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rAKA akantu
gauss_integration_tmpl.hh
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/**
* @file gauss_integration_tmpl.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date Tue May 10 10:48:21 2016
*
* @brief implementation of the gauss integration helpers
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_GAUSS_INTEGRATION_TMPL_HH__
#define __AKANTU_GAUSS_INTEGRATION_TMPL_HH__
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
/* GaussIntegrationElement */
/* -------------------------------------------------------------------------- */
namespace
_aka_gauss_helpers
{
template
<
GaussIntegrationType
type
,
UInt
n
>
struct
GaussIntegrationNbPoints
{
};
template
<
UInt
n
>
struct
GaussIntegrationNbPoints
<
_git_point
,
n
>
{
static
const
UInt
nb_points
=
1
;
};
template
<
UInt
n
>
struct
GaussIntegrationNbPoints
<
_git_segment
,
n
>
{
static
const
UInt
nb_points
=
(
n
+
1
)
/
2
+
((
n
+
1
)
%
2
?
1
:
0
);
};
#define DECLARE_GAUSS_NB_POINTS(type, order, points) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static const UInt nb_points = points; \
}
#define DECLARE_GAUSS_NB_POINTS_PENT(type, order, xo, yo) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static const UInt x_order = xo; \
static const UInt yz_order = yo; \
static const UInt 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(_git_pentahedron, 1, 6); // order 3 in x, order 2 in y and z
//DECLARE_GAUSS_NB_POINTS(_git_pentahedron, 2, 6); // order 3 in x, order 2 in y and z
//DECLARE_GAUSS_NB_POINTS(_git_pentahedron, 3, 8); // order 3 in x, order 3 in y and z
//DECLARE_GAUSS_NB_POINTS(_git_pentahedron, 4, 21);// order 5 in x, order 5 in y and z
//DECLARE_GAUSS_NB_POINTS(_git_pentahedron, 5, 21);// order 5 in x, order 5 in y and z
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
,
UInt
n
,
UInt
on
=
n
,
bool
end_recurse
=
false
>
struct
GaussIntegrationNbPointsHelper
{
static
const
UInt
pnp
=
GaussIntegrationNbPoints
<
type
,
n
>::
nb_points
;
static
const
UInt
order
=
n
;
static
const
UInt
nb_points
=
pnp
;
};
template
<
GaussIntegrationType
type
,
UInt
n
,
UInt
on
>
struct
GaussIntegrationNbPointsHelper
<
type
,
n
,
on
,
true
>
{
static
const
UInt
nb_points
=
0
;
};
/* ------------------------------------------------------------------------ */
/* Generic helper */
/* ------------------------------------------------------------------------ */
template
<
GaussIntegrationType
type
,
UInt
dimension
,
UInt
n
>
struct
GaussIntegrationTypeDataHelper
{
typedef
GaussIntegrationNbPoints
<
type
,
n
>
git_np
;
typedef
GaussIntegrationTypeData
<
type
,
git_np
::
nb_points
>
git_data
;
static
UInt
getNbQuadraturePoints
()
{
return
git_np
::
nb_points
;
}
static
const
Matrix
<
Real
>
getQuadraturePoints
()
{
return
Matrix
<
Real
>
(
git_data
::
quad_positions
,
dimension
,
git_np
::
nb_points
);
}
static
const
Vector
<
Real
>
getWeights
()
{
return
Vector
<
Real
>
(
git_data
::
quad_weights
,
git_np
::
nb_points
);
}
};
/* ------------------------------------------------------------------------ */
/* helper for _segment _quadrangle _hexahedron */
/* ------------------------------------------------------------------------ */
template
<
UInt
dimension
,
UInt
dp
>
struct
GaussIntegrationTypeDataHelper
<
_git_segment
,
dimension
,
dp
>
{
typedef
GaussIntegrationNbPoints
<
_git_segment
,
dp
>
git_np
;
typedef
GaussIntegrationTypeData
<
_git_segment
,
git_np
::
nb_points
>
git_data
;
static
UInt
getNbQuadraturePoints
()
{
return
Math
::
pow
<
dimension
>
(
git_np
::
nb_points
);
}
static
const
Matrix
<
Real
>
getQuadraturePoints
()
{
UInt
tot_nquad
=
getNbQuadraturePoints
();
UInt
nquad
=
git_np
::
nb_points
;
Matrix
<
Real
>
quads
(
dimension
,
tot_nquad
);
Vector
<
Real
>
pos
(
git_data
::
quad_positions
,
nquad
);
UInt
offset
=
1
;
for
(
UInt
d
=
0
;
d
<
dimension
;
++
d
)
{
for
(
UInt
n
=
0
,
q
=
0
;
n
<
tot_nquad
;
++
n
,
q
+=
offset
)
{
UInt
rq
=
q
%
tot_nquad
+
q
/
tot_nquad
;
quads
(
d
,
rq
)
=
pos
(
n
%
nquad
);
}
offset
*=
nquad
;
}
return
quads
;
}
static
const
Vector
<
Real
>
getWeights
()
{
UInt
tot_nquad
=
getNbQuadraturePoints
();
UInt
nquad
=
git_np
::
nb_points
;
Vector
<
Real
>
quads_weights
(
tot_nquad
,
1.
