xref: /libCEED/examples/petsc/bpsraw.c (revision 17be3a414c6fae47654f1361bae9c9dbcdd66795)
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
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 is intentionally "raw", using only low-level communication
14 // primitives.
15 //
16 // Build with:
17 //
18 //     make bpsraw [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
19 //
20 // Sample runs:
21 //
22 //     ./bpsraw -problem bp1
23 //     ./bpsraw -problem bp2
24 //     ./bpsraw -problem bp3
25 //     ./bpsraw -problem bp4
26 //     ./bpsraw -problem bp5 -ceed /cpu/self
27 //     ./bpsraw -problem bp6 -ceed /gpu/cuda
28 //
29 //TESTARGS -ceed {ceed_resource} -test -problem bp2 -degree 5 -q_extra 1 -ksp_max_it_clip 15,15
30 
31 /// @file
32 /// CEED BPs example using PETSc
33 /// See bps.c for an implementation using DMPlex unstructured grids.
34 const char help[] = "Solve CEED BPs using PETSc\n";
35 
36 #include <ceed.h>
37 #include <petscksp.h>
38 #include <petscsys.h>
39 #include <stdbool.h>
40 #include <string.h>
41 #include "qfunctions/bps/bp1.h"
42 #include "qfunctions/bps/bp2.h"
43 #include "qfunctions/bps/bp3.h"
44 #include "qfunctions/bps/bp4.h"
45 #include "qfunctions/bps/common.h"
46 
47 #if PETSC_VERSION_LT(3,12,0)
48 #ifdef PETSC_HAVE_CUDA
49 #include <petsccuda.h>
50 // Note: With PETSc prior to version 3.12.0, providing the source path to
51 //       include 'cublas_v2.h' will be needed to use 'petsccuda.h'.
52 #endif
53 #endif
54 
55 static CeedMemType MemTypeP2C(PetscMemType mem_type) {
56   return PetscMemTypeDevice(mem_type) ? CEED_MEM_DEVICE : CEED_MEM_HOST;
57 }
58 
59 static void Split3(PetscInt size, PetscInt m[3], bool reverse) {
60   for (PetscInt d=0, size_left=size; d<3; d++) {
61     PetscInt try = (PetscInt)PetscCeilReal(PetscPowReal(size_left, 1./(3 - d)));
62     while (try * (size_left / try) != size_left) try++;
63     m[reverse ? 2-d : d] = try;
64     size_left /= try;
65   }
66 }
67 
68 static PetscInt Max3(const PetscInt a[3]) {
69   return PetscMax(a[0], PetscMax(a[1], a[2]));
70 }
71 static PetscInt Min3(const PetscInt a[3]) {
72   return PetscMin(a[0], PetscMin(a[1], a[2]));
73 }
74 static void GlobalNodes(const PetscInt p[3], const PetscInt i_rank[3],
75                         PetscInt degree, const PetscInt mesh_elem[3],
76                         PetscInt m_nodes[3]) {
77   for (int d=0; d<3; d++)
78     m_nodes[d] = degree*mesh_elem[d] + (i_rank[d] == p[d]-1);
79 }
80 static PetscInt GlobalStart(const PetscInt p[3], const PetscInt i_rank[3],
81                             PetscInt degree, const PetscInt mesh_elem[3]) {
82   PetscInt start = 0;
83   // Dumb brute-force is easier to read
84   for (PetscInt i=0; i<p[0]; i++) {
85     for (PetscInt j=0; j<p[1]; j++) {
86       for (PetscInt k=0; k<p[2]; k++) {
87         PetscInt m_nodes[3], ijk_rank[] = {i,j,k};
88         if (i == i_rank[0] && j == i_rank[1] && k == i_rank[2]) return start;
89         GlobalNodes(p, ijk_rank, degree, mesh_elem, m_nodes);
90         start += m_nodes[0] * m_nodes[1] * m_nodes[2];
91       }
92     }
93   }
94   return -1;
95 }
96 static int CreateRestriction(Ceed ceed, const CeedInt mesh_elem[3], CeedInt P,
97                              CeedInt num_comp, CeedElemRestriction *elem_restr) {
98   const PetscInt num_elem = mesh_elem[0]*mesh_elem[1]*mesh_elem[2];
99   PetscInt m_nodes[3], *idx, *idx_p;
100 
101   // Get indicies
102   for (int d=0; d<3; d++) m_nodes[d] = mesh_elem[d]*(P-1) + 1;
103   idx_p = idx = malloc(num_elem*P*P*P*sizeof idx[0]);
104   for (CeedInt i=0; i<mesh_elem[0]; i++)
105     for (CeedInt j=0; j<mesh_elem[1]; j++)
106       for (CeedInt k=0; k<mesh_elem[2]; k++,idx_p += P*P*P)
107         for (CeedInt ii=0; ii<P; ii++)
108           for (CeedInt jj=0; jj<P; jj++)
109             for (CeedInt kk=0; kk<P; kk++) {
110               if (0) { // This is the C-style (i,j,k) ordering that I prefer
111                 idx_p[(ii*P+jj)*P+kk] = num_comp*(((i*(P-1)+ii)*m_nodes[1]
112                                                    + (j*(P-1)+jj))*m_nodes[2]
113                                                   + (k*(P-1)+kk));
114               } else { // (k,j,i) ordering for consistency with MFEM example
115                 idx_p[ii+P*(jj+P*kk)] = num_comp*(((i*(P-1)+ii)*m_nodes[1]
116                                                    + (j*(P-1)+jj))*m_nodes[2]
117                                                   + (k*(P-1)+kk));
118               }
119             }
120 
121   // Setup CEED restriction
122   CeedElemRestrictionCreate(ceed, num_elem, P*P*P, num_comp, 1,
123                             m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp,
124                             CEED_MEM_HOST, CEED_OWN_POINTER, idx, elem_restr);
125 
126   PetscFunctionReturn(0);
127 }
128 
129 // Data for PETSc
130 typedef struct User_ *User;
131 struct User_ {
132   MPI_Comm comm;
133   VecScatter l_to_g;              // Scatter for all entries
134   VecScatter l_to_g_0;            // Skip Dirichlet values
135   VecScatter g_to_g_D;            // global-to-global; only Dirichlet values
136   Vec X_loc, Y_loc;
137   CeedVector x_ceed, y_ceed;
138   CeedOperator op;
139   CeedVector q_data;
140   Ceed ceed;
141 };
142 
143 // BP Options
144 typedef enum {
