LinearTet.cpp

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#include "moab/LocalDiscretization/LinearTet.hpp"
#include "moab/Forward.hpp"
#include <algorithm>
#include <cmath>
#include <limits>

namespace moab
{

const double LinearTet::corner[4][3] = { { 0, 0, 0 }, { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } };

ErrorCode LinearTet::initFcn( const double* verts, const int nverts, double*& work )
{
    // allocate work array as:
    // work[0..8] = T
    // work[9..17] = Tinv
    // work[18] = detT
    // work[19] = detTinv
    if( nverts != 4 )
    {
        std::cout << "Invalid Tetrahedron. Expected 4 vertices.\n";
        return MB_FAILURE;
    }

    assert( verts );

    Matrix3 J( verts[1 * 3 + 0] - verts[0 * 3 + 0], verts[2 * 3 + 0] - verts[0 * 3 + 0],
               verts[3 * 3 + 0] - verts[0 * 3 + 0], verts[1 * 3 + 1] - verts[0 * 3 + 1],
               verts[2 * 3 + 1] - verts[0 * 3 + 1], verts[3 * 3 + 1] - verts[0 * 3 + 1],
               verts[1 * 3 + 2] - verts[0 * 3 + 2], verts[2 * 3 + 2] - verts[0 * 3 + 2],
               verts[3 * 3 + 2] - verts[0 * 3 + 2] );

    // Update the work array
    if( !work ) work = new double[20];

    J.copyto( work );
    J.inverse().copyto( work + Matrix3::size );
    work[18] = J.determinant();
    work[19] = ( work[18] < 1e-12 ? std::numeric_limits< double >::max() : 1.0 / work[18] );

    return MB_SUCCESS;
}

ErrorCode LinearTet::evalFcn( const double* params,
                              const double* field,
                              const int /*ndim*/,
                              const int num_tuples,
                              double* /*work*/,
                              double* result )
{
    assert( params && field && num_tuples > 0 );
    std::vector< double > f0( num_tuples );
    std::copy( field, field + num_tuples, f0.begin() );
    std::copy( field, field + num_tuples, result );

    for( unsigned i = 1; i < 4; ++i )
    {
        double p = 0.5 * ( params[i - 1] + 1 );  // transform from -1 <= p <= 1 to 0 <= p <= 1
        for( int j = 0; j < num_tuples; j++ )
            result[j] += ( field[i * num_tuples + j] - f0[j] ) * p;
    }

    return MB_SUCCESS;
}

ErrorCode LinearTet::integrateFcn( const double* field,
                                   const double* /*verts*/,
                                   const int nverts,
                                   const int /*ndim*/,
                                   const int num_tuples,
                                   double* work,
                                   double* result )
{
    assert( field && num_tuples > 0 );
    std::fill( result, result + num_tuples, 0.0 );
    for( int i = 0; i < nverts; ++i )
    {
        for( int j = 0; j < num_tuples; j++ )
            result[j] += field[i * num_tuples + j];
    }
    double tmp = work[18] / 24.0;
    for( int i = 0; i < num_tuples; i++ )
        result[i] *= tmp;

    return MB_SUCCESS;
}

ErrorCode LinearTet::jacobianFcn( const double*, const double*, const int, const int, double* work, double* result )
{
    // jacobian is cached in work array
    assert( work );
    std::copy( work, work + 9, result );
    return MB_SUCCESS;
}

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

int LinearTet::insideFcn( const double* params, const int, const double tol )
{
    return ( params[0] >= -1.0 - tol && params[1] >= -1.0 - tol && params[2] >= -1.0 - tol &&
             params[0] + params[1] + params[2] <= 1.0 + tol );
}

ErrorCode LinearTet::evaluate_reverse( EvalFcn eval,
                                       JacobianFcn jacob,
                                       InsideFcn inside_f,
                                       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* inside )
{
    // TODO: should differentiate between epsilons used for
    // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
    // right now, fix the tolerance used for NR
    const double error_tol_sqr = iter_tol * iter_tol;
    CartVect* cvparams         = reinterpret_cast< CartVect* >( params );
    const CartVect* cvposn     = reinterpret_cast< const CartVect* >( posn );

    // find best initial guess to improve convergence
    CartVect tmp_params[] = { CartVect( -1, -1, -1 ), CartVect( 1, -1, -1 ), CartVect( -1, 1, -1 ),
                              CartVect( -1, -1, 1 ) };
    double resl           = std::numeric_limits< double >::max();
    CartVect new_pos, tmp_pos;
    ErrorCode rval;
    for( unsigned int i = 0; i < 4; i++ )
    {
        rval = ( *eval )( tmp_params[i].array(), verts, ndim, ndim, work, tmp_pos.array() );
        if( MB_SUCCESS != rval ) return rval;
        double tmp_resl = ( tmp_pos - *cvposn ).length_squared();
        if( tmp_resl < resl )
        {
            *cvparams = tmp_params[i];
            new_pos   = tmp_pos;
            resl      = tmp_resl;
        }
    }

    // residual is diff between old and new pos; need to minimize that
    CartVect res = new_pos - *cvposn;
    Matrix3 J;
    rval = ( *jacob )( cvparams->array(), verts, nverts, ndim, work, J.array() );
#ifndef NDEBUG
    double det = J.determinant();
    assert( det > std::numeric_limits< double >::epsilon() );
#endif
    Matrix3 Ji = J.inverse();

    int iters = 0;
    // while |res| larger than tol
    int dum, *tmp_inside = ( inside ? inside : &dum );
    while( res % res > error_tol_sqr )
    {
        if( ++iters > 25 )
        {
            // if we haven't converged but we're outside, that's defined as success
            *tmp_inside = ( *inside_f )( params, ndim, inside_tol );
            if( !( *tmp_inside ) )
                return MB_SUCCESS;
            else
                return MB_INDEX_OUT_OF_RANGE;
        }

        // new params tries to eliminate residual
        *cvparams -= Ji * res;

        // get the new forward-evaluated position, and its difference from the target pt
        rval = ( *eval )( params, verts, ndim, ndim, work, new_pos.array() );
        if( MB_SUCCESS != rval ) return rval;
        res = new_pos - *cvposn;
    }

    if( inside ) *inside = ( *inside_f )( params, ndim, inside_tol );

    return MB_SUCCESS;
}  // Map::evaluate_reverse()

ErrorCode LinearTet::normalFcn( const int ientDim,
                                const int facet,
                                const int nverts,
                                const double* verts,
                                double normal[3] )
{
    // assert(facet < 4 && ientDim == 2 && nverts == 4);
    if( nverts != 4 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed tet :: expected value = 4 " );
    if( ientDim != 2 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 2 " );
    if( facet > 4 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local face id :: expected value = one of 0-3" );

    int id0 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][0];
    int id1 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][1];
    int id2 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][2];

    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