xref: /libCEED/examples/petsc/bpsraw.c (revision 868092e36f1622fa90aa3e8805129ee32196fd24)
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 -ceed /cpu/self
33 //     ./bpsraw -problem bp3 -ceed /gpu/occa
34 //     ./bpsraw -problem bp4 -ceed /cpu/occa
35 //     ./bpsraw -problem bp5 -ceed /omp/occa
36 //     ./bpsraw -problem bp6 -ceed /ocl/occa
37 //
38 //TESTARGS -ceed {ceed_resource} -test -problem bp2 -degree 5 -qextra 1 -ksp_max_it_clip 20,20
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 <stdbool.h>
46 #include <string.h>
47 #include <petscksp.h>
48 #include <ceed.h>
49 #include "qfunctions/bps/common.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 
55 #include <petscsys.h>
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 void Split3(PetscInt size, PetscInt m[3], bool reverse) {
65   for (PetscInt d=0,sizeleft=size; d<3; d++) {
66     PetscInt try = (PetscInt)PetscCeilReal(PetscPowReal(sizeleft, 1./(3 - d)));
67     while (try * (sizeleft / try) != sizeleft) try++;
68     m[reverse ? 2-d : d] = try;
69     sizeleft /= try;
70   }
71 }
72 
73 static PetscInt Max3(const PetscInt a[3]) {
74   return PetscMax(a[0], PetscMax(a[1], a[2]));
75 }
76 static PetscInt Min3(const PetscInt a[3]) {
77   return PetscMin(a[0], PetscMin(a[1], a[2]));
78 }
79 static void GlobalNodes(const PetscInt p[3], const PetscInt irank[3],
80                         PetscInt degree, const PetscInt melem[3],
81                         PetscInt mnodes[3]) {
82   for (int d=0; d<3; d++)
83     mnodes[d] = degree*melem[d] + (irank[d] == p[d]-1);
84 }
85 static PetscInt GlobalStart(const PetscInt p[3], const PetscInt irank[3],
86                             PetscInt degree, const PetscInt melem[3]) {
87   PetscInt start = 0;
88   // Dumb brute-force is easier to read
89   for (PetscInt i=0; i<p[0]; i++) {
90     for (PetscInt j=0; j<p[1]; j++) {
91       for (PetscInt k=0; k<p[2]; k++) {
92         PetscInt mnodes[3], ijkrank[] = {i,j,k};
93         if (i == irank[0] && j == irank[1] && k == irank[2]) return start;
94         GlobalNodes(p, ijkrank, degree, melem, mnodes);
95         start += mnodes[0] * mnodes[1] * mnodes[2];
96       }
97     }
98   }
99   return -1;
100 }
101 static int CreateRestriction(Ceed ceed, const CeedInt melem[3], CeedInt P,
102                              CeedInt ncomp, CeedElemRestriction *Erestrict) {
103   const PetscInt nelem = melem[0]*melem[1]*melem[2];
104   PetscInt mnodes[3], *idx, *idxp;
105 
106   // Get indicies
107   for (int d=0; d<3; d++) mnodes[d] = melem[d]*(P-1) + 1;
108   idxp = idx = malloc(nelem*P*P*P*sizeof idx[0]);
109   for (CeedInt i=0; i<melem[0]; i++)
110     for (CeedInt j=0; j<melem[1]; j++)
111       for (CeedInt k=0; k<melem[2]; k++,idxp += P*P*P)
112         for (CeedInt ii=0; ii<P; ii++)
113           for (CeedInt jj=0; jj<P; jj++)
114             for (CeedInt kk=0; kk<P; kk++) {
115               if (0) { // This is the C-style (i,j,k) ordering that I prefer
116                 idxp[(ii*P+jj)*P+kk] = ncomp*(((i*(P-1)+ii)*mnodes[1]
117                                                + (j*(P-1)+jj))*mnodes[2]
118                                               + (k*(P-1)+kk));
119               } else { // (k,j,i) ordering for consistency with MFEM example
120                 idxp[ii+P*(jj+P*kk)] = ncomp*(((i*(P-1)+ii)*mnodes[1]
121                                                + (j*(P-1)+jj))*mnodes[2]
122                                               + (k*(P-1)+kk));
123               }
124             }
125 
126   // Setup CEED restriction
127   CeedElemRestrictionCreate(ceed, nelem, P*P*P, ncomp, 1,
128                             mnodes[0]*mnodes[1]*mnodes[2]*ncomp,
