xref: /libCEED/examples/petsc/multigrid.c (revision bd4df46207a63b48a485389a63848eb7a2477f6b)
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
32 //     multigrid -problem bp5 -ceed /cpu/self
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   PetscMemType memtype;
62   UserO *userO;
63   UserProlongRestr *userPR;
64   Ceed ceed;
65   CeedData *ceeddata;
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   // Parse command line options
77   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
78   bpchoice = CEED_BP3;
79   ierr = PetscOptionsEnum("-problem",
80                           "CEED benchmark problem to solve", NULL,
81                           bpTypes, (PetscEnum)bpchoice, (PetscEnum *)&bpchoice,
82                           NULL); CHKERRQ(ierr);
83   ncompu = bpOptions[bpchoice].ncompu;
84   test_mode = PETSC_FALSE;
85   ierr = PetscOptionsBool("-test",
86                           "Testing mode (do not print unless error is large)",
87                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
88   benchmark_mode = PETSC_FALSE;
89   ierr = PetscOptionsBool("-benchmark",
90                           "Benchmarking mode (prints benchmark statistics)",
91                           NULL, benchmark_mode, &benchmark_mode, NULL);
92   CHKERRQ(ierr);
93   write_solution = PETSC_FALSE;
94   ierr = PetscOptionsBool("-write_solution",
95                           "Write solution for visualization",
96                           NULL, write_solution, &write_solution, NULL);
97   CHKERRQ(ierr);
98   degree = test_mode ? 3 : 2;
99   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
100                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
101   if (degree < 1) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
102                              "-degree %D must be at least 1", degree);
103   qextra = bpOptions[bpchoice].qextra;
104   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
105                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
106   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
107                             NULL, ceedresource, ceedresource,
108                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
109   coarsen = COARSEN_UNIFORM;
110   ierr = PetscOptionsEnum("-coarsen",
111                           "Coarsening strategy to use", NULL,
112                           coarsenTypes, (PetscEnum)coarsen,
113                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
114   read_mesh = PETSC_FALSE;
115   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
116                             filename, filename, sizeof(filename), &read_mesh);
117   CHKERRQ(ierr);
118   if (!read_mesh) {
119     PetscInt tmp = dim;
120     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
121                                 melem, &tmp, NULL); CHKERRQ(ierr);
122   }
123   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
124 
125   // Set up libCEED
126   CeedInit(ceedresource, &ceed);
127   CeedMemType memtypebackend;
128   CeedGetPreferredMemType(ceed, &memtypebackend);
129 
130   // Setup DM
131   if (read_mesh) {
132     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, PETSC_TRUE, &dmorig);
133     CHKERRQ(ierr);
134   } else {
135     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, PETSC_FALSE, melem, NULL,
136                                NULL, NULL, PETSC_TRUE,&dmorig); CHKERRQ(ierr);
137   }
138 
139   {
140     DM dmDist = NULL;
141     PetscPartitioner part;
142 
143     ierr = DMPlexGetPartitioner(dmorig, &part); CHKERRQ(ierr);
144     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
145     ierr = DMPlexDistribute(dmorig, 0, NULL, &dmDist); CHKERRQ(ierr);
146     if (dmDist) {
147       ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
148       dmorig = dmDist;
149     }
150   }
151 
152   VecType vectype;
153   switch (memtypebackend) {
154   case CEED_MEM_HOST: vectype = VECSTANDARD; break;
155   case CEED_MEM_DEVICE: {
156     const char *resolved;
157     CeedGetResource(ceed, &resolved);
