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element_class.cc
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/**
* @file element_class.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Tue Jul 20 10:12:44 2010
*
* @brief Common part of element_classes
*
* @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 "element_class.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template<ElementType type> ElementKind ElementClass<type>::kind = _ek_regular;
template<ElementType type> UInt ElementClass<type>::nb_nodes_per_element = 0;
template<ElementType type> ElementType ElementClass<type>::p1_element_type = _not_defined;
template<ElementType type> UInt ElementClass<type>::nb_quadrature_points = 0;
template<ElementType type> UInt ElementClass<type>::spatial_dimension = 0;
template<ElementType type> ElementType ElementClass<type>::facet_type = _not_defined;
template<ElementType type> UInt ElementClass<type>::nb_shape_functions = 1;
template<> ElementKind ElementClass<_not_defined>::kind = _ek_regular;
template<> UInt ElementClass<_not_defined>::nb_nodes_per_element = 0;
template<> ElementType ElementClass<_not_defined>::p1_element_type = _not_defined;
template<> UInt ElementClass<_not_defined>::nb_quadrature_points = 0;
template<> UInt ElementClass<_not_defined>::spatial_dimension = 0;
template<> ElementType ElementClass<_not_defined>::facet_type = _not_defined;
template<> UInt ElementClass<_not_defined>::nb_shape_functions = 1;
template<> Real ElementClass<_not_defined>::quad[] = {};
template<> UInt ElementClass<_not_defined>::nb_facets = 0;
template<> UInt * ElementClass<_not_defined>::facet_connectivity[] = {};
template<> Real ElementClass<_not_defined>::gauss_integration_weights[] = {2.};
/* -------------------------------------------------------------------------- */
/* Element Kind */
/* -------------------------------------------------------------------------- */
template<> ElementKind ElementClass<_segment_2 >::kind = _ek_regular;
template<> ElementKind ElementClass<_segment_3 >::kind = _ek_regular;
template<> ElementKind ElementClass<_triangle_3 >::kind = _ek_regular;
template<> ElementKind ElementClass<_triangle_6 >::kind = _ek_regular;
template<> ElementKind ElementClass<_tetrahedron_4 >::kind = _ek_regular;
template<> ElementKind ElementClass<_tetrahedron_10 >::kind = _ek_regular;
template<> ElementKind ElementClass<_quadrangle_4 >::kind = _ek_regular;
template<> ElementKind ElementClass<_quadrangle_8 >::kind = _ek_regular;
template<> ElementKind ElementClass<_hexahedron_8 >::kind = _ek_regular;
template<> ElementKind ElementClass<_point >::kind = _ek_regular;
template<> ElementKind ElementClass<_bernoulli_beam_2>::kind = _ek_regular;
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_COHESIVE_ELEMENT)
template<> ElementKind ElementClass<_cohesive_2d_4 >::kind = _ek_cohesive;
template<> ElementKind ElementClass<_cohesive_2d_6 >::kind = _ek_cohesive;
#endif
/* -------------------------------------------------------------------------- */
/* Regular Elements */
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_point>::nb_shape_functions = 1;
template<> UInt ElementClass<_point>::nb_nodes_per_element = 1;
template<> ElementType ElementClass<_point>::p1_element_type = _point;
template<> UInt ElementClass<_point>::nb_quadrature_points = 1;
template<> Real ElementClass<_point>::quad[] = {0};
template<> ElementType ElementClass<_point>::facet_type = _not_defined;
template<> UInt ElementClass<_point>::spatial_dimension = 0;
template<> UInt ElementClass<_point>::nb_facets = 0;
template<> UInt * ElementClass<_point>::facet_connectivity[] = {};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_segment_2>::nb_shape_functions = 1;
template<> UInt ElementClass<_segment_2>::nb_nodes_per_element = 2;
template<> ElementType ElementClass<_segment_2>::p1_element_type = _segment_2;
template<> UInt ElementClass<_segment_2>::nb_quadrature_points = 1;
template<> Real ElementClass<_segment_2>::quad[] = {0};
template<> UInt ElementClass<_segment_2>::spatial_dimension = 1;
template<> UInt ElementClass<_segment_2>::nb_facets = 2;
template<> ElementType ElementClass<_segment_2>::facet_type = _point;
template<> UInt ElementClass<_segment_2>::vec_facet_connectivity[]= {0,
1};
template<> UInt * ElementClass<_segment_2>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[1]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_segment_3>::nb_shape_functions = 1;
template<> UInt ElementClass<_segment_3>::nb_nodes_per_element = 3;
