Intrepid
example_12.cpp
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38// Denis Ridzal (dridzal@sandia.gov), or
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43
83// Intrepid includes
87//#include "Intrepid_ArrayTools.hpp"
89//#include "Intrepid_RealSpaceTools.hpp"
91#include "Intrepid_Utils.hpp"
92
93// Epetra includes
94#include "Epetra_Time.h"
95#include "Epetra_Map.h"
96#include "Epetra_FEVector.h"
97#include "Epetra_FECrsMatrix.h"
98#include "Epetra_SerialComm.h"
99
100// Teuchos includes
101#include "Teuchos_oblackholestream.hpp"
102#include "Teuchos_RCP.hpp"
103//#include "Teuchos_BLAS.hpp"
104//#include "Teuchos_BLAS_types.hpp"
105
106// Shards includes
107#include "Shards_CellTopology.hpp"
108
109// EpetraExt includes
110#include "EpetraExt_MultiVectorOut.h"
111
112using namespace std;
113using namespace Intrepid;
114
115int main(int argc, char *argv[]) {
116
117 //Check number of arguments
118 if (argc < 4) {
119 std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
120 std::cout <<"Usage:\n\n";
121 std::cout <<" ./Intrepid_example_Drivers_Example_10.exe deg NX NY NZ verbose\n\n";
122 std::cout <<" where \n";
123 std::cout <<" int deg - polynomial degree to be used (assumed >= 1) \n";
124 std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n";
125 std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n";
126 std::cout <<" int NZ - num intervals in y direction (assumed box domain, 0,1) \n";
127 std::cout <<" verbose (optional) - any character, indicates verbose output \n\n";
128 exit(1);
129 }
130
131 // This little trick lets us print to std::cout only if
132 // a (dummy) command-line argument is provided.
133 int iprint = argc - 1;
134 Teuchos::RCP<std::ostream> outStream;
135 Teuchos::oblackholestream bhs; // outputs nothing
136 if (iprint > 2)
137 outStream = Teuchos::rcp(&std::cout, false);
138 else
139 outStream = Teuchos::rcp(&bhs, false);
140
141 // Save the format state of the original std::cout.
142 Teuchos::oblackholestream oldFormatState;
143 oldFormatState.copyfmt(std::cout);
144
145 *outStream \
146 << "===============================================================================\n" \
147 << "| |\n" \
148 << "| Example: Build Stiffness Matrix for |\n" \
149 << "| Poisson Equation on Hexahedral Mesh |\n" \
150 << "| |\n" \
151 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \
152 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \
153 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \
154 << "| |\n" \
155 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
156 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
157 << "| |\n" \
158 << "===============================================================================\n";
159
160
161 // ************************************ GET INPUTS **************************************
162
163 int deg = atoi(argv[1]); // polynomial degree to use
164 int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1)
165 int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1)
166 int NZ = atoi(argv[4]); // num intervals in y direction (assumed box domain, 0,1)
167
168
169 // *********************************** CELL TOPOLOGY **********************************
170
171 // Get cell topology for base hexahedron
172 typedef shards::CellTopology CellTopology;
173 CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() );
174
175 // Get dimensions
176 int numNodesPerElem = hex_8.getNodeCount();
177 int spaceDim = hex_8.getDimension();
178
