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shape_igfem_inline_impl.cc
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/**
* @file shape_igfem_inline_impl.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief ShapeIGFEM inline implementation
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_SHAPE_IGFEM_INLINE_IMPL_CC__
#define __AKANTU_SHAPE_IGFEM_INLINE_IMPL_CC__
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
inline const Array<Real> & ShapeLagrange<_ek_igfem>::getShapes(const ElementType & el_type,
const GhostType & ghost_type) const {
return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
}
/* -------------------------------------------------------------------------- */
inline const Array<Real> & ShapeLagrange<_ek_igfem>::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); \
setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_1>(integration_points_1, ghost_type); \
setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_2>(integration_points_2, ghost_type); \
precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
if (ElementClass<type>::getNaturalSpaceDimension() == \
mesh.getSpatialDimension()) \
precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type); \
precomputeShapesOnEnrichedNodes<type>(nodes, ghost_type);
inline void ShapeLagrange<_ek_igfem>::initShapeFunctions(const Array<Real> & nodes,
const Matrix<Real> & integration_points,
const Matrix<Real> & integration_points_1,
const Matrix<Real> & integration_points_2,
const ElementType & type,
const GhostType & ghost_type) {
AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
}
#undef INIT_SHAPE_FUNCTIONS
/* -------------------------------------------------------------------------- */
template <ElementType type>
inline void ShapeLagrange<_ek_igfem>::
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 <ElementType type>
void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
UInt elem,
Vector<Real> & natural_coords,
UInt sub_element,
const GhostType & ghost_type) const{
AKANTU_DEBUG_IN();
/// typedef for the two subelement_types and the parent element type
const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
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);
if (!sub_element) {
UInt nb_nodes_sub_el = ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords, sub_element);
ElementClass<sub_type_1>::inverseMap(real_coords,
sub_el_coords,
natural_coords);
}
else {
UInt nb_nodes_sub_el = ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords, sub_element);
ElementClass<sub_type_2>::inverseMap(real_coords,
sub_el_coords,
natural_coords);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
UInt elem,
Vector<Real> & natural_coords,
const GhostType & ghost_type) const{
/// map point into parent reference domain
AKANTU_DEBUG_IN();
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
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);
UInt nb_nodes_parent_el = ElementClass<parent_type>::getNbNodesPerInterpolationElement();
Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
ElementClass<type>::getParentCoords(nodes_coord, parent_coords);
ElementClass<parent_type>::inverseMap(real_coords,
parent_coords,
natural_coords);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
bool ShapeLagrange<_ek_igfem>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::computeShapes(const Vector<Real> & real_coords,
UInt elem,
Vector<Real> & shapes,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
/// typedef for the two subelement_types and the parent element type
const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
UInt spatial_dimension = mesh.getSpatialDimension();
/// parent contribution
/// get the size of the parent shapes
UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
Vector<Real> parent_shapes(size_of_parent_shapes);
/// compute parent shapes -> map shapes in the physical domain of the parent
Vector<Real> natural_coords(spatial_dimension);
Real tol = Math::getTolerance();
Math::setTolerance(1e-14);
inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
natural_coords.clear();
/// sub-element contribution
/// check which sub-element contains the physical point
/// check if point is in sub-element 1
inverseMap<type>(real_coords, elem, natural_coords, 0, ghost_type);
if (ElementClass<sub_type_1>::contains(natural_coords)) {
UInt size_of_sub_shapes = ElementClass<sub_type_1>::getShapeSize();
Vector<Real> sub_shapes(size_of_sub_shapes);
ElementClass<sub_type_1>::computeShapes(natural_coords, sub_shapes);
/// assemble shape functions
ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
}
else {
natural_coords.clear();
inverseMap<type>(real_coords, elem, natural_coords, 1, ghost_type);
AKANTU_DEBUG_ASSERT(ElementClass<sub_type_2>::contains(natural_coords),
