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gauss_integration_tmpl.hh
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/**
* @file gauss_integration_tmpl.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Tue May 10 2016
* @date last modification: Tue Sep 29 2020
*
* @brief implementation of the gauss integration helpers
*
*
* @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 "aka_math.hh"
#ifndef AKANTU_GAUSS_INTEGRATION_TMPL_HH_
#define AKANTU_GAUSS_INTEGRATION_TMPL_HH_
#include "element_class.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
/* GaussIntegrationElement */
/* -------------------------------------------------------------------------- */
namespace _aka_gauss_helpers {
template <GaussIntegrationType type, Int n>
struct GaussIntegrationNbPoints {};
template <Int n> struct GaussIntegrationNbPoints<_git_not_defined, n> {
static constexpr Int nb_points = 0;
};
template <Int n> struct GaussIntegrationNbPoints<_git_point, n> {
static constexpr Int nb_points = 1;
};
template <Int n> struct GaussIntegrationNbPoints<_git_segment, n> {
static constexpr Int nb_points = (n + 1) / 2 + (bool((n + 1) % 2) ? 1 : 0);
};
#define DECLARE_GAUSS_NB_POINTS(type, order, points) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static constexpr Int nb_points = points; \
}
#define DECLARE_GAUSS_NB_POINTS_PENT(type, order, xo, yo) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static constexpr Int x_order = xo; \
static constexpr Int yz_order = yo; \
static constexpr Int nb_points = 1; \
}
DECLARE_GAUSS_NB_POINTS(_git_triangle, 1, 1);
DECLARE_GAUSS_NB_POINTS(_git_triangle, 2, 3);
DECLARE_GAUSS_NB_POINTS(_git_triangle, 3, 4);
DECLARE_GAUSS_NB_POINTS(_git_triangle, 4, 6);
DECLARE_GAUSS_NB_POINTS(_git_triangle, 5, 7);
DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 1, 1);
DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 2, 4);
DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 3, 5);
DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 4, 15);
DECLARE_GAUSS_NB_POINTS(_git_tetrahedron, 5, 15);
DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 1, 3,
2); // order 3 in x, order 2 in y and z
DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 2, 3,
2); // order 3 in x, order 2 in y and z
DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 3, 3,
3); // order 3 in x, order 3 in y and z
DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 4, 5,
5); // order 5 in x, order 5 in y and z
DECLARE_GAUSS_NB_POINTS_PENT(_git_pentahedron, 5, 5,
5); // order 5 in x, order 5 in y and z
template <GaussIntegrationType type, Int n, Int on = n,
bool end_recurse = false>
struct GaussIntegrationNbPointsHelper {
static constexpr Int pnp = GaussIntegrationNbPoints<type, n>::nb_points;
static constexpr Int order = n;
static constexpr Int nb_points = pnp;
};
template <GaussIntegrationType type, Int n, Int on>
struct GaussIntegrationNbPointsHelper<type, n, on, true> {
static constexpr Int nb_points = 0;
};
/* ------------------------------------------------------------------------ */
/* Generic helper */
/* ------------------------------------------------------------------------ */
template <GaussIntegrationType type, Int dimension, Int n>
struct GaussIntegrationTypeDataHelper {
using git_np = GaussIntegrationNbPoints<type, n>;
using git_data = GaussIntegrationTypeData<type, git_np::nb_points>;
static constexpr Int getNbQuadraturePoints() { return git_np::nb_points; }
static constexpr auto getQuadraturePoints()
-> Matrix<Real, std::max(1, dimension),
GaussIntegrationTypeDataHelper::getNbQuadraturePoints()> {
constexpr auto nb_points = git_np::nb_points;
using Matrix = Eigen::Matrix<Real, std::max(1, dimension), nb_points>;
Matrix quads = Eigen::Map<const Matrix>(git_data::quad_positions);
return quads;
}
static constexpr auto getWeights()
-> Vector<Real,
GaussIntegrationTypeDataHelper::getNbQuadraturePoints()> {
constexpr auto nb_points = git_np::nb_points;
using Vector = Eigen::Matrix<Real, nb_points, 1>;
Vector weights = Eigen::Map<const Vector>(git_data::quad_weights);
return weights;
}
};
#if !defined(DOXYGEN)
/* ------------------------------------------------------------------------ */
/* helper for _segment _quadrangle _hexahedron */
/* ------------------------------------------------------------------------ */
template <Int dimension, Int dp>
struct GaussIntegrationTypeDataHelper<_git_segment, dimension, dp> {
using git_np = GaussIntegrationNbPoints<_git_segment, dp>;
using git_data = GaussIntegrationTypeData<_git_segment, git_np::nb_points>;
static constexpr Int getNbQuadraturePoints() {
return Math::pow(git_np::nb_points, dimension);
