xref: /libCEED/examples/petsc/multigrid.c (revision 2c58efb6e21741e7a04026bb6e2331c4d2d8bd66)
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 #include "bps.h"
42 
43 int main(int argc, char **argv) {
44   PetscInt ierr;
45   MPI_Comm comm;
46   char filename[PETSC_MAX_PATH_LEN],
47        ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self";
48   double my_rt_start, my_rt, rt_min, rt_max;
49   PetscInt degree = 3, qextra, *lsize, *xlsize, *gsize, dim = 3, fineLevel,
50            melem[3] = {3, 3, 3}, ncompu = 1, numlevels = degree, *leveldegrees;
51   PetscScalar *r;
52   PetscScalar eps = 1.0;
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   ierr = PetscOptionsScalar("-eps",
99                             "Epsilon parameter for Kershaw mesh transformation",
100                             NULL, eps, &eps, NULL);
101   if (eps > 1 || eps <= 0) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
102                                       "-eps %D must be (0,1]", eps);
103   degree = test_mode ? 3 : 2;
104   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
105                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
106   if (degree < 1) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
107                              "-degree %D must be at least 1", degree);
108   qextra = bpOptions[bpchoice].qextra;
109   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
110                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
111   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
112                             NULL, ceedresource, ceedresource,
113                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
114   coarsen = COARSEN_UNIFORM;
115   ierr = PetscOptionsEnum("-coarsen",
116                           "Coarsening strategy to use", NULL,
117                           coarsenTypes, (PetscEnum)coarsen,
118                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
119   read_mesh = PETSC_FALSE;
120   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
121                             filename, filename, sizeof(filename), &read_mesh);
122   CHKERRQ(ierr);
123   if (!read_mesh) {
124     PetscInt tmp = dim;
125     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
126                                 melem, &tmp, NULL); CHKERRQ(ierr);
127   }
128   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
129 
130   // Set up libCEED
131   CeedInit(ceedresource, &ceed);
132   CeedMemType memtypebackend;
133   CeedGetPreferredMemType(ceed, &memtypebackend);
134 
135   // Setup DM
136   if (read_mesh) {
137     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, PETSC_TRUE, &dmorig);
138     CHKERRQ(ierr);
139   } else {
140     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, PETSC_FALSE, melem, NULL,
141                                NULL, NULL, PETSC_TRUE,&dmorig); CHKERRQ(ierr);
142   }
143 
144   {
145     DM dmDist = NULL;
146     PetscPartitioner part;
147 
148     ierr = DMPlexGetPartitioner(dmorig, &part); CHKERRQ(ierr);
149     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
150     ierr = DMPlexDistribute(dmorig, 0, NULL, &dmDist); CHKERRQ(ierr);
151     if (dmDist) {
152       ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
153       dmorig = dmDist;
154     }
155   }
156 
157   // apply Kershaw mesh transformation
158   ierr = kershaw(dmorig, eps); CHKERRQ(ierr);
159 
160   VecType vectype;
161   switch (memtypebackend) {
162   case CEED_MEM_HOST: vectype = VECSTANDARD; break;
163   case CEED_MEM_DEVICE: {
164     const char *resolved;
165     CeedGetResource(ceed, &resolved);
166     if (strstr(resolved, "/gpu/cuda")) vectype = VECCUDA;
167     else if (strstr(resolved, "/gpu/hip/occa"))
168       vectype = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
169     else if (strstr(resolved, "/gpu/hip")) vectype = VECHIP;
170     else vectype = VECSTANDARD;
171   }
172   }
173   ierr = DMSetVecType(dmorig, vectype); CHKERRQ(ierr);
174   ierr = DMSetFromOptions(dmorig); CHKERRQ(ierr);
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 = DMGetVecType(dmorig, &vectype); CHKERRQ(ierr);
214     ierr = DMSetVecType(dm[i], vectype); CHKERRQ(ierr);
215     PetscInt dim;
216     ierr = DMGetDimension(dm[i], &dim); CHKERRQ(ierr);
217     ierr = SetupDMByDegree(dm[i], leveldegrees[i], ncompu, dim,
218                            bpOptions[bpchoice].enforcebc, bpOptions[bpchoice].bcsfunc);