"Physical point not contained in any element");
UInt size_of_sub_shapes = ElementClass<sub_type_2>::getShapeSize();
Vector<Real> sub_shapes(size_of_sub_shapes);
ElementClass<sub_type_2>::computeShapes(natural_coords, sub_shapes);
/// assemble shape functions
ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 1);
}
Math::setTolerance(tol);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::computeShapeDerivatives(const Matrix<Real> & real_coords,
UInt elem,
Tensor3<Real> & shapesd,
const GhostType & ghost_type) const {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::precomputeShapesOnIntegrationPoints(__attribute__((unused)) const Array<Real> & nodes,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
/// typedef for the two subelement_types and the parent element type
const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
/// get the spatial dimension for the given element type
UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
/// get the integration points for the subelements
Matrix<Real> & natural_coords_sub_1 = integration_points(sub_type_1, ghost_type);
Matrix<Real> & natural_coords_sub_2 = integration_points(sub_type_2, ghost_type);
/// store the number of quadrature points on each subelement and the toal number
UInt nb_points_sub_1 = natural_coords_sub_1.cols();
UInt nb_points_sub_2 = natural_coords_sub_2.cols();
UInt nb_total_points = nb_points_sub_1 + nb_points_sub_2;
// get the integration points for the parent element
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
Array<Real> & natural_coords_parent = igfem_integration_points.alloc(nb_element*nb_total_points,
spatial_dimension,
type,
ghost_type);
Array<Real>::matrix_iterator natural_coords_parent_it = natural_coords_parent.begin_reinterpret(spatial_dimension, nb_total_points, nb_element);
/// get the size of the shapes
UInt size_of_shapes = ElementClass<type>::getShapeSize();
UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
UInt size_of_sub_1_shapes = ElementClass<sub_type_1>::getShapeSize();
UInt size_of_sub_2_shapes = ElementClass<sub_type_2>::getShapeSize();
/// initialize the matrices to store the shape functions of the subelements and the parent
Matrix<Real> sub_1_shapes(size_of_sub_1_shapes, nb_points_sub_1);
Matrix<Real> sub_2_shapes(size_of_sub_2_shapes, nb_points_sub_2);
Matrix<Real> parent_1_shapes(size_of_parent_shapes, nb_points_sub_1);
Matrix<Real> parent_2_shapes(size_of_parent_shapes, nb_points_sub_2);
/// compute the shape functions of the subelements
ElementClass<sub_type_1>::computeShapes(natural_coords_sub_1, sub_1_shapes);
ElementClass<sub_type_2>::computeShapes(natural_coords_sub_2, sub_2_shapes);
/// get the nodal coordinates per element
UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el,
type, ghost_type);
Array<Real>::matrix_iterator x_it = x_el.begin(spatial_dimension,
nb_nodes_per_element);
/// allocate the shapes for the given element type
Array<Real> & shapes_tmp = shapes.alloc(nb_element*nb_total_points,
size_of_shapes,
itp_type,
ghost_type);
Array<Real>::matrix_iterator shapes_it =
shapes_tmp.begin_reinterpret(ElementClass<type>::getNbNodesPerInterpolationElement(), nb_total_points, nb_element);
Matrix<Real> physical_points_1(spatial_dimension, nb_points_sub_1);
Matrix<Real> physical_points_2(spatial_dimension, nb_points_sub_2);
Matrix<Real> parent_natural_coords_1(spatial_dimension, nb_points_sub_1);
Matrix<Real> parent_natural_coords_2(spatial_dimension, nb_points_sub_2);
/// intialize the matrices for the parent and subelement coordinates
UInt nb_nodes_parent_el = ElementClass<parent_type>::getNbNodesPerInterpolationElement();
UInt nb_nodes_sub_el_1 = ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
UInt nb_nodes_sub_el_2 = ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);
/// loop over all elements of the given type and compute the shape functions
Vector<Real> all_shapes(size_of_shapes);
for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it, ++x_it, ++natural_coords_parent_it) {
Matrix<Real> & N = *shapes_it;
const Matrix<Real> & X = *x_it;
Matrix<Real> & nc_parent = *natural_coords_parent_it;
/// map the sub element integration points into the parent reference domain
ElementClass<type>::mapFromSubRefToParentRef(X, sub_el_1_coords, parent_coords, sub_1_shapes, physical_points_1, parent_natural_coords_1, 0);
ElementClass<type>::mapFromSubRefToParentRef(X, sub_el_2_coords, parent_coords, sub_2_shapes, physical_points_2, parent_natural_coords_2, 1);
/// compute the parent shape functions on all integration points
ElementClass<sub_type_1>::computeShapes(parent_natural_coords_1, parent_1_shapes);
ElementClass<sub_type_1>::computeShapes(parent_natural_coords_2, parent_2_shapes);
/// copy the results into the shape functions iterator and natural coords iterator
