LinearHexahedron.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]

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

/** \file LinearHexahedron.cpp
 *  \brief Implement shape function for linear hexahedron
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "MsqError.hpp"
#include "LinearHexahedron.hpp"

namespace MBMesquite
{

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

EntityTopology LinearHexahedron::element_topology() const
{
    return HEXAHEDRON;
}

int LinearHexahedron::num_nodes() const
{
    return 8;
}

static inline int coeff_xi_sign( unsigned coeff )
{
    return 2 * ( ( ( coeff + 1 ) / 2 ) % 2 ) - 1;
}
static inline int coeff_eta_sign( unsigned coeff )
{
    return 2 * ( ( coeff / 2 ) % 2 ) - 1;
}
static inline int coeff_zeta_sign( unsigned coeff )
{
    return 2 * ( coeff / 4 ) - 1;
}

static void coefficients_at_corner( unsigned corner, double* coeff_out, size_t* indices_out, size_t& num_coeff )
{
    num_coeff      = 1;
    coeff_out[0]   = 1.0;
    indices_out[0] = corner;
}

const unsigned xi = 0, eta = 1, zeta = 2;
const int edge_dir[]       = { xi, eta, xi, eta, zeta, zeta, zeta, zeta, xi, eta, xi, eta };
const int edge_beg[]       = { 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7 };    // start vertex by edge number
const int edge_end[]       = { 1, 2, 3, 0, 4, 5, 6, 7, 5, 6, 7, 4 };    // end vetex by edge number
const int edge_opposite[]  = { 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1 };  // opposite edge
const int edge_beg_orth1[] = { 3, 5, 1, 7, 1, 0,
                               3, 2, 7, 1, 5, 3 };  // vtx adjacent to edge start in edge_dir[e]+1 direction
const int edge_beg_orth2[] = { 4, 0, 6, 2, 3, 2,
                               1, 0, 0, 4, 2, 6 };  // vtx adjacent to edge start in edge_dir[e]+2 direction
const int edge_end_orth1[] = { 2, 6, 0, 4, 5, 4,
                               7, 6, 6, 2, 4, 0 };  // vtx adjacent to edge end in edge_dir[e]+1 direction
const int edge_end_orth2[] = { 5, 3, 7, 1, 7, 6,
                               5, 4, 1, 7, 3, 5 };  // vtx adjacent to edge end in edge_dir[e]+2 direction

static void coefficients_at_mid_edge( unsigned edge, double* coeff_out, size_t* indices_out, size_t& num_coeff )
{
    num_coeff      = 2;
    coeff_out[0]   = 0.5;
    coeff_out[1]   = 0.5;
    indices_out[0] = edge_beg[edge];
    indices_out[1] = edge_end[edge];
}

const int face_vtx[6][4] = { { 0, 1, 4, 5 },                  // face 0 vertices
                             { 1, 2, 5, 6 },                  // face 1 vertices
                             { 2, 3, 6, 7 },                  // face 2
                             { 0, 3, 4, 7 },                  // face 3
                             { 0, 1, 2, 3 },                  // face 4
                             { 4, 5, 6, 7 } };                // face 5
const int face_opp[6]    = { 2, 3, 0, 1, 5, 4 };              // opposite faces on hex
const int face_dir[6]    = { eta, xi, eta, xi, zeta, zeta };  // normal direction

static void coefficients_at_mid_face( unsigned face, double* coeff_out, size_t* indices_out, size_t& num_coeff )
{
    num_coeff      = 4;
    coeff_out[0]   = 0.25;
    coeff_out[1]   = 0.25;
    coeff_out[2]   = 0.25;
    coeff_out[3]   = 0.25;
    indices_out[0] = face_vtx[face][0];
    indices_out[1] = face_vtx[face][1];
    indices_out[2] = face_vtx[face][2];
    indices_out[3] = face_vtx[face][3];
}

static void coefficients_at_mid_elem( double* coeff_out, size_t* indices_out, size_t& num_coeff )
{
    num_coeff      = 8;
    coeff_out[0]   = 0.125;
    coeff_out[1]   = 0.125;
    coeff_out[2]   = 0.125;
    coeff_out[3]   = 0.125;
    coeff_out[4]   = 0.125;
    coeff_out[5]   = 0.125;
    coeff_out[6]   = 0.125;
    coeff_out[7]   = 0.125;
    indices_out[0] = 0;
    indices_out[1] = 1;
    indices_out[2] = 2;
    indices_out[3] = 3;
    indices_out[4] = 4;
    indices_out[5] = 5;
    indices_out[6] = 6;
    indices_out[7] = 7;
}

