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integration_element.cc
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rAKA akantu
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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