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235 | #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() );<--- Variable 'rval' is assigned a value that is never used.
#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
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