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element_class_pentahedron_6_inline_impl.hh
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rAKA akantu
element_class_pentahedron_6_inline_impl.hh
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/**
* @file element_class_pentahedron_6_inline_impl.hh
*
* @author Marion Estelle Chambart <mchambart@stucky.ch>
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Thomas Menouillard <tmenouillard@stucky.ch>
*
* @date creation: Mon Mar 14 2011
* @date last modification: Wed Oct 11 2017
*
* @brief Specialization of the element_class class for the type _pentahedron_6
*
*
* Copyright (©) 2010-2018 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/>.
*
*
* @verbatim
/z
|
|
| 1
| /|\
|/ | \
/ | \
/ | \
/ | \
4 2-----0
| \ / /
| \/ /
| \ /----------/y
| / \ /
|/ \ /
5---.--3
/
/
/
\x
x y z
* N0 -1 1 0
* N1 -1 0 1
* N2 -1 0 0
* N3 1 1 0
* N4 1 0 1
* N5 1 0 0
\endverbatim
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_pentahedron_6
,
_gt_pentahedron_6
,
_itp_lagrange_pentahedron_6
,
_ek_regular
,
3
,
_git_pentahedron
,
1
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_lagrange_pentahedron_6
>::
computeShapes
(
const
vector_type
&
c
,
vector_type
&
N
)
{
/// Natural coordinates
N
(
0
)
=
0.5
*
c
(
1
)
*
(
1
-
c
(
0
));
// N1(q)
N
(
1
)
=
0.5
*
c
(
2
)
*
(
1
-
c
(
0
));
// N2(q)
N
(
2
)
=
0.5
*
(
1
-
c
(
1
)
-
c
(
2
))
*
(
1
-
c
(
0
));
// N3(q)
N
(
3
)
=
0.5
*
c
(
1
)
*
(
1
+
c
(
0
));
// N4(q)
N
(
4
)
=
0.5
*
c
(
2
)
*
(
1
+
c
(
0
));
// N5(q)
N
(
5
)
=
0.5
*
(
1
-
c
(
1
)
-
c
(
2
))
*
(
1
+
c
(
0
));
// N6(q)
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_pentahedron_6
>::
computeDNDS
(
const
vector_type
&
c
,
matrix_type
&
dnds
)
{
dnds
(
0
,
0
)
=
-
0.5
*
c
(
1
);
dnds
(
0
,
1
)
=
-
0.5
*
c
(
2
);
dnds
(
0
,
2
)
=
-
0.5
*
(
1
-
c
(
1
)
-
c
(
2
));
dnds
(
0
,
3
)
=
0.5
*
c
(
1
);
dnds
(
0
,
4
)
=
0.5
*
c
(
2
);
dnds
(
0
,
5
)
=
0.5
*
(
1
-
c
(
1
)
-
c
(
2
));
dnds
(
1
,
0
)
=
0.5
*
(
1
-
c
(
0
));
dnds
(
1
,
1
)
=
0.0
;
dnds
(
1
,
2
)
=
-
0.5
*
(
1
-
c
(
0
));
dnds
(
1
,
3
)
=
0.5
*
(
1
+
c
(
0
));
dnds
(
1
,
4
)
=
0.0
;
dnds
(
1
,
5
)
=
-
0.5
*
(
1
+
c
(
0
));
dnds
(
2
,
0
)
=
0.0
;
dnds
(
2
,
1
)
=
0.5
*
(
1
-
c
(
0
));
dnds
(
2
,
2
)
=
-
0.5
*
(
1
-
c
(
0
));
dnds
(
2
,
3
)
=
0.0
;
dnds
(
2
,
4
)
=
0.5
*
(
1
+
c
(
0
));
dnds
(
2
,
5
)
=
-
0.5
*
(
1
+
c
(
0
));
}
/* -------------------------------------------------------------------------- */
// I have to duplicate this code since the Real * coords do not know their size
// in the Math module.
// If later we use eigen or Vector to implement this function
// there should be only one function in akantu::Math
// -> this is temporary for the release deadline which was so extended
inline
Real
triangle_inradius
(
const
Real
*
coord1
,
const
Real
*
coord2
,
const
Real
*
coord3
)
{
/**
* @f{eqnarray*}{
* r &=& A / s \\
* A &=& 1/4 * \sqrt{(a + b + c) * (a - b + c) * (a + b - c) (-a + b + c)} \\
* s &=& \frac{a + b + c}{2}
* @f}
*/
auto
a
=
Math
::
distance_3d
(
coord1
,
coord2
);
auto
b
=
Math
::
distance_3d
(
coord2
,
coord3
);
auto
c
=
Math
::
distance_3d
(
coord1
,
coord3
);
auto
s
=
(
a
+
b
+
c
)
*
0.5
;
return
std
::
sqrt
((
s
-
a
)
*
(
s
-
b
)
*
(
s
-
c
)
/
s
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_pentahedron_6
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
Vector
<
Real
>
u0
=
coord
(
0
);
Vector
<
Real
>
u1
=
coord
(
1
);
Vector
<
Real
>
u2
=
coord
(
2
);
Vector
<
Real
>
u3
=
coord
(
3
);
Vector
<
Real
>
u4
=
coord
(
4
);
Vector
<
Real
>
u5
=
coord
(
5
);
auto
inradius_triangle_1
=
triangle_inradius
(
u0
.
storage
(),
u1
.
storage
(),
u2
.
storage
());
auto
inradius_triangle_2
=
triangle_inradius
(
u3
.
storage
(),
u4
.
storage
(),
u5
.
storage
());
auto
d1
=
u3
.
distance
(
u0
)
*
0.5
;
auto
d2
=
u5
.
distance
(
u2
)
*
0.5
;
auto
d3
=
u4
.
distance
(
u1
)
*
0.5
;
auto
p
=
2.
*
std
::
min
({
inradius_triangle_1
,
inradius_triangle_2
,
d1
,
d2
,
d3
});
return
p
;
}
}
// namespace akantu
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