xref: /libCEED/examples/petsc/multigrid.c (revision 81f92cf0318b9f3402d1efd37c448462967c3131)
1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
3 // reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 //                        libCEED + PETSc Example: CEED BPs 3-6 with Multigrid
18 //
19 // This example demonstrates a simple usage of libCEED with PETSc to solve the
20 // CEED BP benchmark problems, see http://ceed.exascaleproject.org/bps.
21 //
22 // The code uses higher level communication protocols in DMPlex.
23 //
24 // Build with:
25 //
26 //     make multigrid [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
27 //
28 // Sample runs:
29 //
30 //     multigrid -problem bp3
31 //     multigrid -problem bp4 -ceed /cpu/self
32 //     multigrid -problem bp5 -ceed /cpu/occa
33 //     multigrid -problem bp6 -ceed /gpu/cuda
34 //
35 //TESTARGS -ceed {ceed_resource} -test -problem bp3 -degree 3
36 
37 /// @file
38 /// CEED BPs 1-6 multigrid example using PETSc
39 const char help[] = "Solve CEED BPs using p-multigrid with PETSc and DMPlex\n";
40 
41 #define multigrid
42 #include "setup.h"
43 
44 int main(int argc, char **argv) {
45   PetscInt ierr;
46   MPI_Comm comm;
47   char filename[PETSC_MAX_PATH_LEN],
48        ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self";
49   double my_rt_start, my_rt, rt_min, rt_max;
50   PetscInt degree = 3, qextra, *lsize, *xlsize, *gsize, dim = 3, fineLevel,
51            melem[3] = {3, 3, 3}, ncompu = 1, numlevels = degree, *leveldegrees;
52   PetscScalar *r;
53   PetscBool test_mode, benchmark_mode, read_mesh, write_solution;
54   PetscLogStage solvestage;
55   DM  *dm, dmorig;
56   SNES snesdummy;
57   KSP ksp;
58   PC pc;
59   Mat *matO, *matPR, matcoarse;
60   Vec *X, *Xloc, *mult, rhs, rhsloc;
61   UserO *userO;
62   UserProlongRestr *userPR;
63   Ceed ceed;
64   CeedData *ceeddata;
65   CeedMemType memtyperequested;
66   CeedVector rhsceed, target;
67   CeedQFunction qferror, qfrestrict, qfprolong;
68   CeedOperator operror;
69   bpType bpchoice;
70   coarsenType coarsen;
71 
72   ierr = PetscInitialize(&argc, &argv, NULL, help);
73   if (ierr) return ierr;
74   comm = PETSC_COMM_WORLD;
75 
76   // Check PETSc CUDA avaliability
77   PetscBool petschavecuda, setmemtyperequest = PETSC_FALSE;
78   // *INDENT-OFF*
79   #ifdef PETSC_HAVE_CUDA
80   petschavecuda = PETSC_TRUE;
81   #else
82   petschavecuda = PETSC_FALSE;
83   #endif
84   // *INDENT-ON*
85 
86   // Parse command line options
87   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
88   bpchoice = CEED_BP3;
89   ierr = PetscOptionsEnum("-problem",
90                           "CEED benchmark problem to solve", NULL,
91                           bpTypes, (PetscEnum)bpchoice, (PetscEnum *)&bpchoice,
92                           NULL); CHKERRQ(ierr);
93   ncompu = bpOptions[bpchoice].ncompu;
94   test_mode = PETSC_FALSE;
95   ierr = PetscOptionsBool("-test",
96                           "Testing mode (do not print unless error is large)",
97                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
98   benchmark_mode = PETSC_FALSE;
99   ierr = PetscOptionsBool("-benchmark",
100                           "Benchmarking mode (prints benchmark statistics)",
101                           NULL, benchmark_mode, &benchmark_mode, NULL);
102   CHKERRQ(ierr);
103   write_solution = PETSC_FALSE;
104   ierr = PetscOptionsBool("-write_solution",
105                           "Write solution for visualization",
106                           NULL, write_solution, &write_solution, NULL);
107   CHKERRQ(ierr);
108   degree = test_mode ? 3 : 2;
109   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
110                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
111   if (degree < 1) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
112                              "-degree %D must be at least 1", degree);
