MOAB: Mesh Oriented datABase  (version 5.4.1)
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) [email protected]
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,
00057                                         double& result,
00058                                         MsqMatrix< 2, 2 >& deriv_wrt_T,
00059                                         MsqError& /*err*/ )
00060 {
00061     const double nT   = sqr_Frobenius( T );
00062     const double tau  = det( T );
00063     const double tau1 = tau - 1;
00064     result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
00065 
00066     deriv_wrt_T = T;
00067     deriv_wrt_T *= 4;
00068     deriv_wrt_T += ( 2 * mGamma * tau1 - 4 ) * transpose_adj( T );
00069 
00070     return true;
00071 }
00072 
00073 bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
00074                                         double& result,
00075                                         MsqMatrix< 2, 2 >& deriv_wrt_T,
00076                                         MsqMatrix< 2, 2 > second[3],
00077                                         MsqError& /*err*/ )
00078 {
00079     const double nT   = sqr_Frobenius( T );
00080     const double tau  = det( T );
00081     const double tau1 = tau - 1;
00082     result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
00083 
00084     const double f               = 2 * mGamma * tau1 - 4;
00085     const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
00086     deriv_wrt_T                  = T;
00087     deriv_wrt_T *= 4;
00088     deriv_wrt_T += f * adjt;
00089 
00090     set_scaled_outer_product( second, 2 * mGamma, adjt );
00091     pluseq_scaled_I( second, 4 );
00092     pluseq_scaled_2nd_deriv_of_det( second, f );
00093 
00094     return true;
00095 }
00096 
00097 bool TShapeSizeNB3::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
00098 {
00099     const double nT   = Frobenius( T );
00100     const double tau  = det( T );
00101     const double tau1 = tau - 1;
00102     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00103     return true;
00104 }
00105 
00106 bool TShapeSizeNB3::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
00107                                         double& result,
00108                                         MsqMatrix< 3, 3 >& wrt_T,
00109                                         MsqError& /*err*/ )
00110 {
00111     const double nT   = Frobenius( T );
00112     const double tau  = det( T );
00113     const double tau1 = tau - 1;
00114     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00115 
00116     wrt_T = T;
00117     wrt_T *= 3 * nT;
00118     wrt_T -= ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ) * transpose_adj( T );
00119 
00120     return true;
00121 }
00122 
00123 bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
00124                                         double& result,
00125                                         MsqMatrix< 3, 3 >& wrt_T,
00126                                         MsqMatrix< 3, 3 > second[6],
00127                                         MsqError& /*err*/ )
00128 {
00129     const double nT   = Frobenius( T );
00130     const double tau  = det( T );
00131     const double tau1 = tau - 1;
00132     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00133 
00134     const double f               = ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 );
00135     const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
00136     wrt_T                        = T;
00137     wrt_T *= 3 * nT;
00138     wrt_T -= f * adjt;
00139 
00140     set_scaled_outer_product( second, 2 * mGamma, adjt );
00141     pluseq_scaled_2nd_deriv_of_det( second, -f, T );
00142     pluseq_scaled_I( second, 3 * nT );
00143     // Could perturb T a bit if the norm is zero, but that would just
00144     // result in the coefficent of the outer product being practically
00145     // zero, so just skip the outer product in that case.
00146     // Anyway nT approaches zero as T does, so the limit of this term
00147     // as nT approaches zero is zero.
00148     if( nT > 1e-100 )  // NOTE: nT is always positive
00149         pluseq_scaled_outer_product( second, 3 / nT, T );
00150 
00151     return true;
00152 }
00153 
00154 }  // namespace MBMesquite
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