xref: /libCEED/examples/petsc/multigrid.c (revision 6c88e6a2c47a72cd5c3efacc26a364b9cb7d40db)
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 //TESTARGS -ceed {ceed_resource} -test -problem bp3 -degree 3 -simplex
28 
29 /// @file
30 /// CEED BPs 1-6 multigrid example using PETSc
31 const char help[] = "Solve CEED BPs using p-multigrid with PETSc and DMPlex\n";
32 
33 #include <stdbool.h>
34 #include <string.h>
35 #include <ceed.h>
36 #include <petsc.h>
37 #include <petscdmplex.h>
38 #include <petscksp.h>
39 #include <petscsys.h>
40 
41 #include "bps.h"
42 #include "include/bpsproblemdata.h"
43 #include "include/petscutils.h"
44 #include "include/petscversion.h"
45 #include "include/matops.h"
46 #include "include/structs.h"
47 #include "include/libceedsetup.h"
48 
49 #if PETSC_VERSION_LT(3,12,0)
50 #ifdef PETSC_HAVE_CUDA
51 #include <petsccuda.h>
52 // Note: With PETSc prior to version 3.12.0, providing the source path to
53 //       include 'cublas_v2.h' will be needed to use 'petsccuda.h'.
54 #endif
55 #endif
56 
57 int main(int argc, char **argv) {
58   PetscInt ierr;
59   MPI_Comm comm;
60   char filename[PETSC_MAX_PATH_LEN],
61        ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
62   double my_rt_start, my_rt, rt_min, rt_max;
63   PetscInt degree = 3, q_extra, *l_size, *xl_size, *g_size, dim = 3, fine_level,
64            mesh_elem[3] = {3, 3, 3}, num_comp_u = 1, num_levels = degree, *level_degrees;
65   PetscScalar *r;
66   PetscScalar eps = 1.0;
67   PetscBool test_mode, benchmark_mode, read_mesh, write_solution, simplex;
68   PetscLogStage solve_stage;
69   PetscLogEvent assemble_event;
70   DM  *dm, dm_orig;
71   KSP ksp;
72   PC pc;
73   Mat *mat_O, *mat_pr, mat_coarse;
74   Vec *X, *X_loc, *mult, rhs, rhs_loc;
75   PetscMemType mem_type;
76   OperatorApplyContext *op_apply_ctx, op_error_ctx;
77   ProlongRestrContext *pr_restr_ctx;
78   Ceed ceed;
79   CeedData *ceed_data;
80   CeedVector rhs_ceed, target;
81   CeedQFunction qf_error;
82   CeedOperator op_error;
83   BPType bp_choice;
84   CoarsenType coarsen;
85 
86   ierr = PetscInitialize(&argc, &argv, NULL, help);
87   if (ierr) return ierr;
88   comm = PETSC_COMM_WORLD;
89 
90   // Parse command line options
91   PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL);
92   bp_choice = CEED_BP3;
93   ierr = PetscOptionsEnum("-problem",
94                           "CEED benchmark problem to solve", NULL,
95                           bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice,
96                           NULL); CHKERRQ(ierr);
97   num_comp_u = bp_options[bp_choice].num_comp_u;
98   test_mode = PETSC_FALSE;
99   ierr = PetscOptionsBool("-test",
100                           "Testing mode (do not print unless error is large)",
101                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
102   benchmark_mode = PETSC_FALSE;
103   ierr = PetscOptionsBool("-benchmark",
104                           "Benchmarking mode (prints benchmark statistics)",
105                           NULL, benchmark_mode, &benchmark_mode, NULL);
106   CHKERRQ(ierr);
107   write_solution = PETSC_FALSE;
108   ierr = PetscOptionsBool("-write_solution",
109                           "Write solution for visualization",
110                           NULL, write_solution, &write_solution, NULL);
111   CHKERRQ(ierr);
112   simplex = PETSC_FALSE;
113   ierr = PetscOptionsBool("-simplex",
114                           "Element topology (default:hex)",
115                           NULL, simplex, &simplex, NULL);
116   CHKERRQ(ierr);
117   if ((bp_choice == CEED_BP5 || bp_choice == CEED_BP6) && (simplex)) {
118     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP,
