xref: /libCEED/examples/petsc/multigrid.c (revision 1c9a79dbea105b3f95768697087571c12d59a016)
1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 //                        libCEED + PETSc Example: CEED BPs 3-6 with Multigrid
9 //
10 // This example demonstrates a simple usage of libCEED with PETSc to solve the
11 // CEED BP benchmark problems, see http://ceed.exascaleproject.org/bps.
12 //
13 // The code uses higher level communication protocols in DMPlex.
14 //
15 // Build with:
16 //
17 //     make multigrid [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
18 //
19 // Sample runs:
20 //
21 //     multigrid -problem bp3
22 //     multigrid -problem bp4
23 //     multigrid -problem bp5 -ceed /cpu/self
24 //     multigrid -problem bp6 -ceed /gpu/cuda
25 //
26 //TESTARGS -ceed {ceed_resource} -test -problem bp3 -degree 3
27 
28 /// @file
29 /// CEED BPs 1-6 multigrid example using PETSc
30 const char help[] = "Solve CEED BPs using p-multigrid with PETSc and DMPlex\n";
31 
32 #include <stdbool.h>
33 #include <string.h>
34 #include <ceed.h>
35 #include <petsc.h>
36 #include <petscdmplex.h>
37 #include <petscksp.h>
38 #include <petscsys.h>
39 
40 #include "bps.h"
41 #include "include/bpsproblemdata.h"
42 #include "include/petscutils.h"
43 #include "include/petscversion.h"
44 #include "include/matops.h"
45 #include "include/structs.h"
46 #include "include/libceedsetup.h"
47 
48 #if PETSC_VERSION_LT(3,12,0)
49 #ifdef PETSC_HAVE_CUDA
50 #include <petsccuda.h>
51 // Note: With PETSc prior to version 3.12.0, providing the source path to
52 //       include 'cublas_v2.h' will be needed to use 'petsccuda.h'.
53 #endif
54 #endif
55 
56 int main(int argc, char **argv) {
57   PetscInt ierr;
58   MPI_Comm comm;
59   char filename[PETSC_MAX_PATH_LEN],
60        ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
61   double my_rt_start, my_rt, rt_min, rt_max;
62   PetscInt degree = 3, q_extra, *l_size, *xl_size, *g_size, dim = 3, fine_level,
63            mesh_elem[3] = {3, 3, 3}, num_comp_u = 1, num_levels = degree, *level_degrees;
64   PetscScalar *r;
65   PetscScalar eps = 1.0;
66   PetscBool test_mode, benchmark_mode, read_mesh, write_solution, simplex;
67   PetscLogStage solve_stage;
68   PetscLogEvent assemble_event;
69   DM  *dm, dm_orig;
70   KSP ksp;
71   PC pc;
72   Mat *mat_O, *mat_pr, mat_coarse;
73   Vec *X, *X_loc, *mult, rhs, rhs_loc;
74   PetscMemType mem_type;
75   UserO *user_O;
76   UserProlongRestr *user_pr;
77   Ceed ceed;
78   CeedData *ceed_data;
79   CeedVector rhs_ceed, target;
80   CeedQFunction qf_error;
81   CeedOperator op_error;
82   BPType bp_choice;
83   CoarsenType coarsen;
84 
85   ierr = PetscInitialize(&argc, &argv, NULL, help);
86   if (ierr) return ierr;
87   comm = PETSC_COMM_WORLD;
88 
89   // Parse command line options
90   PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL);
91   bp_choice = CEED_BP3;
92   ierr = PetscOptionsEnum("-problem",
93                           "CEED benchmark problem to solve", NULL,
94                           bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice,
95                           NULL); CHKERRQ(ierr);
96   num_comp_u = bp_options[bp_choice].num_comp_u;
97   test_mode = PETSC_FALSE;
98   ierr = PetscOptionsBool("-test",
99                           "Testing mode (do not print unless error is large)",
100                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
101   benchmark_mode = PETSC_FALSE;
102   ierr = PetscOptionsBool("-benchmark",
103                           "Benchmarking mode (prints benchmark statistics)",
104                           NULL, benchmark_mode, &benchmark_mode, NULL);
105   CHKERRQ(ierr);
106   write_solution = PETSC_FALSE;
107   ierr = PetscOptionsBool("-write_solution",
108                           "Write solution for visualization",
109                           NULL, write_solution, &write_solution, NULL);
110   CHKERRQ(ierr);
111   simplex = PETSC_FALSE;
112   ierr = PetscOptionsBool("-simplex",
113                           "Element topology (default:hex)",
114                           NULL, simplex, &simplex, NULL);
