xref: /libCEED/examples/petsc/multigrid.c (revision 53b04fa6da4b584296fd192b66fdd6cbd83ea08e)
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 <stdbool.h>
42 #include <string.h>
43 #include <ceed.h>
44 #include <petsc.h>
45 #include <petscdmplex.h>
46 #include <petscksp.h>
47 #include <petscsys.h>
48 
49 #include "bps.h"
50 #include "include/bpsproblemdata.h"
51 #include "include/petscmacros.h"
52 #include "include/petscutils.h"
53 #include "include/matops.h"
54 #include "include/structs.h"
55 #include "include/libceedsetup.h"
56 
57 #if PETSC_VERSION_LT(3,12,0)
58 #ifdef PETSC_HAVE_CUDA
59 #include <petsccuda.h>
60 // Note: With PETSc prior to version 3.12.0, providing the source path to
61 //       include 'cublas_v2.h' will be needed to use 'petsccuda.h'.
62 #endif
63 #endif
64 
65 int main(int argc, char **argv) {
66   PetscInt ierr;
67   MPI_Comm comm;
68   char filename[PETSC_MAX_PATH_LEN],
69        ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
70   double my_rt_start, my_rt, rt_min, rt_max;
71   PetscInt degree = 3, q_extra, *l_size, *xl_size, *g_size, dim = 3, fine_level,
72            mesh_elem[3] = {3, 3, 3}, num_comp_u = 1, num_levels = degree, *level_degrees;
73   PetscScalar *r;
74   PetscScalar eps = 1.0;
75   PetscBool test_mode, benchmark_mode, read_mesh, write_solution;
76   PetscLogStage solve_stage;
77   DM  *dm, dm_orig;
78   KSP ksp;
79   PC pc;
80   Mat *mat_O, *mat_pr, mat_coarse;
81   Vec *X, *X_loc, *mult, rhs, rhs_loc;
82   PetscMemType mem_type;
83   UserO *user_O;
84   UserProlongRestr *user_pr;
85   Ceed ceed;
86   CeedData *ceed_data;
87   CeedVector rhs_ceed, target;
88   CeedQFunction qf_error, qf_restrict, qf_prolong;
89   CeedOperator op_error;
90   BPType bp_choice;
91   CoarsenType coarsen;
92 
93   ierr = PetscInitialize(&argc, &argv, NULL, help);
94   if (ierr) return ierr;
95   comm = PETSC_COMM_WORLD;
96 
97   // Parse command line options
98   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
99   bp_choice = CEED_BP3;
100   ierr = PetscOptionsEnum("-problem",
101                           "CEED benchmark problem to solve", NULL,
102                           bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice,
103                           NULL); CHKERRQ(ierr);
104   num_comp_u = bp_options[bp_choice].num_comp_u;
105   test_mode = PETSC_FALSE;
106   ierr = PetscOptionsBool("-test",
107                           "Testing mode (do not print unless error is large)",
108                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
109   benchmark_mode = PETSC_FALSE;
110   ierr = PetscOptionsBool("-benchmark",
111                           "Benchmarking mode (prints benchmark statistics)",
112                           NULL, benchmark_mode, &benchmark_mode, NULL);
113   CHKERRQ(ierr);
114   write_solution = PETSC_FALSE;
115   ierr = PetscOptionsBool("-write_solution",
116                           "Write solution for visualization",
117                           NULL, write_solution, &write_solution, NULL);
118   CHKERRQ(ierr);
119   ierr = PetscOptionsScalar("-eps",
120                             "Epsilon parameter for Kershaw mesh transformation",
121                             NULL, eps, &eps, NULL);
122   if (eps > 1 || eps <= 0) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
123                                       "-eps %D must be (0,1]", eps);
124   degree = test_mode ? 3 : 2;
125   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
126                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
127   if (degree < 1) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
128                              "-degree %D must be at least 1", degree);
129   q_extra = bp_options[bp_choice].q_extra;
130   ierr = PetscOptionsInt("-q_extra", "Number of extra quadrature points",
131                          NULL, q_extra, &q_extra, NULL); CHKERRQ(ierr);
132   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
133                             NULL, ceed_resource, ceed_resource,
