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