129                             CEED_MEM_HOST, CEED_OWN_POINTER, idx, Erestrict);
130 
131   PetscFunctionReturn(0);
132 }
133 
134 // Data for PETSc
135 typedef struct User_ *User;
136 struct User_ {
137   MPI_Comm comm;
138   VecScatter ltog;              // Scatter for all entries
139   VecScatter ltog0;             // Skip Dirichlet values
140   VecScatter gtogD;             // global-to-global; only Dirichlet values
141   Vec Xloc, Yloc;
142   CeedVector xceed, yceed;
143   CeedOperator op;
144   CeedVector qdata;
145   Ceed ceed;
146   CeedMemType memtype;
147   int (*VecGetArray)(Vec, PetscScalar **);
148   int (*VecGetArrayRead)(Vec, const PetscScalar **);
149   int (*VecRestoreArray)(Vec, PetscScalar **);
150   int (*VecRestoreArrayRead)(Vec, const PetscScalar **);
151 };
152 
153 // MemType Options
154 static const char *const memTypes[] = {"host","device","memType",
155                                        "CEED_MEM_",0
156                                       };
157 
158 // BP Options
159 typedef enum {
160   CEED_BP1 = 0, CEED_BP2 = 1, CEED_BP3 = 2,
161   CEED_BP4 = 3, CEED_BP5 = 4, CEED_BP6 = 5
162 } bpType;
163 static const char *const bpTypes[] = {"bp1","bp2","bp3","bp4","bp5","bp6",
164                                       "bpType","CEED_BP",0
165                                      };
166 
167 // BP specific data
168 typedef struct {
169   CeedInt ncompu, qdatasize, qextra;
170   CeedQFunctionUser setupgeo, setuprhs, apply, error;
171   const char *setupgeofname, *setuprhsfname, *applyfname, *errorfname;
172   CeedEvalMode inmode, outmode;
173   CeedQuadMode qmode;
174 } bpData;
175 
176 bpData bpOptions[6] = {
177   [CEED_BP1] = {
178     .ncompu = 1,
179     .qdatasize = 1,
180     .qextra = 1,
181     .setupgeo = SetupMassGeo,
182     .setuprhs = SetupMassRhs,
183     .apply = Mass,
184     .error = Error,
185     .setupgeofname = SetupMassGeo_loc,
186     .setuprhsfname = SetupMassRhs_loc,
187     .applyfname = Mass_loc,
188     .errorfname = Error_loc,
189     .inmode = CEED_EVAL_INTERP,
190     .outmode = CEED_EVAL_INTERP,
191     .qmode = CEED_GAUSS
192   },
193   [CEED_BP2] = {
194     .ncompu = 3,
195     .qdatasize = 1,
196     .qextra = 1,
197     .setupgeo = SetupMassGeo,
198     .setuprhs = SetupMassRhs3,
199     .apply = Mass3,
200     .error = Error3,
201     .setupgeofname = SetupMassGeo_loc,
202     .setuprhsfname = SetupMassRhs3_loc,
203     .applyfname = Mass3_loc,
204     .errorfname = Error3_loc,
205     .inmode = CEED_EVAL_INTERP,
206     .outmode = CEED_EVAL_INTERP,
207     .qmode = CEED_GAUSS
208   },
209   [CEED_BP3] = {
210     .ncompu = 1,
211     .qdatasize = 6,
212     .qextra = 1,
213     .setupgeo = SetupDiffGeo,
214     .setuprhs = SetupDiffRhs,
215     .apply = Diff,
216     .error = Error,
217     .setupgeofname = SetupDiffGeo_loc,
218     .setuprhsfname = SetupDiffRhs_loc,
219     .applyfname = Diff_loc,
220     .errorfname = Error_loc,
221     .inmode = CEED_EVAL_GRAD,
222     .outmode = CEED_EVAL_GRAD,
223     .qmode = CEED_GAUSS
224   },
225   [CEED_BP4] = {
226     .ncompu = 3,
227     .qdatasize = 6,
228     .qextra = 1,
229     .setupgeo = SetupDiffGeo,
230     .setuprhs = SetupDiffRhs3,
231     .apply = Diff3,
232     .error = Error3,
233     .setupgeofname = SetupDiffGeo_loc,
234     .setuprhsfname = SetupDiffRhs3_loc,
235     .applyfname = Diff_loc,
236     .errorfname = Error3_loc,
237     .inmode = CEED_EVAL_GRAD,
238     .outmode = CEED_EVAL_GRAD,
239     .qmode = CEED_GAUSS
240   },
241   [CEED_BP5] = {
242     .ncompu = 1,
243     .qdatasize = 6,
244     .qextra = 0,
245     .setupgeo = SetupDiffGeo,
246     .setuprhs = SetupDiffRhs,
247     .apply = Diff,
248     .error = Error,
249     .setupgeofname = SetupDiffGeo_loc,
