Intrepid
test_02.cpp
Go to the documentation of this file.
1// @HEADER
2// ************************************************************************
3//
4// Intrepid Package
5// Copyright (2007) Sandia Corporation
6//
7// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
8// license for use of this work by or on behalf of the U.S. Government.
9//
10// Redistribution and use in source and binary forms, with or without
11// modification, are permitted provided that the following conditions are
12// met:
13//
14// 1. Redistributions of source code must retain the above copyright
15// notice, this list of conditions and the following disclaimer.
16//
17// 2. Redistributions in binary form must reproduce the above copyright
18// notice, this list of conditions and the following disclaimer in the
19// documentation and/or other materials provided with the distribution.
20//
21// 3. Neither the name of the Corporation nor the names of the
22// contributors may be used to endorse or promote products derived from
23// this software without specific prior written permission.
24//
25// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
26// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
28// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
29// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
33// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
34// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36//
37// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
38// Denis Ridzal (dridzal@sandia.gov), or
39// Kara Peterson (kjpeter@sandia.gov)
40//
41// ************************************************************************
42// @HEADER
43
50#include "Intrepid_HGRAD_TET_Cn_FEM_ORTH.hpp"
57#include "Teuchos_oblackholestream.hpp"
58#include "Teuchos_RCP.hpp"
59#include "Teuchos_GlobalMPISession.hpp"
60#include "Teuchos_SerialDenseMatrix.hpp"
61#include "Teuchos_SerialDenseVector.hpp"
62#include "Teuchos_LAPACK.hpp"
63
64using namespace std;
65using namespace Intrepid;
66
67void rhsFunc( FieldContainer<double> &, const FieldContainer<double> &, int, int, int );
68void u_exact( FieldContainer<double> &, const FieldContainer<double> &, int, int, int );
69
70// This is the rhs for (div tau,w) = (f,w),
71// which makes f the negative Laplacian of scalar solution
72void rhsFunc( FieldContainer<double> &result,
73 const FieldContainer<double> &points,
74 int xd,
75 int yd ,
76 int zd)
77{
78 for (int cell=0;cell<result.dimension(0);cell++) {
79 for (int pt=0;pt<result.dimension(1);pt++) {
80 result(cell,pt) = 0.0;
81 if (xd >=2) {
82 result(cell,pt) += xd*(xd-1)*pow(points(cell,pt,0),xd-2)*pow(points(cell,pt,1),yd)
83 *pow(points(cell,pt,2),zd);
84 }
85 if (yd >=2) {
86 result(cell,pt) += yd*(yd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd-2)
87 *pow(points(cell,pt,2),zd);
88 }
89 if (zd>=2) {
90 result(cell,pt) += zd*(zd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd)
91 *pow(points(cell,pt,2),zd-2);
92
93 }
94 }
95 }
96}
97
98void u_exact( FieldContainer<double> &result,
99 const FieldContainer<double> &points,
100 int xd,
101 int yd,
102 int zd)
103{
104 for (int cell=0;cell<result.dimension(0);cell++){
105 for (int pt=0;pt<result.dimension(1);pt++) {
106 result(cell,pt) = std::pow(points(cell,pt,0),xd)*std::pow(points(cell,pt,1),yd)
107 *std::pow(points(cell,pt,2),zd);
108 }
109 }
110 return;
111}
112
113int main(int argc, char *argv[]) {
114 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
115
116 // This little trick lets us print to std::cout only if
117 // a (dummy) command-line argument is provided.
118 int iprint = argc - 1;
119 Teuchos::RCP<std::ostream> outStream;
120 Teuchos::oblackholestream bhs; // outputs nothing
121 if (iprint > 0)
122 outStream = Teuchos::rcp(&std::cout, false);
123 else
124 outStream = Teuchos::rcp(&bhs, false);
125
126 // Save the format state of the original std::cout.