134                             sizeof(ceed_resource), NULL); CHKERRQ(ierr);
135   coarsen = COARSEN_UNIFORM;
136   ierr = PetscOptionsEnum("-coarsen",
137                           "Coarsening strategy to use", NULL,
138                           coarsen_types, (PetscEnum)coarsen,
139                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
140   read_mesh = PETSC_FALSE;
141   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
142                             filename, filename, sizeof(filename), &read_mesh);
143   CHKERRQ(ierr);
144   if (!read_mesh) {
145     PetscInt tmp = dim;
146     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
147                                 mesh_elem, &tmp, NULL); CHKERRQ(ierr);
148   }
149   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
150 
151   // Set up libCEED
152   CeedInit(ceed_resource, &ceed);
153   CeedMemType mem_type_backend;
154   CeedGetPreferredMemType(ceed, &mem_type_backend);
155 
156   // Setup DM
157   if (read_mesh) {
158     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, NULL, PETSC_TRUE,
159                                 &dm_orig);
160     CHKERRQ(ierr);
161   } else {
162     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, PETSC_FALSE, mesh_elem, NULL,
163                                NULL, NULL, PETSC_TRUE, &dm_orig); CHKERRQ(ierr);
164   }
165 
166   {
167     DM dm_dist = NULL;
168     PetscPartitioner part;
169 
170     ierr = DMPlexGetPartitioner(dm_orig, &part); CHKERRQ(ierr);
171     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
172     ierr = DMPlexDistribute(dm_orig, 0, NULL, &dm_dist); CHKERRQ(ierr);
173     if (dm_dist) {
174       ierr = DMDestroy(&dm_orig); CHKERRQ(ierr);
175       dm_orig = dm_dist;
176     }
177   }
178 
179   // Apply Kershaw mesh transformation
180   ierr = Kershaw(dm_orig, eps); CHKERRQ(ierr);
181 
182   VecType vec_type;
183   switch (mem_type_backend) {
184   case CEED_MEM_HOST: vec_type = VECSTANDARD; break;
185   case CEED_MEM_DEVICE: {
186     const char *resolved;
187     CeedGetResource(ceed, &resolved);
188     if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
189     else if (strstr(resolved, "/gpu/hip/occa"))
190       vec_type = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
191     else if (strstr(resolved, "/gpu/hip")) vec_type = VECHIP;
192     else vec_type = VECSTANDARD;
193   }
194   }
195   ierr = DMSetVecType(dm_orig, vec_type); CHKERRQ(ierr);
196   ierr = DMSetFromOptions(dm_orig); CHKERRQ(ierr);
197 
198   // Allocate arrays for PETSc objects for each level
199   switch (coarsen) {
200   case COARSEN_UNIFORM:
201     num_levels = degree;
202     break;
203   case COARSEN_LOGARITHMIC:
204     num_levels = ceil(log(degree)/log(2)) + 1;
205     break;
206   }
207   ierr = PetscMalloc1(num_levels, &level_degrees); CHKERRQ(ierr);
208   fine_level = num_levels - 1;
209 
210   switch (coarsen) {
211   case COARSEN_UNIFORM:
212     for (int i=0; i<num_levels; i++) level_degrees[i] = i + 1;
213     break;
214   case COARSEN_LOGARITHMIC:
215     for (int i=0; i<num_levels - 1; i++) level_degrees[i] = pow(2,i);
216     level_degrees[fine_level] = degree;
217     break;
218   }
219   ierr = PetscMalloc1(num_levels, &dm); CHKERRQ(ierr);
220   ierr = PetscMalloc1(num_levels, &X); CHKERRQ(ierr);
221   ierr = PetscMalloc1(num_levels, &X_loc); CHKERRQ(ierr);
222   ierr = PetscMalloc1(num_levels, &mult); CHKERRQ(ierr);
223   ierr = PetscMalloc1(num_levels, &user_O); CHKERRQ(ierr);
224   ierr = PetscMalloc1(num_levels, &user_pr); CHKERRQ(ierr);
225   ierr = PetscMalloc1(num_levels, &mat_O); CHKERRQ(ierr);
226   ierr = PetscMalloc1(num_levels, &mat_pr); CHKERRQ(ierr);
227   ierr = PetscMalloc1(num_levels, &l_size); CHKERRQ(ierr);
228   ierr = PetscMalloc1(num_levels, &xl_size); CHKERRQ(ierr);
229   ierr = PetscMalloc1(num_levels, &g_size); CHKERRQ(ierr);
230 
231   // Setup DM and Operator Mat Shells for each level
232   for (CeedInt i=0; i<num_levels; i++) {
233     // Create DM
234     ierr = DMClone(dm_orig, &dm[i]); CHKERRQ(ierr);