145   CEED_BP1 = 0, CEED_BP2 = 1, CEED_BP3 = 2,
146   CEED_BP4 = 3, CEED_BP5 = 4, CEED_BP6 = 5
147 } BPType;
148 static const char *const bp_types[] = {"bp1","bp2","bp3","bp4","bp5","bp6",
149                                        "BPType","CEED_BP",0
150                                       };
151 
152 // BP specific data
153 typedef struct {
154   CeedInt num_comp_u, q_data_size, q_extra;
155   CeedQFunctionUser setup_geo, setup_rhs, apply, error;
156   const char *setup_geo_loc, *setup_rhs_loc, *apply_loc, *error_loc;
157   CeedEvalMode in_mode, out_mode;
158   CeedQuadMode q_mode;
159 } BPData;
160 
161 BPData bp_options[6] = {
162   [CEED_BP1] = {
163     .num_comp_u = 1,
164     .q_data_size = 1,
165     .q_extra = 1,
166     .setup_geo = SetupMassGeo,
167     .setup_rhs = SetupMassRhs,
168     .apply = Mass,
169     .error = Error,
170     .setup_geo_loc = SetupMassGeo_loc,
171     .setup_rhs_loc = SetupMassRhs_loc,
172     .apply_loc = Mass_loc,
173     .error_loc = Error_loc,
174     .in_mode = CEED_EVAL_INTERP,
175     .out_mode = CEED_EVAL_INTERP,
176     .q_mode = CEED_GAUSS
177   },
178   [CEED_BP2] = {
179     .num_comp_u = 3,
180     .q_data_size = 1,
181     .q_extra = 1,
182     .setup_geo = SetupMassGeo,
183     .setup_rhs = SetupMassRhs3,
184     .apply = Mass3,
185     .error = Error3,
186     .setup_geo_loc = SetupMassGeo_loc,
187     .setup_rhs_loc = SetupMassRhs3_loc,
188     .apply_loc = Mass3_loc,
189     .error_loc = Error3_loc,
190     .in_mode = CEED_EVAL_INTERP,
191     .out_mode = CEED_EVAL_INTERP,
192     .q_mode = CEED_GAUSS
193   },
194   [CEED_BP3] = {
195     .num_comp_u = 1,
196     .q_data_size = 7,
197     .q_extra = 1,
198     .setup_geo = SetupDiffGeo,
199     .setup_rhs = SetupDiffRhs,
200     .apply = Diff,
201     .error = Error,
202     .setup_geo_loc = SetupDiffGeo_loc,
203     .setup_rhs_loc = SetupDiffRhs_loc,
204     .apply_loc = Diff_loc,
205     .error_loc = Error_loc,
206     .in_mode = CEED_EVAL_GRAD,
207     .out_mode = CEED_EVAL_GRAD,
208     .q_mode = CEED_GAUSS
209   },
210   [CEED_BP4] = {
211     .num_comp_u = 3,
212     .q_data_size = 7,
213     .q_extra = 1,
214     .setup_geo = SetupDiffGeo,
215     .setup_rhs = SetupDiffRhs3,
216     .apply = Diff3,
217     .error = Error3,
218     .setup_geo_loc = SetupDiffGeo_loc,
219     .setup_rhs_loc = SetupDiffRhs3_loc,
220     .apply_loc = Diff3_loc,
221     .error_loc = Error3_loc,
222     .in_mode = CEED_EVAL_GRAD,
223     .out_mode = CEED_EVAL_GRAD,
224     .q_mode = CEED_GAUSS
225   },
226   [CEED_BP5] = {
227     .num_comp_u = 1,
228     .q_data_size = 7,
229     .q_extra = 0,
230     .setup_geo = SetupDiffGeo,
231     .setup_rhs = SetupDiffRhs,
232     .apply = Diff,
233     .error = Error,
234     .setup_geo_loc = SetupDiffGeo_loc,
235     .setup_rhs_loc = SetupDiffRhs_loc,
236     .apply_loc = Diff_loc,
237     .error_loc = Error_loc,
238     .in_mode = CEED_EVAL_GRAD,
239     .out_mode = CEED_EVAL_GRAD,
240     .q_mode = CEED_GAUSS_LOBATTO
241   },
242   [CEED_BP6] = {
243     .num_comp_u = 3,
244     .q_data_size = 7,
245     .q_extra = 0,
246     .setup_geo = SetupDiffGeo,
247     .setup_rhs = SetupDiffRhs3,
248     .apply = Diff3,
249     .error = Error3,
250     .setup_geo_loc = SetupDiffGeo_loc,
251     .setup_rhs_loc = SetupDiffRhs3_loc,
252     .apply_loc = Diff3_loc,
253     .error_loc = Error3_loc,
254     .in_mode = CEED_EVAL_GRAD,
255     .out_mode = CEED_EVAL_GRAD,
256     .q_mode = CEED_GAUSS_LOBATTO
257   }
258 };
259 
260 // This function uses libCEED to compute the action of the mass matrix
261 static PetscErrorCode MatMult_Mass(Mat A, Vec X, Vec Y) {
262   PetscErrorCode ierr;
263   User user;
264   PetscScalar *x, *y;
265   PetscMemType x_mem_type, y_mem_type;
266 
267   PetscFunctionBeginUser;
268 
269   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
270 
271   // Global-to-local
272   ierr = VecScatterBegin(user->l_to_g, X, user->X_loc, INSERT_VALUES,
273                          SCATTER_REVERSE); CHKERRQ(ierr);
274   ierr = VecScatterEnd(user->l_to_g, X, user->X_loc, INSERT_VALUES,
275                        SCATTER_REVERSE); CHKERRQ(ierr);
276 
277   // Setup libCEED vectors
278   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
279                                    &x_mem_type); CHKERRQ(ierr);
280   ierr = VecGetArrayAndMemType(user->Y_loc, &y, &y_mem_type); CHKERRQ(ierr);
281   CeedVectorSetArray(user->x_ceed, MemTypeP2C(x_mem_type), CEED_USE_POINTER, x);
282   CeedVectorSetArray(user->y_ceed, MemTypeP2C(y_mem_type), CEED_USE_POINTER, y);
283 
284   // Apply libCEED operator
285   CeedOperatorApply(user->op, user->x_ceed, user->y_ceed,
286                     CEED_REQUEST_IMMEDIATE);
287 
288   // Restore PETSc vectors
289   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(x_mem_type), NULL);
290   CeedVectorTakeArray(user->y_ceed, MemTypeP2C(y_mem_type), NULL);
291   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
292   CHKERRQ(ierr);
293   ierr = VecRestoreArrayAndMemType(user->Y_loc, &y); CHKERRQ(ierr);
294 
295   // Local-to-global
296   if (Y) {
297     ierr = VecZeroEntries(Y); CHKERRQ(ierr);
298     ierr = VecScatterBegin(user->l_to_g, user->Y_loc, Y, ADD_VALUES,
299                            SCATTER_FORWARD); CHKERRQ(ierr);
