MOAB: Mesh Oriented datABase  (version 5.2.1)
TShapeSize2DNB1.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 TShapeSize2DNB1.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TShapeSize2DNB1.hpp"
00034 #include "MsqMatrix.hpp"
00035 #include "TMPDerivs.hpp"
00036 
00037 #include <iostream>
00038 
00039 namespace MBMesquite
00040 {
00041 
00042 std::string TShapeSize2DNB1::get_name() const
00043 {
00044     return "TShapeSize2DNB1";
00045 }
00046 
00047 TShapeSize2DNB1::~TShapeSize2DNB1() {}
00048 
00049 /** \f$ \mu(T) = |T|^2 - 2 \psi(T) + 2 \f$
00050  *  \f$ \psi(T) = \sqrt{|T|^2 + 2 \tau} \f$
00051  *  \f$ \tau = det(T) \f$
00052  */
00053 bool TShapeSize2DNB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& /*err*/ )
00054 {
00055     double frob_sqr = sqr_Frobenius( T );
00056     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00057 
00058     MsqMatrix< 2, 2 > Tdelta( T );
00059     while( fabs( psi ) < DBL_EPSILON )
00060     {
00061         Tdelta( 0, 0 ) += 1e-12;
00062         Tdelta( 1, 1 ) += 1e-12;
00063         frob_sqr = sqr_Frobenius( Tdelta );
00064         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00065     }
00066 
00067     result = frob_sqr - 2.0 * psi + 2.0;
00068     return true;
00069 }
00070 
00071 bool TShapeSize2DNB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00072                                           MsqError& /*err*/ )
00073 {
00074     double frob_sqr = sqr_Frobenius( T );
00075     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00076 
00077     MsqMatrix< 2, 2 > Tdelta( T );
00078     while( fabs( psi ) < DBL_EPSILON )
00079     {
00080         Tdelta( 0, 0 ) += 1e-12;
00081         Tdelta( 1, 1 ) += 1e-12;
00082         frob_sqr = sqr_Frobenius( Tdelta );
00083         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00084     }
00085 
00086     result = frob_sqr - 2.0 * psi + 2.0;
00087 
00088     deriv_wrt_T = T;
00089     if( psi > 1e-50 )
00090     {
00091         deriv_wrt_T *= ( 1.0 - 1.0 / psi );
00092         deriv_wrt_T -= 1.0 / psi * transpose_adj( T );
00093         deriv_wrt_T *= 2;
00094     }
00095     else
00096     {
00097         std::cout << "Warning: Division by zero avoided in TShapeSize2DNB2::evaluate_with_grad()" << std::endl;
00098     }
00099 
00100     return true;
00101 }
00102 
00103 bool TShapeSize2DNB1::evaluate_with_hess( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00104                                           MsqMatrix< 2, 2 > second[3], MsqError& /*err*/ )
00105 {
00106     double frob_sqr = sqr_Frobenius( T );
00107     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00108 
00109     MsqMatrix< 2, 2 > Tdelta( T );
00110     while( fabs( psi ) < DBL_EPSILON )
00111     {
00112         Tdelta( 0, 0 ) += 1e-12;
00113         Tdelta( 1, 1 ) += 1e-12;
00114         frob_sqr = sqr_Frobenius( Tdelta );
00115         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00116     }
00117 
00118     result = frob_sqr - 2.0 * psi + 2.0;
00119 
00120     deriv_wrt_T = T;
00121     if( psi > 1e-50 )
00122     {
00123         deriv_wrt_T *= ( 1.0 - 1.0 / psi );
00124         deriv_wrt_T -= 1.0 / psi * transpose_adj( T );
00125         deriv_wrt_T *= 2;
00126     }
00127     else
00128     {
00129         std::cout << "Warning: Division by zero avoided in TShapeSize2DNB2::evaluate_with_hess()" << std::endl;
00130     }
00131 
00132     set_scaled_2nd_deriv_wrt_psi( second, -2.0, psi, T );
00133     pluseq_scaled_I( second, 2 );
00134 
00135     return true;
00136 }
00137 
00138 }  // namespace MBMesquite
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