235     ierr = DMGetVecType(dm_orig, &vec_type); CHKERRQ(ierr);
236     ierr = DMSetVecType(dm[i], vec_type); CHKERRQ(ierr);
237     PetscInt dim;
238     ierr = DMGetDimension(dm[i], &dim); CHKERRQ(ierr);
239     ierr = SetupDMByDegree(dm[i], level_degrees[i], num_comp_u, dim,
240                            bp_options[bp_choice].enforce_bc, bp_options[bp_choice].bc_func);
241     CHKERRQ(ierr);
242 
243     // Create vectors
244     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
245     ierr = VecGetLocalSize(X[i], &l_size[i]); CHKERRQ(ierr);
246     ierr = VecGetSize(X[i], &g_size[i]); CHKERRQ(ierr);
247     ierr = DMCreateLocalVector(dm[i], &X_loc[i]); CHKERRQ(ierr);
248     ierr = VecGetSize(X_loc[i], &xl_size[i]); CHKERRQ(ierr);
249 
250     // Operator
251     ierr = PetscMalloc1(1, &user_O[i]); CHKERRQ(ierr);
252     ierr = MatCreateShell(comm, l_size[i], l_size[i], g_size[i], g_size[i],
253                           user_O[i], &mat_O[i]); CHKERRQ(ierr);
254     ierr = MatShellSetOperation(mat_O[i], MATOP_MULT,
255                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
256     ierr = MatShellSetOperation(mat_O[i], MATOP_GET_DIAGONAL,
257                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
258     ierr = MatShellSetVecType(mat_O[i], vec_type); CHKERRQ(ierr);
259 
260     // Level transfers
261     if (i > 0) {
262       // Interp
263       ierr = PetscMalloc1(1, &user_pr[i]); CHKERRQ(ierr);
264       ierr = MatCreateShell(comm, l_size[i], l_size[i-1], g_size[i], g_size[i-1],
265                             user_pr[i], &mat_pr[i]); CHKERRQ(ierr);
266       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT,
267                                   (void(*)(void))MatMult_Prolong);
268       CHKERRQ(ierr);
269       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT_TRANSPOSE,
270                                   (void(*)(void))MatMult_Restrict);
271       CHKERRQ(ierr);
272       ierr = MatShellSetVecType(mat_pr[i], vec_type); CHKERRQ(ierr);
273     }
274   }
275   ierr = VecDuplicate(X[fine_level], &rhs); CHKERRQ(ierr);
276 
277   // Print global grid information
278   if (!test_mode) {
279     PetscInt P = degree + 1, Q = P + q_extra;
280 
281     const char *used_resource;
282     CeedGetResource(ceed, &used_resource);
283 
284     ierr = VecGetType(X[0], &vec_type); CHKERRQ(ierr);
285 
286     ierr = PetscPrintf(comm,
287                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc + PCMG --\n"
288                        "  PETSc:\n"
289                        "    PETSc Vec Type                     : %s\n"
290                        "  libCEED:\n"
291                        "    libCEED Backend                    : %s\n"
292                        "    libCEED Backend MemType            : %s\n"
293                        "  Mesh:\n"
294                        "    Number of 1D Basis Nodes (p)       : %d\n"
295                        "    Number of 1D Quadrature Points (q) : %d\n"
296                        "    Global Nodes                       : %D\n"
297                        "    Owned Nodes                        : %D\n"
298                        "    DoF per node                       : %D\n"
299                        "  Multigrid:\n"
300                        "    Number of Levels                   : %d\n",
301                        bp_choice+1, vec_type, used_resource,
302                        CeedMemTypes[mem_type_backend],
303                        P, Q, g_size[fine_level]/num_comp_u, l_size[fine_level]/num_comp_u,
304                        num_comp_u, num_levels); CHKERRQ(ierr);
305   }
306 
307   // Create RHS vector
308   ierr = VecDuplicate(X_loc[fine_level], &rhs_loc); CHKERRQ(ierr);
309   ierr = VecZeroEntries(rhs_loc); CHKERRQ(ierr);
310   ierr = VecGetArrayAndMemType(rhs_loc, &r, &mem_type); CHKERRQ(ierr);
311   CeedVectorCreate(ceed, xl_size[fine_level], &rhs_ceed);
312   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
313 
314   // Set up libCEED operators on each level
315   ierr = PetscMalloc1(num_levels, &ceed_data); CHKERRQ(ierr);