300     ierr = VecScatterEnd(user->l_to_g, user->Y_loc, Y, ADD_VALUES,
301                          SCATTER_FORWARD); CHKERRQ(ierr);
302   }
303   PetscFunctionReturn(0);
304 }
305 
306 // This function uses libCEED to compute the action of the Laplacian with
307 // Dirichlet boundary conditions
308 static PetscErrorCode MatMult_Diff(Mat A, Vec X, Vec Y) {
309   PetscErrorCode ierr;
310   User user;
311   PetscScalar *x, *y;
312   PetscMemType x_mem_type, y_mem_type;
313 
314   PetscFunctionBeginUser;
315 
316   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
317 
318   // Global-to-local
319   ierr = VecScatterBegin(user->l_to_g_0, X, user->X_loc, INSERT_VALUES,
320                          SCATTER_REVERSE); CHKERRQ(ierr);
321   ierr = VecScatterEnd(user->l_to_g_0, X, user->X_loc, INSERT_VALUES,
322                        SCATTER_REVERSE);
323   CHKERRQ(ierr);
324 
325   // Setup libCEED vectors
326   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
327                                    &x_mem_type); CHKERRQ(ierr);
328   ierr = VecGetArrayAndMemType(user->Y_loc, &y, &y_mem_type); CHKERRQ(ierr);
329   CeedVectorSetArray(user->x_ceed, MemTypeP2C(x_mem_type), CEED_USE_POINTER, x);
330   CeedVectorSetArray(user->y_ceed, MemTypeP2C(y_mem_type), CEED_USE_POINTER, y);
331 
332   // Apply libCEED operator
333   CeedOperatorApply(user->op, user->x_ceed, user->y_ceed,
334                     CEED_REQUEST_IMMEDIATE);
335 
336   // Restore PETSc vectors
337   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(x_mem_type), NULL);
338   CeedVectorTakeArray(user->y_ceed, MemTypeP2C(y_mem_type), NULL);
339   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
340   CHKERRQ(ierr);
341   ierr = VecRestoreArrayAndMemType(user->Y_loc, &y); CHKERRQ(ierr);
342 
343   // Local-to-global
344   ierr = VecZeroEntries(Y); CHKERRQ(ierr);
345   ierr = VecScatterBegin(user->g_to_g_D, X, Y, INSERT_VALUES, SCATTER_FORWARD);
346   CHKERRQ(ierr);
347   ierr = VecScatterEnd(user->g_to_g_D, X, Y, INSERT_VALUES, SCATTER_FORWARD);
348   CHKERRQ(ierr);
349   ierr = VecScatterBegin(user->l_to_g_0, user->Y_loc, Y, ADD_VALUES,
350                          SCATTER_FORWARD); CHKERRQ(ierr);
351   ierr = VecScatterEnd(user->l_to_g_0, user->Y_loc, Y, ADD_VALUES,
352                        SCATTER_FORWARD);
353   CHKERRQ(ierr);
354 
355   PetscFunctionReturn(0);
356 }
357 
358 // This function calculates the error in the final solution
359 static PetscErrorCode ComputeErrorMax(User user, CeedOperator op_error, Vec X,
360                                       CeedVector target, PetscReal *max_error) {
361   PetscErrorCode ierr;
362   PetscScalar *x;
363   PetscMemType mem_type;
364   CeedVector collocated_error;
365   CeedSize length;
366 
367   PetscFunctionBeginUser;
368 
369   CeedVectorGetLength(target, &length);
370   CeedVectorCreate(user->ceed, length, &collocated_error);
371 
372   // Global-to-local
373   ierr = VecScatterBegin(user->l_to_g, X, user->X_loc, INSERT_VALUES,
374                          SCATTER_REVERSE); CHKERRQ(ierr);
375   ierr = VecScatterEnd(user->l_to_g, X, user->X_loc, INSERT_VALUES,
376                        SCATTER_REVERSE); CHKERRQ(ierr);
377 
378   // Setup libCEED vector
379   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
380                                    &mem_type); CHKERRQ(ierr);
381   CeedVectorSetArray(user->x_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, x);
382 
383   // Apply libCEED operator
384   CeedOperatorApply(op_error, user->x_ceed, collocated_error,
385                     CEED_REQUEST_IMMEDIATE);
386 
387   // Restore PETSc vector
388   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(mem_type), NULL);
389   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
390   CHKERRQ(ierr);
391 
392   // Reduce max error
393   *max_error = 0;
394   const CeedScalar *e;
395   CeedVectorGetArrayRead(collocated_error, CEED_MEM_HOST, &e);
396   for (CeedInt i=0; i<length; i++) {
397     *max_error = PetscMax(*max_error, PetscAbsScalar(e[i]));
398   }
399   CeedVectorRestoreArrayRead(collocated_error, &e);
400   ierr = MPI_Allreduce(MPI_IN_PLACE, max_error, 1, MPIU_REAL, MPIU_MAX,
401                        user->comm); CHKERRQ(ierr);
402 
403   // Cleanup
404   CeedVectorDestroy(&collocated_error);
405 
406   PetscFunctionReturn(0);
407 }
408 
409 int main(int argc, char **argv) {
410   PetscInt ierr;
411   MPI_Comm comm;
412   char ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
413   double my_rt_start, my_rt, rt_min, rt_max;
414   PetscInt degree, q_extra, local_nodes, local_elem, mesh_elem[3], m_nodes[3],
415            p[3],
416            i_rank[3], l_nodes[3], l_size, num_comp_u = 1, ksp_max_it_clip[2];
417   PetscScalar *r;
418   PetscBool test_mode, benchmark_mode, write_solution;
419   PetscMPIInt size, rank;
420   PetscLogStage solve_stage;
421   Vec X, X_loc, rhs, rhs_loc;
422   Mat mat;
423   KSP ksp;
424   VecScatter l_to_g, l_to_g_0, g_to_g_D;
425   PetscMemType mem_type;
426   User user;
427   Ceed ceed;
428   CeedBasis basis_x, basis_u;
429   CeedElemRestriction elem_restr_x, elem_restr_u, elem_restr_u_i, elem_restr_qd_i;
430   CeedQFunction qf_setup_geo, qf_setup_rhs, qf_apply, qf_error;
431   CeedOperator op_setup_geo, op_setup_rhs, op_apply, op_error;
