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rAKA/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.hh
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/**
* @file element_class_hexahedron_20_inline_impl.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Sacha Laffely <sacha.laffely@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
*
* @date creation: Tue Mar 31 2015
* @date last modification: Fri Feb 07 2020
*
* @brief Specialization of the element_class class for the type _hexahedron_20
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 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
\y
\z /
| /
7-----|18--------6
/| | / /|
/ | | / / |
19 | | / 17 |
/ 15 | / / 14
/ | | / / |
4-------16---/---5 |
| | +----|------------\x
| 3-------10-|-----2
| / | /
12 / 13 /
| 11 | 9
| / | /
|/ |/
0--------8-------1
x y z
* N0 -1 -1 -1
* N1 1 -1 -1
* N2 1 1 -1
* N3 -1 1 -1
* N4 -1 -1 1
* N5 1 -1 1
* N6 1 1 1
* N7 -1 1 1
* N8 0 -1 -1
* N9 1 0 -1
* N10 0 1 -1
* N11 -1 0 -1
* N12 -1 -1 0
* N13 1 -1 0
* N14 1 1 0
* N15 -1 1 0
* N16 0 -1 1
* N17 1 0 1
* N18 0 1 1
* N19 -1 0 1
* \endverbatim
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_hexahedron_20, _gt_hexahedron_20,
_itp_serendip_hexahedron_20, _ek_regular,
3, _git_segment, 3);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void InterpolationElement<_itp_serendip_hexahedron_20>::computeShapes(
const vector_type & c, vector_type & N) {
// Shape function , Natural coordinates
N(0) =
0.125 * (1 - c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 - c(0) - c(1) - c(2));
N(1) =
0.125 * (1 + c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 + c(0) - c(1) - c(2));
N(2) =
0.125 * (1 + c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 + c(0) + c(1) - c(2));
N(3) =
0.125 * (1 - c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 - c(0) + c(1) - c(2));
N(4) =
0.125 * (1 - c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 - c(0) - c(1) + c(2));
N(5) =
0.125 * (1 + c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 + c(0) - c(1) + c(2));
N(6) =
0.125 * (1 + c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 + c(0) + c(1) + c(2));
N(7) =
0.125 * (1 - c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 - c(0) + c(1) + c(2));
N(8) = 0.25 * (1 - c(0) * c(0)) * (1 - c(1)) * (1 - c(2));
N(9) = 0.25 * (1 - c(1) * c(1)) * (1 + c(0)) * (1 - c(2));
N(10) = 0.25 * (1 - c(0) * c(0)) * (1 + c(1)) * (1 - c(2));
N(11) = 0.25 * (1 - c(1) * c(1)) * (1 - c(0)) * (1 - c(2));
N(12) = 0.25 * (1 - c(2) * c(2)) * (1 - c(0)) * (1 - c(1));
N(13) = 0.25 * (1 - c(2) * c(2)) * (1 + c(0)) * (1 - c(1));
N(14) = 0.25 * (1 - c(2) * c(2)) * (1 + c(0)) * (1 + c(1));
N(15) = 0.25 * (1 - c(2) * c(2)) * (1 - c(0)) * (1 + c(1));
N(16) = 0.25 * (1 - c(0) * c(0)) * (1 - c(1)) * (1 + c(2));
N(17) = 0.25 * (1 - c(1) * c(1)) * (1 + c(0)) * (1 + c(2));
N(18) = 0.25 * (1 - c(0) * c(0)) * (1 + c(1)) * (1 + c(2));
N(19) = 0.25 * (1 - c(1) * c(1)) * (1 - c(0)) * (1 + c(2));
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void InterpolationElement<_itp_serendip_hexahedron_20>::computeDNDS(
const vector_type & c, matrix_type & dnds) {
// derivatives
// ddx
dnds(0, 0) =
0.25 * (c(0) + 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
dnds(0, 1) =
0.25 * (c(0) - 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
dnds(0, 2) =
-0.25 * (c(0) + 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
dnds(0, 3) =
-0.25 * (c(0) - 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
dnds(0, 4) =
-0.25 * (c(0) + 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
dnds(0, 5) =
-0.25 * (c(0) - 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
dnds(0, 6) =
