Intrepid
test_02.cpp
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43 
49 #include "Intrepid_FieldContainer.hpp"
50 #include "Intrepid_HGRAD_WEDGE_C1_FEM.hpp"
51 #include "Intrepid_DefaultCubatureFactory.hpp"
52 #include "Intrepid_RealSpaceTools.hpp"
53 #include "Intrepid_ArrayTools.hpp"
54 #include "Intrepid_FunctionSpaceTools.hpp"
55 #include "Intrepid_CellTools.hpp"
56 #include "Teuchos_oblackholestream.hpp"
57 #include "Teuchos_RCP.hpp"
58 #include "Teuchos_GlobalMPISession.hpp"
59 #include "Teuchos_SerialDenseMatrix.hpp"
60 #include "Teuchos_SerialDenseVector.hpp"
61 #include "Teuchos_LAPACK.hpp"
62 
63 using namespace std;
64 using namespace Intrepid;
65 
66 void rhsFunc(FieldContainer<double> &, const FieldContainer<double> &, int, int, int);
67 void neumann(FieldContainer<double> & ,
68  const FieldContainer<double> & ,
69  const FieldContainer<double> & ,
70  const shards::CellTopology & ,
71  int, int, int, int);
72 void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int, int);
73 
75 void rhsFunc(FieldContainer<double> & result,
76  const FieldContainer<double> & points,
77  int xd,
78  int yd,
79  int zd) {
80 
81  int x = 0, y = 1, z = 2;
82 
83  // second x-derivatives of u
84  if (xd > 1) {
85  for (int cell=0; cell<result.dimension(0); cell++) {
86  for (int pt=0; pt<result.dimension(1); pt++) {
87  result(cell,pt) = - xd*(xd-1)*std::pow(points(cell,pt,x), xd-2) *
88  std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd);
89  }
90  }
91  }
92 
93  // second y-derivatives of u
94  if (yd > 1) {
95  for (int cell=0; cell<result.dimension(0); cell++) {
96  for (int pt=0; pt<result.dimension(1); pt++) {
97  result(cell,pt) -= yd*(yd-1)*std::pow(points(cell,pt,y), yd-2) *
98  std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd);
99  }
100  }
101  }
102 
103  // second z-derivatives of u
104  if (zd > 1) {
105  for (int cell=0; cell<result.dimension(0); cell++) {
106  for (int pt=0; pt<result.dimension(1); pt++) {
107  result(cell,pt) -= zd*(zd-1)*std::pow(points(cell,pt,z), zd-2) *
108  std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd);
109  }
110  }
111  }
112 
113  // add u
114  for (int cell=0; cell<result.dimension(0); cell++) {
115  for (int pt=0; pt<result.dimension(1); pt++) {
116  result(cell,pt) += std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd);
117  }
118  }
119 
120 }
121 
122 
124 void neumann(FieldContainer<double> & result,
125  const FieldContainer<double> & points,
126  const FieldContainer<double> & jacs,
127  const shards::CellTopology & parentCell,
128  int sideOrdinal, int xd, int yd, int zd) {
129 
130  int x = 0, y = 1, z = 2;
131 
132  int numCells = result.dimension(0);
133  int numPoints = result.dimension(1);
134 
135  FieldContainer<double> grad_u(numCells, numPoints, 3);
136  FieldContainer<double> side_normals(numCells, numPoints, 3);
137  FieldContainer<double> normal_lengths(numCells, numPoints);
138 
139  // first x-derivatives of u
140  if (xd > 0) {
141  for (int cell=0; cell<numCells; cell++) {
142  for (int pt=0; pt<numPoints; pt++) {
143  grad_u(cell,pt,x) = xd*std::pow(points(cell,pt,x), xd-1) *
144  std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd);
145  }
146  }
147  }
148 
149  // first y-derivatives of u
150  if (yd > 0) {
151  for (int cell=0; cell<numCells; cell++) {
152  for (int pt=0; pt<numPoints; pt++) {
153  grad_u(cell,pt,y) = yd*std::pow(points(cell,pt,y), yd-1) *
154  std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd);
155  }
156  }
157  }
158 
159  // first z-derivatives of u