for (UInt i = 0; i < nb_points_sub_1; ++i) {
ElementClass<type>::assembleShapes(parent_1_shapes(i), sub_1_shapes(i), all_shapes, 0);
N(i) = all_shapes;
nc_parent(i) = parent_natural_coords_1(i);
}
for (UInt i = 0; i < nb_points_sub_2; ++i) {
ElementClass<type>::assembleShapes(parent_2_shapes(i), sub_2_shapes(i), all_shapes, 1);
N(i + nb_points_sub_1) = all_shapes;
///N(i + nb_points_sub_2) = all_shapes;
nc_parent(i + nb_points_sub_1) = parent_natural_coords_2(i);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes, GhostType ghost_type) {
AKANTU_DEBUG_IN();
/// typedef for the two subelement_types and the parent element type
const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
UInt spatial_dimension = mesh.getSpatialDimension();
/// get the integration points for the subelements
Matrix<Real> & natural_coords_sub_1 = integration_points(sub_type_1, ghost_type);
Matrix<Real> & natural_coords_sub_2 = integration_points(sub_type_2, ghost_type);
/// store the number of quadrature points on each subelement and the toal number
UInt nb_points_sub_1 = natural_coords_sub_1.cols();
UInt nb_points_sub_2 = natural_coords_sub_2.cols();
UInt nb_points_total = nb_points_sub_1 + nb_points_sub_2;
UInt nb_nodes_per_element = ElementClass<type>::getNbNodesPerInterpolationElement();
UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();
/// intialize the matrices for the parent and subelement coordinates
UInt nb_nodes_parent_el = ElementClass<parent_type>::getNbNodesPerInterpolationElement();
UInt nb_nodes_sub_el_1 = ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
UInt nb_nodes_sub_el_2 = ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
Array<Real> & shapes_derivatives_tmp = shapes_derivatives.alloc(nb_element*nb_points_total,
size_of_shapesd,
itp_type,
ghost_type);
/// get an iterator to the coordiantes of the elements
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el,
type, ghost_type);
Real * shapesd_val = shapes_derivatives_tmp.storage();
Array<Real>::matrix_iterator x_it = x_el.begin(spatial_dimension,
nb_nodes_per_element);
/// get an iterator to the integration points of the parent element
Array<Real> & natural_coords_parent = igfem_integration_points(type, ghost_type);
Array<Real>::matrix_iterator natural_coords_parent_it = natural_coords_parent.begin_reinterpret(spatial_dimension, nb_points_total, nb_element);
Tensor3<Real> B_sub_1(spatial_dimension, nb_nodes_sub_el_1, nb_points_sub_1);
Tensor3<Real> B_sub_2(spatial_dimension, nb_nodes_sub_el_2, nb_points_sub_2);
Tensor3<Real> B_parent(spatial_dimension, nb_nodes_parent_el, nb_points_total);
/// assemble the shape derivatives
Matrix<Real> all_shapes(spatial_dimension, nb_nodes_per_element);
for (UInt elem = 0; elem < nb_element; ++elem, ++x_it, ++natural_coords_parent_it) {
Matrix<Real> & X = *x_it;
Matrix<Real> & nc_parent = *natural_coords_parent_it;
Tensor3<Real> B(shapesd_val,
spatial_dimension, nb_nodes_per_element, nb_points_total);
/// get the coordinates of the two sub elements and the parent element
ElementClass<type>::getSubElementCoords(X, sub_el_1_coords, 0);
ElementClass<type>::getSubElementCoords(X, sub_el_2_coords, 1);
ElementClass<type>::getParentCoords(X, parent_coords);
/// compute the subelements' shape derivatives and the parent shape derivatives
computeShapeDerivativesOnCPointsByElement<sub_type_1>(sub_el_1_coords,
natural_coords_sub_1,
B_sub_1);
computeShapeDerivativesOnCPointsByElement<sub_type_2>(sub_el_2_coords,
natural_coords_sub_2,
B_sub_2);
computeShapeDerivativesOnCPointsByElement<parent_type>(parent_coords,
nc_parent,
B_parent);
for (UInt i = 0; i < nb_points_sub_1; ++i) {
ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_1(i), all_shapes, 0);
B(i) = all_shapes;
}
for (UInt i = 0; i < nb_points_sub_2; ++i) {
ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_2(i), all_shapes, 1);
B(i + nb_points_sub_1) = all_shapes;
}
shapesd_val += size_of_shapesd*nb_points_total;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::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));
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(itp_type, ghost_type),
filter_elements);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::interpolateOnPhysicalPoint(const Vector<Real> & real_coords,
UInt elem,
const Array<Real> & field,
Vector<Real> & interpolated,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
Vector<Real> shapes(ElementClass<type>::getShapeSize());
computeShapes<type>(real_coords, elem, shapes, ghost_type);
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_val(spatial_dimension, nb_nodes_per_element);
mesh.extractNodalValuesFromElement(field,
nodes_val.storage(),
elem_val + elem * nb_nodes_per_element,
nb_nodes_per_element,
spatial_dimension);