432   CeedVector x_coord, q_data, rhs_ceed, target;
433   CeedInt P, Q;
434   const CeedInt dim = 3, num_comp_x = 3;
435   BPType bp_choice;
436 
437   ierr = PetscInitialize(&argc, &argv, NULL, help);
438   if (ierr) return ierr;
439   comm = PETSC_COMM_WORLD;
440 
441   // Read command line options
442   PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL);
443   bp_choice = CEED_BP1;
444   ierr = PetscOptionsEnum("-problem",
445                           "CEED benchmark problem to solve", NULL,
446                           bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice,
447                           NULL); CHKERRQ(ierr);
448   num_comp_u = bp_options[bp_choice].num_comp_u;
449   test_mode = PETSC_FALSE;
450   ierr = PetscOptionsBool("-test",
451                           "Testing mode (do not print unless error is large)",
452                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
453   benchmark_mode = PETSC_FALSE;
454   ierr = PetscOptionsBool("-benchmark",
455                           "Benchmarking mode (prints benchmark statistics)",
456                           NULL, benchmark_mode, &benchmark_mode, NULL);
457   CHKERRQ(ierr);
458   write_solution = PETSC_FALSE;
459   ierr = PetscOptionsBool("-write_solution",
460                           "Write solution for visualization",
461                           NULL, write_solution, &write_solution, NULL);
462   CHKERRQ(ierr);
463   degree = test_mode ? 3 : 1;
464   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
465                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
466   q_extra = bp_options[bp_choice].q_extra;
467   ierr = PetscOptionsInt("-q_extra", "Number of extra quadrature points",
468                          NULL, q_extra, &q_extra, NULL); CHKERRQ(ierr);
469   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
470                             NULL, ceed_resource, ceed_resource,
471                             sizeof(ceed_resource), NULL); CHKERRQ(ierr);
472   local_nodes = 1000;
473   ierr = PetscOptionsInt("-local",
474                          "Target number of locally owned nodes per process",
475                          NULL, local_nodes, &local_nodes, NULL); CHKERRQ(ierr);
476   PetscInt two = 2;
477   ksp_max_it_clip[0] = 5;
478   ksp_max_it_clip[1] = 20;
479   ierr = PetscOptionsIntArray("-ksp_max_it_clip",
480                               "Min and max number of iterations to use during benchmarking",
481                               NULL, ksp_max_it_clip, &two, NULL);
482   CHKERRQ(ierr);
483   PetscOptionsEnd();
484   P = degree + 1;
485   Q = P + q_extra;
486 
487   // Set up libCEED
488   CeedInit(ceed_resource, &ceed);
489   CeedMemType mem_type_backend;
490   CeedGetPreferredMemType(ceed, &mem_type_backend);
491 
492   VecType default_vec_type = NULL, vec_type;
493   switch (mem_type_backend) {
494   case CEED_MEM_HOST: default_vec_type = VECSTANDARD; break;
495   case CEED_MEM_DEVICE: {
496     const char *resolved;
497     CeedGetResource(ceed, &resolved);
498     if (strstr(resolved, "/gpu/cuda")) default_vec_type = VECCUDA;
499     else if (strstr(resolved, "/gpu/hip/occa"))
500       default_vec_type = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
501     else if (strstr(resolved, "/gpu/hip")) default_vec_type = VECHIP;
502     else default_vec_type = VECSTANDARD;
503   }
504   }
505 
506   // Determine size of process grid
507   ierr = MPI_Comm_size(comm, &size); CHKERRQ(ierr);
508   Split3(size, p, false);
509 
510   // Find a nicely composite number of elements no less than local_nodes
511   for (local_elem = PetscMax(1, local_nodes / (degree*degree*degree)); ;
512        local_elem++) {
513     Split3(local_elem, mesh_elem, true);
514     if (Max3(mesh_elem) / Min3(mesh_elem) <= 2) break;
515   }
516 
517   // Find my location in the process grid
518   ierr = MPI_Comm_rank(comm, &rank); CHKERRQ(ierr);
519   for (int d=0, rank_left=rank; d<dim; d++) {
520     const int pstride[3] = {p[1] *p[2], p[2], 1};
521     i_rank[d] = rank_left / pstride[d];
522     rank_left -= i_rank[d] * pstride[d];
523   }
524 
525   GlobalNodes(p, i_rank, degree, mesh_elem, m_nodes);
526 
527   // Setup global vector
528   ierr = VecCreate(comm, &X); CHKERRQ(ierr);
529   ierr = VecSetType(X, default_vec_type); CHKERRQ(ierr);
530   ierr = VecSetSizes(X, m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
531                      PETSC_DECIDE);
532   CHKERRQ(ierr);
533   ierr = VecSetFromOptions(X); CHKERRQ(ierr);
534   ierr = VecSetUp(X); CHKERRQ(ierr);
535 
536   // Set up libCEED
537   CeedInit(ceed_resource, &ceed);
538 
539   // Print summary
540   CeedInt gsize;
541   ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
542   if (!test_mode) {
543     const char *used_resource;
544     CeedGetResource(ceed, &used_resource);
545 
546     ierr = VecGetType(X, &vec_type); CHKERRQ(ierr);
547 
548     ierr = PetscPrintf(comm,
549                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc --\n"
550                        "  PETSc:\n"
551                        "    PETSc Vec Type                     : %s\n"
552                        "  libCEED:\n"
553                        "    libCEED Backend                    : %s\n"
554                        "    libCEED Backend MemType            : %s\n"
