MOAB: Mesh Oriented datABase  (version 5.2.1)
TShapeSizeNB3.cpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2009 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     (2009) kraftche@cae.wisc.edu
00024 
00025   ***************************************************************** */
00026 
00027 /** \file TShapeSizeNB3.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TShapeSizeNB3.hpp"
00034 #include "MsqMatrix.hpp"
00035 #include "TMPDerivs.hpp"
00036 
00037 namespace MBMesquite
00038 {
00039 
00040 std::string TShapeSizeNB3::get_name() const
00041 {
00042     return "TShapeSizeNB3";
00043 }
00044 
00045 TShapeSizeNB3::~TShapeSizeNB3() {}
00046 
00047 bool TShapeSizeNB3::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& )
00048 {
00049     const double nT   = sqr_Frobenius( T );
00050     const double tau  = det( T );
00051     const double tau1 = tau - 1;
00052     result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
00053     return true;
00054 }
00055 
00056 bool TShapeSizeNB3::evaluate_with_grad( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00057                                         MsqError& /*err*/ )
00058 {
00059     const double nT   = sqr_Frobenius( T );
00060     const double tau  = det( T );
00061     const double tau1 = tau - 1;
00062     result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
00063 
00064     deriv_wrt_T = T;
00065     deriv_wrt_T *= 4;
00066     deriv_wrt_T += ( 2 * mGamma * tau1 - 4 ) * transpose_adj( T );
00067 
00068     return true;
00069 }
00070 
00071 bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00072                                         MsqMatrix< 2, 2 > second[3], MsqError& /*err*/ )
00073 {
00074     const double nT   = sqr_Frobenius( T );
00075     const double tau  = det( T );
00076     const double tau1 = tau - 1;
00077     result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
00078 
00079     const double f               = 2 * mGamma * tau1 - 4;
00080     const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
00081     deriv_wrt_T                  = T;
00082     deriv_wrt_T *= 4;
00083     deriv_wrt_T += f * adjt;
00084 
00085     set_scaled_outer_product( second, 2 * mGamma, adjt );
00086     pluseq_scaled_I( second, 4 );
00087     pluseq_scaled_2nd_deriv_of_det( second, f );
00088 
00089     return true;
00090 }
00091 
00092 bool TShapeSizeNB3::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
00093 {
00094     const double nT   = Frobenius( T );
00095     const double tau  = det( T );
00096     const double tau1 = tau - 1;
00097     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00098     return true;
00099 }
00100 
00101 bool TShapeSizeNB3::evaluate_with_grad( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T,
00102                                         MsqError& /*err*/ )
00103 {
00104     const double nT   = Frobenius( T );
00105     const double tau  = det( T );
00106     const double tau1 = tau - 1;
00107     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00108 
00109     wrt_T = T;
00110     wrt_T *= 3 * nT;
00111     wrt_T -= ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ) * transpose_adj( T );
00112 
00113     return true;
00114 }
00115 
00116 bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T,
00117                                         MsqMatrix< 3, 3 > second[6], MsqError& /*err*/ )
00118 {
00119     const double nT   = Frobenius( T );
00120     const double tau  = det( T );
00121     const double tau1 = tau - 1;
00122     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00123 
00124     const double f               = ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 );
00125     const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
00126     wrt_T                        = T;
00127     wrt_T *= 3 * nT;
00128     wrt_T -= f * adjt;
00129 
00130     set_scaled_outer_product( second, 2 * mGamma, adjt );
00131     pluseq_scaled_2nd_deriv_of_det( second, -f, T );
00132     pluseq_scaled_I( second, 3 * nT );
00133     // Could perturb T a bit if the norm is zero, but that would just
00134     // result in the coefficent of the outer product being practically
00135     // zero, so just skip the outer product in that case.
00136     // Anyway nT approaches zero as T does, so the limit of this term
00137     // as nT approaches zero is zero.
00138     if( nT > 1e-100 )  // NOTE: nT is always positive
00139         pluseq_scaled_outer_product( second, 3 / nT, T );
00140 
00141     return true;
00142 }
00143 
00144 }  // namespace MBMesquite
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