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rAKA/src/shape_igfem_inline_impl.cc
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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)
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
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) \
setControlPointsByType<type>(control_points, ghost_type); \
setControlPointsByType<ElementClassProperty<type>::sub_element_type_1>(control_points_1, ghost_type); \
setControlPointsByType<ElementClassProperty<type>::sub_element_type_2>(control_points_2, ghost_type); \
precomputeShapesOnControlPoints<type>(nodes, ghost_type); \
if (ElementClass<type>::getNaturalSpaceDimension() == \
mesh.getSpatialDimension()) \
precomputeShapeDerivativesOnControlPoints<type>(nodes, ghost_type);
inline void ShapeLagrange<_ek_igfem>::initShapeFunctions(const Array<Real> & nodes,
const Matrix<Real> & control_points,
const Matrix<Real> & control_points_1,
const Matrix<Real> & control_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,
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 <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>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::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 <ElementType type>
void ShapeLagrange<_ek_igfem>::precomputeShapesOnControlPoints(__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 = control_points(sub_type_1, ghost_type);
Matrix<Real> natural_coords_sub_2 = control_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_control_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
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 control 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 control 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
Vector<Real> all_shapes(size_of_shapes);
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;
Vector<Real> tmp(nc_parent(i));
tmp = 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, 0);
N(i + nb_points_sub_2) = all_shapes;
Vector<Real> tmp(nc_parent(i + nb_points_sub_1));
tmp = parent_natural_coords_2(i);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::precomputeShapeDerivativesOnControlPoints(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 = control_points(sub_type_1, ghost_type);
Matrix<Real> natural_coords_sub_2 = control_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 control points of the parent element
Array<Real> & natural_coords_parent = igfem_control_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);
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_1,
B_sub_2);
computeShapeDerivativesOnCPointsByElement<parent_type>(parent_coords,
nc_parent,
B_parent);
/// assemble the shape derivatives
Matrix<Real> all_shapes(spatial_dimension, nb_nodes_per_element);
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_2) = all_shapes;
}
shapesd_val += size_of_shapesd*nb_points_total;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::interpolateOnControlPoints(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->interpolateElementalFieldOnControlPoints<type>(u_el, out_uq, ghost_type,
shapes(itp_type, ghost_type),
filter_elements);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void ShapeLagrange<_ek_igfem>::gradientOnControlPoints(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->gradientElementalFieldOnControlPoints<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();
}
/* -------------------------------------------------------------------------- */
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