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rAKA/fem/element_classes/element_class_segment_3.cc
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element_class_segment_3.cc
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/**
* @file element_class_segment_3.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Sun Oct 3 10:28:28 2010
*
* @brief Specialization of the element_class class for the type _segment_3
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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
-1 0 1
-----x---------x---------x-----> x
1 3 2
@endverbatim
*
* @subsection coords Nodes coordinates
*
* @f[
* \begin{array}{lll}
* x_{1} = -1 & x_{2} = 1 & x_{3} = 0
* \end{array}
* @f]
*
* @subsection shapes Shape functions
* @f[
* \begin{array}{ll}
* w_1(x) = \frac{x}{2}(x - 1) & w'_1(x) = x - \frac{1}{2}\\
* w_2(x) = \frac{x}{2}(x + 1) & w'_2(x) = x + \frac{1}{2}\\
* w_3(x) = 1-x^2 & w'_3(x) = -2x
* \end{array}
* @f]
*
* @subsection quad_points Position of quadrature points
* @f[
* \begin{array}{ll}
* x_{q1} = -1/\sqrt{3} & x_{q2} = 1/\sqrt{3}
* \end{array}
* @f]
*/
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_segment_3>::nb_nodes_per_element;
template<> UInt ElementClass<_segment_3>::nb_quadrature_points;
template<> UInt ElementClass<_segment_3>::spatial_dimension;
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_3>::computeShapes(const Real * natural_coords,
Real * shapes){
Real c = natural_coords[0];
shapes[0] = (c - 1) * c / 2;
shapes[1] = (c + 1) * c / 2;
shapes[2] = 1 - c * c;
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_3>::computeDNDS(const Real * natural_coords,
Real * dnds){
Real c = natural_coords[0];
dnds[0] = c - .5;
dnds[1] = c + .5;
dnds[2] = -2 * c;
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_3>::computeJacobian(const Real * dxds,
const UInt dimension,
Real & jac){
if (dimension == spatial_dimension){
jac = dxds[0];
} else {
jac = Math::norm2(dxds);
}
}
/* -------------------------------------------------------------------------- */
template<> inline Real ElementClass<_segment_3>::getInradius(const Real * coord) {
Real dist1 = sqrt((coord[0] - coord[1])*(coord[0] - coord[1]));
Real dist2 = sqrt((coord[1] - coord[2])*(coord[1] - coord[2]));
return dist1 < dist2 ? dist1 : dist2;
}
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