MOAB: Mesh Oriented datABase  (version 5.3.1)
LinearHexahedron.hpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2006 Lawrence Livermore National Laboratory.  Under
00005     the terms of Contract B545069 with the University of Wisconsin --
00006     Madison, Lawrence Livermore National Laboratory retains certain
00007     rights in 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 #ifndef MSQ_LINEAR_HEXAHEDRON_HPP
00028 #define MSQ_LINEAR_HEXAHEDRON_HPP
00029 
00030 #include "Mesquite.hpp"
00031 #include "MappingFunction.hpp"
00032 
00033 namespace MBMesquite
00034 {
00035 
00036 /**\brief Linear mapping function for a hexahedral element
00037  *
00038  * This class implements the MappingFunction interface, providing
00039  * a Linear shape function for hexahedral elements.
00040  *
00041  * \f$\vec{x}(\xi,\eta,\zeta) = \sum_{i=0}^{7} N_i(\xi,\eta,\zeta) \vec{x_i}\f$
00042  *
00043  * \f$N_0(\xi,\eta,\zeta) = (1-\xi)(1-\eta)(1-\zeta)\f$
00044  *
00045  * \f$N_1(\xi,\eta,\zeta) =    \xi (1-\eta)(1-\zeta)\f$
00046  *
00047  * \f$N_2(\xi,\eta,\zeta) =    \xi    \eta (1-\zeta)\f$
00048  *
00049  * \f$N_3(\xi,\eta,\zeta) = (1-\xi)   \eta (1-\zeta)\f$
00050  *
00051  * \f$N_4(\xi,\eta,\zeta) = (1-\xi)(1-\eta)   \zeta \f$
00052  *
00053  * \f$N_5(\xi,\eta,\zeta) =    \xi (1-\eta)   \zeta \f$
00054  *
00055  * \f$N_6(\xi,\eta,\zeta) =    \xi    \eta    \zeta \f$
00056  *
00057  * \f$N_7(\xi,\eta,\zeta) = (1-\xi)   \eta    \zeta \f$
00058  *
00059  */
00060 class MESQUITE_EXPORT LinearHexahedron : public MappingFunction3D
00061 {
00062   public:
00063     virtual EntityTopology element_topology() const;
00064 
00065     virtual int num_nodes() const;
00066 
00067     virtual void coefficients( Sample location, NodeSet nodeset, double* coeff_out, size_t* indices_out,
00068                                size_t& num_coeff_out, MsqError& err ) const;
00069 
00070     virtual void derivatives( Sample location, NodeSet nodeset, size_t* vertex_indices_out,
00071                               MsqVector< 3 >* d_coeff_d_xi_out, size_t& num_vtx, MsqError& err ) const;
00072 
00073     virtual void ideal( Sample location, MsqMatrix< 3, 3 >& jacobian_out, MsqError& err ) const;
00074 };
00075 
00076 }  // namespace MBMesquite
00077 
00078 #endif
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