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element_class_triangle_3_inline_impl.cc
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element_class_triangle_3_inline_impl.cc
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/**
* @file element_class_triangle_3_inline_impl.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Sun Oct 19 2014
*
* @brief Specialization of the element_class class for the type _triangle_3
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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
\eta
^
|
x (0,0,1)
|`
| `
| q `
| ° `
x--------x-----> \xi
(1,0,0) (0,1,0)
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta \\
* N2 &=& \xi \\
* N3 &=& \eta
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* \xi_{q0} &=& 1/3 \qquad \eta_{q0} = 1/3
* @f}
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_triangle_3, _gt_triangle_3, _itp_lagrange_triangle_3, _ek_regular, 2,
_git_triangle, 1);
AKANTU_DEFINE_SHAPE(_gt_triangle_3, _gst_triangle);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void
InterpolationElement<_itp_lagrange_triangle_3>::computeShapes(const vector_type & natural_coords,
vector_type & N) {
/// Natural coordinates
Real c0 = 1 - natural_coords(0) - natural_coords(1); /// @f$ c0 = 1 - \xi - \eta @f$
Real c1 = natural_coords(0); /// @f$ c1 = \xi @f$
Real c2 = natural_coords(1); /// @f$ c2 = \eta @f$
N(0) = c0; /// N1(q_0)
N(1) = c1; /// N2(q_0)
N(2) = c2; /// N3(q_0)
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void
InterpolationElement<_itp_lagrange_triangle_3>::computeDNDS(__attribute__ ((unused)) const vector_type & natural_coords,
matrix_type & dnds) {
/**
* @f[
* dnds = \left(
* \begin{array}{cccccc}
* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial \xi} & \frac{\partial N3}{\partial \xi} \\
* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial \eta} & \frac{\partial N3}{\partial \eta}
* \end{array}
* \right)
* @f]
*/
dnds(0, 0) = -1.; dnds(0, 1) = 1.; dnds(0, 2) = 0.;
dnds(1, 0) = -1.; dnds(1, 1) = 0.; dnds(1, 2) = 1.;
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_lagrange_triangle_3>::computeSpecialJacobian(const Matrix<Real> & J,
Real & jac) {
Vector<Real> vprod(J.cols());
Matrix<Real> Jt(J.transpose(), true);
vprod.crossProduct(Jt(0), Jt(1));
jac = vprod.norm();
}
/* -------------------------------------------------------------------------- */
template<>
inline Real
GeometricalElement<_gt_triangle_3>::getInradius(const Matrix<Real> & coord) {
return Math::triangle_inradius(coord(0).storage(),
coord(1).storage(),
coord(2).storage());
}
/* -------------------------------------------------------------------------- */
// template<> inline bool ElementClass<_triangle_3>::contains(const Vector<Real> & natural_coords) {
// if (natural_coords[0] < 0.) return false;
// if (natural_coords[0] > 1.) return false;
// if (natural_coords[1] < 0.) return false;
// if (natural_coords[1] > 1.) return false;
// if (natural_coords[0]+natural_coords[1] > 1.) return false;
// return true;
// }
/* -------------------------------------------------------------------------- */

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