/usr/include/trilinos/HexLagrangeShape.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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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
***************************************************************** */
#ifndef MSQ_HEX_LAGRANGE_SHAPE_HPP
#define MSQ_HEX_LAGRANGE_SHAPE_HPP
/** \file HexLagrangeShape.hpp
* \brief Lagrange mapping funtion for a 27-node hex.
* \author Nicholas Voshell
*/
#include "MappingFunction.hpp"
namespace MESQUITE_NS {
/**\brief Lagrange shape function for 27-node hexahedral elements
*
* This class implements the MappingFunction interface, providing
* a Lagrange shape function for hexahedral elements.
*
* \f$\vec{x}(\xi,\eta) = \sum_{i=0}^{n-1} N_i(r, s, t) \vec{x_i}\f$
*
* \f$N_a = l^2_b(r) l^2_c(s) l^2_d(t)\f$
*
* \f$l^2_1(\xi) = (\xi - 1) (2 \xi - 1)\f$
*
* \f$l^2_2(\xi) = 4 \xi (1 - \xi)\f$
*
* \f$l^2_3(\xi) = \xi (2 \xi - 1)\f$
*
* Mesquite / iTAPS / MBCN order
*
* \f$\begin{array}{cccc}
* a & b & c & d \\ \hline
* 0 & 1 & 1 & 1 \\
* 1 & 3 & 1 & 1 \\
* 2 & 3 & 3 & 1 \\
* 3 & 1 & 3 & 1 \\
* 4 & 1 & 1 & 3 \\
* 5 & 3 & 1 & 3 \\
* 6 & 3 & 3 & 3 \\
* 7 & 1 & 3 & 3 \\
* 8 & 2 & 1 & 1 \\
* 9 & 3 & 2 & 1 \\
* 10 & 2 & 3 & 1 \\
* 11 & 1 & 2 & 1 \\
* 12 & 1 & 1 & 2 \\
* 13 & 3 & 1 & 2 \\
* 14 & 3 & 3 & 2 \\
* 15 & 1 & 3 & 2 \\
* 16 & 2 & 1 & 3 \\
* 17 & 3 & 2 & 3 \\
* 18 & 2 & 3 & 3 \\
* 19 & 1 & 2 & 3 \\
* 20 & 2 & 1 & 2 \\
* 21 & 3 & 2 & 2 \\
* 22 & 2 & 3 & 2 \\
* 23 & 1 & 2 & 2 \\
* 24 & 2 & 2 & 1 \\
* 25 & 2 & 2 & 3 \\
* 26 & 2 & 2 & 2 \end{array}\f$
*
* MBCN ORDER
*
* 7 - 18- 6
* / /
* 19 25 17
* / /
* 4 - 16- 6
*
* 15- 22- 14
* / /
* 23 26 21
* / /
* 12- 20- 13
*
* 3 - 10- 2
* / /
* 11 24 9 t s
* / / |/
* 0 - 8 - 1 +-r
*/
class MESQUITE_EXPORT HexLagrangeShape : public MappingFunction3D
{
public:
virtual
EntityTopology element_topology() const;
virtual
int num_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>& jacobian_out,
MsqError& err ) const;
};
} // namespace Mesquite
#endif
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