119             "BP5/6 is not supported with simplex");
120   }
121   ierr = PetscOptionsScalar("-eps",
122                             "Epsilon parameter for Kershaw mesh transformation",
123                             NULL, eps, &eps, NULL);
124   if (eps > 1 || eps <= 0) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
125                                      "-eps %g must be (0,1]", (double)PetscRealPart(eps));
126   degree = test_mode ? 3 : 2;
127   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
128                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
129   if (degree < 1) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
130                             "-degree %" PetscInt_FMT " must be at least 1", degree);
131   q_extra = bp_options[bp_choice].q_extra;
132   ierr = PetscOptionsInt("-q_extra", "Number of extra quadrature points",
133                          NULL, q_extra, &q_extra, NULL); CHKERRQ(ierr);
134   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
135                             NULL, ceed_resource, ceed_resource,
136                             sizeof(ceed_resource), NULL); CHKERRQ(ierr);
137   coarsen = COARSEN_UNIFORM;
138   ierr = PetscOptionsEnum("-coarsen",
139                           "Coarsening strategy to use", NULL,
140                           coarsen_types, (PetscEnum)coarsen,
141                           (PetscEnum *)&coarsen, NULL); CHKERRQ(ierr);
142   read_mesh = PETSC_FALSE;
143   ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL,
144                             filename, filename, sizeof(filename), &read_mesh);
145   CHKERRQ(ierr);
146   if (!read_mesh) {
147     PetscInt tmp = dim;
148     ierr = PetscOptionsIntArray("-cells","Number of cells per dimension", NULL,
149                                 mesh_elem, &tmp, NULL); CHKERRQ(ierr);
150   }
151   PetscOptionsEnd();
152 
153   // Set up libCEED
154   CeedInit(ceed_resource, &ceed);
155   CeedMemType mem_type_backend;
156   CeedGetPreferredMemType(ceed, &mem_type_backend);
157 
158   // Setup DM
159   if (read_mesh) {
160     ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, NULL, PETSC_TRUE,
161                                 &dm_orig);
162     CHKERRQ(ierr);
163   } else {
164     ierr = DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, simplex, mesh_elem, NULL,
165                                NULL, NULL, PETSC_TRUE, &dm_orig); CHKERRQ(ierr);
166   }
167 
168   VecType vec_type;
169   switch (mem_type_backend) {
170   case CEED_MEM_HOST: vec_type = VECSTANDARD; break;
171   case CEED_MEM_DEVICE: {
172     const char *resolved;
173     CeedGetResource(ceed, &resolved);
174     if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
175     else if (strstr(resolved, "/gpu/hip/occa"))
176       vec_type = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
177     else if (strstr(resolved, "/gpu/hip")) vec_type = VECHIP;
178     else vec_type = VECSTANDARD;
179   }
180   }
181   ierr = DMSetVecType(dm_orig, vec_type); CHKERRQ(ierr);
182   ierr = DMSetFromOptions(dm_orig); CHKERRQ(ierr);
183   ierr = DMViewFromOptions(dm_orig, NULL, "-dm_view"); CHKERRQ(ierr);
184 
185   // Apply Kershaw mesh transformation
186   ierr = Kershaw(dm_orig, eps); CHKERRQ(ierr);
187 
188   // Allocate arrays for PETSc objects for each level
189   switch (coarsen) {
190   case COARSEN_UNIFORM:
191     num_levels = degree;
192     break;
193   case COARSEN_LOGARITHMIC:
194     num_levels = ceil(log(degree)/log(2)) + 1;
195     break;
196   }
197   ierr = PetscMalloc1(num_levels, &level_degrees); CHKERRQ(ierr);
198   fine_level = num_levels - 1;
199 
200   switch (coarsen) {
