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rAKA/src/fe_engine/element_classes/element_class_pentahedron_15_inline_impl.cc
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element_class_pentahedron_15_inline_impl.cc
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/**
* @file element_class_pentahedron_15_inline_impl.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Sacha Laffely <sacha.laffely@epfl.ch>
* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
*
* @date creation: Tue Mar 31 2015
* @date last modification: Wed Sep 16 2015
*
* @brief Specialization of the element_class class for the type _pentahedron_15
*
* @section LICENSE
*
* Copyright (©) 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
z
^
|
|
| 1
| /|\
|/ | \
10 7 6
/ | \
/ | \
4 2--8--0
| \ / /
| \11 /
13 12 9---------->y
| / \ /
|/ \ /
5--14--3
/
/
/
v
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
* N6 -1 0.5 0.5
* N7 -1 0 0.5
* N8 -1 0.5 0
* N9 0 1 0
* N10 0 0 1
* N11 0 0 0
* N12 1 0.5 0.5
* N13 1 0 0.5
* N14 1 0.5 0
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_pentahedron_15,
_gt_pentahedron_15,
_itp_lagrange_pentahedron_15,
_ek_regular,
3,
_git_pentahedron,
2);
AKANTU_DEFINE_SHAPE(_gt_pentahedron_15, _gst_prism);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void
InterpolationElement<_itp_lagrange_pentahedron_15>::computeShapes(const vector_type & c,
vector_type & N) {
// Shape Functions, Natural coordinates
N( 0) = 0.5 * c(1) * (1 - c(0)) * (2 * c(1) - 2 - c(0));
N( 1) = 0.5 * c(2) * (1 - c(0)) * (2 * c(2) - 2 - c(0));
N( 2) = 0.5 * (c(0) - 1) * (1 - c(1) - c(2)) * (c(0) + 2 * c(1) + 2 * c(2));
N( 3) = 0.5 * c(1) * (1 + c(0)) * (2 * c(1) - 2 + c(0));
N( 4) = 0.5 * c(2) * (1 + c(0)) * (2 * c(2) - 2 + c(0));
N( 5) = 0.5 * (-c(0) - 1) * (1 - c(1) - c(2)) * (-c(0) + 2 * c(1) + 2 * c(2));
N( 6) = 2.0 * c(1) * c(2) * (1 - c(0));
N( 7) = 2.0 * c(2) * (1 - c(1) - c(2)) * (1 - c(0));
N( 8) = 2.0 * c(1) * (1 - c(0)) * (1 - c(1) - c(2));
N( 9) = c(1) * (1 - c(0) * c(0));
N(10) = c(2) * (1 - c(0) * c(0));
N(11) = (1 - c(1) - c(2)) * (1 - c(0) * c(0));
N(12) = 2.0 * c(1) * c(2) * (1 + c(0));
N(13) = 2.0 * c(2) * (1 - c(1) - c(2)) * (1 + c(0));
N(14) = 2.0 * c(1) * (1 - c(1) - c(2)) * (1 + c(0));
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void
InterpolationElement<_itp_lagrange_pentahedron_15>::computeDNDS(const vector_type & c,
matrix_type & dnds) {
//ddx
dnds(0, 0) = 0.5 * c(1) * (2 * c(0) - 2 * c(1) + 1);
dnds(0, 1) = 0.5 * c(2) * (2 * c(0) - 2 * c(2) + 1);
dnds(0, 2) = -0.5 * (2 * c(0) + 2 * c(1) + 2 * c(2) - 1) * (c(1) + c(2) -1);
dnds(0, 3) = 0.5 * c(1) * (2 * c(0) + 2 * c(1) - 1);
dnds(0, 4) = 0.5 * c(2) * (2 * c(0) + 2 * c(2) - 1);
dnds(0, 5) = -0.5 * (c(1) + c(2) - 1) * (2 * c(0) - 2 * c(1) - 2 * c(2) + 1);
dnds(0, 6) = -2.0 * c(1) * c(2);
dnds(0, 7) = 2.0 * c(2) * (c(1) + c(2) - 1);
dnds(0, 8) = 2.0 * c(1) * (c(1) + c(2) - 1);
dnds(0, 9) = -2.0 * c(0) * c(1);
dnds(0,10) = -2.0 * c(0) * c(2);
dnds(0,11) = 2.0 * c(0) * (c(1) + c(2) - 1);
dnds(0,12) = 2.0 * c(1) * c(2);
dnds(0,13) = -2.0 * c(2) * (c(1) + c(2) - 1);
dnds(0,14) = -2.0 * c(1) * (c(1) + c(2) - 1);
//ddy
dnds(1, 0) = -0.5 * (c(0) - 1) * (4 * c(1) - c(0) - 2);
dnds(1, 1) = 0.0;
dnds(1, 2) = -0.5 * (c(0) - 1) * (4 * c(1) + c(0) + 2 * (2 * c(2) - 1));
dnds(1, 3) = 0.5 * (c(0) + 1) * (4 * c(1) + c(0) - 2);
dnds(1, 4) = 0.0;
dnds(1, 5) = 0.5 * (c(0) + 1) * (4 * c(1) - c(0) + 2 * (2 * c(2) - 1));
dnds(1, 6) = -2.0 * (c(0) - 1) * c(2);
dnds(1, 7) = 2.0 * c(2) * (c(0) - 1);
dnds(1, 8) = 2.0 * (2 * c(1) + c(2) - 1) * (c(0) - 1);
dnds(1, 9) = -(c(0) * c(0) - 1);
dnds(1,10) = 0.0;
dnds(1,11) = (c(0) * c(0) - 1);
dnds(1,12) = 2.0 * c(2) * (c(0) + 1);
dnds(1,13) = -2.0 * c(2) * (c(0) + 1);
dnds(1,14) = -2.0 * (2 * c(1) + c(2) - 1) * (c(0) + 1);
//ddz
dnds(2, 0) = 0.0;
dnds(2, 1) = -0.5 * (c(0) - 1) * (4 * c(2) - c(0) - 2);
dnds(2, 2) = -0.5 * (c(0) - 1) * (4 * c(2) + c(0) + 2 * (2 * c(1) - 1));
dnds(2, 3) = 0.0;
dnds(2, 4) = 0.5 * (c(0) + 1) * (4 * c(2) + c(0) - 2);
dnds(2, 5) = 0.5 * (c(0) + 1) * (4 * c(2) - c(0) + 2 * (2 * c(1) - 1));
dnds(2, 6) = -2.0 * (c(0) - 1) * c(1);
dnds(2, 7) = 2.0 * (c(0) - 1) * (2 * c(2) + c(1) - 1);
dnds(2, 8) = 2.0 * c(1) * (c(0) - 1);
dnds(2, 9) = 0.0;
dnds(2,10) = -(c(0) * c(0) - 1);
dnds(2,11) = (c(0) * c(0) - 1);
dnds(2,12) = 2.0 * (c(0) + 1) * c(1);
dnds(2,13) = -2.0 * (c(0) + 1) * (2 * c(2) + c(1) - 1);
dnds(2,14) = -2.0 * (c(0) + 1) * c(1);
}
/* -------------------------------------------------------------------------- */
template<>
inline Real
GeometricalElement<_gt_pentahedron_15>::getInradius(const Matrix<Real> & coord) {
return GeometricalElement<_gt_pentahedron_6>::getInradius(coord);
}
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