113   qextra = bpOptions[bpchoice].qextra;
114   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
115                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
116   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
117                             NULL, ceedresource, ceedresource,
118                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
119   coarsen = COARSEN_UNIFORM;
120   ierr = PetscOptionsEnum("-coarsen",
121                           "Coarsening strategy to use", NULL,
122                           coarsenTypes, (PetscEnum)coarsen,
123                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
124   read_mesh = PETSC_FALSE;
125   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
126                             filename, filename, sizeof(filename), &read_mesh);
127   CHKERRQ(ierr);
128   if (!read_mesh) {
129     PetscInt tmp = dim;
130     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
131                                 melem, &tmp, NULL); CHKERRQ(ierr);
132   }
133   memtyperequested = petschavecuda ? CEED_MEM_DEVICE : CEED_MEM_HOST;
134   ierr = PetscOptionsEnum("-memtype",
135                           "CEED MemType requested", NULL,
136                           memTypes, (PetscEnum)memtyperequested,
137                           (PetscEnum *)&memtyperequested, &setmemtyperequest);
138   CHKERRQ(ierr);
139   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
140 
141   // Set up libCEED
142   CeedInit(ceedresource, &ceed);
143   CeedMemType memtypebackend;
144   CeedGetPreferredMemType(ceed, &memtypebackend);
145 
146   // Check memtype compatibility
147   if (!setmemtyperequest)
148     memtyperequested = memtypebackend;
149   else if (!petschavecuda && memtyperequested == CEED_MEM_DEVICE)
150     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP_SYS,
151              "PETSc was not built with CUDA. "
152              "Requested MemType CEED_MEM_DEVICE is not supported.", NULL);
153 
154   // Setup DM
155   if (read_mesh) {
156     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, PETSC_TRUE, &dmorig);
157     CHKERRQ(ierr);
158   } else {
159     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, PETSC_FALSE, melem, NULL,
160                                NULL, NULL, PETSC_TRUE,&dmorig); CHKERRQ(ierr);
161   }
162 
163   {
164     DM dmDist = NULL;
165     PetscPartitioner part;
166 
167     ierr = DMPlexGetPartitioner(dmorig, &part); CHKERRQ(ierr);
168     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
169     ierr = DMPlexDistribute(dmorig, 0, NULL, &dmDist); CHKERRQ(ierr);
170     if (dmDist) {
171       ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
172       dmorig = dmDist;
173     }
174   }
175 
176   // Allocate arrays for PETSc objects for each level
177   switch (coarsen) {
178   case COARSEN_UNIFORM:
179     numlevels = degree;
180     break;
181   case COARSEN_LOGARITHMIC:
182     numlevels = ceil(log(degree)/log(2)) + 1;
183     break;
184   }
185   ierr = PetscMalloc1(numlevels, &leveldegrees); CHKERRQ(ierr);
186   fineLevel = numlevels - 1;
187 
188   switch (coarsen) {
189   case COARSEN_UNIFORM:
190     for (int i=0; i<numlevels; i++) leveldegrees[i] = i + 1;
191     break;
192   case COARSEN_LOGARITHMIC:
193     for (int i=0; i<numlevels - 1; i++) leveldegrees[i] = pow(2,i);
194     leveldegrees[fineLevel] = degree;
195     break;
196   }
197   ierr = PetscMalloc1(numlevels, &dm); CHKERRQ(ierr);
198   ierr = PetscMalloc1(numlevels, &X); CHKERRQ(ierr);
199   ierr = PetscMalloc1(numlevels, &Xloc); CHKERRQ(ierr);
200   ierr = PetscMalloc1(numlevels, &mult); CHKERRQ(ierr);
201   ierr = PetscMalloc1(numlevels, &userO); CHKERRQ(ierr);
202   ierr = PetscMalloc1(numlevels, &userPR); CHKERRQ(ierr);
203   ierr = PetscMalloc1(numlevels, &matO); CHKERRQ(ierr);
204   ierr = PetscMalloc1(numlevels, &matPR); CHKERRQ(ierr);
