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integration_element.cc
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/**
* @file integration_element.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Jan 16 2013
* @date last modification: Mon Jul 07 2014
*
* @brief Definition of the intagration constants
*
* @section LICENSE
*
* Copyright (©) 2014 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_common.hh"
#include "element_class.hh"
using std::sqrt;
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
/* Points */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_point, 1>::nb_quadrature_points = 1;
template<> Real GaussIntegrationTypeData<_git_point, 1>::quad_positions[] = {0};
template<> Real GaussIntegrationTypeData<_git_point, 1>::quad_weights[] = {1.};
/* -------------------------------------------------------------------------- */
/* Segments */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_segment, 1>::nb_quadrature_points = 1;
template<> Real GaussIntegrationTypeData<_git_segment, 1>::quad_positions[] = {0.};
template<> Real GaussIntegrationTypeData<_git_segment, 1>::quad_weights[] = {2.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_segment, 2>::nb_quadrature_points = 2;
template<> Real GaussIntegrationTypeData<_git_segment, 2>::quad_positions[] = {-1./sqrt(3.), 1./sqrt(3.)};
template<> Real GaussIntegrationTypeData<_git_segment, 2>::quad_weights[] = {1., 1.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_segment, 3>::nb_quadrature_points = 3;
template<> Real GaussIntegrationTypeData<_git_segment, 3>::quad_positions[] = {-sqrt(3./5.), 0., sqrt(3./5.)};
template<> Real GaussIntegrationTypeData<_git_segment, 3>::quad_weights[] = {5./9., 8./9., 5./9.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_segment, 4>::nb_quadrature_points = 4;
template<> Real GaussIntegrationTypeData<_git_segment, 4>::quad_positions[] = {-sqrt((3. + 2.*sqrt(6./5.))/7.),
-sqrt((3. - 2.*sqrt(6./5.))/7.),
sqrt((3. - 2.*sqrt(6./5.))/7.),
sqrt((3. + 2.*sqrt(6./5.))/7.)};
template<> Real GaussIntegrationTypeData<_git_segment, 4>::quad_weights[] = {(18. - sqrt(30.))/36.,
(18. + sqrt(30.))/36.,
(18. + sqrt(30.))/36.,
(18. - sqrt(30.))/36.};
/* -------------------------------------------------------------------------- */
/* Triangles */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_triangle, 1>::nb_quadrature_points = 1;
template<> Real GaussIntegrationTypeData<_git_triangle, 1>::quad_positions[] = {1./3., 1./3.};
template<> Real GaussIntegrationTypeData<_git_triangle, 1>::quad_weights[] = {1./2.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_triangle, 2>::nb_quadrature_points = 3;
template<> Real GaussIntegrationTypeData<_git_triangle, 2>::quad_positions[] = {1./6., 1./6.,
2./3., 1./6.,
1./6., 2./3.};
template<> Real GaussIntegrationTypeData<_git_triangle, 2>::quad_weights[] = {1./6., 1./6., 1./6.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_triangle, 3>::nb_quadrature_points = 4;
template<> Real GaussIntegrationTypeData<_git_triangle, 3>::quad_positions[] = {1./5., 1./5.,
3./5., 1./5.,
1./5., 3./5.,
1./3., 1./3.};
template<> Real GaussIntegrationTypeData<_git_triangle, 3>::quad_weights[] = {25./(24.*4.), 25./(24.*4.), 25./(24.*4.), -27/(24.*4.)};
/* -------------------------------------------------------------------------- */
/* Tetrahedrons */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_tetrahedron, 1>::nb_quadrature_points = 1;
template<> Real GaussIntegrationTypeData<_git_tetrahedron, 1>::quad_positions[] = {1./4., 1./4., 1./4.};
template<> Real GaussIntegrationTypeData<_git_tetrahedron, 1>::quad_weights[] = {1./6.};
/* -------------------------------------------------------------------------- */
static const Real tet_2_a = (5. - std::sqrt(5.))/20.;
static const Real tet_2_b = (5. + 3.*std::sqrt(5.))/20.;
template<> UInt GaussIntegrationTypeData<_git_tetrahedron, 2>::nb_quadrature_points = 4;
template<> Real GaussIntegrationTypeData<_git_tetrahedron, 2>::quad_positions[] = {tet_2_a, tet_2_a, tet_2_a,
tet_2_b, tet_2_a, tet_2_a,
tet_2_a, tet_2_b, tet_2_a,
tet_2_a, tet_2_a, tet_2_b};
template<> Real GaussIntegrationTypeData<_git_tetrahedron, 2>::quad_weights[] = {1./24., 1./24., 1./24., 1./24.};
/* -------------------------------------------------------------------------- */
/* Pentahedrons */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_pentahedron, 1>::nb_quadrature_points = 6;
template<> Real GaussIntegrationTypeData<_git_pentahedron, 1>::quad_positions[] = {-1./sqrt(3.), 0.5, 0.5,
-1./sqrt(3.), 0. , 0.5,
-1./sqrt(3.), 0.5, 0.,
1./sqrt(3.), 0.5, 0.5,
1./sqrt(3.), 0. , 0.5,
1./sqrt(3.), 0.5 ,0.};
template<> Real GaussIntegrationTypeData<_git_pentahedron, 1>::quad_weights[] = {1./6, 1./6, 1./6,
1./6, 1./6, 1./6};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationTypeData<_git_pentahedron, 2>::nb_quadrature_points = 8;
template<> Real GaussIntegrationTypeData<_git_pentahedron, 2>::quad_positions[] = {-sqrt(3.)/3., 1./3., 1./3.,
-sqrt(3.)/3., 0.6 , 0.2,
-sqrt(3.)/3., 0.2, 0.6,
-sqrt(3.)/3., 0.2, 0.2,
sqrt(3.)/3., 1./3., 1./3.,
sqrt(3.)/3., 0.6 , 0.2,
sqrt(3.)/3., 0.2, 0.6,
sqrt(3.)/3., 0.2, 0.2,};
template<> Real GaussIntegrationTypeData<_git_pentahedron, 2>::quad_weights[] = {-27./96., 25./96., 25./96., 25./96.,
-27./96., 25./96., 25./96., 25./96.};
__END_AKANTU__

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