MOAB: Mesh Oriented datABase
(version 5.2.1)
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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 TShape3DB2.cpp 00028 * \brief 00029 * \author Jason Kraftcheck 00030 */ 00031 00032 #include "Mesquite.hpp" 00033 #include "TShape3DB2.hpp" 00034 #include "MsqMatrix.hpp" 00035 #include "MsqError.hpp" 00036 #include "TMPDerivs.hpp" 00037 00038 namespace MBMesquite 00039 { 00040 00041 TShape3DB2::~TShape3DB2() {} 00042 00043 std::string TShape3DB2::get_name() const 00044 { 00045 return "TShape3DB2"; 00046 } 00047 00048 // \mu_3(T) = \frac{ |T|^2 |adj(T)|^2 } {9 \tau^2} - 1 00049 bool TShape3DB2::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err ) 00050 { 00051 double f = sqr_Frobenius( T ); 00052 double g = sqr_Frobenius( adj( T ) ); 00053 double d = det( T ); 00054 if( invalid_determinant( d ) ) 00055 { 00056 MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED ); 00057 return false; 00058 } 00059 result = ( f * g ) / ( 9 * d * d ) - 1; 00060 return true; 00061 } 00062 00063 bool TShape3DB2::evaluate_with_grad( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T, 00064 MsqError& err ) 00065 { 00066 double f = sqr_Frobenius( T ); 00067 double g = sqr_Frobenius( adj( T ) ); 00068 double d = det( T ); 00069 if( invalid_determinant( d ) ) 00070 { 00071 MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED ); 00072 return false; 00073 } 00074 result = ( f * g ) / ( 9 * d * d ) - 1; 00075 00076 wrt_T = T; 00077 wrt_T *= ( g + f * f ); 00078 wrt_T -= f * ( T * transpose( T ) * T ); 00079 wrt_T -= f * g / d * transpose_adj( T ); 00080 wrt_T *= 2 / ( 9 * d * d ); 00081 00082 return true; 00083 } 00084 00085 bool TShape3DB2::evaluate_with_hess( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T, 00086 MsqMatrix< 3, 3 > second[6], MsqError& err ) 00087 { 00088 double f = sqr_Frobenius( T ); 00089 double g = sqr_Frobenius( adj( T ) ); 00090 double d = det( T ); 00091 if( invalid_determinant( d ) ) 00092 { 00093 MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED ); 00094 return false; 00095 } 00096 const double den = 1.0 / ( 9 * d * d ); 00097 result = f * g * den - 1; 00098 00099 MsqMatrix< 3, 3 > dg = 2 * ( f * T - T * transpose( T ) * T ); 00100 MsqMatrix< 3, 3 > df = 2 * T; 00101 MsqMatrix< 3, 3 > dtau = transpose_adj( T ); 00102 00103 wrt_T = g * df + f * dg - 2 * f * g / d * transpose_adj( T ); 00104 wrt_T *= den; 00105 00106 set_scaled_2nd_deriv_norm_sqr_adj( second, den * f, T ); 00107 pluseq_scaled_I( second, 2 * den * g ); 00108 pluseq_scaled_sum_outer_product( second, den, dg, df ); 00109 pluseq_scaled_sum_outer_product( second, -2 * den * g / d, df, dtau ); 00110 pluseq_scaled_sum_outer_product( second, -2 * den * f / d, dg, dtau ); 00111 pluseq_scaled_outer_product( second, 6 * den * f * g / ( d * d ), dtau ); 00112 pluseq_scaled_2nd_deriv_of_det( second, -2 * den * f * g / d, T ); 00113 00114 return true; 00115 } 00116 00117 } // namespace MBMesquite