MOAB: Mesh Oriented datABase  (version 5.4.0)
LinearTetrahedron.cpp
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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 #include "Mesquite.hpp"
00028 #include "MsqError.hpp"
00029 #include "LinearTetrahedron.hpp"
00030 
00031 namespace MBMesquite
00032 {
00033 
00034 static const char* nonlinear_error = "Attempt to use LinearTetrahedron mapping function for a nonlinear element\n";
00035 
00036 EntityTopology LinearTetrahedron::element_topology() const
00037 {
00038     return TETRAHEDRON;
00039 }
00040 
00041 int LinearTetrahedron::num_nodes() const
00042 {
00043     return 4;
00044 }
00045 
00046 NodeSet LinearTetrahedron::sample_points( NodeSet ) const
00047 {
00048     NodeSet result;
00049     result.set_mid_region_node();
00050     return result;
00051 }
00052 
00053 static const unsigned faces[][3] = { { 1, 0, 3 }, { 3, 2, 1 }, { 0, 2, 3 }, { 0, 1, 2 } };
00054 
00055 void LinearTetrahedron::coefficients( Sample location,
00056                                       NodeSet nodeset,
00057                                       double* coeff_out,
00058                                       size_t* indices_out,
00059                                       size_t& num_coeff,
00060                                       MsqError& err ) const
00061 {
00062     if( nodeset.have_any_mid_node() )
00063     {
00064         MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT );
00065         return;
00066     }
00067 
00068     switch( location.dimension )
00069     {
00070         case 0:
00071             num_coeff      = 1;
00072             indices_out[0] = location.number;
00073             coeff_out[0]   = 1.0;
00074             break;
00075         case 1:
00076             num_coeff    = 2;
00077             coeff_out[0] = 0.5;
00078             coeff_out[1] = 0.5;
00079             if( location.number < 3 )
00080             {
00081                 indices_out[0] = location.number;
00082                 indices_out[1] = ( location.number + 1 ) % 3;
00083             }
00084             else
00085             {
00086                 indices_out[0] = location.number - 3;
00087                 indices_out[1] = 3;
00088             }
00089             break;
00090         case 2:
00091             num_coeff      = 3;
00092             indices_out[0] = faces[location.number][0];
00093             indices_out[1] = faces[location.number][1];
00094             indices_out[2] = faces[location.number][2];
00095             coeff_out[0] = coeff_out[1] = coeff_out[2] = coeff_out[3] = MSQ_ONE_THIRD;
00096             break;
00097         case 3:
00098             num_coeff      = 4;
00099             indices_out[0] = 0;
00100             indices_out[1] = 1;
00101             indices_out[2] = 2;
00102             indices_out[3] = 3;
00103             coeff_out[0] = coeff_out[1] = coeff_out[2] = coeff_out[3] = 0.25;
00104             break;
00105         default:
00106             MSQ_SETERR( err )( "Invalid/unsupported logical dimension", MsqError::INVALID_ARG );
00107     }
00108 }
00109 
00110 void LinearTetrahedron::derivatives( Sample,
00111                                      NodeSet nodeset,
00112                                      size_t* vertices,
00113                                      MsqVector< 3 >* coeff_derivs,
00114                                      size_t& num_vtx,
00115                                      MsqError& err ) const
00116 {
00117     if( nodeset.have_any_mid_node() )
00118     {
00119         MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT );
00120         return;
00121     }
00122     else
00123     {
00124         num_vtx     = 4;
00125         vertices[0] = 0;
00126         vertices[1] = 1;
00127         vertices[2] = 2;
00128         vertices[3] = 3;
00129 
00130         coeff_derivs[0][0] = -1.0;
00131         coeff_derivs[0][1] = -1.0;
00132         coeff_derivs[0][2] = -1.0;
00133 
00134         coeff_derivs[1][0] = 1.0;
00135         coeff_derivs[1][1] = 0.0;
00136         coeff_derivs[1][2] = 0.0;
00137 
00138         coeff_derivs[2][0] = 0.0;
00139         coeff_derivs[2][1] = 1.0;
00140         coeff_derivs[2][2] = 0.0;
00141 
00142         coeff_derivs[3][0] = 0.0;
00143         coeff_derivs[3][1] = 0.0;
00144         coeff_derivs[3][2] = 1.0;
00145     }
00146 }
00147 
00148 void LinearTetrahedron::ideal( Sample, MsqMatrix< 3, 3 >& J, MsqError& ) const
00149 {
00150     const double a = 1.122462048309373;   // 6th root of 2
00151     const double b = 1.7320508075688772;  // sqrt(3)
00152     const double c = 1.5874010519681994;  // 2 to the 2/3
00153     J( 0, 0 )      = a;
00154     J( 0, 1 )      = 0.5 * a;
00155     J( 0, 2 )      = 0.5 * a;
00156     J( 1, 0 )      = 0.0;
00157     J( 1, 1 )      = 0.5 * a * b;
00158     J( 1, 2 )      = 0.5 * a / b;
00159     J( 2, 0 )      = 0.0;
00160     J( 2, 1 )      = 0.0;
00161     J( 2, 2 )      = c / b;
00162 }
00163 
00164 }  // namespace MBMesquite
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