316   for (int i=0; i<num_levels; i++) {
317     // Print level information
318     if (!test_mode && (i == 0 || i == fine_level)) {
319       ierr = PetscPrintf(comm,"    Level %D (%s):\n"
320                          "      Number of 1D Basis Nodes (p)     : %d\n"
321                          "      Global Nodes                     : %D\n"
322                          "      Owned Nodes                      : %D\n",
323                          i, (i? "fine" : "coarse"), level_degrees[i] + 1,
324                          g_size[i]/num_comp_u, l_size[i]/num_comp_u); CHKERRQ(ierr);
325     }
326     ierr = PetscMalloc1(1, &ceed_data[i]); CHKERRQ(ierr);
327     ierr = SetupLibceedByDegree(dm[i], ceed, level_degrees[i], dim, q_extra,
328                                 dim, num_comp_u, g_size[i], xl_size[i], bp_options[bp_choice],
329                                 ceed_data[i], i==(fine_level), rhs_ceed, &target);
330     CHKERRQ(ierr);
331   }
332 
333   // Gather RHS
334   CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL);
335   ierr = VecRestoreArrayAndMemType(rhs_loc, &r); CHKERRQ(ierr);
336   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
337   ierr = DMLocalToGlobal(dm[fine_level], rhs_loc, ADD_VALUES, rhs); CHKERRQ(ierr);
338   CeedVectorDestroy(&rhs_ceed);
339 
340   // Create the restriction/interpolation QFunction
341   CeedQFunctionCreateIdentity(ceed, num_comp_u, CEED_EVAL_NONE, CEED_EVAL_INTERP,
342                               &qf_restrict);
343   CeedQFunctionCreateIdentity(ceed, num_comp_u, CEED_EVAL_INTERP, CEED_EVAL_NONE,
344                               &qf_prolong);
345 
346   // Set up libCEED level transfer operators
347   ierr = CeedLevelTransferSetup(ceed, num_levels, num_comp_u, ceed_data,
348                                 level_degrees,
349                                 qf_restrict, qf_prolong); CHKERRQ(ierr);
350 
351   // Create the error QFunction
352   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error,
353                               bp_options[bp_choice].error_loc, &qf_error);
354   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
355   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
356   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_NONE);
357 
358   // Create the error operator
359   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
360                      &op_error);
361   CeedOperatorSetField(op_error, "u", ceed_data[fine_level]->elem_restr_u,
362                        ceed_data[fine_level]->basis_u, CEED_VECTOR_ACTIVE);
363   CeedOperatorSetField(op_error, "true_soln",
364                        ceed_data[fine_level]->elem_restr_u_i,
365                        CEED_BASIS_COLLOCATED, target);
366   CeedOperatorSetField(op_error, "error", ceed_data[fine_level]->elem_restr_u_i,
367                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
368 
369   // Calculate multiplicity
370   for (int i=0; i<num_levels; i++) {
371     PetscScalar *x;
372 
373     // CEED vector
374     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
375     ierr = VecGetArray(X_loc[i], &x); CHKERRQ(ierr);
376     CeedVectorSetArray(ceed_data[i]->x_ceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
377 
378     // Multiplicity
379     CeedElemRestrictionGetMultiplicity(ceed_data[i]->elem_restr_u,
380                                        ceed_data[i]->x_ceed);
381     CeedVectorSyncArray(ceed_data[i]->x_ceed, CEED_MEM_HOST);
382 
383     // Restore vector
384     ierr = VecRestoreArray(X_loc[i], &x); CHKERRQ(ierr);
385 
386     // Creat mult vector
387     ierr = VecDuplicate(X_loc[i], &mult[i]); CHKERRQ(ierr);
388 
389     // Local-to-global
390     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
391     ierr = DMLocalToGlobal(dm[i], X_loc[i], ADD_VALUES, X[i]);
392     CHKERRQ(ierr);
393     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
394 
395     // Global-to-local
396     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
397     CHKERRQ(ierr);
