Intrepid
test_02.cpp
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43 
49 #include "Intrepid_FieldContainer.hpp"
50 #include "Intrepid_HGRAD_PYR_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_PYR_C1_FEM) |\n" \
214  << "| |\n" \
215  << "| 1) Patch test involving mass and stiffness matrices, |\n" \
216  << "| for the Neumann problem on a pyramid 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::Pyramid<> >()); // 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 Pyramid.
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, 5, cellDim);
270  // funky Pyramid (affine mapping)
271  cell_nodes(0, 0, 0) = -1.0;
272  cell_nodes(0, 0, 1) = 3.0;
273  cell_nodes(0, 0, 2) = 2.0;
274  cell_nodes(0, 1, 0) = 3.0;
275  cell_nodes(0, 1, 1) = -2.0;
276  cell_nodes(0, 1, 2) = -1.0;
277  cell_nodes(0, 2, 0) = 6.0;
278  cell_nodes(0, 2, 1) = 3.0;
279  cell_nodes(0, 2, 2) = -1.0;
280  cell_nodes(0, 3, 0) = 4.0;
281  cell_nodes(0, 3, 1) = 2.0;
282  cell_nodes(0, 3, 2) = -2.0;
283  cell_nodes(0, 4, 0) = 5.0;
284  cell_nodes(0, 4, 1) = -1.0;
285  cell_nodes(0, 4, 2) = 1.0;
286 
287  // perturbed reference Pyramid
288  /*cell_nodes(0, 0, 0) = -1.1;
289  cell_nodes(0, 0, 1) = -1.1;
290  cell_nodes(0, 0, 2) = 0.2;
291  cell_nodes(0, 1, 0) = 1.2;
292  cell_nodes(0, 1, 1) = -1.1;
293  cell_nodes(0, 1, 2) = 0.05;
294  cell_nodes(0, 2, 0) = 1.0;
295  cell_nodes(0, 2, 1) = 0.9;
296  cell_nodes(0, 2, 2) = 0.1;
297  cell_nodes(0, 3, 0) = -1.1;
298  cell_nodes(0, 3, 1) = 0.9;
299  cell_nodes(0, 3, 2) = -0.1;
300  cell_nodes(0, 4, 0) = 0.1;
301  cell_nodes(0, 4, 1) = -0.1;
302  cell_nodes(0, 4, 2) = 1.1; */
303 
304  // reference Pyramid
305  /*cell_nodes(0, 0, 0) = -1.0;
306  cell_nodes(0, 0, 1) = -1.0;
307  cell_nodes(0, 0, 2) = 0.0;
308  cell_nodes(0, 1, 0) = 1.0;
309  cell_nodes(0, 1, 1) = -1.0;
310  cell_nodes(0, 1, 2) = 0.0;
311  cell_nodes(0, 2, 0) = 1.0;
312  cell_nodes(0, 2, 1) = 1.0;
313  cell_nodes(0, 2, 2) = 0.0;
314  cell_nodes(0, 3, 0) = -1.0;
315  cell_nodes(0, 3, 1) = 1.0;
316  cell_nodes(0, 3, 2) = 1.0;
317  cell_nodes(0, 4, 0) = 0.0;
318  cell_nodes(0, 4, 1) = 0.0;
319  cell_nodes(0, 4, 2) = 1.0; */
320 
321 
322  FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
323  CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell);
324  interp_points.resize(numInterpPoints, cellDim);
325 
326  for (int x_order=0; x_order <= max_order; x_order++) {
327  for (int y_order=0; y_order <= max_order-x_order; y_order++) {
328  for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
329 
330  // evaluate exact solution
331  FieldContainer<double> exact_solution(1, numInterpPoints);
332  u_exact(exact_solution, interp_points, x_order, y_order, z_order);
333 
334  int basis_order = 1;
335 
336  // set test tolerance;
337  double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
338 
339  //create basis
340  Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
341  Teuchos::rcp(new Basis_HGRAD_PYR_C1_FEM<double,FieldContainer<double> >() );
342  int numFields = basis->getCardinality();
343 
344  // create cubatures
345  Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
346  Teuchos::RCP<Cubature<double> > sideQCub = cubFactory.create(sideQ, 2*basis_order);
347  Teuchos::RCP<Cubature<double> > sideTCub = cubFactory.create(sideT, 2*basis_order);
348  int numCubPointsCell = cellCub->getNumPoints();
349  int numCubPointsSideQ = sideQCub->getNumPoints();
350  int numCubPointsSideT = sideTCub->getNumPoints();
351 
352  /* Computational arrays. */
353  /* Section 1: Related to parent cell integration. */
354  FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
355  FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
356  FieldContainer<double> cub_weights_cell(numCubPointsCell);
357  FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
358  FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
359  FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
360  FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
361 
362  FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
363  FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
364  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
