Intrepid
test_02.cpp
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43
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
63using namespace std;
64using namespace Intrepid;
65
66void rhsFunc(FieldContainer<double> &, const FieldContainer<double> &, int, int, int);
70 const shards::CellTopology & ,
71 int, int, int, int);
72void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int, int);
73
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
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
180void 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
192int 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_TET_C2_FEM) |\n" \
214 << "| |\n" \
215 << "| 1) Patch test involving mass and stiffness matrices, |\n" \
216 << "| for the Neumann problem on a tetrahedral 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 << "| |\n" \
225 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
226 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
227 << "| |\n" \
228 << "===============================================================================\n"\
229 << "| TEST 1: Patch test |\n"\
230 << "===============================================================================\n";
231
232
233 int errorFlag = 0;
234
235 outStream -> precision(16);
236
237
238 try {
239
240 int max_order = 2; // max total order of polynomial solution
241 DefaultCubatureFactory<double> cubFactory; // create factory
242 shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology
243 shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology
244 int cellDim = cell.getDimension();
245 int sideDim = side.getDimension();
246
247 // Define array containing points at which the solution is evaluated, on the reference tet.
248 int numIntervals = 10;
249 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6;
250 FieldContainer<double> interp_points_ref(numInterpPoints, 3);
251 int counter = 0;
252 for (int k=0; k<=numIntervals; k++) {
253 for (int j=0; j<=numIntervals; j++) {
254 for (int i=0; i<=numIntervals; i++) {
255 if (i+j+k <= numIntervals) {
256 interp_points_ref(counter,0) = i*(1.0/numIntervals);
257 interp_points_ref(counter,1) = j*(1.0/numIntervals);
258 interp_points_ref(counter,2) = k*(1.0/numIntervals);
259 counter++;
260 }
261 }
262 }
263 }
264
265 /* Definition of parent cell. */
266 FieldContainer<double> cell_nodes(1, 4, cellDim);
267 // funky tet
268 cell_nodes(0, 0, 0) = -1.0;
269 cell_nodes(0, 0, 1) = -2.0;
270 cell_nodes(0, 0, 2) = 0.0;
271 cell_nodes(0, 1, 0) = 6.0;
272 cell_nodes(0, 1, 1) = 2.0;
273 cell_nodes(0, 1, 2) = 0.0;
274 cell_nodes(0, 2, 0) = -5.0;
275 cell_nodes(0, 2, 1) = 1.0;
276 cell_nodes(0, 2, 2) = 0.0;
277 cell_nodes(0, 3, 0) = -4.0;
278 cell_nodes(0, 3, 1) = -1.0;
279 cell_nodes(0, 3, 2) = 3.0;
280 // perturbed reference tet
281 /*cell_nodes(0, 0, 0) = 0.1;
282 cell_nodes(0, 0, 1) = -0.1;
283 cell_nodes(0, 0, 2) = 0.2;
284 cell_nodes(0, 1, 0) = 1.2;
285 cell_nodes(0, 1, 1) = -0.1;
286 cell_nodes(0, 1, 2) = 0.05;
287 cell_nodes(0, 2, 0) = 0.0;
288 cell_nodes(0, 2, 1) = 0.9;
289 cell_nodes(0, 2, 2) = 0.1;
290 cell_nodes(0, 3, 0) = 0.1;
291 cell_nodes(0, 3, 1) = -0.1;
292 cell_nodes(0, 3, 2) = 1.1;*/
293 // reference tet
294 /*cell_nodes(0, 0, 0) = 0.0;
295 cell_nodes(0, 0, 1) = 0.0;
296 cell_nodes(0, 0, 2) = 0.0;
297 cell_nodes(0, 1, 0) = 1.0;
298 cell_nodes(0, 1, 1) = 0.0;
299 cell_nodes(0, 1, 2) = 0.0;
300 cell_nodes(0, 2, 0) = 0.0;
301 cell_nodes(0, 2, 1) = 1.0;
302 cell_nodes(0, 2, 2) = 0.0;
303 cell_nodes(0, 3, 0) = 0.0;
304 cell_nodes(0, 3, 1) = 0.0;
305 cell_nodes(0, 3, 2) = 1.0;*/
306
307 FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
308 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell);
309 interp_points.resize(numInterpPoints, cellDim);
310
311 for (int x_order=0; x_order <= max_order; x_order++) {
312 for (int y_order=0; y_order <= max_order-x_order; y_order++) {
313 for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
314
315 // evaluate exact solution
316 FieldContainer<double> exact_solution(1, numInterpPoints);
317 u_exact(exact_solution, interp_points, x_order, y_order, z_order);
318
319 int basis_order = 2;
320
321 // set test tolerance;
322 double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
323
324 //create basis
325 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
326 Teuchos::rcp(new Basis_HGRAD_TET_C2_FEM<double,FieldContainer<double> >() );
327 int numFields = basis->getCardinality();
328
329 // create cubatures
330 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
331 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order);
332 int numCubPointsCell = cellCub->getNumPoints();
333 int numCubPointsSide = sideCub->getNumPoints();
334
335 /* Computational arrays. */
336 /* Section 1: Related to parent cell integration. */
337 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
338 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
339 FieldContainer<double> cub_weights_cell(numCubPointsCell);
340 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
341 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
342 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