template<> ElementType ElementClass<_segment_3>::p1_element_type = _segment_2;
template<> UInt ElementClass<_segment_3>::nb_quadrature_points = 2;
template<> Real ElementClass<_segment_3>::quad[] = {-1./sqrt(3.), 1./sqrt(3.)};
template<> UInt ElementClass<_segment_3>::spatial_dimension = 1;
template<> UInt ElementClass<_segment_3>::nb_facets = 2;
template<> ElementType ElementClass<_segment_3>::facet_type = _point;
template<> UInt ElementClass<_segment_3>::vec_facet_connectivity[]= {0,
1};
template<> UInt * ElementClass<_segment_3>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[1]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_triangle_3>::nb_shape_functions = 1;
template<> UInt ElementClass<_triangle_3>::nb_nodes_per_element = 3;
template<> ElementType ElementClass<_triangle_3>::p1_element_type = _triangle_3;
template<> UInt ElementClass<_triangle_3>::nb_quadrature_points = 1;
template<> Real ElementClass<_triangle_3>::quad[] = {1./3., 1./3.};
template<> UInt ElementClass<_triangle_3>::spatial_dimension = 2;
template<> UInt ElementClass<_triangle_3>::nb_facets = 3;
template<> ElementType ElementClass<_triangle_3>::facet_type = _segment_2;
template<> UInt ElementClass<_triangle_3>::vec_facet_connectivity[]= {0, 1,
1, 2,
2, 0};
template<> UInt * ElementClass<_triangle_3>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[2],
&vec_facet_connectivity[4]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_triangle_6>::nb_shape_functions = 1;
template<> UInt ElementClass<_triangle_6>::nb_nodes_per_element = 6;
template<> ElementType ElementClass<_triangle_6>::p1_element_type = _triangle_3;
template<> UInt ElementClass<_triangle_6>::nb_quadrature_points = 3;
template<> Real ElementClass<_triangle_6>::quad[] = {1./6., 1./6.,
2./3., 1./6.,
1./6., 2./3.};
template<> UInt ElementClass<_triangle_6>::spatial_dimension = 2;
template<> UInt ElementClass<_triangle_6>::nb_facets = 3;
template<> ElementType ElementClass<_triangle_6>::facet_type = _segment_3;
template<> UInt ElementClass<_triangle_6>::vec_facet_connectivity[]= {0, 1, 3,
1, 2, 4,
2, 0, 5};
template<> UInt * ElementClass<_triangle_6>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[3],
&vec_facet_connectivity[6]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_tetrahedron_4>::nb_shape_functions = 1;
template<> UInt ElementClass<_tetrahedron_4>::nb_nodes_per_element = 4;
template<> ElementType ElementClass<_tetrahedron_4>::p1_element_type = _tetrahedron_4;
template<> UInt ElementClass<_tetrahedron_4>::nb_quadrature_points = 1;
template<> Real ElementClass<_tetrahedron_4>::quad[] = {1./4., 1./4., 1./4.};
template<> UInt ElementClass<_tetrahedron_4>::spatial_dimension = 3;
template<> UInt ElementClass<_tetrahedron_4>::nb_facets = 4;
template<> ElementType ElementClass<_tetrahedron_4>::facet_type = _triangle_3;
template<> UInt ElementClass<_tetrahedron_4>::vec_facet_connectivity[]= {0, 2, 1,
1, 2, 3,
2, 0, 3,
0, 1, 3};
template<> UInt * ElementClass<_tetrahedron_4>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[3],
&vec_facet_connectivity[6],
&vec_facet_connectivity[9]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_tetrahedron_10>::nb_shape_functions = 1;
template<> UInt ElementClass<_tetrahedron_10>::nb_nodes_per_element = 10;
template<> ElementType ElementClass<_tetrahedron_10>::p1_element_type = _tetrahedron_4;
template<> UInt ElementClass<_tetrahedron_10>::nb_quadrature_points = 4;
template<> Real ElementClass<_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<> UInt ElementClass<_tetrahedron_10>::spatial_dimension = 3;
template<> UInt ElementClass<_tetrahedron_10>::nb_facets = 4;
template<> ElementType ElementClass<_tetrahedron_10>::facet_type = _triangle_6;
template<> UInt ElementClass<_tetrahedron_10>::vec_facet_connectivity[]= {0, 2, 1, 6, 5, 4,
1, 2, 3, 5, 9, 8,
2, 0, 3, 6, 7, 9,
0, 1, 3, 4, 8, 7};
template<> UInt * ElementClass<_tetrahedron_10>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[6],
&vec_facet_connectivity[12],
&vec_facet_connectivity[18]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_quadrangle_4>::nb_shape_functions = 1;
template<> UInt ElementClass<_quadrangle_4>::nb_nodes_per_element = 4;
template<> ElementType ElementClass<_quadrangle_4>::p1_element_type = _quadrangle_4;
template<> UInt ElementClass<_quadrangle_4>::nb_quadrature_points = 4;
//template<> Real ElementClass<_quadrangle_4>::quad[] = {0, 0};
template<> Real ElementClass<_quadrangle_4>::quad[] = {-1./std::sqrt(3), -1./sqrt(3),
1./sqrt(3), -1./sqrt(3),
1./sqrt(3), 1./sqrt(3),
-1./sqrt(3), 1./sqrt(3)};