158     if (strstr(resolved, "/gpu/cuda")) vectype = VECCUDA;
159     else if (strstr(resolved, "/gpu/hip/occa"))
160       vectype = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
161     else if (strstr(resolved, "/gpu/hip")) vectype = VECHIP;
162     else vectype = VECSTANDARD;
163   }
164   }
165   ierr = DMSetVecType(dmorig, vectype); CHKERRQ(ierr);
166   ierr = DMSetFromOptions(dmorig); CHKERRQ(ierr);
167 
168   // Allocate arrays for PETSc objects for each level
169   switch (coarsen) {
170   case COARSEN_UNIFORM:
171     numlevels = degree;
172     break;
173   case COARSEN_LOGARITHMIC:
174     numlevels = ceil(log(degree)/log(2)) + 1;
175     break;
176   }
177   ierr = PetscMalloc1(numlevels, &leveldegrees); CHKERRQ(ierr);
178   fineLevel = numlevels - 1;
179 
180   switch (coarsen) {
181   case COARSEN_UNIFORM:
182     for (int i=0; i<numlevels; i++) leveldegrees[i] = i + 1;
183     break;
184   case COARSEN_LOGARITHMIC:
185     for (int i=0; i<numlevels - 1; i++) leveldegrees[i] = pow(2,i);
186     leveldegrees[fineLevel] = degree;
187     break;
188   }
189   ierr = PetscMalloc1(numlevels, &dm); CHKERRQ(ierr);
190   ierr = PetscMalloc1(numlevels, &X); CHKERRQ(ierr);
191   ierr = PetscMalloc1(numlevels, &Xloc); CHKERRQ(ierr);
192   ierr = PetscMalloc1(numlevels, &mult); CHKERRQ(ierr);
193   ierr = PetscMalloc1(numlevels, &userO); CHKERRQ(ierr);
194   ierr = PetscMalloc1(numlevels, &userPR); CHKERRQ(ierr);
195   ierr = PetscMalloc1(numlevels, &matO); CHKERRQ(ierr);
196   ierr = PetscMalloc1(numlevels, &matPR); CHKERRQ(ierr);
197   ierr = PetscMalloc1(numlevels, &lsize); CHKERRQ(ierr);
198   ierr = PetscMalloc1(numlevels, &xlsize); CHKERRQ(ierr);
199   ierr = PetscMalloc1(numlevels, &gsize); CHKERRQ(ierr);
200 
201   // Setup DM and Operator Mat Shells for each level
202   for (CeedInt i=0; i<numlevels; i++) {
203     // Create DM
204     ierr = DMClone(dmorig, &dm[i]); CHKERRQ(ierr);
205     ierr = DMGetVecType(dmorig, &vectype); CHKERRQ(ierr);
206     ierr = DMSetVecType(dm[i], vectype); CHKERRQ(ierr);
207     ierr = SetupDMByDegree(dm[i], leveldegrees[i], ncompu, bpchoice);
208     CHKERRQ(ierr);
209 
210     // Create vectors
211     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
212     ierr = VecGetLocalSize(X[i], &lsize[i]); CHKERRQ(ierr);
213     ierr = VecGetSize(X[i], &gsize[i]); CHKERRQ(ierr);
214     ierr = DMCreateLocalVector(dm[i], &Xloc[i]); CHKERRQ(ierr);
215     ierr = VecGetSize(Xloc[i], &xlsize[i]); CHKERRQ(ierr);
216 
217     // Operator
218     ierr = PetscMalloc1(1, &userO[i]); CHKERRQ(ierr);
219     ierr = MatCreateShell(comm, lsize[i], lsize[i], gsize[i], gsize[i],
220                           userO[i], &matO[i]); CHKERRQ(ierr);
221     ierr = MatShellSetOperation(matO[i], MATOP_MULT,
222                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
223     ierr = MatShellSetOperation(matO[i], MATOP_GET_DIAGONAL,
224                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
225     ierr = MatShellSetVecType(matO[i], vectype); CHKERRQ(ierr);
226 
227     // Level transfers
228     if (i > 0) {
229       // Interp
230       ierr = PetscMalloc1(1, &userPR[i]); CHKERRQ(ierr);
231       ierr = MatCreateShell(comm, lsize[i], lsize[i-1], gsize[i], gsize[i-1],
232                             userPR[i], &matPR[i]); CHKERRQ(ierr);
233       ierr = MatShellSetOperation(matPR[i], MATOP_MULT,
234                                   (void(*)(void))MatMult_Prolong);
235       CHKERRQ(ierr);
236       ierr = MatShellSetOperation(matPR[i], MATOP_MULT_TRANSPOSE,
237                                   (void(*)(void))MatMult_Restrict);
238       CHKERRQ(ierr);
239       ierr = MatShellSetVecType(matPR[i], vectype); CHKERRQ(ierr);
240     }
241   }
242   ierr = VecDuplicate(X[fineLevel], &rhs); CHKERRQ(ierr);
243 
244   // Print global grid information
245   if (!test_mode) {
246     PetscInt P = degree + 1, Q = P + qextra;
247 
248     const char *usedresource;
249     CeedGetResource(ceed, &usedresource);
250 
251     ierr = VecGetType(X[0], &vectype); CHKERRQ(ierr);
252 
253     ierr = PetscPrintf(comm,
