MOAB: Mesh Oriented datABase  (version 5.2.1)
TShapeSize2DNB2.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 TShapeSize2DNB2.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TShapeSize2DNB2.hpp"
00034 #include "MsqMatrix.hpp"
00035 #include "TMPDerivs.hpp"
00036 
00037 namespace MBMesquite
00038 {
00039 
00040 std::string TShapeSize2DNB2::get_name() const
00041 {
00042     return "TShapeSize2DNB2";
00043 }
00044 
00045 TShapeSize2DNB2::~TShapeSize2DNB2() {}
00046 
00047 /** \f$ \mu(T) = \frac{|T|^2+2}{2\psi(T)} - 1 \f$
00048  *  \f$ \psi(T) = \sqrt{|T|^2 + 2 \tau}\f$
00049  *  \f$ \tau = det(T) \f$
00050  */
00051 bool TShapeSize2DNB2::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& )
00052 {
00053     double frob_sqr = sqr_Frobenius( T );
00054     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00055 
00056     double a = 1e-12;
00057     while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
00058     {
00059         MsqMatrix< 2, 2 > Tdelta( T );
00060         Tdelta( 0, 0 ) += a;
00061         Tdelta( 1, 1 ) += a;
00062         a *= 2.0;
00063         frob_sqr = sqr_Frobenius( Tdelta );
00064         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00065         if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
00066     }
00067 
00068     result -= 1.0;
00069     return true;
00070 }
00071 
00072 bool TShapeSize2DNB2::evaluate_with_grad( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00073                                           MsqError& /*err*/ )
00074 {
00075     double frob_sqr = sqr_Frobenius( T );
00076     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00077 
00078     double a = 1e-12;
00079     while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
00080     {
00081         MsqMatrix< 2, 2 > Tdelta( T );
00082         Tdelta( 0, 0 ) += a;
00083         Tdelta( 1, 1 ) += a;
00084         a *= 2.0;
00085         frob_sqr = sqr_Frobenius( Tdelta );
00086         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00087         if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
00088     }
00089 
00090     // MsqMatrix<2,2> d_psi = 1.0/psi * (T + transpose_adj(T));
00091     // deriv_wrt_T = (1.0/psi) * (T - result * d_psi);
00092     if( psi > 1e-50 )
00093     {
00094         const double f = result / ( psi * psi );
00095         deriv_wrt_T    = transpose_adj( T );
00096         deriv_wrt_T *= -f;
00097         deriv_wrt_T += ( 1.0 / psi - f ) * T;
00098     }
00099 
00100     result -= 1.0;
00101 
00102     return true;
00103 }
00104 
00105 bool TShapeSize2DNB2::evaluate_with_hess( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& deriv_wrt_T,
00106                                           MsqMatrix< 2, 2 > second[3], MsqError& /*err*/ )
00107 {
00108     double frob_sqr = sqr_Frobenius( T );
00109     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00110 
00111     double a = 1e-12;
00112     while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
00113     {
00114         MsqMatrix< 2, 2 > Tdelta( T );
00115         Tdelta( 0, 0 ) += a;
00116         Tdelta( 1, 1 ) += a;
00117         a *= 2.0;
00118         frob_sqr = sqr_Frobenius( Tdelta );
00119         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00120         if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
00121     }
00122 
00123     const double inv_psi    = 1.0 / psi;
00124     MsqMatrix< 2, 2 > d_psi = T + transpose_adj( T );
00125     d_psi *= inv_psi;
00126 
00127     deriv_wrt_T = d_psi;
00128     deriv_wrt_T *= -result;
00129     deriv_wrt_T += T;
00130     deriv_wrt_T *= inv_psi;
00131 
00132     set_scaled_2nd_deriv_wrt_psi( second, -result * inv_psi, psi, T );
00133     pluseq_scaled_outer_product( second, 2 * result * inv_psi * inv_psi, d_psi );
00134     pluseq_scaled_sum_outer_product( second, -inv_psi * inv_psi, d_psi, T );
00135     pluseq_scaled_I( second, inv_psi );
00136 
00137     result -= 1.0;
00138 
00139     return true;
00140 }
00141 
00142 }  // namespace MBMesquite
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