void LinearHexahedron::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:
            coefficients_at_corner( loc.number, coeff_out, indices_out, num_coeff );
            break;
        case 1:
            coefficients_at_mid_edge( loc.number, coeff_out, indices_out, num_coeff );
            break;
        case 2:
            coefficients_at_mid_face( loc.number, coeff_out, indices_out, num_coeff );
            break;
        case 3:
            coefficients_at_mid_elem( coeff_out, indices_out, num_coeff );
            break;
        default:
            MSQ_SETERR( err )( "Invalid/unsupported logical dimension", MsqError::INVALID_ARG );
    }
}

static void derivatives_at_corner( unsigned corner,
                                   size_t* vertex_indices_out,
                                   MsqVector< 3 >* d_coeff_d_xi_out,
                                   size_t& num_vtx )
{
    const int xi_sign   = coeff_xi_sign( corner );
    const int eta_sign  = coeff_eta_sign( corner );
    const int zeta_sign = coeff_zeta_sign( corner );
    const int offset    = 4 * ( corner / 4 );
    // const int adj_in_xi   = offset + (9 - corner)%4;
    const int adj_in_xi   = corner + 1 - 2 * ( corner % 2 );
    const int adj_in_eta  = 3 + 2 * offset - (int)corner;
    const int adj_in_zeta = corner - zeta_sign * 4;

    num_vtx               = 4;
    vertex_indices_out[0] = corner;
    vertex_indices_out[1] = adj_in_xi;
    vertex_indices_out[2] = adj_in_eta;
    vertex_indices_out[3] = adj_in_zeta;

    d_coeff_d_xi_out[0][0] = xi_sign;
    d_coeff_d_xi_out[0][1] = eta_sign;
    d_coeff_d_xi_out[0][2] = zeta_sign;

    d_coeff_d_xi_out[1][0] = -xi_sign;
    d_coeff_d_xi_out[1][1] = 0.0;
    d_coeff_d_xi_out[1][2] = 0.0;

    d_coeff_d_xi_out[2][0] = 0.0;
    d_coeff_d_xi_out[2][1] = -eta_sign;
    d_coeff_d_xi_out[2][2] = 0.0;

    d_coeff_d_xi_out[3][0] = 0.0;
    d_coeff_d_xi_out[3][1] = 0.0;
    d_coeff_d_xi_out[3][2] = -zeta_sign;
}

static void derivatives_at_mid_edge( unsigned edge,
                                     size_t* vertex_indices_out,
                                     MsqVector< 3 >* d_coeff_d_xi_out,
                                     size_t& num_vtx )
{
    const int direction = edge_dir[edge];
    const int ortho1    = ( direction + 1 ) % 3;
    const int ortho2    = ( direction + 2 ) % 3;
    const int vtx       = edge_beg[edge];
    const int signs[]   = { coeff_xi_sign( vtx ), coeff_eta_sign( vtx ), coeff_zeta_sign( vtx ) };
    const int sign_dir  = signs[direction];
    const int sign_or1  = signs[ortho1];
    const int sign_or2  = signs[ortho2];

    num_vtx               = 6;
    vertex_indices_out[0] = edge_beg[edge];
    vertex_indices_out[1] = edge_end[edge];
    vertex_indices_out[2] = edge_beg_orth1[edge];
    vertex_indices_out[3] = edge_end_orth1[edge];
    vertex_indices_out[4] = edge_beg_orth2[edge];
    vertex_indices_out[5] = edge_end_orth2[edge];

    d_coeff_d_xi_out[0][direction] = sign_dir;
    d_coeff_d_xi_out[0][ortho1]    = sign_or1 * 0.5;
    d_coeff_d_xi_out[0][ortho2]    = sign_or2 * 0.5;

    d_coeff_d_xi_out[1][direction] = -sign_dir;
    d_coeff_d_xi_out[1][ortho1]    = sign_or1 * 0.5;
    d_coeff_d_xi_out[1][ortho2]    = sign_or2 * 0.5;