250     .setuprhsfname = SetupDiffRhs_loc,
251     .applyfname = Diff_loc,
252     .errorfname = Error_loc,
253     .inmode = CEED_EVAL_GRAD,
254     .outmode = CEED_EVAL_GRAD,
255     .qmode = CEED_GAUSS_LOBATTO
256   },
257   [CEED_BP6] = {
258     .ncompu = 3,
259     .qdatasize = 6,
260     .qextra = 0,
261     .setupgeo = SetupDiffGeo,
262     .setuprhs = SetupDiffRhs3,
263     .apply = Diff3,
264     .error = Error3,
265     .setupgeofname = SetupDiffGeo_loc,
266     .setuprhsfname = SetupDiffRhs3_loc,
267     .applyfname = Diff_loc,
268     .errorfname = Error3_loc,
269     .inmode = CEED_EVAL_GRAD,
270     .outmode = CEED_EVAL_GRAD,
271     .qmode = CEED_GAUSS_LOBATTO
272   }
273 };
274 
275 // This function uses libCEED to compute the action of the mass matrix
276 static PetscErrorCode MatMult_Mass(Mat A, Vec X, Vec Y) {
277   PetscErrorCode ierr;
278   User user;
279   PetscScalar *x, *y;
280 
281   PetscFunctionBeginUser;
282 
283   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
284 
285   // Global-to-local
286   ierr = VecScatterBegin(user->ltog, X, user->Xloc, INSERT_VALUES,
287                          SCATTER_REVERSE); CHKERRQ(ierr);
288   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES,
289                        SCATTER_REVERSE); CHKERRQ(ierr);
290 
291   // Setup libCEED vectors
292   ierr = user->VecGetArrayRead(user->Xloc, (const PetscScalar **)&x);
293   CHKERRQ(ierr);
294   ierr = user->VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
295   CeedVectorSetArray(user->xceed, user->memtype, CEED_USE_POINTER, x);
296   CeedVectorSetArray(user->yceed, user->memtype, CEED_USE_POINTER, y);
297 
298   // Apply libCEED operator
299   CeedOperatorApply(user->op, user->xceed, user->yceed,
300                     CEED_REQUEST_IMMEDIATE);
301   CeedVectorSyncArray(user->yceed, user->memtype);
302 
303   // Restore PETSc vectors
304   ierr = user->VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x);
305   CHKERRQ(ierr);
306   ierr = user->VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
307 
308   // Local-to-global
309   if (Y) {
310     ierr = VecZeroEntries(Y); CHKERRQ(ierr);
311     ierr = VecScatterBegin(user->ltog, user->Yloc, Y, ADD_VALUES,
312                            SCATTER_FORWARD); CHKERRQ(ierr);
313     ierr = VecScatterEnd(user->ltog, user->Yloc, Y, ADD_VALUES,
314                          SCATTER_FORWARD); CHKERRQ(ierr);
315   }
316   PetscFunctionReturn(0);
317 }
318 
319 // This function uses libCEED to compute the action of the Laplacian with
320 // Dirichlet boundary conditions
321 static PetscErrorCode MatMult_Diff(Mat A, Vec X, Vec Y) {
322   PetscErrorCode ierr;
323   User user;
324   PetscScalar *x, *y;
325 
326   PetscFunctionBeginUser;
327 
328   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
329 
330   // Global-to-local
331   ierr = VecScatterBegin(user->ltog0, X, user->Xloc, INSERT_VALUES,
332                          SCATTER_REVERSE); CHKERRQ(ierr);
333   ierr = VecScatterEnd(user->ltog0, X, user->Xloc, INSERT_VALUES,
334                        SCATTER_REVERSE);
335   CHKERRQ(ierr);
336 
337   // Setup libCEED vectors
338   ierr = user->VecGetArrayRead(user->Xloc, (const PetscScalar **)&x);
339   CHKERRQ(ierr);
340   ierr = user->VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
341   CeedVectorSetArray(user->xceed, user->memtype, CEED_USE_POINTER, x);
342   CeedVectorSetArray(user->yceed, user->memtype, CEED_USE_POINTER, y);
343 
344   // Apply libCEED operator
345   CeedOperatorApply(user->op, user->xceed, user->yceed,
346                     CEED_REQUEST_IMMEDIATE);
347   CeedVectorSyncArray(user->yceed, user->memtype);
348 
349   // Restore PETSc vectors
