xref: /libCEED/examples/petsc/bpsraw.c (revision e79b91d9f61753a734e6e21c778d772fcdbcc265)
1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
3 // reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 //                        libCEED + PETSc Example: CEED BPs
18 //
19 // This example demonstrates a simple usage of libCEED with PETSc to solve the
20 // CEED BP benchmark problems, see http://ceed.exascaleproject.org/bps.
21 //
22 // The code is intentionally "raw", using only low-level communication
23 // primitives.
24 //
25 // Build with:
26 //
27 //     make bpsraw [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
28 //
29 // Sample runs:
30 //
31 //     ./bpsraw -problem bp1
32 //     ./bpsraw -problem bp2
33 //     ./bpsraw -problem bp3
34 //     ./bpsraw -problem bp4
35 //     ./bpsraw -problem bp5 -ceed /cpu/self
36 //     ./bpsraw -problem bp6 -ceed /gpu/cuda
37 //
38 //TESTARGS -ceed {ceed_resource} -test -problem bp2 -degree 5 -q_extra 1 -ksp_max_it_clip 15,15
39 
40 /// @file
41 /// CEED BPs example using PETSc
42 /// See bps.c for an implementation using DMPlex unstructured grids.
43 const char help[] = "Solve CEED BPs using PETSc\n";
44 
45 #include <ceed.h>
46 #include <petscksp.h>
47 #include <petscsys.h>
48 #include <stdbool.h>
49 #include <string.h>
50 #include "qfunctions/bps/bp1.h"
51 #include "qfunctions/bps/bp2.h"
52 #include "qfunctions/bps/bp3.h"
53 #include "qfunctions/bps/bp4.h"
54 #include "qfunctions/bps/common.h"
55 
56 #if PETSC_VERSION_LT(3,12,0)
57 #ifdef PETSC_HAVE_CUDA
58 #include <petsccuda.h>
59 // Note: With PETSc prior to version 3.12.0, providing the source path to
60 //       include 'cublas_v2.h' will be needed to use 'petsccuda.h'.
61 #endif
62 #endif
63 
64 static CeedMemType MemTypeP2C(PetscMemType mem_type) {
65   return PetscMemTypeDevice(mem_type) ? CEED_MEM_DEVICE : CEED_MEM_HOST;
66 }
67 
68 static void Split3(PetscInt size, PetscInt m[3], bool reverse) {
69   for (PetscInt d=0, size_left=size; d<3; d++) {
70     PetscInt try = (PetscInt)PetscCeilReal(PetscPowReal(size_left, 1./(3 - d)));
71     while (try * (size_left / try) != size_left) try++;
72     m[reverse ? 2-d : d] = try;
73     size_left /= try;
74   }
75 }
76 
77 static PetscInt Max3(const PetscInt a[3]) {
78   return PetscMax(a[0], PetscMax(a[1], a[2]));
79 }
80 static PetscInt Min3(const PetscInt a[3]) {
81   return PetscMin(a[0], PetscMin(a[1], a[2]));
82 }
83 static void GlobalNodes(const PetscInt p[3], const PetscInt i_rank[3],
84                         PetscInt degree, const PetscInt mesh_elem[3],
85                         PetscInt m_nodes[3]) {
86   for (int d=0; d<3; d++)
87     m_nodes[d] = degree*mesh_elem[d] + (i_rank[d] == p[d]-1);
88 }
89 static PetscInt GlobalStart(const PetscInt p[3], const PetscInt i_rank[3],
90                             PetscInt degree, const PetscInt mesh_elem[3]) {
91   PetscInt start = 0;
92   // Dumb brute-force is easier to read
93   for (PetscInt i=0; i<p[0]; i++) {
94     for (PetscInt j=0; j<p[1]; j++) {
95       for (PetscInt k=0; k<p[2]; k++) {
96         PetscInt m_nodes[3], ijk_rank[] = {i,j,k};
97         if (i == i_rank[0] && j == i_rank[1] && k == i_rank[2]) return start;
98         GlobalNodes(p, ijk_rank, degree, mesh_elem, m_nodes);
99         start += m_nodes[0] * m_nodes[1] * m_nodes[2];
100       }
101     }
102   }
103   return -1;
104 }
105 static int CreateRestriction(Ceed ceed, const CeedInt mesh_elem[3], CeedInt P,
106                              CeedInt num_comp, CeedElemRestriction *elem_restr) {
107   const PetscInt num_elem = mesh_elem[0]*mesh_elem[1]*mesh_elem[2];
108   PetscInt m_nodes[3], *idx, *idx_p;
109 
110   // Get indicies
111   for (int d=0; d<3; d++) m_nodes[d] = mesh_elem[d]*(P-1) + 1;
112   idx_p = idx = malloc(num_elem*P*P*P*sizeof idx[0]);
113   for (CeedInt i=0; i<mesh_elem[0]; i++)
114     for (CeedInt j=0; j<mesh_elem[1]; j++)
115       for (CeedInt k=0; k<mesh_elem[2]; k++,idx_p += P*P*P)
116         for (CeedInt ii=0; ii<P; ii++)
117           for (CeedInt jj=0; jj<P; jj++)
118             for (CeedInt kk=0; kk<P; kk++) {
119               if (0) { // This is the C-style (i,j,k) ordering that I prefer
120                 idx_p[(ii*P+jj)*P+kk] = num_comp*(((i*(P-1)+ii)*m_nodes[1]
121                                                    + (j*(P-1)+jj))*m_nodes[2]
122                                                   + (k*(P-1)+kk));
123               } else { // (k,j,i) ordering for consistency with MFEM example
124                 idx_p[ii+P*(jj+P*kk)] = num_comp*(((i*(P-1)+ii)*m_nodes[1]
125                                                    + (j*(P-1)+jj))*m_nodes[2]
126                                                   + (k*(P-1)+kk));
127               }
128             }
129 
130   // Setup CEED restriction
131   CeedElemRestrictionCreate(ceed, num_elem, P*P*P, num_comp, 1,
132                             m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp,
133                             CEED_MEM_HOST, CEED_OWN_POINTER, idx, elem_restr);
134 
135   PetscFunctionReturn(0);
136 }
137 
138 // Data for PETSc
139 typedef struct User_ *User;
140 struct User_ {
141   MPI_Comm comm;
142   VecScatter l_to_g;              // Scatter for all entries
143   VecScatter l_to_g_0;            // Skip Dirichlet values
