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rAKA/src/fe_engine/shape_functions_inline_impl.hh
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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 UInt ShapeFunctions::getShapeSize(ElementType type) {
AKANTU_DEBUG_IN();
UInt shape_size = 0;
#define GET_SHAPE_SIZE(type) shape_size = ElementClass<type>::getShapeSize()
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_SIZE); // ,
#undef GET_SHAPE_SIZE
AKANTU_DEBUG_OUT();
return shape_size;
}
/* -------------------------------------------------------------------------- */
inline UInt ShapeFunctions::getShapeDerivativesSize(ElementType type) {
AKANTU_DEBUG_IN();
UInt shape_derivatives_size = 0;
#define GET_SHAPE_DERIVATIVES_SIZE(type) \
shape_derivatives_size = ElementClass<type>::getShapeDerivativesSize()
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPE_DERIVATIVES_SIZE); // ,
#undef GET_SHAPE_DERIVATIVES_SIZE
AKANTU_DEBUG_OUT();
return shape_derivatives_size;
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeFunctions::setIntegrationPointsByType(const Matrix<Real> & points,
GhostType ghost_type) {
if (not this->integration_points.exists(type, ghost_type)) {
this->integration_points(type, ghost_type).shallowCopy(points);
}
}
/* -------------------------------------------------------------------------- */
inline void
ShapeFunctions::buildInterpolationMatrix(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) {
switch (integration_order) {
case 1: {
for (UInt i = 0; i < coordinates.cols(); ++i) {
coordMatrix(i, 0) = 1;
}
break;
}
case 2: {
UInt nb_quadrature_points = coordMatrix.cols();
for (UInt i = 0; i < coordinates.cols(); ++i) {
coordMatrix(i, 0) = 1;
for (UInt j = 1; j < nb_quadrature_points; ++j) {
coordMatrix(i, j) = coordinates(j - 1, i);
}
}
break;
}
default: {
AKANTU_TO_IMPLEMENT();
break;
}
}
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix(
const Matrix<Real> & /*unused*/, Matrix<Real> & /*unused*/,
UInt /*unused*/) const {
AKANTU_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template <>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_2>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template <>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_3>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template <>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_3>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template <>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_6>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_4>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_10>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/**
* @todo Write a more efficient interpolation for quadrangles by
* dropping unnecessary quadrature points
*
*/
/* -------------------------------------------------------------------------- */
template <>
inline void
ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_4>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
if (integration_order !=
ElementClassProperty<_quadrangle_4>::polynomial_degree) {
AKANTU_TO_IMPLEMENT();
} else {
for (UInt i = 0; i < coordinates.cols(); ++i) {
Real x = coordinates(0, i);
Real y = coordinates(1, i);
coordMatrix(i, 0) = 1;
coordMatrix(i, 1) = x;
coordMatrix(i, 2) = y;
coordMatrix(i, 3) = x * y;
}
}
}
/* -------------------------------------------------------------------------- */
template <>
inline void
ShapeFunctions::buildElementalFieldInterpolationMatrix<_quadrangle_8>(
const Matrix<Real> & /*unused*/ coordinates,
Matrix<Real> & /*unused*/ coordMatrix,
UInt /*unused*/ integration_order) const {
if (integration_order !=
ElementClassProperty<_quadrangle_8>::polynomial_degree) {
AKANTU_TO_IMPLEMENT();
} else {
for (UInt i = 0; i < coordinates.cols(); ++i) {
// UInt j = 0;
Real x = coordinates(0, i);
Real y = coordinates(1, i);
coordMatrix(i, 0) = 1;
coordMatrix(i, 1) = x;
coordMatrix(i, 2) = y;
coordMatrix(i, 3) = x * y;
// for (UInt e = 0; e <= 2; ++e) {
// for (UInt n = 0; n <= 2; ++n) {
// coordMatrix(i, j) = std::pow(x, e) * std::pow(y, n);
// ++j;
// }
// }
}
}
}
/* -------------------------------------------------------------------------- */
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<UInt> & element_filter) const {
AKANTU_DEBUG_IN();
auto nb_element = this->mesh.getNbElement(type, ghost_type);