350   ierr = user->VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x);
351   CHKERRQ(ierr);
352   ierr = user->VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
353 
354   // Local-to-global
355   ierr = VecZeroEntries(Y); CHKERRQ(ierr);
356   ierr = VecScatterBegin(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
357   CHKERRQ(ierr);
358   ierr = VecScatterEnd(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
359   CHKERRQ(ierr);
360   ierr = VecScatterBegin(user->ltog0, user->Yloc, Y, ADD_VALUES,
361                          SCATTER_FORWARD); CHKERRQ(ierr);
362   ierr = VecScatterEnd(user->ltog0, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
363   CHKERRQ(ierr);
364 
365   PetscFunctionReturn(0);
366 }
367 
368 // This function calculates the error in the final solution
369 static PetscErrorCode ComputeErrorMax(User user, CeedOperator operror, Vec X,
370                                       CeedVector target, PetscReal *maxerror) {
371   PetscErrorCode ierr;
372   PetscScalar *x;
373   CeedVector collocated_error;
374   CeedInt 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->ltog, X, user->Xloc, INSERT_VALUES,
383                          SCATTER_REVERSE); CHKERRQ(ierr);
384   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES,
385                        SCATTER_REVERSE); CHKERRQ(ierr);
386 
387   // Setup libCEED vector
388   ierr = user->VecGetArrayRead(user->Xloc, (const PetscScalar **)&x);
389   CHKERRQ(ierr);
390   CeedVectorSetArray(user->xceed, user->memtype, CEED_USE_POINTER, x);
391 
392   // Apply libCEED operator
393   CeedOperatorApply(operror, user->xceed, collocated_error,
394                     CEED_REQUEST_IMMEDIATE);
395 
396   // Restore PETSc vector
397   ierr = user->VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x);
398   CHKERRQ(ierr);
399 
400   // Reduce max error
401   *maxerror = 0;
402   const CeedScalar *e;
403   CeedVectorGetArrayRead(collocated_error, CEED_MEM_HOST, &e);
404   for (CeedInt i=0; i<length; i++) {
405     *maxerror = PetscMax(*maxerror, PetscAbsScalar(e[i]));
406   }
407   CeedVectorRestoreArrayRead(collocated_error, &e);
408   ierr = MPI_Allreduce(MPI_IN_PLACE, maxerror, 1, MPIU_REAL, MPIU_MAX,
409                        user->comm); CHKERRQ(ierr);
410 
411   // Cleanup
412   CeedVectorDestroy(&collocated_error);
413 
414   PetscFunctionReturn(0);
415 }
416 
417 int main(int argc, char **argv) {
418   PetscInt ierr;
419   MPI_Comm comm;
420   char ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self";
421   double my_rt_start, my_rt, rt_min, rt_max;
422   PetscInt degree, qextra, localnodes, localelem, melem[3], mnodes[3], p[3],
423            irank[3], lnodes[3], lsize, ncompu = 1, ksp_max_it_clip[2];
424   PetscScalar *r;
425   PetscBool test_mode, benchmark_mode, write_solution;
426   PetscMPIInt size, rank;
427   PetscLogStage solvestage;
428   Vec X, Xloc, rhs, rhsloc;
429   Mat mat;
430   KSP ksp;
431   VecScatter ltog, ltog0, gtogD;
432   User user;
433   Ceed ceed;
434   CeedBasis basisx, basisu;
435   CeedElemRestriction Erestrictx, Erestrictu, Erestrictui, Erestrictqdi;
436   CeedQFunction qfsetupgeo, qfsetuprhs, qfapply, qferror;
437   CeedOperator opsetupgeo, opsetuprhs, opapply, operror;
438   CeedVector xcoord, qdata, rhsceed, target;
439   CeedMemType memtyperequested;
440   CeedInt P, Q;
441   const CeedInt dim = 3, ncompx = 3;
442   bpType bpchoice;
443 
444   // Check for PETSc CUDA availability
445   PetscBool petschavecuda, setmemtyperequest = PETSC_FALSE;
446   // *INDENT-OFF*
447   #ifdef PETSC_HAVE_CUDA
448   petschavecuda = PETSC_TRUE;
449   #else
450   petschavecuda = PETSC_FALSE;
451   #endif
452   // *INDENT-ON*
453 
