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rAKA/src/fe_engine/element_classes/element_class_pentahedron_6_inline_impl.cc
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element_class_pentahedron_6_inline_impl.cc
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/**
* @file element_class_pentahedron_6_inline_impl.cc
*
* @author Marion Estelle Chambart <mchambart@stucky.ch>
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Thomas Menouillard <tmenouillard@stucky.ch>
*
* @date creation: Mon Mar 14 2011
* @date last modification: Wed Oct 11 2017
*
* @brief Specialization of the element_class class for the type _pentahedron_6
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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
| /|\
|/ | \
/ | \
/ | \
/ | \
4 2-----0
| \ / /
| \/ /
| \ /----------/y
| / \ /
|/ \ /
5---.--3
/
/
/
\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
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_pentahedron_6, _gt_pentahedron_6,
_itp_lagrange_pentahedron_6, _ek_regular,
3, _git_pentahedron, 1);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeShapes(
const vector_type & c, vector_type & N) {
/// Natural coordinates
N(0) = 0.5 * c(1) * (1 - c(0)); // N1(q)
N(1) = 0.5 * c(2) * (1 - c(0)); // N2(q)
N(2) = 0.5 * (1 - c(1) - c(2)) * (1 - c(0)); // N3(q)
N(3) = 0.5 * c(1) * (1 + c(0)); // N4(q)
N(4) = 0.5 * c(2) * (1 + c(0)); // N5(q)
N(5) = 0.5 * (1 - c(1) - c(2)) * (1 + c(0)); // N6(q)
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeDNDS(
const vector_type & c, matrix_type & dnds) {
dnds(0, 0) = -0.5 * c(1);
dnds(0, 1) = -0.5 * c(2);
dnds(0, 2) = -0.5 * (1 - c(1) - c(2));
dnds(0, 3) = 0.5 * c(1);
dnds(0, 4) = 0.5 * c(2);
dnds(0, 5) = 0.5 * (1 - c(1) - c(2));
dnds(1, 0) = 0.5 * (1 - c(0));
dnds(1, 1) = 0.0;
dnds(1, 2) = -0.5 * (1 - c(0));
dnds(1, 3) = 0.5 * (1 + c(0));
dnds(1, 4) = 0.0;
dnds(1, 5) = -0.5 * (1 + c(0));
dnds(2, 0) = 0.0;
dnds(2, 1) = 0.5 * (1 - c(0));
dnds(2, 2) = -0.5 * (1 - c(0));
dnds(2, 3) = 0.0;
dnds(2, 4) = 0.5 * (1 + c(0));
dnds(2, 5) = -0.5 * (1 + c(0));
}
/* -------------------------------------------------------------------------- */
// I have to duplicate this code since the Real * coords do not know their size
// in the Math module.
// If later we use eigen or Vector to implement this function
// there should be only one function in akantu::Math
// -> this is temporary for the release deadline which was so extended
inline Real triangle_inradius(const Real * coord1, const Real * coord2,
const Real * coord3) {
/**
* @f{eqnarray*}{
* r &=& A / s \\
* A &=& 1/4 * \sqrt{(a + b + c) * (a - b + c) * (a + b - c) (-a + b + c)} \\
* s &=& \frac{a + b + c}{2}
* @f}
*/
Real a, b, c;
a = Math::distance_3d(coord1, coord2);
b = Math::distance_3d(coord2, coord3);
c = Math::distance_3d(coord1, coord3);
Real s;
s = (a + b + c) * 0.5;
return sqrt((s - a) * (s - b) * (s - c) / s);
}
/* -------------------------------------------------------------------------- */
template <>
inline Real
GeometricalElement<_gt_pentahedron_6>::getInradius(const Matrix<Real> & coord) {
Vector<Real> u0 = coord(0);
Vector<Real> u1 = coord(1);
Vector<Real> u2 = coord(2);
Vector<Real> u3 = coord(3);
Vector<Real> u4 = coord(4);
Vector<Real> u5 = coord(5);
Real inradius_triangle_1 =
triangle_inradius(u0.storage(), u1.storage(), u2.storage());
Real inradius_triangle_2 =
triangle_inradius(u3.storage(), u4.storage(), u5.storage());
Real d1 = u3.distance(u0) * 0.5;
Real d2 = u5.distance(u2) * 0.5;
Real d3 = u4.distance(u1) * 0.5;
Real p =
2. * std::min({inradius_triangle_1, inradius_triangle_2, d1, d2, d3});
return p;
}
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