TShapeB1.cpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2006 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2006) kraftche@cae.wisc.edu

  ***************************************************************** */

/** \file TShapeB1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeB1.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string TShapeB1::get_name() const
{
    return "TShapeB1";
}

TShapeB1::~TShapeB1() {}

bool TShapeB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    result = 0.5 * sqr_Frobenius( T ) / d - 1;
    return true;
}

bool TShapeB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                   double& result,
                                   MsqMatrix< 2, 2 >& deriv_wrt_T,
                                   MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    double inv_d = 1.0 / d;
    result       = 0.5 * sqr_Frobenius( T ) * inv_d;
    deriv_wrt_T  = T;
    deriv_wrt_T -= result * transpose_adj( T );
    deriv_wrt_T *= inv_d;

    result -= 1.0;
    return true;
}

/** \f$ \frac{\partial^2 \mu}{\partial T^2}
      = \frac{1}{\tau} I_4
      - \frac{1}{\tau^2} \left( T \otimes \frac{\partial \tau}{\partial T}
                          + \frac{\partial \tau}{\partial T} \otimes T \right)
      + \frac{|T|^2}{\tau^3} \left( \frac{\partial \tau}{\partial T} \otimes
                               \frac{\partial \tau}{\partial T} \right)
      - \frac{|T|^2}{2 \tau^3} \frac{\partial^2 \tau}{\partial T^2} \f$
  */
bool TShapeB1::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                   double& result,
                                   MsqMatrix< 2, 2 >& deriv_wrt_T,
                                   MsqMatrix< 2, 2 > second_wrt_T[3],
                                   MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    double inv_d                 = 1.0 / d;
    double f1                    = sqr_Frobenius( T ) * inv_d;
    result                       = 0.5 * f1;
    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    deriv_wrt_T                  = T;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= inv_d;

    set_scaled_outer_product( second_wrt_T, f1 * inv_d * inv_d, adjt );
    pluseq_scaled_sum_outer_product( second_wrt_T, -inv_d * inv_d, T, adjt );
    pluseq_scaled_I( second_wrt_T, inv_d );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * inv_d );

    result -= 1.0;
    return true;
}

bool TShapeB1::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    double f   = Frobenius( T );
    double d   = det( T );
    double den = 3 * MSQ_SQRT_THREE * d;

    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = ( f * f * f ) / den - 1.0;
    return true;
}

bool TShapeB1::evaluate_with_grad( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T, MsqError& err )
{
    double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    double norm      = Frobenius( T );
    double den       = 1.0 / ( 3 * MSQ_SQRT_THREE * d );
    double norm_cube = norm * norm * norm;
    result           = norm_cube * den - 1.0;
    wrt_T            = T;
    wrt_T *= 3 * norm * den;
    wrt_T -= norm_cube * den / d * transpose_adj( T );
    return true;
}

bool TShapeB1::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                   double& result,
                                   MsqMatrix< 3, 3 >& deriv_wrt_T,
                                   MsqMatrix< 3, 3 > second_wrt_T[6],
                                   MsqError& err )
{
    double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    double id              = 1.0 / d;
    double norm            = Frobenius( T );
    double den             = 1.0 / ( 3 * MSQ_SQRT_THREE * d );
    double norm_cube       = norm * norm * norm;
    result                 = norm_cube * den - 1.0;
    MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    deriv_wrt_T            = T;
    deriv_wrt_T *= 3 * norm * den;
    deriv_wrt_T -= norm_cube * den * id * transpose_adj( T );

    set_scaled_outer_product( second_wrt_T, 3 * den / norm, T );
    pluseq_scaled_I( second_wrt_T, 3 * norm * den );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -den * norm_cube * id, T );
    pluseq_scaled_outer_product( second_wrt_T, 2 * den * norm_cube * id * id, adjt );
    pluseq_scaled_sum_outer_product( second_wrt_T, -3 * norm * den * id, T, adjt );

    return true;
}

}  // namespace MBMesquite