398     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
399 
400     // Multiplicity scaling
401     ierr = VecReciprocal(mult[i]);
402   }
403 
404   // Set up Mat
405   for (int i=0; i<num_levels; i++) {
406     // User Operator
407     user_O[i]->comm = comm;
408     user_O[i]->dm = dm[i];
409     user_O[i]->X_loc = X_loc[i];
410     ierr = VecDuplicate(X_loc[i], &user_O[i]->Y_loc); CHKERRQ(ierr);
411     user_O[i]->x_ceed = ceed_data[i]->x_ceed;
412     user_O[i]->y_ceed = ceed_data[i]->y_ceed;
413     user_O[i]->op = ceed_data[i]->op_apply;
414     user_O[i]->ceed = ceed;
415 
416     if (i > 0) {
417       // Prolongation/Restriction Operator
418       user_pr[i]->comm = comm;
419       user_pr[i]->dmf = dm[i];
420       user_pr[i]->dmc = dm[i-1];
421       user_pr[i]->loc_vec_c = X_loc[i-1];
422       user_pr[i]->loc_vec_f = user_O[i]->Y_loc;
423       user_pr[i]->mult_vec = mult[i];
424       user_pr[i]->ceed_vec_c = user_O[i-1]->x_ceed;
425       user_pr[i]->ceed_vec_f = user_O[i]->y_ceed;
426       user_pr[i]->op_prolong = ceed_data[i]->op_prolong;
427       user_pr[i]->op_restrict = ceed_data[i]->op_restrict;
428       user_pr[i]->ceed = ceed;
429     }
430   }
431 
432   // Assemble coarse grid Jacobian for AMG (or other sparse matrix) solve
433   ierr = DMCreateMatrix(dm[0], &mat_coarse); CHKERRQ(ierr);
434 
435   if (PETSC_VERSION_GE(3,16,0)) { // Assemble matrix analytically
436     CeedInt num_entries, *rows, *cols;
437     CeedVector coo_values;
438     CeedOperatorLinearAssembleSymbolic(user_O[0]->op, &num_entries, &rows, &cols);
439     ISLocalToGlobalMapping ltog_row, ltog_col;
440     ierr = MatGetLocalToGlobalMapping(mat_coarse, &ltog_row, &ltog_col);
441     CHKERRQ(ierr);
442     ierr = ISLocalToGlobalMappingApply(ltog_row, num_entries, rows, rows);
443     CHKERRQ(ierr);
444     ierr = ISLocalToGlobalMappingApply(ltog_col, num_entries, cols, cols);
445     CHKERRQ(ierr);
446     ierr = MatSetPreallocationCOO(mat_coarse, num_entries, rows, cols);
447     CHKERRQ(ierr);
448     free(rows);
449     free(cols);
450     CeedVectorCreate(ceed, num_entries, &coo_values);
451     CeedOperatorLinearAssemble(user_O[0]->op, coo_values);
452     const CeedScalar *values;
453     CeedVectorGetArrayRead(coo_values, CEED_MEM_HOST, &values);
454     ierr = MatSetValuesCOO(mat_coarse, values, ADD_VALUES); CHKERRQ(ierr);
455     CeedVectorRestoreArrayRead(coo_values, &values);
456     CeedVectorDestroy(&coo_values);
457   } else { // Assemble matrix using coloring. Our interfaces match SNES so it's convenient
458     SNES snes_dummy;
459 
460     // Setup dummy SNES for AMG coarse solve
461     ierr = SNESCreate(comm, &snes_dummy); CHKERRQ(ierr);
462     ierr = SNESSetDM(snes_dummy, dm[0]); CHKERRQ(ierr);
463     ierr = SNESSetSolution(snes_dummy, X[0]); CHKERRQ(ierr);
464     ierr = SNESSetFunction(snes_dummy, X[0], FormResidual_Ceed,
465                            user_O[0]); CHKERRQ(ierr);
466     ierr = SNESSetJacobian(snes_dummy, mat_coarse, mat_coarse, NULL,
467                            NULL); CHKERRQ(ierr);
468     ierr = SNESComputeJacobianDefaultColor(snes_dummy, X[0], mat_O[0],
469                                            mat_coarse, NULL); CHKERRQ(ierr);
470     ierr = SNESDestroy(&snes_dummy); CHKERRQ(ierr);
471   }
472 
473   // Set up KSP
474   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
475   {
476     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
477     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
478     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
479                             PETSC_DEFAULT); CHKERRQ(ierr);
480   }
481   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
482   ierr = KSPSetOperators(ksp, mat_O[fine_level], mat_O[fine_level]);
483   CHKERRQ(ierr);
484 
485   // Set up PCMG
486   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
487   PCMGCycleType pcmg_cycle_type = PC_MG_CYCLE_V;
488   {
489     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
490 
491     // PCMG levels
492     ierr = PCMGSetLevels(pc, num_levels, NULL); CHKERRQ(ierr);