201   case COARSEN_UNIFORM:
202     for (int i=0; i<num_levels; i++) level_degrees[i] = i + 1;
203     break;
204   case COARSEN_LOGARITHMIC:
205     for (int i=0; i<num_levels - 1; i++) level_degrees[i] = pow(2,i);
206     level_degrees[fine_level] = degree;
207     break;
208   }
209   ierr = PetscMalloc1(num_levels, &dm); CHKERRQ(ierr);
210   ierr = PetscMalloc1(num_levels, &X); CHKERRQ(ierr);
211   ierr = PetscMalloc1(num_levels, &X_loc); CHKERRQ(ierr);
212   ierr = PetscMalloc1(num_levels, &mult); CHKERRQ(ierr);
213   ierr = PetscMalloc1(num_levels, &op_apply_ctx); CHKERRQ(ierr);
214   ierr = PetscMalloc1(num_levels, &pr_restr_ctx); CHKERRQ(ierr);
215   ierr = PetscMalloc1(num_levels, &mat_O); CHKERRQ(ierr);
216   ierr = PetscMalloc1(num_levels, &mat_pr); CHKERRQ(ierr);
217   ierr = PetscMalloc1(num_levels, &l_size); CHKERRQ(ierr);
218   ierr = PetscMalloc1(num_levels, &xl_size); CHKERRQ(ierr);
219   ierr = PetscMalloc1(num_levels, &g_size); CHKERRQ(ierr);
220 
221   PetscInt c_start, c_end;
222   ierr = DMPlexGetHeightStratum(dm_orig, 0, &c_start, &c_end); CHKERRQ(ierr);
223   DMPolytopeType  cell_type;
224   ierr = DMPlexGetCellType(dm_orig, c_start, &cell_type); CHKERRQ(ierr);
225   CeedElemTopology elem_topo = ElemTopologyP2C(cell_type);
226 
227   // Setup DM and Operator Mat Shells for each level
228   for (CeedInt i=0; i<num_levels; i++) {
229     // Create DM
230     ierr = DMClone(dm_orig, &dm[i]); CHKERRQ(ierr);
231     ierr = DMGetVecType(dm_orig, &vec_type); CHKERRQ(ierr);
232     ierr = DMSetVecType(dm[i], vec_type); CHKERRQ(ierr);
233     PetscInt dim;
234     ierr = DMGetDimension(dm[i], &dim); CHKERRQ(ierr);
235     ierr = SetupDMByDegree(dm[i], level_degrees[fine_level], q_extra,
236                            num_comp_u, dim,
237                            bp_options[bp_choice].enforce_bc, bp_options[bp_choice].bc_func);
238     CHKERRQ(ierr);
239 
240     // Create vectors
241     ierr = DMCreateGlobalVector(dm[i], &X[i]); CHKERRQ(ierr);
242     ierr = VecGetLocalSize(X[i], &l_size[i]); CHKERRQ(ierr);
243     ierr = VecGetSize(X[i], &g_size[i]); CHKERRQ(ierr);
244     ierr = DMCreateLocalVector(dm[i], &X_loc[i]); CHKERRQ(ierr);
245     ierr = VecGetSize(X_loc[i], &xl_size[i]); CHKERRQ(ierr);
246 
247     // Operator
248     ierr = PetscMalloc1(1, &op_apply_ctx[i]); CHKERRQ(ierr);
249     ierr = PetscMalloc1(1, &op_error_ctx); CHKERRQ(ierr);
250     ierr = MatCreateShell(comm, l_size[i], l_size[i], g_size[i], g_size[i],
251                           op_apply_ctx[i], &mat_O[i]); CHKERRQ(ierr);
252     ierr = MatShellSetOperation(mat_O[i], MATOP_MULT,
253                                 (void(*)(void))MatMult_Ceed); CHKERRQ(ierr);
254     ierr = MatShellSetOperation(mat_O[i], MATOP_GET_DIAGONAL,
255                                 (void(*)(void))MatGetDiag); CHKERRQ(ierr);
256     ierr = MatShellSetVecType(mat_O[i], vec_type); CHKERRQ(ierr);
257 
258     // Level transfers
259     if (i > 0) {
260       // Interp
261       ierr = PetscMalloc1(1, &pr_restr_ctx[i]); CHKERRQ(ierr);
262       ierr = MatCreateShell(comm, l_size[i], l_size[i-1], g_size[i], g_size[i-1],
263                             pr_restr_ctx[i], &mat_pr[i]); CHKERRQ(ierr);
264       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT,
265                                   (void(*)(void))MatMult_Prolong);
266       CHKERRQ(ierr);
267       ierr = MatShellSetOperation(mat_pr[i], MATOP_MULT_TRANSPOSE,
268                                   (void(*)(void))MatMult_Restrict);
269       CHKERRQ(ierr);
270       ierr = MatShellSetVecType(mat_pr[i], vec_type); CHKERRQ(ierr);
271     }
272   }
273   ierr = VecDuplicate(X[fine_level], &rhs); CHKERRQ(ierr);