219     CHKERRQ(ierr);
220 
221     // Create vectors
222     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
223     ierr = VecGetLocalSize(X[i], &lsize[i]); CHKERRQ(ierr);
224     ierr = VecGetSize(X[i], &gsize[i]); CHKERRQ(ierr);
225     ierr = DMCreateLocalVector(dm[i], &Xloc[i]); CHKERRQ(ierr);
226     ierr = VecGetSize(Xloc[i], &xlsize[i]); CHKERRQ(ierr);
227 
228     // Operator
229     ierr = PetscMalloc1(1, &userO[i]); CHKERRQ(ierr);
230     ierr = MatCreateShell(comm, lsize[i], lsize[i], gsize[i], gsize[i],
231                           userO[i], &matO[i]); CHKERRQ(ierr);
232     ierr = MatShellSetOperation(matO[i], MATOP_MULT,
233                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
234     ierr = MatShellSetOperation(matO[i], MATOP_GET_DIAGONAL,
235                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
236     ierr = MatShellSetVecType(matO[i], vectype); CHKERRQ(ierr);
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       ierr = MatShellSetVecType(matPR[i], vectype); CHKERRQ(ierr);
251     }
252   }
253   ierr = VecDuplicate(X[fineLevel], &rhs); CHKERRQ(ierr);
254 
255   // Print global grid information
256   if (!test_mode) {
257     PetscInt P = degree + 1, Q = P + qextra;
258 
259     const char *usedresource;
260     CeedGetResource(ceed, &usedresource);
261 
262     ierr = VecGetType(X[0], &vectype); CHKERRQ(ierr);
263 
264     ierr = PetscPrintf(comm,
265                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc + PCMG --\n"
266                        "  PETSc:\n"
267                        "    PETSc Vec Type                     : %s\n"
268                        "  libCEED:\n"
269                        "    libCEED Backend                    : %s\n"
270                        "    libCEED Backend MemType            : %s\n"
271                        "  Mesh:\n"
272                        "    Number of 1D Basis Nodes (p)       : %d\n"
273                        "    Number of 1D Quadrature Points (q) : %d\n"
274                        "    Global Nodes                       : %D\n"
275                        "    Owned Nodes                        : %D\n"
276                        "    DoF per node                       : %D\n"
277                        "  Multigrid:\n"
278                        "    Number of Levels                   : %d\n",
279                        bpchoice+1, vectype, usedresource,
280                        CeedMemTypes[memtypebackend],
281                        P, Q, gsize[fineLevel]/ncompu, lsize[fineLevel]/ncompu,
282                        ncompu, numlevels); CHKERRQ(ierr);
283   }
284 
285   // Create RHS vector
286   ierr = VecDuplicate(Xloc[fineLevel], &rhsloc); CHKERRQ(ierr);
287   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
288   ierr = VecGetArrayAndMemType(rhsloc, &r, &memtype); CHKERRQ(ierr);
289   CeedVectorCreate(ceed, xlsize[fineLevel], &rhsceed);
290   CeedVectorSetArray(rhsceed, MemTypeP2C(memtype), CEED_USE_POINTER, r);
291 
292   // Set up libCEED operators on each level
293   ierr = PetscMalloc1(numlevels, &ceeddata); CHKERRQ(ierr);
294   for (int i=0; i<numlevels; i++) {
295     // Print level information
296     if (!test_mode && (i == 0 || i == fineLevel)) {
297       ierr = PetscPrintf(comm,"    Level %D (%s):\n"
298                          "      Number of 1D Basis Nodes (p)     : %d\n"
299                          "      Global Nodes                     : %D\n"
300                          "      Owned Nodes                      : %D\n",
301                          i, (i? "fine" : "coarse"), leveldegrees[i] + 1,
302                          gsize[i]/ncompu, lsize[i]/ncompu); CHKERRQ(ierr);
303     }
304     ierr = PetscMalloc1(1, &ceeddata[i]); CHKERRQ(ierr);
305     ierr = SetupLibceedByDegree(dm[i], ceed, leveldegrees[i], dim, qextra,
306                                 dim, ncompu, gsize[i], xlsize[i], bpOptions[bpchoice],
307                                 ceeddata[i], i==(fineLevel), rhsceed, &target);
308     CHKERRQ(ierr);
309   }
310 
311   // Gather RHS
312   CeedVectorTakeArray(rhsceed, MemTypeP2C(memtype), NULL);
313   ierr = VecRestoreArrayAndMemType(rhsloc, &r); CHKERRQ(ierr);
314   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
315   ierr = DMLocalToGlobal(dm[fineLevel], rhsloc, ADD_VALUES, rhs); CHKERRQ(ierr);
316   CeedVectorDestroy(&rhsceed);
317 
318   // Create the restriction/interpolation QFunction