160  if (zd > 0) {
161  for (int cell=0; cell<numCells; cell++) {
162  for (int pt=0; pt<numPoints; pt++) {
163  grad_u(cell,pt,z) = zd*std::pow(points(cell,pt,z), zd-1) *
164  std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd);
165  }
166  }
167  }
168 
169  CellTools<double>::getPhysicalSideNormals(side_normals, jacs, sideOrdinal, parentCell);
170 
171  // scale normals
172  RealSpaceTools<double>::vectorNorm(normal_lengths, side_normals, NORM_TWO);
173  FunctionSpaceTools::scalarMultiplyDataData<double>(side_normals, normal_lengths, side_normals, true);
174 
175  FunctionSpaceTools::dotMultiplyDataData<double>(result, grad_u, side_normals);
176 
177 }
178 
180 void u_exact(FieldContainer<double> & result, const FieldContainer<double> & points, int xd, int yd, int zd) {
181  int x = 0, y = 1, z = 2;
182  for (int cell=0; cell<result.dimension(0); cell++) {
183  for (int pt=0; pt<result.dimension(1); pt++) {
184  result(cell,pt) = std::pow(points(pt,x), xd)*std::pow(points(pt,y), yd)*std::pow(points(pt,z), zd);
185  }
186  }
187 }
188 
189 
190 
191 
192 int main(int argc, char *argv[]) {
193 
194  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
195 
196  // This little trick lets us print to std::cout only if
197  // a (dummy) command-line argument is provided.
198  int iprint = argc - 1;
199  Teuchos::RCP<std::ostream> outStream;
200  Teuchos::oblackholestream bhs; // outputs nothing
201  if (iprint > 0)
202  outStream = Teuchos::rcp(&std::cout, false);
203  else
204  outStream = Teuchos::rcp(&bhs, false);
205 
206  // Save the format state of the original std::cout.
207  Teuchos::oblackholestream oldFormatState;
208  oldFormatState.copyfmt(std::cout);
209 
210  *outStream \
211  << "===============================================================================\n" \
212  << "| |\n" \
213  << "| Unit Test (Basis_HGRAD_WEDGE_C1_FEM) |\n" \
214  << "| |\n" \
215  << "| 1) Patch test involving mass and stiffness matrices, |\n" \
216  << "| for the Neumann problem on a wedge patch |\n" \
217  << "| Omega with boundary Gamma. |\n" \
218  << "| |\n" \
219  << "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \
220  << "| |\n" \
221  << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \
222  << "| Denis Ridzal (dridzal@sandia.gov), |\n" \
223  << "| Kara Peterson (kjpeter@sandia.gov). |\n" \
224  << "| Mauro Perego (mperego@sandia.gov). |\n" \
225  << "| |\n" \
226  << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
227  << "| Trilinos website: http://trilinos.sandia.gov |\n" \
228  << "| |\n" \
229  << "===============================================================================\n"\
230  << "| TEST 1: Patch test |\n"\
231  << "===============================================================================\n";
232 
233 
234  int errorFlag = 0;
235 
236  outStream -> precision(16);
237 
238 
239  try {
240 
241  int max_order = 1; // max total order of polynomial solution
242  DefaultCubatureFactory<double> cubFactory; // create factory
243  shards::CellTopology cell(shards::getCellTopologyData< shards::Wedge<> >()); // create parent cell topology
244  shards::CellTopology sideQ(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology
245  shards::CellTopology sideT(shards::getCellTopologyData< shards::Triangle<> >());
246  int cellDim = cell.getDimension();
247  int sideQDim = sideQ.getDimension();
248  int sideTDim = sideT.getDimension();
249 
250  // Define array containing points at which the solution is evaluated, on the reference Wedge.
