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fem_template_tmpl.hh
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/**
* @file fem_template_tmpl.hh
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Mon Nov 5 17:08:50 2012
*
* @brief Template implementation of FEMTemplate
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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/>.
*
*/
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
FEMTemplate<I, S, kind>::FEMTemplate(Mesh & mesh, UInt spatial_dimension,
ID id, MemoryID memory_id) :
FEM(mesh,spatial_dimension,id,memory_id),
integrator(mesh, id, memory_id),
shape_functions(mesh, id, memory_id) { }
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
FEMTemplate<I, S, kind>::~FEMTemplate() { }
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::gradientOnQuadraturePoints(const Array<Real> &u,
Array<Real> &nablauq,
const UInt nb_degree_of_freedom,
const ElementType & type,
const GhostType & ghost_type,
const Array<UInt> & filter_elements) const {
AKANTU_DEBUG_IN();
UInt nb_element = mesh.getNbElement(type, ghost_type);
if(filter_elements != empty_filter) nb_element = filter_elements.getSize();
UInt nb_points = shape_functions.getControlPoints(type, ghost_type).cols();
#ifndef AKANTU_NDEBUG
UInt element_dimension = mesh.getSpatialDimension(type);
AKANTU_DEBUG_ASSERT(u.getSize() == mesh.getNbNodes(),
"The vector u(" << u.getID()
<< ") has not the good size.");
AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom ,
"The vector u(" << u.getID()
<< ") has not the good number of component.");
AKANTU_DEBUG_ASSERT(nablauq.getNbComponent()
== nb_degree_of_freedom * element_dimension,
"The vector nablauq(" << nablauq.getID()
<< ") has not the good number of component.");
// AKANTU_DEBUG_ASSERT(nablauq.getSize() == nb_element * nb_points,
// "The vector nablauq(" << nablauq.getID()
// << ") has not the good size.");
#endif
nablauq.resize(nb_element * nb_points);
#define COMPUTE_GRADIENT(type) \
if (element_dimension == ElementClass<type>::getSpatialDimension()) \
shape_functions.template gradientOnControlPoints<type>(u, \
nablauq, \
nb_degree_of_freedom, \
ghost_type, \
filter_elements);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(COMPUTE_GRADIENT);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_GRADIENT);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef COMPUTE_GRADIENT
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::initShapeFunctions(const GhostType & ghost_type) {
initShapeFunctions(mesh.getNodes(), ghost_type);
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::initShapeFunctions(const Array<Real> & nodes,
const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
Mesh::type_iterator it = mesh.firstType(element_dimension, ghost_type, kind);
Mesh::type_iterator end = mesh.lastType(element_dimension, ghost_type, kind);
for(; it != end; ++it) {
ElementType type = *it;
integrator.initIntegrator(nodes, type, ghost_type);
const Matrix<Real> & control_points =
getQuadraturePoints(type, ghost_type);
shape_functions.initShapeFunctions(nodes, control_points, type, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::integrate(const Array<Real> & f,
Array<Real> &intf,
UInt nb_degree_of_freedom,
const ElementType & type,
const GhostType & ghost_type,
const Array<UInt> & filter_elements) const{
UInt nb_element = mesh.getNbElement(type, ghost_type);
if(filter_elements != empty_filter) nb_element = filter_elements.getSize();
#ifndef AKANTU_NDEBUG
UInt nb_quadrature_points = getNbQuadraturePoints(type);
AKANTU_DEBUG_ASSERT(f.getSize() == nb_element * nb_quadrature_points,
"The vector f(" << f.getID() << " size " << f.getSize()
<< ") has not the good size (" << nb_element << ").");
AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom ,
"The vector f(" << f.getID()
<< ") has not the good number of component.");
AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
"The vector intf(" << intf.getID()
<< ") has not the good number of component.");
#endif
intf.resize(nb_element);
#define INTEGRATE(type) \
integrator.template integrate<type>(f, \
intf, \
nb_degree_of_freedom, \
ghost_type, \
filter_elements);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_structural)
AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INTEGRATE);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef INTEGRATE
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
Real FEMTemplate<I, S, kind>::integrate(const Array<Real> & f,
const ElementType & type,
const GhostType & ghost_type,
const Array<UInt> & filter_elements) const{
AKANTU_DEBUG_IN();
#ifndef AKANTU_NDEBUG
// std::stringstream sstr; sstr << ghost_type;
// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
// "The vector " << nablauq.getID() << " is not taged " << ghost_type);
UInt nb_element = mesh.getNbElement(type, ghost_type);
if(filter_elements != empty_filter) nb_element = filter_elements.getSize();
UInt nb_quadrature_points = getNbQuadraturePoints(type, ghost_type);
AKANTU_DEBUG_ASSERT(f.getSize() == nb_element * nb_quadrature_points,
"The vector f(" << f.getID()
<< ") has not the good size. (" << f.getSize() << "!=" << nb_quadrature_points * nb_element << ")");
AKANTU_DEBUG_ASSERT(f.getNbComponent() == 1,
"The vector f(" << f.getID()
<< ") has not the good number of component.");
#endif
Real integral = 0.;
#define INTEGRATE(type) \
integral = integrator.template integrate<type>(f, \
ghost_type, \
filter_elements);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_structural)
AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INTEGRATE);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef INTEGRATE
AKANTU_DEBUG_OUT();
return integral;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
Real FEMTemplate<I, S, kind>::integrate(const Vector<Real> & f,
const ElementType & type,
UInt index,
const GhostType & ghost_type) const{
Real res = 0.;
#define INTEGRATE(type) \
res = integrator.template integrate<type>(f, \
index, \
ghost_type);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_structural)
AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INTEGRATE);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef INTEGRATE
return res;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::integrateOnQuadraturePoints(const Array<Real> & f,
Array<Real> &intf,
UInt nb_degree_of_freedom,
const ElementType & type,
const GhostType & ghost_type,
const Array<UInt> & filter_elements) const{
UInt nb_element = mesh.getNbElement(type, ghost_type);
if(filter_elements != empty_filter) nb_element = filter_elements.getSize();
UInt nb_quadrature_points = getNbQuadraturePoints(type);
#ifndef AKANTU_NDEBUG
// std::stringstream sstr; sstr << ghost_type;
// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
// "The vector " << nablauq.getID() << " is not taged " << ghost_type);
AKANTU_DEBUG_ASSERT(f.getSize() == nb_element * nb_quadrature_points,
"The vector f(" << f.getID() << " size " << f.getSize()
<< ") has not the good size (" << nb_element << ").");
AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom ,
"The vector f(" << f.getID()
<< ") has not the good number of component.");
AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
"The vector intf(" << intf.getID()
<< ") has not the good number of component.");
#endif
intf.resize(nb_element*nb_quadrature_points);
#define INTEGRATE(type) \
integrator.template integrateOnQuadraturePoints<type>(f, \
intf, \
nb_degree_of_freedom, \
ghost_type, \
filter_elements);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTEGRATE);
else if(kind == _ek_structural)
AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(INTEGRATE);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef INTEGRATE
