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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: Thu Dec 28 2017
*
* @brief Specialization of the element_class class for the type
* _pentahedron_15
*
* @section LICENSE
*
* Copyright (©) 2015-2018 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/>.
*
* @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);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void InterpolationElement<_itp_lagrange_pentahedron_15>::computeShapes(
const vector_type & c, vector_type & N) {
auto & x = c(0);
auto & y = c(1);
auto & z = c(2);
// Shape Functions, Natural coordinates
N(0) = 0.5 * y * (1 - x) * (2 * y - 2 - x);
N(1) = 0.5 * z * (1 - x) * (2 * z - 2 - x);
N(2) = 0.5 * (x - 1) * (1 - y - z) * (x + 2 * y + 2 * z);
N(3) = 0.5 * y * (1 + x) * (2 * y - 2 + x);
N(4) = 0.5 * z * (1 + x) * (2 * z - 2 + x);
N(5) = 0.5 * (-x - 1) * (1 - y - z) * (-x + 2 * y + 2 * z);
N(6) = 2.0 * y * z * (1 - x);
N(7) = 2.0 * z * (1 - y - z) * (1 - x);
N(8) = 2.0 * y * (1 - x) * (1 - y - z);
N(9) = y * (1 - x * x);
N(10) = z * (1 - x * x);
N(11) = (1 - y - z) * (1 - x * x);
N(12) = 2.0 * y * z * (1 + x);
N(13) = 2.0 * z * (1 - y - z) * (1 + x);
N(14) = 2.0 * y * (1 - y - z) * (1 + x);
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void InterpolationElement<_itp_lagrange_pentahedron_15>::computeDNDS(
const vector_type & c, matrix_type & dnds) {
auto & x = c(0);
auto & y = c(1);
auto & z = c(2);
// ddx
dnds(0, 0) = 0.5 * y * (2 * x - 2 * y + 1);
dnds(0, 1) = 0.5 * z * (2 * x - 2 * z + 1);
dnds(0, 2) = -0.5 * (2 * x + 2 * y + 2 * z - 1) * (y + z - 1);
dnds(0, 3) = 0.5 * y * (2 * x + 2 * y - 1);
dnds(0, 4) = 0.5 * z * (2 * x + 2 * z - 1);
dnds(0, 5) = -0.5 * (y + z - 1) * (2 * x - 2 * y - 2 * z + 1);
dnds(0, 6) = -2.0 * y * z;
dnds(0, 7) = 2.0 * z * (y + z - 1);
dnds(0, 8) = 2.0 * y * (y + z - 1);
dnds(0, 9) = -2.0 * x * y;
dnds(0, 10) = -2.0 * x * z;
dnds(0, 11) = 2.0 * x * (y + z - 1);
dnds(0, 12) = 2.0 * y * z;
dnds(0, 13) = -2.0 * z * (y + z - 1);
dnds(0, 14) = -2.0 * y * (y + z - 1);
// ddy
dnds(1, 0) = -0.5 * (x - 1) * (4 * y - x - 2);
dnds(1, 1) = 0.0;
dnds(1, 2) = -0.5 * (x - 1) * (4 * y + x + 2 * (2 * z - 1));
dnds(1, 3) = 0.5 * (x + 1) * (4 * y + x - 2);
dnds(1, 4) = 0.0;
dnds(1, 5) = 0.5 * (x + 1) * (4 * y - x + 2 * (2 * z - 1));
dnds(1, 6) = -2.0 * (x - 1) * z;
dnds(1, 7) = 2.0 * z * (x - 1);
dnds(1, 8) = 2.0 * (2 * y + z - 1) * (x - 1);
dnds(1, 9) = -(x * x - 1);
dnds(1, 10) = 0.0;
dnds(1, 11) = (x * x - 1);
dnds(1, 12) = 2.0 * z * (x + 1);
dnds(1, 13) = -2.0 * z * (x + 1);
dnds(1, 14) = -2.0 * (2 * y + z - 1) * (x + 1);
// ddz
dnds(2, 0) = 0.0;
dnds(2, 1) = -0.5 * (x - 1) * (4 * z - x - 2);
dnds(2, 2) = -0.5 * (x - 1) * (4 * z + x + 2 * (2 * y - 1));
dnds(2, 3) = 0.0;
dnds(2, 4) = 0.5 * (x + 1) * (4 * z + x - 2);
dnds(2, 5) = 0.5 * (x + 1) * (4 * z - x + 2 * (2 * y - 1));
dnds(2, 6) = -2.0 * (x - 1) * y;
dnds(2, 7) = 2.0 * (x - 1) * (2 * z + y - 1);
dnds(2, 8) = 2.0 * y * (x - 1);
dnds(2, 9) = 0.0;
dnds(2, 10) = -(x * x - 1);
dnds(2, 11) = (x * x - 1);
dnds(2, 12) = 2.0 * (x + 1) * y;
dnds(2, 13) = -2.0 * (x + 1) * (2 * z + y - 1);
dnds(2, 14) = -2.0 * (x + 1) * y;
}
/* -------------------------------------------------------------------------- */
template <>
inline Real GeometricalElement<_gt_pentahedron_15>::getInradius(
const Matrix<Real> & coord) {
return GeometricalElement<_gt_pentahedron_6>::getInradius(coord) * 0.5;
}

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