493     for (int i=0; i<num_levels; i++) {
494       // Smoother
495       KSP smoother;
496       PC smoother_pc;
497       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
498       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
499       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
500       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
501       ierr = KSPSetOperators(smoother, mat_O[i], mat_O[i]); CHKERRQ(ierr);
502       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
503       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
504       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
505 
506       // Work vector
507       if (i < num_levels - 1) {
508         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
509       }
510 
511       // Level transfers
512       if (i > 0) {
513         // Interpolation
514         ierr = PCMGSetInterpolation(pc, i, mat_pr[i]); CHKERRQ(ierr);
515       }
516 
517       // Coarse solve
518       KSP coarse;
519       PC coarse_pc;
520       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
521       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
522       ierr = KSPSetOperators(coarse, mat_coarse, mat_coarse); CHKERRQ(ierr);
523 
524       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
525       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
526 
527       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
528       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
529       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
530       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
531     }
532 
533     // PCMG options
534     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
535     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
536     ierr = PCMGSetCycleType(pc, pcmg_cycle_type); CHKERRQ(ierr);
537   }
538 
539   // First run, if benchmarking
540   if (benchmark_mode) {
541     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
542     CHKERRQ(ierr);
543     ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
544     my_rt_start = MPI_Wtime();
545     ierr = KSPSolve(ksp, rhs, X[fine_level]); CHKERRQ(ierr);
546     my_rt = MPI_Wtime() - my_rt_start;
547     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
548     CHKERRQ(ierr);
549     // Set maxits based on first iteration timing
550     if (my_rt > 0.02) {
551       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
552       CHKERRQ(ierr);
553     } else {
554       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
555       CHKERRQ(ierr);
556     }
557   }
558 
559   // Timed solve
560   ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
561   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
562 
563   // -- Performance logging
564   ierr = PetscLogStageRegister("Solve Stage", &solve_stage); CHKERRQ(ierr);
565   ierr = PetscLogStagePush(solve_stage); CHKERRQ(ierr);
566 
567   // -- Solve
568   my_rt_start = MPI_Wtime();
569   ierr = KSPSolve(ksp, rhs, X[fine_level]); CHKERRQ(ierr);
570   my_rt = MPI_Wtime() - my_rt_start;
571 
572 
573   // -- Performance logging
574   ierr = PetscLogStagePop();
575 
576   // Output results
577   {
578     KSPType ksp_type;
579     PCMGType pcmg_type;
580     KSPConvergedReason reason;
581     PetscReal rnorm;
582     PetscInt its;
583     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
584     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
585     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
586     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
587     ierr = PCMGGetType(pc, &pcmg_type); CHKERRQ(ierr);
588     if (!test_mode || reason < 0 || rnorm > 1e-8) {
589       ierr = PetscPrintf(comm,
590                          "  KSP:\n"
591                          "    KSP Type                           : %s\n"
592                          "    KSP Convergence                    : %s\n"
593                          "    Total KSP Iterations               : %D\n"
