xref: /libCEED/examples/petsc/multigrid.c (revision d31f425a588330e8e8161e7ae186baa9c4fe27b5)
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 CEED BP benchmark problems, see http://ceed.exascaleproject.org/bps.
11 //
12 // The code uses higher level communication protocols in DMPlex.
13 //
14 // Build with:
15 //
16 //     make multigrid [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
17 //
18 // Sample runs:
19 //
20 //     multigrid -problem bp3
21 //     multigrid -problem bp4
22 //     multigrid -problem bp5 -ceed /cpu/self
23 //     multigrid -problem bp6 -ceed /gpu/cuda
24 //
25 //TESTARGS(name="BP3, hex elements") -ceed {ceed_resource} -test -problem bp3 -degree 3
26 //TESTARGS(name="BP3, tet elements") -ceed {ceed_resource} -test -problem bp3 -degree 3 -simplex
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 <ceed.h>
33 #include <petsc.h>
34 #include <petscdmplex.h>
35 #include <petscksp.h>
36 #include <petscsys.h>
37 #include <stdbool.h>
38 #include <string.h>
39 
40 #include "bps.h"
41 #include "include/bpsproblemdata.h"
42 #include "include/libceedsetup.h"
43 #include "include/matops.h"
44 #include "include/petscutils.h"
45 #include "include/petscversion.h"
46 #include "include/structs.h"
47 
48 int main(int argc, char **argv) {
49   MPI_Comm comm;
50   char     filename[PETSC_MAX_PATH_LEN], ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
51   double   my_rt_start, my_rt, rt_min, rt_max;
52   PetscInt degree = 3, q_extra, *l_size, *xl_size, *g_size, dim = 3, fine_level, mesh_elem[3] = {3, 3, 3}, num_comp_u = 1, num_levels = degree,
53            *level_degrees;
54   PetscScalar          *r;
55   PetscScalar           eps = 1.0;
56   PetscBool             test_mode, benchmark_mode, read_mesh, write_solution, simplex;
57   PetscLogStage         solve_stage;
58   PetscLogEvent         assemble_event;
59   DM                   *dm, dm_orig;
60   KSP                   ksp;
61   PC                    pc;
62   Mat                  *mat_O, *mat_pr, mat_coarse;
63   Vec                  *X, *X_loc, *mult, rhs, rhs_loc;
64   PetscMemType          mem_type;
65   OperatorApplyContext *op_apply_ctx, op_error_ctx;
66   ProlongRestrContext  *pr_restr_ctx;
67   Ceed                  ceed;
68   CeedData             *ceed_data;
69   CeedVector            rhs_ceed, target;
70   CeedQFunction         qf_error;
71   CeedOperator          op_error;
72   BPType                bp_choice;
73   CoarsenType           coarsen;
74 
75   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
76   comm = PETSC_COMM_WORLD;
77 
78   // Parse command line options
79   PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL);
80   bp_choice = CEED_BP3;
81   PetscCall(PetscOptionsEnum("-problem", "CEED benchmark problem to solve", NULL, bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice, NULL));
82   num_comp_u = bp_options[bp_choice].num_comp_u;
83   test_mode  = PETSC_FALSE;
84   PetscCall(PetscOptionsBool("-test", "Testing mode (do not print unless error is large)", NULL, test_mode, &test_mode, NULL));
85   benchmark_mode = PETSC_FALSE;
86   PetscCall(PetscOptionsBool("-benchmark", "Benchmarking mode (prints benchmark statistics)", NULL, benchmark_mode, &benchmark_mode, NULL));
87   write_solution = PETSC_FALSE;
88   PetscCall(PetscOptionsBool("-write_solution", "Write solution for visualization", NULL, write_solution, &write_solution, NULL));
89   simplex = PETSC_FALSE;
90   PetscCall(PetscOptionsBool("-simplex", "Element topology (default:hex)", NULL, simplex, &simplex, NULL));
91   if ((bp_choice == CEED_BP5 || bp_choice == CEED_BP6) && (simplex)) {
92     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "BP5/6 is not supported with simplex");