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::interpolateOnQuadraturePoints(const Array<Real> &u,
Array<Real> &uq,
UInt nb_degree_of_freedom,
const ElementType & type,
const GhostType & ghost_type,
const Array<UInt> & filter_elements) const{
AKANTU_DEBUG_IN();
UInt nb_points = shape_functions.getControlPoints(type, ghost_type).cols();
UInt nb_element = mesh.getNbElement(type, ghost_type);
if(filter_elements != empty_filter) nb_element = filter_elements.getSize();
#ifndef AKANTU_NDEBUG
// std::stringstream sstr; sstr << ghost_type;
// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
// "The vector " << nablauq.getID() << " is not taged " << ghost_type);
AKANTU_DEBUG_ASSERT(u.getSize() == mesh.getNbNodes(),
"The vector u(" << u.getID()
<< ") has not the good size.");
AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom ,
"The vector u(" << u.getID()
<< ") has not the good number of component.");
AKANTU_DEBUG_ASSERT(uq.getNbComponent() == nb_degree_of_freedom,
"The vector uq(" << uq.getID()
<< ") has not the good number of component.");
#endif
uq.resize(nb_element * nb_points);
#define INTERPOLATE(type) \
shape_functions.template interpolateOnControlPoints<type>(u, \
uq, \
nb_degree_of_freedom, \
ghost_type, \
filter_elements);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(INTERPOLATE);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(INTERPOLATE);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef INTERPOLATE
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::interpolateOnQuadraturePoints(const Array<Real> & u,
ByElementTypeReal & uq,
const ByElementTypeUInt * filter_elements) const {
AKANTU_DEBUG_IN();
const Array<UInt> * filter = NULL;
for (ghost_type_t::iterator gt = ghost_type_t::begin();
gt != ghost_type_t::end(); ++gt) {
GhostType ghost_type = *gt;
ByElementTypeReal::type_iterator it = uq.firstType(_all_dimensions, ghost_type, kind);
ByElementTypeReal::type_iterator last = uq.lastType(_all_dimensions, ghost_type, kind);
for (; it != last; ++it) {
ElementType type = *it;
UInt nb_quad_per_element = getNbQuadraturePoints(type, ghost_type);
UInt nb_element = 0;
if (filter_elements) {
filter = &((*filter_elements)(type, ghost_type));
nb_element = filter->getSize();
}
else {
filter = &empty_filter;
nb_element = mesh.getNbElement(type, ghost_type);
}
UInt nb_tot_quad = nb_quad_per_element * nb_element;
Array<Real> & quad = uq(type, ghost_type);
quad.resize(nb_tot_quad);
interpolateOnQuadraturePoints(u,
quad,
mesh.getSpatialDimension(),
type,
ghost_type,
*filter);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::computeNormalsOnControlPoints(const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
computeNormalsOnControlPoints(mesh.getNodes(),
ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::computeNormalsOnControlPoints(const Array<Real> & field,
const GhostType & ghost_type) {
AKANTU_DEBUG_IN();
// Real * coord = mesh.getNodes().storage();
UInt spatial_dimension = mesh.getSpatialDimension();
//allocate the normal arrays
Mesh::type_iterator it = mesh.firstType(element_dimension, ghost_type, kind);
Mesh::type_iterator end = mesh.lastType(element_dimension, ghost_type, kind);
for(; it != end; ++it) {
ElementType type = *it;
UInt size = mesh.getNbElement(type, ghost_type);
if(normals_on_quad_points.exists(type, ghost_type)) {
normals_on_quad_points(type, ghost_type).resize(size);
} else {
normals_on_quad_points.alloc(size, spatial_dimension, type, ghost_type);
}
}
//loop over the type to build the normals
it = mesh.firstType(element_dimension, ghost_type, kind);
for(; it != end; ++it) {
Array<Real> & normals_on_quad = normals_on_quad_points(*it, ghost_type);
computeNormalsOnControlPoints(field, normals_on_quad, *it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::computeNormalsOnControlPoints(const Array<Real> & field,
Array<Real> & normal,
const ElementType & type,
const GhostType & ghost_type) const {
