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/**
* Copyright (©) 2011-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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.hh"
#include "mesh_iterators.hh"
/* -------------------------------------------------------------------------- */
#include "integrator_gauss.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
namespace debug {
struct IntegratorGaussException : public Exception {};
} // namespace debug
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrateOnElement(
const Array<Real> & f, Real * intf, Int nb_degree_of_freedom, Idx elem,
GhostType ghost_type) const {
auto & jac_loc = jacobians(type, ghost_type);
auto nb_quadrature_points = ElementClass<type>::getNbQuadraturePoints();
AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
"The vector f do not have the good number of component.");
auto * f_val = f.data() + elem * f.getNbComponent();
auto * jac_val = jac_loc.data() + elem * nb_quadrature_points;
integrate(f_val, jac_val, intf, nb_degree_of_freedom, nb_quadrature_points);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Vector<Real> & in_f, Idx index, GhostType ghost_type) const {
const Array<Real> & jac_loc = jacobians(type, ghost_type);
auto nb_quadrature_points =
GaussIntegrationElement<type>::getNbQuadraturePoints();
AKANTU_DEBUG_ASSERT(in_f.size() == nb_quadrature_points,
"The vector f do not have nb_quadrature_points entries.");
auto * jac_val = jac_loc.data() + index * nb_quadrature_points;
Real intf{};
integrate(in_f.data(), jac_val, &intf, 1, nb_quadrature_points);
return intf;
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Real * f, const Real * jac, Real * inte, Int nb_degree_of_freedom,
Int nb_quadrature_points) const {
Eigen::Map<VectorXr> inte_v(inte, nb_quadrature_points);
Eigen::Map<const VectorXr> cjac(jac, nb_quadrature_points);
Eigen::Map<const MatrixXr> fq(f, nb_degree_of_freedom, nb_quadrature_points);
inte_v.zero();
inte_v = fq * cjac;
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline const Matrix<Real> &
IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints(
GhostType ghost_type) const {
AKANTU_DEBUG_ASSERT(
quadrature_points.exists(type, ghost_type),
"Quadrature points for type "
<< quadrature_points.printType(type, ghost_type)
<< " have not been initialized."
<< " Did you use 'computeQuadraturePoints' function ?");
return (quadrature_points(type, ghost_type));
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline Int
IntegratorGauss<kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
GhostType ghost_type) const {
if (not quadrature_points.exists(type, ghost_type)) {
constexpr auto polynomial_degree =
IntegrationOrderFunctor::template getOrder<type>();
return GaussIntegrationElement<type,
polynomial_degree>::getQuadraturePoints()
.cols();
}
return quadrature_points(type, ghost_type).cols();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline Int
IntegratorGauss<kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
GhostType ghost_type) {
if (not quadrature_points.exists(type, ghost_type)) {
this->template computeQuadraturePoints<type>(ghost_type);
}
return quadrature_points(type, ghost_type).cols();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, Int polynomial_degree>
inline Matrix<Real>
IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints() const {
return GaussIntegrationElement<type,
polynomial_degree>::getQuadraturePoints();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, Int polynomial_degree>
inline Vector<Real>
IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationWeights() const {
return GaussIntegrationElement<type, polynomial_degree>::getWeights();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline void
IntegratorGauss<kind, IntegrationOrderFunctor>::computeQuadraturePoints(
GhostType ghost_type) {
auto & quads = quadrature_points(type, ghost_type);
constexpr auto polynomial_degree =
IntegrationOrderFunctor::template getOrder<type>();
quads =
GaussIntegrationElement<type, polynomial_degree>::getQuadraturePoints();
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, class D1, class D2, class D3>
inline void IntegratorGauss<kind, IntegrationOrderFunctor>::