254                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc + PCMG --\n"
255                        "  PETSc:\n"
256                        "    PETSc Vec Type                     : %s\n"
257                        "  libCEED:\n"
258                        "    libCEED Backend                    : %s\n"
259                        "    libCEED Backend MemType            : %s\n"
260                        "  Mesh:\n"
261                        "    Number of 1D Basis Nodes (p)       : %d\n"
262                        "    Number of 1D Quadrature Points (q) : %d\n"
263                        "    Global Nodes                       : %D\n"
264                        "    Owned Nodes                        : %D\n"
265                        "    DoF per node                       : %D\n"
266                        "  Multigrid:\n"
267                        "    Number of Levels                   : %d\n",
268                        bpchoice+1, vectype, usedresource,
269                        CeedMemTypes[memtypebackend],
270                        P, Q, gsize[fineLevel]/ncompu, lsize[fineLevel]/ncompu,
271                        ncompu, numlevels); CHKERRQ(ierr);
272   }
273 
274   // Create RHS vector
275   ierr = VecDuplicate(Xloc[fineLevel], &rhsloc); CHKERRQ(ierr);
276   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
277   ierr = VecGetArrayAndMemType(rhsloc, &r, &memtype); CHKERRQ(ierr);
278   CeedVectorCreate(ceed, xlsize[fineLevel], &rhsceed);
279   CeedVectorSetArray(rhsceed, MemTypeP2C(memtype), CEED_USE_POINTER, r);
280 
281   // Set up libCEED operators on each level
282   ierr = PetscMalloc1(numlevels, &ceeddata); CHKERRQ(ierr);
283   for (int i=0; i<numlevels; i++) {
284     // Print level information
285     if (!test_mode && (i == 0 || i == fineLevel)) {
286       ierr = PetscPrintf(comm,"    Level %D (%s):\n"
287                          "      Number of 1D Basis Nodes (p)     : %d\n"
288                          "      Global Nodes                     : %D\n"
289                          "      Owned Nodes                      : %D\n",
290                          i, (i? "fine" : "coarse"), leveldegrees[i] + 1,
291                          gsize[i]/ncompu, lsize[i]/ncompu); CHKERRQ(ierr);
292     }
293     ierr = PetscMalloc1(1, &ceeddata[i]); CHKERRQ(ierr);
294     ierr = SetupLibceedByDegree(dm[i], ceed, leveldegrees[i], dim, qextra,
295                                 ncompu, gsize[i], xlsize[i], bpchoice,
296                                 ceeddata[i], i==(fineLevel), rhsceed, &target);
297     CHKERRQ(ierr);
298   }
299 
300   // Gather RHS
301   CeedVectorTakeArray(rhsceed, MemTypeP2C(memtype), NULL);
302   ierr = VecRestoreArrayAndMemType(rhsloc, &r); CHKERRQ(ierr);
303   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
304   ierr = DMLocalToGlobal(dm[fineLevel], rhsloc, ADD_VALUES, rhs); CHKERRQ(ierr);
305   CeedVectorDestroy(&rhsceed);
306 
307   // Create the restriction/interpolation QFunction
308   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
309                               &qfrestrict);
310   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
311                               &qfprolong);
312 
313   // Set up libCEED level transfer operators
314   ierr = CeedLevelTransferSetup(ceed, numlevels, ncompu, bpchoice, ceeddata,
315                                 leveldegrees, qfrestrict, qfprolong);
316   CHKERRQ(ierr);
317 
318   // Create the error QFunction
319   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].error,
320                               bpOptions[bpchoice].errorfname, &qferror);
321   CeedQFunctionAddInput(qferror, "u", ncompu, CEED_EVAL_INTERP);
322   CeedQFunctionAddInput(qferror, "true_soln", ncompu, CEED_EVAL_NONE);
323   CeedQFunctionAddOutput(qferror, "error", ncompu, CEED_EVAL_NONE);
324 
325   // Create the error operator
326   CeedOperatorCreate(ceed, qferror, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
327                      &operror);
328   CeedOperatorSetField(operror, "u", ceeddata[fineLevel]->Erestrictu,
