MOAB: Mesh Oriented datABase  (version 5.4.0)
TShapeSize3DNB1.cpp
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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 TShapeSize3DNB1.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TShapeSize3DNB1.hpp"
00034 #include "MsqMatrix.hpp"
00035 #include "TMPDerivs.hpp"
00036 
00037 namespace MBMesquite
00038 {
00039 
00040 std::string TShapeSize3DNB1::get_name() const
00041 {
00042     return "TShapeSize3DNB1";
00043 }
00044 
00045 TShapeSize3DNB1::~TShapeSize3DNB1() {}
00046 
00047 bool TShapeSize3DNB1::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
00048 {
00049     const double nT   = Frobenius( T );
00050     const double tau  = det( T );
00051     const double tau1 = tau - 1;
00052     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00053     return true;
00054 }
00055 
00056 bool TShapeSize3DNB1::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
00057                                           double& result,
00058                                           MsqMatrix< 3, 3 >& wrt_T,
00059                                           MsqError& /*err*/ )
00060 {
00061     const double nT   = Frobenius( T );
00062     const double tau  = det( T );
00063     const double tau1 = tau - 1;
00064     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00065 
00066     wrt_T = T;
00067     wrt_T *= 3 * nT;
00068     wrt_T -= ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ) * transpose_adj( T );
00069 
00070     return true;
00071 }
00072 
00073 bool TShapeSize3DNB1::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
00074                                           double& result,
00075                                           MsqMatrix< 3, 3 >& wrt_T,
00076                                           MsqMatrix< 3, 3 > second[6],
00077                                           MsqError& /*err*/ )
00078 {
00079     const double nT   = Frobenius( T );
00080     const double tau  = det( T );
00081     const double tau1 = tau - 1;
00082     result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
00083 
00084     const double f               = ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 );
00085     const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
00086     wrt_T                        = T;
00087     wrt_T *= 3 * nT;
00088     wrt_T -= f * adjt;
00089 
00090     set_scaled_outer_product( second, 2 * mGamma, adjt );
00091     pluseq_scaled_2nd_deriv_of_det( second, -f, T );
00092     pluseq_scaled_I( second, 3 * nT );
00093     // Could perturb T a bit if the norm is zero, but that would just
00094     // result in the coefficent of the outer product being practically
00095     // zero, so just skip the outer product in that case.
00096     // Anyway nT approaches zero as T does, so the limit of this term
00097     // as nT approaches zero is zero.
00098     if( nT > 1e-100 )  // NOTE: nT is always positive
00099         pluseq_scaled_outer_product( second, 3 / nT, T );
00100 
00101     return true;
00102 }
00103 
00104 }  // namespace MBMesquite
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