computeJacobianOnQuadPointsByElement(
const Eigen::MatrixBase<D1> & node_coords,
const Eigen::MatrixBase<D2> & quad,
Eigen::MatrixBase<D3> & jacobians) const {
// jacobian
ElementClass<type>::computeJacobian(quad, node_coords, jacobians);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
IntegratorGauss<kind, IntegrationOrderFunctor>::IntegratorGauss(
const Mesh & mesh, Int spatial_dimension, const ID & id)
: Integrator(mesh, spatial_dimension, id) {}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void IntegratorGauss<kind, IntegrationOrderFunctor>::checkJacobians(
GhostType ghost_type) const {
auto nb_quadrature_points = this->quadrature_points(type, ghost_type).cols();
auto nb_element = mesh.getConnectivity(type, ghost_type).size();
auto * jacobians_val = jacobians(type, ghost_type).data();
for (Idx i = 0; i < nb_element * nb_quadrature_points; ++i, ++jacobians_val) {
if (*jacobians_val < 0) {
AKANTU_CUSTOM_EXCEPTION_INFO(debug::IntegratorGaussException{},
"Negative jacobian computed,"
<< " possible problem in the element "
"node ordering (Quadrature Point "
<< i % nb_quadrature_points << ":"
<< i / nb_quadrature_points << ":"
<< type << ":" << ghost_type << ")");
}
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void IntegratorGauss<kind, IntegrationOrderFunctor>::
computeJacobiansOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & quad_points,
Array<Real> & jacobians, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
auto spatial_dimension = mesh.getSpatialDimension();
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_quadrature_points = quad_points.cols();
auto nb_element = mesh.getNbElement(type, ghost_type);
jacobians.resize(nb_element * nb_quadrature_points);
auto jacobians_it = make_view(jacobians, nb_quadrature_points).begin();
auto jacobians_begin = jacobians_it;
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
filter_elements);
auto x_it = make_view(x_el, spatial_dimension, nb_nodes_per_element).begin();
nb_element = x_el.size();
// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
for (Idx elem = 0; elem < nb_element; ++elem, ++x_it) {
const auto & x = *x_it;
if (filter_elements != empty_filter) {
jacobians_it = jacobians_begin + filter_elements(elem);
}
computeJacobianOnQuadPointsByElement<type>(x, quad_points, *jacobians_it);
if (filter_elements == empty_filter) {
++jacobians_it;
}
}
}
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_STRUCTURAL_MECHANICS)
template <>
template <ElementType type>
void IntegratorGauss<_ek_structural, DefaultIntegrationOrderFunctor>::
computeJacobiansOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & quad_points,
Array<Real> & jacobians, GhostType ghost_type,
const Array<Int> & filter_elements) const {
const auto spatial_dimension = mesh.getSpatialDimension();
const auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
const auto nb_quadrature_points = quad_points.cols();
const auto nb_dofs = ElementClass<type>::getNbDegreeOfFreedom();
auto nb_element = mesh.getNbElement(type, ghost_type);
jacobians.resize(nb_element * nb_quadrature_points);
auto jacobians_it = make_view(jacobians, nb_quadrature_points).begin();
auto jacobians_begin = jacobians_it;
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
filter_elements);
auto x_it = make_view(x_el, spatial_dimension, nb_nodes_per_element).begin();
nb_element = x_el.size();
Array<Real> zeros(nb_element, spatial_dimension, 0.);
const auto has_extra_normal =
mesh.hasData<Real>("extra_normal", type, ghost_type);
auto extra_normal_begin = make_const_view(zeros, spatial_dimension).begin();
if (has_extra_normal) {
extra_normal_begin =
make_const_view(mesh.getData<Real>("extra_normal", type, ghost_type),
spatial_dimension)
.begin();
}
auto extra_normal = extra_normal_begin;
// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
for (Idx elem = 0; elem < nb_element; ++elem, ++x_it) {
if (filter_elements != empty_filter) {
jacobians_it = jacobians_begin + filter_elements(elem);
if (has_extra_normal) {
extra_normal = extra_normal_begin + filter_elements(elem);
}
}
const auto & X = *x_it;
auto & J = *jacobians_it;
Matrix<Real, nb_dofs, nb_dofs> R;
ElementClass<type>::computeRotationMatrix(R, X, *extra_normal);