#define COMPUTE_NORMALS_ON_QUAD(type) \
computeNormalsOnControlPoints<type>(field, normal, ghost_type);
if(kind == _ek_regular)
AKANTU_BOOST_REGULAR_ELEMENT_SWITCH(COMPUTE_NORMALS_ON_QUAD);
else if(kind == _ek_cohesive)
AKANTU_BOOST_COHESIVE_ELEMENT_SWITCH(COMPUTE_NORMALS_ON_QUAD);
else
AKANTU_DEBUG_TO_IMPLEMENT();
#undef COMPUTE_NORMALS_ON_QUAD
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
template<ElementType type>
void FEMTemplate<I, S, kind>::computeNormalsOnControlPoints(const Array<Real> & field,
Array<Real> & normal,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt spatial_dimension = mesh.getSpatialDimension();
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_points = getNbQuadraturePoints(type, ghost_type);
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
normal.resize(nb_element * nb_points);
Array<Real>::matrix_iterator normals_on_quad = normal.begin_reinterpret(spatial_dimension,
nb_points,
nb_element);
Array<Real> f_el(0, spatial_dimension * nb_nodes_per_element);
FEM::extractNodalToElementField(mesh, field, f_el, type, ghost_type);
const Matrix<Real> & quads =
integrator. template getQuadraturePoints<type>(ghost_type);
Array<Real>::matrix_iterator f_it = f_el.begin(spatial_dimension, nb_nodes_per_element);
for (UInt elem = 0; elem < nb_element; ++elem) {
ElementClass<type>::computeNormalsOnNaturalCoordinates(quads,
*f_it,
*normals_on_quad);
++normals_on_quad;
++f_it;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/* Matrix lumping functions */
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::assembleFieldLumped(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
ElementType type,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
#define ASSEMBLE_LUMPED(type) \
assembleLumpedTemplate<type>(field_1, nb_degree_of_freedom,lumped, equation_number,ghost_type)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(ASSEMBLE_LUMPED);;
#undef ASSEMBLE_LUMPED
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
void FEMTemplate<I, S, kind>::assembleFieldMatrix(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
SparseMatrix & matrix,
ElementType type,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
#define ASSEMBLE_MATRIX(type) \
assembleFieldMatrix<type>(field_1, nb_degree_of_freedom, \
matrix, \
ghost_type)
AKANTU_BOOST_ALL_ELEMENT_SWITCH(ASSEMBLE_MATRIX);;
#undef ASSEMBLE_MATRIX
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
template <ElementType type>
void FEMTemplate<I, S, kind>::assembleLumpedTemplate(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
this->template assembleLumpedRowSum<type>(field_1, nb_degree_of_freedom,lumped, equation_number,ghost_type);
}
/* -------------------------------------------------------------------------- */
/**
* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV = \int \rho \varphi_i dV @f$
*/
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
template <ElementType type>
void FEMTemplate<I, S, kind>::assembleLumpedRowSum(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt shapes_size = ElementClass<type>::getShapeSize();
Array<Real> * field_times_shapes = new Array<Real>(0, shapes_size * nb_degree_of_freedom);
Array<Real> * field = new Array<Real>(field_1.getSize(), nb_degree_of_freedom);
Array<Real>::const_scalar_iterator f1_it = field_1.begin();
Array<Real>::const_scalar_iterator f1_end = field_1.end();
Array<Real>::vector_iterator f_it = field->begin(nb_degree_of_freedom);
for(;f1_it != f1_end; ++f1_it, ++f_it) {
f_it->set(*f1_it);
}
shape_functions.template fieldTimesShapes<type>(*field, *field_times_shapes, ghost_type);
delete field;
UInt nb_element = mesh.getNbElement(type, ghost_type);
Array<Real> * int_field_times_shapes = new Array<Real>(nb_element, shapes_size * nb_degree_of_freedom,
"inte_rho_x_shapes");
integrator.template integrate<type>(*field_times_shapes, *int_field_times_shapes,