205   ierr = PetscMalloc1(numlevels, &lsize); CHKERRQ(ierr);
206   ierr = PetscMalloc1(numlevels, &xlsize); CHKERRQ(ierr);
207   ierr = PetscMalloc1(numlevels, &gsize); CHKERRQ(ierr);
208 
209   // Setup DM and Operator Mat Shells for each level
210   for (CeedInt i=0; i<numlevels; i++) {
211     // Create DM
212     ierr = DMClone(dmorig, &dm[i]); CHKERRQ(ierr);
213     ierr = SetupDMByDegree(dm[i], leveldegrees[i], ncompu, bpchoice);
214     CHKERRQ(ierr);
215 
216     // Create vectors
217     if (memtyperequested == CEED_MEM_DEVICE) {
218       ierr = DMSetVecType(dm[i], VECCUDA); CHKERRQ(ierr);
219     }
220     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
221     ierr = VecGetLocalSize(X[i], &lsize[i]); CHKERRQ(ierr);
222     ierr = VecGetSize(X[i], &gsize[i]); CHKERRQ(ierr);
223     ierr = DMCreateLocalVector(dm[i], &Xloc[i]); CHKERRQ(ierr);
224     ierr = VecGetSize(Xloc[i], &xlsize[i]); CHKERRQ(ierr);
225 
226     // Operator
227     ierr = PetscMalloc1(1, &userO[i]); CHKERRQ(ierr);
228     ierr = MatCreateShell(comm, lsize[i], lsize[i], gsize[i], gsize[i],
229                           userO[i], &matO[i]); CHKERRQ(ierr);
230     ierr = MatShellSetOperation(matO[i], MATOP_MULT,
231                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
232     ierr = MatShellSetOperation(matO[i], MATOP_GET_DIAGONAL,
233                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
234     if (memtyperequested == CEED_MEM_DEVICE) {
235       ierr = MatShellSetVecType(matO[i], VECCUDA); CHKERRQ(ierr);
236     }
237 
238     // Level transfers
239     if (i > 0) {
240       // Interp
241       ierr = PetscMalloc1(1, &userPR[i]); CHKERRQ(ierr);
242       ierr = MatCreateShell(comm, lsize[i], lsize[i-1], gsize[i], gsize[i-1],
243                             userPR[i], &matPR[i]); CHKERRQ(ierr);
244       ierr = MatShellSetOperation(matPR[i], MATOP_MULT,
245                                   (void(*)(void))MatMult_Prolong);
246       CHKERRQ(ierr);
247       ierr = MatShellSetOperation(matPR[i], MATOP_MULT_TRANSPOSE,
248                                   (void(*)(void))MatMult_Restrict);
249       CHKERRQ(ierr);
250       if (memtyperequested == CEED_MEM_DEVICE) {
251         ierr = MatShellSetVecType(matPR[i], VECCUDA); CHKERRQ(ierr);
252       }
253     }
254   }
255   ierr = VecDuplicate(X[fineLevel], &rhs); CHKERRQ(ierr);
256 
257   // Print global grid information
258   if (!test_mode) {
259     PetscInt P = degree + 1, Q = P + qextra;
260 
261     const char *usedresource;
262     CeedGetResource(ceed, &usedresource);
263 
264     VecType vectype;
265     ierr = VecGetType(X[0], &vectype); CHKERRQ(ierr);
266 
267     ierr = PetscPrintf(comm,
268                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc + PCMG --\n"
269                        "  PETSc:\n"
270                        "    PETSc Vec Type                     : %s\n"
271                        "  libCEED:\n"
272                        "    libCEED Backend                    : %s\n"
273                        "    libCEED Backend MemType            : %s\n"
274                        "    libCEED User Requested MemType     : %s\n"
275                        "  Mesh:\n"
276                        "    Number of 1D Basis Nodes (p)       : %d\n"
277                        "    Number of 1D Quadrature Points (q) : %d\n"
278                        "    Global Nodes                       : %D\n"
279                        "    Owned Nodes                        : %D\n"
280                        "    DoF per node                       : %D\n"
281                        "  Multigrid:\n"
282                        "    Number of Levels                   : %d\n",
283                        bpchoice+1, vectype, usedresource,
284                        CeedMemTypes[memtypebackend],
285                        (setmemtyperequest) ?