const Int natural_space = ElementClass<type>::getNaturalSpaceDimension();
const Int nb_nodes = ElementClass<type>::getNbNodesPerElement();
// Extracting relevant lines
Matrix<Real> RX = R.block(0, 0, spatial_dimension, spatial_dimension) * X;
auto x = RX.template block<natural_space, nb_nodes>(0, 0);
computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);
if (filter_elements == empty_filter) {
++jacobians_it;
if (has_extra_normal) {
++extra_normal;
}
}
}
}
#endif
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_COHESIVE_ELEMENT)
template <>
template <ElementType type>
void IntegratorGauss<_ek_cohesive, DefaultIntegrationOrderFunctor>::
computeJacobiansOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & quad_points,
Array<Real> & jacobians, GhostType ghost_type,
const Array<Int> & filter_elements) const {
auto spatial_dimension = mesh.getSpatialDimension();
auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
auto nb_quadrature_points = quad_points.cols();
auto nb_element = mesh.getNbElement(type, ghost_type);
jacobians.resize(nb_element * nb_quadrature_points);
auto jacobians_begin = make_view(jacobians, nb_quadrature_points).begin();
Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
filter_elements);
auto x_it = make_view(x_el, spatial_dimension, nb_nodes_per_element).begin();
auto nb_nodes_per_subelement = nb_nodes_per_element / 2;
Matrix<Real> x(spatial_dimension, nb_nodes_per_subelement);
nb_element = x_el.size();
Idx l_el = 0;
auto compute = [&](const auto & el) {
auto && J = jacobians_begin[el];
auto && X = x_it[l_el];
++l_el;
for (Int n = 0; n < nb_nodes_per_subelement; ++n) {
x(n) = (X(n) + X(n + nb_nodes_per_subelement)) / 2.;
}
if (type == _cohesive_1d_2) {
J(0) = 1;
} else {
this->computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);
}
};
for_each_element(nb_element, filter_elements, compute);
}
#endif
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void IntegratorGauss<kind, IntegrationOrderFunctor>::
precomputeJacobiansOnQuadraturePoints(const Array<Real> & nodes,
GhostType ghost_type) {
auto & jacobians_tmp = jacobians.alloc(0, 1, type, ghost_type);
this->computeJacobiansOnIntegrationPoints<type>(
nodes, quadrature_points(type, ghost_type), jacobians_tmp, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, Int polynomial_degree>
void IntegratorGauss<kind, IntegrationOrderFunctor>::multiplyJacobiansByWeights(
Array<Real> & jacobians, const Array<Int> & filter_elements) const {
constexpr auto nb_quadrature_points =
GaussIntegrationElement<type, polynomial_degree>::getNbQuadraturePoints();
auto && weights =
GaussIntegrationElement<type, polynomial_degree>::getWeights();
auto && view = make_view<nb_quadrature_points>(jacobians);
if (filter_elements != empty_filter) {
for (auto && J : filter(filter_elements, view)) {
J.array() *= weights.array();
}
} else {
for (auto && J : view) {
J.array() *= weights.array();
}
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Array<Real> & in_f, Array<Real> & intf, Int nb_degree_of_freedom,
const Array<Real> & jacobians, Int nb_element) const {
intf.resize(nb_element);
if (nb_element == 0) {
return;
}
auto nb_points = jacobians.size() / nb_element;
for (auto && [f, int_f, J] :
zip(make_view(in_f, nb_degree_of_freedom, nb_points),
make_view(intf, nb_degree_of_freedom),
make_view(jacobians, nb_points))) {
int_f = f * J;
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Array<Real> & in_f, Array<Real> & intf, Int nb_degree_of_freedom,
GhostType ghost_type, const Array<Int> & filter_elements) const {
AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
"No jacobians for the type "
<< jacobians.printType(type, ghost_type));
const auto & jac_loc = jacobians(type, ghost_type);
if (filter_elements != empty_filter) {
auto nb_element = filter_elements.size();
Array<Real> filtered_J(0, jac_loc.getNbComponent());
FEEngine::filterElementalData(mesh, jac_loc, filtered_J, type, ghost_type,
filter_elements);
this->integrate(in_f, intf, nb_degree_of_freedom, filtered_J, nb_element);
} else {
auto nb_element = mesh.getNbElement(type, ghost_type);
this->integrate(in_f, intf, nb_degree_of_freedom, jac_loc, nb_element);