555                        "  Mesh:\n"
556                        "    Number of 1D Basis Nodes (P)       : %d\n"
557                        "    Number of 1D Quadrature Points (Q) : %d\n"
558                        "    Global nodes                       : %" PetscInt_FMT "\n"
559                        "    Process Decomposition              : %" PetscInt_FMT
560                        " %" PetscInt_FMT " %" PetscInt_FMT "\n"
561                        "    Local Elements                     : %" PetscInt_FMT
562                        " = %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n"
563                        "    Owned nodes                        : %" PetscInt_FMT
564                        " = %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n"
565                        "    DoF per node                       : %" PetscInt_FMT "\n",
566                        bp_choice+1, vec_type, used_resource,
567                        CeedMemTypes[mem_type_backend],
568                        P, Q,  gsize/num_comp_u, p[0], p[1], p[2], local_elem,
569                        mesh_elem[0], mesh_elem[1], mesh_elem[2],
570                        m_nodes[0]*m_nodes[1]*m_nodes[2], m_nodes[0], m_nodes[1],
571                        m_nodes[2], num_comp_u); CHKERRQ(ierr);
572   }
573 
574   {
575     l_size = 1;
576     for (int d=0; d<dim; d++) {
577       l_nodes[d] = mesh_elem[d]*degree + 1;
578       l_size *= l_nodes[d];
579     }
580     ierr = VecCreate(PETSC_COMM_SELF, &X_loc); CHKERRQ(ierr);
581     ierr = VecSetType(X_loc, default_vec_type); CHKERRQ(ierr);
582     ierr = VecSetSizes(X_loc, l_size*num_comp_u, PETSC_DECIDE); CHKERRQ(ierr);
583     ierr = VecSetFromOptions(X_loc); CHKERRQ(ierr);
584     ierr = VecSetUp(X_loc); CHKERRQ(ierr);
585 
586     // Create local-to-global scatter
587     PetscInt *l_to_g_ind, *l_to_g_ind_0, *loc_ind, l_0_count;
588     IS l_to_g_is, l_to_g_is_0, loc_is;
589     PetscInt g_start[2][2][2], g_m_nodes[2][2][2][dim];
590 
591     for (int i=0; i<2; i++) {
592       for (int j=0; j<2; j++) {
593         for (int k=0; k<2; k++) {
594           PetscInt ijk_rank[3] = {i_rank[0]+i, i_rank[1]+j, i_rank[2]+k};
595           g_start[i][j][k] = GlobalStart(p, ijk_rank, degree, mesh_elem);
596           GlobalNodes(p, ijk_rank, degree, mesh_elem, g_m_nodes[i][j][k]);
597         }
598       }
599     }
600 
601     ierr = PetscMalloc1(l_size, &l_to_g_ind); CHKERRQ(ierr);
602     ierr = PetscMalloc1(l_size, &l_to_g_ind_0); CHKERRQ(ierr);
603     ierr = PetscMalloc1(l_size, &loc_ind); CHKERRQ(ierr);
604     l_0_count = 0;
605     for (PetscInt i=0,ir,ii; ir=i>=m_nodes[0], ii=i-ir*m_nodes[0], i<l_nodes[0];
606          i++)
607       for (PetscInt j=0,jr,jj; jr=j>=m_nodes[1], jj=j-jr*m_nodes[1], j<l_nodes[1];
608            j++)
609         for (PetscInt k=0,kr,kk; kr=k>=m_nodes[2], kk=k-kr*m_nodes[2], k<l_nodes[2];
610              k++) {
611           PetscInt here = (i*l_nodes[1]+j)*l_nodes[2]+k;
612           l_to_g_ind[here] =
613             g_start[ir][jr][kr] + (ii*g_m_nodes[ir][jr][kr][1]+jj)*g_m_nodes[ir][jr][kr][2]
614             +kk;
615           if ((i_rank[0] == 0 && i == 0)
616               || (i_rank[1] == 0 && j == 0)
617               || (i_rank[2] == 0 && k == 0)
618               || (i_rank[0]+1 == p[0] && i+1 == l_nodes[0])
619               || (i_rank[1]+1 == p[1] && j+1 == l_nodes[1])
620               || (i_rank[2]+1 == p[2] && k+1 == l_nodes[2]))
621             continue;
622           l_to_g_ind_0[l_0_count] = l_to_g_ind[here];
623           loc_ind[l_0_count++] = here;
624         }
625     ierr = ISCreateBlock(comm, num_comp_u, l_size, l_to_g_ind, PETSC_OWN_POINTER,
626                          &l_to_g_is); CHKERRQ(ierr);
627     ierr = VecScatterCreate(X_loc, NULL, X, l_to_g_is, &l_to_g); CHKERRQ(ierr);
628     CHKERRQ(ierr);
629     ierr = ISCreateBlock(comm, num_comp_u, l_0_count, l_to_g_ind_0,
630                          PETSC_OWN_POINTER,
631                          &l_to_g_is_0); CHKERRQ(ierr);
632     ierr = ISCreateBlock(comm, num_comp_u, l_0_count, loc_ind, PETSC_OWN_POINTER,
633                          &loc_is); CHKERRQ(ierr);
634     ierr = VecScatterCreate(X_loc, loc_is, X, l_to_g_is_0, &l_to_g_0);
635     CHKERRQ(ierr);
636     {
637       // Create global-to-global scatter for Dirichlet values (everything not in
638       // l_to_g_is_0, which is the range of l_to_g_0)
639       PetscInt x_start, x_end, *ind_D, count_D = 0;
640       IS is_D;
641       const PetscScalar *x;
642       ierr = VecZeroEntries(X_loc); CHKERRQ(ierr);
643       ierr = VecSet(X, 1.0); CHKERRQ(ierr);
644       ierr = VecScatterBegin(l_to_g_0, X_loc, X, INSERT_VALUES, SCATTER_FORWARD);
645       CHKERRQ(ierr);
646       ierr = VecScatterEnd(l_to_g_0, X_loc, X, INSERT_VALUES, SCATTER_FORWARD);
647       CHKERRQ(ierr);
648       ierr = VecGetOwnershipRange(X, &x_start, &x_end); CHKERRQ(ierr);
649       ierr = PetscMalloc1(x_end-x_start, &ind_D); CHKERRQ(ierr);
650       ierr = VecGetArrayRead(X, &x); CHKERRQ(ierr);
651       for (PetscInt i=0; i<x_end-x_start; i++) {
652         if (x[i] == 1.) ind_D[count_D++] = x_start + i;
653       }
654       ierr = VecRestoreArrayRead(X, &x); CHKERRQ(ierr);
655       ierr = ISCreateGeneral(comm, count_D, ind_D, PETSC_COPY_VALUES, &is_D);
