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rAKA/src/fe_engine/shape_lagrange_inline_impl.cc
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shape_lagrange_inline_impl.cc
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/**
* @file shape_lagrange_inline_impl.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Oct 27 2010
* @date last modification: Thu Oct 15 2015
*
* @brief ShapeLagrange 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/>.
*
*/
__END_AKANTU__
#include "fe_engine.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
inline const Array<Real> &
ShapeLagrange<kind>::getShapes(const ElementType & el_type,
const GhostType & ghost_type) const {
return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
inline const Array<Real> &
ShapeLagrange<kind>::getShapesDerivatives(const ElementType & el_type,
const GhostType & ghost_type) const {
return shapes_derivatives(FEEngine::getInterpolationType(el_type),
ghost_type);
}
/* -------------------------------------------------------------------------- */
#define INIT_SHAPE_FUNCTIONS(type) \
setIntegrationPointsByType<type>(integration_points, ghost_type); \
precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
if (ElementClass<type>::getNaturalSpaceDimension() == \
mesh.getSpatialDimension() || \
kind != _ek_regular) \
precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type);
template <ElementKind kind>
inline void ShapeLagrange<kind>::initShapeFunctions(
const Array<Real> & nodes, const Matrix<Real> & integration_points,
const ElementType & type, const GhostType & ghost_type) {
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
}
#if defined(AKANTU_STRUCTURAL_MECHANICS)
/* -------------------------------------------------------------------------- */
template <>
inline void ShapeLagrange<_ek_structural>::initShapeFunctions(
__attribute__((unused)) const Array<Real> & nodes,
__attribute__((unused)) const Matrix<Real> & integration_points,
__attribute__((unused)) const ElementType & type,
__attribute__((unused)) const GhostType & ghost_type) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
#endif
#undef INIT_SHAPE_FUNCTIONS
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
inline void ShapeLagrange<kind>::computeShapeDerivativesOnCPointsByElement(
const Matrix<Real> & node_coords, const Matrix<Real> & natural_coords,
Tensor3<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 dxds
Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
natural_coords.cols());
ElementClass<type>::computeJMat(dnds, node_coords, J);
// compute shape derivatives
ElementClass<type>::computeShapeDerivatives(J, dnds, shapesd);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::inverseMap(const Vector<Real> & real_coords,
UInt elem, Vector<Real> & natural_coords,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = mesh.getSpatialDimension();
UInt nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);
mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
elem_val + elem * nb_nodes_per_element,
nb_nodes_per_element, spatial_dimension);
ElementClass<type>::inverseMap(real_coords, nodes_coord, natural_coords);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
bool ShapeLagrange<kind>::contains(const Vector<Real> & real_coords, UInt elem,
const GhostType & ghost_type) const {
UInt 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>
void ShapeLagrange<kind>::interpolate(const Vector<Real> & real_coords,
UInt elem,
const Matrix<Real> & nodal_values,
Vector<Real> & interpolated,
const GhostType & ghost_type) const {
UInt nb_shapes = ElementClass<type>::getShapeSize();
Vector<Real> shapes(nb_shapes);
computeShapes<type>(real_coords, elem, shapes, ghost_type);
ElementClass<type>::interpolate(nodal_values, shapes, interpolated);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::computeShapes(const Vector<Real> & real_coords,
UInt elem, Vector<Real> & shapes,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt 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>
void ShapeLagrange<kind>::computeShapeDerivatives(
const Matrix<Real> & real_coords, UInt elem, Tensor3<Real> & shapesd,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = mesh.getSpatialDimension();
UInt nb_points = real_coords.cols();
UInt 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");
Matrix<Real> natural_coords(spatial_dimension, nb_points);
// Creates the matrix of natural coordinates
for (UInt i = 0; i < nb_points; i++) {
Vector<Real> real_point = real_coords(i);
Vector<Real> natural_point = natural_coords(i);
inverseMap<type>(real_point, elem, natural_point, ghost_type);
}
UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);
mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
elem_val + elem * nb_nodes_per_element,
nb_nodes_per_element, spatial_dimension);
computeShapeDerivativesOnCPointsByElement<type>(nodes_coord, natural_coords,
shapesd);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
ShapeLagrange<kind>::ShapeLagrange(const Mesh & mesh, const ID & id,
const MemoryID & memory_id)
: ShapeFunctions(mesh, id, memory_id),
shapes("shapes_generic", id, memory_id),
shapes_derivatives("shapes_derivatives_generic", id, memory_id) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::computeShapesOnIntegrationPoints(
__attribute__((unused)) const Array<Real> & nodes,
const Matrix<Real> & integration_points, Array<Real> & shapes,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt nb_points = integration_points.cols();
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
shapes.resize(nb_element * nb_points);
#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
Array<Real>::matrix_iterator shapes_it = shapes.begin_reinterpret(
ElementClass<type>::getNbNodesPerInterpolationElement(), nb_points,
nb_element);
for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it) {
Matrix<Real> & N = *shapes_it;
ElementClass<type>::computeShapes(integration_points, N);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::precomputeShapesOnIntegrationPoints(
const Array<Real> & nodes, const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
Matrix<Real> & natural_coords = integration_points(type, ghost_type);
UInt 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>::computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & integration_points,
Array<Real> & shape_derivatives, const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = mesh.getSpatialDimension();
UInt nb_nodes_per_element =
ElementClass<type>::getNbNodesPerInterpolationElement();
UInt nb_points = integration_points.cols();
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
UInt 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);
Real * shapesd_val = shape_derivatives.storage();
Array<Real>::matrix_iterator x_it =
x_el.begin(spatial_dimension, nb_nodes_per_element);
for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
Matrix<Real> & X = *x_it;
Tensor3<Real> B(shapesd_val, spatial_dimension, nb_nodes_per_element,
nb_points);
computeShapeDerivativesOnCPointsByElement<type>(X, integration_points, B);
shapesd_val += size_of_shapesd * nb_points;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
template <ElementType type>
void ShapeLagrange<kind>::precomputeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
Matrix<Real> & natural_coords = integration_points(type, ghost_type);
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
UInt 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, UInt nb_degree_of_freedom,
const Array<Real> & shapes, GhostType ghost_type,
const Array<UInt> & filter_elements) const {
AKANTU_DEBUG_IN();
UInt 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, UInt nb_degree_of_freedom,
GhostType ghost_type, const Array<UInt> & 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,
UInt nb_degree_of_freedom, GhostType ghost_type,
const Array<UInt> & 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));
UInt 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>::fieldTimesShapes(const Array<Real> & field,
Array<Real> & field_times_shapes,
GhostType ghost_type) const {
AKANTU_DEBUG_IN();
field_times_shapes.resize(field.getSize());
UInt size_of_shapes = ElementClass<type>::getShapeSize();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
UInt nb_degree_of_freedom = field.getNbComponent();
const Array<Real> & shape = shapes(itp_type, ghost_type);
Array<Real>::const_matrix_iterator field_it =
field.begin(nb_degree_of_freedom, 1);
Array<Real>::const_matrix_iterator shapes_it = shape.begin(1, size_of_shapes);
Array<Real>::matrix_iterator it =
field_times_shapes.begin(nb_degree_of_freedom, size_of_shapes);
Array<Real>::matrix_iterator end =
field_times_shapes.end(nb_degree_of_freedom, size_of_shapes);
for (; it != end; ++it, ++field_it, ++shapes_it) {
it->mul<false, false>(*field_it, *shapes_it);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind>
void ShapeLagrange<kind>::printself(std::ostream & stream, int indent) const {
std::string space;
for (Int i = 0; i < indent; i++, space += AKANTU_INDENT)
;
stream << space << "Shapes Lagrange [" << std::endl;
ShapeFunctions::printself(stream, indent + 1);
shapes.printself(stream, indent + 1);
shapes_derivatives.printself(stream, indent + 1);
stream << space << "]" << std::endl;
}
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