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, Int polynomial_degree>
void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Array<Real> & in_f, Array<Real> & intf, Int nb_degree_of_freedom,
GhostType ghost_type) const {
auto quads = this->getIntegrationPoints<type, polynomial_degree>();
Array<Real> jacobians;
this->computeJacobiansOnIntegrationPoints<type>(mesh.getNodes(), quads,
jacobians, ghost_type);
this->multiplyJacobiansByWeights<type, polynomial_degree>(jacobians);
this->integrate(in_f, intf, nb_degree_of_freedom, jacobians,
mesh.getNbElement(type, ghost_type));
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type, Int polynomial_degree>
Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Array<Real> & in_f, GhostType ghost_type) const {
Array<Real> intfv(0, 1);
integrate<type, polynomial_degree>(in_f, intfv, 1, ghost_type);
auto res = Math::reduce(intfv);
return res;
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
const Array<Real> & in_f, GhostType ghost_type,
const Array<Int> & filter_elements) const {
if (in_f.empty()) {
return 0;
}
AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
"No jacobians for the type "
<< jacobians.printType(type, ghost_type));
Array<Real> intfv(0, 1);
integrate<type>(in_f, intfv, 1, ghost_type, filter_elements);
auto res = Math::reduce(intfv);
return res;
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline void
IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAddedByType(
const Array<Idx> & elements, GhostType ghost_type) {
const auto & nodes = mesh.getNodes();
computeQuadraturePoints<type>(ghost_type);
if (not jacobians.exists(type, ghost_type)) {
jacobians.alloc(0, 1, type, ghost_type);
}
this->computeJacobiansOnIntegrationPoints(
nodes, quadrature_points(type, ghost_type), jacobians(type, ghost_type),
type, ghost_type, elements);
constexpr auto polynomial_degree =
IntegrationOrderFunctor::template getOrder<type>();
this->multiplyJacobiansByWeights<type, polynomial_degree>(
this->jacobians(type, ghost_type), elements);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
void IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAdded(
const Array<Element> & new_elements) {
for (auto elements_range : MeshElementsByTypes(new_elements)) {
auto type = elements_range.getType();
auto ghost_type = elements_range.getGhostType();
if (mesh.getSpatialDimension(type) != _spatial_dimension) {
continue;
}
if (Mesh::getKind(type) != kind) {
continue;
}
tuple_dispatch<ElementTypes_t<kind>>(
[&](auto && enum_type) {
constexpr auto type = aka::decay_v<decltype(enum_type)>;
this->template onElementsAddedByType<type>(
elements_range.getElements(), ghost_type);
},
type);
}
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
template <ElementType type>
inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
const Array<Real> & nodes, GhostType ghost_type) {
computeQuadraturePoints<type>(ghost_type);
precomputeJacobiansOnQuadraturePoints<type>(nodes, ghost_type);
checkJacobians<type>(ghost_type);
constexpr auto polynomial_degree =
IntegrationOrderFunctor::template getOrder<type>();
multiplyJacobiansByWeights<type, polynomial_degree>(
this->jacobians(type, ghost_type));
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
const Array<Real> & nodes, ElementType type, GhostType ghost_type) {
tuple_dispatch<ElementTypes_t<kind>>(
[&](auto && enum_type) {
constexpr auto type = aka::decay_v<decltype(enum_type)>;
this->template initIntegrator<type>(nodes, ghost_type);
},
type);
}
/* -------------------------------------------------------------------------- */
template <ElementKind kind, class IntegrationOrderFunctor>
void IntegratorGauss<kind, IntegrationOrderFunctor>::
computeJacobiansOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & quad_points,
Array<Real> & jacobians, ElementType type, GhostType ghost_type,
const Array<Idx> & filter_elements) const {
tuple_dispatch<ElementTypes_t<kind>>(
[&](auto && enum_type) {
constexpr auto type = aka::decay_v<decltype(enum_type)>;
this->template computeJacobiansOnIntegrationPoints<type>(
nodes, quad_points, jacobians, ghost_type, filter_elements);
},
type);
}
} // namespace akantu
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