274 
275   // Print global grid information
276   if (!test_mode) {
277     PetscInt P = degree + 1, Q = P + q_extra;
278 
279     const char *used_resource;
280     CeedGetResource(ceed, &used_resource);
281 
282     ierr = VecGetType(X[0], &vec_type); CHKERRQ(ierr);
283 
284     ierr = PetscPrintf(comm,
285                        "\n-- CEED Benchmark Problem %" CeedInt_FMT " -- libCEED + PETSc + PCMG --\n"
286                        "  PETSc:\n"
287                        "    PETSc Vec Type                          : %s\n"
288                        "  libCEED:\n"
289                        "    libCEED Backend                         : %s\n"
290                        "    libCEED Backend MemType                 : %s\n"
291                        "  Mesh:\n"
292                        "    Solution Order (P)                      : %" CeedInt_FMT "\n"
293                        "    Quadrature  Order (Q)                   : %" CeedInt_FMT "\n"
294                        "    Additional quadrature points (q_extra)  : %" CeedInt_FMT "\n"
295                        "    Global Nodes                            : %" PetscInt_FMT "\n"
296                        "    Owned Nodes                             : %" PetscInt_FMT "\n"
297                        "    DoF per node                            : %" PetscInt_FMT "\n"
298                        "    Element topology                        : %s\n"
299                        "  Multigrid:\n"
300                        "    Number of Levels                        : %" CeedInt_FMT "\n",
301                        bp_choice+1, vec_type, used_resource,
302                        CeedMemTypes[mem_type_backend], P, Q, q_extra,
303                        g_size[fine_level]/num_comp_u, l_size[fine_level]/num_comp_u,
304                        num_comp_u, CeedElemTopologies[elem_topo],
305                        num_levels); CHKERRQ(ierr);
306   }
307 
308   // Create RHS vector
309   ierr = VecDuplicate(X_loc[fine_level], &rhs_loc); CHKERRQ(ierr);
310   ierr = VecZeroEntries(rhs_loc); CHKERRQ(ierr);
311   ierr = VecGetArrayAndMemType(rhs_loc, &r, &mem_type); CHKERRQ(ierr);
312   CeedVectorCreate(ceed, xl_size[fine_level], &rhs_ceed);
313   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
314 
315   // Set up libCEED operators on each level
316   ierr = PetscMalloc1(num_levels, &ceed_data); CHKERRQ(ierr);
317   for (PetscInt i=0; i<num_levels; i++) {
318     // Print level information
319     if (!test_mode && (i == 0 || i == fine_level)) {
320       ierr = PetscPrintf(comm,"    Level %" PetscInt_FMT " (%s):\n"
321                          "      Solution Order (P)                    : %" CeedInt_FMT "\n"
322                          "      Global Nodes                          : %" PetscInt_FMT "\n"
323                          "      Owned Nodes                           : %" PetscInt_FMT "\n",
324                          i, (i? "fine" : "coarse"), level_degrees[i] + 1,
325                          g_size[i]/num_comp_u, l_size[i]/num_comp_u); CHKERRQ(ierr);
326     }
327     ierr = PetscMalloc1(1, &ceed_data[i]); CHKERRQ(ierr);
328     ierr = SetupLibceedByDegree(dm[i], ceed, level_degrees[i], dim, q_extra,
329                                 dim, num_comp_u, g_size[i], xl_size[i], bp_options[bp_choice],
330                                 ceed_data[i], i==(fine_level), rhs_ceed, &target);
331     CHKERRQ(ierr);
332   }
333 
334   // Gather RHS
335   CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL);
336   ierr = VecRestoreArrayAndMemType(rhs_loc, &r); CHKERRQ(ierr);
337   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
