TShapeSizeNB3.cpp

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

    Copyright 2009 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

    (2009) kraftche@cae.wisc.edu

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

/** \file TShapeSizeNB3.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSizeNB3.hpp"
#include "MsqMatrix.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string TShapeSizeNB3::get_name() const
{
    return "TShapeSizeNB3";
}

TShapeSizeNB3::~TShapeSizeNB3() {}

bool TShapeSizeNB3::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& )
{
    const double nT   = sqr_Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;
    return true;
}

bool TShapeSizeNB3::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                        double& result,
                                        MsqMatrix< 2, 2 >& deriv_wrt_T,
                                        MsqError& /*err*/ )
{
    const double nT   = sqr_Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;

    deriv_wrt_T = T;
    deriv_wrt_T *= 4;
    deriv_wrt_T += ( 2 * mGamma * tau1 - 4 ) * transpose_adj( T );

    return true;
}

bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                        double& result,
                                        MsqMatrix< 2, 2 >& deriv_wrt_T,
                                        MsqMatrix< 2, 2 > second[3],
                                        MsqError& /*err*/ )
{
    const double nT   = sqr_Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = 2 * nT - 4 * tau + mGamma * tau1 * tau1;

    const double f               = 2 * mGamma * tau1 - 4;
    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    deriv_wrt_T                  = T;
    deriv_wrt_T *= 4;
    deriv_wrt_T += f * adjt;

    set_scaled_outer_product( second, 2 * mGamma, adjt );
    pluseq_scaled_I( second, 4 );
    pluseq_scaled_2nd_deriv_of_det( second, f );

    return true;
}

bool TShapeSizeNB3::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
{
    const double nT   = Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;
    return true;
}

bool TShapeSizeNB3::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                        double& result,
                                        MsqMatrix< 3, 3 >& wrt_T,
                                        MsqError& /*err*/ )
{
    const double nT   = Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;

    wrt_T = T;
    wrt_T *= 3 * nT;
    wrt_T -= ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ) * transpose_adj( T );

    return true;
}

bool TShapeSizeNB3::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                        double& result,
                                        MsqMatrix< 3, 3 >& wrt_T,
                                        MsqMatrix< 3, 3 > second[6],
                                        MsqError& /*err*/ )
{
    const double nT   = Frobenius( T );
    const double tau  = det( T );
    const double tau1 = tau - 1;
    result            = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1;

    const double f               = ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 );
    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    wrt_T                        = T;
    wrt_T *= 3 * nT;
    wrt_T -= f * adjt;

    set_scaled_outer_product( second, 2 * mGamma, adjt );
    pluseq_scaled_2nd_deriv_of_det( second, -f, T );
    pluseq_scaled_I( second, 3 * nT );
    // Could perturb T a bit if the norm is zero, but that would just
    // result in the coefficent of the outer product being practically
    // zero, so just skip the outer product in that case.
    // Anyway nT approaches zero as T does, so the limit of this term
    // as nT approaches zero is zero.
    if( nT > 1e-100 )  // NOTE: nT is always positive
        pluseq_scaled_outer_product( second, 3 / nT, T );

    return true;
}

}  // namespace MBMesquite