MOAB: Mesh Oriented datABase  (version 5.2.1)
LinearTet.cpp
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00001 #include "moab/LocalDiscretization/LinearTet.hpp"
00002 #include "moab/Forward.hpp"
00003 #include <algorithm>
00004 #include <math.h>
00005 #include <limits>
00006 
00007 namespace moab
00008 {
00009 
00010 const double LinearTet::corner[4][3] = { { 0, 0, 0 }, { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } };
00011 
00012 ErrorCode LinearTet::initFcn( const double* verts, const int nverts, double*& work )
00013 {
00014     // allocate work array as:
00015     // work[0..8] = T
00016     // work[9..17] = Tinv
00017     // work[18] = detT
00018     // work[19] = detTinv
00019     assert( nverts == 4 && verts );
00020     if( !work ) work = new double[20];
00021 
00022     Matrix3 J( verts[1 * 3 + 0] - verts[0 * 3 + 0], verts[2 * 3 + 0] - verts[0 * 3 + 0],
00023                verts[3 * 3 + 0] - verts[0 * 3 + 0], verts[1 * 3 + 1] - verts[0 * 3 + 1],
00024                verts[2 * 3 + 1] - verts[0 * 3 + 1], verts[3 * 3 + 1] - verts[0 * 3 + 1],
00025                verts[1 * 3 + 2] - verts[0 * 3 + 2], verts[2 * 3 + 2] - verts[0 * 3 + 2],
00026                verts[3 * 3 + 2] - verts[0 * 3 + 2] );
00027     J.copyto( work );
00028     J.inverse().copyto( work + Matrix3::size );
00029     work[18] = J.determinant();
00030     work[19] = ( work[18] < 1e-12 ? std::numeric_limits< double >::max() : 1.0 / work[18] );
00031 
00032     return MB_SUCCESS;
00033 }
00034 
00035 ErrorCode LinearTet::evalFcn( const double* params, const double* field, const int /*ndim*/, const int num_tuples,
00036                               double* /*work*/, double* result )
00037 {
00038     assert( params && field && num_tuples > 0 );
00039     std::vector< double > f0( num_tuples );
00040     std::copy( field, field + num_tuples, f0.begin() );
00041     std::copy( field, field + num_tuples, result );
00042 
00043     for( unsigned i = 1; i < 4; ++i )
00044     {
00045         double p = 0.5 * ( params[i - 1] + 1 );  // transform from -1 <= p <= 1 to 0 <= p <= 1
00046         for( int j = 0; j < num_tuples; j++ )
00047             result[j] += ( field[i * num_tuples + j] - f0[j] ) * p;
00048     }
00049 
00050     return MB_SUCCESS;
00051 }
00052 
00053 ErrorCode LinearTet::integrateFcn( const double* field, const double* /*verts*/, const int nverts, const int /*ndim*/,
00054                                    const int num_tuples, double* work, double* result )
00055 {
00056     assert( field && num_tuples > 0 );
00057     std::fill( result, result + num_tuples, 0.0 );
00058     for( int i = 0; i < nverts; ++i )
00059     {
00060         for( int j = 0; j < num_tuples; j++ )
00061             result[j] += field[i * num_tuples + j];
00062     }
00063     double tmp = work[18] / 24.0;
00064     for( int i = 0; i < num_tuples; i++ )
00065         result[i] *= tmp;
00066 
00067     return MB_SUCCESS;
00068 }
00069 
00070 ErrorCode LinearTet::jacobianFcn( const double*, const double*, const int, const int, double* work, double* result )
00071 {
00072     // jacobian is cached in work array
00073     assert( work );
00074     std::copy( work, work + 9, result );
00075     return MB_SUCCESS;
00076 }
00077 
00078 ErrorCode LinearTet::reverseEvalFcn( EvalFcn eval, JacobianFcn jacob, InsideFcn ins, const double* posn,
00079                                      const double* verts, const int nverts, const int ndim, const double iter_tol,
00080                                      const double inside_tol, double* work, double* params, int* is_inside )
00081 {
00082     assert( posn && verts );
00083     return evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
00084                              is_inside );
00085 }
00086 
00087 int LinearTet::insideFcn( const double* params, const int, const double tol )
00088 {
00089     return ( params[0] >= -1.0 - tol && params[1] >= -1.0 - tol && params[2] >= -1.0 - tol &&
00090              params[0] + params[1] + params[2] <= 1.0 + tol );
00091 }
00092 
00093 ErrorCode LinearTet::evaluate_reverse( EvalFcn eval, JacobianFcn jacob, InsideFcn inside_f, const double* posn,
00094                                        const double* verts, const int nverts, const int ndim, const double iter_tol,
00095                                        const double inside_tol, double* work, double* params, int* inside )