115   CHKERRQ(ierr);
116   ierr = PetscOptionsScalar("-eps",
117                             "Epsilon parameter for Kershaw mesh transformation",
118                             NULL, eps, &eps, NULL);
119   if (eps > 1 || eps <= 0) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
120                                      "-eps %g must be (0,1]", (double)PetscRealPart(eps));
121   degree = test_mode ? 3 : 2;
122   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
123                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
124   if (degree < 1) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
125                             "-degree %" PetscInt_FMT " must be at least 1", degree);
126   q_extra = bp_options[bp_choice].q_extra;
127   ierr = PetscOptionsInt("-q_extra", "Number of extra quadrature points",
128                          NULL, q_extra, &q_extra, NULL); CHKERRQ(ierr);
129   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
130                             NULL, ceed_resource, ceed_resource,
131                             sizeof(ceed_resource), NULL); CHKERRQ(ierr);
132   coarsen = COARSEN_UNIFORM;
133   ierr = PetscOptionsEnum("-coarsen",
134                           "Coarsening strategy to use", NULL,
135                           coarsen_types, (PetscEnum)coarsen,
136                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
137   read_mesh = PETSC_FALSE;
138   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
139                             filename, filename, sizeof(filename), &read_mesh);
140   CHKERRQ(ierr);
141   if (!read_mesh) {
142     PetscInt tmp = dim;
143     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
144                                 mesh_elem, &tmp, NULL); CHKERRQ(ierr);
145   }
146   PetscOptionsEnd();
147 
148   // Set up libCEED
149   CeedInit(ceed_resource, &ceed);
150   CeedMemType mem_type_backend;
151   CeedGetPreferredMemType(ceed, &mem_type_backend);
152 
153   // Setup DM
154   if (read_mesh) {
155     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, NULL, PETSC_TRUE,
156                                 &dm_orig);
157     CHKERRQ(ierr);
158   } else {
159     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, simplex, mesh_elem, NULL,
160                                NULL, NULL, PETSC_TRUE, &dm_orig); CHKERRQ(ierr);
161   }
162 
163   VecType vec_type;
164   switch (mem_type_backend) {
165   case CEED_MEM_HOST: vec_type = VECSTANDARD; break;
166   case CEED_MEM_DEVICE: {
167     const char *resolved;
168     CeedGetResource(ceed, &resolved);
169     if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
170     else if (strstr(resolved, "/gpu/hip/occa"))
171       vec_type = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
172     else if (strstr(resolved, "/gpu/hip")) vec_type = VECHIP;
173     else vec_type = VECSTANDARD;
174   }
175   }
176   ierr = DMSetVecType(dm_orig, vec_type); CHKERRQ(ierr);
177   ierr = DMSetFromOptions(dm_orig); CHKERRQ(ierr);
178   ierr = DMViewFromOptions(dm_orig, NULL, "-dm_view"); CHKERRQ(ierr);
179 
180   // Apply Kershaw mesh transformation
181   ierr = Kershaw(dm_orig, eps); CHKERRQ(ierr);
182 
183   // Allocate arrays for PETSc objects for each level
184   switch (coarsen) {
185   case COARSEN_UNIFORM:
186     num_levels = degree;
187     break;
188   case COARSEN_LOGARITHMIC:
189     num_levels = ceil(log(degree)/log(2)) + 1;
190     break;
191   }
192   ierr = PetscMalloc1(num_levels, &level_degrees); CHKERRQ(ierr);
193   fine_level = num_levels - 1;
194 
195   switch (coarsen) {
196   case COARSEN_UNIFORM:
197     for (int i=0; i<num_levels; i++) level_degrees[i] = i + 1;
198     break;
199   case COARSEN_LOGARITHMIC:
200     for (int i=0; i<num_levels - 1; i++) level_degrees[i] = pow(2,i);
201     level_degrees[fine_level] = degree;
202     break;
203   }
204   ierr = PetscMalloc1(num_levels, &dm); CHKERRQ(ierr);
205   ierr = PetscMalloc1(num_levels, &X); CHKERRQ(ierr);
206   ierr = PetscMalloc1(num_levels, &X_loc); CHKERRQ(ierr);
207   ierr = PetscMalloc1(num_levels, &mult); CHKERRQ(ierr);