179 // *********************************** GENERATE MESH ************************************
180
181 *outStream << "Generating mesh ... \n\n";
182
183 *outStream << " NX" << " NY" << " NZ\n";
184 *outStream << std::setw(5) << NX <<
185 std::setw(5) << NY << std::setw(5) << NZ << "\n\n";
186
187 // Print mesh information
188 int numElems = NX*NY*NZ;
189 int numNodes = (NX+1)*(NY+1)*(NZ+1);
190 *outStream << " Number of Elements: " << numElems << " \n";
191 *outStream << " Number of Nodes: " << numNodes << " \n\n";
192
193 // Cube
194 double leftX = 0.0, rightX = 1.0;
195 double leftY = 0.0, rightY = 1.0;
196 double leftZ = 0.0, rightZ = 1.0;
197
198 // Mesh spacing
199 double hx = (rightX-leftX)/((double)NX);
200 double hy = (rightY-leftY)/((double)NY);
201 double hz = (rightZ-leftZ)/((double)NZ);
202
203 // Get nodal coordinates
204 FieldContainer<double> nodeCoord(numNodes, spaceDim);
205 FieldContainer<int> nodeOnBoundary(numNodes);
206 int inode = 0;
207 for (int k=0; k<NZ+1; k++)
208 {
209 for (int j=0; j<NY+1; j++)
210 {
211 for (int i=0; i<NX+1; i++)
212 {
213 nodeCoord(inode,0) = leftX + (double)i*hx;
214 nodeCoord(inode,1) = leftY + (double)j*hy;
215 nodeCoord(inode,2) = leftZ + (double)k*hz;
216 if (k==0 || k==NZ || j==0 || i==0 || j==NY || i==NX)
217 {
218 nodeOnBoundary(inode)=1;
219 }
220 else
221 {
222 nodeOnBoundary(inode)=0;
223 }
224 inode++;
225 }
226 }
227 }
228#define DUMP_DATA
229#ifdef DUMP_DATA
230 // Print nodal coords
231 ofstream fcoordout("coords.dat");
232 for (int i=0; i<numNodes; i++) {
233 fcoordout << nodeCoord(i,0) <<" ";
234 fcoordout << nodeCoord(i,1) <<" ";
235 fcoordout << nodeCoord(i,2) <<"\n";
236 }
237 fcoordout.close();
238#endif
239
240
241 // Element to Node map
242 // We'll keep it around, but this is only the DOFMap if you are in the lowest order case.
243 FieldContainer<int> elemToNode(numElems, numNodesPerElem);
244 int ielem = 0;
245 for (int k=0; k<NZ; k++)
246 {
247 for (int j=0; j<NY; j++)
248 {
249 for (int i=0; i<NX; i++)
250 {
251 elemToNode(ielem,0) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
252 elemToNode(ielem,1) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
253 elemToNode(ielem,2) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
254 elemToNode(ielem,3) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
255 elemToNode(ielem,4) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
256 elemToNode(ielem,5) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
257 elemToNode(ielem,6) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
258 elemToNode(ielem,7) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
259 ielem++;
260 }
261 }
262 }
263#ifdef DUMP_DATA
264 // Output connectivity
265 ofstream fe2nout("elem2node.dat");
266 for (int k=0;k<NZ;k++)
267 {
268 for (int j=0; j<NY; j++)
269 {
270 for (int i=0; i<NX; i++)
271 {
272 ielem = i + j * NX + k * NY * NY;
273 for (int m=0; m<numNodesPerElem; m++)
274 {
275 fe2nout << elemToNode(ielem,m) <<" ";
276 }
277 fe2nout <<"\n";
278 }
279 }
280 }
281 fe2nout.close();
282#endif
283
284 // ************************************ CUBATURE **************************************
285 *outStream << "Getting cubature ... \n\n";
286
287 // Get numerical integration points and weights
288 DefaultCubatureFactory<double> cubFactory;
289 int cubDegree = 2*deg;
290 Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(hex_8, cubDegree);
291
292 int cubDim = quadCub->getDimension();
293 int numCubPoints = quadCub->getNumPoints();
