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rAKA akantu
gauss_integration_tmpl.hh
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/**
* Copyright (©) 2016-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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_math.hh"
#ifndef AKANTU_GAUSS_INTEGRATION_TMPL_HH_
#define AKANTU_GAUSS_INTEGRATION_TMPL_HH_
#include "element_class.hh"
namespace
akantu
{
/* -------------------------------------------------------------------------- */
/* GaussIntegrationElement */
/* -------------------------------------------------------------------------- */
namespace
_aka_gauss_helpers
{
template
<
GaussIntegrationType
type
,
Int
n
>
struct
GaussIntegrationNbPoints
{};
template
<
Int
n
>
struct
GaussIntegrationNbPoints
<
_git_not_defined
,
n
>
{
static
constexpr
Int
nb_points
=
0
;
};
template
<
Int
n
>
struct
GaussIntegrationNbPoints
<
_git_point
,
n
>
{
static
constexpr
Int
nb_points
=
1
;
};
template
<
Int
n
>
struct
GaussIntegrationNbPoints
<
_git_segment
,
n
>
{
static
constexpr
Int
nb_points
=
(
n
+
1
)
/
2
+
(
bool
((
n
+
1
)
%
2
)
?
1
:
0
);
};
#define DECLARE_GAUSS_NB_POINTS(type, order, points) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static constexpr Int nb_points = points; \
}
#define DECLARE_GAUSS_NB_POINTS_PENT(type, order, xo, yo) \
template <> struct GaussIntegrationNbPoints<type, order> { \
static constexpr Int x_order = xo; \
static constexpr Int yz_order = yo; \
static constexpr Int 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_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
,
Int
n
,
Int
on
=
n
,
bool
end_recurse
=
false
>
struct
GaussIntegrationNbPointsHelper
{
static
constexpr
Int
pnp
=
GaussIntegrationNbPoints
<
type
,
n
>::
nb_points
;
static
constexpr
Int
order
=
n
;
static
constexpr
Int
nb_points
=
pnp
;
};
template
<
GaussIntegrationType
type
,
Int
n
,
Int
on
>
struct
GaussIntegrationNbPointsHelper
<
type
,
n
,
on
,
true
>
{
static
constexpr
Int
nb_points
=
0
;
};
/* ------------------------------------------------------------------------ */
/* Generic helper */
/* ------------------------------------------------------------------------ */
template
<
GaussIntegrationType
type
,
Int
dimension
,
Int
n
>
struct
GaussIntegrationTypeDataHelper
{
using
git_np
=
GaussIntegrationNbPoints
<
type
,
n
>
;
using
git_data
=
GaussIntegrationTypeData
<
type
,
git_np
::
nb_points
>
;
static
constexpr
Int
getNbQuadraturePoints
()
{
return
git_np
::
nb_points
;
}
static
constexpr
auto
getQuadraturePoints
()
->
Matrix
<
Real
,
std
::
max
(
1
,
dimension
),
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
{
constexpr
auto
nb_points
=
git_np
::
nb_points
;
using
Matrix
=
Eigen
::
Matrix
<
Real
,
std
::
max
(
1
,
dimension
),
nb_points
>
;
Matrix
quads
=
Eigen
::
Map
<
const
Matrix
>
(
git_data
::
quad_positions
);
return
quads
;
}
static
constexpr
auto
getWeights
()
->
Vector
<
Real
,
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
{
constexpr
auto
nb_points
=
git_np
::
nb_points
;
using
Vector
=
Eigen
::
Matrix
<
Real
,
nb_points
,
1
>
;
Vector
weights
=
Eigen
::
Map
<
const
Vector
>
(
git_data
::
quad_weights
);
return
weights
;
}
};
#if !defined(DOXYGEN)
/* ------------------------------------------------------------------------ */
/* helper for _segment _quadrangle _hexahedron */
/* ------------------------------------------------------------------------ */
template
<
Int
dimension
,
Int
dp
>
struct
GaussIntegrationTypeDataHelper
<
_git_segment
,
dimension
,
dp
>
{
using
git_np
=
GaussIntegrationNbPoints
<
_git_segment
,
dp
>
;
using
git_data
=
GaussIntegrationTypeData
<
_git_segment
,
git_np
::
nb_points
>
;
static
constexpr
Int
getNbQuadraturePoints
()
{
return
Math
::
pow
(
git_np
::
nb_points
,
dimension
);
}
static
constexpr
auto
getQuadraturePoints
()
->
Matrix
<
Real
,
dimension
,
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
{
const
auto
tot_nquad
=
getNbQuadraturePoints
();
const
auto
nquad
=
git_np
::
nb_points
;
Eigen
::
Matrix
<
Real
,
dimension
,
tot_nquad
>
quads
;
Eigen
::
Map
<
const
Eigen
::
Matrix
<
Real
,
nquad
,
1
>>
pos
(
git_data
::
quad_positions
);
Int
offset
=
1
;
for
(
Int
d
=
0
;
d
<
dimension
;
++
d
)
{
for
(
Int
n
=
0
,
q
=
0
;
n
<
tot_nquad
;
++
n
,
q
+=
offset
)
{
Int
rq
=
q
%
tot_nquad
+
q
/
tot_nquad
;
quads
(
d
,
rq
)
=
pos
(
n
%
nquad
);
}
offset
*=
nquad
;
}
return
quads
;
}
static
constexpr
Vector
<
Real
,
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
getWeights
()
{
const
auto
tot_nquad
=
getNbQuadraturePoints
();
const
auto
nquad
=
git_np
::
nb_points
;
Eigen
::
Matrix
<
Real
,
tot_nquad
,
1
>
quads_weights
;
quads_weights
.
