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rAKA/src/fe_engine/element_classes/element_class_tetrahedron_4_inline_impl.cc
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element_class_tetrahedron_4_inline_impl.cc
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/**
* @file element_class_tetrahedron_4_inline_impl.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @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 _tetrahedron_4
*
* @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
\eta
^
|
x (0,0,1,0)
|`
| ` ° \xi
| ` ° -
| ` x (0,0,0,1)
| q.` - '
| -` '
| - ` '
| - ` '
x------------------x-----> \zeta
(1,0,0,0) (0,1,0,0)
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta - \zeta \\
* N2 &=& \xi \\
* N3 &=& \eta \\
* N4 &=& \zeta
* @f}
*
* @subsection quad_points Position of quadrature points
* @f[
* \xi_{q0} = 1/4 \qquad \eta_{q0} = 1/4 \qquad \zeta_{q0} = 1/4
* @f]
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_tetrahedron_4, _gt_tetrahedron_4, _itp_lagrange_tetrahedron_4, _ek_regular, 3,
_git_tetrahedron, 1);
AKANTU_DEFINE_SHAPE(_gt_tetrahedron_4, _gst_triangle);
/* -------------------------------------------------------------------------- */
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$ c2 = 1 - \xi - \eta - \zeta @f$
Real c1 = natural_coords(1); /// @f$ c0 = \xi @f$
Real c2 = natural_coords(2); /// @f$ c1 = \eta @f$
Real c3 = natural_coords(0); /// @f$ c2 = \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(0, 1) = 1.; dnds(0, 2) = 0.; dnds(0, 3) = 0.;
dnds(1, 0) = -1.; dnds(1, 1) = 0.; dnds(1, 2) = 1.; dnds(1, 3) = 0.;
dnds(2, 0) = -1.; dnds(2, 1) = 0.; dnds(2, 2) = 0.; dnds(2, 3) = 1.;
}
/* -------------------------------------------------------------------------- */
template<>
inline Real
GeometricalElement<_gt_tetrahedron_4>::getInradius(const Matrix<Real> & coord) {
return Math::tetrahedron_inradius(coord(0).storage(),
coord(1).storage(),
coord(2).storage(),
coord(3).storage());
}
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