343 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
344
345 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
346 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
347 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
348 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
349 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
350 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
351 FieldContainer<double> fe_matrix(1, numFields, numFields);
352
353 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
354 FieldContainer<double> rhs_and_soln_vector(1, numFields);
355
356 /* Section 2: Related to subcell (side) integration. */
357 unsigned numSides = 4;
358 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim);
359 FieldContainer<double> cub_weights_side(numCubPointsSide);
360 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim);
361 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim);
362 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim);
363 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide);
364 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide);
365
366 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide);
367 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
368 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
369 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide);
370 FieldContainer<double> neumann_fields_per_side(1, numFields);
371
372 /* Section 3: Related to global interpolant. */
373 FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
374 FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
375 FieldContainer<double> interpolant(1, numInterpPoints);
376
377 FieldContainer<int> ipiv(numFields);
378
379
380
381 /******************* START COMPUTATION ***********************/
382
383 // get cubature points and weights
384 cellCub->getCubature(cub_points_cell, cub_weights_cell);
385
386 // compute geometric cell information
387 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
388 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
389 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
390
391 // compute weighted measure
392 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
393
395 // Computing mass matrices:
396 // tabulate values of basis functions at (reference) cubature points
397 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
398
399 // transform values of basis functions
400 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
401 value_of_basis_at_cub_points_cell);
402
403 // multiply with weighted measure
404 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
405 weighted_measure_cell,
406 transformed_value_of_basis_at_cub_points_cell);
407
408 // compute mass matrices
409 FunctionSpaceTools::integrate<double>(fe_matrix,
410 transformed_value_of_basis_at_cub_points_cell,
411 weighted_transformed_value_of_basis_at_cub_points_cell,
412 COMP_BLAS);
414
416 // Computing stiffness matrices:
417 // tabulate gradients of basis functions at (reference) cubature points
418 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
419
420 // transform gradients of basis functions
421 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
422 jacobian_inv_cell,
423 grad_of_basis_at_cub_points_cell);
424
425 // multiply with weighted measure
426 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
427 weighted_measure_cell,
428 transformed_grad_of_basis_at_cub_points_cell);
429
430 // compute stiffness matrices and sum into fe_matrix
431 FunctionSpaceTools::integrate<double>(fe_matrix,
432 transformed_grad_of_basis_at_cub_points_cell,
433 weighted_transformed_grad_of_basis_at_cub_points_cell,
434 COMP_BLAS,
435 true);
437
439 // Computing RHS contributions:
440 // map cell (reference) cubature points to physical space
441 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
442
443 // evaluate rhs function
444 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
445
446 // compute rhs
447 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
448 rhs_at_cub_points_cell_physical,
449 weighted_transformed_value_of_basis_at_cub_points_cell,
450 COMP_BLAS);
451
452 // compute neumann b.c. contributions and adjust rhs
453 sideCub->getCubature(cub_points_side, cub_weights_side);
454 for (unsigned i=0; i<numSides; i++) {
455 // compute geometric cell information
456 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell);
457 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell);
458 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell);
459
460 // compute weighted face measure
461 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell,
462 jacobian_side_refcell,
463 cub_weights_side,
464 i,
465 cell);
466
467 // tabulate values of basis functions at side cubature points, in the reference parent cell domain
468 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE);
469 // transform
470 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell,
471 value_of_basis_at_cub_points_side_refcell);
472
473 // multiply with weighted measure
474 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell,
475 weighted_measure_side_refcell,
476 transformed_value_of_basis_at_cub_points_side_refcell);
477