127 Teuchos::oblackholestream oldFormatState;
128 oldFormatState.copyfmt(std::cout);
129
130 *outStream \
131 << "===============================================================================\n" \
132 << "| |\n" \
133 << "| Unit Test (Basis_HGRAD_TET_In_FEM) |\n" \
134 << "| |\n" \
135 << "| 1) Patch test involving H(div) matrices |\n" \
136 << "| for the Dirichlet problem on a tetrahedral patch |\n" \
137 << "| Omega with boundary Gamma. |\n" \
138 << "| |\n" \
139 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \
140 << "| Robert Kirby (robert.c.kirby@ttu.edu), |\n" \
141 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \
142 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \
143 << "| |\n" \
144 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
145 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
146 << "| |\n" \
147 << "===============================================================================\n" \
148 << "| TEST 1: Patch test |\n" \
149 << "===============================================================================\n";
150
151
152 int errorFlag = 0;
153
154 outStream -> precision(16);
155
156 try {
157 DefaultCubatureFactory<double> cubFactory; // create cubature factory
158 shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology
159 shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology
160
161 int cellDim = cell.getDimension();
162 int sideDim = side.getDimension();
163
164 int min_order = 0;
165 int max_order = 5;
166
167 int numIntervals = max_order;
168 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals+3))/6;
169 FieldContainer<double> interp_points_ref(numInterpPoints, cellDim);
170 int counter = 0;
171 for (int j=0; j<=numIntervals; j++) {
172 for (int i=0; i<=numIntervals-j; i++) {
173 for (int k=0;k<numIntervals-j-i;k++) {
174 interp_points_ref(counter,0) = i*(1.0/numIntervals);
175 interp_points_ref(counter,1) = j*(1.0/numIntervals);
176 interp_points_ref(counter,2) = k*(1.0/numIntervals);
177 counter++;
178 }
179 }
180 }
181
182 //interp_points_ref.resize(numInterpPoints,cellDim);
183
184 for (int basis_order=min_order;basis_order<=max_order;basis_order++) {
185 // create bases
186 Teuchos::RCP<Basis<double,FieldContainer<double> > > vectorBasis =
187 Teuchos::rcp(new Basis_HDIV_TET_In_FEM<double,FieldContainer<double> >(basis_order+1,POINTTYPE_EQUISPACED) );
188 Teuchos::RCP<Basis<double,FieldContainer<double> > > scalarBasis =
189 Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM_ORTH<double,FieldContainer<double> >(basis_order) );
190
191 int numVectorFields = vectorBasis->getCardinality();
192 int numScalarFields = scalarBasis->getCardinality();
193 int numTotalFields = numVectorFields + numScalarFields;
194
195 // create cubatures
196 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1));
197 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*(basis_order+1));
198
199 int numCubPointsCell = cellCub->getNumPoints();
200 int numCubPointsSide = sideCub->getNumPoints();
201
202 // hold cubature information
203 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
204 FieldContainer<double> cub_weights_cell(numCubPointsCell);
205 FieldContainer<double> cub_points_side( numCubPointsSide, sideDim );
206 FieldContainer<double> cub_weights_side( numCubPointsSide );
207 FieldContainer<double> cub_points_side_refcell( numCubPointsSide , cellDim );
208
209 // hold basis function information on refcell
210 FieldContainer<double> value_of_v_basis_at_cub_points_cell(numVectorFields, numCubPointsCell, cellDim );
211 FieldContainer<double> w_value_of_v_basis_at_cub_points_cell(1, numVectorFields, numCubPointsCell, cellDim);
212 FieldContainer<double> div_of_v_basis_at_cub_points_cell( numVectorFields, numCubPointsCell );
213 FieldContainer<double> w_div_of_v_basis_at_cub_points_cell( 1, numVectorFields , numCubPointsCell );
214 FieldContainer<double> value_of_s_basis_at_cub_points_cell(numScalarFields,numCubPointsCell);
215 FieldContainer<double> w_value_of_s_basis_at_cub_points_cell(1,numScalarFields,numCubPointsCell);
216
217 // containers for side integration:
218 // I just need the normal component of the vector basis
219 // and the exact solution at the cub points