656       CHKERRQ(ierr);
657       ierr = PetscFree(ind_D); CHKERRQ(ierr);
658       ierr = VecScatterCreate(X, is_D, X, is_D, &g_to_g_D); CHKERRQ(ierr);
659       ierr = ISDestroy(&is_D); CHKERRQ(ierr);
660     }
661     ierr = ISDestroy(&l_to_g_is); CHKERRQ(ierr);
662     ierr = ISDestroy(&l_to_g_is_0); CHKERRQ(ierr);
663     ierr = ISDestroy(&loc_is); CHKERRQ(ierr);
664   }
665 
666   // CEED bases
667   CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_u, P, Q,
668                                   bp_options[bp_choice].q_mode, &basis_u);
669   CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, 2, Q,
670                                   bp_options[bp_choice].q_mode, &basis_x);
671 
672   // CEED restrictions
673   CreateRestriction(ceed, mesh_elem, P, num_comp_u, &elem_restr_u);
674   CreateRestriction(ceed, mesh_elem, 2, dim, &elem_restr_x);
675   CeedInt num_elem = mesh_elem[0]*mesh_elem[1]*mesh_elem[2];
676   CeedElemRestrictionCreateStrided(ceed, num_elem, Q*Q*Q, num_comp_u,
677                                    num_comp_u*num_elem*Q*Q*Q,
678                                    CEED_STRIDES_BACKEND, &elem_restr_u_i);
679   CeedElemRestrictionCreateStrided(ceed, num_elem, Q*Q*Q,
680                                    bp_options[bp_choice].q_data_size,
681                                    bp_options[bp_choice].q_data_size*num_elem*Q*Q*Q,
682                                    CEED_STRIDES_BACKEND, &elem_restr_qd_i);
683   {
684     CeedScalar *x_loc;
685     CeedInt shape[3] = {mesh_elem[0]+1, mesh_elem[1]+1, mesh_elem[2]+1}, len =
686                          shape[0]*shape[1]*shape[2];
687     x_loc = malloc(len*num_comp_x*sizeof x_loc[0]);
688     for (CeedInt i=0; i<shape[0]; i++) {
689       for (CeedInt j=0; j<shape[1]; j++) {
690         for (CeedInt k=0; k<shape[2]; k++) {
691           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 0] = 1.*(i_rank[0]*mesh_elem[0]+i) /
692               (p[0]*mesh_elem[0]);
693           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 1] = 1.*(i_rank[1]*mesh_elem[1]+j) /
694               (p[1]*mesh_elem[1]);
695           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 2] = 1.*(i_rank[2]*mesh_elem[2]+k) /
696               (p[2]*mesh_elem[2]);
697         }
698       }
699     }
700     CeedVectorCreate(ceed, len*num_comp_x, &x_coord);
701     CeedVectorSetArray(x_coord, CEED_MEM_HOST, CEED_OWN_POINTER, x_loc);
702   }
703 
704   // Create the QFunction that builds the operator quadrature data
705   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].setup_geo,
706                               bp_options[bp_choice].setup_geo_loc, &qf_setup_geo);
707   CeedQFunctionAddInput(qf_setup_geo, "x", num_comp_x, CEED_EVAL_INTERP);
708   CeedQFunctionAddInput(qf_setup_geo, "dx", num_comp_x*dim, CEED_EVAL_GRAD);
709   CeedQFunctionAddInput(qf_setup_geo, "weight", 1, CEED_EVAL_WEIGHT);
710   CeedQFunctionAddOutput(qf_setup_geo, "q_data",
711                          bp_options[bp_choice].q_data_size,
712                          CEED_EVAL_NONE);
713 
714   // Create the QFunction that sets up the RHS and true solution
715   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].setup_rhs,
716                               bp_options[bp_choice].setup_rhs_loc, &qf_setup_rhs);
717   CeedQFunctionAddInput(qf_setup_rhs, "x", num_comp_x, CEED_EVAL_INTERP);
718   CeedQFunctionAddInput(qf_setup_rhs, "q_data", bp_options[bp_choice].q_data_size,
719                         CEED_EVAL_NONE);
720   CeedQFunctionAddOutput(qf_setup_rhs, "true_soln", num_comp_u, CEED_EVAL_NONE);
721   CeedQFunctionAddOutput(qf_setup_rhs, "rhs", num_comp_u, CEED_EVAL_INTERP);
722 
723   // Set up PDE operator
724   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].apply,
725                               bp_options[bp_choice].apply_loc, &qf_apply);
726   // Add inputs and outputs
727   CeedInt in_scale = bp_options[bp_choice].in_mode==CEED_EVAL_GRAD ? 3 : 1;
728   CeedInt out_scale = bp_options[bp_choice].out_mode==CEED_EVAL_GRAD ? 3 : 1;
729   CeedQFunctionAddInput(qf_apply, "u", num_comp_u*in_scale,
730                         bp_options[bp_choice].in_mode);
731   CeedQFunctionAddInput(qf_apply, "q_data", bp_options[bp_choice].q_data_size,
732                         CEED_EVAL_NONE);
733   CeedQFunctionAddOutput(qf_apply, "v", num_comp_u*out_scale,
734                          bp_options[bp_choice].out_mode);
735 
736   // Create the error qfunction
737   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error,
738                               bp_options[bp_choice].error_loc, &qf_error);
739   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
740   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
741   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_NONE);
742 
743   // Create the persistent vectors that will be needed in setup
744   CeedInt num_qpts;
745   CeedBasisGetNumQuadraturePoints(basis_u, &num_qpts);
746   CeedVectorCreate(ceed, bp_options[bp_choice].q_data_size*num_elem*num_qpts,
747                    &q_data);
748   CeedVectorCreate(ceed, num_elem*num_qpts*num_comp_u, &target);
749   CeedVectorCreate(ceed, l_size*num_comp_u, &rhs_ceed);
750 
751   // Create the operator that builds the quadrature data for the ceed operator