208   ierr = PetscMalloc1(num_levels, &user_O); CHKERRQ(ierr);
209   ierr = PetscMalloc1(num_levels, &user_pr); CHKERRQ(ierr);
210   ierr = PetscMalloc1(num_levels, &mat_O); CHKERRQ(ierr);
211   ierr = PetscMalloc1(num_levels, &mat_pr); CHKERRQ(ierr);
212   ierr = PetscMalloc1(num_levels, &l_size); CHKERRQ(ierr);
213   ierr = PetscMalloc1(num_levels, &xl_size); CHKERRQ(ierr);
214   ierr = PetscMalloc1(num_levels, &g_size); CHKERRQ(ierr);
215 
216   PetscInt c_start, c_end;
217   ierr = DMPlexGetHeightStratum(dm_orig, 0, &c_start, &c_end); CHKERRQ(ierr);
218   DMPolytopeType  cell_type;
219   ierr = DMPlexGetCellType(dm_orig, c_start, &cell_type); CHKERRQ(ierr);
220   CeedElemTopology elem_topo = ElemTopologyP2C(cell_type);
221 
222   // Setup DM and Operator Mat Shells for each level
223   for (CeedInt i=0; i<num_levels; i++) {
224     // Create DM
225     ierr = DMClone(dm_orig, &dm[i]); CHKERRQ(ierr);
226     ierr = DMGetVecType(dm_orig, &vec_type); CHKERRQ(ierr);
227     ierr = DMSetVecType(dm[i], vec_type); CHKERRQ(ierr);
228     PetscInt dim;
229     ierr = DMGetDimension(dm[i], &dim); CHKERRQ(ierr);
230     ierr = SetupDMByDegree(dm[i], level_degrees[i], q_extra, num_comp_u, dim,
231                            bp_options[bp_choice].enforce_bc, bp_options[bp_choice].bc_func);
232     CHKERRQ(ierr);
233 
234     // Create vectors
235     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
236     ierr = VecGetLocalSize(X[i], &l_size[i]); CHKERRQ(ierr);
237     ierr = VecGetSize(X[i], &g_size[i]); CHKERRQ(ierr);
238     ierr = DMCreateLocalVector(dm[i], &X_loc[i]); CHKERRQ(ierr);
239     ierr = VecGetSize(X_loc[i], &xl_size[i]); CHKERRQ(ierr);
240 
241     // Operator
242     ierr = PetscMalloc1(1, &user_O[i]); CHKERRQ(ierr);
243     ierr = MatCreateShell(comm, l_size[i], l_size[i], g_size[i], g_size[i],
244                           user_O[i], &mat_O[i]); CHKERRQ(ierr);
245     ierr = MatShellSetOperation(mat_O[i], MATOP_MULT,
246                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
247     ierr = MatShellSetOperation(mat_O[i], MATOP_GET_DIAGONAL,
248                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
249     ierr = MatShellSetVecType(mat_O[i], vec_type); CHKERRQ(ierr);
250 
251     // Level transfers
252     if (i > 0) {
253       // Interp
254       ierr = PetscMalloc1(1, &user_pr[i]); CHKERRQ(ierr);
255       ierr = MatCreateShell(comm, l_size[i], l_size[i-1], g_size[i], g_size[i-1],
256                             user_pr[i], &mat_pr[i]); CHKERRQ(ierr);
257       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT,
258                                   (void(*)(void))MatMult_Prolong);
259       CHKERRQ(ierr);
260       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT_TRANSPOSE,
261                                   (void(*)(void))MatMult_Restrict);
262       CHKERRQ(ierr);
263       ierr = MatShellSetVecType(mat_pr[i], vec_type); CHKERRQ(ierr);
264     }
265   }
266   ierr = VecDuplicate(X[fine_level], &rhs); CHKERRQ(ierr);
267 
268   // Print global grid information
269   if (!test_mode) {
270     PetscInt P = degree + 1, Q = P + q_extra;
271 
272     const char *used_resource;
273     CeedGetResource(ceed, &used_resource);
274 
275     ierr = VecGetType(X[0], &vec_type); CHKERRQ(ierr);
276 
277     ierr = PetscPrintf(comm,
278                        "\n-- CEED Benchmark Problem %" CeedInt_FMT " -- libCEED + PETSc + PCMG --\n"
279                        "  PETSc:\n"
280                        "    PETSc Vec Type                          : %s\n"
281                        "  libCEED:\n"
282                        "    libCEED Backend                         : %s\n"
283                        "    libCEED Backend MemType                 : %s\n"
284                        "  Mesh:\n"
285                        "    Number of 1D Basis Nodes (p)            : %" CeedInt_FMT "\n"
286                        "    Number of 1D Quadrature Points (q)      : %" CeedInt_FMT "\n"
287                        "    Additional quadrature points (q_extra)  : %" CeedInt_FMT "\n"
