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/**
* @file fe_engine_template_tmpl_field.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Aug 09 2017
* @date last modification: Sat Mar 13 2021
*
* @brief implementation of the assemble field s functions
*
*
* @section LICENSE
*
* Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
//#include "fe_engine_template.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_
#define AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
/* Matrix lumping functions */
/* -------------------------------------------------------------------------- */
namespace fe_engine {
namespace details {
namespace {
template <class Functor>
void fillField(const Functor & field_funct, Array<Real> & field,
Int nb_element, Int nb_integration_points,
ElementType type, GhostType ghost_type) {
auto nb_degree_of_freedom = field.getNbComponent();
field.resize(nb_integration_points * nb_element);
Matrix<Real> mat(nb_degree_of_freedom, nb_integration_points);
Element el{type, 0, ghost_type};
for (auto && data : enumerate(make_view(field, nb_degree_of_freedom,
nb_integration_points))) {
el.element = std::get<0>(data);
mat.fill(0.);
field_funct(mat, el);
mat = std::get<1>(data);
}
}
} // namespace
} // namespace details
} // namespace fe_engine
#define DISPATCH_HELPER(Func, ...) \
auto && call = [&](auto && enum_type) { \
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value; \
this->Func<type>(__VA_ARGS__); \
}; \
tuple_dispatch<ElementTypes_t<kind>>(call, type);
/* -------------------------------------------------------------------------- */
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind, class IOF>
void FEEngineTemplate<I, S, kind, IOF>::assembleFieldLumped(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const {
DISPATCH_HELPER(assembleFieldLumped, field_funct, matrix_id, dof_id,
dof_manager, ghost_type);
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldLumped(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const {
AKANTU_DEBUG_IN();
auto nb_degree_of_freedom = dof_manager.getDOFs(dof_id).getNbComponent();
auto nb_element = mesh.getNbElement(type, ghost_type);
auto nb_integration_points = this->getNbIntegrationPoints(type);
Array<Real> field(0, nb_degree_of_freedom);
fe_engine::details::fillField(field_funct, field, nb_element,
nb_integration_points, type, ghost_type);
switch (type) {
case _triangle_6:
case _quadrangle_8:
case _tetrahedron_10:
case _hexahedron_20:
case _pentahedron_15:
this->template assembleLumpedDiagonalScaling<type>(field, matrix_id, dof_id,
dof_manager, ghost_type);
break;
default:
this->template assembleLumpedRowSum<type>(field, matrix_id, dof_id,
dof_manager, ghost_type);
}
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> class I, template <ElementKind> class S,
ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
assembleLumpedRowSum(const Array<Real> & field, const ID & matrix_id,
const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const {
AKANTU_DEBUG_IN();
auto shapes_size = ElementClass<type>::getShapeSize();
auto nb_degree_of_freedom = field.getNbComponent();
auto field_times_shapes =
std::make_shared<Array<Real>>(0, shapes_size * nb_degree_of_freedom);
shape_functions.template computeNtb<type>(field, *field_times_shapes,
ghost_type);
auto nb_element = mesh.getNbElement(type, ghost_type);
auto int_field_times_shapes = std::make_shared<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);
dof_manager.assembleElementalArrayToLumpedMatrix(
dof_id, *int_field_times_shapes, matrix_id, type, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
*/
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
assembleLumpedDiagonalScaling(const Array<Real> & field,
const ID & matrix_id, const ID & dof_id,
DOFManager & dof_manager,
GhostType ghost_type) const {
AKANTU_DEBUG_IN();
const auto & type_p1 = ElementClass<type>::getP1ElementType();
auto nb_nodes_per_element_p1 = Mesh::getNbNodesPerElement(type_p1);
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_degree_of_freedom = field.getNbComponent();