93   }
94   PetscCall(PetscOptionsScalar("-eps", "Epsilon parameter for Kershaw mesh transformation", NULL, eps, &eps, NULL));
95   if (eps > 1 || eps <= 0) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "-eps %g must be (0,1]", (double)PetscRealPart(eps));
96   degree = test_mode ? 3 : 2;
97   PetscCall(PetscOptionsInt("-degree", "Polynomial degree of tensor product basis", NULL, degree, &degree, NULL));
98   if (degree < 1) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "-degree %" PetscInt_FMT " must be at least 1", degree);
99   q_extra = bp_options[bp_choice].q_extra;
100   PetscCall(PetscOptionsInt("-q_extra", "Number of extra quadrature points", NULL, q_extra, &q_extra, NULL));
101   PetscCall(PetscOptionsString("-ceed", "CEED resource specifier", NULL, ceed_resource, ceed_resource, sizeof(ceed_resource), NULL));
102   coarsen = COARSEN_UNIFORM;
103   PetscCall(PetscOptionsEnum("-coarsen", "Coarsening strategy to use", NULL, coarsen_types, (PetscEnum)coarsen, (PetscEnum *)&coarsen, NULL));
104   read_mesh = PETSC_FALSE;
105   PetscCall(PetscOptionsString("-mesh", "Read mesh from file", NULL, filename, filename, sizeof(filename), &read_mesh));
106   if (!read_mesh) {
107     PetscInt tmp = dim;
108     PetscCall(PetscOptionsIntArray("-cells", "Number of cells per dimension", NULL, mesh_elem, &tmp, NULL));
109   }
110   PetscOptionsEnd();
111 
112   // Set up libCEED
113   CeedInit(ceed_resource, &ceed);
114   CeedMemType mem_type_backend;
115   CeedGetPreferredMemType(ceed, &mem_type_backend);
116 
117   // Setup DM
118   if (read_mesh) {
119     PetscCall(DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, NULL, PETSC_TRUE, &dm_orig));
120   } else {
121     PetscCall(DMPlexCreateBoxMesh(PETSC_COMM_WORLD, dim, simplex, mesh_elem, NULL, NULL, NULL, PETSC_TRUE, &dm_orig));
122   }
123 
124   VecType vec_type;
125   switch (mem_type_backend) {
126     case CEED_MEM_HOST:
127       vec_type = VECSTANDARD;
128       break;
129     case CEED_MEM_DEVICE: {
130       const char *resolved;
131       CeedGetResource(ceed, &resolved);
132       if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
133       else if (strstr(resolved, "/gpu/hip/occa")) vec_type = VECSTANDARD;  // https://github.com/CEED/libCEED/issues/678
134       else if (strstr(resolved, "/gpu/hip")) vec_type = VECHIP;
135       else vec_type = VECSTANDARD;
136     }
137   }
138   PetscCall(DMSetVecType(dm_orig, vec_type));
139   PetscCall(DMSetFromOptions(dm_orig));
140   PetscCall(DMViewFromOptions(dm_orig, NULL, "-dm_view"));
141 
142   // Apply Kershaw mesh transformation
143   PetscCall(Kershaw(dm_orig, eps));
144 
145   // Allocate arrays for PETSc objects for each level
146   switch (coarsen) {
147     case COARSEN_UNIFORM:
148       num_levels = degree;
149       break;
150     case COARSEN_LOGARITHMIC:
151       num_levels = ceil(log(degree) / log(2)) + 1;
152       break;
153   }
154   PetscCall(PetscMalloc1(num_levels, &level_degrees));
155   fine_level = num_levels - 1;
156 
157   switch (coarsen) {
158     case COARSEN_UNIFORM:
159       for (int i = 0; i < num_levels; i++) level_degrees[i] = i + 1;
160       break;
161     case COARSEN_LOGARITHMIC:
162       for (int i = 0; i < num_levels - 1; i++) level_degrees[i] = pow(2, i);
163       level_degrees[fine_level] = degree;
164       break;
165   }
166   PetscCall(PetscMalloc1(num_levels, &dm));
167   PetscCall(PetscMalloc1(num_levels, &X));
168   PetscCall(PetscMalloc1(num_levels, &X_loc));
169   PetscCall(PetscMalloc1(num_levels, &mult));
170   PetscCall(PetscMalloc1(num_levels, &op_apply_ctx));
171   PetscCall(PetscMalloc1(num_levels, &pr_restr_ctx));
172   PetscCall(PetscMalloc1(num_levels, &mat_O));