594                          "    Final rnorm                        : %e\n",
595                          ksp_type, KSPConvergedReasons[reason], its,
596                          (double)rnorm); CHKERRQ(ierr);
597       ierr = PetscPrintf(comm,
598                          "  PCMG:\n"
599                          "    PCMG Type                          : %s\n"
600                          "    PCMG Cycle Type                    : %s\n",
601                          PCMGTypes[pcmg_type],
602                          PCMGCycleTypes[pcmg_cycle_type]); CHKERRQ(ierr);
603     }
604     if (!test_mode) {
605       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
606     }
607     {
608       PetscReal max_error;
609       ierr = ComputeErrorMax(user_O[fine_level], op_error, X[fine_level], target,
610                              &max_error); CHKERRQ(ierr);
611       PetscReal tol = 5e-2;
612       if (!test_mode || max_error > tol) {
613         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
614         CHKERRQ(ierr);
615         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
616         CHKERRQ(ierr);
617         ierr = PetscPrintf(comm,
618                            "    Pointwise Error (max)              : %e\n"
619                            "    CG Solve Time                      : %g (%g) sec\n",
620                            (double)max_error, rt_max, rt_min); CHKERRQ(ierr);
621       }
622     }
623     if (benchmark_mode && (!test_mode)) {
624       ierr = PetscPrintf(comm,
625                          "    DoFs/Sec in CG                     : %g (%g) million\n",
626                          1e-6*g_size[fine_level]*its/rt_max,
627                          1e-6*g_size[fine_level]*its/rt_min);
628       CHKERRQ(ierr);
629     }
630   }
631 
632   if (write_solution) {
633     PetscViewer vtk_viewer_soln;
634 
635     ierr = PetscViewerCreate(comm, &vtk_viewer_soln); CHKERRQ(ierr);
636     ierr = PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK); CHKERRQ(ierr);
637     ierr = PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"); CHKERRQ(ierr);
638     ierr = VecView(X[fine_level], vtk_viewer_soln); CHKERRQ(ierr);
639     ierr = PetscViewerDestroy(&vtk_viewer_soln); CHKERRQ(ierr);
640   }
641 
642   // Cleanup
643   for (int i=0; i<num_levels; i++) {
644     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
645     ierr = VecDestroy(&X_loc[i]); CHKERRQ(ierr);
646     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
647     ierr = VecDestroy(&user_O[i]->Y_loc); CHKERRQ(ierr);
648     ierr = MatDestroy(&mat_O[i]); CHKERRQ(ierr);
649     ierr = PetscFree(user_O[i]); CHKERRQ(ierr);
650     if (i > 0) {
651       ierr = MatDestroy(&mat_pr[i]); CHKERRQ(ierr);
652       ierr = PetscFree(user_pr[i]); CHKERRQ(ierr);
653     }
654     ierr = CeedDataDestroy(i, ceed_data[i]); CHKERRQ(ierr);
655     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
656   }
657   ierr = PetscFree(level_degrees); CHKERRQ(ierr);
658   ierr = PetscFree(dm); CHKERRQ(ierr);
659   ierr = PetscFree(X); CHKERRQ(ierr);
660   ierr = PetscFree(X_loc); CHKERRQ(ierr);
661   ierr = PetscFree(mult); CHKERRQ(ierr);
662   ierr = PetscFree(mat_O); CHKERRQ(ierr);
663   ierr = PetscFree(mat_pr); CHKERRQ(ierr);
664   ierr = PetscFree(ceed_data); CHKERRQ(ierr);
665   ierr = PetscFree(user_O); CHKERRQ(ierr);
666   ierr = PetscFree(user_pr); CHKERRQ(ierr);
667   ierr = PetscFree(l_size); CHKERRQ(ierr);
668   ierr = PetscFree(xl_size); CHKERRQ(ierr);
669   ierr = PetscFree(g_size); CHKERRQ(ierr);
670   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
671   ierr = VecDestroy(&rhs_loc); CHKERRQ(ierr);
672   ierr = MatDestroy(&mat_coarse); CHKERRQ(ierr);
673   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
674   ierr = DMDestroy(&dm_orig); CHKERRQ(ierr);
675   CeedVectorDestroy(&target);
676   CeedQFunctionDestroy(&qf_error);
677   CeedQFunctionDestroy(&qf_restrict);
678   CeedQFunctionDestroy(&qf_prolong);
679   CeedOperatorDestroy(&op_error);
680   CeedDestroy(&ceed);
681   return PetscFinalize();
682 }
683