286                        CeedMemTypes[memtyperequested] : "none",
287                        P, Q, gsize[fineLevel]/ncompu, lsize[fineLevel]/ncompu,
288                        ncompu, numlevels); CHKERRQ(ierr);
289   }
290 
291   // Create RHS vector
292   ierr = VecDuplicate(Xloc[fineLevel], &rhsloc); CHKERRQ(ierr);
293   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
294   if (memtyperequested == CEED_MEM_HOST) {
295     ierr = VecGetArray(rhsloc, &r); CHKERRQ(ierr);
296   } else {
297     ierr = VecCUDAGetArray(rhsloc, &r); CHKERRQ(ierr);
298   }
299   CeedVectorCreate(ceed, xlsize[fineLevel], &rhsceed);
300   CeedVectorSetArray(rhsceed, memtyperequested, CEED_USE_POINTER, r);
301 
302   // Set up libCEED operators on each level
303   ierr = PetscMalloc1(numlevels, &ceeddata); CHKERRQ(ierr);
304   for (int i=0; i<numlevels; i++) {
305     // Print level information
306     if (!test_mode && (i == 0 || i == fineLevel)) {
307       ierr = PetscPrintf(comm,"    Level %D (%s):\n"
308                          "      Number of 1D Basis Nodes (p)     : %d\n"
309                          "      Global Nodes                     : %D\n"
310                          "      Owned Nodes                      : %D\n",
311                          i, (i? "fine" : "coarse"), leveldegrees[i] + 1,
312                          gsize[i]/ncompu, lsize[i]/ncompu); CHKERRQ(ierr);
313     }
314     ierr = PetscMalloc1(1, &ceeddata[i]); CHKERRQ(ierr);
315     ierr = SetupLibceedByDegree(dm[i], ceed, leveldegrees[i], dim, qextra,
316                                 ncompu, gsize[i], xlsize[i], bpchoice,
317                                 ceeddata[i], i==(fineLevel), rhsceed, &target);
318     CHKERRQ(ierr);
319   }
320 
321   // Gather RHS
322   CeedVectorTakeArray(rhsceed, memtyperequested, NULL);
323   if (memtyperequested == CEED_MEM_HOST) {
324     ierr = VecRestoreArray(rhsloc, &r); CHKERRQ(ierr);
325   } else {
326     ierr = VecCUDARestoreArray(rhsloc, &r); CHKERRQ(ierr);
327   }
328   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
329   ierr = DMLocalToGlobal(dm[fineLevel], rhsloc, ADD_VALUES, rhs); CHKERRQ(ierr);
330   CeedVectorDestroy(&rhsceed);
331 
332   // Create the restriction/interpolation QFunction
333   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
334                               &qfrestrict);
335   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
336                               &qfprolong);
337 
338   // Set up libCEED level transfer operators
339   ierr = CeedLevelTransferSetup(ceed, numlevels, ncompu, bpchoice, ceeddata,
340                                 leveldegrees, qfrestrict, qfprolong);
341   CHKERRQ(ierr);
342 
343   // Create the error QFunction
344   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].error,
345                               bpOptions[bpchoice].errorfname, &qferror);
346   CeedQFunctionAddInput(qferror, "u", ncompu, CEED_EVAL_INTERP);
347   CeedQFunctionAddInput(qferror, "true_soln", ncompu, CEED_EVAL_NONE);
348   CeedQFunctionAddOutput(qferror, "error", ncompu, CEED_EVAL_NONE);
349 
350   // Create the error operator
351   CeedOperatorCreate(ceed, qferror, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
352                      &operror);
353   CeedOperatorSetField(operror, "u", ceeddata[fineLevel]->Erestrictu,
354                        ceeddata[fineLevel]->basisu, CEED_VECTOR_ACTIVE);
355   CeedOperatorSetField(operror, "true_soln", ceeddata[fineLevel]->Erestrictui,
356                        CEED_BASIS_COLLOCATED, target);
357   CeedOperatorSetField(operror, "error", ceeddata[fineLevel]->Erestrictui,
358                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
359 
360   // Calculate multiplicity
361   for (int i=0; i<numlevels; i++) {
362     PetscScalar *x;
363 
364     // CEED vector
365     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
366     ierr = VecGetArray(Xloc[i], &x); CHKERRQ(ierr);
367     CeedVectorSetArray(ceeddata[i]->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
368 
369     // Multiplicity
370     CeedElemRestrictionGetMultiplicity(ceeddata[i]->Erestrictu,
