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rAKA/src/fe_engine/element_classes/element_class_segment_2_inline_impl.hh
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element_class_segment_2_inline_impl.hh
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/**
* @file element_class_segment_2_inline_impl.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Wed Oct 11 2017
*
* @brief Specialization of the element_class class for the type _segment_2
*
*
* 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/>.
*
*
* @verbatim
q
--x--------|--------x---> x
-1 0 1
@endverbatim
*
* @f{eqnarray*}{
* w_1(x) &=& 1/2(1 - x) \\
* w_2(x) &=& 1/2(1 + x)
* @f}
*
* @f{eqnarray*}{
* x_{q} &=& 0
* @f}
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_segment_2, _gt_segment_2,
_itp_lagrange_segment_2, _ek_regular, 1,
_git_segment, 1);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void InterpolationElement<_itp_lagrange_segment_2>::computeShapes(
const vector_type & natural_coords, vector_type & N) {
/// natural coordinate
Real c = natural_coords(0);
/// shape functions
N(0) = 0.5 * (1 - c);
N(1) = 0.5 * (1 + c);
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void InterpolationElement<_itp_lagrange_segment_2>::computeDNDS(
__attribute__((unused)) const vector_type & natural_coords,
matrix_type & dnds) {
/// dN1/de
dnds(0, 0) = -.5;
/// dN2/de
dnds(0, 1) = .5;
}
/* -------------------------------------------------------------------------- */
template<>
template <class vector_type, class matrix_type>
inline void InterpolationElement<_itp_lagrange_segment_2>::computeD2NDS2(
const vector_type & /*natural_coords*/, matrix_type & d2nds2) {
d2nds2.zero();
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_lagrange_segment_2>::computeSpecialJacobian(
const Matrix<Real> & dxds, Real & jac) {
jac = dxds.norm<L_2>();
}
/* -------------------------------------------------------------------------- */
template <>
inline Real
GeometricalElement<_gt_segment_2>::getInradius(const Matrix<Real> & coord) {
if (coord.rows() == 2) {
return Math::distance_2d(coord(0).storage(), coord(1).storage());
}
if (coord.rows() == 3) {
return Math::distance_3d(coord(0).storage(), coord(1).storage());
}
return std::abs(coord(0, 0) - coord(0, 1));
}
// /* --------------------------------------------------------------------------
// */
// template<> inline bool ElementClass<_segment_2>::contains(const Vector<Real>
// & natural_coords) {
// if (natural_coords(0) < -1.) return false;
// if (natural_coords(0) > 1.) return false;
// return true;
// }
/* -------------------------------------------------------------------------- */
} // namespace akantu
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