288                        "    Global Nodes                            : %" PetscInt_FMT "\n"
289                        "    Owned Nodes                             : %" PetscInt_FMT "\n"
290                        "    DoF per node                            : %" PetscInt_FMT "\n"
291                        "  Multigrid:\n"
292                        "    Number of Levels                        : %" CeedInt_FMT "\n",
293                        bp_choice+1, vec_type, used_resource,
294                        CeedMemTypes[mem_type_backend], P, Q, q_extra,
295                        g_size[fine_level]/num_comp_u, l_size[fine_level]/num_comp_u,
296                        num_comp_u, CeedElemTopologies[elem_topo],
297                        num_levels); CHKERRQ(ierr);
298   }
299 
300   // Create RHS vector
301   ierr = VecDuplicate(X_loc[fine_level], &rhs_loc); CHKERRQ(ierr);
302   ierr = VecZeroEntries(rhs_loc); CHKERRQ(ierr);
303   ierr = VecGetArrayAndMemType(rhs_loc, &r, &mem_type); CHKERRQ(ierr);
304   CeedVectorCreate(ceed, xl_size[fine_level], &rhs_ceed);
305   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
306 
307   // Set up libCEED operators on each level
308   ierr = PetscMalloc1(num_levels, &ceed_data); CHKERRQ(ierr);
309   for (PetscInt i=0; i<num_levels; i++) {
310     // Print level information
311     if (!test_mode && (i == 0 || i == fine_level)) {
312       ierr = PetscPrintf(comm,"    Level %" PetscInt_FMT " (%s):\n"
313                          "      Number of 1D Basis Nodes (p)     : %" CeedInt_FMT "\n"
314                          "      Global Nodes                     : %" PetscInt_FMT "\n"
315                          "      Owned Nodes                      : %" PetscInt_FMT "\n",
316                          i, (i? "fine" : "coarse"), level_degrees[i] + 1,
317                          g_size[i]/num_comp_u, l_size[i]/num_comp_u); CHKERRQ(ierr);
318     }
319     ierr = PetscMalloc1(1, &ceed_data[i]); CHKERRQ(ierr);
320     ierr = SetupLibceedByDegree(dm[i], ceed, level_degrees[i], dim, q_extra,
321                                 dim, num_comp_u, g_size[i], xl_size[i], bp_options[bp_choice],
322                                 ceed_data[i], i==(fine_level), rhs_ceed, &target);
323     CHKERRQ(ierr);
324   }
325 
326   // Gather RHS
327   CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL);
328   ierr = VecRestoreArrayAndMemType(rhs_loc, &r); CHKERRQ(ierr);
329   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
330   ierr = DMLocalToGlobal(dm[fine_level], rhs_loc, ADD_VALUES, rhs); CHKERRQ(ierr);
331   CeedVectorDestroy(&rhs_ceed);
332 
333   // Create the error QFunction
334   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error,
335                               bp_options[bp_choice].error_loc, &qf_error);
336   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
337   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
338   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_NONE);
339 
340   // Create the error operator
341   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
342                      &op_error);
343   CeedOperatorSetField(op_error, "u", ceed_data[fine_level]->elem_restr_u,
344                        ceed_data[fine_level]->basis_u, CEED_VECTOR_ACTIVE);
345   CeedOperatorSetField(op_error, "true_soln",
346                        ceed_data[fine_level]->elem_restr_u_i,
347                        CEED_BASIS_COLLOCATED, target);
348   CeedOperatorSetField(op_error, "error", ceed_data[fine_level]->elem_restr_u_i,
349                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
350 
351   // Calculate multiplicity
352   for (int i=0; i<num_levels; i++) {
353     PetscScalar *x;
354 
355     // CEED vector
356     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
357     ierr = VecGetArray(X_loc[i], &x); CHKERRQ(ierr);
358     CeedVectorSetArray(ceed_data[i]->x_ceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
359 
360     // Multiplicity
361     CeedElemRestrictionGetMultiplicity(ceed_data[i]->elem_restr_u,
362                                        ceed_data[i]->x_ceed);