319   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
320                               &qfrestrict);
321   CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
322                               &qfprolong);
323 
324   // Set up libCEED level transfer operators
325   ierr = CeedLevelTransferSetup(ceed, numlevels, ncompu, ceeddata, leveldegrees,
326                                 qfrestrict, qfprolong); CHKERRQ(ierr);
327 
328   // Create the error QFunction
329   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].error,
330                               bpOptions[bpchoice].errorfname, &qferror);
331   CeedQFunctionAddInput(qferror, "u", ncompu, CEED_EVAL_INTERP);
332   CeedQFunctionAddInput(qferror, "true_soln", ncompu, CEED_EVAL_NONE);
333   CeedQFunctionAddOutput(qferror, "error", ncompu, CEED_EVAL_NONE);
334 
335   // Create the error operator
336   CeedOperatorCreate(ceed, qferror, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
337                      &operror);
338   CeedOperatorSetField(operror, "u", ceeddata[fineLevel]->Erestrictu,
339                        ceeddata[fineLevel]->basisu, CEED_VECTOR_ACTIVE);
340   CeedOperatorSetField(operror, "true_soln", ceeddata[fineLevel]->Erestrictui,
341                        CEED_BASIS_COLLOCATED, target);
342   CeedOperatorSetField(operror, "error", ceeddata[fineLevel]->Erestrictui,
343                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
344 
345   // Calculate multiplicity
346   for (int i=0; i<numlevels; i++) {
347     PetscScalar *x;
348 
349     // CEED vector
350     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
351     ierr = VecGetArray(Xloc[i], &x); CHKERRQ(ierr);
352     CeedVectorSetArray(ceeddata[i]->Xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
353 
354     // Multiplicity
355     CeedElemRestrictionGetMultiplicity(ceeddata[i]->Erestrictu,
356                                        ceeddata[i]->Xceed);
357     CeedVectorSyncArray(ceeddata[i]->Xceed, CEED_MEM_HOST);
358 
359     // Restore vector
360     ierr = VecRestoreArray(Xloc[i], &x); CHKERRQ(ierr);
361 
362     // Creat mult vector
363     ierr = VecDuplicate(Xloc[i], &mult[i]); CHKERRQ(ierr);
364 
365     // Local-to-global
366     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
367     ierr = DMLocalToGlobal(dm[i], Xloc[i], ADD_VALUES, X[i]);
368     CHKERRQ(ierr);
369     ierr = VecZeroEntries(Xloc[i]); CHKERRQ(ierr);
370 
371     // Global-to-local
372     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
373     CHKERRQ(ierr);
374     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
375 
376     // Multiplicity scaling
377     ierr = VecReciprocal(mult[i]);
378   }
379 
380   // Set up Mat
381   for (int i=0; i<numlevels; i++) {
382     // User Operator
383     userO[i]->comm = comm;
384     userO[i]->dm = dm[i];
385     userO[i]->Xloc = Xloc[i];
386     ierr = VecDuplicate(Xloc[i], &userO[i]->Yloc); CHKERRQ(ierr);
387     userO[i]->Xceed = ceeddata[i]->Xceed;
388     userO[i]->Yceed = ceeddata[i]->Yceed;
389     userO[i]->op = ceeddata[i]->opApply;
390     userO[i]->ceed = ceed;
391 
392     if (i > 0) {
393       // Prolongation/Restriction Operator
394       userPR[i]->comm = comm;
395       userPR[i]->dmf = dm[i];
396       userPR[i]->dmc = dm[i-1];
397       userPR[i]->locvecc = Xloc[i-1];
398       userPR[i]->locvecf = userO[i]->Yloc;
399       userPR[i]->multvec = mult[i];
400       userPR[i]->ceedvecc = userO[i-1]->Xceed;
401       userPR[i]->ceedvecf = userO[i]->Yceed;
402       userPR[i]->opProlong = ceeddata[i]->opProlong;
403       userPR[i]->opRestrict = ceeddata[i]->opRestrict;
404       userPR[i]->ceed = ceed;
405     }
406   }
407 
408   // Setup dummy SNES for AMG coarse solve
409   ierr = SNESCreate(comm, &snesdummy); CHKERRQ(ierr);
410   ierr = SNESSetDM(snesdummy, dm[0]); CHKERRQ(ierr);
411   ierr = SNESSetSolution(snesdummy, X[0]); CHKERRQ(ierr);
412 
413   // -- Jacobian matrix
414   ierr = DMSetMatType(dm[0], MATAIJ); CHKERRQ(ierr);
415   ierr = DMCreateMatrix(dm[0], &matcoarse); CHKERRQ(ierr);
416   ierr = SNESSetJacobian(snesdummy, matcoarse, matcoarse, NULL,
417                          NULL); CHKERRQ(ierr);
418 
419   // -- Residual evaluation function
420   ierr = SNESSetFunction(snesdummy, X[0], FormResidual_Ceed,
421                          userO[0]); CHKERRQ(ierr);
422 
423   // -- Form Jacobian
424   ierr = SNESComputeJacobianDefaultColor(snesdummy, X[0], matO[0],
