MOAB: Mesh Oriented datABase  (version 5.2.1)
TetLagrangeShape.hpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2006 Sandia National Laboratories.  Developed at the
00005     University of Wisconsin--Madison under SNL contract number
00006     624796.  The U.S. Government and the University of Wisconsin
00007     retain certain rights to this software.
00008 
00009     This library is free software; you can redistribute it and/or
00010     modify it under the terms of the GNU Lesser General Public
00011     License as published by the Free Software Foundation; either
00012     version 2.1 of the License, or (at your option) any later version.
00013 
00014     This library is distributed in the hope that it will be useful,
00015     but WITHOUT ANY WARRANTY; without even the implied warranty of
00016     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00017     Lesser General Public License for more details.
00018 
00019     You should have received a copy of the GNU Lesser General Public License
00020     (lgpl.txt) along with this library; if not, write to the Free Software
00021     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
00022 
00023     (2006) kraftche@cae.wisc.edu
00024 
00025   ***************************************************************** */
00026 
00027 /** \file TetLagrangeShape.hpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #ifndef MSQ_TET_LAGRANGE_SHAPE_HPP
00033 #define MSQ_TET_LAGRANGE_SHAPE_HPP
00034 
00035 #include "Mesquite.hpp"
00036 #include "MappingFunction.hpp"
00037 
00038 namespace MBMesquite
00039 {
00040 
00041 /**\brief Lagrange shape function for tetrahedral elements
00042  *
00043  * This class implements the MappingFunction interface, providing
00044  * a Lagrange shape function for a 10-node tet.
00045  *
00046  * \f$\vec{x}(r,s,t) = sum_{i=0}^{n-1} N_i(r,s,t) \vec{x_i}\f$
00047  *
00048  * \f$N_1 = u(2u - 1)\f$
00049  *
00050  * \f$N_2 = r(2r - 1)\f$
00051  *
00052  * \f$N_3 = s(2s - 1)\f$
00053  *
00054  * \f$N_4 = t(2t - 1)\f$
00055  *
00056  * \f$N_5 = 4ru\f$
00057  *
00058  * \f$N_6 = 4rs\f$
00059  *
00060  * \f$N_7 = 4su\f$
00061  *
00062  * \f$N_8 = 4tu\f$
00063  *
00064  * \f$N_9 = 4rt\f$
00065  *
00066  * \f$N_10 = 4st\f$
00067  *
00068  * \f$u = 1 - r - s - t\f$
00069  */
00070 class MESQUITE_EXPORT TetLagrangeShape : public MappingFunction3D
00071 {
00072   public:
00073     virtual EntityTopology element_topology() const;
00074 
00075     virtual int num_nodes() const;
00076 
00077     virtual NodeSet sample_points( NodeSet higher_order_nodes ) const;
00078 
00079     virtual void coefficients( Sample location, NodeSet nodeset, double* coeff_out, size_t* indices_out,
00080                                size_t& num_coeff_out, MsqError& err ) const;
00081 
00082     virtual void derivatives( Sample location, NodeSet nodeset, size_t* vertex_indices_out,
00083                               MsqVector< 3 >* d_coeff_d_xi_out, size_t& num_vtx, MsqError& err ) const;
00084 
00085     virtual void ideal( Sample location, MsqMatrix< 3, 3 >& jacobian_out, MsqError& err ) const;
00086 };
00087 
00088 }  // namespace MBMesquite
00089 
00090 #endif
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