auto nb_element = mesh.getNbElement(type, ghost_type);
Vector<Real> nodal_factor(nb_nodes_per_element);
auto assign_weight_to_nodes = [&nodal_factor, nb_nodes_per_element,
nb_nodes_per_element_p1](Real corner,
Real mid) {
for (Int n = 0; n < nb_nodes_per_element_p1; n++) {
nodal_factor(n) = corner;
}
for (Int n = nb_nodes_per_element_p1; n < nb_nodes_per_element; n++) {
nodal_factor(n) = mid;
}
};
if (type == _triangle_6) {
assign_weight_to_nodes(1. / 12., 1. / 4.);
}
if (type == _tetrahedron_10) {
assign_weight_to_nodes(1. / 32., 7. / 48.);
}
if (type == _quadrangle_8) {
assign_weight_to_nodes(
3. / 76.,
16. / 76.); /** coeff. derived by scaling
* the diagonal terms of the corresponding
* consistent mass computed with 3x3 gauss points;
* coeff. are (1./36., 8./36.) for 2x2 gauss points */
}
if (type == _hexahedron_20) {
assign_weight_to_nodes(
7. / 248., 16. / 248.); /** coeff. derived by scaling
* the diagonal terms of the corresponding
* consistent mass computed with 3x3x3 gauss
* points; coeff. are (1./40.,
* 1./15.) for 2x2x2 gauss points */
}
if (type == _pentahedron_15) {
// coefficients derived by scaling the diagonal terms of the corresponding
// consistent mass computed with 8 gauss points;
for (Int n = 0; n < nb_nodes_per_element_p1; n++) {
nodal_factor(n) = 51. / 2358.;
}
Real mid_triangle = 192. / 2358.;
Real mid_quadrangle = 300. / 2358.;
nodal_factor(6) = mid_triangle;
nodal_factor(7) = mid_triangle;
nodal_factor(8) = mid_triangle;
nodal_factor(9) = mid_quadrangle;
nodal_factor(10) = mid_quadrangle;
nodal_factor(11) = mid_quadrangle;
nodal_factor(12) = mid_triangle;
nodal_factor(13) = mid_triangle;
nodal_factor(14) = mid_triangle;
}
if (nb_element == 0) {
AKANTU_DEBUG_OUT();
return;
}
/// compute @f$ \int \rho dV = \rho V @f$ for each element
auto int_field = std::make_unique<Array<Real>>(
field.size(), nb_degree_of_freedom, "inte_rho_x");
integrator.template integrate<type>(field, *int_field, nb_degree_of_freedom,
ghost_type, empty_filter);
/// distribute the mass of the element to the nodes
auto lumped_per_node = std::make_unique<Array<Real>>(
nb_element, nb_degree_of_freedom * nb_nodes_per_element, "mass_per_node");
auto int_field_it = int_field->begin(nb_degree_of_freedom);
auto lumped_per_node_it =
lumped_per_node->begin(nb_degree_of_freedom, nb_nodes_per_element);
for (Int e = 0; e < nb_element; ++e) {
for (Int n = 0; n < nb_nodes_per_element; ++n) {
auto && l = (*lumped_per_node_it)(n);
l = *int_field_it * nodal_factor(n);
}
++int_field_it;
++lumped_per_node_it;
}
dof_manager.assembleElementalArrayToLumpedMatrix(dof_id, *lumped_per_node,
matrix_id, type, ghost_type);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind, class IOF>
template <ElementKind kind_, std::enable_if_t<kind_ != _ek_cohesive> *>
void FEEngineTemplate<I, S, kind, IOF>::assembleFieldMatrixImpl(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const {
DISPATCH_HELPER(assembleFieldMatrix, field_funct, matrix_id, dof_id,
dof_manager, ghost_type);
}
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind, class IOF>
template <ElementKind kind_, std::enable_if_t<kind_ == _ek_cohesive> *>
void FEEngineTemplate<I, S, kind, IOF>::assembleFieldMatrixImpl(
const std::function<void(Matrix<Real> &,
const Element &)> & /*field_funct*/,
const ID & /*matrix_id*/, const ID & /*dof_id*/,
DOFManager & /*dof_manager*/, ElementType /*type*/,
GhostType /*ghost_type*/) const {
AKANTU_TO_IMPLEMENT();
}
namespace fe_engine {
namespace details {
template <ElementKind kind> struct ShapesForMassHelper {
template <ElementType type, class ShapeFunctions>
static auto getShapes(ShapeFunctions & shape_functions,
const Matrix<Real> & integration_points,
const Array<Real> & nodes,
Int & nb_degree_of_freedom, Int nb_element,
GhostType ghost_type) {
auto shapes_size = ElementClass<type>::getShapeSize();
Array<Real> shapes(0, shapes_size);
shape_functions.template computeShapesOnIntegrationPoints<type>(
nodes, integration_points, shapes, ghost_type);