294
295 FieldContainer<double> cubPoints(numCubPoints, cubDim);
296 FieldContainer<double> cubWeights(numCubPoints);
297
298 quadCub->getCubature(cubPoints, cubWeights);
299
300
301 // ************************************** BASIS ***************************************
302
303 *outStream << "Getting basis ... \n\n";
304
305 // Define basis
306 Basis_HGRAD_HEX_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL);
307 int numFieldsG = quadHGradBasis.getCardinality();
308 FieldContainer<double> quadGVals(numFieldsG, numCubPoints);
309 FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim);
310
311 // Evaluate basis values and gradients at cubature points
312 quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE);
313 quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD);
314
315 // create the local-global mapping
316 FieldContainer<int> ltgMapping(numElems,numFieldsG);
317 const int numDOF = (NX*deg+1)*(NY*deg+1)*(NZ*deg+1);
318 ielem=0;
319 for (int k=0;k<NZ;k++)
320 {
321 for (int j=0;j<NY;j++)
322 {
323 for (int i=0;i<NX;i++)
324 {
325 const int start = k * ( NY * deg + 1 ) * ( NX * deg + 1 ) + j * ( NX * deg + 1 ) + i * deg;
326 // loop over local dof on this cell
327 int local_dof_cur=0;
328 for (int kloc=0;kloc<=deg;kloc++)
329 {
330 for (int jloc=0;jloc<=deg;jloc++)
331 {
332 for (int iloc=0;iloc<=deg;iloc++)
333 {
334 ltgMapping(ielem,local_dof_cur) = start
335 + kloc * ( NX * deg + 1 ) * ( NY * deg + 1 )
336 + jloc * ( NX * deg + 1 )
337 + iloc;
338 local_dof_cur++;
339 }
340 }
341 }
342 ielem++;
343 }
344 }
345 }
346#ifdef DUMP_DATA
347 // Output ltg mapping
348 ielem = 0;
349 ofstream ltgout("ltg.dat");
350 for (int k=0;k<NZ;k++)
351 {
352 for (int j=0; j<NY; j++)
353 {
354 for (int i=0; i<NX; i++)
355 {
356 ielem = i + j * NX + k * NX * NY;
357 for (int m=0; m<numFieldsG; m++)
358 {
359 ltgout << ltgMapping(ielem,m) <<" ";
360 }
361 ltgout <<"\n";
362 }
363 }
364 }
365 ltgout.close();
366#endif
367
368 // ********** DECLARE GLOBAL OBJECTS *************
369 Epetra_SerialComm Comm;
370 Epetra_Map globalMapG(numDOF, 0, Comm);
371 Epetra_FEVector u(globalMapG); u.Random();
372 Epetra_FEVector Ku(globalMapG);
373
374 // Let's preallocate the graph before we instantiate the matrix
375 Epetra_Time graphTimer(Comm);
376 Epetra_CrsGraph grph( Copy , globalMapG , 4 * numFieldsG );
377 for (int k=0;k<numElems;k++)
378 {
379 for (int i=0;i<numFieldsG;i++)
380 {
381 grph.InsertGlobalIndices(ltgMapping(k,i),numFieldsG,&ltgMapping(k,0));
382 }
383 }
384 grph.FillComplete();
385 const double graphTime = graphTimer.ElapsedTime();
386
387
388 // time the instantiation
389 Epetra_Time instantiateTimer(Comm);
390 Epetra_FECrsMatrix StiffMatrix(Copy,grph);
391 const double instantiateTime = instantiateTimer.ElapsedTime();
392
393
394 // ********** CONSTRUCT AND INSERT LOCAL STIFFNESS MATRICES ***********
395 *outStream << "Building local stiffness matrices...\n\n";
396 typedef CellTools<double> CellTools;
397 typedef FunctionSpaceTools fst;
398// int numCells = numElems;
399
400
401 // jacobian information
402 FieldContainer<double> refCellNodes(1,numNodesPerElem,spaceDim);
403 FieldContainer<double> cellJacobian(1,numCubPoints,spaceDim,spaceDim);
404 FieldContainer<double> cellJacobInv(1,numCubPoints,spaceDim,spaceDim);
405 FieldContainer<double> cellJacobDet(1,numCubPoints);
406
407 // element stiffness matrices and supporting storage space
408 FieldContainer<double> localStiffMatrix(1, numFieldsG, numFieldsG);
