LinearQuad.cpp

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

namespace moab
{

const double LinearQuad::corner[4][2] = { { -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 LinearQuad::gauss[1][2] = { { 2.0, 0.0 } };

ErrorCode LinearQuad::jacobianFcn( const double* params, const double* verts, const int /*nverts*/, const int /*ndim*/,
                                   double*, double* result )
{
    Matrix3* J = reinterpret_cast< Matrix3* >( result );
    *J         = Matrix3( 0.0 );
    for( unsigned i = 0; i < 4; ++i )
    {
        const double xi_p     = 1 + params[0] * corner[i][0];
        const double eta_p    = 1 + params[1] * corner[i][1];
        const double dNi_dxi  = corner[i][0] * eta_p;
        const double dNi_deta = corner[i][1] * xi_p;
        ( *J )( 0, 0 ) += dNi_dxi * verts[i * 3 + 0];
        ( *J )( 1, 0 ) += dNi_dxi * verts[i * 3 + 1];
        ( *J )( 0, 1 ) += dNi_deta * verts[i * 3 + 0];
        ( *J )( 1, 1 ) += dNi_deta * verts[i * 3 + 1];
    }
    ( *J ) *= 0.25;
    ( *J )( 2, 2 ) = 1.0; /* to make sure the Jacobian determinant is non-zero */
    return MB_SUCCESS;
}  // LinearQuad::jacobian()

ErrorCode LinearQuad::evalFcn( const double* params, const double* field, const int /*ndim*/, const int num_tuples,
                               double*, double* result )
{
    for( int i = 0; i < num_tuples; i++ )
        result[i] = 0.0;
    for( unsigned i = 0; i < 4; ++i )
    {
        const double N_i = ( 1 + params[0] * corner[i][0] ) * ( 1 + params[1] * corner[i][1] );
        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] *= 0.25;

    return MB_SUCCESS;
}

ErrorCode LinearQuad::integrateFcn( const double* field, const double* verts, const int nverts, const int ndim,
                                    const int num_tuples, double* work, double* result )
{
    double tmp_result[4];
    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 < LinearQuad::gauss_count; ++j1 )
    {
        x[0]      = LinearQuad::gauss[j1][1];
        double w1 = LinearQuad::gauss[j1][0];
        for( unsigned int j2 = 0; j2 < LinearQuad::gauss_count; ++j2 )
        {
            x[1]      = LinearQuad::gauss[j2][1];
            double w2 = LinearQuad::gauss[j2][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 * J.determinant();
            for( int i = 0; i < num_tuples; i++ )
                result[i] += tmp_result[i] * tmp_det;
        }
    }
    return MB_SUCCESS;
}  // LinearHex::integrate_vector()

ErrorCode LinearQuad::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 )
{
    return EvalSet::evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
                                      is_inside );
}

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

ErrorCode LinearQuad::normalFcn( const int ientDim, const int facet, const int nverts, const double* verts,
                                 double normal[3] )
{
    // assert(facet <4 && ientDim == 1 && nverts==4);
    if( nverts != 4 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed quad :: expected value = 4" );
    if( ientDim != 1 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 1 " );
    if( facet > 4 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local edge id :: expected value = one of 0-3" );

    // Get the local vertex ids of  local edge
    int id0 = CN::mConnectivityMap[MBQUAD][ientDim - 1].conn[facet][0];
    int id1 = CN::mConnectivityMap[MBQUAD][ientDim - 1].conn[facet][1];

    // Find a vector along the edge
    double edge[3];
    for( int i = 0; i < 3; i++ )
    {
        edge[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
    }
    // Find the normal of the face
    double x0[3], x1[3], fnrm[3];
    for( int i = 0; i < 3; i++ )
    {
        x0[i] = verts[3 * 1 + i] - verts[3 * 0 + i];
        x1[i] = verts[3 * 3 + i] - verts[3 * 0 + i];
    }
    fnrm[0] = x0[1] * x1[2] - x1[1] * x0[2];
    fnrm[1] = x1[0] * x0[2] - x0[0] * x1[2];
    fnrm[2] = x0[0] * x1[1] - x1[0] * x0[1];

    // Find the normal of the edge as the cross product of edge and face normal

    double a   = edge[1] * fnrm[2] - fnrm[1] * edge[2];
    double b   = edge[2] * fnrm[0] - fnrm[2] * edge[0];
    double c   = edge[0] * fnrm[1] - fnrm[0] * edge[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