365  FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
366  FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
367  FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
368  FieldContainer<double> fe_matrix(1, numFields, numFields);
369 
370  FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
371  FieldContainer<double> rhs_and_soln_vector(1, numFields);
372 
373  /* Section 2: Related to subcell (side) integration. */
374  unsigned numSides = 5;
375  unsigned numSidesT = 4;
376  FieldContainer<double> cub_points_sideQ(numCubPointsSideQ, sideQDim);
377  FieldContainer<double> cub_points_sideT(numCubPointsSideT, sideTDim);
378  FieldContainer<double> cub_weights_sideQ(numCubPointsSideQ);
379  FieldContainer<double> cub_weights_sideT(numCubPointsSideT);
380  FieldContainer<double> cub_points_sideQ_refcell(numCubPointsSideQ, cellDim);
381  FieldContainer<double> cub_points_sideT_refcell(numCubPointsSideT, cellDim);
382  FieldContainer<double> cub_points_sideQ_physical(1, numCubPointsSideQ, cellDim);
383  FieldContainer<double> cub_points_sideT_physical(1, numCubPointsSideT, cellDim);
384  FieldContainer<double> jacobian_sideQ_refcell(1, numCubPointsSideQ, cellDim, cellDim);
385  FieldContainer<double> jacobian_sideT_refcell(1, numCubPointsSideT, cellDim, cellDim);
386  FieldContainer<double> jacobian_det_sideQ_refcell(1, numCubPointsSideQ);
387  FieldContainer<double> jacobian_det_sideT_refcell(1, numCubPointsSideT);
388  FieldContainer<double> weighted_measure_sideQ_refcell(1, numCubPointsSideQ);
389  FieldContainer<double> weighted_measure_sideT_refcell(1, numCubPointsSideT);
390 
391  FieldContainer<double> value_of_basis_at_cub_points_sideQ_refcell(numFields, numCubPointsSideQ);
392  FieldContainer<double> value_of_basis_at_cub_points_sideT_refcell(numFields, numCubPointsSideT);
393  FieldContainer<double> transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ);
394  FieldContainer<double> transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT);
395  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ);
396  FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT);
397  FieldContainer<double> neumann_data_at_cub_points_sideQ_physical(1, numCubPointsSideQ);
398  FieldContainer<double> neumann_data_at_cub_points_sideT_physical(1, numCubPointsSideT);
399  FieldContainer<double> neumann_fields_per_side(1, numFields);
400 
401  /* Section 3: Related to global interpolant. */
402  FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
403  FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
404  FieldContainer<double> interpolant(1, numInterpPoints);
405 
406  FieldContainer<int> ipiv(numFields);
407 
408 
409 
410  /******************* START COMPUTATION ***********************/
411 
412  // get cubature points and weights
413  cellCub->getCubature(cub_points_cell, cub_weights_cell);
414 
415  // compute geometric cell information
416  CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
417  CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
418  CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
419 
420  // compute weighted measure
421  FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
422 
424  // Computing mass matrices:
425  // tabulate values of basis functions at (reference) cubature points
426  basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
427 
428  // transform values of basis functions
429  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
430  value_of_basis_at_cub_points_cell);
431 
432  // multiply with weighted measure
433  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
434  weighted_measure_cell,
435  transformed_value_of_basis_at_cub_points_cell);
436 
437  // compute mass matrices
438  FunctionSpaceTools::integrate<double>(fe_matrix,
439  transformed_value_of_basis_at_cub_points_cell,
440  weighted_transformed_value_of_basis_at_cub_points_cell,
441  COMP_BLAS);
443 
445  // Computing stiffness matrices:
446  // tabulate gradients of basis functions at (reference) cubature points
447  basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
448 
449  // transform gradients of basis functions
450  FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