338   ierr = DMLocalToGlobal(dm[fine_level], rhs_loc, ADD_VALUES, rhs); CHKERRQ(ierr);
339   CeedVectorDestroy(&rhs_ceed);
340 
341   // Create the error QFunction
342   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error,
343                               bp_options[bp_choice].error_loc, &qf_error);
344   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
345   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
346   CeedQFunctionAddInput(qf_error, "qdata", ceed_data[fine_level]->q_data_size,
347                         CEED_EVAL_NONE);
348   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_NONE);
349 
350   // Create the error operator
351   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
352                      &op_error);
353   CeedOperatorSetField(op_error, "u", ceed_data[fine_level]->elem_restr_u,
354                        ceed_data[fine_level]->basis_u, CEED_VECTOR_ACTIVE);
355   CeedOperatorSetField(op_error, "true_soln",
356                        ceed_data[fine_level]->elem_restr_u_i,
357                        CEED_BASIS_COLLOCATED, target);
358   CeedOperatorSetField(op_error, "qdata", ceed_data[fine_level]->elem_restr_qd_i,
359                        CEED_BASIS_COLLOCATED, ceed_data[fine_level]->q_data);
360   CeedOperatorSetField(op_error, "error", ceed_data[fine_level]->elem_restr_u_i,
361                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
362 
363   // Calculate multiplicity
364   for (int i=0; i<num_levels; i++) {
365     PetscScalar *x;
366 
367     // CEED vector
368     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
369     ierr = VecGetArray(X_loc[i], &x); CHKERRQ(ierr);
370     CeedVectorSetArray(ceed_data[i]->x_ceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
371 
372     // Multiplicity
373     CeedElemRestrictionGetMultiplicity(ceed_data[i]->elem_restr_u,
374                                        ceed_data[i]->x_ceed);
375     CeedVectorSyncArray(ceed_data[i]->x_ceed, CEED_MEM_HOST);
376 
377     // Restore vector
378     ierr = VecRestoreArray(X_loc[i], &x); CHKERRQ(ierr);
379 
380     // Creat mult vector
381     ierr = VecDuplicate(X_loc[i], &mult[i]); CHKERRQ(ierr);
382 
383     // Local-to-global
384     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
385     ierr = DMLocalToGlobal(dm[i], X_loc[i], ADD_VALUES, X[i]);
386     CHKERRQ(ierr);
387     ierr = VecZeroEntries(X_loc[i]); CHKERRQ(ierr);
388 
389     // Global-to-local
390     ierr = DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]);
391     CHKERRQ(ierr);
392     ierr = VecZeroEntries(X[i]); CHKERRQ(ierr);
393 
394     // Multiplicity scaling
395     ierr = VecReciprocal(mult[i]);
396   }
397 
398   // Set up Mat
399   for (int i=0; i<num_levels; i++) {
400     // Set up apply operator context
401     ierr = SetupApplyOperatorCtx(comm, dm[i], ceed,
402                                  ceed_data[i], X_loc[i],
403                                  op_apply_ctx[i]); CHKERRQ(ierr);
404 
405     if (i > 0) {
406       // Prolongation/Restriction Operator
407       ierr = CeedLevelTransferSetup(dm[i-1], ceed, i, num_comp_u, ceed_data,
408                                     bp_options[bp_choice], mult[i]); CHKERRQ(ierr);
409       pr_restr_ctx[i]->comm = comm;
410       pr_restr_ctx[i]->dmf = dm[i];
411       pr_restr_ctx[i]->dmc = dm[i-1];
412       pr_restr_ctx[i]->loc_vec_c = X_loc[i-1];
413       pr_restr_ctx[i]->loc_vec_f = op_apply_ctx[i]->Y_loc;
414       pr_restr_ctx[i]->mult_vec = mult[i];
415       pr_restr_ctx[i]->ceed_vec_c = op_apply_ctx[i-1]->x_ceed;
416       pr_restr_ctx[i]->ceed_vec_f = op_apply_ctx[i]->y_ceed;
417       pr_restr_ctx[i]->op_prolong = ceed_data[i]->op_prolong;