    d_coeff_d_xi_out[2][direction] = 0.0;
    d_coeff_d_xi_out[2][ortho1]    = -sign_or1 * 0.5;
    d_coeff_d_xi_out[2][ortho2]    = 0.0;

    d_coeff_d_xi_out[3][direction] = 0.0;
    d_coeff_d_xi_out[3][ortho1]    = -sign_or1 * 0.5;
    d_coeff_d_xi_out[3][ortho2]    = 0.0;

    d_coeff_d_xi_out[4][direction] = 0.0;
    d_coeff_d_xi_out[4][ortho1]    = 0.0;
    d_coeff_d_xi_out[4][ortho2]    = -sign_or2 * 0.5;

    d_coeff_d_xi_out[5][direction] = 0.0;
    d_coeff_d_xi_out[5][ortho1]    = 0.0;
    d_coeff_d_xi_out[5][ortho2]    = -sign_or2 * 0.5;
}

static void derivatives_at_mid_face( unsigned face,
                                     size_t* vertex_indices_out,
                                     MsqVector< 3 >* d_coeff_d_xi_out,
                                     size_t& num_vtx )
{
    const int vtx_signs[4][3] = { { coeff_xi_sign( face_vtx[face][0] ), coeff_eta_sign( face_vtx[face][0] ),
                                    coeff_zeta_sign( face_vtx[face][0] ) },
                                  { coeff_xi_sign( face_vtx[face][1] ), coeff_eta_sign( face_vtx[face][1] ),
                                    coeff_zeta_sign( face_vtx[face][1] ) },
                                  { coeff_xi_sign( face_vtx[face][2] ), coeff_eta_sign( face_vtx[face][2] ),
                                    coeff_zeta_sign( face_vtx[face][2] ) },
                                  { coeff_xi_sign( face_vtx[face][3] ), coeff_eta_sign( face_vtx[face][3] ),
                                    coeff_zeta_sign( face_vtx[face][3] ) } };
    const int ortho_dir       = face_dir[face];
    const int face_dir1       = ( ortho_dir + 1 ) % 3;
    const int face_dir2       = ( ortho_dir + 2 ) % 3;
    const int ortho_sign      = vtx_signs[0][ortho_dir];  // same for all 4 verts

    num_vtx               = 8;
    vertex_indices_out[0] = face_vtx[face][0];
    vertex_indices_out[1] = face_vtx[face][1];
    vertex_indices_out[2] = face_vtx[face][2];
    vertex_indices_out[3] = face_vtx[face][3];
    vertex_indices_out[4] = face_vtx[face_opp[face]][0];
    vertex_indices_out[5] = face_vtx[face_opp[face]][1];
    vertex_indices_out[6] = face_vtx[face_opp[face]][2];
    vertex_indices_out[7] = face_vtx[face_opp[face]][3];

    d_coeff_d_xi_out[0][ortho_dir] = ortho_sign * 0.25;
    d_coeff_d_xi_out[0][face_dir1] = vtx_signs[0][face_dir1] * 0.5;
    d_coeff_d_xi_out[0][face_dir2] = vtx_signs[0][face_dir2] * 0.5;

    d_coeff_d_xi_out[1][ortho_dir] = ortho_sign * 0.25;
    d_coeff_d_xi_out[1][face_dir1] = vtx_signs[1][face_dir1] * 0.5;
    d_coeff_d_xi_out[1][face_dir2] = vtx_signs[1][face_dir2] * 0.5;

    d_coeff_d_xi_out[2][ortho_dir] = ortho_sign * 0.25;
    d_coeff_d_xi_out[2][face_dir1] = vtx_signs[2][face_dir1] * 0.5;
    d_coeff_d_xi_out[2][face_dir2] = vtx_signs[2][face_dir2] * 0.5;

    d_coeff_d_xi_out[3][ortho_dir] = ortho_sign * 0.25;
    d_coeff_d_xi_out[3][face_dir1] = vtx_signs[3][face_dir1] * 0.5;
    d_coeff_d_xi_out[3][face_dir2] = vtx_signs[3][face_dir2] * 0.5;

    d_coeff_d_xi_out[4][ortho_dir] = -ortho_sign * 0.25;
    d_coeff_d_xi_out[4][face_dir1] = 0.0;
    d_coeff_d_xi_out[4][face_dir2] = 0.0;