173   PetscCall(PetscMalloc1(num_levels, &mat_pr));
174   PetscCall(PetscMalloc1(num_levels, &l_size));
175   PetscCall(PetscMalloc1(num_levels, &xl_size));
176   PetscCall(PetscMalloc1(num_levels, &g_size));
177 
178   PetscInt c_start, c_end;
179   PetscCall(DMPlexGetHeightStratum(dm_orig, 0, &c_start, &c_end));
180   DMPolytopeType cell_type;
181   PetscCall(DMPlexGetCellType(dm_orig, c_start, &cell_type));
182   CeedElemTopology elem_topo = ElemTopologyP2C(cell_type);
183 
184   // Setup DM and Operator Mat Shells for each level
185   for (CeedInt i = 0; i < num_levels; i++) {
186     // Create DM
187     PetscCall(DMClone(dm_orig, &dm[i]));
188     PetscCall(DMGetVecType(dm_orig, &vec_type));
189     PetscCall(DMSetVecType(dm[i], vec_type));
190     PetscInt dim;
191     PetscCall(DMGetDimension(dm[i], &dim));
192     PetscCall(SetupDMByDegree(dm[i], level_degrees[fine_level], q_extra, num_comp_u, dim, bp_options[bp_choice].enforce_bc));
193 
194     // Create vectors
195     PetscCall(DMCreateGlobalVector(dm[i], &X[i]));
196     PetscCall(VecGetLocalSize(X[i], &l_size[i]));
197     PetscCall(VecGetSize(X[i], &g_size[i]));
198     PetscCall(DMCreateLocalVector(dm[i], &X_loc[i]));
199     PetscCall(VecGetSize(X_loc[i], &xl_size[i]));
200 
201     // Operator
202     PetscCall(PetscMalloc1(1, &op_apply_ctx[i]));
203     PetscCall(PetscMalloc1(1, &op_error_ctx));
204     PetscCall(MatCreateShell(comm, l_size[i], l_size[i], g_size[i], g_size[i], op_apply_ctx[i], &mat_O[i]));
205     PetscCall(MatShellSetOperation(mat_O[i], MATOP_MULT, (void (*)(void))MatMult_Ceed));
206     PetscCall(MatShellSetOperation(mat_O[i], MATOP_GET_DIAGONAL, (void (*)(void))MatGetDiag));
207     PetscCall(MatShellSetVecType(mat_O[i], vec_type));
208 
209     // Level transfers
210     if (i > 0) {
211       // Interp
212       PetscCall(PetscMalloc1(1, &pr_restr_ctx[i]));
213       PetscCall(MatCreateShell(comm, l_size[i], l_size[i - 1], g_size[i], g_size[i - 1], pr_restr_ctx[i], &mat_pr[i]));
214       PetscCall(MatShellSetOperation(mat_pr[i], MATOP_MULT, (void (*)(void))MatMult_Prolong));
215       PetscCall(MatShellSetOperation(mat_pr[i], MATOP_MULT_TRANSPOSE, (void (*)(void))MatMult_Restrict));
216       PetscCall(MatShellSetVecType(mat_pr[i], vec_type));
217     }
218   }
219   PetscCall(VecDuplicate(X[fine_level], &rhs));
220 
221   // Print global grid information
222   if (!test_mode) {
223     PetscInt P = degree + 1, Q = P + q_extra;
224 
225     const char *used_resource;
226     CeedGetResource(ceed, &used_resource);
227 
228     PetscCall(VecGetType(X[0], &vec_type));
229 
230     PetscCall(PetscPrintf(comm,
231                           "\n-- CEED Benchmark Problem %" CeedInt_FMT " -- libCEED + PETSc + PCMG --\n"
232                           "  PETSc:\n"
233                           "    PETSc Vec Type                          : %s\n"
234                           "  libCEED:\n"
235                           "    libCEED Backend                         : %s\n"
236                           "    libCEED Backend MemType                 : %s\n"
237                           "  Mesh:\n"
238                           "    Solution Order (P)                      : %" CeedInt_FMT "\n"
239                           "    Quadrature  Order (Q)                   : %" CeedInt_FMT "\n"
240                           "    Additional quadrature points (q_extra)  : %" CeedInt_FMT "\n"
241                           "    Global Nodes                            : %" PetscInt_FMT "\n"
242                           "    Owned Nodes                             : %" PetscInt_FMT "\n"
243                           "    DoF per node                            : %" PetscInt_FMT "\n"