nb_degree_of_freedom * shapes_size, ghost_type, empty_filter);
delete field_times_shapes;
assembleArray(*int_field_times_shapes, lumped, equation_number,nb_degree_of_freedom, type, ghost_type);
delete int_field_times_shapes;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
*/
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
template <ElementType type>
void FEMTemplate<I, S, kind>::assembleLumpedDiagonalScaling(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
const ElementType & type_p1 = ElementClass<type>::getP1ElementType();
UInt nb_nodes_per_element_p1 = Mesh::getNbNodesPerElement(type_p1);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = integrator.template getQuadraturePoints<type>(ghost_type).cols();
UInt nb_element = field_1.getSize() / nb_quadrature_points;
Real corner_factor = 0;
Real mid_factor = 0;
if(type == _triangle_6) {
corner_factor = 1./12.;
mid_factor = 1./4.;
}
if (type == _tetrahedron_10) {
corner_factor = 1./32.;
mid_factor = 7./48.;
}
if (type == _quadrangle_8) {
corner_factor = 1./36.;
mid_factor = 8./36.;
}
if (nb_element == 0) {
AKANTU_DEBUG_OUT();
return;
}
/// compute @f$ \int \rho dV = \rho V @f$ for each element
Array<Real> * int_field_1 = new Array<Real>(field_1.getSize(), 1,
"inte_rho_x_1");
integrator.template integrate<type>(field_1, *int_field_1, 1, ghost_type, empty_filter);
/// distribute the mass of the element to the nodes
Array<Real> * lumped_per_node = new Array<Real>(nb_element, nb_degree_of_freedom * nb_nodes_per_element, "mass_per_node");
Array<Real>::const_scalar_iterator int_field_1_it = int_field_1->begin();
Array<Real>::matrix_iterator lumped_per_node_it
= lumped_per_node->begin(nb_degree_of_freedom, nb_nodes_per_element);
for (UInt e = 0; e < nb_element; ++e) {
Real lmass = *int_field_1_it * corner_factor;
for (UInt n = 0; n < nb_nodes_per_element_p1; ++n) {
Vector<Real> l = (*lumped_per_node_it)(n);
l.set(lmass); /// corner points
}
lmass = *int_field_1_it * mid_factor;
for (UInt n = nb_nodes_per_element_p1; n < nb_nodes_per_element; ++n) {
Vector<Real> l = (*lumped_per_node_it)(n);
l.set(lmass); /// mid points
}
++int_field_1_it;
++lumped_per_node_it;
}
delete int_field_1;
// lumped_per_node->extendComponentsInterlaced(nb_degree_of_freedom,1);
assembleArray(*lumped_per_node, lumped, equation_number, nb_degree_of_freedom, type, ghost_type);
delete lumped_per_node;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV = \int \rho \varphi_i dV @f$
*/
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
template <ElementType type>
void FEMTemplate<I, S, kind>::assembleFieldMatrix(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
SparseMatrix & matrix,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt vect_size = field_1.getSize();
UInt shapes_size = ElementClass<type>::getShapeSize();
UInt lmat_size = nb_degree_of_freedom * shapes_size;
const Array<Real> & shapes = shape_functions.getShapes(type,ghost_type);
Array<Real> * modified_shapes = new Array<Real>(vect_size, lmat_size * nb_degree_of_freedom);
modified_shapes->clear();
Array<Real> * local_mat = new Array<Real>(vect_size, lmat_size * lmat_size);
Array<Real>::matrix_iterator shape_vect = modified_shapes->begin(nb_degree_of_freedom, lmat_size);
Real * sh = shapes.storage();
for(UInt q = 0; q < vect_size; ++q) {
Real * msh = shape_vect->storage();
for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
Real * msh_tmp = msh + d * (lmat_size + 1);
for (UInt s = 0; s < shapes_size; ++s) {
*msh_tmp = sh[s];
msh_tmp += nb_degree_of_freedom;
}
}
++shape_vect;
sh += shapes_size;
}
shape_vect = modified_shapes->begin(nb_degree_of_freedom, lmat_size);
Array<Real>::matrix_iterator lmat = local_mat->begin(lmat_size, lmat_size);
Real * field_val = field_1.storage();
for(UInt q = 0; q < vect_size; ++q) {
(*lmat).mul<true, false>(*shape_vect, *shape_vect, *field_val);