425                                          matcoarse, NULL); CHKERRQ(ierr);
426 
427   // Set up KSP
428   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
429   {
430     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
431     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
432     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
433                             PETSC_DEFAULT); CHKERRQ(ierr);
434   }
435   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
436   ierr = KSPSetOperators(ksp, matO[fineLevel], matO[fineLevel]);
437   CHKERRQ(ierr);
438 
439   // Set up PCMG
440   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
441   PCMGCycleType pcgmcycletype = PC_MG_CYCLE_V;
442   {
443     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
444 
445     // PCMG levels
446     ierr = PCMGSetLevels(pc, numlevels, NULL); CHKERRQ(ierr);
447     for (int i=0; i<numlevels; i++) {
448       // Smoother
449       KSP smoother;
450       PC smoother_pc;
451       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
452       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
453       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
454       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
455       ierr = KSPSetOperators(smoother, matO[i], matO[i]); CHKERRQ(ierr);
456       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
457       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
458       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
459 
460       // Work vector
461       if (i < numlevels - 1) {
462         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
463       }
464 
465       // Level transfers
466       if (i > 0) {
467         // Interpolation
468         ierr = PCMGSetInterpolation(pc, i, matPR[i]); CHKERRQ(ierr);
469       }
470 
471       // Coarse solve
472       KSP coarse;
473       PC coarse_pc;
474       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
475       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
476       ierr = KSPSetOperators(coarse, matcoarse, matcoarse); CHKERRQ(ierr);
477 
478       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
479       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
480 
481       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
482       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
483       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
484       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
485     }
486 
487     // PCMG options
488     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
489     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
490     ierr = PCMGSetCycleType(pc, pcgmcycletype); CHKERRQ(ierr);
491   }
492 
493   // First run, if benchmarking
494   if (benchmark_mode) {
495     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
496     CHKERRQ(ierr);
497     ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
498     my_rt_start = MPI_Wtime();
499     ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
500     my_rt = MPI_Wtime() - my_rt_start;
501     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
502     CHKERRQ(ierr);
503     // Set maxits based on first iteration timing
504     if (my_rt > 0.02) {
505       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
506       CHKERRQ(ierr);
507     } else {
508       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
509       CHKERRQ(ierr);
510     }
511   }
512 
513   // Timed solve
514   ierr = VecZeroEntries(X[fineLevel]); CHKERRQ(ierr);
515   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
516 
517   // -- Performance logging
518   ierr = PetscLogStageRegister("Solve Stage", &solvestage); CHKERRQ(ierr);
519   ierr = PetscLogStagePush(solvestage); CHKERRQ(ierr);
520 
521   // -- Solve
522   my_rt_start = MPI_Wtime();
523   ierr = KSPSolve(ksp, rhs, X[fineLevel]); CHKERRQ(ierr);
524   my_rt = MPI_Wtime() - my_rt_start;
525 
526 
527   // -- Performance logging
528   ierr = PetscLogStagePop();
529 
530   // Output results
531   {
532     KSPType ksptype;
533     PCMGType pcmgtype;
534     KSPConvergedReason reason;
535     PetscReal rnorm;
536     PetscInt its;
537     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
538     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
539     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
540     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