244                           "    Element topology                        : %s\n"
245                           "  Multigrid:\n"
246                           "    Number of Levels                        : %" CeedInt_FMT "\n",
247                           bp_choice + 1, vec_type, used_resource, CeedMemTypes[mem_type_backend], P, Q, q_extra, g_size[fine_level] / num_comp_u,
248                           l_size[fine_level] / num_comp_u, num_comp_u, CeedElemTopologies[elem_topo], num_levels));
249   }
250 
251   // Create RHS vector
252   PetscCall(VecDuplicate(X_loc[fine_level], &rhs_loc));
253   PetscCall(VecZeroEntries(rhs_loc));
254   PetscCall(VecGetArrayAndMemType(rhs_loc, &r, &mem_type));
255   CeedVectorCreate(ceed, xl_size[fine_level], &rhs_ceed);
256   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
257 
258   // Set up libCEED operators on each level
259   PetscCall(PetscMalloc1(num_levels, &ceed_data));
260   for (PetscInt i = 0; i < num_levels; i++) {
261     // Print level information
262     if (!test_mode && (i == 0 || i == fine_level)) {
263       PetscCall(PetscPrintf(comm,
264                             "    Level %" PetscInt_FMT " (%s):\n"
265                             "      Solution Order (P)                    : %" CeedInt_FMT "\n"
266                             "      Global Nodes                          : %" PetscInt_FMT "\n"
267                             "      Owned Nodes                           : %" PetscInt_FMT "\n",
268                             i, (i ? "fine" : "coarse"), level_degrees[i] + 1, g_size[i] / num_comp_u, l_size[i] / num_comp_u));
269     }
270     PetscCall(PetscMalloc1(1, &ceed_data[i]));
271     PetscCall(SetupLibceedByDegree(dm[i], ceed, level_degrees[i], dim, q_extra, dim, num_comp_u, g_size[i], xl_size[i], bp_options[bp_choice],
272                                    ceed_data[i], i == (fine_level), rhs_ceed, &target));
273   }
274 
275   // Gather RHS
276   CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL);
277   PetscCall(VecRestoreArrayAndMemType(rhs_loc, &r));
278   PetscCall(VecZeroEntries(rhs));
279   PetscCall(DMLocalToGlobal(dm[fine_level], rhs_loc, ADD_VALUES, rhs));
280   CeedVectorDestroy(&rhs_ceed);
281 
282   // Create the error QFunction
283   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error, bp_options[bp_choice].error_loc, &qf_error);
284   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
285   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
286   CeedQFunctionAddInput(qf_error, "qdata", ceed_data[fine_level]->q_data_size, CEED_EVAL_NONE);
287   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_INTERP);
288 
289   // Create the error operator
290   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_error);
291   CeedOperatorSetField(op_error, "u", ceed_data[fine_level]->elem_restr_u, ceed_data[fine_level]->basis_u, CEED_VECTOR_ACTIVE);
292   CeedOperatorSetField(op_error, "true_soln", ceed_data[fine_level]->elem_restr_u_i, CEED_BASIS_NONE, target);
293   CeedOperatorSetField(op_error, "qdata", ceed_data[fine_level]->elem_restr_qd_i, CEED_BASIS_NONE, ceed_data[fine_level]->q_data);
294   CeedOperatorSetField(op_error, "error", ceed_data[fine_level]->elem_restr_u, ceed_data[fine_level]->basis_u, CEED_VECTOR_ACTIVE);
295 
296   // Calculate multiplicity
297   for (int i = 0; i < num_levels; i++) {
298     PetscScalar *x;
299 
300     // CEED vector
301     PetscCall(VecZeroEntries(X_loc[i]));
302     PetscCall(VecGetArray(X_loc[i], &x));
303     CeedVectorSetArray(ceed_data[i]->x_ceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
304 
305     // Multiplicity
306     CeedElemRestrictionGetMultiplicity(ceed_data[i]->elem_restr_u, ceed_data[i]->x_ceed);