454   ierr = PetscInitialize(&argc, &argv, NULL, help);
455   if (ierr) return ierr;
456   comm = PETSC_COMM_WORLD;
457 
458   // Read command line options
459   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
460   bpchoice = CEED_BP1;
461   ierr = PetscOptionsEnum("-problem",
462                           "CEED benchmark problem to solve", NULL,
463                           bpTypes, (PetscEnum)bpchoice, (PetscEnum *)&bpchoice,
464                           NULL); CHKERRQ(ierr);
465   ncompu = bpOptions[bpchoice].ncompu;
466   test_mode = PETSC_FALSE;
467   ierr = PetscOptionsBool("-test",
468                           "Testing mode (do not print unless error is large)",
469                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
470   benchmark_mode = PETSC_FALSE;
471   ierr = PetscOptionsBool("-benchmark",
472                           "Benchmarking mode (prints benchmark statistics)",
473                           NULL, benchmark_mode, &benchmark_mode, NULL);
474   CHKERRQ(ierr);
475   write_solution = PETSC_FALSE;
476   ierr = PetscOptionsBool("-write_solution",
477                           "Write solution for visualization",
478                           NULL, write_solution, &write_solution, NULL);
479   CHKERRQ(ierr);
480   degree = test_mode ? 3 : 1;
481   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
482                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
483   qextra = bpOptions[bpchoice].qextra;
484   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
485                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
486   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
487                             NULL, ceedresource, ceedresource,
488                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
489   localnodes = 1000;
490   ierr = PetscOptionsInt("-local",
491                          "Target number of locally owned nodes per process",
492                          NULL, localnodes, &localnodes, NULL); CHKERRQ(ierr);
493   PetscInt two = 2;
494   ksp_max_it_clip[0] = 5;
495   ksp_max_it_clip[1] = 20;
496   ierr = PetscOptionsIntArray("-ksp_max_it_clip",
497                               "Min and max number of iterations to use during benchmarking",
498                               NULL, ksp_max_it_clip, &two, NULL);
499   CHKERRQ(ierr);
500   memtyperequested = petschavecuda ? CEED_MEM_DEVICE : CEED_MEM_HOST;
501   ierr = PetscOptionsEnum("-memtype",
502                           "CEED MemType requested", NULL,
503                           memTypes, (PetscEnum)memtyperequested,
504                           (PetscEnum *)&memtyperequested, &setmemtyperequest);
505   CHKERRQ(ierr);
506   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
507   P = degree + 1;
508   Q = P + qextra;
509 
510   // Set up libCEED
511   CeedInit(ceedresource, &ceed);
512   CeedMemType memtypebackend;
513   CeedGetPreferredMemType(ceed, &memtypebackend);
514 
515   // Check memtype compatibility
516   if (!setmemtyperequest)
517     memtyperequested = memtypebackend;
518   else if (!petschavecuda && memtyperequested == CEED_MEM_DEVICE)
519     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP_SYS,
520              "PETSc was not built with CUDA. "
521              "Requested MemType CEED_MEM_DEVICE is not supported.", NULL);
522 
523   // Determine size of process grid
524   ierr = MPI_Comm_size(comm, &size); CHKERRQ(ierr);
525   Split3(size, p, false);
526 
527   // Find a nicely composite number of elements no less than localnodes
528   for (localelem = PetscMax(1, localnodes / (degree*degree*degree)); ;
529        localelem++) {
530     Split3(localelem, melem, true);
