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rAKA/src/fe_engine/shape_functions_inline_impl.cc
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shape_functions_inline_impl.cc
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/**
* @file shape_functions_inline_impl.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Fabian Barras <fabian.barras@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Fri Jun 13 2014
*
* @brief ShapeFunctions inline implementation
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 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/>.
*
*/
/* -------------------------------------------------------------------------- */
__END_AKANTU__
#include "fe_engine.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
inline UInt ShapeFunctions::getShapeSize(const 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(const 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::setControlPointsByType(const Matrix<Real> & points,
const GhostType & ghost_type) {
control_points(type, ghost_type).shallowCopy(points);
}
/* -------------------------------------------------------------------------- */
inline void ShapeFunctions::initElementalFieldInterpolationFromControlPoints(const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
const ElementTypeMapArray<Real> & quadrature_points_coordinates,
const ElementTypeMapArray<UInt> * element_filter) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = this->mesh.getSpatialDimension();
for (ghost_type_t::iterator gt = ghost_type_t::begin();
gt != ghost_type_t::end(); ++gt) {
GhostType ghost_type = *gt;
Mesh::type_iterator it, last;
if(element_filter) {
it = element_filter->firstType(spatial_dimension, ghost_type);
last = element_filter->lastType(spatial_dimension, ghost_type);
}
else {
it = mesh.firstType(spatial_dimension, ghost_type);
last = mesh.lastType(spatial_dimension, ghost_type);
}
for (; it != last; ++it) {
ElementType type = *it;
UInt nb_element = mesh.getNbElement(type, ghost_type);
if (nb_element == 0) continue;
const Array<UInt> * elem_filter;
if(element_filter) elem_filter = &((*element_filter)(type, ghost_type));
else elem_filter = &(empty_filter);
#define AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS(type) \
initElementalFieldInterpolationFromControlPoints<type>(interpolation_points_coordinates(type, ghost_type), \
interpolation_points_coordinates_matrices, \
quad_points_coordinates_inv_matrices, \
quadrature_points_coordinates(type, ghost_type), \
ghost_type, \
*elem_filter) \
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS);
#undef AKANTU_INIT_ELEMENTAL_FIELD_INTERPOLATION_FROM_C_POINTS
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
inline void ShapeFunctions::initElementalFieldInterpolationFromControlPoints(const Array<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
const Array<Real> & quadrature_points_coordinates,
GhostType & ghost_type,
const Array<UInt> & element_filter) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = this->mesh.getSpatialDimension();
UInt nb_element = this->mesh.getNbElement(type, ghost_type);
UInt nb_element_filter;
if(element_filter == empty_filter)
nb_element_filter = element_filter.getSize();
else nb_element_filter = nb_element;
UInt nb_quad_per_element = GaussIntegrationElement<type>::getNbQuadraturePoints();
UInt nb_interpolation_points_per_elem = interpolation_points_coordinates.getSize() / nb_element;
AKANTU_DEBUG_ASSERT(interpolation_points_coordinates.getSize() % nb_element == 0,
"Number of interpolation points should be a multiple of total number of elements");
if(!quad_points_coordinates_inv_matrices.exists(type, ghost_type))
quad_points_coordinates_inv_matrices.alloc(nb_element_filter,
nb_quad_per_element*nb_quad_per_element,
type, ghost_type);
else
quad_points_coordinates_inv_matrices(type, ghost_type).resize(nb_element_filter);
if(!interpolation_points_coordinates_matrices.exists(type, ghost_type))
interpolation_points_coordinates_matrices.alloc(nb_element_filter,
nb_interpolation_points_per_elem * nb_quad_per_element,
type, ghost_type);
else
interpolation_points_coordinates_matrices(type, ghost_type).resize(nb_element_filter);
Array<Real> & quad_inv_mat = quad_points_coordinates_inv_matrices(type, ghost_type);
Array<Real> & interp_points_mat = interpolation_points_coordinates_matrices(type, ghost_type);
Matrix<Real> quad_coord_matrix(nb_quad_per_element, nb_quad_per_element);
Array<Real>::const_matrix_iterator quad_coords_it =