144   VecScatter g_to_g_D;            // global-to-global; only Dirichlet values
145   Vec X_loc, Y_loc;
146   CeedVector x_ceed, y_ceed;
147   CeedOperator op;
148   CeedVector q_data;
149   Ceed ceed;
150 };
151 
152 // BP Options
153 typedef enum {
154   CEED_BP1 = 0, CEED_BP2 = 1, CEED_BP3 = 2,
155   CEED_BP4 = 3, CEED_BP5 = 4, CEED_BP6 = 5
156 } BPType;
157 static const char *const bp_types[] = {"bp1","bp2","bp3","bp4","bp5","bp6",
158                                        "BPType","CEED_BP",0
159                                       };
160 
161 // BP specific data
162 typedef struct {
163   CeedInt num_comp_u, q_data_size, q_extra;
164   CeedQFunctionUser setup_geo, setup_rhs, apply, error;
165   const char *setup_geo_loc, *setup_rhs_loc, *apply_loc, *error_loc;
166   CeedEvalMode in_mode, out_mode;
167   CeedQuadMode q_mode;
168 } BPData;
169 
170 BPData bp_options[6] = {
171   [CEED_BP1] = {
172     .num_comp_u = 1,
173     .q_data_size = 1,
174     .q_extra = 1,
175     .setup_geo = SetupMassGeo,
176     .setup_rhs = SetupMassRhs,
177     .apply = Mass,
178     .error = Error,
179     .setup_geo_loc = SetupMassGeo_loc,
180     .setup_rhs_loc = SetupMassRhs_loc,
181     .apply_loc = Mass_loc,
182     .error_loc = Error_loc,
183     .in_mode = CEED_EVAL_INTERP,
184     .out_mode = CEED_EVAL_INTERP,
185     .q_mode = CEED_GAUSS
186   },
187   [CEED_BP2] = {
188     .num_comp_u = 3,
189     .q_data_size = 1,
190     .q_extra = 1,
191     .setup_geo = SetupMassGeo,
192     .setup_rhs = SetupMassRhs3,
193     .apply = Mass3,
194     .error = Error3,
195     .setup_geo_loc = SetupMassGeo_loc,
196     .setup_rhs_loc = SetupMassRhs3_loc,
197     .apply_loc = Mass3_loc,
198     .error_loc = Error3_loc,
199     .in_mode = CEED_EVAL_INTERP,
200     .out_mode = CEED_EVAL_INTERP,
201     .q_mode = CEED_GAUSS
202   },
203   [CEED_BP3] = {
204     .num_comp_u = 1,
205     .q_data_size = 7,
206     .q_extra = 1,
207     .setup_geo = SetupDiffGeo,
208     .setup_rhs = SetupDiffRhs,
209     .apply = Diff,
210     .error = Error,
211     .setup_geo_loc = SetupDiffGeo_loc,
212     .setup_rhs_loc = SetupDiffRhs_loc,
213     .apply_loc = Diff_loc,
214     .error_loc = Error_loc,
215     .in_mode = CEED_EVAL_GRAD,
216     .out_mode = CEED_EVAL_GRAD,
217     .q_mode = CEED_GAUSS
218   },
219   [CEED_BP4] = {
220     .num_comp_u = 3,
221     .q_data_size = 7,
222     .q_extra = 1,
223     .setup_geo = SetupDiffGeo,
224     .setup_rhs = SetupDiffRhs3,
225     .apply = Diff3,
226     .error = Error3,
227     .setup_geo_loc = SetupDiffGeo_loc,
228     .setup_rhs_loc = SetupDiffRhs3_loc,
229     .apply_loc = Diff3_loc,
230     .error_loc = Error3_loc,
231     .in_mode = CEED_EVAL_GRAD,
232     .out_mode = CEED_EVAL_GRAD,
233     .q_mode = CEED_GAUSS
234   },
235   [CEED_BP5] = {
236     .num_comp_u = 1,
237     .q_data_size = 7,
238     .q_extra = 0,
239     .setup_geo = SetupDiffGeo,
240     .setup_rhs = SetupDiffRhs,
241     .apply = Diff,
242     .error = Error,
243     .setup_geo_loc = SetupDiffGeo_loc,
244     .setup_rhs_loc = SetupDiffRhs_loc,
245     .apply_loc = Diff_loc,
246     .error_loc = Error_loc,
247     .in_mode = CEED_EVAL_GRAD,
248     .out_mode = CEED_EVAL_GRAD,
249     .q_mode = CEED_GAUSS_LOBATTO
250   },
251   [CEED_BP6] = {
252     .num_comp_u = 3,
253     .q_data_size = 7,
254     .q_extra = 0,
255     .setup_geo = SetupDiffGeo,
256     .setup_rhs = SetupDiffRhs3,
257     .apply = Diff3,
258     .error = Error3,
259     .setup_geo_loc = SetupDiffGeo_loc,
260     .setup_rhs_loc = SetupDiffRhs3_loc,
261     .apply_loc = Diff3_loc,
262     .error_loc = Error3_loc,
263     .in_mode = CEED_EVAL_GRAD,
264     .out_mode = CEED_EVAL_GRAD,
265     .q_mode = CEED_GAUSS_LOBATTO
266   }
267 };
268 
269 // This function uses libCEED to compute the action of the mass matrix
270 static PetscErrorCode MatMult_Mass(Mat A, Vec X, Vec Y) {
271   PetscErrorCode ierr;
272   User user;
273   PetscScalar *x, *y;
274   PetscMemType x_mem_type, y_mem_type;
275 
276   PetscFunctionBeginUser;
277 
278   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
279 
280   // Global-to-local
281   ierr = VecScatterBegin(user->l_to_g, X, user->X_loc, INSERT_VALUES,
282                          SCATTER_REVERSE); CHKERRQ(ierr);
283   ierr = VecScatterEnd(user->l_to_g, X, user->X_loc, INSERT_VALUES,
284                        SCATTER_REVERSE); CHKERRQ(ierr);
285 
286   // Setup libCEED vectors
287   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
288                                    &x_mem_type); CHKERRQ(ierr);
289   ierr = VecGetArrayAndMemType(user->Y_loc, &y, &y_mem_type); CHKERRQ(ierr);
290   CeedVectorSetArray(user->x_ceed, MemTypeP2C(x_mem_type), CEED_USE_POINTER, x);
291   CeedVectorSetArray(user->y_ceed, MemTypeP2C(y_mem_type), CEED_USE_POINTER, y);
292 
293   // Apply libCEED operator
294   CeedOperatorApply(user->op, user->x_ceed, user->y_ceed,
295                     CEED_REQUEST_IMMEDIATE);
296 
297   // Restore PETSc vectors
298   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(x_mem_type), NULL);
299   CeedVectorTakeArray(user->y_ceed, MemTypeP2C(y_mem_type), NULL);
300   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
301   CHKERRQ(ierr);
302   ierr = VecRestoreArrayAndMemType(user->Y_loc, &y); CHKERRQ(ierr);
303 
304   // Local-to-global