531     if (Max3(melem) / Min3(melem) <= 2) break;
532   }
533 
534   // Find my location in the process grid
535   ierr = MPI_Comm_rank(comm, &rank); CHKERRQ(ierr);
536   for (int d=0,rankleft=rank; d<dim; d++) {
537     const int pstride[3] = {p[1] *p[2], p[2], 1};
538     irank[d] = rankleft / pstride[d];
539     rankleft -= irank[d] * pstride[d];
540   }
541 
542   GlobalNodes(p, irank, degree, melem, mnodes);
543 
544   // Setup global vector
545   ierr = VecCreate(comm, &X); CHKERRQ(ierr);
546   if (memtyperequested == CEED_MEM_DEVICE) {
547     ierr = VecSetType(X, VECCUDA); CHKERRQ(ierr);
548   }
549   ierr = VecSetSizes(X, mnodes[0]*mnodes[1]*mnodes[2]*ncompu, PETSC_DECIDE);
550   CHKERRQ(ierr);
551   ierr = VecSetUp(X); CHKERRQ(ierr);
552 
553   // Set up libCEED
554   CeedInit(ceedresource, &ceed);
555 
556   // Print summary
557   CeedInt gsize;
558   ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
559   if (!test_mode) {
560     const char *usedresource;
561     CeedGetResource(ceed, &usedresource);
562 
563     VecType vectype;
564     ierr = VecGetType(X, &vectype); CHKERRQ(ierr);
565 
566     ierr = PetscPrintf(comm,
567                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc --\n"
568                        "  PETSc:\n"
569                        "    PETSc Vec Type                     : %s\n"
570                        "  libCEED:\n"
571                        "    libCEED Backend                    : %s\n"
572                        "    libCEED Backend MemType            : %s\n"
573                        "    libCEED User Requested MemType     : %s\n"
574                        "  Mesh:\n"
575                        "    Number of 1D Basis Nodes (P)       : %d\n"
576                        "    Number of 1D Quadrature Points (Q) : %d\n"
577                        "    Global nodes                       : %D\n"
578                        "    Process Decomposition              : %D %D %D\n"
579                        "    Local Elements                     : %D = %D %D %D\n"
580                        "    Owned nodes                        : %D = %D %D %D\n"
581                        "    DoF per node                       : %D\n",
582                        bpchoice+1, vectype, usedresource,
583                        CeedMemTypes[memtypebackend],
584                        (setmemtyperequest) ?
585                        CeedMemTypes[memtyperequested] : "none",
586                        P, Q,  gsize/ncompu, p[0], p[1], p[2], localelem,
587                        melem[0], melem[1], melem[2],
588                        mnodes[0]*mnodes[1]*mnodes[2], mnodes[0], mnodes[1],
589                        mnodes[2], ncompu); CHKERRQ(ierr);
590   }
591 
592   {
593     lsize = 1;
594     for (int d=0; d<dim; d++) {
595       lnodes[d] = melem[d]*degree + 1;
596       lsize *= lnodes[d];
597     }
598     ierr = VecCreate(PETSC_COMM_SELF, &Xloc); CHKERRQ(ierr);
599     if (memtyperequested == CEED_MEM_DEVICE) {
600       ierr = VecSetType(Xloc, VECCUDA); CHKERRQ(ierr);
601     }
602     ierr = VecSetSizes(Xloc, lsize*ncompu, PETSC_DECIDE); CHKERRQ(ierr);
603     ierr = VecSetUp(Xloc); CHKERRQ(ierr);
604 
605     // Create local-to-global scatter
606     PetscInt *ltogind, *ltogind0, *locind, l0count;
607     IS ltogis, ltogis0, locis;
608     PetscInt gstart[2][2][2], gmnodes[2][2][2][dim];
609 
610     for (int i=0; i<2; i++) {
611       for (int j=0; j<2; j++) {
612         for (int k=0; k<2; k++) {
613           PetscInt ijkrank[3] = {irank[0]+i, irank[1]+j, irank[2]+k};
614           gstart[i][j][k] = GlobalStart(p, ijkrank, degree, melem);
615           GlobalNodes(p, ijkrank, degree, melem, gmnodes[i][j][k]);
616         }
617       }
