; ++el, ++u_it) {
const auto & u = *u_it;
for (Int q = 0; q < nb_points; ++q, ++B_it, ++nabla_u_it) {
const auto & B = *B_it;
auto & nabla_u = *nabla_u_it;
nabla_u.noalias() = u * B.transpose();
}
}
delete filtered_B;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
} // namespace akantu
//#endif /* AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_ */
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