/usr/include/trilinos/LinearPyramid.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
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MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2006 Lawrence Livermore National Laboratory. Under
the terms of Contract B545069 with the University of Wisconsin --
Madison, Lawrence Livermore National Laboratory retains certain
rights in this software.
This library 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 2.1 of the License, or (at your option) any later version.
This library 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
(lgpl.txt) along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
(2006) kraftche@cae.wisc.edu
***************************************************************** */
/** \file LinearPyramid.hpp
* \brief mapping function for linear prism
* \author Jason Kraftcheck
*/
#ifndef MSQ_LINEAR_PYRAMID_HPP
#define MSQ_LINEAR_PYRAMID_HPP
#include "Mesquite.hpp"
#include "MappingFunction.hpp"
namespace MESQUITE_NS {
/**\brief Linear mapping function for a pyramid element
*
* \f$\vec{x}(\vec{\xi})=\sum_{i=0}^5 N_i(\vec{\xi})\vec{x_i}\f$
* - \f$ N_0(\vec{\xi})=(1-\xi)(1-\eta)(1-\zeta) \f$
* - \f$ N_1(\vec{\xi})= \xi (1-\eta)(1-\zeta) \f$
* - \f$ N_2(\vec{\xi})= \xi \eta (1-\zeta) \f$
* - \f$ N_3(\vec{\xi})=(1-\xi) \eta (1-\zeta) \f$
* - \f$ N_4(\vec{\xi})=\zeta \f$
*
* Where the mid-edge coordinates are:
* - \f$ \vec{\xi}_{e0}=( \frac{1}{2}, 0, 0) \f$
* - \f$ \vec{\xi}_{e1}=( 1, \frac{1}{2}, 0) \f$
* - \f$ \vec{\xi}_{e2}=( \frac{1}{2}, 1, 0) \f$
* - \f$ \vec{\xi}_{e3}=( 0, \frac{1}{2}, 0) \f$
* - \f$ \vec{\xi}_{e4}=( 0, 0, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{e5}=( 1, 0, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{e6}=( 1, 1, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{e7}=( 0, 1, \frac{1}{2}) \f$
*
* and mid-face the coordinates are:
* - \f$ \vec{\xi}_{f0}=( \frac{1}{2}, 0, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{f1}=( 1, \frac{1}{2}, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{f2}=( \frac{1}{2}, 1, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{f3}=( 0, \frac{1}{2}, \frac{1}{2}) \f$
* - \f$ \vec{\xi}_{f4}=( \frac{1}{2}, \frac{1}{2}, 0) \f$
*
* and the mid-element coorindates are
* - \f$ \vec{\xi}_m=( \frac{1}{2}, \frac{1}{2}, \frac{1}{2}) \f$
*/
class MESQUITE_EXPORT LinearPyramid : public MappingFunction3D
{
public:
virtual
EntityTopology element_topology() const;
virtual
int num_nodes() const;
virtual
NodeSet sample_points( NodeSet higher_order_nodes ) const;
virtual
void coefficients( Sample location,
NodeSet nodeset,
double* coeff_out,
size_t* indices_out,
size_t& num_coeff_out,
MsqError& err ) const;
virtual
void derivatives( Sample location,
NodeSet nodeset,
size_t* vertex_indices_out,
MsqVector<3>* d_coeff_d_xi_out,
size_t& num_vtx,
MsqError& err ) const;
virtual
void ideal( Sample location,
MsqMatrix<3,3>& J,
MsqError& err ) const;
};
} // namespace Mesquite
#endif
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