00096 {
00097     // TODO: should differentiate between epsilons used for
00098     // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
00099     // right now, fix the tolerance used for NR
00100     const double error_tol_sqr = iter_tol * iter_tol;
00101     CartVect* cvparams         = reinterpret_cast< CartVect* >( params );
00102     const CartVect* cvposn     = reinterpret_cast< const CartVect* >( posn );
00103 
00104     // find best initial guess to improve convergence
00105     CartVect tmp_params[] = { CartVect( -1, -1, -1 ), CartVect( 1, -1, -1 ), CartVect( -1, 1, -1 ),
00106                               CartVect( -1, -1, 1 ) };
00107     double resl           = std::numeric_limits< double >::max();
00108     CartVect new_pos, tmp_pos;
00109     ErrorCode rval;
00110     for( unsigned int i = 0; i < 4; i++ )
00111     {
00112         rval = ( *eval )( tmp_params[i].array(), verts, ndim, ndim, work, tmp_pos.array() );
00113         if( MB_SUCCESS != rval ) return rval;
00114         double tmp_resl = ( tmp_pos - *cvposn ).length_squared();
00115         if( tmp_resl < resl )
00116         {
00117             *cvparams = tmp_params[i];
00118             new_pos   = tmp_pos;
00119             resl      = tmp_resl;
00120         }
00121     }
00122 
00123     // residual is diff between old and new pos; need to minimize that
00124     CartVect res = new_pos - *cvposn;
00125     Matrix3 J;
00126     rval = ( *jacob )( cvparams->array(), verts, nverts, ndim, work, J.array() );
00127 #ifndef NDEBUG
00128     double det = J.determinant();
00129     assert( det > std::numeric_limits< double >::epsilon() );
00130 #endif
00131     Matrix3 Ji = J.inverse();
00132 
00133     int iters = 0;
00134     // while |res| larger than tol
00135     int dum, *tmp_inside = ( inside ? inside : &dum );
00136     while( res % res > error_tol_sqr )
00137     {
00138         if( ++iters > 25 )
00139         {
00140             // if we haven't converged but we're outside, that's defined as success
00141             *tmp_inside = ( *inside_f )( params, ndim, inside_tol );
00142             if( !( *tmp_inside ) )
00143                 return MB_SUCCESS;
00144             else
00145                 return MB_INDEX_OUT_OF_RANGE;
00146         }
00147 
00148         // new params tries to eliminate residual
00149         *cvparams -= Ji * res;
00150 
00151         // get the new forward-evaluated position, and its difference from the target pt
00152         rval = ( *eval )( params, verts, ndim, ndim, work, new_pos.array() );
00153         if( MB_SUCCESS != rval ) return rval;
00154         res = new_pos - *cvposn;
00155     }
00156 
00157     if( inside ) *inside = ( *inside_f )( params, ndim, inside_tol );
00158 
00159     return MB_SUCCESS;
00160 }  // Map::evaluate_reverse()
00161 
00162 ErrorCode LinearTet::normalFcn( const int ientDim, const int facet, const int nverts, const double* verts,
00163                                 double normal[3] )
00164 {
00165     // assert(facet < 4 && ientDim == 2 && nverts == 4);
00166     if( nverts != 4 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed tet :: expected value = 4 " );
00167     if( ientDim != 2 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 2 " );
00168     if( facet > 4 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local face id :: expected value = one of 0-3" );
00169 
00170     int id0 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][0];
00171     int id1 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][1];
00172     int id2 = CN::mConnectivityMap[MBTET][ientDim - 1].conn[facet][2];
00173 
00174     double x0[3], x1[3];
00175 
00176     for( int i = 0; i < 3; i++ )
00177     {
00178         x0[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
00179         x1[i] = verts[3 * id2 + i] - verts[3 * id0 + i];
00180     }
00181 
00182     double a   = x0[1] * x1[2] - x1[1] * x0[2];
00183     double b   = x1[0] * x0[2] - x0[0] * x1[2];
00184     double c   = x0[0] * x1[1] - x1[0] * x0[1];
00185     double nrm = sqrt( a * a + b * b + c * c );
00186 
00187     if( nrm > std::numeric_limits< double >::epsilon() )
00188     {
00189         normal[0] = a / nrm;
00190         normal[1] = b / nrm;
00191         normal[2] = c / nrm;
00192     }
00193     return MB_SUCCESS;
00194 }
00195 
00196 }  // namespace moab
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