363     CeedVectorSyncArray(ceed_data[i]->x_ceed, CEED_MEM_HOST);
364 
365     // Restore vector
366     ierr = VecRestoreArray(X_loc[i], &x); CHKERRQ(ierr);
367 
368     // Creat mult vector
369     ierr = VecDuplicate(X_loc[i], &mult[i]); CHKERRQ(ierr);
370 
371     // Local-to-global
372     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
373     ierr = DMLocalToGlobal(dm[i], X_loc[i], ADD_VALUES, X[i]);
374     CHKERRQ(ierr);
375     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
376 
377     // Global-to-local
378     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
379     CHKERRQ(ierr);
380     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
381 
382     // Multiplicity scaling
383     ierr = VecReciprocal(mult[i]);
384   }
385 
386   // Set up Mat
387   for (int i=0; i<num_levels; i++) {
388     // User Operator
389     user_O[i]->comm = comm;
390     user_O[i]->dm = dm[i];
391     user_O[i]->X_loc = X_loc[i];
392     ierr = VecDuplicate(X_loc[i], &user_O[i]->Y_loc); CHKERRQ(ierr);
393     user_O[i]->x_ceed = ceed_data[i]->x_ceed;
394     user_O[i]->y_ceed = ceed_data[i]->y_ceed;
395     user_O[i]->op = ceed_data[i]->op_apply;
396     user_O[i]->ceed = ceed;
397 
398     if (i > 0) {
399       // Prolongation/Restriction Operator
400       ierr = CeedLevelTransferSetup(dm[i], ceed, i, num_comp_u, ceed_data,
401                                     mult[i]); CHKERRQ(ierr);
402       user_pr[i]->comm = comm;
403       user_pr[i]->dmf = dm[i];
404       user_pr[i]->dmc = dm[i-1];
405       user_pr[i]->loc_vec_c = X_loc[i-1];
406       user_pr[i]->loc_vec_f = user_O[i]->Y_loc;
407       user_pr[i]->mult_vec = mult[i];
408       user_pr[i]->ceed_vec_c = user_O[i-1]->x_ceed;
409       user_pr[i]->ceed_vec_f = user_O[i]->y_ceed;
410       user_pr[i]->op_prolong = ceed_data[i]->op_prolong;
411       user_pr[i]->op_restrict = ceed_data[i]->op_restrict;
412       user_pr[i]->ceed = ceed;
413     }
414   }
415 
416   // Assemble coarse grid Jacobian for AMG (or other sparse matrix) solve
417   ierr = DMCreateMatrix(dm[0], &mat_coarse); CHKERRQ(ierr);
418 
419   ierr = PetscLogEventRegister("AssembleMatrix", MAT_CLASSID, &assemble_event);
420   CHKERRQ(ierr);
421   {
422     // Assemble matrix analytically
423     PetscCount num_entries;
424     CeedInt *rows, *cols;
425     CeedVector coo_values;
426     CeedOperatorLinearAssembleSymbolic(user_O[0]->op, &num_entries, &rows, &cols);
427     ISLocalToGlobalMapping ltog_row, ltog_col;
428     ierr = MatGetLocalToGlobalMapping(mat_coarse, &ltog_row, &ltog_col);
429     CHKERRQ(ierr);
430     ierr = ISLocalToGlobalMappingApply(ltog_row, num_entries, rows, rows);
431     CHKERRQ(ierr);
432     ierr = ISLocalToGlobalMappingApply(ltog_col, num_entries, cols, cols);
433     CHKERRQ(ierr);
434     ierr = MatSetPreallocationCOO(mat_coarse, num_entries, rows, cols);
435     CHKERRQ(ierr);
436     free(rows);
437     free(cols);
438     CeedVectorCreate(ceed, num_entries, &coo_values);
439     ierr = PetscLogEventBegin(assemble_event, mat_coarse, 0, 0, 0); CHKERRQ(ierr);
440     CeedOperatorLinearAssemble(user_O[0]->op, coo_values);
441     const CeedScalar *values;
442     CeedVectorGetArrayRead(coo_values, CEED_MEM_HOST, &values);
443     ierr = MatSetValuesCOO(mat_coarse, values, ADD_VALUES); CHKERRQ(ierr);
444     CeedVectorRestoreArrayRead(coo_values, &values);
445     ierr = PetscLogEventEnd(assemble_event, mat_coarse, 0, 0, 0); CHKERRQ(ierr);
446     CeedVectorDestroy(&coo_values);
447   }
448 
449   // Set up KSP
450   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
451   {
452     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
453     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
454     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
455                             PETSC_DEFAULT); CHKERRQ(ierr);
456   }
457   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
458   ierr = KSPSetOperators(ksp, mat_O[fine_level], mat_O[fine_level]);
459   CHKERRQ(ierr);
460 
461   // Set up PCMG
462   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
