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rAKA/src/fem/integration_element.cc
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integration_element.cc
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/**
* @file integration_element.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date Sun Nov 18 00:45:16 2012
*
* @brief Definition of the intagration constants
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "element_class.hh"
using std::sqrt;
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_point_1>::nb_quadrature_points = 1;
template<> Real GaussIntegrationElement<_point_1>::quad[] = {0};
template<> Real GaussIntegrationElement<_point_1>::weights[] = {1.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_segment_2>::nb_quadrature_points = 1;
template<> Real GaussIntegrationElement<_segment_2>::quad[] = {0};
template<> Real GaussIntegrationElement<_segment_2>::weights[] = {2.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_segment_3>::nb_quadrature_points = 2;
template<> Real GaussIntegrationElement<_segment_3>::quad[] = {-1./sqrt(3.), 1./sqrt(3.)};
template<> Real GaussIntegrationElement<_segment_3>::weights[] = {1., 1.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_triangle_3>::nb_quadrature_points = 1;
template<> Real GaussIntegrationElement<_triangle_3>::quad[] = {1./3., 1./3.};
template<> Real GaussIntegrationElement<_triangle_3>::weights[] = {1./2.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_triangle_6>::nb_quadrature_points = 3;
template<> Real GaussIntegrationElement<_triangle_6>::quad[] = {1./6., 1./6.,
2./3., 1./6.,
1./6., 2./3.};
template<> Real GaussIntegrationElement<_triangle_6>::weights[] = {1./6., 1./6., 1./6.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_tetrahedron_4>::nb_quadrature_points = 1;
template<> Real GaussIntegrationElement<_tetrahedron_4>::quad[] = {1./4., 1./4., 1./4.};
template<> Real GaussIntegrationElement<_tetrahedron_4>::weights[] = {1./6.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_tetrahedron_10>::nb_quadrature_points = 4;
template<> Real GaussIntegrationElement<_tetrahedron_10>::quad[] = {0.1381966011250, 0.1381966011250, 0.1381966011250, // a = (5-sqrt(5))/20
0.5854101966250, 0.1381966011250, 0.1381966011250, // b = (5+3*sqrt(5))/20
0.1381966011250, 0.5854101966250, 0.1381966011250,
0.1381966011250, 0.1381966011250, 0.5854101966250};
template<> Real GaussIntegrationElement<_tetrahedron_10>::weights[] = {1./24., 1./24., 1./24., 1./24.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_quadrangle_4>::nb_quadrature_points = 4;
template<> Real GaussIntegrationElement<_quadrangle_4>::quad[] = {-1./sqrt(3.), -1./sqrt(3.),
1./sqrt(3.), -1./sqrt(3.),
1./sqrt(3.), 1./sqrt(3.),
-1./sqrt(3.), 1./sqrt(3.)};
template<> Real GaussIntegrationElement<_quadrangle_4>::weights[] = {1., 1., 1., 1.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_quadrangle_8>::nb_quadrature_points = 9;
template<> Real GaussIntegrationElement<_quadrangle_8>::quad[] = {0. , 0.,
sqrt(3./5.) , sqrt(3./5.),
-sqrt(3./5.), sqrt(3./5.),
-sqrt(3./5.), -sqrt(3./5.),
sqrt(3./5.) , -sqrt(3./5.),
0. , sqrt(3./5.),
-sqrt(3./5.), 0.,
0. , -sqrt(3./5.),
sqrt(3./5.) , 0.};
template<> Real GaussIntegrationElement<_quadrangle_8 >::weights[] = {64./81.,
25./81., 25./81., 25./81., 25./81.,
40./81., 40./81., 40./81., 40./81.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_hexahedron_8>::nb_quadrature_points = 8;
template<> Real GaussIntegrationElement<_hexahedron_8>::quad[] = {-1./sqrt(3.), -1./sqrt(3.), -1./sqrt(3.),
1./sqrt(3.) , -1./sqrt(3.), -1./sqrt(3.),
1./sqrt(3.) , 1./sqrt(3.), -1./sqrt(3.),
-1./sqrt(3.), 1./sqrt(3.), -1./sqrt(3.),
-1./sqrt(3.), -1./sqrt(3.), 1./sqrt(3.),
1./sqrt(3.) , -1./sqrt(3.), 1./sqrt(3.),
1./sqrt(3.) , 1./sqrt(3.), 1./sqrt(3.),
-1./sqrt(3.), 1./sqrt(3.), 1./sqrt(3.)};
template<> Real GaussIntegrationElement<_hexahedron_8>::weights[] = {1., 1., 1., 1.,
1., 1., 1., 1.};
#if defined(AKANTU_STRUCTURAL_MECHANICS)
/* -------------------------------------------------------------------------- */
/* Structural elements */
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_bernoulli_beam_2>::nb_quadrature_points = 2;
template<> Real GaussIntegrationElement<_bernoulli_beam_2>::quad[] = {-1./sqrt(3.), 0,
1./sqrt(3.), 0.};
template<> Real GaussIntegrationElement<_bernoulli_beam_2>::weights[] = {1., 1.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_bernoulli_beam_3>::nb_quadrature_points = 3;
template<> Real GaussIntegrationElement<_bernoulli_beam_3>::quad[] = {-sqrt(3./5.), 0., 0.,
0., 0., 0.,
sqrt(3./5.), 0., 0.};
template<> Real GaussIntegrationElement<_bernoulli_beam_3>::weights[] = {5./9., 8./9., 5./9.};
#endif
#if defined(AKANTU_COHESIVE_ELEMENT)
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_cohesive_2d_4>::nb_quadrature_points = 1;
template<> Real GaussIntegrationElement<_cohesive_2d_4>::quad[] = {0};
template<> Real GaussIntegrationElement<_cohesive_2d_4>::weights[] = {2.};
/* -------------------------------------------------------------------------- */
template<> UInt GaussIntegrationElement<_cohesive_2d_6>::nb_quadrature_points = 2;
template<> Real GaussIntegrationElement<_cohesive_2d_6>::quad[] = {-1./sqrt(3.), 1./sqrt(3.)};
template<> Real GaussIntegrationElement<_cohesive_2d_6>::weights[] = {1., 1.};
/* -------------------------------------------------------------------------- */
#endif
__END_AKANTU__
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