auto nb_integration_points = integration_points.cols();
auto vect_size = nb_integration_points * nb_element;
auto lmat_size = nb_degree_of_freedom * shapes_size;
// Extending the shape functions
/// \todo move this in the shape functions as Voigt format shapes to
/// have the code in common with the structural elements
auto shapes_voigt = std::make_unique<Array<Real>>(
vect_size, lmat_size * nb_degree_of_freedom, 0.);
auto mshapes_it = shapes_voigt->begin(nb_degree_of_freedom, lmat_size);
auto shapes_it = shapes.begin(shapes_size);
for (Int q = 0; q < vect_size; ++q, ++mshapes_it, ++shapes_it) {
for (Int d = 0; d < nb_degree_of_freedom; ++d) {
for (Int s = 0; s < shapes_size; ++s) {
(*mshapes_it)(d, s * nb_degree_of_freedom + d) = (*shapes_it)(s);
}
}
}
return shapes_voigt;
}
};
#if defined(AKANTU_STRUCTURAL_MECHANICS)
template <> struct ShapesForMassHelper<_ek_structural> {
template <ElementType type, class ShapeFunctions>
static auto getShapes(ShapeFunctions & shape_functions,
const Matrix<Real> & integration_points,
const Array<Real> & nodes,
UInt & nb_degree_of_freedom, UInt /*nb_element*/,
GhostType ghost_type) {
auto nb_unknown = ElementClass<type>::getNbStressComponents();
auto nb_degree_of_freedom_ = ElementClass<type>::getNbDegreeOfFreedom();
auto nb_nodes_per_element = ElementClass<type>::getNbNodesPerElement();
auto shapes = std::make_unique<Array<Real>>(
0, nb_unknown * nb_nodes_per_element * nb_degree_of_freedom_);
nb_degree_of_freedom = nb_unknown;
shape_functions.template computeShapesMassOnIntegrationPoints<type>(
nodes, integration_points, *shapes, ghost_type);
return shapes;
}
};
#endif
} // namespace details
} // namespace fe_engine
//
/* -------------------------------------------------------------------------- */
/**
* @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> class I, template <ElementKind> class S,
ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const {
AKANTU_DEBUG_IN();
auto shapes_size = ElementClass<type>::getShapeSize();
auto nb_degree_of_freedom = dof_manager.getDOFs(dof_id).getNbComponent();
auto lmat_size = nb_degree_of_freedom * shapes_size;
auto nb_element = mesh.getNbElement(type, ghost_type);
// \int N * N so degree 2 * degree of N
const auto polynomial_degree =
2 * ElementClassProperty<type>::polynomial_degree;
// getting the integration points
auto integration_points =
integrator.template getIntegrationPoints<type, polynomial_degree>();
auto nb_integration_points = integration_points.cols();
auto vect_size = nb_integration_points * nb_element;
// getting the shapes on the integration points
auto shapes_voigt =
fe_engine::details::ShapesForMassHelper<kind>::template getShapes<type>(
shape_functions, integration_points, mesh.getNodes(),
nb_degree_of_freedom, nb_element, ghost_type);
// getting the value to assemble on the integration points
Array<Real> field(vect_size, nb_degree_of_freedom);
fe_engine::details::fillField(field_funct, field, nb_element,
integration_points.cols(), type, ghost_type);
Array<Real> local_mat(vect_size, lmat_size * lmat_size);
// computing \rho * N
for (auto && data :
zip(make_view(local_mat, lmat_size, lmat_size),
make_view(*shapes_voigt, nb_degree_of_freedom, lmat_size),
make_view(field, nb_degree_of_freedom))) {
const auto & rho = std::get<2>(data);
const auto & N = std::get<1>(data);
auto & mat = std::get<0>(data);
Matrix<Real> Nt = N.transpose();
for (Int d = 0; d < Nt.cols(); ++d) {
Nt(d) *= rho(d);
}
mat = Nt * N;
}
// integrate the elemental values
Array<Real> int_field_times_shapes(nb_element, lmat_size * lmat_size,
"inte_rho_x_shapes");
this->integrator.template integrate<type, polynomial_degree>(
local_mat, int_field_times_shapes, lmat_size * lmat_size, ghost_type);
// assemble the elemental values to the matrix
dof_manager.assembleElementalMatricesToMatrix(
matrix_id, dof_id, int_field_times_shapes, type, ghost_type);
AKANTU_DEBUG_OUT();
}
} // namespace akantu
#endif /* AKANTU_FE_ENGINE_TEMPLATE_TMPL_FIELD_HH_ */

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