463   PCMGCycleType pcmg_cycle_type = PC_MG_CYCLE_V;
464   {
465     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
466 
467     // PCMG levels
468     ierr = PCMGSetLevels(pc, num_levels, NULL); CHKERRQ(ierr);
469     for (int i=0; i<num_levels; i++) {
470       // Smoother
471       KSP smoother;
472       PC smoother_pc;
473       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
474       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
475       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
476       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
477       ierr = KSPSetOperators(smoother, mat_O[i], mat_O[i]); CHKERRQ(ierr);
478       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
479       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
480       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
481 
482       // Work vector
483       if (i < num_levels - 1) {
484         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
485       }
486 
487       // Level transfers
488       if (i > 0) {
489         // Interpolation
490         ierr = PCMGSetInterpolation(pc, i, mat_pr[i]); CHKERRQ(ierr);
491       }
492 
493       // Coarse solve
494       KSP coarse;
495       PC coarse_pc;
496       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
497       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
498       ierr = KSPSetOperators(coarse, mat_coarse, mat_coarse); CHKERRQ(ierr);
499 
500       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
501       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
502 
503       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
504       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
505       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
506       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
507     }
508 
509     // PCMG options
510     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
511     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
512     ierr = PCMGSetCycleType(pc, pcmg_cycle_type); CHKERRQ(ierr);
513   }
514 
515   // First run, if benchmarking
516   if (benchmark_mode) {
517     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
518     CHKERRQ(ierr);
519     ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
520     my_rt_start = MPI_Wtime();
521     ierr = KSPSolve(ksp, rhs, X[fine_level]); CHKERRQ(ierr);
522     my_rt = MPI_Wtime() - my_rt_start;
523     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
524     CHKERRQ(ierr);
525     // Set maxits based on first iteration timing
526     if (my_rt > 0.02) {
527       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
528       CHKERRQ(ierr);
529     } else {
530       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
531       CHKERRQ(ierr);
532     }
533   }
534 
535   // Timed solve
536   ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
537   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
538 
539   // -- Performance logging
540   ierr = PetscLogStageRegister("Solve Stage", &solve_stage); CHKERRQ(ierr);
541   ierr = PetscLogStagePush(solve_stage); CHKERRQ(ierr);
542 
543   // -- Solve
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 
548 
549   // -- Performance logging
550   ierr = PetscLogStagePop();
551 
552   // Output results
553   {
554     KSPType ksp_type;
555     PCMGType pcmg_type;
556     KSPConvergedReason reason;
557     PetscReal rnorm;
558     PetscInt its;
559     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
560     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
561     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
562     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
563     ierr = PCMGGetType(pc, &pcmg_type); CHKERRQ(ierr);
564     if (!test_mode || reason < 0 || rnorm > 1e-8) {
565       ierr = PetscPrintf(comm,
566                          "  KSP:\n"
567                          "    KSP Type                                : %s\n"
568                          "    KSP Convergence                         : %s\n"