fill
(
1
);
Eigen
::
Map
<
const
Eigen
::
Matrix
<
Real
,
nquad
,
1
>>
weights
(
git_data
::
quad_weights
);
Int
offset
=
1
;
for
(
Int
d
=
0
;
d
<
dimension
;
++
d
)
{
for
(
Int
n
=
0
,
q
=
0
;
n
<
tot_nquad
;
++
n
,
q
+=
offset
)
{
Int
rq
=
q
%
tot_nquad
+
q
/
tot_nquad
;
quads_weights
(
rq
)
*=
weights
(
n
%
nquad
);
}
offset
*=
nquad
;
}
return
quads_weights
;
}
};
/* ------------------------------------------------------------------------ */
/* helper for _pentahedron */
/* ------------------------------------------------------------------------ */
template
<
Int
dimension
,
Int
dp
>
struct
GaussIntegrationTypeDataHelper
<
_git_pentahedron
,
dimension
,
dp
>
{
using
git_info
=
GaussIntegrationNbPoints
<
_git_pentahedron
,
dp
>
;
using
git_np_seg
=
GaussIntegrationNbPoints
<
_git_segment
,
git_info
::
x_order
>
;
using
git_np_tri
=
GaussIntegrationNbPoints
<
_git_triangle
,
git_info
::
yz_order
>
;
using
git_data_seg
=
GaussIntegrationTypeData
<
_git_segment
,
git_np_seg
::
nb_points
>
;
using
git_data_tri
=
GaussIntegrationTypeData
<
_git_triangle
,
git_np_tri
::
nb_points
>
;
static
constexpr
Int
getNbQuadraturePoints
()
{
return
git_np_seg
::
nb_points
*
git_np_tri
::
nb_points
;
}
static
constexpr
auto
getQuadraturePoints
()
->
Matrix
<
Real
,
dimension
,
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
{
constexpr
auto
tot_nquad
=
getNbQuadraturePoints
();
constexpr
auto
nquad_seg
=
git_np_seg
::
nb_points
;
constexpr
auto
nquad_tri
=
git_np_tri
::
nb_points
;
Matrix
<
Real
,
dimension
,
tot_nquad
>
quads
;
Eigen
::
Map
<
Vector
<
Real
,
nquad_seg
>>
pos_seg
(
git_data_seg
::
quad_positions
);
Eigen
::
Map
<
Matrix
<
Real
,
2
,
nquad_tri
>>
pos_tri
(
git_data_tri
::
quad_positions
);
for
(
Int
ns
=
0
,
q
=
0
;
ns
<
nquad_seg
;
++
ns
)
{
for
(
Int
nt
=
0
;
nt
<
nquad_tri
;
++
nt
,
++
q
)
{
auto
&&
quad
=
quads
(
q
);
quad
(
_x
)
=
pos_seg
(
ns
);
quad
(
_y
)
=
pos_tri
(
_x
,
nt
);
quad
(
_z
)
=
pos_tri
(
_y
,
nt
);
}
}
return
quads
;
}
static
constexpr
auto
getWeights
()
->
Vector
<
Real
,
GaussIntegrationTypeDataHelper
::
getNbQuadraturePoints
()
>
{
constexpr
auto
tot_nquad
=
getNbQuadraturePoints
();
constexpr
auto
nquad_seg
=
git_np_seg
::
nb_points
;
constexpr
auto
nquad_tri
=
git_np_tri
::
nb_points
;
Vector
<
Real
,
tot_nquad
>
quads_weights
;
Eigen
::
Map
<
const
Vector
<
Real
,
nquad_seg
>>
weight_seg
(
git_data_seg
::
quad_weights
);
Eigen
::
Map
<
const
Vector
<
Real
,
nquad_tri
>>
weight_tri
(
git_data_tri
::
quad_weights
);
for
(
Int
ns
=
0
,
q
=
0
;
ns
<
nquad_seg
;
++
ns
)
{
for
(
Int
nt
=
0
;
nt
<
nquad_tri
;
++
nt
,
++
q
)
{
quads_weights
(
q
)
=
weight_seg
(
ns
)
*
weight_tri
(
nt
);
}
}
return
quads_weights
;
}
};
#endif
}
// namespace _aka_gauss_helpers
/* -------------------------------------------------------------------------- */
template
<
ElementType
element_type
,
Int
n
>
constexpr
Int
GaussIntegrationElement
<
element_type
,
n
>::
getNbQuadraturePoints
()
{
using
data_helper
=
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
element_type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
;
return
data_helper
::
getNbQuadraturePoints
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
element_type
,
Int
n
>
constexpr
auto
GaussIntegrationElement
<
element_type
,
n
>::
getWeights
()
{
using
data_helper
=
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
element_type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
;
return
data_helper
::
getWeights
();
}
template
<
ElementType
type
,
Int
n
>
constexpr
auto
GaussIntegrationElement
<
type
,
n
>::
getQuadraturePoints
()
{
using
data_helper
=
_aka_gauss_helpers
::
GaussIntegrationTypeDataHelper
<
ElementClassProperty
<
type
>::
gauss_integration_type
,
interpolation_property
::
natural_space_dimension
,
n
>
;
return
data_helper
::
getQuadraturePoints
();
}
}
// namespace akantu
#endif
/* AKANTU_GAUSS_INTEGRATION_TMPL_HH_ */
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