305   if (Y) {
306     ierr = VecZeroEntries(Y); CHKERRQ(ierr);
307     ierr = VecScatterBegin(user->l_to_g, user->Y_loc, Y, ADD_VALUES,
308                            SCATTER_FORWARD); CHKERRQ(ierr);
309     ierr = VecScatterEnd(user->l_to_g, user->Y_loc, Y, ADD_VALUES,
310                          SCATTER_FORWARD); CHKERRQ(ierr);
311   }
312   PetscFunctionReturn(0);
313 }
314 
315 // This function uses libCEED to compute the action of the Laplacian with
316 // Dirichlet boundary conditions
317 static PetscErrorCode MatMult_Diff(Mat A, Vec X, Vec Y) {
318   PetscErrorCode ierr;
319   User user;
320   PetscScalar *x, *y;
321   PetscMemType x_mem_type, y_mem_type;
322 
323   PetscFunctionBeginUser;
324 
325   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
326 
327   // Global-to-local
328   ierr = VecScatterBegin(user->l_to_g_0, X, user->X_loc, INSERT_VALUES,
329                          SCATTER_REVERSE); CHKERRQ(ierr);
330   ierr = VecScatterEnd(user->l_to_g_0, X, user->X_loc, INSERT_VALUES,
331                        SCATTER_REVERSE);
332   CHKERRQ(ierr);
333 
334   // Setup libCEED vectors
335   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
336                                    &x_mem_type); CHKERRQ(ierr);
337   ierr = VecGetArrayAndMemType(user->Y_loc, &y, &y_mem_type); CHKERRQ(ierr);
338   CeedVectorSetArray(user->x_ceed, MemTypeP2C(x_mem_type), CEED_USE_POINTER, x);
339   CeedVectorSetArray(user->y_ceed, MemTypeP2C(y_mem_type), CEED_USE_POINTER, y);
340 
341   // Apply libCEED operator
342   CeedOperatorApply(user->op, user->x_ceed, user->y_ceed,
343                     CEED_REQUEST_IMMEDIATE);
344 
345   // Restore PETSc vectors
346   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(x_mem_type), NULL);
347   CeedVectorTakeArray(user->y_ceed, MemTypeP2C(y_mem_type), NULL);
348   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
349   CHKERRQ(ierr);
350   ierr = VecRestoreArrayAndMemType(user->Y_loc, &y); CHKERRQ(ierr);
351 
352   // Local-to-global
353   ierr = VecZeroEntries(Y); CHKERRQ(ierr);
354   ierr = VecScatterBegin(user->g_to_g_D, X, Y, INSERT_VALUES, SCATTER_FORWARD);
355   CHKERRQ(ierr);
356   ierr = VecScatterEnd(user->g_to_g_D, X, Y, INSERT_VALUES, SCATTER_FORWARD);
357   CHKERRQ(ierr);
358   ierr = VecScatterBegin(user->l_to_g_0, user->Y_loc, Y, ADD_VALUES,
359                          SCATTER_FORWARD); CHKERRQ(ierr);
360   ierr = VecScatterEnd(user->l_to_g_0, user->Y_loc, Y, ADD_VALUES,
361                        SCATTER_FORWARD);
362   CHKERRQ(ierr);
363 
364   PetscFunctionReturn(0);
365 }
366 
367 // This function calculates the error in the final solution
368 static PetscErrorCode ComputeErrorMax(User user, CeedOperator op_error, Vec X,
369                                       CeedVector target, PetscReal *max_error) {
370   PetscErrorCode ierr;
371   PetscScalar *x;
372   PetscMemType mem_type;
373   CeedVector collocated_error;
374   CeedSize length;
375 
376   PetscFunctionBeginUser;
377 
378   CeedVectorGetLength(target, &length);
379   CeedVectorCreate(user->ceed, length, &collocated_error);
380 
381   // Global-to-local
382   ierr = VecScatterBegin(user->l_to_g, X, user->X_loc, INSERT_VALUES,
383                          SCATTER_REVERSE); CHKERRQ(ierr);
384   ierr = VecScatterEnd(user->l_to_g, X, user->X_loc, INSERT_VALUES,
385                        SCATTER_REVERSE); CHKERRQ(ierr);
386 
387   // Setup libCEED vector
388   ierr = VecGetArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x,
389                                    &mem_type); CHKERRQ(ierr);
390   CeedVectorSetArray(user->x_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, x);
391 
392   // Apply libCEED operator
393   CeedOperatorApply(op_error, user->x_ceed, collocated_error,
394                     CEED_REQUEST_IMMEDIATE);
395 
396   // Restore PETSc vector
397   CeedVectorTakeArray(user->x_ceed, MemTypeP2C(mem_type), NULL);
398   ierr = VecRestoreArrayReadAndMemType(user->X_loc, (const PetscScalar **)&x);
399   CHKERRQ(ierr);
400 
401   // Reduce max error
402   *max_error = 0;
403   const CeedScalar *e;
404   CeedVectorGetArrayRead(collocated_error, CEED_MEM_HOST, &e);
405   for (CeedInt i=0; i<length; i++) {
406     *max_error = PetscMax(*max_error, PetscAbsScalar(e[i]));
407   }
408   CeedVectorRestoreArrayRead(collocated_error, &e);
409   ierr = MPI_Allreduce(MPI_IN_PLACE, max_error, 1, MPIU_REAL, MPIU_MAX,
410                        user->comm); CHKERRQ(ierr);
411 
412   // Cleanup
413   CeedVectorDestroy(&collocated_error);
414 
415   PetscFunctionReturn(0);
416 }
417 
418 int main(int argc, char **argv) {
419   PetscInt ierr;
420   MPI_Comm comm;
421   char ceed_resource[PETSC_MAX_PATH_LEN] = "/cpu/self";
422   double my_rt_start, my_rt, rt_min, rt_max;
423   PetscInt degree, q_extra, local_nodes, local_elem, mesh_elem[3], m_nodes[3],
424            p[3],
425            i_rank[3], l_nodes[3], l_size, num_comp_u = 1, ksp_max_it_clip[2];
426   PetscScalar *r;
427   PetscBool test_mode, benchmark_mode, write_solution;
428   PetscMPIInt size, rank;
429   PetscLogStage solve_stage;
430   Vec X, X_loc, rhs, rhs_loc;
431   Mat mat;
432   KSP ksp;
433   VecScatter l_to_g, l_to_g_0, g_to_g_D;
434   PetscMemType mem_type;
435   User user;
436   Ceed ceed;
437   CeedBasis basis_x, basis_u;