451  jacobian_inv_cell,
452  grad_of_basis_at_cub_points_cell);
453 
454  // multiply with weighted measure
455  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
456  weighted_measure_cell,
457  transformed_grad_of_basis_at_cub_points_cell);
458 
459  // compute stiffness matrices and sum into fe_matrix
460  FunctionSpaceTools::integrate<double>(fe_matrix,
461  transformed_grad_of_basis_at_cub_points_cell,
462  weighted_transformed_grad_of_basis_at_cub_points_cell,
463  COMP_BLAS,
464  true);
466 
468  // Computing RHS contributions:
469  // map cell (reference) cubature points to physical space
470  CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
471 
472  // evaluate rhs function
473  rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
474 
475  // compute rhs
476  FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
477  rhs_at_cub_points_cell_physical,
478  weighted_transformed_value_of_basis_at_cub_points_cell,
479  COMP_BLAS);
480 
481  // compute neumann b.c. contributions and adjust rhs
482  sideQCub->getCubature(cub_points_sideQ, cub_weights_sideQ);
483  sideTCub->getCubature(cub_points_sideT, cub_weights_sideT);
484 
485  for (unsigned i=0; i<numSidesT; i++) {
486  // compute geometric cell information
487  CellTools<double>::mapToReferenceSubcell(cub_points_sideT_refcell, cub_points_sideT, sideTDim, (int)i, cell);
488  CellTools<double>::setJacobian(jacobian_sideT_refcell, cub_points_sideT_refcell, cell_nodes, cell);
489  CellTools<double>::setJacobianDet(jacobian_det_sideT_refcell, jacobian_sideT_refcell);
490 
491  // compute weighted face measure
492  FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideT_refcell,
493  jacobian_sideT_refcell,
494  cub_weights_sideT,
495  i,
496  cell);
497 
498  // tabulate values of basis functions at side cubature points, in the reference parent cell domain
499  basis->getValues(value_of_basis_at_cub_points_sideT_refcell, cub_points_sideT_refcell, OPERATOR_VALUE);
500  // transform
501  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideT_refcell,
502  value_of_basis_at_cub_points_sideT_refcell);
503 
504  // multiply with weighted measure
505  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideT_refcell,
506  weighted_measure_sideT_refcell,
507  transformed_value_of_basis_at_cub_points_sideT_refcell);
508 
509  // compute Neumann data
510  // map side cubature points in reference parent cell domain to physical space
511  CellTools<double>::mapToPhysicalFrame(cub_points_sideT_physical, cub_points_sideT_refcell, cell_nodes, cell);
512  // now compute data
513  neumann(neumann_data_at_cub_points_sideT_physical, cub_points_sideT_physical, jacobian_sideT_refcell,
514  cell, (int)i, x_order, y_order, z_order);
515 
516  FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
517  neumann_data_at_cub_points_sideT_physical,
518  weighted_transformed_value_of_basis_at_cub_points_sideT_refcell,
519  COMP_BLAS);
520 
521  // adjust RHS
522  RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
523  }
524 
525  for (unsigned i=numSidesT; i<numSides; i++) {
526  // compute geometric cell information
527  CellTools<double>::mapToReferenceSubcell(cub_points_sideQ_refcell, cub_points_sideQ, sideQDim, (int)i, cell);
528  CellTools<double>::setJacobian(jacobian_sideQ_refcell, cub_points_sideQ_refcell, cell_nodes, cell);
529  CellTools<double>::setJacobianDet(jacobian_det_sideQ_refcell, jacobian_sideQ_refcell);
530 
531  // compute weighted face measure
532  FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideQ_refcell,
533  jacobian_sideQ_refcell,
534  cub_weights_sideQ,
535  i,
536  cell);
537 
538  // tabulate values of basis functions at side cubature points, in the reference parent cell domain
539  basis->getValues(value_of_basis_at_cub_points_sideQ_refcell, cub_points_sideQ_refcell, OPERATOR_VALUE);
540  // transform
541  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideQ_refcell,
542  value_of_basis_at_cub_points_sideQ_refcell);
543 
544  // multiply with weighted measure
545  FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell,
546  weighted_measure_sideQ_refcell,
547  transformed_value_of_basis_at_cub_points_sideQ_refcell);