418       pr_restr_ctx[i]->op_restrict = ceed_data[i]->op_restrict;
419       pr_restr_ctx[i]->ceed = ceed;
420     }
421   }
422 
423   // Assemble coarse grid Jacobian for AMG (or other sparse matrix) solve
424   ierr = DMCreateMatrix(dm[0], &mat_coarse); CHKERRQ(ierr);
425 
426   ierr = PetscLogEventRegister("AssembleMatrix", MAT_CLASSID, &assemble_event);
427   CHKERRQ(ierr);
428   {
429     // Assemble matrix analytically
430     PetscCount num_entries;
431     CeedInt *rows, *cols;
432     CeedVector coo_values;
433     CeedOperatorLinearAssembleSymbolic(op_apply_ctx[0]->op, &num_entries, &rows,
434                                        &cols);
435     ISLocalToGlobalMapping ltog_row, ltog_col;
436     ierr = MatGetLocalToGlobalMapping(mat_coarse, &ltog_row, &ltog_col);
437     CHKERRQ(ierr);
438     ierr = ISLocalToGlobalMappingApply(ltog_row, num_entries, rows, rows);
439     CHKERRQ(ierr);
440     ierr = ISLocalToGlobalMappingApply(ltog_col, num_entries, cols, cols);
441     CHKERRQ(ierr);
442     ierr = MatSetPreallocationCOO(mat_coarse, num_entries, rows, cols);
443     CHKERRQ(ierr);
444     free(rows);
445     free(cols);
446     CeedVectorCreate(ceed, num_entries, &coo_values);
447     ierr = PetscLogEventBegin(assemble_event, mat_coarse, 0, 0, 0); CHKERRQ(ierr);
448     CeedOperatorLinearAssemble(op_apply_ctx[0]->op, coo_values);
449     const CeedScalar *values;
450     CeedVectorGetArrayRead(coo_values, CEED_MEM_HOST, &values);
451     ierr = MatSetValuesCOO(mat_coarse, values, ADD_VALUES); CHKERRQ(ierr);
452     CeedVectorRestoreArrayRead(coo_values, &values);
453     ierr = PetscLogEventEnd(assemble_event, mat_coarse, 0, 0, 0); CHKERRQ(ierr);
454     CeedVectorDestroy(&coo_values);
455   }
456 
457   // Set up KSP
458   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
459   {
460     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
461     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
462     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
463                             PETSC_DEFAULT); CHKERRQ(ierr);
464   }
465   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
466   ierr = KSPSetOperators(ksp, mat_O[fine_level], mat_O[fine_level]);
467   CHKERRQ(ierr);
468 
469   // Set up PCMG
470   ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
471   PCMGCycleType pcmg_cycle_type = PC_MG_CYCLE_V;
472   {
473     ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
474 
475     // PCMG levels
476     ierr = PCMGSetLevels(pc, num_levels, NULL); CHKERRQ(ierr);
477     for (int i=0; i<num_levels; i++) {
478       // Smoother
479       KSP smoother;
480       PC smoother_pc;
481       ierr = PCMGGetSmoother(pc, i, &smoother); CHKERRQ(ierr);
482       ierr = KSPSetType(smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
483       ierr = KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1); CHKERRQ(ierr);
484       ierr = KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE); CHKERRQ(ierr);
485       ierr = KSPSetOperators(smoother, mat_O[i], mat_O[i]); CHKERRQ(ierr);
486       ierr = KSPGetPC(smoother, &smoother_pc); CHKERRQ(ierr);
487       ierr = PCSetType(smoother_pc, PCJACOBI); CHKERRQ(ierr);
488       ierr = PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
489 
490       // Work vector
491       if (i < num_levels - 1) {
492         ierr = PCMGSetX(pc, i, X[i]); CHKERRQ(ierr);
493       }
494 
495       // Level transfers
496       if (i > 0) {
497         // Interpolation
498         ierr = PCMGSetInterpolation(pc, i, mat_pr[i]); CHKERRQ(ierr);
499       }
500 
501       // Coarse solve
502       KSP coarse;
503       PC coarse_pc;
504       ierr = PCMGGetCoarseSolve(pc, &coarse); CHKERRQ(ierr);