++lmat; ++shape_vect; ++field_val;
}
delete modified_shapes;
UInt nb_element = mesh.getNbElement(type, ghost_type);
Array<Real> * int_field_times_shapes = new Array<Real>(nb_element, lmat_size * lmat_size,
"inte_rho_x_shapes");
integrator.template integrate<type>(*local_mat, *int_field_times_shapes,
lmat_size * lmat_size, ghost_type, empty_filter);
delete local_mat;
assembleMatrix(*int_field_times_shapes, matrix, nb_degree_of_freedom, type, ghost_type);
delete int_field_times_shapes;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline void FEMTemplate<I, S, kind>::inverseMap(const Vector<Real> & real_coords,
UInt element,
const ElementType & type,
Vector<Real> & natural_coords,
const GhostType & ghost_type) const{
AKANTU_DEBUG_IN();
#define INVERSE_MAP(type) \
shape_functions.template inverseMap<type>(real_coords, element, natural_coords, ghost_type);
AKANTU_BOOST_ELEMENT_SWITCH(INVERSE_MAP, AKANTU_NOT_STRUCTURAL_ELEMENT_TYPE);
#undef INVERSE_MAP
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline bool FEMTemplate<I, S, kind>::contains(const Vector<Real> & real_coords,
UInt element,
const ElementType & type,
const GhostType & ghost_type) const{
AKANTU_DEBUG_IN();
bool contain = false;
#define CONTAINS(type) \
contain = shape_functions.template contains<type>(real_coords, element, ghost_type);
AKANTU_BOOST_ELEMENT_SWITCH(CONTAINS, AKANTU_NOT_STRUCTURAL_ELEMENT_TYPE);
#undef CONTAINS
AKANTU_DEBUG_OUT();
return contain;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline void FEMTemplate<I, S, kind>::computeShapes(const Vector<Real> & real_coords,
UInt element,
const ElementType & type,
Vector<Real> & shapes,
const GhostType & ghost_type) const{
AKANTU_DEBUG_IN();
#define COMPUTE_SHAPES(type) \
shape_functions.template computeShapes<type>(real_coords,element,shapes,ghost_type);
AKANTU_BOOST_ALL_ELEMENT_SWITCH(COMPUTE_SHAPES);
#undef COMPUTE_SHAPES
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline UInt FEMTemplate<I, S, kind>::getNbQuadraturePoints(const ElementType & type,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
UInt nb_quad_points = 0;
#define GET_NB_QUAD(type) \
nb_quad_points = \
integrator. template getQuadraturePoints<type>(ghost_type).cols();
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_NB_QUAD);
#undef GET_NB_QUAD
AKANTU_DEBUG_OUT();
return nb_quad_points;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline const Array<Real> & FEMTemplate<I, S, kind>::getShapes(const ElementType & type,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
const Array<Real> * ret = NULL;
#define GET_SHAPES(type) \
ret = &(shape_functions.getShapes(type, ghost_type));
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPES);
#undef GET_SHAPES
AKANTU_DEBUG_OUT();
return *ret;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline const Array<Real> & FEMTemplate<I, S, kind>::getShapesDerivatives(const ElementType & type,
const GhostType & ghost_type,
__attribute__((unused)) UInt id) const {
AKANTU_DEBUG_IN();
const Array<Real> * ret = NULL;
#define GET_SHAPES(type) \
ret = &(shape_functions.getShapesDerivatives(type, ghost_type));
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_SHAPES);
#undef GET_SHAPES
AKANTU_DEBUG_OUT();
return *ret;
}
/* -------------------------------------------------------------------------- */
template<template <ElementKind> class I,
template <ElementKind> class S,
ElementKind kind>
inline const Matrix<Real> &
FEMTemplate<I, S, kind>::getQuadraturePoints(const ElementType & type,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
const Matrix<Real> * ret = NULL;
#define GET_QUADS(type) \
ret = &(integrator. template getQuadraturePoints<type>(ghost_type));
AKANTU_BOOST_ALL_ELEMENT_SWITCH(GET_QUADS);
#undef GET_QUADS
AKANTU_DEBUG_OUT();
return *ret;
}
/* -------------------------------------------------------------------------- */