618     }
619 
620     ierr = PetscMalloc1(lsize, &ltogind); CHKERRQ(ierr);
621     ierr = PetscMalloc1(lsize, &ltogind0); CHKERRQ(ierr);
622     ierr = PetscMalloc1(lsize, &locind); CHKERRQ(ierr);
623     l0count = 0;
624     for (PetscInt i=0,ir,ii; ir=i>=mnodes[0], ii=i-ir*mnodes[0], i<lnodes[0]; i++)
625       for (PetscInt j=0,jr,jj; jr=j>=mnodes[1], jj=j-jr*mnodes[1], j<lnodes[1]; j++)
626         for (PetscInt k=0,kr,kk; kr=k>=mnodes[2], kk=k-kr*mnodes[2], k<lnodes[2]; k++) {
627           PetscInt here = (i*lnodes[1]+j)*lnodes[2]+k;
628           ltogind[here] =
629             gstart[ir][jr][kr] + (ii*gmnodes[ir][jr][kr][1]+jj)*gmnodes[ir][jr][kr][2]+kk;
630           if ((irank[0] == 0 && i == 0)
631               || (irank[1] == 0 && j == 0)
632               || (irank[2] == 0 && k == 0)
633               || (irank[0]+1 == p[0] && i+1 == lnodes[0])
634               || (irank[1]+1 == p[1] && j+1 == lnodes[1])
635               || (irank[2]+1 == p[2] && k+1 == lnodes[2]))
636             continue;
637           ltogind0[l0count] = ltogind[here];
638           locind[l0count++] = here;
639         }
640     ierr = ISCreateBlock(comm, ncompu, lsize, ltogind, PETSC_OWN_POINTER,
641                          &ltogis); CHKERRQ(ierr);
642     ierr = VecScatterCreate(Xloc, NULL, X, ltogis, &ltog); CHKERRQ(ierr);
643     CHKERRQ(ierr);
644     ierr = ISCreateBlock(comm, ncompu, l0count, ltogind0, PETSC_OWN_POINTER,
645                          &ltogis0); CHKERRQ(ierr);
646     ierr = ISCreateBlock(comm, ncompu, l0count, locind, PETSC_OWN_POINTER,
647                          &locis); CHKERRQ(ierr);
648     ierr = VecScatterCreate(Xloc, locis, X, ltogis0, &ltog0); CHKERRQ(ierr);
649     {
650       // Create global-to-global scatter for Dirichlet values (everything not in
651       // ltogis0, which is the range of ltog0)
652       PetscInt xstart, xend, *indD, countD = 0;
653       IS isD;
654       const PetscScalar *x;
655       ierr = VecZeroEntries(Xloc); CHKERRQ(ierr);
656       ierr = VecSet(X, 1.0); CHKERRQ(ierr);
657       ierr = VecScatterBegin(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
658       CHKERRQ(ierr);
659       ierr = VecScatterEnd(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
660       CHKERRQ(ierr);
661       ierr = VecGetOwnershipRange(X, &xstart, &xend); CHKERRQ(ierr);
662       ierr = PetscMalloc1(xend-xstart, &indD); CHKERRQ(ierr);
663       ierr = VecGetArrayRead(X, &x); CHKERRQ(ierr);
664       for (PetscInt i=0; i<xend-xstart; i++) {
665         if (x[i] == 1.) indD[countD++] = xstart + i;
666       }
667       ierr = VecRestoreArrayRead(X, &x); CHKERRQ(ierr);
668       ierr = ISCreateGeneral(comm, countD, indD, PETSC_COPY_VALUES, &isD);
669       CHKERRQ(ierr);
670       ierr = PetscFree(indD); CHKERRQ(ierr);
671       ierr = VecScatterCreate(X, isD, X, isD, &gtogD); CHKERRQ(ierr);
672       ierr = ISDestroy(&isD); CHKERRQ(ierr);
673     }
674     ierr = ISDestroy(&ltogis); CHKERRQ(ierr);
675     ierr = ISDestroy(&ltogis0); CHKERRQ(ierr);
676     ierr = ISDestroy(&locis); CHKERRQ(ierr);
677   }
678 
679   // CEED bases
680   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompu, P, Q,
681                                   bpOptions[bpchoice].qmode, &basisu);
682   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, Q,
683                                   bpOptions[bpchoice].qmode, &basisx);
684 
685   // CEED restrictions
686   CreateRestriction(ceed, melem, P, ncompu, &Erestrictu);
687   CreateRestriction(ceed, melem, 2, dim, &Erestrictx);
688   CeedInt nelem = melem[0]*melem[1]*melem[2];
689   CeedElemRestrictionCreateStrided(ceed, nelem, Q*Q*Q, ncompu,
690                                    ncompu*nelem*Q*Q*Q,