548 
549  // compute Neumann data
550  // map side cubature points in reference parent cell domain to physical space
551  CellTools<double>::mapToPhysicalFrame(cub_points_sideQ_physical, cub_points_sideQ_refcell, cell_nodes, cell);
552  // now compute data
553  neumann(neumann_data_at_cub_points_sideQ_physical, cub_points_sideQ_physical, jacobian_sideQ_refcell,
554  cell, (int)i, x_order, y_order, z_order);
555 
556  FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
557  neumann_data_at_cub_points_sideQ_physical,
558  weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell,
559  COMP_BLAS);
560 
561  // adjust RHS
562  RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
563  }
565 
567  // Solution of linear system:
568  int info = 0;
569  Teuchos::LAPACK<int, double> solver;
570  solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
572 
574  // Building interpolant:
575  // evaluate basis at interpolation points
576  basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
577  // transform values of basis functions
578  FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
579  value_of_basis_at_interp_points_ref);
580  FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
582 
583  /******************* END COMPUTATION ***********************/
584 
585  RealSpaceTools<double>::subtract(interpolant, exact_solution);
586 
587  *outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
588  << x_order << ", " << y_order << ", " << z_order
589  << ") and finite element interpolant of order " << basis_order << ": "
590  << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
591  RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
592 
593  if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
594  RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
595  *outStream << "\n\nPatch test failed for solution polynomial order ("
596  << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
597  errorFlag++;
598  }
599  } // end for z_order
600  } // end for y_order
601  } // end for x_order
602 
603  }
604  // Catch unexpected errors
605  catch (const std::logic_error & err) {
606  *outStream << err.what() << "\n\n";
607  errorFlag = -1000;
608  };
609 
610  if (errorFlag != 0)
611  std::cout << "End Result: TEST FAILED\n";
612  else
613  std::cout << "End Result: TEST PASSED\n";
614 
615  // reset format state of std::cout
616  std::cout.copyfmt(oldFormatState);
617 
618  return errorFlag;
619 }
rhsFunc
void rhsFunc(FieldContainer< double > &, const FieldContainer< double > &, int, int, int)
right-hand side function
Definition: test_02.cpp:73
u_exact
void u_exact(FieldContainer< double > &, const FieldContainer< double > &, int, int, int)
exact solution
Definition: test_02.cpp:99
neumann
void neumann(FieldContainer< double > &, const FieldContainer< double > &, const FieldContainer< double > &, const shards::CellTopology &, int, int, int, int)
neumann boundary conditions
Definition: test_02.cpp:124
main
int main(int argc, char *argv[])
outdated tests for orthogonal bases
Definition: test_02.cpp:63
Intrepid_ArrayTools.hpp
Header file for utility class to provide array tools, such as tensor contractions,...
Intrepid_CellTools.hpp
Header file for the Intrepid::CellTools class.
Intrepid_DefaultCubatureFactory.hpp
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
Intrepid_FieldContainer.hpp
Header file for utility class to provide multidimensional containers.
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::Basis_HGRAD_PYR_C1_FEM
Implementation of the default H(grad)-compatible FEM basis of degree 1 on Pyramid cell.
Definition: Intrepid_HGRAD_PYR_C1_FEM.hpp:83
Intrepid::CellTools
A stateless class for operations on cell data. Provides methods for:
Definition: Intrepid_CellTools.hpp:109
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::FieldContainer::dimension
int dimension(const int whichDim) const
Returns the specified dimension.
Definition: Intrepid_FieldContainerDef.hpp:658
Intrepid::RealSpaceTools
Implementation of basic linear algebra functionality in Euclidean space.
Definition: Intrepid_RealSpaceTools.hpp:65
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