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)) {
result.alloc(nb_element * nb_interpolation_points_per_elem,
field.getNbComponent(), type, ghost_type);
}
if (element_filter != empty_filter) {
nb_element = element_filter.size();
}
Matrix<Real> coefficients(nb_quad_per_element, field.getNbComponent());
auto & result_vec = result(type, ghost_type);
auto field_it = field.begin_reinterpret(field.getNbComponent(),
nb_quad_per_element, nb_element);
auto interpolation_points_coordinates_it =
interpolation_points_coordinates_matrices.begin(
nb_interpolation_points_per_elem, nb_quad_per_element);
auto result_begin = result_vec.begin_reinterpret(
field.getNbComponent(), nb_interpolation_points_per_elem,
result_vec.size() / nb_interpolation_points_per_elem);
auto inv_quad_coord_it = quad_points_coordinates_inv_matrices.begin(
nb_quad_per_element, nb_quad_per_element);
/// loop over the elements of the current filter and element type
for (UInt el = 0; el < nb_element; ++el, ++field_it, ++inv_quad_coord_it,
++interpolation_points_coordinates_it) {
/**
* matrix containing the inversion of the quadrature points'
* coordinates
*/
const auto & inv_quad_coord_matrix = *inv_quad_coord_it;
/**
* multiply it by the field values over quadrature points to get
* the interpolation coefficients
*/
coefficients.mul<false, true>(inv_quad_coord_matrix, *field_it);
/// matrix containing the points' coordinates
const auto & coord = *interpolation_points_coordinates_it;
/// multiply the coordinates matrix by the coefficients matrix and store the
/// result
Matrix<Real> res(result_begin[element_filter(el)]);
res.mul<true, true>(coefficients, coord);
}
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<UInt> & filter_elements) const {
auto nb_element = mesh.getNbElement(type, ghost_type);
auto nb_nodes_per_element = ElementClass<type>::getShapeSize();
auto nb_points = shapes.size() / mesh.getNbElement(type, ghost_type);
auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
Array<Real>::const_matrix_iterator N_it;
Array<Real> * filtered_N = nullptr;
if (filter_elements != empty_filter) {
nb_element = filter_elements.size();
filtered_N = new Array<Real>(0, shapes.getNbComponent());
FEEngine::filterElementalData(mesh, shapes, *filtered_N, type, ghost_type,
filter_elements);
N_it = filtered_N->begin_reinterpret(nb_nodes_per_element, nb_points,
nb_element);
} else {
N_it =
shapes.begin_reinterpret(nb_nodes_per_element, nb_points, nb_element);
}
uq.resize(nb_element * nb_points);
auto u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
auto inter_u_it =
uq.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);
for (UInt el = 0; el < nb_element; ++el, ++N_it, ++u_it, ++inter_u_it) {
const auto & u = *u_it;
const auto & N = *N_it;
auto & inter_u = *inter_u_it;
inter_u.template mul<false, false>(u, N);
}
delete filtered_N;
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeFunctions::gradientElementalFieldOnIntegrationPoints(
const Array<Real> & u_el, Array<Real> & out_nablauq, GhostType ghost_type,
const Array<Real> & shapes_derivatives,
const Array<UInt> & filter_elements) const {
AKANTU_DEBUG_IN();
auto nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
auto nb_points = integration_points(type, ghost_type).cols();
auto element_dimension = ElementClass<type>::getNaturalSpaceDimension();
auto nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
auto nb_element = mesh.getNbElement(type, ghost_type);
Array<Real>::const_matrix_iterator B_it;
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 = filtered_B->begin(element_dimension, nb_nodes_per_element);
} else {
B_it = shapes_derivatives.begin(element_dimension, nb_nodes_per_element);
}
out_nablauq.resize(nb_element * nb_points);
auto u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
auto nabla_u_it = out_nablauq.begin(nb_degree_of_freedom, element_dimension);
for (UInt el = 0; el < nb_element; ++el, ++u_it) {
const auto & u = *u_it;
for (UInt q = 0; q < nb_points; ++q, ++B_it, ++nabla_u_it) {
const auto & B = *B_it;
auto & nabla_u = *nabla_u_it;
nabla_u.template mul<false, true>(u, B);
}
}
delete filtered_B;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
} // namespace akantu
#endif /* AKANTU_SHAPE_FUNCTIONS_INLINE_IMPL_HH_ */
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