220 FieldContainer<double> value_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide,cellDim);
221 FieldContainer<double> n_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide);
222 FieldContainer<double> w_n_of_v_basis_at_cub_points_side(1,numVectorFields,numCubPointsSide);
223 FieldContainer<double> diri_data_at_cub_points_side(1,numCubPointsSide);
224 FieldContainer<double> side_normal(cellDim);
225
226 // holds rhs data
227 FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell);
228
229 // FEM matrices and vectors
230 FieldContainer<double> fe_matrix_M(1,numVectorFields,numVectorFields);
231 FieldContainer<double> fe_matrix_B(1,numVectorFields,numScalarFields);
232 FieldContainer<double> fe_matrix(1,numTotalFields,numTotalFields);
233
234 FieldContainer<double> rhs_vector_vec(1,numVectorFields);
235 FieldContainer<double> rhs_vector_scal(1,numScalarFields);
236 FieldContainer<double> rhs_and_soln_vec(1,numTotalFields);
237
238 FieldContainer<int> ipiv(numTotalFields);
239 FieldContainer<double> value_of_s_basis_at_interp_points( numScalarFields , numInterpPoints);
240 FieldContainer<double> interpolant( 1 , numInterpPoints );
241
242 // set test tolerance
243 double zero = (basis_order+1)*(basis_order+1)*100*INTREPID_TOL;
244
245 // build matrices outside the loop, and then just do the rhs
246 // for each iteration
247
248 cellCub->getCubature(cub_points_cell, cub_weights_cell);
249 sideCub->getCubature(cub_points_side, cub_weights_side);
250
251 // need the vector basis & its divergences
252 vectorBasis->getValues(value_of_v_basis_at_cub_points_cell,
253 cub_points_cell,
254 OPERATOR_VALUE);
255 vectorBasis->getValues(div_of_v_basis_at_cub_points_cell,
256 cub_points_cell,
257 OPERATOR_DIV);
258
259 // need the scalar basis as well
260 scalarBasis->getValues(value_of_s_basis_at_cub_points_cell,
261 cub_points_cell,
262 OPERATOR_VALUE);
263
264 // construct mass matrix
265 cub_weights_cell.resize(1,numCubPointsCell);
266 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_v_basis_at_cub_points_cell ,
267 cub_weights_cell ,
268 value_of_v_basis_at_cub_points_cell );
269 cub_weights_cell.resize(numCubPointsCell);
270
271
272 value_of_v_basis_at_cub_points_cell.resize( 1 , numVectorFields , numCubPointsCell , cellDim );
273 FunctionSpaceTools::integrate<double>(fe_matrix_M,
274 w_value_of_v_basis_at_cub_points_cell ,
275 value_of_v_basis_at_cub_points_cell ,
276 COMP_BLAS );
277 value_of_v_basis_at_cub_points_cell.resize( numVectorFields , numCubPointsCell , cellDim );
278
279 // div matrix
280 cub_weights_cell.resize(1,numCubPointsCell);
281 FunctionSpaceTools::multiplyMeasure<double>(w_div_of_v_basis_at_cub_points_cell,
282 cub_weights_cell,
283 div_of_v_basis_at_cub_points_cell);
284 cub_weights_cell.resize(numCubPointsCell);
285
286 value_of_s_basis_at_cub_points_cell.resize(1,numScalarFields,numCubPointsCell);
287 FunctionSpaceTools::integrate<double>(fe_matrix_B,
288 w_div_of_v_basis_at_cub_points_cell ,
289 value_of_s_basis_at_cub_points_cell ,
290 COMP_BLAS );
291 value_of_s_basis_at_cub_points_cell.resize(numScalarFields,numCubPointsCell);
292
293
294 // construct div matrix
295
296 for (int x_order=0;x_order<=basis_order;x_order++) {
297 for (int y_order=0;y_order<=basis_order-x_order;y_order++) {
298 for (int z_order=0;z_order<=basis_order-x_order-y_order;z_order++) {
299
300
301 // reset global matrix since I destroyed it in LU factorization.
302 fe_matrix.initialize();
303 // insert mass matrix into global matrix
304 for (int i=0;i<numVectorFields;i++) {
305 for (int j=0;j<numVectorFields;j++) {
306 fe_matrix(0,i,j) = fe_matrix_M(0,i,j);
307 }
308 }
309
310 // insert div matrix into global matrix
311 for (int i=0;i<numVectorFields;i++) {
312 for (int j=0;j<numScalarFields;j++) {
313 fe_matrix(0,i,numVectorFields+j)=-fe_matrix_B(0,i,j);
314 fe_matrix(0,j+numVectorFields,i)=fe_matrix_B(0,i,j);
315 }
316 }
317
318 // clear old vector data
319 rhs_vector_vec.initialize();
320 rhs_vector_scal.initialize();
321 rhs_and_soln_vec.initialize();
322
323 // now get rhs vector
324 // rhs_vector_scal is just (rhs,w) for w in the scalar basis
325 // I already have the scalar basis tabulated.