478 // compute Neumann data
479 // map side cubature points in reference parent cell domain to physical space
480 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell);
481 // now compute data
482 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell,
483 cell, (int)i, x_order, y_order, z_order);
484
485 FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
486 neumann_data_at_cub_points_side_physical,
487 weighted_transformed_value_of_basis_at_cub_points_side_refcell,
488 COMP_BLAS);
489
490 // adjust RHS
491 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
492 }
494
496 // Solution of linear system:
497 int info = 0;
498 Teuchos::LAPACK<int, double> solver;
499 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
501
503 // Building interpolant:
504 // evaluate basis at interpolation points
505 basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
506 // transform values of basis functions
507 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
508 value_of_basis_at_interp_points_ref);
509 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
511
512 /******************* END COMPUTATION ***********************/
513
514 RealSpaceTools<double>::subtract(interpolant, exact_solution);
515
516 *outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
517 << x_order << ", " << y_order << ", " << z_order
518 << ") and finite element interpolant of order " << basis_order << ": "
519 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
520 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
521
522 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
523 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
524 *outStream << "\n\nPatch test failed for solution polynomial order ("
525 << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
526 errorFlag++;
527 }
528 } // end for z_order
529 } // end for y_order
530 } // end for x_order
531
532 }
533 // Catch unexpected errors
534 catch (const std::logic_error & err) {
535 *outStream << err.what() << "\n\n";
536 errorFlag = -1000;
537 };
538
539 if (errorFlag != 0)
540 std::cout << "End Result: TEST FAILED\n";
541 else
542 std::cout << "End Result: TEST PASSED\n";
543
544 // reset format state of std::cout
545 std::cout.copyfmt(oldFormatState);
546
547 return errorFlag;
548}
void rhsFunc(FieldContainer< double > &, const FieldContainer< double > &, int, int, int)
right-hand side function
Definition: test_02.cpp:75
void u_exact(FieldContainer< double > &, const FieldContainer< double > &, int, int, int)
exact solution
Definition: test_02.cpp:180
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
Header file for utility class to provide array tools, such as tensor contractions,...
Header file for the Intrepid::CellTools class.
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
Header file for utility class to provide multidimensional containers.
Header file for the Intrepid::FunctionSpaceTools class.
Header file for the Intrepid::HGRAD_TET_C2_FEM class.
Header file for classes providing basic linear algebra functionality in 1D, 2D and 3D.
Implementation of the default H(grad)-compatible FEM basis of degree 2 on Tetrahedron cell.
A stateless class for operations on cell data. Provides methods for:
static void mapToReferenceSubcell(ArraySubcellPoint &refSubcellPoints, const ArrayParamPoint &paramPoints, const int subcellDim, const int subcellOrd, const shards::CellTopology &parentCell)
Computes parameterization maps of 1- and 2-subcells of reference cells.
static void mapToPhysicalFrame(ArrayPhysPoint &physPoints, const ArrayRefPoint &refPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)
Computes F, the reference-to-physical frame map.
static void getPhysicalSideNormals(ArraySideNormal &sideNormals, const ArrayJac &worksetJacobians, const int &worksetSideOrd, const shards::CellTopology &parentCell)
Computes non-normalized normal vectors to physical sides in a side workset .
static void setJacobianDet(ArrayJacDet &jacobianDet, const ArrayJac &jacobian)
Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F.
static void setJacobianInv(ArrayJacInv &jacobianInv, const ArrayJac &jacobian)
Computes the inverse of the Jacobian matrix DF of the reference-to-physical frame map F.
A factory class that generates specific instances of cubatures.
Teuchos::RCP< Cubature< Scalar, ArrayPoint, ArrayWeight > > create(const shards::CellTopology &cellTopology, const std::vector< int > &degree)
Factory method.
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
int dimension(const int whichDim) const
Returns the specified dimension.
Implementation of basic linear algebra functionality in Euclidean space.
static void subtract(Scalar *diffArray, const Scalar *inArray1, const Scalar *inArray2, const int size)
Subtracts contiguous data inArray2 from inArray1 of size size: diffArray = inArray1 - inArray2.
static Scalar vectorNorm(const Scalar *inVec, const size_t dim, const ENorm normType)
Computes norm (1, 2, infinity) of the vector inVec of size dim.
static void add(Scalar *sumArray, const Scalar *inArray1, const Scalar *inArray2, const int size)
Adds contiguous data inArray1 and inArray2 of size size: sumArray = inArray1 + inArray2.