LinearTriangle.cpp

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

    Copyright 2006 Lawrence Livermore National Laboratory.  Under
    the terms of Contract B545069 with the University of Wisconsin --
    Madison, Lawrence Livermore National Laboratory retains certain
    rights in 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

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

#include "Mesquite.hpp"
#include "MsqError.hpp"
#include "LinearTriangle.hpp"

namespace MBMesquite
{

static const char* nonlinear_error = "Attempt to use LinearTriangle mapping function for a nonlinear element\n";

EntityTopology LinearTriangle::element_topology() const
{
    return TRIANGLE;
}

int LinearTriangle::num_nodes() const
{
    return 3;
}

NodeSet LinearTriangle::sample_points( NodeSet ) const
{
    NodeSet result;
    result.set_mid_face_node( 0 );
    return result;
}

void LinearTriangle::coefficients( Sample loc, NodeSet nodeset, double* coeff_out, size_t* indices_out,
                                   size_t& num_coeff, MsqError& err ) const
{
    if( nodeset.have_any_mid_node() )
    {
        MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT );
        return;
    }

    switch( loc.dimension )
    {
        case 0:
            num_coeff      = 1;
            indices_out[0] = loc.number;
            coeff_out[0]   = 1.0;
            break;
        case 1:
            num_coeff      = 2;
            indices_out[0] = loc.number;
            indices_out[1] = ( loc.number + 1 ) % 3;
            coeff_out[0]   = 0.5;
            coeff_out[1]   = 0.5;
            break;
        case 2:
            num_coeff      = 3;
            indices_out[0] = 0;
            indices_out[1] = 1;
            indices_out[2] = 2;
            coeff_out[0] = coeff_out[1] = coeff_out[2] = MSQ_ONE_THIRD;
            break;
        default:
            MSQ_SETERR( err )( "Invalid/unsupported logical dimension", MsqError::INVALID_ARG );
    }
}

void LinearTriangle::derivatives( Sample, NodeSet nodeset, size_t* vertices, MsqVector< 2 >* coeff_derivs,
                                  size_t& num_vtx, MsqError& err ) const
{
    if( nodeset.have_any_mid_node() ) { MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT ); }
    else
    {
        num_vtx     = 3;
        vertices[0] = 0;
        vertices[1] = 1;
        vertices[2] = 2;

        coeff_derivs[0][0] = -1.0;
        coeff_derivs[0][1] = -1.0;
        coeff_derivs[1][0] = 1.0;
        coeff_derivs[1][1] = 0.0;
        coeff_derivs[2][0] = 0.0;
        coeff_derivs[2][1] = 1.0;
    }
}

void LinearTriangle::ideal( Sample, MsqMatrix< 3, 2 >& J, MsqError& ) const
{
    //  const double g = 1.074569931823542; // sqrt(2/sqrt(3));
    //  J(0,0) = g;    J(0,1) = 0.5*g;
    //  J(1,0) = 0.0;  J(1,1) = 1.0/g;
    //  J(2,0) = 0.0;  J(2,1) = 0.0;
    const double a = 0.70710678118654746;  // 1/sqrt(2)
    const double b = 1.3160740129524924;   // 4th root of 3
    J( 0, 0 )      = -a / b;
    J( 0, 1 )      = a / b;
    J( 1, 0 )      = -a * b;
    J( 1, 1 )      = -a * b;
    J( 2, 0 )      = 0.0;
    J( 2, 1 )      = 0.0;
}

}  // namespace MBMesquite