438   CeedElemRestriction elem_restr_x, elem_restr_u, elem_restr_u_i, elem_restr_qd_i;
439   CeedQFunction qf_setup_geo, qf_setup_rhs, qf_apply, qf_error;
440   CeedOperator op_setup_geo, op_setup_rhs, op_apply, op_error;
441   CeedVector x_coord, q_data, rhs_ceed, target;
442   CeedInt P, Q;
443   const CeedInt dim = 3, num_comp_x = 3;
444   BPType bp_choice;
445 
446   ierr = PetscInitialize(&argc, &argv, NULL, help);
447   if (ierr) return ierr;
448   comm = PETSC_COMM_WORLD;
449 
450   // Read command line options
451   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
452   bp_choice = CEED_BP1;
453   ierr = PetscOptionsEnum("-problem",
454                           "CEED benchmark problem to solve", NULL,
455                           bp_types, (PetscEnum)bp_choice, (PetscEnum *)&bp_choice,
456                           NULL); CHKERRQ(ierr);
457   num_comp_u = bp_options[bp_choice].num_comp_u;
458   test_mode = PETSC_FALSE;
459   ierr = PetscOptionsBool("-test",
460                           "Testing mode (do not print unless error is large)",
461                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
462   benchmark_mode = PETSC_FALSE;
463   ierr = PetscOptionsBool("-benchmark",
464                           "Benchmarking mode (prints benchmark statistics)",
465                           NULL, benchmark_mode, &benchmark_mode, NULL);
466   CHKERRQ(ierr);
467   write_solution = PETSC_FALSE;
468   ierr = PetscOptionsBool("-write_solution",
469                           "Write solution for visualization",
470                           NULL, write_solution, &write_solution, NULL);
471   CHKERRQ(ierr);
472   degree = test_mode ? 3 : 1;
473   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
474                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
475   q_extra = bp_options[bp_choice].q_extra;
476   ierr = PetscOptionsInt("-q_extra", "Number of extra quadrature points",
477                          NULL, q_extra, &q_extra, NULL); CHKERRQ(ierr);
478   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
479                             NULL, ceed_resource, ceed_resource,
480                             sizeof(ceed_resource), NULL); CHKERRQ(ierr);
481   local_nodes = 1000;
482   ierr = PetscOptionsInt("-local",
483                          "Target number of locally owned nodes per process",
484                          NULL, local_nodes, &local_nodes, NULL); CHKERRQ(ierr);
485   PetscInt two = 2;
486   ksp_max_it_clip[0] = 5;
487   ksp_max_it_clip[1] = 20;
488   ierr = PetscOptionsIntArray("-ksp_max_it_clip",
489                               "Min and max number of iterations to use during benchmarking",
490                               NULL, ksp_max_it_clip, &two, NULL);
491   CHKERRQ(ierr);
492   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
493   P = degree + 1;
494   Q = P + q_extra;
495 
496   // Set up libCEED
497   CeedInit(ceed_resource, &ceed);
498   CeedMemType mem_type_backend;
499   CeedGetPreferredMemType(ceed, &mem_type_backend);
500 
501   VecType default_vec_type = NULL, vec_type;
502   switch (mem_type_backend) {
503   case CEED_MEM_HOST: default_vec_type = VECSTANDARD; break;
504   case CEED_MEM_DEVICE: {
505     const char *resolved;
506     CeedGetResource(ceed, &resolved);
507     if (strstr(resolved, "/gpu/cuda")) default_vec_type = VECCUDA;
508     else if (strstr(resolved, "/gpu/hip/occa"))
509       default_vec_type = VECSTANDARD; // https://github.com/CEED/libCEED/issues/678
510     else if (strstr(resolved, "/gpu/hip")) default_vec_type = VECHIP;
511     else default_vec_type = VECSTANDARD;
512   }
513   }
514 
515   // Determine size of process grid
516   ierr = MPI_Comm_size(comm, &size); CHKERRQ(ierr);
517   Split3(size, p, false);
518 
519   // Find a nicely composite number of elements no less than local_nodes
520   for (local_elem = PetscMax(1, local_nodes / (degree*degree*degree)); ;
521        local_elem++) {
522     Split3(local_elem, mesh_elem, true);
523     if (Max3(mesh_elem) / Min3(mesh_elem) <= 2) break;
524   }
525 
526   // Find my location in the process grid
527   ierr = MPI_Comm_rank(comm, &rank); CHKERRQ(ierr);
528   for (int d=0, rank_left=rank; d<dim; d++) {
529     const int pstride[3] = {p[1] *p[2], p[2], 1};
530     i_rank[d] = rank_left / pstride[d];
531     rank_left -= i_rank[d] * pstride[d];
532   }
533 
534   GlobalNodes(p, i_rank, degree, mesh_elem, m_nodes);
535 
536   // Setup global vector
537   ierr = VecCreate(comm, &X); CHKERRQ(ierr);
538   ierr = VecSetType(X, default_vec_type); CHKERRQ(ierr);
539   ierr = VecSetSizes(X, m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
540                      PETSC_DECIDE);
541   CHKERRQ(ierr);
542   ierr = VecSetFromOptions(X); CHKERRQ(ierr);
543   ierr = VecSetUp(X); CHKERRQ(ierr);
544 
545   // Set up libCEED
546   CeedInit(ceed_resource, &ceed);
547 
548   // Print summary
549   CeedInt gsize;
550   ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
551   if (!test_mode) {
552     const char *used_resource;
553     CeedGetResource(ceed, &used_resource);
554 
555     ierr = VecGetType(X, &vec_type); CHKERRQ(ierr);
556 
557     ierr = PetscPrintf(comm,
558                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc --\n"
559                        "  PETSc:\n"