409 FieldContainer<double> transformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim);
410 FieldContainer<double> weightedTransformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim);
411 FieldContainer<double> weightedMeasure(1, numCubPoints);
412
413
414 Epetra_Time localConstructTimer( Comm );
415 refCellNodes(0,0,0) = 0.0; refCellNodes(0,0,1) = 0.0; refCellNodes(0,0,2) = 0.0;
416 refCellNodes(0,1,0) = hx; refCellNodes(0,1,1) = 0.0; refCellNodes(0,1,2) = 0.0;
417 refCellNodes(0,2,0) = hx; refCellNodes(0,2,1) = hy; refCellNodes(0,2,2) = 0.0;
418 refCellNodes(0,3,0) = 0.0; refCellNodes(0,3,1) = hy; refCellNodes(0,3,2) = 0.0;
419 refCellNodes(0,4,0) = 0.0; refCellNodes(0,4,1) = 0.0; refCellNodes(0,4,2) = hz;
420 refCellNodes(0,5,0) = hx; refCellNodes(0,5,1) = 0.0; refCellNodes(0,5,2) = hz;
421 refCellNodes(0,6,0) = hx; refCellNodes(0,6,1) = hy; refCellNodes(0,6,2) = hz;
422 refCellNodes(0,7,0) = 0.0; refCellNodes(0,7,1) = hy; refCellNodes(0,7,2) = hz;
423
424
425 // jacobian evaluation
426 CellTools::setJacobian(cellJacobian,cubPoints,refCellNodes,hex_8);
427 CellTools::setJacobianInv(cellJacobInv, cellJacobian );
428 CellTools::setJacobianDet(cellJacobDet, cellJacobian );
429
430 // transform reference element gradients to each cell
431 fst::HGRADtransformGRAD<double>(transformedBasisGradients, cellJacobInv, quadGrads);
432
433 // compute weighted measure
434 fst::computeCellMeasure<double>(weightedMeasure, cellJacobDet, cubWeights);
435
436 // multiply values with weighted measure
437 fst::multiplyMeasure<double>(weightedTransformedBasisGradients,
438 weightedMeasure, transformedBasisGradients);
439
440 // integrate to compute element stiffness matrix
441 fst::integrate<double>(localStiffMatrix,
442 transformedBasisGradients, weightedTransformedBasisGradients , COMP_BLAS);
443
444 const double localConstructTime = localConstructTimer.ElapsedTime();
445
446
447 Epetra_Time insertionTimer(Comm);
448
449 // *** Element loop ***
450 for (int k=0; k<numElems; k++)
451 {
452 // assemble into global matrix
453 StiffMatrix.InsertGlobalValues(numFieldsG,&ltgMapping(k,0),numFieldsG,&ltgMapping(k,0),&localStiffMatrix(0,0,0));
454
455 }
456 StiffMatrix.GlobalAssemble(); StiffMatrix.FillComplete();
457 const double insertionTime = insertionTimer.ElapsedTime( );
458
459 *outStream << "Time to construct matrix graph: " << graphTime << "\n";
460 *outStream << "Time to instantiate global stiffness matrix: " << instantiateTime << "\n";
461 *outStream << "Time to build local matrices (including Jacobian computation): "<< localConstructTime << "\n";
462 *outStream << "Time to assemble global matrix from local matrices: " << insertionTime << "\n";
463 *outStream << "Total construction time: " << graphTime + instantiateTime + localConstructTime + insertionTime << "\n";
464
465 Epetra_Time applyTimer(Comm);
466 StiffMatrix.Apply(u,Ku);
467 const double multTime = applyTimer.ElapsedTime();
468 *outStream << "Time to multiply onto a vector: " << multTime << "\n";
469
470 *outStream << "End Result: TEST PASSED\n";
471
472 // reset format state of std::cout
473 std::cout.copyfmt(oldFormatState);
474
475 return 0;
476}
477
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_HEX_Cn_FEM class.
Intrepid utilities.
A stateless class for operations on cell data. Provides methods for:
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.
Defines expert-level interfaces for the evaluation of functions and operators in physical space (supp...