329                        ceeddata[fineLevel]->basisu, CEED_VECTOR_ACTIVE);
330   CeedOperatorSetField(operror, "true_soln", ceeddata[fineLevel]->Erestrictui,
331                        CEED_BASIS_COLLOCATED, target);
332   CeedOperatorSetField(operror, "error", ceeddata[fineLevel]->Erestrictui,
333                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
334 
335   // Calculate multiplicity
336   for (int i=0; i<numlevels; i++) {
337     PetscScalar *x;
338 
339     // CEED vector
340     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
341     ierr = VecGetArray(Xloc[i], &x); CHKERRQ(ierr);
342     CeedVectorSetArray(ceeddata[i]->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
343 
344     // Multiplicity
345     CeedElemRestrictionGetMultiplicity(ceeddata[i]->Erestrictu,
346                                        ceeddata[i]->xceed);
347     CeedVectorSyncArray(ceeddata[i]->xceed, CEED_MEM_HOST);
348 
349     // Restore vector
350     ierr = VecRestoreArray(Xloc[i], &x); CHKERRQ(ierr);
351 
352     // Creat mult vector
353     ierr = VecDuplicate(Xloc[i], &mult[i]); CHKERRQ(ierr);
354 
355     // Local-to-global
356     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
357     ierr = DMLocalToGlobal(dm[i], Xloc[i], ADD_VALUES, X[i]);
358     CHKERRQ(ierr);
359     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
360 
361     // Global-to-local
362     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
363     CHKERRQ(ierr);
364     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
365 
366     // Multiplicity scaling
367     ierr = VecReciprocal(mult[i]);
368   }
369 
370   // Set up Mat
371   for (int i=0; i<numlevels; i++) {
372     // User Operator
373     userO[i]->comm = comm;
374     userO[i]->dm = dm[i];
375     userO[i]->Xloc = Xloc[i];
376     ierr = VecDuplicate(Xloc[i], &userO[i]->Yloc); CHKERRQ(ierr);
377     userO[i]->xceed = ceeddata[i]->xceed;
378     userO[i]->yceed = ceeddata[i]->yceed;
379     userO[i]->op = ceeddata[i]->opapply;
380     userO[i]->ceed = ceed;
381 
382     if (i > 0) {
383       // Prolongation/Restriction Operator
384       userPR[i]->comm = comm;
385       userPR[i]->dmf = dm[i];
386       userPR[i]->dmc = dm[i-1];
387       userPR[i]->locvecc = Xloc[i-1];
388       userPR[i]->locvecf = userO[i]->Yloc;
389       userPR[i]->multvec = mult[i];
390       userPR[i]->ceedvecc = userO[i-1]->xceed;
391       userPR[i]->ceedvecf = userO[i]->yceed;
392       userPR[i]->opprolong = ceeddata[i]->opprolong;
393       userPR[i]->oprestrict = ceeddata[i]->oprestrict;
394       userPR[i]->ceed = ceed;
395     }
396   }
397 
398   // Setup dummy SNES for AMG coarse solve
399   ierr = SNESCreate(comm, &snesdummy); CHKERRQ(ierr);
400   ierr = SNESSetDM(snesdummy, dm[0]); CHKERRQ(ierr);
401   ierr = SNESSetSolution(snesdummy, X[0]); CHKERRQ(ierr);
402 
403   // -- Jacobian matrix
404   ierr = DMSetMatType(dm[0], MATAIJ); CHKERRQ(ierr);
405   ierr = DMCreateMatrix(dm[0], &matcoarse); CHKERRQ(ierr);
406   ierr = SNESSetJacobian(snesdummy, matcoarse, matcoarse, NULL,
407                          NULL); CHKERRQ(ierr);
408 
409   // -- Residual evaluation function
410   ierr = SNESSetFunction(snesdummy, X[0], FormResidual_Ceed,
411                          userO[0]); CHKERRQ(ierr);
412 
413   // -- Form Jacobian
414   ierr = SNESComputeJacobianDefaultColor(snesdummy, X[0], matO[0],
415                                          matcoarse, NULL); CHKERRQ(ierr);
416 
417   // Set up KSP
418   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
419   {
420     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
421     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
422     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
423                             PETSC_DEFAULT); CHKERRQ(ierr);
424   }
425   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
426   ierr = KSPSetOperators(ksp, matO[fineLevel], matO[fineLevel]);
427   CHKERRQ(ierr);
428 
429   // Set up PCMG
430   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
431   PCMGCycleType pcgmcycletype = PC_MG_CYCLE_V;
432   {