);
Vector
<
Real
>
weights
(
git_data
::
quad_weights
,
nquad
);
UInt
offset
=
1
;
for
(
UInt
d
=
0
;
d
<
dimension
;
++
d
)
{
for
(
UInt
n
=
0
,
q
=
0
;
n
<
tot_nquad
;
++
n
,
q
+=
offset
)
{
UInt
rq
=
q
%
tot_nquad
+
q
/
tot_nquad
;
quads_weights
(
rq
)
*=
weights
(
n
%
nquad
);
}
offset
*=
nquad
;
}
return
quads_weights
;
}
};
/* ------------------------------------------------------------------------ */
/* helper for _pentahedron */
/* ------------------------------------------------------------------------ */
template
<
UInt
dimension
,
UInt
dp
>
struct
GaussIntegrationTypeDataHelper
<
_git_pentahedron
,
dimension
,
dp
>
{
typedef
GaussIntegrationNbPoints
<
_git_pentahedron
,
dp
>
git_info
;
typedef
GaussIntegrationNbPoints
<
_git_segment
,
git_info
::
x_order
>
git_np_seg
;
typedef
GaussIntegrationNbPoints
<
_git_triangle
,
git_info
::
yz_order
>
git_np_tri
;
typedef
GaussIntegrationTypeData
<
_git_segment
,
git_np_seg
::
nb_points
>
git_data_seg
;
typedef
GaussIntegrationTypeData
<
_git_triangle
,
git_np_tri
::
nb_points
>
git_data_tri
;
static
UInt
getNbQuadraturePoints
()
{
return
git_np_seg
::
nb_points
*
git_np_tri
::
nb_points
;
}
static
const
Matrix
<
Real
>
getQuadraturePoints
()
{
UInt
tot_nquad
=
getNbQuadraturePoints
();
UInt
nquad_seg
=
git_np_seg
::
nb_points
;
UInt
nquad_tri
=
git_np_tri
::
nb_points
;
Matrix
<
Real
>
quads
(
dimension
,
tot_nquad
);
Matrix
<
Real
>
pos_seg_w
(
git_data_seg
::
quad_positions
,
1
,
nquad_seg
);
Matrix
<
Real
>
pos_tri_w
(
git_data_tri
::
quad_positions
,
2
,
nquad_tri
);
for
(
UInt
ns
=
0
,
q
=
0
;
ns
<
nquad_seg
;
++
ns
)
{
Vector
<
Real
>
pos_seg
=
pos_seg_w
(
ns
);
for
(
UInt
nt
=
0
;
nt
<
nquad_tri
;
++
nt
,
++
q
)
{
Vector
<
Real
>
pos_tri
=
pos_tri_w
(
nt
);
Vector
<
Real
>
quad
=
quads
(
q
);
quad
(
_x
)
=
pos_seg
(
_x
);
quad
(
_y
)
=
pos_tri
(
_x
);
quad
(
_z
)
=
pos_tri
(
_y
);
}
}
return
quads
;
}
static
const
Vector
<
Real
>
getWeights
()
{
UInt
tot_nquad
=
getNbQuadraturePoints
();
UInt
nquad_seg
=
git_np_seg
::
nb_points
;
UInt
nquad_tri
=
git_np_tri
::
nb_points
;
Vector
<
Real
>
quads_weights
(
tot_nquad
);
Vector
<
Real
>
weight_seg
(
git_data_seg
::
quad_weights
,
nquad_seg
);
Vector
<
Real
>
weight_tri
(
git_data_tri
::
quad_weights
,
nquad_tri
);
for
(
UInt
ns
=
0
,
q
=
0
;
ns
<
nquad_seg
;
++
ns
)
{
for
(
UInt
nt
=
0
;
nt
<
nquad_tri
;
++
nt
,
++
q
)
{
quads_weights
(
q
)
=
weight_seg
(
ns
)
*
weight_tri
(
nt
);
}
}
return
quads_weights
;
}
};
}
template
<
ElementType
element_type
,
UInt
n
>
const
Matrix
<
Real
>
GaussIntegrationElement
<
element_type
,
n
>::
getQuadraturePoints
()
{
const
InterpolationType
itp_type
=
ElementClassProperty
<
element_type
>::
interpolation_type
;
typedef
InterpolationPorperty
<
itp_type
>
interpolation_property
;
typedef
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
element_type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
data_helper
;
Matrix
<
Real
>
tmp
(
data_helper
::
getQuadraturePoints
());
return
tmp
;
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
element_type
,
UInt
n
>
const
Vector
<
Real
>
GaussIntegrationElement
<
element_type
,
n
>::
getWeights
()
{
const
InterpolationType
itp_type
=
ElementClassProperty
<
element_type
>::
interpolation_type
;
typedef
InterpolationPorperty
<
itp_type
>
interpolation_property
;
typedef
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
element_type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
data_helper
;
Vector
<
Real
>
tmp
(
data_helper
::
getWeights
());
return
tmp
;
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
element_type
,
UInt
n
>
UInt
GaussIntegrationElement
<
element_type
,
n
>::
getNbQuadraturePoints
()
{
const
InterpolationType
itp_type
=
ElementClassProperty
<
element_type
>::
interpolation_type
;
typedef
InterpolationPorperty
<
itp_type
>
interpolation_property
;
typedef
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
element_type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
data_helper
;
return
data_helper
::
getNbQuadraturePoints
();
}
__END_AKANTU__
#endif
/* __AKANTU_GAUSS_INTEGRATION_TMPL_HH__ */
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