541     ierr = PCMGGetType(pc, &pcmgtype); CHKERRQ(ierr);
542     if (!test_mode || reason < 0 || rnorm > 1e-8) {
543       ierr = PetscPrintf(comm,
544                          "  KSP:\n"
545                          "    KSP Type                           : %s\n"
546                          "    KSP Convergence                    : %s\n"
547                          "    Total KSP Iterations               : %D\n"
548                          "    Final rnorm                        : %e\n",
549                          ksptype, KSPConvergedReasons[reason], its,
550                          (double)rnorm); CHKERRQ(ierr);
551       ierr = PetscPrintf(comm,
552                          "  PCMG:\n"
553                          "    PCMG Type                          : %s\n"
554                          "    PCMG Cycle Type                    : %s\n",
555                          PCMGTypes[pcmgtype],
556                          PCMGCycleTypes[pcgmcycletype]); CHKERRQ(ierr);
557     }
558     if (!test_mode) {
559       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
560     }
561     {
562       PetscReal maxerror;
563       ierr = ComputeErrorMax(userO[fineLevel], operror, X[fineLevel], target,
564                              &maxerror); CHKERRQ(ierr);
565       PetscReal tol = 5e-2;
566       if (!test_mode || maxerror > tol) {
567         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
568         CHKERRQ(ierr);
569         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
570         CHKERRQ(ierr);
571         ierr = PetscPrintf(comm,
572                            "    Pointwise Error (max)              : %e\n"
573                            "    CG Solve Time                      : %g (%g) sec\n",
574                            (double)maxerror, rt_max, rt_min); CHKERRQ(ierr);
575       }
576     }
577     if (benchmark_mode && (!test_mode)) {
578       ierr = PetscPrintf(comm,
579                          "    DoFs/Sec in CG                     : %g (%g) million\n",
580                          1e-6*gsize[fineLevel]*its/rt_max,
581                          1e-6*gsize[fineLevel]*its/rt_min);
582       CHKERRQ(ierr);
583     }
584   }
585 
586   if (write_solution) {
587     PetscViewer vtkviewersoln;
588 
589     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
590     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
591     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtu"); CHKERRQ(ierr);
592     ierr = VecView(X[fineLevel], vtkviewersoln); CHKERRQ(ierr);
593     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
594   }
595 
596   // Cleanup
597   for (int i=0; i<numlevels; i++) {
598     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
599     ierr = VecDestroy(&Xloc[i]); CHKERRQ(ierr);
600     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
601     ierr = VecDestroy(&userO[i]->Yloc); CHKERRQ(ierr);
602     ierr = MatDestroy(&matO[i]); CHKERRQ(ierr);
603     ierr = PetscFree(userO[i]); CHKERRQ(ierr);
604     if (i > 0) {
605       ierr = MatDestroy(&matPR[i]); CHKERRQ(ierr);
606       ierr = PetscFree(userPR[i]); CHKERRQ(ierr);
607     }
608     ierr = CeedDataDestroy(i, ceeddata[i]); CHKERRQ(ierr);
609     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
610   }
611   ierr = PetscFree(leveldegrees); CHKERRQ(ierr);
612   ierr = PetscFree(dm); CHKERRQ(ierr);
613   ierr = PetscFree(X); CHKERRQ(ierr);
614   ierr = PetscFree(Xloc); CHKERRQ(ierr);
615   ierr = PetscFree(mult); CHKERRQ(ierr);
616   ierr = PetscFree(matO); CHKERRQ(ierr);
617   ierr = PetscFree(matPR); CHKERRQ(ierr);
618   ierr = PetscFree(ceeddata); CHKERRQ(ierr);
619   ierr = PetscFree(userO); CHKERRQ(ierr);
620   ierr = PetscFree(userPR); CHKERRQ(ierr);
621   ierr = PetscFree(lsize); CHKERRQ(ierr);
622   ierr = PetscFree(xlsize); CHKERRQ(ierr);
623   ierr = PetscFree(gsize); CHKERRQ(ierr);
624   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
625   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
626   ierr = MatDestroy(&matcoarse); CHKERRQ(ierr);
627   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
628   ierr = SNESDestroy(&snesdummy); CHKERRQ(ierr);
629   ierr = DMDestroy(&dmorig); CHKERRQ(ierr);
630   CeedVectorDestroy(&target);
631   CeedQFunctionDestroy(&qferror);
632   CeedQFunctionDestroy(&qfrestrict);
633   CeedQFunctionDestroy(&qfprolong);
634   CeedOperatorDestroy(&operror);
635   CeedDestroy(&ceed);
636   return PetscFinalize();
637 }
638