251  int numIntervals = 10;
252  int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6;
253  FieldContainer<double> interp_points_ref(numInterpPoints, 3);
254  int counter = 0;
255  for (int k=0; k<=numIntervals; k++) {
256  for (int j=0; j<=numIntervals; j++) {
257  for (int i=0; i<=numIntervals; i++) {
258  if (i+j+k <= numIntervals) {
259  interp_points_ref(counter,0) = i*(1.0/numIntervals);
260  interp_points_ref(counter,1) = j*(1.0/numIntervals);
261  interp_points_ref(counter,2) = k*(1.0/numIntervals);
262  counter++;
263  }
264  }
265  }
266  }
267 
268  /* Definition of parent cell. */
269  FieldContainer<double> cell_nodes(1, 6, cellDim);
270  // funky Wedge (affine mapping)
271  cell_nodes(0, 0, 0) = -3.0;
272  cell_nodes(0, 0, 1) = -5.0;
273  cell_nodes(0, 0, 2) = -5.0;
274  cell_nodes(0, 1, 0) = -1.0;
275  cell_nodes(0, 1, 1) = -4.0;
276  cell_nodes(0, 1, 2) = -4.0;
277  cell_nodes(0, 2, 0) = 0.0;
278  cell_nodes(0, 2, 1) = 0.0;
279  cell_nodes(0, 2, 2) = -5.0;
280  cell_nodes(0, 3, 0) = 5.0;
281  cell_nodes(0, 3, 1) = -1.0;
282  cell_nodes(0, 3, 2) = 1.0;
283  cell_nodes(0, 4, 0) = 7.0;
284  cell_nodes(0, 4, 1) = 0.0;
285  cell_nodes(0, 4, 2) = 2.0;
286  cell_nodes(0, 5, 0) = 8.0;
287  cell_nodes(0, 5, 1) = 4.0;
288  cell_nodes(0, 5, 2) = 1.0;
289 
290  // perturbed reference Wedge
291  /*cell_nodes(0, 0, 0) = 0.1;
292  cell_nodes(0, 0, 1) = 0.1;
293  cell_nodes(0, 0, 2) = -0.8;
294  cell_nodes(0, 1, 0) = 1.2;
295  cell_nodes(0, 1, 1) = 0.1;
296  cell_nodes(0, 1, 2) = -0.95;
297  cell_nodes(0, 2, 0) = 0.0;
298  cell_nodes(0, 2, 1) = 0.9;
299  cell_nodes(0, 2, 2) = -0.0;
300  cell_nodes(0, 3, 0) = 0.1;
301  cell_nodes(0, 3, 1) = 0.0;
302  cell_nodes(0, 3, 2) = 0.9;
303  cell_nodes(0, 4, 0) = 0.9;
304  cell_nodes(0, 4, 1) = 0.1;
305  cell_nodes(0, 4, 2) = 1.1;
306  cell_nodes(0, 5, 0) = -0.1;
307  cell_nodes(0, 5, 1) = 1.0;
308  cell_nodes(0, 5, 2) = 1.0;*/
309 
310  // reference Wedge
311  /*cell_nodes(0, 0, 0) = 0.0;
312  cell_nodes(0, 0, 1) = 0.0;
313  cell_nodes(0, 0, 2) = -1.0;
314  cell_nodes(0, 1, 0) = 1.0;
315  cell_nodes(0, 1, 1) = 0.0;
316  cell_nodes(0, 1, 2) = -1.0;
317  cell_nodes(0, 2, 0) = 0.0;
318  cell_nodes(0, 2, 1) = 1.0;
319  cell_nodes(0, 2, 2) = -1.0;
320  cell_nodes(0, 3, 0) = 0.0;
321  cell_nodes(0, 3, 1) = 0.0;
322  cell_nodes(0, 3, 2) = 1.0;
323  cell_nodes(0, 4, 0) = 1.0;
324  cell_nodes(0, 4, 1) = 0.0;
325  cell_nodes(0, 4, 2) = 1.0;
326  cell_nodes(0, 5, 0) = 0.0;
327  cell_nodes(0, 5, 1) = 1.0;
328  cell_nodes(0, 5, 2) = 1.0;*/
329 
330 
331  FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
332  CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell);
333  interp_points.resize(numInterpPoints, cellDim);
334 
335  for (int x_order=0; x_order <= max_order; x_order++) {
336  for (int y_order=0; y_order <= max_order-x_order; y_order++) {
337  for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
338 
339  // evaluate exact solution
340  FieldContainer<double> exact_solution(1, numInterpPoints);
341  u_exact(exact_solution, interp_points, x_order, y_order, z_order);
342 
343  int basis_order = 1;
344 
345  // set test tolerance;
346  double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
347 
348  //create basis
349  Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
350  Teuchos::rcp(new Basis_HGRAD_WEDGE_C1_FEM<double,FieldContainer<double> >() );
351  int numFields = basis->getCardinality();
352 
353  // create cubatures
354  Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
355  Teuchos::RCP<Cubature<double> > sideQCub = cubFactory.create(sideQ, 2*basis_order);
356  Teuchos::RCP<Cubature<double> > sideTCub = cubFactory.create(sideT, 2*basis_order);
357  int numCubPointsCell = cellCub->getNumPoints();
358  int numCubPointsSideQ = sideQCub->getNumPoints();
359  int numCubPointsSideT = sideTCub->getNumPoints();
360 
361  /* Computational arrays. */
362  /* Section 1: Related to parent cell integration. */
363  FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
364  FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
365  FieldContainer<double> cub_weights_cell(numCubPointsCell);
366  FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
367  FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