560                        "    PETSc Vec Type                     : %s\n"
561                        "  libCEED:\n"
562                        "    libCEED Backend                    : %s\n"
563                        "    libCEED Backend MemType            : %s\n"
564                        "  Mesh:\n"
565                        "    Number of 1D Basis Nodes (P)       : %d\n"
566                        "    Number of 1D Quadrature Points (Q) : %d\n"
567                        "    Global nodes                       : %D\n"
568                        "    Process Decomposition              : %D %D %D\n"
569                        "    Local Elements                     : %D = %D %D %D\n"
570                        "    Owned nodes                        : %D = %D %D %D\n"
571                        "    DoF per node                       : %D\n",
572                        bp_choice+1, vec_type, used_resource,
573                        CeedMemTypes[mem_type_backend],
574                        P, Q,  gsize/num_comp_u, p[0], p[1], p[2], local_elem,
575                        mesh_elem[0], mesh_elem[1], mesh_elem[2],
576                        m_nodes[0]*m_nodes[1]*m_nodes[2], m_nodes[0], m_nodes[1],
577                        m_nodes[2], num_comp_u); CHKERRQ(ierr);
578   }
579 
580   {
581     l_size = 1;
582     for (int d=0; d<dim; d++) {
583       l_nodes[d] = mesh_elem[d]*degree + 1;
584       l_size *= l_nodes[d];
585     }
586     ierr = VecCreate(PETSC_COMM_SELF, &X_loc); CHKERRQ(ierr);
587     ierr = VecSetType(X_loc, default_vec_type); CHKERRQ(ierr);
588     ierr = VecSetSizes(X_loc, l_size*num_comp_u, PETSC_DECIDE); CHKERRQ(ierr);
589     ierr = VecSetFromOptions(X_loc); CHKERRQ(ierr);
590     ierr = VecSetUp(X_loc); CHKERRQ(ierr);
591 
592     // Create local-to-global scatter
593     PetscInt *l_to_g_ind, *l_to_g_ind_0, *loc_ind, l_0_count;
594     IS l_to_g_is, l_to_g_is_0, loc_is;
595     PetscInt g_start[2][2][2], g_m_nodes[2][2][2][dim];
596 
597     for (int i=0; i<2; i++) {
598       for (int j=0; j<2; j++) {
599         for (int k=0; k<2; k++) {
600           PetscInt ijk_rank[3] = {i_rank[0]+i, i_rank[1]+j, i_rank[2]+k};
601           g_start[i][j][k] = GlobalStart(p, ijk_rank, degree, mesh_elem);
602           GlobalNodes(p, ijk_rank, degree, mesh_elem, g_m_nodes[i][j][k]);
603         }
604       }
605     }
606 
607     ierr = PetscMalloc1(l_size, &l_to_g_ind); CHKERRQ(ierr);
608     ierr = PetscMalloc1(l_size, &l_to_g_ind_0); CHKERRQ(ierr);
609     ierr = PetscMalloc1(l_size, &loc_ind); CHKERRQ(ierr);
610     l_0_count = 0;
611     for (PetscInt i=0,ir,ii; ir=i>=m_nodes[0], ii=i-ir*m_nodes[0], i<l_nodes[0];
612          i++)
613       for (PetscInt j=0,jr,jj; jr=j>=m_nodes[1], jj=j-jr*m_nodes[1], j<l_nodes[1];
614            j++)
615         for (PetscInt k=0,kr,kk; kr=k>=m_nodes[2], kk=k-kr*m_nodes[2], k<l_nodes[2];
616              k++) {
617           PetscInt here = (i*l_nodes[1]+j)*l_nodes[2]+k;
618           l_to_g_ind[here] =
619             g_start[ir][jr][kr] + (ii*g_m_nodes[ir][jr][kr][1]+jj)*g_m_nodes[ir][jr][kr][2]
620             +kk;
621           if ((i_rank[0] == 0 && i == 0)
622               || (i_rank[1] == 0 && j == 0)
623               || (i_rank[2] == 0 && k == 0)
624               || (i_rank[0]+1 == p[0] && i+1 == l_nodes[0])
625               || (i_rank[1]+1 == p[1] && j+1 == l_nodes[1])
626               || (i_rank[2]+1 == p[2] && k+1 == l_nodes[2]))
627             continue;
628           l_to_g_ind_0[l_0_count] = l_to_g_ind[here];
629           loc_ind[l_0_count++] = here;
630         }
631     ierr = ISCreateBlock(comm, num_comp_u, l_size, l_to_g_ind, PETSC_OWN_POINTER,
632                          &l_to_g_is); CHKERRQ(ierr);
633     ierr = VecScatterCreate(X_loc, NULL, X, l_to_g_is, &l_to_g); CHKERRQ(ierr);
634     CHKERRQ(ierr);
635     ierr = ISCreateBlock(comm, num_comp_u, l_0_count, l_to_g_ind_0,
636                          PETSC_OWN_POINTER,
637                          &l_to_g_is_0); CHKERRQ(ierr);
638     ierr = ISCreateBlock(comm, num_comp_u, l_0_count, loc_ind, PETSC_OWN_POINTER,
639                          &loc_is); CHKERRQ(ierr);
640     ierr = VecScatterCreate(X_loc, loc_is, X, l_to_g_is_0, &l_to_g_0);
641     CHKERRQ(ierr);
642     {
643       // Create global-to-global scatter for Dirichlet values (everything not in
644       // l_to_g_is_0, which is the range of l_to_g_0)
645       PetscInt x_start, x_end, *ind_D, count_D = 0;
646       IS is_D;
647       const PetscScalar *x;
648       ierr = VecZeroEntries(X_loc); CHKERRQ(ierr);
649       ierr = VecSet(X, 1.0); CHKERRQ(ierr);
650       ierr = VecScatterBegin(l_to_g_0, X_loc, X, INSERT_VALUES, SCATTER_FORWARD);
651       CHKERRQ(ierr);
652       ierr = VecScatterEnd(l_to_g_0, X_loc, X, INSERT_VALUES, SCATTER_FORWARD);
653       CHKERRQ(ierr);
654       ierr = VecGetOwnershipRange(X, &x_start, &x_end); CHKERRQ(ierr);
655       ierr = PetscMalloc1(x_end-x_start, &ind_D); CHKERRQ(ierr);
656       ierr = VecGetArrayRead(X, &x); CHKERRQ(ierr);
657       for (PetscInt i=0; i<x_end-x_start; i++) {
658         if (x[i] == 1.) ind_D[count_D++] = x_start + i;
659       }
660       ierr = VecRestoreArrayRead(X, &x); CHKERRQ(ierr);
661       ierr = ISCreateGeneral(comm, count_D, ind_D, PETSC_COPY_VALUES, &is_D);