752   CeedOperatorCreate(ceed, qf_setup_geo, CEED_QFUNCTION_NONE,
753                      CEED_QFUNCTION_NONE, &op_setup_geo);
754   CeedOperatorSetField(op_setup_geo, "x", elem_restr_x, basis_x,
755                        CEED_VECTOR_ACTIVE);
756   CeedOperatorSetField(op_setup_geo, "dx", elem_restr_x, basis_x,
757                        CEED_VECTOR_ACTIVE);
758   CeedOperatorSetField(op_setup_geo, "weight", CEED_ELEMRESTRICTION_NONE, basis_x,
759                        CEED_VECTOR_NONE);
760   CeedOperatorSetField(op_setup_geo, "q_data", elem_restr_qd_i,
761                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
762 
763   // Create the operator that builds the RHS and true solution
764   CeedOperatorCreate(ceed, qf_setup_rhs, CEED_QFUNCTION_NONE,
765                      CEED_QFUNCTION_NONE, &op_setup_rhs);
766   CeedOperatorSetField(op_setup_rhs, "x", elem_restr_x, basis_x,
767                        CEED_VECTOR_ACTIVE);
768   CeedOperatorSetField(op_setup_rhs, "q_data", elem_restr_qd_i,
769                        CEED_BASIS_COLLOCATED,
770                        q_data);
771   CeedOperatorSetField(op_setup_rhs, "true_soln", elem_restr_u_i,
772                        CEED_BASIS_COLLOCATED, target);
773   CeedOperatorSetField(op_setup_rhs, "rhs", elem_restr_u, basis_u,
774                        CEED_VECTOR_ACTIVE);
775 
776   // Create the mass or diff operator
777   CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
778                      &op_apply);
779   CeedOperatorSetField(op_apply, "u", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
780   CeedOperatorSetField(op_apply, "q_data", elem_restr_qd_i, CEED_BASIS_COLLOCATED,
781                        q_data);
782   CeedOperatorSetField(op_apply, "v", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
783 
784   // Create the error operator
785   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
786                      &op_error);
787   CeedOperatorSetField(op_error, "u", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
788   CeedOperatorSetField(op_error, "true_soln", elem_restr_u_i,
789                        CEED_BASIS_COLLOCATED, target);
790   CeedOperatorSetField(op_error, "error", elem_restr_u_i, CEED_BASIS_COLLOCATED,
791                        CEED_VECTOR_ACTIVE);
792 
793   // Set up Mat
794   ierr = PetscMalloc1(1, &user); CHKERRQ(ierr);
795   user->comm = comm;
796   user->l_to_g = l_to_g;
797   if (bp_choice != CEED_BP1 && bp_choice != CEED_BP2) {
798     user->l_to_g_0 = l_to_g_0;
799     user->g_to_g_D = g_to_g_D;
800   }
801   user->X_loc = X_loc;
802   ierr = VecDuplicate(X_loc, &user->Y_loc); CHKERRQ(ierr);
803   CeedVectorCreate(ceed, l_size*num_comp_u, &user->x_ceed);
804   CeedVectorCreate(ceed, l_size*num_comp_u, &user->y_ceed);
805   user->op = op_apply;
806   user->q_data = q_data;
807   user->ceed = ceed;
808 
809   ierr = MatCreateShell(comm, m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
810                         m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
811                         PETSC_DECIDE, PETSC_DECIDE, user, &mat); CHKERRQ(ierr);
812   if (bp_choice == CEED_BP1 || bp_choice == CEED_BP2) {
813     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Mass);
814     CHKERRQ(ierr);
815   } else {
816     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Diff);
817     CHKERRQ(ierr);
818   }
819   ierr = VecGetType(X, &vec_type); CHKERRQ(ierr);
820   ierr = MatShellSetVecType(mat, vec_type); CHKERRQ(ierr);
821 
822   // Get RHS vector
823   ierr = VecDuplicate(X, &rhs); CHKERRQ(ierr);
824   ierr = VecDuplicate(X_loc, &rhs_loc); CHKERRQ(ierr);
825   ierr = VecZeroEntries(rhs_loc); CHKERRQ(ierr);
826   ierr = VecGetArrayAndMemType(rhs_loc, &r, &mem_type); CHKERRQ(ierr);
827   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
828 
829   // Setup q_data, rhs, and target
830   CeedOperatorApply(op_setup_geo, x_coord, q_data, CEED_REQUEST_IMMEDIATE);
831   CeedOperatorApply(op_setup_rhs, x_coord, rhs_ceed, CEED_REQUEST_IMMEDIATE);
832   CeedVectorDestroy(&x_coord);
833 
834   // Gather RHS
835   ierr = CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL); CHKERRQ(ierr);
836   ierr = VecRestoreArrayAndMemType(rhs_loc, &r); CHKERRQ(ierr);
837   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
838   ierr = VecScatterBegin(l_to_g, rhs_loc, rhs, ADD_VALUES, SCATTER_FORWARD);
839   CHKERRQ(ierr);
840   ierr = VecScatterEnd(l_to_g, rhs_loc, rhs, ADD_VALUES, SCATTER_FORWARD);
841   CHKERRQ(ierr);
842   CeedVectorDestroy(&rhs_ceed);
843 
844   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
845   {
846     PC pc;
847     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
848     if (bp_choice == CEED_BP1 || bp_choice == CEED_BP2) {
849       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
850       ierr = PCJacobiSetType(pc, PC_JACOBI_ROWSUM); CHKERRQ(ierr);
851     } else {
852       ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
853     }
854     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
855     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
856     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
857                             PETSC_DEFAULT); CHKERRQ(ierr);
858   }
859   ierr = KSPSetOperators(ksp, mat, mat); CHKERRQ(ierr);