433     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
434 
435     // PCMG levels
436     ierr = PCMGSetLevels(pc, numlevels, NULL); CHKERRQ(ierr);
437     for (int i=0; i<numlevels; i++) {
438       // Smoother
439       KSP smoother;
440       PC smoother_pc;
441       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
442       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
443       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
444       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
445       ierr = KSPSetOperators(smoother, matO[i], matO[i]); CHKERRQ(ierr);
446       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
447       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
448       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
449 
450       // Work vector
451       if (i < numlevels - 1) {
452         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
453       }
454 
455       // Level transfers
456       if (i > 0) {
457         // Interpolation
458         ierr = PCMGSetInterpolation(pc, i, matPR[i]); CHKERRQ(ierr);
459       }
460 
461       // Coarse solve
462       KSP coarse;
463       PC coarse_pc;
464       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
465       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
466       ierr = KSPSetOperators(coarse, matcoarse, matcoarse); CHKERRQ(ierr);
467 
468       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
469       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
470 
471       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
472       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
473       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
474       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
475     }
476 
477     // PCMG options
478     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
479     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
480     ierr = PCMGSetCycleType(pc, pcgmcycletype); CHKERRQ(ierr);
481   }
482 
483   // First run, if benchmarking
484   if (benchmark_mode) {
485     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
486     CHKERRQ(ierr);
487     ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
488     my_rt_start = MPI_Wtime();
489     ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
490     my_rt = MPI_Wtime() - my_rt_start;
491     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
492     CHKERRQ(ierr);
493     // Set maxits based on first iteration timing
494     if (my_rt > 0.02) {
495       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
496       CHKERRQ(ierr);
497     } else {
498       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
499       CHKERRQ(ierr);
500     }
501   }
502 
503   // Timed solve
504   ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
505   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
506 
507   // -- Performance logging
508   ierr = PetscLogStageRegister("Solve Stage", &solvestage); CHKERRQ(ierr);
509   ierr = PetscLogStagePush(solvestage); CHKERRQ(ierr);
510 
511   // -- Solve
512   my_rt_start = MPI_Wtime();
513   ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
514   my_rt = MPI_Wtime() - my_rt_start;
515 
516 
517   // -- Performance logging
518   ierr = PetscLogStagePop();
519 
520   // Output results
521   {
522     KSPType ksptype;
523     PCMGType pcmgtype;
524     KSPConvergedReason reason;
525     PetscReal rnorm;
526     PetscInt its;
527     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
528     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
529     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
530     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
531     ierr = PCMGGetType(pc, &pcmgtype); CHKERRQ(ierr);
532     if (!test_mode || reason < 0 || rnorm > 1e-8) {
533       ierr = PetscPrintf(comm,
534                          "  KSP:\n"
535                          "    KSP Type                           : %s\n"
536                          "    KSP Convergence                    : %s\n"
