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rAKA/src/fe_engine/shape_structural_inline_impl.cc
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shape_structural_inline_impl.cc
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/**
* @file shape_structural_inline_impl.cc
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Dec 13 2010
* @date last modification: Thu Oct 15 2015
*
* @brief ShapeStructural inline implementation
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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_CC__
#define __AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_CC__
namespace akantu {
template <ElementKind kind>
inline void ShapeStructural<kind>::initShapeFunctions(
const Array<Real> & /* unused */, const Matrix<Real> & /* unused */,
const ElementType & /* unused */, const GhostType & /* unused */) {
AKANTU_DEBUG_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,
const ElementType & type, const 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, const GhostType & ghost_type,
const Array<UInt> & filter_elements) const {
/// \TODO this code differs from ShapeLagrangeBase only in the size of N
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();
}
for (UInt elem = 0; elem < nb_element; ++elem) {
if (filter_elements != empty_filter)
shapes_it = shapes_begin + filter_elements(elem);
Tensor3<Real> & N = *shapes_it;
ElementClass<type>::computeShapes(integration_points, N);
if (filter_elements == empty_filter)
++shapes_it;
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeStructural<kind>::precomputeRotationMatrices(
const Array<Real> & nodes, const 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>::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>());
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeStructural<kind>::precomputeShapesOnIntegrationPoints(
const Array<Real> & /*nodes*/, const 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();
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 shapes_it = shapes_.begin_reinterpret(
nb_dof, nb_dof * nb_nodes_per_element, nb_points, nb_element);
for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it) {
auto & N = *shapes_it;
ElementClass<type>::computeShapes(natural_coords, N);
}
AKANTU_DEBUG_OUT();
} // namespace akantu
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeStructural<kind>::precomputeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const 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);
Matrix<Real> R(spatial_dimension, spatial_dimension);
for (UInt j = 0; j < spatial_dimension; ++j)
for (UInt i = 0; i < spatial_dimension; ++i)
R(i, j) = RDOFs(i, j);
// Rotate to local basis
auto x = R * X;
Matrix<Real> node_coords(natural_spatial_dimension, nb_nodes_per_element);
// Extract relevant first lines
for (UInt j = 0; j < node_coords.cols(); ++j)
for (UInt i = 0; i < node_coords.rows(); ++i)
node_coords(i, j) = x(i, j);
Tensor3<Real> dnds(B.size(0), B.size(1), B.size(2));
ElementClass<type>::computeDNDS(natural_coords, dnds);
Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
natural_coords.cols());
ElementClass<type>::computeJMat(dnds, node_coords, J);
ElementClass<type>::computeShapeDerivatives(J, dnds, 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,
const 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<type>(mesh, in_u, u_el, 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_elements(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, u);
}
++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,
const 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<type>(mesh, in_u, u_el, 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_elements(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>(uq(q));
auto u_q = Matrix<Real>(u(q));
auto B_q = Matrix<Real>(N(q));
nablau_q.mul<false, false>(B, u);
}
++out_it;
++u_it;
});
AKANTU_DEBUG_OUT();
}
} // namespace akantu
#endif /* __AKANTU_SHAPE_STRUCTURAL_INLINE_IMPL_CC__ */
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