}
static constexpr auto getQuadraturePoints()
-> Matrix<Real, dimension,
GaussIntegrationTypeDataHelper::getNbQuadraturePoints()> {
const auto tot_nquad = getNbQuadraturePoints();
const auto nquad = git_np::nb_points;
Eigen::Matrix<Real, dimension, tot_nquad> quads;
Eigen::Map<const Eigen::Matrix<Real, nquad, 1>> pos(
git_data::quad_positions);
Int offset = 1;
for (Int d = 0; d < dimension; ++d) {
for (Int n = 0, q = 0; n < tot_nquad; ++n, q += offset) {
Int rq = q % tot_nquad + q / tot_nquad;
quads(d, rq) = pos(n % nquad);
}
offset *= nquad;
}
return quads;
}
static constexpr Vector<
Real, GaussIntegrationTypeDataHelper::getNbQuadraturePoints()>
getWeights() {
const auto tot_nquad = getNbQuadraturePoints();
const auto nquad = git_np::nb_points;
Eigen::Matrix<Real, tot_nquad, 1> quads_weights;
quads_weights.fill(1);
Eigen::Map<const Eigen::Matrix<Real, nquad, 1>> weights(
git_data::quad_weights);
Int offset = 1;
for (Int d = 0; d < dimension; ++d) {
for (Int n = 0, q = 0; n < tot_nquad; ++n, q += offset) {
Int rq = q % tot_nquad + q / tot_nquad;
quads_weights(rq) *= weights(n % nquad);
}
offset *= nquad;
}
return quads_weights;
}
};
/* ------------------------------------------------------------------------ */
/* helper for _pentahedron */
/* ------------------------------------------------------------------------ */
template <Int dimension, Int dp>
struct GaussIntegrationTypeDataHelper<_git_pentahedron, dimension, dp> {
using git_info = GaussIntegrationNbPoints<_git_pentahedron, dp>;
using git_np_seg =
GaussIntegrationNbPoints<_git_segment, git_info::x_order>;
using git_np_tri =
GaussIntegrationNbPoints<_git_triangle, git_info::yz_order>;
using git_data_seg =
GaussIntegrationTypeData<_git_segment, git_np_seg::nb_points>;
using git_data_tri =
GaussIntegrationTypeData<_git_triangle, git_np_tri::nb_points>;
static constexpr Int getNbQuadraturePoints() {
return git_np_seg::nb_points * git_np_tri::nb_points;
}
static constexpr auto getQuadraturePoints()
-> Matrix<Real, dimension,
GaussIntegrationTypeDataHelper::getNbQuadraturePoints()> {
constexpr auto tot_nquad = getNbQuadraturePoints();
constexpr auto nquad_seg = git_np_seg::nb_points;
constexpr auto nquad_tri = git_np_tri::nb_points;
Matrix<Real, dimension, tot_nquad> quads;
Eigen::Map<Vector<Real, nquad_seg>> pos_seg(git_data_seg::quad_positions);
Eigen::Map<Matrix<Real, 2, nquad_tri>> pos_tri(
git_data_tri::quad_positions);
for (Int ns = 0, q = 0; ns < nquad_seg; ++ns) {
for (Int nt = 0; nt < nquad_tri; ++nt, ++q) {
auto && quad = quads(q);
quad(_x) = pos_seg(ns);
quad(_y) = pos_tri(_x, nt);
quad(_z) = pos_tri(_y, nt);
}
}
return quads;
}
static constexpr auto getWeights()
-> Vector<Real,
GaussIntegrationTypeDataHelper::getNbQuadraturePoints()> {
constexpr auto tot_nquad = getNbQuadraturePoints();
constexpr auto nquad_seg = git_np_seg::nb_points;
constexpr auto nquad_tri = git_np_tri::nb_points;
Vector<Real, tot_nquad> quads_weights;
Eigen::Map<const Vector<Real, nquad_seg>> weight_seg(
git_data_seg::quad_weights);
Eigen::Map<const Vector<Real, nquad_tri>> weight_tri(
git_data_tri::quad_weights);
for (Int ns = 0, q = 0; ns < nquad_seg; ++ns) {
for (Int nt = 0; nt < nquad_tri; ++nt, ++q) {
quads_weights(q) = weight_seg(ns) * weight_tri(nt);
}
}
return quads_weights;
}
};
#endif
} // namespace _aka_gauss_helpers
/* -------------------------------------------------------------------------- */
template <ElementType element_type, Int n>
constexpr Int
GaussIntegrationElement<element_type, n>::getNbQuadraturePoints() {
using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
ElementClassProperty<element_type>::gauss_integration_type,
interpolation_property::natural_space_dimension, n>;
return data_helper::getNbQuadraturePoints();
}
/* -------------------------------------------------------------------------- */
template <ElementType element_type, Int n>
constexpr auto GaussIntegrationElement<element_type, n>::getWeights() {
using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
ElementClassProperty<element_type>::gauss_integration_type,
interpolation_property::natural_space_dimension, n>;
return data_helper::getWeights();
}
template <ElementType type, Int n>
constexpr auto GaussIntegrationElement<type, n>::getQuadraturePoints() {
using data_helper = _aka_gauss_helpers::GaussIntegrationTypeDataHelper<
ElementClassProperty<type>::gauss_integration_type,
interpolation_property::natural_space_dimension, n>;
return data_helper::getQuadraturePoints();
}
} // namespace akantu
#endif /* AKANTU_GAUSS_INTEGRATION_TMPL_HH_ */

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