326 cub_points_cell.resize(1,numCubPointsCell,cellDim);
327 rhsFunc(rhs_at_cub_points_cell,
328 cub_points_cell,
329 x_order,
330 y_order,
331 z_order);
332
333 cub_points_cell.resize(numCubPointsCell,cellDim);
334
335 cub_weights_cell.resize(1,numCubPointsCell);
336 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_s_basis_at_cub_points_cell,
337 cub_weights_cell,
338 value_of_s_basis_at_cub_points_cell);
339 cub_weights_cell.resize(numCubPointsCell);
340 FunctionSpaceTools::integrate<double>(rhs_vector_scal,
341 rhs_at_cub_points_cell,
342 w_value_of_s_basis_at_cub_points_cell,
343 COMP_BLAS);
344
345 for (int i=0;i<numScalarFields;i++) {
346 rhs_and_soln_vec(0,numVectorFields+i) = rhs_vector_scal(0,i);
347 }
348
349
350 // now get <u,v.n> on boundary
351 for (unsigned side_cur=0;side_cur<4;side_cur++) {
352 // map side cubature to current side
353 CellTools<double>::mapToReferenceSubcell( cub_points_side_refcell ,
354 cub_points_side ,
355 sideDim ,
356 (int)side_cur ,
357 cell );
358
359 // Evaluate dirichlet data
360 cub_points_side_refcell.resize(1,numCubPointsSide,cellDim);
361 u_exact(diri_data_at_cub_points_side,
362 cub_points_side_refcell,x_order,y_order,z_order);
363 cub_points_side_refcell.resize(numCubPointsSide,cellDim);
364
365 // get normal direction, this has the edge weight factored into it already
367 (int)side_cur,cell );
368
369 // v.n at cub points on side
370 vectorBasis->getValues(value_of_v_basis_at_cub_points_side ,
371 cub_points_side_refcell ,
372 OPERATOR_VALUE );
373
374
375 for (int i=0;i<numVectorFields;i++) {
376 for (int j=0;j<numCubPointsSide;j++) {
377 n_of_v_basis_at_cub_points_side(i,j) = 0.0;
378 for (int k=0;k<cellDim;k++) {
379 n_of_v_basis_at_cub_points_side(i,j) += side_normal(k) *
380 value_of_v_basis_at_cub_points_side(i,j,k);
381 }
382 }
383 }
384
385 cub_weights_side.resize(1,numCubPointsSide);
386 FunctionSpaceTools::multiplyMeasure<double>(w_n_of_v_basis_at_cub_points_side,
387 cub_weights_side,
388 n_of_v_basis_at_cub_points_side);
389 cub_weights_side.resize(numCubPointsSide);
390
391 FunctionSpaceTools::integrate<double>(rhs_vector_vec,
392 diri_data_at_cub_points_side,
393 w_n_of_v_basis_at_cub_points_side,
394 COMP_BLAS,
395 false);
396 for (int i=0;i<numVectorFields;i++) {
397 rhs_and_soln_vec(0,i) -= rhs_vector_vec(0,i);
398 }
399
400 }
401
402 // solve linear system
403 int info = 0;
404 Teuchos::LAPACK<int, double> solver;
405 solver.GESV(numTotalFields, 1, &fe_matrix[0], numTotalFields, &ipiv(0), &rhs_and_soln_vec[0],
406 numTotalFields, &info);
407
408 // compute interpolant; the scalar entries are last
409 scalarBasis->getValues(value_of_s_basis_at_interp_points,
410 interp_points_ref,
411 OPERATOR_VALUE);
412 for (int pt=0;pt<numInterpPoints;pt++) {
413 interpolant(0,pt)=0.0;
414 for (int i=0;i<numScalarFields;i++) {
415 interpolant(0,pt) += rhs_and_soln_vec(0,numVectorFields+i)
416 * value_of_s_basis_at_interp_points(i,pt);
417 }
418 }
419
420 interp_points_ref.resize(1,numInterpPoints,cellDim);
421 // get exact solution for comparison
422 FieldContainer<double> exact_solution(1,numInterpPoints);
423 u_exact( exact_solution , interp_points_ref , x_order, y_order, z_order);
424 interp_points_ref.resize(numInterpPoints,cellDim);
425
426 RealSpaceTools<double>::add(interpolant,exact_solution);
427
428 double nrm= RealSpaceTools<double>::vectorNorm(&interpolant[0],interpolant.dimension(1), NORM_TWO);
429
430 *outStream << "\nNorm-2 error between scalar components of exact solution of order ("
431 << x_order << ", " << y_order << ", " << z_order
432 << ") and finite element interpolant of order " << basis_order << ": "
433 << nrm << "\n";
434
435 if (nrm > zero) {
436 *outStream << "\n\nPatch test failed for solution polynomial order ("
437 << x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) ("
438 << basis_order << ", " << basis_order+1 << ")\n\n";
439 errorFlag++;
440 }
441
442 }
443 }
444 }
445 }
446
447 }
448
449 catch (const std::logic_error & err) {
450 *outStream << err.what() << "\n\n";
451 errorFlag = -1000;
452 };
453
454 if (errorFlag != 0)
455 std::cout << "End Result: TEST FAILED\n";
456 else
457 std::cout << "End Result: TEST PASSED\n";
458
459 // reset format state of std::cout
460 std::cout.copyfmt(oldFormatState);
461
462 return errorFlag;
463}
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::HDIV_TET_In_FEM class.
Header file for classes providing basic linear algebra functionality in 1D, 2D and 3D.
Implementation of the default H(div)-compatible Raviart-Thomas basis of arbitrary degree on Tetrahedr...
Implementation of the default H(grad)-compatible orthogonal basis of arbitrary degree on tetrahedron.
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 getReferenceSideNormal(ArraySideNormal &refSideNormal, const int &sideOrd, const shards::CellTopology &parentCell)
Computes constant normal vectors to sides of 2D or 3D reference cells.
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.