    d_coeff_d_xi_out[5][ortho_dir] = -ortho_sign * 0.25;
    d_coeff_d_xi_out[5][face_dir1] = 0.0;
    d_coeff_d_xi_out[5][face_dir2] = 0.0;

    d_coeff_d_xi_out[6][ortho_dir] = -ortho_sign * 0.25;
    d_coeff_d_xi_out[6][face_dir1] = 0.0;
    d_coeff_d_xi_out[6][face_dir2] = 0.0;

    d_coeff_d_xi_out[7][ortho_dir] = -ortho_sign * 0.25;
    d_coeff_d_xi_out[7][face_dir1] = 0.0;
    d_coeff_d_xi_out[7][face_dir2] = 0.0;
}

static void derivatives_at_mid_elem( size_t* vertex_indices_out, MsqVector< 3 >* d_coeff_d_xi_out, size_t& num_vtx )

{
    num_vtx               = 8;
    vertex_indices_out[0] = 0;
    vertex_indices_out[1] = 1;
    vertex_indices_out[2] = 2;
    vertex_indices_out[3] = 3;
    vertex_indices_out[4] = 4;
    vertex_indices_out[5] = 5;
    vertex_indices_out[6] = 6;
    vertex_indices_out[7] = 7;

    d_coeff_d_xi_out[0][0] = -0.25;
    d_coeff_d_xi_out[0][1] = -0.25;
    d_coeff_d_xi_out[0][2] = -0.25;

    d_coeff_d_xi_out[1][0] = 0.25;
    d_coeff_d_xi_out[1][1] = -0.25;
    d_coeff_d_xi_out[1][2] = -0.25;

    d_coeff_d_xi_out[2][0] = 0.25;
    d_coeff_d_xi_out[2][1] = 0.25;
    d_coeff_d_xi_out[2][2] = -0.25;

    d_coeff_d_xi_out[3][0] = -0.25;
    d_coeff_d_xi_out[3][1] = 0.25;
    d_coeff_d_xi_out[3][2] = -0.25;

    d_coeff_d_xi_out[4][0] = -0.25;
    d_coeff_d_xi_out[4][1] = -0.25;
    d_coeff_d_xi_out[4][2] = 0.25;

    d_coeff_d_xi_out[5][0] = 0.25;
    d_coeff_d_xi_out[5][1] = -0.25;
    d_coeff_d_xi_out[5][2] = 0.25;

    d_coeff_d_xi_out[6][0] = 0.25;
    d_coeff_d_xi_out[6][1] = 0.25;
    d_coeff_d_xi_out[6][2] = 0.25;

    d_coeff_d_xi_out[7][0] = -0.25;
    d_coeff_d_xi_out[7][1] = 0.25;
    d_coeff_d_xi_out[7][2] = 0.25;
}

void LinearHexahedron::derivatives( Sample loc,
                                    NodeSet nodeset,
                                    size_t* vertex_indices_out,
                                    MsqVector< 3 >* d_coeff_d_xi_out,
                                    size_t& num_vtx,
                                    MsqError& err ) const
{
    if( nodeset.have_any_mid_node() )
    {
        MSQ_SETERR( err )( nonlinear_error, MsqError::UNSUPPORTED_ELEMENT );
        return;
    }

    switch( loc.dimension )
    {
        case 0:
            derivatives_at_corner( loc.number, vertex_indices_out, d_coeff_d_xi_out, num_vtx );
            break;
        case 1:
            derivatives_at_mid_edge( loc.number, vertex_indices_out, d_coeff_d_xi_out, num_vtx );
            break;
        case 2:
            derivatives_at_mid_face( loc.number, vertex_indices_out, d_coeff_d_xi_out, num_vtx );
            break;
        case 3:
            derivatives_at_mid_elem( vertex_indices_out, d_coeff_d_xi_out, num_vtx );
            break;
        default:
            MSQ_SETERR( err )( "Invalid/unsupported logical dimension", MsqError::INVALID_ARG );
    }
}

void LinearHexahedron::ideal( Sample, MsqMatrix< 3, 3 >& J, MsqError& ) const
{
    J( 0, 0 ) = J( 1, 1 ) = J( 2, 2 ) = 1.0;
    J( 1, 0 ) = J( 0, 1 ) = J( 0, 2 ) = 0.0;
    J( 2, 0 ) = J( 2, 1 ) = J( 1, 2 ) = 0.0;
}

}  // namespace MBMesquite