LinearHex.cpp

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#include "moab/LocalDiscretization/LinearHex.hpp"
#include "moab/Matrix3.hpp"
#include "moab/Forward.hpp"
#include <cmath>
#include <limits>

namespace moab
{

const double LinearHex::corner[8][3] = { { -1, -1, -1 }, { 1, -1, -1 }, { 1, 1, -1 }, { -1, 1, -1 },
                                         { -1, -1, 1 },  { 1, -1, 1 },  { 1, 1, 1 },  { -1, 1, 1 } };

/* For each point, its weight and location are stored as an array.
   Hence, the inner dimension is 2, the outer dimension is gauss_count.
   We use a one-point Gaussian quadrature, since it integrates linear functions exactly.
*/
const double LinearHex::gauss[1][2] = { { 2.0, 0.0 } };

ErrorCode LinearHex::jacobianFcn( const double* params,
                                  const double* verts,
                                  const int /*nverts*/,
                                  const int ndim,
                                  double*,
                                  double* result )
{
    assert( params && verts );
    Matrix3* J = reinterpret_cast< Matrix3* >( result );
    *J         = Matrix3( 0.0 );
    for( unsigned i = 0; i < 8; ++i )
    {
        const double params_p    = 1 + params[0] * corner[i][0];
        const double eta_p       = 1 + params[1] * corner[i][1];
        const double zeta_p      = 1 + params[2] * corner[i][2];
        const double dNi_dparams = corner[i][0] * eta_p * zeta_p;
        const double dNi_deta    = corner[i][1] * params_p * zeta_p;
        const double dNi_dzeta   = corner[i][2] * params_p * eta_p;
        ( *J )( 0, 0 ) += dNi_dparams * verts[i * ndim + 0];
        ( *J )( 1, 0 ) += dNi_dparams * verts[i * ndim + 1];
        ( *J )( 2, 0 ) += dNi_dparams * verts[i * ndim + 2];
        ( *J )( 0, 1 ) += dNi_deta * verts[i * ndim + 0];
        ( *J )( 1, 1 ) += dNi_deta * verts[i * ndim + 1];
        ( *J )( 2, 1 ) += dNi_deta * verts[i * ndim + 2];
        ( *J )( 0, 2 ) += dNi_dzeta * verts[i * ndim + 0];
        ( *J )( 1, 2 ) += dNi_dzeta * verts[i * ndim + 1];
        ( *J )( 2, 2 ) += dNi_dzeta * verts[i * ndim + 2];
    }
    ( *J ) *= 0.125;
    return MB_SUCCESS;
}  // LinearHex::jacobian()

ErrorCode LinearHex::evalFcn( const double* params,
                              const double* field,
                              const int /*ndim*/,
                              const int num_tuples,
                              double*,
                              double* result )
{
    assert( params && field && num_tuples != -1 );
    for( int i = 0; i < num_tuples; i++ )
        result[i] = 0.0;
    for( unsigned i = 0; i < 8; ++i )
    {
        const double N_i =
            ( 1 + params[0] * corner[i][0] ) * ( 1 + params[1] * corner[i][1] ) * ( 1 + params[2] * corner[i][2] );
        for( int j = 0; j < num_tuples; j++ )
            result[j] += N_i * field[i * num_tuples + j];
    }
    for( int i = 0; i < num_tuples; i++ )
        result[i] *= 0.125;

    return MB_SUCCESS;
}

ErrorCode LinearHex::integrateFcn( const double* field,
                                   const double* verts,
                                   const int nverts,
                                   const int ndim,
                                   const int num_tuples,
                                   double* work,
                                   double* result )
{
    assert( field && verts && num_tuples != -1 );
    double tmp_result[8];
    ErrorCode rval = MB_SUCCESS;
    for( int i = 0; i < num_tuples; i++ )
        result[i] = 0.0;
    CartVect x;
    Matrix3 J;
    for( unsigned int j1 = 0; j1 < LinearHex::gauss_count; ++j1 )
    {
        x[0]      = LinearHex::gauss[j1][1];
        double w1 = LinearHex::gauss[j1][0];
        for( unsigned int j2 = 0; j2 < LinearHex::gauss_count; ++j2 )
        {
            x[1]      = LinearHex::gauss[j2][1];
            double w2 = LinearHex::gauss[j2][0];
            for( unsigned int j3 = 0; j3 < LinearHex::gauss_count; ++j3 )
            {
                x[2]      = LinearHex::gauss[j3][1];
                double w3 = LinearHex::gauss[j3][0];
                rval      = evalFcn( x.array(), field, ndim, num_tuples, NULL, tmp_result );
                if( MB_SUCCESS != rval ) return rval;
                rval = jacobianFcn( x.array(), verts, nverts, ndim, work, J[0] );
                if( MB_SUCCESS != rval ) return rval;
                double tmp_det = w1 * w2 * w3 * J.determinant();
                for( int i = 0; i < num_tuples; i++ )
                    result[i] += tmp_result[i] * tmp_det;
            }
        }
    }

    return MB_SUCCESS;
}  // LinearHex::integrate_vector()

ErrorCode LinearHex::reverseEvalFcn( EvalFcn eval,
                                     JacobianFcn jacob,
                                     InsideFcn ins,
                                     const double* posn,
                                     const double* verts,
                                     const int nverts,
                                     const int ndim,
                                     const double iter_tol,
                                     const double inside_tol,
                                     double* work,
                                     double* params,
                                     int* is_inside )
{
    assert( posn && verts );
    return EvalSet::evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
                                      is_inside );
}

int LinearHex::insideFcn( const double* params, const int ndim, const double tol )
{
    return EvalSet::inside_function( params, ndim, tol );
}

ErrorCode LinearHex::normalFcn( const int ientDim,
                                const int facet,
                                const int nverts,
                                const double* verts,
                                double normal[3] )
{
    // assert(facet < 6 && ientDim == 2 && nverts == 8);
    if( nverts != 8 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed hex :: expected value = 8 " );
    if( ientDim != 2 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 2 " );
    if( facet > 6 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local face id :: expected value = one of 0-5" );

    int id0 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][0];
    int id1 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][1];
    int id2 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][3];

    double x0[3], x1[3];

    for( int i = 0; i < 3; i++ )
    {
        x0[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
        x1[i] = verts[3 * id2 + i] - verts[3 * id0 + i];
    }

    double a   = x0[1] * x1[2] - x1[1] * x0[2];
    double b   = x1[0] * x0[2] - x0[0] * x1[2];
    double c   = x0[0] * x1[1] - x1[0] * x0[1];
    double nrm = sqrt( a * a + b * b + c * c );

    if( nrm > std::numeric_limits< double >::epsilon() )
    {
        normal[0] = a / nrm;
        normal[1] = b / nrm;
        normal[2] = c / nrm;
    }
    return MB_SUCCESS;
}

}  // namespace moab