662       CHKERRQ(ierr);
663       ierr = PetscFree(ind_D); CHKERRQ(ierr);
664       ierr = VecScatterCreate(X, is_D, X, is_D, &g_to_g_D); CHKERRQ(ierr);
665       ierr = ISDestroy(&is_D); CHKERRQ(ierr);
666     }
667     ierr = ISDestroy(&l_to_g_is); CHKERRQ(ierr);
668     ierr = ISDestroy(&l_to_g_is_0); CHKERRQ(ierr);
669     ierr = ISDestroy(&loc_is); CHKERRQ(ierr);
670   }
671 
672   // CEED bases
673   CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_u, P, Q,
674                                   bp_options[bp_choice].q_mode, &basis_u);
675   CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, 2, Q,
676                                   bp_options[bp_choice].q_mode, &basis_x);
677 
678   // CEED restrictions
679   CreateRestriction(ceed, mesh_elem, P, num_comp_u, &elem_restr_u);
680   CreateRestriction(ceed, mesh_elem, 2, dim, &elem_restr_x);
681   CeedInt num_elem = mesh_elem[0]*mesh_elem[1]*mesh_elem[2];
682   CeedElemRestrictionCreateStrided(ceed, num_elem, Q*Q*Q, num_comp_u,
683                                    num_comp_u*num_elem*Q*Q*Q,
684                                    CEED_STRIDES_BACKEND, &elem_restr_u_i);
685   CeedElemRestrictionCreateStrided(ceed, num_elem, Q*Q*Q,
686                                    bp_options[bp_choice].q_data_size,
687                                    bp_options[bp_choice].q_data_size*num_elem*Q*Q*Q,
688                                    CEED_STRIDES_BACKEND, &elem_restr_qd_i);
689   {
690     CeedScalar *x_loc;
691     CeedInt shape[3] = {mesh_elem[0]+1, mesh_elem[1]+1, mesh_elem[2]+1}, len =
692                          shape[0]*shape[1]*shape[2];
693     x_loc = malloc(len*num_comp_x*sizeof x_loc[0]);
694     for (CeedInt i=0; i<shape[0]; i++) {
695       for (CeedInt j=0; j<shape[1]; j++) {
696         for (CeedInt k=0; k<shape[2]; k++) {
697           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 0] = 1.*(i_rank[0]*mesh_elem[0]+i) /
698               (p[0]*mesh_elem[0]);
699           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 1] = 1.*(i_rank[1]*mesh_elem[1]+j) /
700               (p[1]*mesh_elem[1]);
701           x_loc[dim*((i*shape[1]+j)*shape[2]+k) + 2] = 1.*(i_rank[2]*mesh_elem[2]+k) /
702               (p[2]*mesh_elem[2]);
703         }
704       }
705     }
706     CeedVectorCreate(ceed, len*num_comp_x, &x_coord);
707     CeedVectorSetArray(x_coord, CEED_MEM_HOST, CEED_OWN_POINTER, x_loc);
708   }
709 
710   // Create the QFunction that builds the operator quadrature data
711   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].setup_geo,
712                               bp_options[bp_choice].setup_geo_loc, &qf_setup_geo);
713   CeedQFunctionAddInput(qf_setup_geo, "x", num_comp_x, CEED_EVAL_INTERP);
714   CeedQFunctionAddInput(qf_setup_geo, "dx", num_comp_x*dim, CEED_EVAL_GRAD);
715   CeedQFunctionAddInput(qf_setup_geo, "weight", 1, CEED_EVAL_WEIGHT);
716   CeedQFunctionAddOutput(qf_setup_geo, "q_data",
717                          bp_options[bp_choice].q_data_size,
718                          CEED_EVAL_NONE);
719 
720   // Create the QFunction that sets up the RHS and true solution
721   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].setup_rhs,
722                               bp_options[bp_choice].setup_rhs_loc, &qf_setup_rhs);
723   CeedQFunctionAddInput(qf_setup_rhs, "x", num_comp_x, CEED_EVAL_INTERP);
724   CeedQFunctionAddInput(qf_setup_rhs, "q_data", bp_options[bp_choice].q_data_size,
725                         CEED_EVAL_NONE);
726   CeedQFunctionAddOutput(qf_setup_rhs, "true_soln", num_comp_u, CEED_EVAL_NONE);
727   CeedQFunctionAddOutput(qf_setup_rhs, "rhs", num_comp_u, CEED_EVAL_INTERP);
728 
729   // Set up PDE operator
730   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].apply,
731                               bp_options[bp_choice].apply_loc, &qf_apply);
732   // Add inputs and outputs
733   CeedInt in_scale = bp_options[bp_choice].in_mode==CEED_EVAL_GRAD ? 3 : 1;
734   CeedInt out_scale = bp_options[bp_choice].out_mode==CEED_EVAL_GRAD ? 3 : 1;
735   CeedQFunctionAddInput(qf_apply, "u", num_comp_u*in_scale,
736                         bp_options[bp_choice].in_mode);
737   CeedQFunctionAddInput(qf_apply, "q_data", bp_options[bp_choice].q_data_size,
738                         CEED_EVAL_NONE);
739   CeedQFunctionAddOutput(qf_apply, "v", num_comp_u*out_scale,
740                          bp_options[bp_choice].out_mode);
741 
742   // Create the error qfunction
743   CeedQFunctionCreateInterior(ceed, 1, bp_options[bp_choice].error,
744                               bp_options[bp_choice].error_loc, &qf_error);
745   CeedQFunctionAddInput(qf_error, "u", num_comp_u, CEED_EVAL_INTERP);
746   CeedQFunctionAddInput(qf_error, "true_soln", num_comp_u, CEED_EVAL_NONE);
747   CeedQFunctionAddOutput(qf_error, "error", num_comp_u, CEED_EVAL_NONE);
748 
749   // Create the persistent vectors that will be needed in setup
750   CeedInt num_qpts;
751   CeedBasisGetNumQuadraturePoints(basis_u, &num_qpts);
752   CeedVectorCreate(ceed, bp_options[bp_choice].q_data_size*num_elem*num_qpts,
753                    &q_data);
754   CeedVectorCreate(ceed, num_elem*num_qpts*num_comp_u, &target);
755   CeedVectorCreate(ceed, l_size*num_comp_u, &rhs_ceed);
756 
757   // Create the operator that builds the quadrature data for the ceed operator