860   // First run's performance log is not considered for benchmarking purposes
861   ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
862   CHKERRQ(ierr);
863   my_rt_start = MPI_Wtime();
864   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
865   my_rt = MPI_Wtime() - my_rt_start;
866   ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
867   CHKERRQ(ierr);
868   // Set maxits based on first iteration timing
869   if (my_rt > 0.02) {
870     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
871                             ksp_max_it_clip[0]); CHKERRQ(ierr);
872   } else {
873     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
874                             ksp_max_it_clip[1]); CHKERRQ(ierr);
875   }
876   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
877 
878   // Timed solve
879   ierr = VecZeroEntries(X); CHKERRQ(ierr);
880   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
881 
882   // -- Performance logging
883   ierr = PetscLogStageRegister("Solve Stage", &solve_stage); CHKERRQ(ierr);
884   ierr = PetscLogStagePush(solve_stage); CHKERRQ(ierr);
885 
886   // -- Solve
887   my_rt_start = MPI_Wtime();
888   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
889   my_rt = MPI_Wtime() - my_rt_start;
890 
891   // -- Performance logging
892   ierr = PetscLogStagePop();
893 
894   // Output results
895   {
896     KSPType ksp_type;
897     KSPConvergedReason reason;
898     PetscReal rnorm;
899     PetscInt its;
900     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
901     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
902     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
903     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
904     if (!test_mode || reason < 0 || rnorm > 1e-8) {
905       ierr = PetscPrintf(comm,
906                          "  KSP:\n"
907                          "    KSP Type                           : %s\n"
908                          "    KSP Convergence                    : %s\n"
909                          "    Total KSP Iterations               : %" PetscInt_FMT "\n"
910                          "    Final rnorm                        : %e\n",
911                          ksp_type, KSPConvergedReasons[reason], its,
912                          (double)rnorm); CHKERRQ(ierr);
913     }
914     if (!test_mode) {
915       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
916     }
917     {
918       PetscReal max_error;
919       ierr = ComputeErrorMax(user, op_error, X, target, &max_error);
920       CHKERRQ(ierr);
921       PetscReal tol = 5e-2;
922       if (!test_mode || max_error > tol) {
923         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
924         CHKERRQ(ierr);
925         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
926         CHKERRQ(ierr);
927         ierr = PetscPrintf(comm,
928                            "    Pointwise Error (max)              : %e\n"
929                            "    CG Solve Time                      : %g (%g) sec\n",
930                            (double)max_error, rt_max, rt_min); CHKERRQ(ierr);
931       }
932     }
933     if (!test_mode) {
934       ierr = PetscPrintf(comm,
935                          "    DoFs/Sec in CG                     : %g (%g) million\n",
936                          1e-6*gsize*its/rt_max,
937                          1e-6*gsize*its/rt_min); CHKERRQ(ierr);
938     }
939   }
940 
941   if (write_solution) {
942     PetscViewer vtk_viewer_soln;
943 
944     ierr = PetscViewerCreate(comm, &vtk_viewer_soln); CHKERRQ(ierr);
945     ierr = PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK); CHKERRQ(ierr);
946     ierr = PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"); CHKERRQ(ierr);
947     ierr = VecView(X, vtk_viewer_soln); CHKERRQ(ierr);
948     ierr = PetscViewerDestroy(&vtk_viewer_soln); CHKERRQ(ierr);
949   }
950 
951   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
952   ierr = VecDestroy(&rhs_loc); CHKERRQ(ierr);
953   ierr = VecDestroy(&X); CHKERRQ(ierr);
954   ierr = VecDestroy(&user->X_loc); CHKERRQ(ierr);
955   ierr = VecDestroy(&user->Y_loc); CHKERRQ(ierr);
956   ierr = VecScatterDestroy(&l_to_g); CHKERRQ(ierr);
957   ierr = VecScatterDestroy(&l_to_g_0); CHKERRQ(ierr);
958   ierr = VecScatterDestroy(&g_to_g_D); CHKERRQ(ierr);
959   ierr = MatDestroy(&mat); CHKERRQ(ierr);
960   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
961 
962   CeedVectorDestroy(&user->x_ceed);
963   CeedVectorDestroy(&user->y_ceed);
964   CeedVectorDestroy(&user->q_data);
965   CeedVectorDestroy(&target);
966   CeedOperatorDestroy(&op_setup_geo);
967   CeedOperatorDestroy(&op_setup_rhs);
968   CeedOperatorDestroy(&op_apply);
969   CeedOperatorDestroy(&op_error);
970   CeedElemRestrictionDestroy(&elem_restr_u);
971   CeedElemRestrictionDestroy(&elem_restr_x);
972   CeedElemRestrictionDestroy(&elem_restr_u_i);
973   CeedElemRestrictionDestroy(&elem_restr_qd_i);
974   CeedQFunctionDestroy(&qf_setup_geo);
975   CeedQFunctionDestroy(&qf_setup_rhs);
976   CeedQFunctionDestroy(&qf_apply);
977   CeedQFunctionDestroy(&qf_error);
978   CeedBasisDestroy(&basis_u);
979   CeedBasisDestroy(&basis_x);
980   CeedDestroy(&ceed);
981   ierr = PetscFree(user); CHKERRQ(ierr);
982   return PetscFinalize();
983 }
984