0.25 * (c(0) + 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
dnds(0, 7) =
0.25 * (c(0) - 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
dnds(0, 8) = -0.5 * c(0) * (c(1) - 1) * (c(2) - 1);
dnds(0, 9) = 0.25 * (c(1) * c(1) - 1) * (c(2) - 1);
dnds(0, 10) = 0.5 * c(0) * (c(1) + 1) * (c(2) - 1);
dnds(0, 11) = -0.25 * (c(1) * c(1) - 1) * (c(2) - 1);
dnds(0, 12) = -0.25 * (c(2) * c(2) - 1) * (c(1) - 1);
dnds(0, 13) = 0.25 * (c(1) - 1) * (c(2) * c(2) - 1);
dnds(0, 14) = -0.25 * (c(1) + 1) * (c(2) * c(2) - 1);
dnds(0, 15) = 0.25 * (c(1) + 1) * (c(2) * c(2) - 1);
dnds(0, 16) = 0.5 * c(0) * (c(1) - 1) * (c(2) + 1);
dnds(0, 17) = -0.25 * (c(2) + 1) * (c(1) * c(1) - 1);
dnds(0, 18) = -0.5 * c(0) * (c(1) + 1) * (c(2) + 1);
dnds(0, 19) = 0.25 * (c(2) + 1) * (c(1) * c(1) - 1);
// ddy
dnds(1, 0) =
0.25 * (c(1) + 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
dnds(1, 1) =
-0.25 * (c(1) - 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
dnds(1, 2) =
-0.25 * (c(1) + 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
dnds(1, 3) =
0.25 * (c(1) - 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
dnds(1, 4) =
-0.25 * (c(1) + 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
dnds(1, 5) =
0.25 * (c(1) - 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
dnds(1, 6) =
0.25 * (c(1) + 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
dnds(1, 7) =
-0.25 * (c(1) - 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
dnds(1, 8) = -0.25 * (c(0) * c(0) - 1) * (c(2) - 1);
dnds(1, 9) = 0.5 * c(1) * (c(0) + 1) * (c(2) - 1);
dnds(1, 10) = 0.25 * (c(0) * c(0) - 1) * (c(2) - 1);
dnds(1, 11) = -0.5 * c(1) * (c(0) - 1) * (c(2) - 1);
dnds(1, 12) = -0.25 * (c(2) * c(2) - 1) * (c(0) - 1);
dnds(1, 13) = 0.25 * (c(0) + 1) * (c(2) * c(2) - 1);
dnds(1, 14) = -0.25 * (c(0) + 1) * (c(2) * c(2) - 1);
dnds(1, 15) = 0.25 * (c(0) - 1) * (c(2) * c(2) - 1);
dnds(1, 16) = 0.25 * (c(2) + 1) * (c(0) * c(0) - 1);
dnds(1, 17) = -0.5 * c(1) * (c(0) + 1) * (c(2) + 1);
dnds(1, 18) = -0.25 * (c(2) + 1) * (c(0) * c(0) - 1);
dnds(1, 19) = 0.5 * c(1) * (c(0) - 1) * (c(2) + 1);
// ddz
dnds(2, 0) =
0.25 * (c(2) + 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
dnds(2, 1) =
-0.25 * (c(2) - 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
dnds(2, 2) =
0.25 * (c(2) - 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
dnds(2, 3) =
-0.25 * (c(2) + 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
dnds(2, 4) =
0.25 * (c(2) - 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
dnds(2, 5) =
-0.25 * (c(2) + 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
dnds(2, 6) =
0.25 * (c(2) + 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
dnds(2, 7) =
-0.25 * (c(2) - 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
dnds(2, 8) = -0.25 * (c(0) * c(0) - 1) * (c(1) - 1);
dnds(2, 9) = 0.25 * (c(1) * c(1) - 1) * (c(0) + 1);
dnds(2, 10) = 0.25 * (c(0) * c(0) - 1) * (c(1) + 1);
dnds(2, 11) = -0.25 * (c(1) * c(1) - 1) * (c(0) - 1);
dnds(2, 12) = -0.5 * c(2) * (c(1) - 1) * (c(0) - 1);
dnds(2, 13) = 0.5 * c(2) * (c(0) + 1) * (c(1) - 1);
dnds(2, 14) = -0.5 * c(2) * (c(0) + 1) * (c(1) + 1);
dnds(2, 15) = 0.5 * c(2) * (c(0) - 1) * (c(1) + 1);
dnds(2, 16) = 0.25 * (c(1) - 1) * (c(0) * c(0) - 1);
dnds(2, 17) = -0.25 * (c(0) + 1) * (c(1) * c(1) - 1);
dnds(2, 18) = -0.25 * (c(1) + 1) * (c(0) * c(0) - 1);
dnds(2, 19) = 0.25 * (c(0) - 1) * (c(1) * c(1) - 1);
}
/* -------------------------------------------------------------------------- */
template <>
inline Real
GeometricalElement<_gt_hexahedron_20>::getInradius(const Matrix<Real> & coord) {
return GeometricalElement<_gt_hexahedron_8>::getInradius(coord) * 0.5;
}
} // namespace akantu
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