371                                        ceeddata[i]->xceed);
372     CeedVectorSyncArray(ceeddata[i]->xceed, CEED_MEM_HOST);
373 
374     // Restore vector
375     ierr = VecRestoreArray(Xloc[i], &x); CHKERRQ(ierr);
376 
377     // Creat mult vector
378     ierr = VecDuplicate(Xloc[i], &mult[i]); CHKERRQ(ierr);
379 
380     // Local-to-global
381     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
382     ierr = DMLocalToGlobal(dm[i], Xloc[i], ADD_VALUES, X[i]);
383     CHKERRQ(ierr);
384     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
385 
386     // Global-to-local
387     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
388     CHKERRQ(ierr);
389     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
390 
391     // Multiplicity scaling
392     ierr = VecReciprocal(mult[i]);
393   }
394 
395   // Set up Mat
396   for (int i=0; i<numlevels; i++) {
397     // User Operator
398     userO[i]->comm = comm;
399     userO[i]->dm = dm[i];
400     userO[i]->Xloc = Xloc[i];
401     ierr = VecDuplicate(Xloc[i], &userO[i]->Yloc); CHKERRQ(ierr);
402     userO[i]->xceed = ceeddata[i]->xceed;
403     userO[i]->yceed = ceeddata[i]->yceed;
404     userO[i]->op = ceeddata[i]->opapply;
405     userO[i]->ceed = ceed;
406     userO[i]->memtype = memtyperequested;
407     if (memtyperequested == CEED_MEM_HOST) {
408       userO[i]->VecGetArray = VecGetArray;
409       userO[i]->VecGetArrayRead = VecGetArrayRead;
410       userO[i]->VecRestoreArray = VecRestoreArray;
411       userO[i]->VecRestoreArrayRead = VecRestoreArrayRead;
412     } else {
413       userO[i]->VecGetArray = VecCUDAGetArray;
414       userO[i]->VecGetArrayRead = VecCUDAGetArrayRead;
415       userO[i]->VecRestoreArray = VecCUDARestoreArray;
416       userO[i]->VecRestoreArrayRead = VecCUDARestoreArrayRead;
417     }
418 
419     if (i > 0) {
420       // Prolongation/Restriction Operator
421       userPR[i]->comm = comm;
422       userPR[i]->dmf = dm[i];
423       userPR[i]->dmc = dm[i-1];
424       userPR[i]->locvecc = Xloc[i-1];
425       userPR[i]->locvecf = userO[i]->Yloc;
426       userPR[i]->multvec = mult[i];
427       userPR[i]->ceedvecc = userO[i-1]->xceed;
428       userPR[i]->ceedvecf = userO[i]->yceed;
429       userPR[i]->opprolong = ceeddata[i]->opprolong;
430       userPR[i]->oprestrict = ceeddata[i]->oprestrict;
431       userPR[i]->ceed = ceed;
432       userPR[i]->memtype = userO[i]->memtype;
433       userPR[i]->VecGetArray = userO[i]->VecGetArray;
434       userPR[i]->VecGetArrayRead = userO[i]->VecGetArrayRead;
435       userPR[i]->VecRestoreArray = userO[i]->VecRestoreArray;
436       userPR[i]->VecRestoreArrayRead = userO[i]->VecRestoreArrayRead;
437     }
438   }
439 
440   // Setup dummy SNES for AMG coarse solve
441   ierr = SNESCreate(comm, &snesdummy); CHKERRQ(ierr);
442   ierr = SNESSetDM(snesdummy, dm[0]); CHKERRQ(ierr);
443   ierr = SNESSetSolution(snesdummy, X[0]); CHKERRQ(ierr);
444 
445   // -- Jacobian matrix
446   ierr = DMSetMatType(dm[0], MATAIJ); CHKERRQ(ierr);
447   ierr = DMCreateMatrix(dm[0], &matcoarse); CHKERRQ(ierr);
448   ierr = SNESSetJacobian(snesdummy, matcoarse, matcoarse, NULL,
449                          NULL); CHKERRQ(ierr);
450 
451   // -- Residual evaluation function
452   ierr = SNESSetFunction(snesdummy, X[0], FormResidual_Ceed,
453                          userO[0]); CHKERRQ(ierr);
454 
455   // -- Form Jacobian
456   ierr = SNESComputeJacobianDefaultColor(snesdummy, X[0], matO[0],
457                                          matcoarse, NULL); CHKERRQ(ierr);
458 
459   // Set up KSP
460   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
461   {
462     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
463     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
464     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
465                             PETSC_DEFAULT); CHKERRQ(ierr);
466   }
467   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
468   ierr = KSPSetOperators(ksp, matO[fineLevel], matO[fineLevel]);
469   CHKERRQ(ierr);
470 
471   // Set up PCMG
472   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