307     CeedVectorSyncArray(ceed_data[i]->x_ceed, CEED_MEM_HOST);
308 
309     // Restore vector
310     PetscCall(VecRestoreArray(X_loc[i], &x));
311 
312     // Creat mult vector
313     PetscCall(VecDuplicate(X_loc[i], &mult[i]));
314 
315     // Local-to-global
316     PetscCall(VecZeroEntries(X[i]));
317     PetscCall(DMLocalToGlobal(dm[i], X_loc[i], ADD_VALUES, X[i]));
318     PetscCall(VecZeroEntries(X_loc[i]));
319 
320     // Global-to-local
321     PetscCall(DMGlobalToLocal(dm[i], X[i], INSERT_VALUES, mult[i]));
322     PetscCall(VecZeroEntries(X[i]));
323 
324     // Multiplicity scaling
325     PetscCall(VecReciprocal(mult[i]));
326   }
327 
328   // Set up Mat
329   for (int i = 0; i < num_levels; i++) {
330     // Set up apply operator context
331     PetscCall(SetupApplyOperatorCtx(comm, dm[i], ceed, ceed_data[i], X_loc[i], op_apply_ctx[i]));
332 
333     if (i > 0) {
334       // Prolongation/Restriction Operator
335       PetscCall(CeedLevelTransferSetup(dm[i - 1], ceed, i, num_comp_u, ceed_data, bp_options[bp_choice], mult[i]));
336       pr_restr_ctx[i]->comm        = comm;
337       pr_restr_ctx[i]->dmf         = dm[i];
338       pr_restr_ctx[i]->dmc         = dm[i - 1];
339       pr_restr_ctx[i]->loc_vec_c   = X_loc[i - 1];
340       pr_restr_ctx[i]->loc_vec_f   = op_apply_ctx[i]->Y_loc;
341       pr_restr_ctx[i]->mult_vec    = mult[i];
342       pr_restr_ctx[i]->ceed_vec_c  = op_apply_ctx[i - 1]->x_ceed;
343       pr_restr_ctx[i]->ceed_vec_f  = op_apply_ctx[i]->y_ceed;
344       pr_restr_ctx[i]->op_prolong  = ceed_data[i]->op_prolong;
345       pr_restr_ctx[i]->op_restrict = ceed_data[i]->op_restrict;
346       pr_restr_ctx[i]->ceed        = ceed;
347     }
348   }
349 
350   // Assemble coarse grid Jacobian for AMG (or other sparse matrix) solve
351   PetscCall(DMCreateMatrix(dm[0], &mat_coarse));
352 
353   PetscCall(PetscLogEventRegister("AssembleMatrix", MAT_CLASSID, &assemble_event));
354   {
355     // Assemble matrix analytically
356     PetscCount num_entries;
357     CeedInt   *rows, *cols;
358     CeedVector coo_values;
359     CeedOperatorLinearAssembleSymbolic(op_apply_ctx[0]->op, &num_entries, &rows, &cols);
360     ISLocalToGlobalMapping ltog_row, ltog_col;
361     PetscCall(MatGetLocalToGlobalMapping(mat_coarse, &ltog_row, &ltog_col));
362     PetscCall(ISLocalToGlobalMappingApply(ltog_row, num_entries, rows, rows));
363     PetscCall(ISLocalToGlobalMappingApply(ltog_col, num_entries, cols, cols));
364     PetscCall(MatSetPreallocationCOO(mat_coarse, num_entries, rows, cols));
365     free(rows);
366     free(cols);
367     CeedVectorCreate(ceed, num_entries, &coo_values);
368     PetscCall(PetscLogEventBegin(assemble_event, mat_coarse, 0, 0, 0));
369     CeedOperatorLinearAssemble(op_apply_ctx[0]->op, coo_values);
370     const CeedScalar *values;
371     CeedVectorGetArrayRead(coo_values, CEED_MEM_HOST, &values);
372     PetscCall(MatSetValuesCOO(mat_coarse, values, ADD_VALUES));
373     CeedVectorRestoreArrayRead(coo_values, &values);
374     PetscCall(PetscLogEventEnd(assemble_event, mat_coarse, 0, 0, 0));
375     CeedVectorDestroy(&coo_values);
376   }
377 
378   // Set up KSP
379   PetscCall(KSPCreate(comm, &ksp));
380   {
381     PetscCall(KSPSetType(ksp, KSPCG));
382     PetscCall(KSPSetNormType(ksp, KSP_NORM_NATURAL));
383     PetscCall(KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
384   }
385   PetscCall(KSPSetFromOptions(ksp));
386   PetscCall(KSPSetOperators(ksp, mat_O[fine_level], mat_O[fine_level]));
387 
388   // Set up PCMG
389   PetscCall(KSPGetPC(ksp, &pc));
390   PCMGCycleType pcmg_cycle_type = PC_MG_CYCLE_V;
391   {
392     PetscCall(PCSetType(pc, PCMG));
393 
394     // PCMG levels
395     PetscCall(PCMGSetLevels(pc, num_levels, NULL));