template<> UInt ElementClass<_quadrangle_4>::spatial_dimension = 2;
template<> UInt ElementClass<_quadrangle_4>::nb_facets = 4;
template<> ElementType ElementClass<_quadrangle_4>::facet_type = _segment_2;
template<> UInt ElementClass<_quadrangle_4>::vec_facet_connectivity[]= {0, 1,
1, 2,
2, 3,
3, 0};
template<> UInt * ElementClass<_quadrangle_4>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[2],
&vec_facet_connectivity[4],
&vec_facet_connectivity[6]};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_quadrangle_8>::nb_shape_functions = 1;
template<> UInt ElementClass<_quadrangle_8>::nb_nodes_per_element = 8;
template<> ElementType ElementClass<_quadrangle_8>::p1_element_type = _quadrangle_8;
template<> UInt ElementClass<_quadrangle_8>::nb_quadrature_points = 9;
template<> Real ElementClass<_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<> UInt ElementClass<_quadrangle_8>::spatial_dimension = 2;
template<> UInt ElementClass<_quadrangle_8>::nb_facets = 4;
template<> ElementType ElementClass<_quadrangle_8>::facet_type = _segment_3;
template<> UInt ElementClass<_quadrangle_8>::vec_facet_connectivity[]= {0, 1, 4,
1, 2, 5,
2, 3, 6,
3, 0, 7};
template<> UInt * ElementClass<_quadrangle_8>::facet_connectivity[] = {vec_facet_connectivity + 0,
vec_facet_connectivity + 3,
vec_facet_connectivity + 6,
vec_facet_connectivity + 9};
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_hexahedron_8>::nb_shape_functions = 1;
template<> UInt ElementClass<_hexahedron_8>::nb_nodes_per_element = 8;
template<> ElementType ElementClass<_hexahedron_8>::p1_element_type = _hexahedron_8;
template<> UInt ElementClass<_hexahedron_8>::nb_quadrature_points = 8;
template<> Real ElementClass<_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<> UInt ElementClass<_hexahedron_8>::spatial_dimension = 3;
template<> UInt ElementClass<_hexahedron_8>::nb_facets = 6;
template<> ElementType ElementClass<_hexahedron_8>::facet_type = _quadrangle_4;
template<> UInt ElementClass<_hexahedron_8>::vec_facet_connectivity[]= {0, 1, 2, 3,
0, 1, 5, 4,
1, 2, 6, 5,
2, 3, 7, 6,
3, 0, 4, 7,
4, 5, 6, 7};
template<> UInt * ElementClass<_hexahedron_8>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[4],
&vec_facet_connectivity[8],
&vec_facet_connectivity[12],
&vec_facet_connectivity[16],
&vec_facet_connectivity[20]};
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
/* Structural elements */
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_bernoulli_beam_2>::nb_nodes_per_element = 2;
template<> ElementType ElementClass<_bernoulli_beam_2>::p1_element_type = _bernoulli_beam_2;
template<> UInt ElementClass<_bernoulli_beam_2>::nb_quadrature_points = 2;
template<> Real ElementClass<_bernoulli_beam_2>::quad[] = {-1/sqrt(3), 0,
1/sqrt(3), 0};
template<> UInt ElementClass<_bernoulli_beam_2>::spatial_dimension = 2;
template<> UInt ElementClass<_bernoulli_beam_2>::nb_facets = 2;
template<> ElementType ElementClass<_bernoulli_beam_2>::facet_type = _point;
template<> UInt ElementClass<_bernoulli_beam_2>::vec_facet_connectivity[]= {0,
1};
template<> UInt * ElementClass<_bernoulli_beam_2>::facet_connectivity[] = {&vec_facet_connectivity[0],
&vec_facet_connectivity[1]};
template<> UInt ElementClass<_bernoulli_beam_2>::nb_shape_functions = 5;
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
/* Gauss integration */
/* -------------------------------------------------------------------------- */
template<> Real ElementClass<_segment_2 >::gauss_integration_weights[] = {2.};
template<> Real ElementClass<_segment_3 >::gauss_integration_weights[] = {1., 1.};
template<> Real ElementClass<_triangle_3 >::gauss_integration_weights[] = {1./2.};
template<> Real ElementClass<_triangle_6 >::gauss_integration_weights[] = {1./6., 1./6., 1./6.};
template<> Real ElementClass<_tetrahedron_4 >::gauss_integration_weights[] = {1./6.};
template<> Real ElementClass<_tetrahedron_10 >::gauss_integration_weights[] = {1./24., 1./24., 1./24., 1./24.};
template<> Real ElementClass<_quadrangle_4 >::gauss_integration_weights[] = {1., 1., 1., 1.};
template<> Real ElementClass<_quadrangle_8 >::gauss_integration_weights[] = {64./81.,
25./81., 25./81., 25./81., 25./81.,
40./81., 40./81., 40./81., 40./81.};
template<> Real ElementClass<_hexahedron_8 >::gauss_integration_weights[] = {1., 1., 1., 1.,
1., 1., 1., 1.};
template<> Real ElementClass<_point >::gauss_integration_weights[] = {1.};
template<> Real ElementClass<_bernoulli_beam_2>::gauss_integration_weights[] = {1., 1.};
__END_AKANTU__

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