473   PCMGCycleType pcgmcycletype = PC_MG_CYCLE_V;
474   {
475     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
476 
477     // PCMG levels
478     ierr = PCMGSetLevels(pc, numlevels, NULL); CHKERRQ(ierr);
479     for (int i=0; i<numlevels; i++) {
480       // Smoother
481       KSP smoother;
482       PC smoother_pc;
483       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
484       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
485       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
486       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
487       ierr = KSPSetOperators(smoother, matO[i], matO[i]); CHKERRQ(ierr);
488       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
489       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
490       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
491 
492       // Work vector
493       if (i < numlevels - 1) {
494         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
495       }
496 
497       // Level transfers
498       if (i > 0) {
499         // Interpolation
500         ierr = PCMGSetInterpolation(pc, i, matPR[i]); CHKERRQ(ierr);
501       }
502 
503       // Coarse solve
504       KSP coarse;
505       PC coarse_pc;
506       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
507       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
508       ierr = KSPSetOperators(coarse, matcoarse, matcoarse); CHKERRQ(ierr);
509 
510       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
511       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
512 
513       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
514       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
515       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
516       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
517     }
518 
519     // PCMG options
520     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
521     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
522     ierr = PCMGSetCycleType(pc, pcgmcycletype); CHKERRQ(ierr);
523   }
524 
525   // First run, if benchmarking
526   if (benchmark_mode) {
527     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
528     CHKERRQ(ierr);
529     ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
530     my_rt_start = MPI_Wtime();
531     ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
532     my_rt = MPI_Wtime() - my_rt_start;
533     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
534     CHKERRQ(ierr);
535     // Set maxits based on first iteration timing
536     if (my_rt > 0.02) {
537       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
538       CHKERRQ(ierr);
539     } else {
540       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
541       CHKERRQ(ierr);
542     }
543   }
544 
545   // Timed solve
546   ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
547   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
548 
549   // -- Performance logging
550   ierr = PetscLogStageRegister("Solve Stage", &solvestage); CHKERRQ(ierr);
551   ierr = PetscLogStagePush(solvestage); CHKERRQ(ierr);
552 
553   // -- Solve
554   my_rt_start = MPI_Wtime();
555   ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
556   my_rt = MPI_Wtime() - my_rt_start;
557 
558 
559   // -- Performance logging
560   ierr = PetscLogStagePop();
561 
562   // Output results
563   {
564     KSPType ksptype;
565     PCMGType pcmgtype;
566     KSPConvergedReason reason;
567     PetscReal rnorm;
568     PetscInt its;
569     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
570     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
571     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
572     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
573     ierr = PCMGGetType(pc, &pcmgtype); CHKERRQ(ierr);
574     if (!test_mode || reason < 0 || rnorm > 1e-8) {
575       ierr = PetscPrintf(comm,
576                          "  KSP:\n"
577                          "    KSP Type                           : %s\n"
578                          "    KSP Convergence                    : %s\n"