ElementClass<type>::interpolate(nodes_val, shapes, interpolated);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::precomputeShapesOnEnrichedNodes(__attribute__((unused)) const Array<Real> & nodes,
const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
const ElementType sub_type = ElementClassProperty<type>::sub_element_type_1;
/// get the spatial dimension for the given element type
UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
// get the integration points for the parent element
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
/// get the size of the shapes
UInt nb_enriched_nodes = ElementClass<type>::getNbEnrichments();
UInt nb_parent_nodes = ElementClass<parent_type>::getNbNodesPerInterpolationElement();
UInt size_of_shapes = ElementClass<type>::getShapeSize();
UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
UInt size_of_sub_shapes = ElementClass<sub_type>::getShapeSize();
Vector<Real> parent_shapes(size_of_parent_shapes);
Vector<Real> sub_shapes(size_of_sub_shapes);
Vector<Real> shapes(size_of_shapes);
/// get the nodal coordinates per element
UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el,
type, ghost_type);
Array<Real>::matrix_iterator x_it = x_el.begin(spatial_dimension,
nb_nodes_per_element);
/// allocate the shapes for the given element type
Array<Real> & shapes_tmp = shapes_at_enrichments.alloc(nb_element * nb_enriched_nodes,
size_of_shapes,
itp_type,
ghost_type);
Array<Real>::matrix_iterator shapes_it =
shapes_tmp.begin_reinterpret(ElementClass<type>::getNbNodesPerInterpolationElement(), nb_enriched_nodes, nb_element);
Vector<Real> real_coords(spatial_dimension);
Vector<Real> natural_coords(spatial_dimension);
Matrix<Real> parent_coords(spatial_dimension, nb_parent_nodes);
UInt * sub_element_enrichments = ElementClass<type>::getSubElementEnrichments();
/// loop over all elements
for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it, ++x_it) {
Matrix<Real> & N = *shapes_it;
const Matrix<Real> & X = *x_it;
for (UInt i = 0; i < nb_enriched_nodes; ++i) {
/// get the parent element coordinates
ElementClass<type>::getParentCoords(X, parent_coords);
/// get the physical coords of the enriched node
real_coords = X(nb_parent_nodes + i);
/// map the physical point into the parent ref domain
ElementClass<parent_type>::inverseMap(real_coords,
parent_coords,
natural_coords);
/// compute the parent shape functions
ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
///Sub-element contribution
sub_shapes.clear();
sub_shapes(sub_element_enrichments[i]) = 1.;
ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
N(i) = shapes;
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::interpolateAtEnrichedNodes(const Array<Real> & src,
Array<Real> & dst,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
const ElementType parent_type = ElementClassProperty<type>::parent_element_type;
UInt nb_element = mesh.getNbElement(type, ghost_type);
UInt nb_nodes_per_element = ElementClass<type>::getNbNodesPerInterpolationElement();
UInt nb_parent_nodes = ElementClass<parent_type>::getNbNodesPerInterpolationElement();
UInt nb_enrichments = ElementClass<type>::getNbEnrichments();
UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
UInt spatial_dimension = mesh.getSpatialDimension();
Matrix<Real> nodes_val(spatial_dimension, nb_nodes_per_element);
InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
const Array<Real> & shapes = shapes_at_enrichments(itp_type, ghost_type);
Array<Real>::const_matrix_iterator shapes_it =
shapes.begin_reinterpret(nb_nodes_per_element, nb_enrichments, nb_element);
Array<Real>::vector_iterator dst_vect = dst.begin(spatial_dimension);
Vector<Real> interpolated(spatial_dimension);
for(UInt e = 0; e < nb_element; ++e, ++shapes_it) {
const Matrix<Real> & el_shapes = *shapes_it;
mesh.extractNodalValuesFromElement(src,
nodes_val.storage(),
elem_val + e * nb_nodes_per_element,
nb_nodes_per_element,
spatial_dimension);;
for (UInt i = 0; i < nb_enrichments; ++i) {
ElementClass<type>::interpolate(nodes_val, el_shapes(i), interpolated);
UInt enr_node_idx = elem_val[e * nb_nodes_per_element + nb_parent_nodes + i];
dst_vect[enr_node_idx] = interpolated;
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
#define COMPUTE_ENRICHED_VALUES(type) \
interpolateAtEnrichedNodes<type>(src, \
dst, \
ghost_type);
inline void ShapeLagrange<_ek_igfem>::interpolateEnrichmentsAllTypes(const Array<Real> & src,
Array<Real> & dst,
const ElementType & type,
const GhostType & ghost_type) const {
AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(COMPUTE_ENRICHED_VALUES);
}
#undef COMPUTE_ENRICHED_VALUES
/* -------------------------------------------------------------------------- */
__END_AKANTU__
#endif /* __AKANTU_SHAPE_IGFEM_INLINE_IMPL_CC__ */
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