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element_class_tetrahedron_4_inline_impl.hh
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rAKA akantu
element_class_tetrahedron_4_inline_impl.hh
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/**
* @file element_class_tetrahedron_4_inline_impl.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Wed Oct 11 2017
*
* @brief Specialization of the element_class class for the type _tetrahedron_4
*
*
* 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
\eta
^
|
x (0,0,1,0)
|`
| ` ° \zeta
| ` ° -
| ` x (0,0,0,1)
| q.` - '
| -` '
| - ` '
| - ` '
x------------------x-----> \xi
(1,0,0,0) (0,1,0,0)
@endverbatim
*
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta - \zeta \\
* N2 &=& \xi \\
* N3 &=& \eta \\
* N4 &=& \zeta
* @f}
*
* @f[
* \xi_{q0} = 1/4 \qquad \eta_{q0} = 1/4 \qquad \zeta_{q0} = 1/4
* @f]
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_tetrahedron_4
,
_gt_tetrahedron_4
,
_itp_lagrange_tetrahedron_4
,
_ek_regular
,
3
,
_git_tetrahedron
,
1
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_lagrange_tetrahedron_4
>::
computeShapes
(
const
vector_type
&
natural_coords
,
vector_type
&
N
)
{
Real
c0
=
1
-
natural_coords
(
0
)
-
natural_coords
(
1
)
-
natural_coords
(
2
);
/// @f$ c0 = 1 - \xi - \eta - \zeta @f$
Real
c1
=
natural_coords
(
1
);
/// @f$ c1 = \xi @f$
Real
c2
=
natural_coords
(
2
);
/// @f$ c2 = \eta @f$
Real
c3
=
natural_coords
(
0
);
/// @f$ c3 = \zeta @f$
N
(
0
)
=
c0
;
N
(
1
)
=
c1
;
N
(
2
)
=
c2
;
N
(
3
)
=
c3
;
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_tetrahedron_4
>::
computeDNDS
(
__attribute__
((
unused
))
const
vector_type
&
natural_coords
,
matrix_type
&
dnds
)
{
/**
* @f[
* dnds = \left(
* \begin{array}{cccccc}
* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
* \xi}
* & \frac{\partial N3}{\partial \xi} & \frac{\partial N4}{\partial
* \xi} \\
* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
* \eta}
* & \frac{\partial N3}{\partial \eta} & \frac{\partial N4}{\partial
* \eta} \\
* \frac{\partial N1}{\partial \zeta} & \frac{\partial N2}{\partial
* \zeta}
* & \frac{\partial N3}{\partial \zeta} & \frac{\partial N4}{\partial
* \zeta}
* \end{array}
* \right)
* @f]
*/
dnds
(
0
,
0
)
=
-
1.
;
dnds
(
1
,
0
)
=
-
1.
;
dnds
(
2
,
0
)
=
-
1.
;
dnds
(
0
,
1
)
=
0.
;
dnds
(
1
,
1
)
=
1.
;
dnds
(
2
,
1
)
=
0.
;
dnds
(
0
,
2
)
=
0.
;
dnds
(
1
,
2
)
=
0.
;
dnds
(
2
,
2
)
=
1.
;
dnds
(
0
,
3
)
=
1.
;
dnds
(
1
,
3
)
=
0.
;
dnds
(
2
,
3
)
=
0.
;
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_tetrahedron_4
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
return
2.
*
Math
::
tetrahedron_inradius
(
coord
(
0
).
storage
(),
coord
(
1
).
storage
(),
coord
(
2
).
storage
(),
coord
(
3
).
storage
());
}
}
// namespace akantu
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