505       ierr = KSPSetType(coarse, KSPPREONLY); CHKERRQ(ierr);
506       ierr = KSPSetOperators(coarse, mat_coarse, mat_coarse); CHKERRQ(ierr);
507 
508       ierr = KSPGetPC(coarse, &coarse_pc); CHKERRQ(ierr);
509       ierr = PCSetType(coarse_pc, PCGAMG); CHKERRQ(ierr);
510 
511       ierr = KSPSetOptionsPrefix(coarse, "coarse_"); CHKERRQ(ierr);
512       ierr = PCSetOptionsPrefix(coarse_pc, "coarse_"); CHKERRQ(ierr);
513       ierr = KSPSetFromOptions(coarse); CHKERRQ(ierr);
514       ierr = PCSetFromOptions(coarse_pc); CHKERRQ(ierr);
515     }
516 
517     // PCMG options
518     ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
519     ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
520     ierr = PCMGSetCycleType(pc, pcmg_cycle_type); CHKERRQ(ierr);
521   }
522 
523   // First run, if benchmarking
524   if (benchmark_mode) {
525     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
526     CHKERRQ(ierr);
527     ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
528     my_rt_start = MPI_Wtime();
529     ierr = KSPSolve(ksp, rhs, X[fine_level]); CHKERRQ(ierr);
530     my_rt = MPI_Wtime() - my_rt_start;
531     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
532     CHKERRQ(ierr);
533     // Set maxits based on first iteration timing
534     if (my_rt > 0.02) {
535       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
536       CHKERRQ(ierr);
537     } else {
538       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
539       CHKERRQ(ierr);
540     }
541   }
542 
543   // Timed solve
544   ierr = VecZeroEntries(X[fine_level]); CHKERRQ(ierr);
545   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
546 
547   // -- Performance logging
548   ierr = PetscLogStageRegister("Solve Stage", &solve_stage); CHKERRQ(ierr);
549   ierr = PetscLogStagePush(solve_stage); CHKERRQ(ierr);
550 
551   // -- Solve
552   my_rt_start = MPI_Wtime();
553   ierr = KSPSolve(ksp, rhs, X[fine_level]); CHKERRQ(ierr);
554   my_rt = MPI_Wtime() - my_rt_start;
555 
556 
557   // -- Performance logging
558   ierr = PetscLogStagePop();
559 
560   // Output results
561   {
562     KSPType ksp_type;
563     PCMGType pcmg_type;
564     KSPConvergedReason reason;
565     PetscReal rnorm;
566     PetscInt its;
567     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
568     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
569     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
570     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
571     ierr = PCMGGetType(pc, &pcmg_type); CHKERRQ(ierr);
572     if (!test_mode || reason < 0 || rnorm > 1e-8) {
573       ierr = PetscPrintf(comm,
574                          "  KSP:\n"
575                          "    KSP Type                                : %s\n"
576                          "    KSP Convergence                         : %s\n"
577                          "    Total KSP Iterations                    : %" PetscInt_FMT "\n"
578                          "    Final rnorm                             : %e\n",
579                          ksp_type, KSPConvergedReasons[reason], its,
580                          (double)rnorm); CHKERRQ(ierr);
581       ierr = PetscPrintf(comm,
582                          "  PCMG:\n"
583                          "    PCMG Type                               : %s\n"
584                          "    PCMG Cycle Type                         : %s\n",
585                          PCMGTypes[pcmg_type],
586                          PCMGCycleTypes[pcmg_cycle_type]); CHKERRQ(ierr);
587     }
588     if (!test_mode) {
589       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
590     }
591     {