368  FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
369  FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
370 
371  FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
372  FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
373  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
374  FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
375  FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
376  FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
377  FieldContainer<double> fe_matrix(1, numFields, numFields);
378 
379  FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
380  FieldContainer<double> rhs_and_soln_vector(1, numFields);
381 
382  /* Section 2: Related to subcell (side) integration. */
383  unsigned numSides = 5;
384  unsigned numSidesQ = 3;
385  FieldContainer<double> cub_points_sideQ(numCubPointsSideQ, sideQDim);
386  FieldContainer<double> cub_points_sideT(numCubPointsSideT, sideTDim);
387  FieldContainer<double> cub_weights_sideQ(numCubPointsSideQ);
388  FieldContainer<double> cub_weights_sideT(numCubPointsSideT);
389  FieldContainer<double> cub_points_sideQ_refcell(numCubPointsSideQ, cellDim);
390  FieldContainer<double> cub_points_sideT_refcell(numCubPointsSideT, cellDim);
391  FieldContainer<double> cub_points_sideQ_physical(1, numCubPointsSideQ, cellDim);
392  FieldContainer<double> cub_points_sideT_physical(1, numCubPointsSideT, cellDim);
393  FieldContainer<double> jacobian_sideQ_refcell(1, numCubPointsSideQ, cellDim, cellDim);
394  FieldContainer<double> jacobian_sideT_refcell(1, numCubPointsSideT, cellDim, cellDim);
395  FieldContainer<double> jacobian_det_sideQ_refcell(1, numCubPointsSideQ);
396  FieldContainer<double> jacobian_det_sideT_refcell(1, numCubPointsSideT);
397  FieldContainer<double> weighted_measure_sideQ_refcell(1, numCubPointsSideQ);
398  FieldContainer<double> weighted_measure_sideT_refcell(1, numCubPointsSideT);
399 
400  FieldContainer<double> value_of_basis_at_cub_points_sideQ_refcell(numFields, numCubPointsSideQ);
401  FieldContainer<double> value_of_basis_at_cub_points_sideT_refcell(numFields, numCubPointsSideT);
402  FieldContainer<double> transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ);
403  FieldContainer<double> transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT);
404  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ);
405  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT);
406  FieldContainer<double> neumann_data_at_cub_points_sideQ_physical(1, numCubPointsSideQ);
407  FieldContainer<double> neumann_data_at_cub_points_sideT_physical(1, numCubPointsSideT);
408  FieldContainer<double> neumann_fields_per_side(1, numFields);
409 
410  /* Section 3: Related to global interpolant. */
411  FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
412  FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
413  FieldContainer<double> interpolant(1, numInterpPoints);
414 
415  FieldContainer<int> ipiv(numFields);
416 
417 
418 
419  /******************* START COMPUTATION ***********************/
420 
421  // get cubature points and weights
422  cellCub->getCubature(cub_points_cell, cub_weights_cell);
423 
424  // compute geometric cell information
425  CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
426  CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
427  CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
428 
429  // compute weighted measure
430  FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
431 
433  // Computing mass matrices:
434  // tabulate values of basis functions at (reference) cubature points
435  basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
436 
437  // transform values of basis functions
438  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
439  value_of_basis_at_cub_points_cell);
440 
441  // multiply with weighted measure
442  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
443  weighted_measure_cell,
444  transformed_value_of_basis_at_cub_points_cell);
445 
446  // compute mass matrices
447  FunctionSpaceTools::integrate<double>(fe_matrix,
448  transformed_value_of_basis_at_cub_points_cell,
449  weighted_transformed_value_of_basis_at_cub_points_cell,
450  COMP_BLAS);
452 
454  // Computing stiffness matrices:
455  // tabulate gradients of basis functions at (reference) cubature points
456  basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
457 
458  // transform gradients of basis functions
459  FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
460  jacobian_inv_cell,
461  grad_of_basis_at_cub_points_cell);
462 
463  // multiply with weighted measure
464  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
465  weighted_measure_cell,
466  transformed_grad_of_basis_at_cub_points_cell);
467 
468  // compute stiffness matrices and sum into fe_matrix
469  FunctionSpaceTools::integrate<double>(fe_matrix,
470  transformed_grad_of_basis_at_cub_points_cell,
471  weighted_transformed_grad_of_basis_at_cub_points_cell,
472  COMP_BLAS,
473  true);
475 
477  // Computing RHS contributions:
478  // map cell (reference) cubature points to physical space
479  CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
480 
481  // evaluate rhs function
482  rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
483 
484  // compute rhs
485  FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
486  rhs_at_cub_points_cell_physical,
487  weighted_transformed_value_of_basis_at_cub_points_cell,
488  COMP_BLAS);
489 
490  // compute neumann b.c. contributions and adjust rhs
491  sideQCub->getCubature(cub_points_sideQ, cub_weights_sideQ);
492  sideTCub->getCubature(cub_points_sideT, cub_weights_sideT);
493 
494  for (unsigned i=0; i<numSidesQ; i++) {
495  // compute geometric cell information
496  CellTools<double>::mapToReferenceSubcell(cub_points_sideQ_refcell, cub_points_sideQ, sideQDim, (int)i, cell);
497  CellTools<double>::setJacobian(jacobian_sideQ_refcell, cub_points_sideQ_refcell, cell_nodes, cell);
498  CellTools<double>::setJacobianDet(jacobian_det_sideQ_refcell, jacobian_sideQ_refcell);
499 
500  // compute weighted face measure
501  FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideQ_refcell,
502  jacobian_sideQ_refcell,
503  cub_weights_sideQ,
504  i,
505  cell);
506 
507  // tabulate values of basis functions at side cubature points, in the reference parent cell domain
508  basis->getValues(value_of_basis_at_cub_points_sideQ_refcell, cub_points_sideQ_refcell, OPERATOR_VALUE);
509  // transform
510  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideQ_refcell,
511  value_of_basis_at_cub_points_sideQ_refcell);
512 
513  // multiply with weighted measure
514  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell,
515  weighted_measure_sideQ_refcell,
516  transformed_value_of_basis_at_cub_points_sideQ_refcell);
517 
518  // compute Neumann data
519  // map side cubature points in reference parent cell domain to physical space
520  CellTools<double>::mapToPhysicalFrame(cub_points_sideQ_physical, cub_points_sideQ_refcell, cell_nodes, cell);
521  // now compute data
522  neumann(neumann_data_at_cub_points_sideQ_physical, cub_points_sideQ_physical, jacobian_sideQ_refcell,
523  cell, (int)i, x_order, y_order, z_order);
524 
525  FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
526  neumann_data_at_cub_points_sideQ_physical,
527  weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell,
528  COMP_BLAS);
529 
530  // adjust RHS
531  RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
532  }
533 
534  for (unsigned i=numSidesQ; i<numSides; i++) {
535  // compute geometric cell information
536  CellTools<double>::mapToReferenceSubcell(cub_points_sideT_refcell, cub_points_sideT, sideTDim, (int)i, cell);
537  CellTools<double>::setJacobian(jacobian_sideT_refcell, cub_points_sideT_refcell, cell_nodes, cell);
538  CellTools<double>::setJacobianDet(jacobian_det_sideT_refcell, jacobian_sideT_refcell);
539 
540  // compute weighted face measure
541  FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideT_refcell,
542  jacobian_sideT_refcell,
543  cub_weights_sideT,
544  i,
545  cell);
546 
547  // tabulate values of basis functions at side cubature points, in the reference parent cell domain
548  basis->getValues(value_of_basis_at_cub_points_sideT_refcell, cub_points_sideT_refcell, OPERATOR_VALUE);
549  // transform
550  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideT_refcell,
551  value_of_basis_at_cub_points_sideT_refcell);
552 
553  // multiply with weighted measure
