Mesh Oriented datABase  (version 5.5.0)
An array-based unstructured mesh library
LinearHex.cpp
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1 #include "moab/LocalDiscretization/LinearHex.hpp"
2 #include "moab/Matrix3.hpp"
3 #include "moab/Forward.hpp"
4 #include <cmath>
5 #include <limits>
6 
7 namespace moab
8 {
9 
10 const double LinearHex::corner[8][3] = { { -1, -1, -1 }, { 1, -1, -1 }, { 1, 1, -1 }, { -1, 1, -1 },
11  { -1, -1, 1 }, { 1, -1, 1 }, { 1, 1, 1 }, { -1, 1, 1 } };
12 
13 /* For each point, its weight and location are stored as an array.
14  Hence, the inner dimension is 2, the outer dimension is gauss_count.
15  We use a one-point Gaussian quadrature, since it integrates linear functions exactly.
16 */
17 const double LinearHex::gauss[1][2] = { { 2.0, 0.0 } };
18 
19 ErrorCode LinearHex::jacobianFcn( const double* params,
20  const double* verts,
21  const int /*nverts*/,
22  const int ndim,
23  double*,
24  double* result )
25 {
26  assert( params && verts );
27  Matrix3* J = reinterpret_cast< Matrix3* >( result );
28  *J = Matrix3( 0.0 );
29  for( unsigned i = 0; i < 8; ++i )
30  {
31  const double params_p = 1 + params[0] * corner[i][0];
32  const double eta_p = 1 + params[1] * corner[i][1];
33  const double zeta_p = 1 + params[2] * corner[i][2];
34  const double dNi_dparams = corner[i][0] * eta_p * zeta_p;
35  const double dNi_deta = corner[i][1] * params_p * zeta_p;
36  const double dNi_dzeta = corner[i][2] * params_p * eta_p;
37  ( *J )( 0, 0 ) += dNi_dparams * verts[i * ndim + 0];
38  ( *J )( 1, 0 ) += dNi_dparams * verts[i * ndim + 1];
39  ( *J )( 2, 0 ) += dNi_dparams * verts[i * ndim + 2];
40  ( *J )( 0, 1 ) += dNi_deta * verts[i * ndim + 0];
41  ( *J )( 1, 1 ) += dNi_deta * verts[i * ndim + 1];
42  ( *J )( 2, 1 ) += dNi_deta * verts[i * ndim + 2];
43  ( *J )( 0, 2 ) += dNi_dzeta * verts[i * ndim + 0];
44  ( *J )( 1, 2 ) += dNi_dzeta * verts[i * ndim + 1];
45  ( *J )( 2, 2 ) += dNi_dzeta * verts[i * ndim + 2];
46  }
47  ( *J ) *= 0.125;
48  return MB_SUCCESS;
49 } // LinearHex::jacobian()
50 
51 ErrorCode LinearHex::evalFcn( const double* params,
52  const double* field,
53  const int /*ndim*/,
54  const int num_tuples,
55  double*,
56  double* result )
57 {
58  assert( params && field && num_tuples != -1 );
59  for( int i = 0; i < num_tuples; i++ )
60  result[i] = 0.0;
61  for( unsigned i = 0; i < 8; ++i )
62  {
63  const double N_i =
64  ( 1 + params[0] * corner[i][0] ) * ( 1 + params[1] * corner[i][1] ) * ( 1 + params[2] * corner[i][2] );
65  for( int j = 0; j < num_tuples; j++ )
66  result[j] += N_i * field[i * num_tuples + j];
67  }
68  for( int i = 0; i < num_tuples; i++ )
69  result[i] *= 0.125;
70 
71  return MB_SUCCESS;
72 }
73 
74 ErrorCode LinearHex::integrateFcn( const double* field,
75  const double* verts,
76  const int nverts,
77  const int ndim,
78  const int num_tuples,
79  double* work,
80  double* result )
81 {
82  assert( field && verts && num_tuples != -1 );
83  double tmp_result[8];
84  ErrorCode rval = MB_SUCCESS;
85  for( int i = 0; i < num_tuples; i++ )
86  result[i] = 0.0;
87  CartVect x;
88  Matrix3 J;
89  for( unsigned int j1 = 0; j1 < LinearHex::gauss_count; ++j1 )
90  {
91  x[0] = LinearHex::gauss[j1][1];
92  double w1 = LinearHex::gauss[j1][0];
93  for( unsigned int j2 = 0; j2 < LinearHex::gauss_count; ++j2 )
94  {
95  x[1] = LinearHex::gauss[j2][1];
96  double w2 = LinearHex::gauss[j2][0];
97  for( unsigned int j3 = 0; j3 < LinearHex::gauss_count; ++j3 )
98  {
99  x[2] = LinearHex::gauss[j3][1];
100  double w3 = LinearHex::gauss[j3][0];
101  rval = evalFcn( x.array(), field, ndim, num_tuples, NULL, tmp_result );
102  if( MB_SUCCESS != rval ) return rval;
103  rval = jacobianFcn( x.array(), verts, nverts, ndim, work, J[0] );
104  if( MB_SUCCESS != rval ) return rval;
105  double tmp_det = w1 * w2 * w3 * J.determinant();
106  for( int i = 0; i < num_tuples; i++ )
107  result[i] += tmp_result[i] * tmp_det;
108  }
109  }
110  }
111 
112  return MB_SUCCESS;
113 } // LinearHex::integrate_vector()
114 
115 ErrorCode LinearHex::reverseEvalFcn( EvalFcn eval,
116  JacobianFcn jacob,
117  InsideFcn ins,
118  const double* posn,
119  const double* verts,
120  const int nverts,
121  const int ndim,
122  const double iter_tol,
123  const double inside_tol,
124  double* work,
125  double* params,
126  int* is_inside )
127 {
128  assert( posn && verts );
129  return EvalSet::evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
130  is_inside );
131 }
132 
133 int LinearHex::insideFcn( const double* params, const int ndim, const double tol )
134 {
135  return EvalSet::inside_function( params, ndim, tol );
136 }
137 
138 ErrorCode LinearHex::normalFcn( const int ientDim,
139  const int facet,
140  const int nverts,
141  const double* verts,
142  double normal[3] )
143 {
144  // assert(facet < 6 && ientDim == 2 && nverts == 8);
145  if( nverts != 8 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed hex :: expected value = 8 " );
146  if( ientDim != 2 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 2 " );
147  if( facet > 6 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local face id :: expected value = one of 0-5" );
148 
149  int id0 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][0];
150  int id1 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][1];
151  int id2 = CN::mConnectivityMap[MBHEX][ientDim - 1].conn[facet][3];
152 
153  double x0[3], x1[3];
154 
155  for( int i = 0; i < 3; i++ )
156  {
157  x0[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
158  x1[i] = verts[3 * id2 + i] - verts[3 * id0 + i];
159  }
160 
161  double a = x0[1] * x1[2] - x1[1] * x0[2];
162  double b = x1[0] * x0[2] - x0[0] * x1[2];
163  double c = x0[0] * x1[1] - x1[0] * x0[1];
164  double nrm = sqrt( a * a + b * b + c * c );
165 
166  if( nrm > std::numeric_limits< double >::epsilon() )
167  {
168  normal[0] = a / nrm;
169  normal[1] = b / nrm;
170  normal[2] = c / nrm;
171  }
172  return MB_SUCCESS;
173 }
174 
175 } // namespace moab