__END_AKANTU__
#include "shape_lagrange.hh"
#include "integrator_gauss.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template <>
template <>
inline void FEMTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>::
assembleLumpedTemplate<_triangle_6>(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
assembleLumpedDiagonalScaling<_triangle_6>(field_1, nb_degree_of_freedom,
lumped, equation_number, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <>
template <>
inline void FEMTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>::
assembleLumpedTemplate<_tetrahedron_10>(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
assembleLumpedDiagonalScaling<_tetrahedron_10>(field_1, nb_degree_of_freedom,
lumped, equation_number, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <>
template <>
inline void
FEMTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>::
assembleLumpedTemplate<_quadrangle_8>(const Array<Real> & field_1,
UInt nb_degree_of_freedom,
Array<Real> & lumped,
const Array<Int> & equation_number,
const GhostType & ghost_type) const {
assembleLumpedDiagonalScaling<_quadrangle_8>(field_1, nb_degree_of_freedom,
lumped, equation_number, ghost_type);
}
/* -------------------------------------------------------------------------- */
template<>
template<>
inline void FEMTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>::computeNormalsOnControlPoints<_point_1>(__attribute__((unused))const Array<Real> & field,
Array<Real> & normal,
const GhostType & ghost_type) const {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == 1, "Mesh dimension must be 1 to compute normals on points!");
const ElementType type = _point_1;
UInt spatial_dimension = mesh.getSpatialDimension();
//UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_points = getNbQuadraturePoints(type, ghost_type);
UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
normal.resize(nb_element * nb_points);
Array<Real>::matrix_iterator normals_on_quad = normal.begin_reinterpret(spatial_dimension,
nb_points,
nb_element);
Array< std::vector<Element> > segments = mesh.getElementToSubelement(type, ghost_type);
Array<Real> coords = mesh.getNodes();
const Mesh * mesh_segment;
if (mesh.isMeshFacets())
mesh_segment = &(mesh.getMeshParent());
else
mesh_segment = &mesh;
for (UInt elem = 0; elem < nb_element; ++elem) {
UInt nb_segment = segments(elem).size();
AKANTU_DEBUG_ASSERT(nb_segment > 0, "Impossible to compute a normal on a point connected to 0 segments");
Real normal_value = 1;
if (nb_segment == 1) {
Element segment = segments(elem)[0];
const Array<UInt> & segment_connectivity = mesh_segment->getConnectivity(segment.type, segment.ghost_type);
//const Vector<UInt> & segment_points = segment_connectivity.begin(Mesh::getNbNodesPerElement(segment.type))[segment.element];
Real difference;
if(segment_connectivity(0) == elem) {
difference = coords(elem)-coords(segment_connectivity(1));
} else {
difference = coords(elem)-coords(segment_connectivity(0));
}
normal_value = difference/std::abs(difference);
}
for(UInt n(0); n < nb_points; ++n) {
(*normals_on_quad)(0, n) = normal_value;
}
++normals_on_quad;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/* Shape Linked specialization */
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_STRUCTURAL_MECHANICS)
__END_AKANTU__
#include "shape_linked.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template <>
inline const Array<Real> &
FEMTemplate<IntegratorGauss, ShapeLinked, _ek_structural>::getShapesDerivatives(const ElementType & type,
const GhostType & ghost_type,
UInt id) const {
AKANTU_DEBUG_IN();
const Array<Real> * ret = NULL;
#define GET_SHAPES(type) \
ret = &(shape_functions.getShapesDerivatives(type, ghost_type, id));
AKANTU_BOOST_STRUCTURAL_ELEMENT_SWITCH(GET_SHAPES);
#undef GET_SHAPES
AKANTU_DEBUG_OUT();
return *ret;
}
#endif
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