396     for (int i = 0; i < num_levels; i++) {
397       // Smoother
398       KSP smoother;
399       PC  smoother_pc;
400       PetscCall(PCMGGetSmoother(pc, i, &smoother));
401       PetscCall(KSPSetType(smoother, KSPCHEBYSHEV));
402       PetscCall(KSPChebyshevEstEigSet(smoother, 0, 0.1, 0, 1.1));
403       PetscCall(KSPChebyshevEstEigSetUseNoisy(smoother, PETSC_TRUE));
404       PetscCall(KSPSetOperators(smoother, mat_O[i], mat_O[i]));
405       PetscCall(KSPGetPC(smoother, &smoother_pc));
406       PetscCall(PCSetType(smoother_pc, PCJACOBI));
407       PetscCall(PCJacobiSetType(smoother_pc, PC_JACOBI_DIAGONAL));
408 
409       // Work vector
410       if (i < num_levels - 1) {
411         PetscCall(PCMGSetX(pc, i, X[i]));
412       }
413 
414       // Level transfers
415       if (i > 0) {
416         // Interpolation
417         PetscCall(PCMGSetInterpolation(pc, i, mat_pr[i]));
418       }
419 
420       // Coarse solve
421       KSP coarse;
422       PC  coarse_pc;
423       PetscCall(PCMGGetCoarseSolve(pc, &coarse));
424       PetscCall(KSPSetType(coarse, KSPPREONLY));
425       PetscCall(KSPSetOperators(coarse, mat_coarse, mat_coarse));
426 
427       PetscCall(KSPGetPC(coarse, &coarse_pc));
428       PetscCall(PCSetType(coarse_pc, PCGAMG));
429 
430       PetscCall(KSPSetOptionsPrefix(coarse, "coarse_"));
431       PetscCall(PCSetOptionsPrefix(coarse_pc, "coarse_"));
432       PetscCall(KSPSetFromOptions(coarse));
433       PetscCall(PCSetFromOptions(coarse_pc));
434     }
435 
436     // PCMG options
437     PetscCall(PCMGSetType(pc, PC_MG_MULTIPLICATIVE));
438     PetscCall(PCMGSetNumberSmooth(pc, 3));
439     PetscCall(PCMGSetCycleType(pc, pcmg_cycle_type));
440   }
441 
442   // First run, if benchmarking
443   if (benchmark_mode) {
444     PetscCall(KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1));
445     PetscCall(VecZeroEntries(X[fine_level]));
446     my_rt_start = MPI_Wtime();
447     PetscCall(KSPSolve(ksp, rhs, X[fine_level]));
448     my_rt = MPI_Wtime() - my_rt_start;
449     PetscCall(MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm));
450     // Set maxits based on first iteration timing
451     if (my_rt > 0.02) {
452       PetscCall(KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5));
453     } else {
454       PetscCall(KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20));
455     }
456   }
457 
458   // Timed solve
459   PetscCall(VecZeroEntries(X[fine_level]));
460   PetscCall(PetscBarrier((PetscObject)ksp));
461 
462   // -- Performance logging
463   PetscCall(PetscLogStageRegister("Solve Stage", &solve_stage));
464   PetscCall(PetscLogStagePush(solve_stage));
465 
466   // -- Solve
467   my_rt_start = MPI_Wtime();
468   PetscCall(KSPSolve(ksp, rhs, X[fine_level]));
469   my_rt = MPI_Wtime() - my_rt_start;
470 
471   // -- Performance logging
472   PetscCall(PetscLogStagePop());
473 
474   // Output results
475   {
476     KSPType            ksp_type;
477     PCMGType           pcmg_type;
478     KSPConvergedReason reason;
479     PetscReal          rnorm;
480     PetscInt           its;
481     PetscCall(KSPGetType(ksp, &ksp_type));
482     PetscCall(KSPGetConvergedReason(ksp, &reason));
483     PetscCall(KSPGetIterationNumber(ksp, &its));
484     PetscCall(KSPGetResidualNorm(ksp, &rnorm));
485     PetscCall(PCMGGetType(pc, &pcmg_type));
486     if (!test_mode || reason < 0 || rnorm > 1e-8) {
487       PetscCall(PetscPrintf(comm,
488                             "  KSP:\n"
489                             "    KSP Type                                : %s\n"
490                             "    KSP Convergence                         : %s\n"
491                             "    Total KSP Iterations                    : %" PetscInt_FMT "\n"
