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element_class_segment_2_inline_impl.cc
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rAKA akantu
element_class_segment_2_inline_impl.cc
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/**
* @file element_class_segment_2_inline_impl.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Sun Oct 19 2014
*
* @brief Specialization of the element_class class for the type _segment_2
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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/>.
*
* @section DESCRIPTION
*
* @verbatim
q
--x--------|--------x---> x
-1 0 1
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* w_1(x) &=& 1/2(1 - x) \\
* w_2(x) &=& 1/2(1 + x)
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* x_{q} &=& 0
* @f}
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_segment_2
,
_gt_segment_2
,
_itp_lagrange_segment_2
,
_ek_regular
,
1
,
_git_segment
,
1
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeShapes
(
const
vector_type
&
natural_coords
,
vector_type
&
N
)
{
/// natural coordinate
Real
c
=
natural_coords
(
0
);
/// shape functions
N
(
0
)
=
0.5
*
(
1
-
c
);
N
(
1
)
=
0.5
*
(
1
+
c
);
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeDNDS
(
__attribute__
((
unused
))
const
vector_type
&
natural_coords
,
matrix_type
&
dnds
)
{
/// dN1/de
dnds
(
0
,
0
)
=
-
.5
;
/// dN2/de
dnds
(
0
,
1
)
=
.5
;
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeSpecialJacobian
(
const
Matrix
<
Real
>
&
dxds
,
Real
&
jac
)
{
jac
=
dxds
.
norm
<
L_2
>
();
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_segment_2
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
return
std
::
abs
(
coord
(
0
,
0
)
-
coord
(
0
,
1
));
}
// /* --------------------------------------------------------------------------
// */
// template<> inline bool ElementClass<_segment_2>::contains(const Vector<Real>
// & natural_coords) {
// if (natural_coords(0) < -1.) return false;
// if (natural_coords(0) > 1.) return false;
// return true;
// }
/* -------------------------------------------------------------------------- */
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