537                          "    Total KSP Iterations               : %D\n"
538                          "    Final rnorm                        : %e\n",
539                          ksptype, KSPConvergedReasons[reason], its,
540                          (double)rnorm); CHKERRQ(ierr);
541       ierr = PetscPrintf(comm,
542                          "  PCMG:\n"
543                          "    PCMG Type                          : %s\n"
544                          "    PCMG Cycle Type                    : %s\n",
545                          PCMGTypes[pcmgtype],
546                          PCMGCycleTypes[pcgmcycletype]); CHKERRQ(ierr);
547     }
548     if (!test_mode) {
549       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
550     }
551     {
552       PetscReal maxerror;
553       ierr = ComputeErrorMax(userO[fineLevel], operror, X[fineLevel], target,
554                              &maxerror); CHKERRQ(ierr);
555       PetscReal tol = 5e-2;
556       if (!test_mode || maxerror > tol) {
557         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
558         CHKERRQ(ierr);
559         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
560         CHKERRQ(ierr);
561         ierr = PetscPrintf(comm,
562                            "    Pointwise Error (max)              : %e\n"
563                            "    CG Solve Time                      : %g (%g) sec\n",
564                            (double)maxerror, rt_max, rt_min); CHKERRQ(ierr);
565       }
566     }
567     if (benchmark_mode && (!test_mode)) {
568       ierr = PetscPrintf(comm,
569                          "    DoFs/Sec in CG                     : %g (%g) million\n",
570                          1e-6*gsize[fineLevel]*its/rt_max,
571                          1e-6*gsize[fineLevel]*its/rt_min);
572       CHKERRQ(ierr);
573     }
574   }
575 
576   if (write_solution) {
577     PetscViewer vtkviewersoln;
578 
579     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
580     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
581     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtk"); CHKERRQ(ierr);
582     ierr = VecView(X[fineLevel], vtkviewersoln); CHKERRQ(ierr);
583     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
584   }
585 
586   // Cleanup
587   for (int i=0; i<numlevels; i++) {
588     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
589     ierr = VecDestroy(&Xloc[i]); CHKERRQ(ierr);
590     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
591     ierr = VecDestroy(&userO[i]->Yloc); CHKERRQ(ierr);
592     ierr = MatDestroy(&matO[i]); CHKERRQ(ierr);
593     ierr = PetscFree(userO[i]); CHKERRQ(ierr);
594     if (i > 0) {
595       ierr = MatDestroy(&matPR[i]); CHKERRQ(ierr);
596       ierr = PetscFree(userPR[i]); CHKERRQ(ierr);
597     }
598     ierr = CeedDataDestroy(i, ceeddata[i]); CHKERRQ(ierr);
599     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
600   }
601   ierr = PetscFree(leveldegrees); CHKERRQ(ierr);
602   ierr = PetscFree(dm); CHKERRQ(ierr);
603   ierr = PetscFree(X); CHKERRQ(ierr);
604   ierr = PetscFree(Xloc); CHKERRQ(ierr);
605   ierr = PetscFree(mult); CHKERRQ(ierr);
606   ierr = PetscFree(matO); CHKERRQ(ierr);
607   ierr = PetscFree(matPR); CHKERRQ(ierr);
608   ierr = PetscFree(ceeddata); CHKERRQ(ierr);
609   ierr = PetscFree(userO); CHKERRQ(ierr);
610   ierr = PetscFree(userPR); CHKERRQ(ierr);
611   ierr = PetscFree(lsize); CHKERRQ(ierr);
612   ierr = PetscFree(xlsize); CHKERRQ(ierr);
613   ierr = PetscFree(gsize); CHKERRQ(ierr);
614   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
615   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
616   ierr = MatDestroy(&matcoarse); CHKERRQ(ierr);
617   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
618   ierr = SNESDestroy(&snesdummy); CHKERRQ(ierr);
619   ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
620   CeedVectorDestroy(&target);
621   CeedQFunctionDestroy(&qferror);
622   CeedQFunctionDestroy(&qfrestrict);
623   CeedQFunctionDestroy(&qfprolong);
624   CeedOperatorDestroy(&operror);
625   CeedDestroy(&ceed);
626   return PetscFinalize();
627 }
628