LinearTetrahedron.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) [email protected]

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

#include "Mesquite.hpp"
#include "MsqError.hpp"
#include "LinearTetrahedron.hpp"

namespace MBMesquite
{

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

EntityTopology LinearTetrahedron::element_topology() const
{
    return TETRAHEDRON;
}

int LinearTetrahedron::num_nodes() const
{
    return 4;
}

NodeSet LinearTetrahedron::sample_points( NodeSet ) const
{
    NodeSet result;
    result.set_mid_region_node();
    return result;
}

static const unsigned faces[][3] = { { 1, 0, 3 }, { 3, 2, 1 }, { 0, 2, 3 }, { 0, 1, 2 } };

void LinearTetrahedron::coefficients( Sample location,
                                      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( location.dimension )
    {
        case 0:
            num_coeff      = 1;
            indices_out[0] = location.number;
            coeff_out[0]   = 1.0;
            break;
        case 1:
            num_coeff    = 2;
            coeff_out[0] = 0.5;
            coeff_out[1] = 0.5;
            if( location.number < 3 )
            {
                indices_out[0] = location.number;
                indices_out[1] = ( location.number + 1 ) % 3;
            }
            else
            {
                indices_out[0] = location.number - 3;
                indices_out[1] = 3;
            }
            break;
        case 2:
            num_coeff      = 3;
            indices_out[0] = faces[location.number][0];
            indices_out[1] = faces[location.number][1];
            indices_out[2] = faces[location.number][2];
            coeff_out[0] = coeff_out[1] = coeff_out[2] = coeff_out[3] = MSQ_ONE_THIRD;
            break;
        case 3:
            num_coeff      = 4;
            indices_out[0] = 0;
            indices_out[1] = 1;
            indices_out[2] = 2;
            indices_out[3] = 3;
            coeff_out[0] = coeff_out[1] = coeff_out[2] = coeff_out[3] = 0.25;
            break;
        default:
            MSQ_SETERR( err )( "Invalid/unsupported logical dimension", MsqError::INVALID_ARG );
    }
}

void LinearTetrahedron::derivatives( Sample,
                                     NodeSet nodeset,
                                     size_t* vertices,
                                     MsqVector< 3 >* coeff_derivs,
                                     size_t& num_vtx,
                                     MsqError& err ) const
{
    if( nodeset.have_any_mid_node() )
    {
        MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT );
        return;
    }
    else
    {
        num_vtx     = 4;
        vertices[0] = 0;
        vertices[1] = 1;
        vertices[2] = 2;
        vertices[3] = 3;

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

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

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

        coeff_derivs[3][0] = 0.0;
        coeff_derivs[3][1] = 0.0;
        coeff_derivs[3][2] = 1.0;
    }
}

void LinearTetrahedron::ideal( Sample, MsqMatrix< 3, 3 >& J, MsqError& ) const
{
    const double a = 1.122462048309373;   // 6th root of 2
    const double b = 1.7320508075688772;  // sqrt(3)
    const double c = 1.5874010519681994;  // 2 to the 2/3
    J( 0, 0 )      = a;
    J( 0, 1 )      = 0.5 * a;
    J( 0, 2 )      = 0.5 * a;
    J( 1, 0 )      = 0.0;
    J( 1, 1 )      = 0.5 * a * b;
    J( 1, 2 )      = 0.5 * a / b;
    J( 2, 0 )      = 0.0;
    J( 2, 1 )      = 0.0;
    J( 2, 2 )      = c / b;
}

}  // namespace MBMesquite