758   CeedOperatorCreate(ceed, qf_setup_geo, CEED_QFUNCTION_NONE,
759                      CEED_QFUNCTION_NONE, &op_setup_geo);
760   CeedOperatorSetField(op_setup_geo, "x", elem_restr_x, basis_x,
761                        CEED_VECTOR_ACTIVE);
762   CeedOperatorSetField(op_setup_geo, "dx", elem_restr_x, basis_x,
763                        CEED_VECTOR_ACTIVE);
764   CeedOperatorSetField(op_setup_geo, "weight", CEED_ELEMRESTRICTION_NONE, basis_x,
765                        CEED_VECTOR_NONE);
766   CeedOperatorSetField(op_setup_geo, "q_data", elem_restr_qd_i,
767                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
768 
769   // Create the operator that builds the RHS and true solution
770   CeedOperatorCreate(ceed, qf_setup_rhs, CEED_QFUNCTION_NONE,
771                      CEED_QFUNCTION_NONE, &op_setup_rhs);
772   CeedOperatorSetField(op_setup_rhs, "x", elem_restr_x, basis_x,
773                        CEED_VECTOR_ACTIVE);
774   CeedOperatorSetField(op_setup_rhs, "q_data", elem_restr_qd_i,
775                        CEED_BASIS_COLLOCATED,
776                        q_data);
777   CeedOperatorSetField(op_setup_rhs, "true_soln", elem_restr_u_i,
778                        CEED_BASIS_COLLOCATED, target);
779   CeedOperatorSetField(op_setup_rhs, "rhs", elem_restr_u, basis_u,
780                        CEED_VECTOR_ACTIVE);
781 
782   // Create the mass or diff operator
783   CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
784                      &op_apply);
785   CeedOperatorSetField(op_apply, "u", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
786   CeedOperatorSetField(op_apply, "q_data", elem_restr_qd_i, CEED_BASIS_COLLOCATED,
787                        q_data);
788   CeedOperatorSetField(op_apply, "v", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
789 
790   // Create the error operator
791   CeedOperatorCreate(ceed, qf_error, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
792                      &op_error);
793   CeedOperatorSetField(op_error, "u", elem_restr_u, basis_u, CEED_VECTOR_ACTIVE);
794   CeedOperatorSetField(op_error, "true_soln", elem_restr_u_i,
795                        CEED_BASIS_COLLOCATED, target);
796   CeedOperatorSetField(op_error, "error", elem_restr_u_i, CEED_BASIS_COLLOCATED,
797                        CEED_VECTOR_ACTIVE);
798 
799   // Set up Mat
800   ierr = PetscMalloc1(1, &user); CHKERRQ(ierr);
801   user->comm = comm;
802   user->l_to_g = l_to_g;
803   if (bp_choice != CEED_BP1 && bp_choice != CEED_BP2) {
804     user->l_to_g_0 = l_to_g_0;
805     user->g_to_g_D = g_to_g_D;
806   }
807   user->X_loc = X_loc;
808   ierr = VecDuplicate(X_loc, &user->Y_loc); CHKERRQ(ierr);
809   CeedVectorCreate(ceed, l_size*num_comp_u, &user->x_ceed);
810   CeedVectorCreate(ceed, l_size*num_comp_u, &user->y_ceed);
811   user->op = op_apply;
812   user->q_data = q_data;
813   user->ceed = ceed;
814 
815   ierr = MatCreateShell(comm, m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
816                         m_nodes[0]*m_nodes[1]*m_nodes[2]*num_comp_u,
817                         PETSC_DECIDE, PETSC_DECIDE, user, &mat); CHKERRQ(ierr);
818   if (bp_choice == CEED_BP1 || bp_choice == CEED_BP2) {
819     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Mass);
820     CHKERRQ(ierr);
821   } else {
822     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Diff);
823     CHKERRQ(ierr);
824   }
825   ierr = VecGetType(X, &vec_type); CHKERRQ(ierr);
826   ierr = MatShellSetVecType(mat, vec_type); CHKERRQ(ierr);
827 
828   // Get RHS vector
829   ierr = VecDuplicate(X, &rhs); CHKERRQ(ierr);
830   ierr = VecDuplicate(X_loc, &rhs_loc); CHKERRQ(ierr);
831   ierr = VecZeroEntries(rhs_loc); CHKERRQ(ierr);
832   ierr = VecGetArrayAndMemType(rhs_loc, &r, &mem_type); CHKERRQ(ierr);
833   CeedVectorSetArray(rhs_ceed, MemTypeP2C(mem_type), CEED_USE_POINTER, r);
834 
835   // Setup q_data, rhs, and target
836   CeedOperatorApply(op_setup_geo, x_coord, q_data, CEED_REQUEST_IMMEDIATE);
837   CeedOperatorApply(op_setup_rhs, x_coord, rhs_ceed, CEED_REQUEST_IMMEDIATE);
838   CeedVectorDestroy(&x_coord);
839 
840   // Gather RHS
841   ierr = CeedVectorTakeArray(rhs_ceed, MemTypeP2C(mem_type), NULL); CHKERRQ(ierr);
842   ierr = VecRestoreArrayAndMemType(rhs_loc, &r); CHKERRQ(ierr);
843   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
844   ierr = VecScatterBegin(l_to_g, rhs_loc, rhs, ADD_VALUES, SCATTER_FORWARD);
845   CHKERRQ(ierr);
846   ierr = VecScatterEnd(l_to_g, rhs_loc, rhs, ADD_VALUES, SCATTER_FORWARD);
847   CHKERRQ(ierr);
848   CeedVectorDestroy(&rhs_ceed);
849 
850   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
851   {
852     PC pc;
853     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
854     if (bp_choice == CEED_BP1 || bp_choice == CEED_BP2) {
855       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
856       ierr = PCJacobiSetType(pc, PC_JACOBI_ROWSUM); CHKERRQ(ierr);
857     } else {
858       ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
859     }
860     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
861     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
862     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
863                             PETSC_DEFAULT); CHKERRQ(ierr);
864   }