quadrature_points_coordinates.begin_reinterpret(spatial_dimension,
nb_quad_per_element,
nb_element);
Array<Real>::const_matrix_iterator points_coords_begin =
interpolation_points_coordinates.begin_reinterpret(spatial_dimension,
nb_interpolation_points_per_elem,
nb_element);
Array<Real>::matrix_iterator inv_quad_coord_it =
quad_inv_mat.begin(nb_quad_per_element, nb_quad_per_element);
Array<Real>::matrix_iterator int_points_mat_it =
interp_points_mat.begin(nb_interpolation_points_per_elem, nb_quad_per_element);
/// loop over the elements of the current material and element type
for (UInt el = 0; el < nb_element; ++el, ++inv_quad_coord_it,
++int_points_mat_it, ++quad_coords_it) {
/// matrix containing the quadrature points coordinates
const Matrix<Real> & quad_coords = *quad_coords_it;
/// matrix to store the matrix inversion result
Matrix<Real> & inv_quad_coord_matrix = *inv_quad_coord_it;
/// insert the quad coordinates in a matrix compatible with the interpolation
buildElementalFieldInterpolationMatrix<type>(quad_coords,
quad_coord_matrix);
/// invert the interpolation matrix
inv_quad_coord_matrix.inverse(quad_coord_matrix);
/// matrix containing the interpolation points coordinates
const Matrix<Real> & points_coords = points_coords_begin[element_filter(el)];
/// matrix to store the interpolation points coordinates
/// compatible with these functions
Matrix<Real> & inv_points_coord_matrix = *int_points_mat_it;
/// insert the quad coordinates in a matrix compatible with the interpolation
buildElementalFieldInterpolationMatrix<type>(points_coords,
inv_points_coord_matrix);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
inline void ShapeFunctions::buildInterpolationMatrix(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
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_DEBUG_TO_IMPLEMENT();
break;
}
}
}
/* -------------------------------------------------------------------------- */
template<ElementType type>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix(__attribute__((unused)) const Matrix<Real> & coordinates,
__attribute__((unused)) Matrix<Real> & coordMatrix,
__attribute__((unused)) UInt integration_order) const {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_2>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_segment_3>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_3>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_triangle_6>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_4>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
buildInterpolationMatrix(coordinates, coordMatrix, integration_order);
}
/* -------------------------------------------------------------------------- */
template<>
inline void ShapeFunctions::buildElementalFieldInterpolationMatrix<_tetrahedron_10>(const Matrix<Real> & coordinates,
Matrix<Real> & coordMatrix,
UInt 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> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
if(integration_order!=ElementClassProperty<_quadrangle_4>::minimal_integration_order){
AKANTU_DEBUG_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> & coordinates,
Matrix<Real> & coordMatrix,
UInt integration_order) const {
if(integration_order!=ElementClassProperty<_quadrangle_8>::minimal_integration_order){
AKANTU_DEBUG_TO_IMPLEMENT();
} else {
for (UInt i = 0; i < coordinates.cols(); ++i) {
UInt j = 0;
Real x = coordinates(0, i);
Real y = coordinates(1, i);
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;
}
}
}
}
}
/* -------------------------------------------------------------------------- */
void ShapeFunctions::interpolateElementalFieldFromControlPoints(const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result,
const GhostType ghost_type,
const ElementTypeMapArray<UInt> * element_filter) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = this->mesh.getSpatialDimension();
Mesh::type_iterator it, last;
if(element_filter) {
it = element_filter->firstType(spatial_dimension, ghost_type);
last = element_filter->lastType(spatial_dimension, ghost_type);
}
else {
it = mesh.firstType(spatial_dimension, ghost_type);
last = mesh.lastType(spatial_dimension, ghost_type);
}
for (; it != last; ++it) {
ElementType type = *it;
UInt nb_element = mesh.getNbElement(type, ghost_type);
if (nb_element == 0) continue;
const Array<UInt> * elem_filter;
if(element_filter) elem_filter = &((*element_filter)(type, ghost_type));
else elem_filter = &(empty_filter);