592       // Set up error operator context
593       ierr = SetupErrorOperatorCtx(comm, dm[fine_level], ceed,
594                                    ceed_data[fine_level], X_loc[fine_level],
595                                    op_error, op_error_ctx); CHKERRQ(ierr);
596       PetscReal max_error;
597       ierr = ComputeErrorMax(op_error_ctx, X[fine_level],
598                              target, &max_error); CHKERRQ(ierr);
599       PetscReal tol = 5e-2;
600       if (!test_mode || max_error > tol) {
601         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
602         CHKERRQ(ierr);
603         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
604         CHKERRQ(ierr);
605         ierr = PetscPrintf(comm,
606                            "    Pointwise Error (max)                   : %e\n"
607                            "    CG Solve Time                           : %g (%g) sec\n",
608                            (double)max_error, rt_max, rt_min); CHKERRQ(ierr);
609       }
610     }
611     if (benchmark_mode && (!test_mode)) {
612       ierr = PetscPrintf(comm,
613                          "    DoFs/Sec in CG                            : %g (%g) million\n",
614                          1e-6*g_size[fine_level]*its/rt_max,
615                          1e-6*g_size[fine_level]*its/rt_min);
616       CHKERRQ(ierr);
617     }
618   }
619 
620   if (write_solution) {
621     PetscViewer vtk_viewer_soln;
622 
623     ierr = PetscViewerCreate(comm, &vtk_viewer_soln); CHKERRQ(ierr);
624     ierr = PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK); CHKERRQ(ierr);
625     ierr = PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"); CHKERRQ(ierr);
626     ierr = VecView(X[fine_level], vtk_viewer_soln); CHKERRQ(ierr);
627     ierr = PetscViewerDestroy(&vtk_viewer_soln); CHKERRQ(ierr);
628   }
629 
630   // Cleanup
631   for (int i=0; i<num_levels; i++) {
632     ierr = VecDestroy(&X[i]); CHKERRQ(ierr);
633     ierr = VecDestroy(&X_loc[i]); CHKERRQ(ierr);
634     ierr = VecDestroy(&mult[i]); CHKERRQ(ierr);
635     ierr = VecDestroy(&op_apply_ctx[i]->Y_loc); CHKERRQ(ierr);
636     ierr = MatDestroy(&mat_O[i]); CHKERRQ(ierr);
637     ierr = PetscFree(op_apply_ctx[i]); CHKERRQ(ierr);
638     if (i > 0) {
639       ierr = MatDestroy(&mat_pr[i]); CHKERRQ(ierr);
640       ierr = PetscFree(pr_restr_ctx[i]); CHKERRQ(ierr);
641     }
642     ierr = CeedDataDestroy(i, ceed_data[i]); CHKERRQ(ierr);
643     ierr = DMDestroy(&dm[i]); CHKERRQ(ierr);
644   }
645   ierr = PetscFree(level_degrees); CHKERRQ(ierr);
646   ierr = PetscFree(dm); CHKERRQ(ierr);
647   ierr = PetscFree(X); CHKERRQ(ierr);
648   ierr = PetscFree(X_loc); CHKERRQ(ierr);
649   ierr = VecDestroy(&op_error_ctx->Y_loc); CHKERRQ(ierr);
650   ierr = PetscFree(mult); CHKERRQ(ierr);
651   ierr = PetscFree(mat_O); CHKERRQ(ierr);
652   ierr = PetscFree(mat_pr); CHKERRQ(ierr);
653   ierr = PetscFree(ceed_data); CHKERRQ(ierr);
654   ierr = PetscFree(op_apply_ctx); CHKERRQ(ierr);
655   ierr = PetscFree(op_error_ctx); CHKERRQ(ierr);
656   ierr = PetscFree(pr_restr_ctx); CHKERRQ(ierr);
657   ierr = PetscFree(l_size); CHKERRQ(ierr);
658   ierr = PetscFree(xl_size); CHKERRQ(ierr);
659   ierr = PetscFree(g_size); CHKERRQ(ierr);
660   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
661   ierr = VecDestroy(&rhs_loc); CHKERRQ(ierr);
662   ierr = MatDestroy(&mat_coarse); CHKERRQ(ierr);
663   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
664   ierr = DMDestroy(&dm_orig); CHKERRQ(ierr);
665   CeedVectorDestroy(&target);
666   CeedQFunctionDestroy(&qf_error);
667   CeedOperatorDestroy(&op_error);
668   CeedDestroy(&ceed);
669   return PetscFinalize();
670 }
671