MOAB: Mesh Oriented datABase  (version 5.4.1)
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,
00073                                           double& result,
00074                                           MsqMatrix< 2, 2 >& deriv_wrt_T,
00075                                           MsqError& /*err*/ )
00076 {
00077     double frob_sqr = sqr_Frobenius( T );
00078     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00079 
00080     double a = 1e-12;
00081     while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
00082     {
00083         MsqMatrix< 2, 2 > Tdelta( T );
00084         Tdelta( 0, 0 ) += a;
00085         Tdelta( 1, 1 ) += a;
00086         a *= 2.0;
00087         frob_sqr = sqr_Frobenius( Tdelta );
00088         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00089         if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
00090     }
00091 
00092     // MsqMatrix<2,2> d_psi = 1.0/psi * (T + transpose_adj(T));
00093     // deriv_wrt_T = (1.0/psi) * (T - result * d_psi);
00094     if( psi > 1e-50 )
00095     {
00096         const double f = result / ( psi * psi );
00097         deriv_wrt_T    = transpose_adj( T );
00098         deriv_wrt_T *= -f;
00099         deriv_wrt_T += ( 1.0 / psi - f ) * T;
00100     }
00101 
00102     result -= 1.0;
00103 
00104     return true;
00105 }
00106 
00107 bool TShapeSize2DNB2::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
00108                                           double& result,
00109                                           MsqMatrix< 2, 2 >& deriv_wrt_T,
00110                                           MsqMatrix< 2, 2 > second[3],
00111                                           MsqError& /*err*/ )
00112 {
00113     double frob_sqr = sqr_Frobenius( T );
00114     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00115 
00116     double a = 1e-12;
00117     while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
00118     {
00119         MsqMatrix< 2, 2 > Tdelta( T );
00120         Tdelta( 0, 0 ) += a;
00121         Tdelta( 1, 1 ) += a;
00122         a *= 2.0;
00123         frob_sqr = sqr_Frobenius( Tdelta );
00124         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00125         if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
00126     }
00127 
00128     const double inv_psi    = 1.0 / psi;
00129     MsqMatrix< 2, 2 > d_psi = T + transpose_adj( T );
00130     d_psi *= inv_psi;
00131 
00132     deriv_wrt_T = d_psi;
00133     deriv_wrt_T *= -result;
00134     deriv_wrt_T += T;
00135     deriv_wrt_T *= inv_psi;
00136 
00137     set_scaled_2nd_deriv_wrt_psi( second, -result * inv_psi, psi, T );
00138     pluseq_scaled_outer_product( second, 2 * result * inv_psi * inv_psi, d_psi );
00139     pluseq_scaled_sum_outer_product( second, -inv_psi * inv_psi, d_psi, T );
00140     pluseq_scaled_I( second, inv_psi );
00141 
00142     result -= 1.0;
00143 
00144     return true;
00145 }
00146 
00147 }  // namespace MBMesquite
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