/usr/include/trilinos/QuadLagrangeShape.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | /* *****************************************************************
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_QUAD_LAGRANGE_SHAPE_HPP
#define MSQ_QUAD_LAGRANGE_SHAPE_HPP
/** \file QuadLagrangeShape.hpp
* \brief Lagrange mapping funtion for a 9-node quad.
* \author Jason Kraftcheck
*/
#include "MappingFunction.hpp"
namespace MESQUITE_NS {
/**\brief Lagrange shape function for 9-node quadrilateral elements
*
* This class implements the MappingFunction interface, providing
* a Lagrange shape function for quadrilateral elements.
*
* \f$\vec{x}(\xi,\eta) = \sum_{i=0}^{n-1} N_i(\xi,\eta) \vec{x_i}\f$
*
* \f$N_a = l^2_b(\xi) l^2_c(\eta)\f$
*
* \f$l^2_1(\xi) = (\xi - 1) (2 \xi - 1)\f$
*
* \f$l^2_2(\xi) = 4 \xi (1 - \xi)\f$
*
* \f$l^2_3(\xi) = \xi (2 \xi - 1)\f$
*
* \f$\begin{array}{ccc}
* a & b & c \\ \hline
* 0 & 1 & 1 \\
* 1 & 3 & 1 \\
* 2 & 3 & 3 \\
* 3 & 1 & 3 \\
* 4 & 2 & 1 \\
* 5 & 3 & 2 \\
* 6 & 2 & 3 \\
* 7 & 1 & 2 \\
* 8 & 2 & 2 \end{array}\f$
*
*/
class MESQUITE_EXPORT QuadLagrangeShape : public MappingFunction2D
{
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<2>* d_coeff_d_xi_out,
size_t& num_vtx,
MsqError& err ) const;
virtual
void ideal( Sample location,
MsqMatrix<3,2>& jacobian_out,
MsqError& err ) const;
};
} // namespace Mesquite
#endif
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