554  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideT_refcell,
555  weighted_measure_sideT_refcell,
556  transformed_value_of_basis_at_cub_points_sideT_refcell);
557 
558  // compute Neumann data
559  // map side cubature points in reference parent cell domain to physical space
560  CellTools<double>::mapToPhysicalFrame(cub_points_sideT_physical, cub_points_sideT_refcell, cell_nodes, cell);
561  // now compute data
562  neumann(neumann_data_at_cub_points_sideT_physical, cub_points_sideT_physical, jacobian_sideT_refcell,
563  cell, (int)i, x_order, y_order, z_order);
564 
565  FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
566  neumann_data_at_cub_points_sideT_physical,
567  weighted_transformed_value_of_basis_at_cub_points_sideT_refcell,
568  COMP_BLAS);
569 
570  // adjust RHS
571  RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
572  }
574 
576  // Solution of linear system:
577  int info = 0;
578  Teuchos::LAPACK<int, double> solver;
579  solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
581 
583  // Building interpolant:
584  // evaluate basis at interpolation points
585  basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
586  // transform values of basis functions
587  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
588  value_of_basis_at_interp_points_ref);
589  FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
591 
592  /******************* END COMPUTATION ***********************/
593 
594  RealSpaceTools<double>::subtract(interpolant, exact_solution);
595 
596  *outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
597  << x_order << ", " << y_order << ", " << z_order
598  << ") and finite element interpolant of order " << basis_order << ": "
599  << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
600  RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
601 
602  if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
603  RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
604  *outStream << "\n\nPatch test failed for solution polynomial order ("
605  << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
606  errorFlag++;
607  }
608  } // end for z_order
609  } // end for y_order
610  } // end for x_order
611 
612  }
613  // Catch unexpected errors
614  catch (const std::logic_error & err) {
615  *outStream << err.what() << "\n\n";
616  errorFlag = -1000;
617  };
618 
619  if (errorFlag != 0)
620  std::cout << "End Result: TEST FAILED\n";
621  else
622  std::cout << "End Result: TEST PASSED\n";
623 
624  // reset format state of std::cout
625  std::cout.copyfmt(oldFormatState);
626 
627  return errorFlag;
628 }
Intrepid::RealSpaceTools
Implementation of basic linear algebra functionality in Euclidean space.
Definition: Intrepid_RealSpaceTools.hpp:65
Intrepid::Basis_HGRAD_WEDGE_C1_FEM
Implementation of the default H(grad)-compatible FEM basis of degree 1 on Wedge cell.
Definition: Intrepid_HGRAD_WEDGE_C1_FEM.hpp:85
Intrepid_CellTools.hpp
Header file for the Intrepid::CellTools class.
Intrepid::FieldContainer::dimension
int dimension(const int whichDim) const
Returns the specified dimension.
Definition: Intrepid_FieldContainerDef.hpp:658
Intrepid_FieldContainer.hpp
Header file for utility class to provide multidimensional containers.
Intrepid_ArrayTools.hpp
Header file for utility class to provide array tools, such as tensor contractions, etc.
Intrepid_DefaultCubatureFactory.hpp
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
Intrepid_FunctionSpaceTools.hpp
Header file for the Intrepid::FunctionSpaceTools class.
Intrepid_RealSpaceTools.hpp
Header file for classes providing basic linear algebra functionality in 1D, 2D and 3D...
Intrepid::DefaultCubatureFactory
A factory class that generates specific instances of cubatures.
Definition: Intrepid_DefaultCubatureFactory.hpp:77
Intrepid::DefaultCubatureFactory::create
Teuchos::RCP< Cubature< Scalar, ArrayPoint, ArrayWeight > > create(const shards::CellTopology &cellTopology, const std::vector< int > &degree)
Factory method.
Definition: Intrepid_DefaultCubatureFactoryDef.hpp:53
Intrepid::CellTools
A stateless class for operations on cell data. Provides methods for:
Definition: Intrepid_CellTools.hpp:109
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