865   ierr = KSPSetOperators(ksp, mat, mat); CHKERRQ(ierr);
866   // First run's performance log is not considered for benchmarking purposes
867   ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
868   CHKERRQ(ierr);
869   my_rt_start = MPI_Wtime();
870   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
871   my_rt = MPI_Wtime() - my_rt_start;
872   ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
873   CHKERRQ(ierr);
874   // Set maxits based on first iteration timing
875   if (my_rt > 0.02) {
876     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
877                             ksp_max_it_clip[0]); CHKERRQ(ierr);
878   } else {
879     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
880                             ksp_max_it_clip[1]); CHKERRQ(ierr);
881   }
882   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
883 
884   // Timed solve
885   ierr = VecZeroEntries(X); CHKERRQ(ierr);
886   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
887 
888   // -- Performance logging
889   ierr = PetscLogStageRegister("Solve Stage", &solve_stage); CHKERRQ(ierr);
890   ierr = PetscLogStagePush(solve_stage); CHKERRQ(ierr);
891 
892   // -- Solve
893   my_rt_start = MPI_Wtime();
894   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
895   my_rt = MPI_Wtime() - my_rt_start;
896 
897   // -- Performance logging
898   ierr = PetscLogStagePop();
899 
900   // Output results
901   {
902     KSPType ksp_type;
903     KSPConvergedReason reason;
904     PetscReal rnorm;
905     PetscInt its;
906     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
907     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
908     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
909     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
910     if (!test_mode || reason < 0 || rnorm > 1e-8) {
911       ierr = PetscPrintf(comm,
912                          "  KSP:\n"
913                          "    KSP Type                           : %s\n"
914                          "    KSP Convergence                    : %s\n"
915                          "    Total KSP Iterations               : %D\n"
916                          "    Final rnorm                        : %e\n",
917                          ksp_type, KSPConvergedReasons[reason], its,
918                          (double)rnorm); CHKERRQ(ierr);
919     }
920     if (!test_mode) {
921       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
922     }
923     {
924       PetscReal max_error;
925       ierr = ComputeErrorMax(user, op_error, X, target, &max_error);
926       CHKERRQ(ierr);
927       PetscReal tol = 5e-2;
928       if (!test_mode || max_error > tol) {
929         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
930         CHKERRQ(ierr);
931         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
932         CHKERRQ(ierr);
933         ierr = PetscPrintf(comm,
934                            "    Pointwise Error (max)              : %e\n"
935                            "    CG Solve Time                      : %g (%g) sec\n",
936                            (double)max_error, rt_max, rt_min); CHKERRQ(ierr);
937       }
938     }
939     if (!test_mode) {
940       ierr = PetscPrintf(comm,
941                          "    DoFs/Sec in CG                     : %g (%g) million\n",
942                          1e-6*gsize*its/rt_max,
943                          1e-6*gsize*its/rt_min); CHKERRQ(ierr);
944     }
945   }
946 
947   if (write_solution) {
948     PetscViewer vtk_viewer_soln;
949 
950     ierr = PetscViewerCreate(comm, &vtk_viewer_soln); CHKERRQ(ierr);
951     ierr = PetscViewerSetType(vtk_viewer_soln, PETSCVIEWERVTK); CHKERRQ(ierr);
952     ierr = PetscViewerFileSetName(vtk_viewer_soln, "solution.vtu"); CHKERRQ(ierr);
953     ierr = VecView(X, vtk_viewer_soln); CHKERRQ(ierr);
954     ierr = PetscViewerDestroy(&vtk_viewer_soln); CHKERRQ(ierr);
955   }
956 
957   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
958   ierr = VecDestroy(&rhs_loc); CHKERRQ(ierr);
959   ierr = VecDestroy(&X); CHKERRQ(ierr);
960   ierr = VecDestroy(&user->X_loc); CHKERRQ(ierr);
961   ierr = VecDestroy(&user->Y_loc); CHKERRQ(ierr);
962   ierr = VecScatterDestroy(&l_to_g); CHKERRQ(ierr);
963   ierr = VecScatterDestroy(&l_to_g_0); CHKERRQ(ierr);
964   ierr = VecScatterDestroy(&g_to_g_D); CHKERRQ(ierr);
965   ierr = MatDestroy(&mat); CHKERRQ(ierr);
966   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
967 
968   CeedVectorDestroy(&user->x_ceed);
969   CeedVectorDestroy(&user->y_ceed);
970   CeedVectorDestroy(&user->q_data);
971   CeedVectorDestroy(&target);
972   CeedOperatorDestroy(&op_setup_geo);
973   CeedOperatorDestroy(&op_setup_rhs);
974   CeedOperatorDestroy(&op_apply);
975   CeedOperatorDestroy(&op_error);
976   CeedElemRestrictionDestroy(&elem_restr_u);
977   CeedElemRestrictionDestroy(&elem_restr_x);
978   CeedElemRestrictionDestroy(&elem_restr_u_i);
979   CeedElemRestrictionDestroy(&elem_restr_qd_i);
980   CeedQFunctionDestroy(&qf_setup_geo);
981   CeedQFunctionDestroy(&qf_setup_rhs);
982   CeedQFunctionDestroy(&qf_apply);
983   CeedQFunctionDestroy(&qf_error);
984   CeedBasisDestroy(&basis_u);
985   CeedBasisDestroy(&basis_x);
986   CeedDestroy(&ceed);
987   ierr = PetscFree(user); CHKERRQ(ierr);
988   return PetscFinalize();
989 }
990