579                          "    Total KSP Iterations               : %D\n"
580                          "    Final rnorm                        : %e\n",
581                          ksptype, KSPConvergedReasons[reason], its,
582                          (double)rnorm); CHKERRQ(ierr);
583       ierr = PetscPrintf(comm,
584                          "  PCMG:\n"
585                          "    PCMG Type                          : %s\n"
586                          "    PCMG Cycle Type                    : %s\n",
587                          PCMGTypes[pcmgtype],
588                          PCMGCycleTypes[pcgmcycletype]); CHKERRQ(ierr);
589     }
590     if (!test_mode) {
591       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
592     }
593     {
594       PetscReal maxerror;
595       ierr = ComputeErrorMax(userO[fineLevel], operror, X[fineLevel], target,
596                              &maxerror); CHKERRQ(ierr);
597       PetscReal tol = 5e-2;
598       if (!test_mode || maxerror > tol) {
599         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
600         CHKERRQ(ierr);
601         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
602         CHKERRQ(ierr);
603         ierr = PetscPrintf(comm,
604                            "    Pointwise Error (max)              : %e\n"
605                            "    CG Solve Time                      : %g (%g) sec\n",
606                            (double)maxerror, rt_max, rt_min); CHKERRQ(ierr);
607       }
608     }
609     if (benchmark_mode && (!test_mode)) {
610       ierr = PetscPrintf(comm,
611                          "    DoFs/Sec in CG                     : %g (%g) million\n",
612                          1e-6*gsize[fineLevel]*its/rt_max,
613                          1e-6*gsize[fineLevel]*its/rt_min);
614       CHKERRQ(ierr);
615     }
616   }
617 
618   if (write_solution) {
619     PetscViewer vtkviewersoln;
620 
621     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
622     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
623     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtk"); CHKERRQ(ierr);
624     ierr = VecView(X[fineLevel], vtkviewersoln); CHKERRQ(ierr);
625     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
626   }
627 
628   // Cleanup
629   for (int i=0; i<numlevels; i++) {
630     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
631     ierr = VecDestroy(&Xloc[i]); CHKERRQ(ierr);
632     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
633     ierr = VecDestroy(&userO[i]->Yloc); CHKERRQ(ierr);
634     ierr = MatDestroy(&matO[i]); CHKERRQ(ierr);
635     ierr = PetscFree(userO[i]); CHKERRQ(ierr);
636     if (i > 0) {
637       ierr = MatDestroy(&matPR[i]); CHKERRQ(ierr);
638       ierr = PetscFree(userPR[i]); CHKERRQ(ierr);
639     }
640     ierr = CeedDataDestroy(i, ceeddata[i]); CHKERRQ(ierr);
641     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
642   }
643   ierr = PetscFree(leveldegrees); CHKERRQ(ierr);
644   ierr = PetscFree(dm); CHKERRQ(ierr);
645   ierr = PetscFree(X); CHKERRQ(ierr);
646   ierr = PetscFree(Xloc); CHKERRQ(ierr);
647   ierr = PetscFree(mult); CHKERRQ(ierr);
648   ierr = PetscFree(matO); CHKERRQ(ierr);
649   ierr = PetscFree(matPR); CHKERRQ(ierr);
650   ierr = PetscFree(ceeddata); CHKERRQ(ierr);
651   ierr = PetscFree(userO); CHKERRQ(ierr);
652   ierr = PetscFree(userPR); CHKERRQ(ierr);
653   ierr = PetscFree(lsize); CHKERRQ(ierr);
654   ierr = PetscFree(xlsize); CHKERRQ(ierr);
655   ierr = PetscFree(gsize); CHKERRQ(ierr);
656   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
657   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
658   ierr = MatDestroy(&matcoarse); CHKERRQ(ierr);
659   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
660   ierr = SNESDestroy(&snesdummy); CHKERRQ(ierr);
661   ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
662   CeedVectorDestroy(&target);
663   CeedQFunctionDestroy(&qferror);
664   CeedQFunctionDestroy(&qfrestrict);
665   CeedQFunctionDestroy(&qfprolong);
666   CeedOperatorDestroy(&operror);
667   CeedDestroy(&ceed);
668   return PetscFinalize();
669 }
670