569                          "    Total KSP Iterations                    : %D\n"
570                          "    Final rnorm                             : %e\n",
571                          ksp_type, KSPConvergedReasons[reason], its,
572                          (double)rnorm); CHKERRQ(ierr);
573       ierr = PetscPrintf(comm,
574                          "  PCMG:\n"
575                          "    PCMG Type                               : %s\n"
576                          "    PCMG Cycle Type                         : %s\n",
577                          PCMGTypes[pcmg_type],
578                          PCMGCycleTypes[pcmg_cycle_type]); CHKERRQ(ierr);
579     }
580     if (!test_mode) {
581       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
582     }
583     {
584       PetscReal max_error;
585       ierr = ComputeErrorMax(user_O[fine_level], op_error, X[fine_level], target,
586                              &max_error); CHKERRQ(ierr);
587       PetscReal tol = 5e-2;
588       if (!test_mode || max_error > tol) {
589         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
590         CHKERRQ(ierr);
591         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
592         CHKERRQ(ierr);
593         ierr = PetscPrintf(comm,
594                            "    Pointwise Error (max)                   : %e\n"
595                            "    CG Solve Time                           : %g (%g) sec\n",
596                            (double)max_error, rt_max, rt_min); CHKERRQ(ierr);
597       }
598     }
599     if (benchmark_mode && (!test_mode)) {
600       ierr = PetscPrintf(comm,
601                          "    DoFs/Sec in CG                     : %g (%g) million\n",
602                          1e-6*g_size[fine_level]*its/rt_max,
603                          1e-6*g_size[fine_level]*its/rt_min);
604       CHKERRQ(ierr);
605     }
606   }
607 
608   if (write_solution) {
609     PetscViewer vtk_viewer_soln;
610 
611     ierr = PetscViewerCreate(comm, &vtk_viewer_soln); CHKERRQ(ierr);
612     ierr = PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK); CHKERRQ(ierr);
613     ierr = PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"); CHKERRQ(ierr);
614     ierr = VecView(X[fine_level], vtk_viewer_soln); CHKERRQ(ierr);
615     ierr = PetscViewerDestroy(&vtk_viewer_soln); CHKERRQ(ierr);
616   }
617 
618   // Cleanup
619   for (int i=0; i<num_levels; i++) {
620     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
621     ierr = VecDestroy(&X_loc[i]); CHKERRQ(ierr);
622     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
623     ierr = VecDestroy(&user_O[i]->Y_loc); CHKERRQ(ierr);
624     ierr = MatDestroy(&mat_O[i]); CHKERRQ(ierr);
625     ierr = PetscFree(user_O[i]); CHKERRQ(ierr);
626     if (i > 0) {
627       ierr = MatDestroy(&mat_pr[i]); CHKERRQ(ierr);
628       ierr = PetscFree(user_pr[i]); CHKERRQ(ierr);
629     }
630     ierr = CeedDataDestroy(i, ceed_data[i]); CHKERRQ(ierr);
631     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
632   }
633   ierr = PetscFree(level_degrees); CHKERRQ(ierr);
634   ierr = PetscFree(dm); CHKERRQ(ierr);
635   ierr = PetscFree(X); CHKERRQ(ierr);
636   ierr = PetscFree(X_loc); CHKERRQ(ierr);
637   ierr = PetscFree(mult); CHKERRQ(ierr);
638   ierr = PetscFree(mat_O); CHKERRQ(ierr);
639   ierr = PetscFree(mat_pr); CHKERRQ(ierr);
640   ierr = PetscFree(ceed_data); CHKERRQ(ierr);
641   ierr = PetscFree(user_O); CHKERRQ(ierr);
642   ierr = PetscFree(user_pr); CHKERRQ(ierr);
643   ierr = PetscFree(l_size); CHKERRQ(ierr);
644   ierr = PetscFree(xl_size); CHKERRQ(ierr);
645   ierr = PetscFree(g_size); CHKERRQ(ierr);
646   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
647   ierr = VecDestroy(&rhs_loc); CHKERRQ(ierr);
648   ierr = MatDestroy(&mat_coarse); CHKERRQ(ierr);
649   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
650   ierr = DMDestroy(&dm_orig); CHKERRQ(ierr);
651   CeedVectorDestroy(&target);
652   CeedQFunctionDestroy(&qf_error);
653   CeedOperatorDestroy(&op_error);
654   CeedDestroy(&ceed);
655   return PetscFinalize();
656 }
657