#define AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS(type) \
interpolateElementalFieldFromControlPoints<type>(field(type, ghost_type), \
interpolation_points_coordinates_matrices(type, ghost_type), \
quad_points_coordinates_inv_matrices(type, ghost_type), \
result, \
ghost_type, \
*elem_filter) \
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS);
#undef AKANTU_INTERPOLATE_ELEMENTAL_FIELD_FROM_C_POINTS
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
inline void ShapeFunctions::interpolateElementalFieldFromControlPoints(const Array<Real> & field,
const Array<Real> & interpolation_points_coordinates_matrices,
const Array<Real> & quad_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result,
const GhostType ghost_type,
const Array<UInt> & element_filter) const {
AKANTU_DEBUG_IN();
UInt nb_element = this->mesh.getNbElement(type, ghost_type);
UInt nb_quad_per_element = GaussIntegrationElement<type>::getNbQuadraturePoints();
UInt nb_interpolation_points_per_elem
= interpolation_points_coordinates_matrices.getNbComponent() / nb_quad_per_element;
if(!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.getSize();
Matrix<Real> coefficients(nb_quad_per_element, field.getNbComponent());
Array<Real> & result_vec = result(type, ghost_type);
Array<Real>::const_matrix_iterator field_it
= field.begin_reinterpret(field.getNbComponent(),
nb_quad_per_element,
nb_element);
Array<Real>::const_matrix_iterator interpolation_points_coordinates_it =
interpolation_points_coordinates_matrices.begin(nb_interpolation_points_per_elem, nb_quad_per_element);
Array<Real>::matrix_iterator result_begin
= result_vec.begin_reinterpret(field.getNbComponent(),
nb_interpolation_points_per_elem,
result_vec.getSize() / nb_interpolation_points_per_elem);
Array<Real>::const_matrix_iterator 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 material 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 Matrix<Real> & 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 Matrix<Real> & 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::interpolateElementalFieldOnControlPoints(const Array<Real> &u_el,
Array<Real> &uq,
GhostType ghost_type,
const Array<Real> & shapes,
const Array<UInt> & filter_elements) const {
UInt nb_element;
UInt nb_points = control_points(type, ghost_type).cols();
UInt nb_nodes_per_element = ElementClass<type>::getShapeSize();
UInt nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
Array<Real>::const_matrix_iterator N_it;
Array<Real>::const_matrix_iterator u_it;
Array<Real>::matrix_iterator inter_u_it;
Array<Real> * filtered_N = NULL;
if(filter_elements != empty_filter) {
nb_element = filter_elements.getSize();
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 {
nb_element = mesh.getNbElement(type,ghost_type);
N_it = shapes.begin_reinterpret(nb_nodes_per_element, nb_points, nb_element);
}
uq.resize(nb_element*nb_points);
u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
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 Matrix<Real> & u = *u_it;
const Matrix<Real> & N = *N_it;
Matrix<Real> & inter_u = *inter_u_it;
inter_u.mul<false, false>(u, N);
}
delete filtered_N;
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeFunctions::gradientElementalFieldOnControlPoints(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();
UInt nb_nodes_per_element = ElementClass<type>::getNbNodesPerInterpolationElement();
UInt nb_points = control_points(type, ghost_type).cols();
UInt element_dimension = ElementClass<type>::getNaturalSpaceDimension();
UInt nb_degree_of_freedom = u_el.getNbComponent() / nb_nodes_per_element;
Array<Real>::const_matrix_iterator B_it;
Array<Real>::const_matrix_iterator u_it;
Array<Real>::matrix_iterator nabla_u_it;
UInt nb_element;
Array<Real> * filtered_B = NULL;
if(filter_elements != empty_filter) {
nb_element = filter_elements.getSize();
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);
nb_element = mesh.getNbElement(type, ghost_type);
}
out_nablauq.resize(nb_element*nb_points);
u_it = u_el.begin(nb_degree_of_freedom, nb_nodes_per_element);
nabla_u_it = out_nablauq.begin(nb_degree_of_freedom, element_dimension);
for (UInt el = 0; el < nb_element; ++el, ++u_it) {
const Matrix<Real> & u = *u_it;
for (UInt q = 0; q < nb_points; ++q, ++B_it, ++nabla_u_it) {
const Matrix<Real> & B = *B_it;
Matrix<Real> & nabla_u = *nabla_u_it;
nabla_u.mul<false, true>(u, B);
}
}
delete filtered_B;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
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