492                             "    Final rnorm                             : %e\n",
493                             ksp_type, KSPConvergedReasons[reason], its, (double)rnorm));
494       PetscCall(PetscPrintf(comm,
495                             "  PCMG:\n"
496                             "    PCMG Type                               : %s\n"
497                             "    PCMG Cycle Type                         : %s\n",
498                             PCMGTypes[pcmg_type], PCMGCycleTypes[pcmg_cycle_type]));
499     }
500     if (!test_mode) {
501       PetscCall(PetscPrintf(comm, "  Performance:\n"));
502     }
503     {
504       // Set up error operator context
505       PetscCall(SetupErrorOperatorCtx(comm, dm[fine_level], ceed, ceed_data[fine_level], X_loc[fine_level], op_error, op_error_ctx));
506       PetscScalar l2_error;
507       PetscCall(ComputeL2Error(X[fine_level], &l2_error, op_error_ctx));
508       PetscReal tol = 5e-2;
509       if (!test_mode || l2_error > tol) {
510         PetscCall(MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm));
511         PetscCall(MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm));
512         PetscCall(PetscPrintf(comm,
513                               "    L2 Error                                : %e\n"
514                               "    CG Solve Time                           : %g (%g) sec\n",
515                               (double)l2_error, rt_max, rt_min));
516       }
517     }
518     if (benchmark_mode && (!test_mode)) {
519       PetscCall(PetscPrintf(comm, "    DoFs/Sec in CG                            : %g (%g) million\n", 1e-6 * g_size[fine_level] * its / rt_max,
520                             1e-6 * g_size[fine_level] * its / rt_min));
521     }
522   }
523 
524   if (write_solution) {
525     PetscViewer vtk_viewer_soln;
526 
527     PetscCall(PetscViewerCreate(comm, &vtk_viewer_soln));
528     PetscCall(PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK));
529     PetscCall(PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"));
530     PetscCall(VecView(X[fine_level], vtk_viewer_soln));
531     PetscCall(PetscViewerDestroy(&vtk_viewer_soln));
532   }
533 
534   // Cleanup
535   for (int i = 0; i < num_levels; i++) {
536     PetscCall(VecDestroy(&X[i]));
537     PetscCall(VecDestroy(&X_loc[i]));
538     PetscCall(VecDestroy(&mult[i]));
539     PetscCall(VecDestroy(&op_apply_ctx[i]->Y_loc));
540     PetscCall(MatDestroy(&mat_O[i]));
541     PetscCall(PetscFree(op_apply_ctx[i]));
542     if (i > 0) {
543       PetscCall(MatDestroy(&mat_pr[i]));
544       PetscCall(PetscFree(pr_restr_ctx[i]));
545     }
546     PetscCall(CeedDataDestroy(i, ceed_data[i]));
547     PetscCall(DMDestroy(&dm[i]));
548   }
549   PetscCall(PetscFree(level_degrees));
550   PetscCall(PetscFree(dm));
551   PetscCall(PetscFree(X));
552   PetscCall(PetscFree(X_loc));
553   PetscCall(VecDestroy(&op_error_ctx->Y_loc));
554   PetscCall(PetscFree(mult));
555   PetscCall(PetscFree(mat_O));
556   PetscCall(PetscFree(mat_pr));
557   PetscCall(PetscFree(ceed_data));
558   PetscCall(PetscFree(op_apply_ctx));
559   PetscCall(PetscFree(op_error_ctx));
560   PetscCall(PetscFree(pr_restr_ctx));
561   PetscCall(PetscFree(l_size));
562   PetscCall(PetscFree(xl_size));
563   PetscCall(PetscFree(g_size));
564   PetscCall(VecDestroy(&rhs));
565   PetscCall(VecDestroy(&rhs_loc));
566   PetscCall(MatDestroy(&mat_coarse));
567   PetscCall(KSPDestroy(&ksp));
568   PetscCall(DMDestroy(&dm_orig));
569   CeedVectorDestroy(&target);
570   CeedQFunctionDestroy(&qf_error);
571   CeedOperatorDestroy(&op_error);
572   CeedDestroy(&ceed);
573   return PetscFinalize();
574 }
575