691                                    CEED_STRIDES_BACKEND, &Erestrictui);
692   CeedElemRestrictionCreateStrided(ceed, nelem, Q*Q*Q,
693                                    bpOptions[bpchoice].qdatasize,
694                                    bpOptions[bpchoice].qdatasize*nelem*Q*Q*Q,
695                                    CEED_STRIDES_BACKEND, &Erestrictqdi);
696   {
697     CeedScalar *xloc;
698     CeedInt shape[3] = {melem[0]+1, melem[1]+1, melem[2]+1}, len =
699                          shape[0]*shape[1]*shape[2];
700     xloc = malloc(len*ncompx*sizeof xloc[0]);
701     for (CeedInt i=0; i<shape[0]; i++) {
702       for (CeedInt j=0; j<shape[1]; j++) {
703         for (CeedInt k=0; k<shape[2]; k++) {
704           xloc[dim*((i*shape[1]+j)*shape[2]+k) + 0] = 1.*(irank[0]*melem[0]+i) /
705               (p[0]*melem[0]);
706           xloc[dim*((i*shape[1]+j)*shape[2]+k) + 1] = 1.*(irank[1]*melem[1]+j) /
707               (p[1]*melem[1]);
708           xloc[dim*((i*shape[1]+j)*shape[2]+k) + 2] = 1.*(irank[2]*melem[2]+k) /
709               (p[2]*melem[2]);
710         }
711       }
712     }
713     CeedVectorCreate(ceed, len*ncompx, &xcoord);
714     CeedVectorSetArray(xcoord, CEED_MEM_HOST, CEED_OWN_POINTER, xloc);
715   }
716 
717   // Create the Qfunction that builds the operator quadrature data
718   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].setupgeo,
719                               bpOptions[bpchoice].setupgeofname, &qfsetupgeo);
720   CeedQFunctionAddInput(qfsetupgeo, "dx", ncompx*dim, CEED_EVAL_GRAD);
721   CeedQFunctionAddInput(qfsetupgeo, "weight", 1, CEED_EVAL_WEIGHT);
722   CeedQFunctionAddOutput(qfsetupgeo, "qdata", bpOptions[bpchoice].qdatasize,
723                          CEED_EVAL_NONE);
724 
725   // Create the Qfunction that sets up the RHS and true solution
726   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].setuprhs,
727                               bpOptions[bpchoice].setuprhsfname, &qfsetuprhs);
728   CeedQFunctionAddInput(qfsetuprhs, "x", ncompx, CEED_EVAL_INTERP);
729   CeedQFunctionAddInput(qfsetuprhs, "dx", ncompx*dim, CEED_EVAL_GRAD);
730   CeedQFunctionAddInput(qfsetuprhs, "weight", 1, CEED_EVAL_WEIGHT);
731   CeedQFunctionAddOutput(qfsetuprhs, "true_soln", ncompu, CEED_EVAL_NONE);
732   CeedQFunctionAddOutput(qfsetuprhs, "rhs", ncompu, CEED_EVAL_INTERP);
733 
734   // Set up PDE operator
735   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].apply,
736                               bpOptions[bpchoice].applyfname, &qfapply);
737   // Add inputs and outputs
738   CeedInt inscale = bpOptions[bpchoice].inmode==CEED_EVAL_GRAD ? 3 : 1;
739   CeedInt outscale = bpOptions[bpchoice].outmode==CEED_EVAL_GRAD ? 3 : 1;
740   CeedQFunctionAddInput(qfapply, "u", ncompu*inscale,
741                         bpOptions[bpchoice].inmode);
742   CeedQFunctionAddInput(qfapply, "qdata", bpOptions[bpchoice].qdatasize,
743                         CEED_EVAL_NONE);
744   CeedQFunctionAddOutput(qfapply, "v", ncompu*outscale,
745                          bpOptions[bpchoice].outmode);
746 
747   // Create the error qfunction
748   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpchoice].error,
749                               bpOptions[bpchoice].errorfname, &qferror);
750   CeedQFunctionAddInput(qferror, "u", ncompu, CEED_EVAL_INTERP);
751   CeedQFunctionAddInput(qferror, "true_soln", ncompu, CEED_EVAL_NONE);
752   CeedQFunctionAddOutput(qferror, "error", ncompu, CEED_EVAL_NONE);
753 
754   // Create the persistent vectors that will be needed in setup
755   CeedInt nqpts;
756   CeedBasisGetNumQuadraturePoints(basisu, &nqpts);
757   CeedVectorCreate(ceed, bpOptions[bpchoice].qdatasize*nelem*nqpts, &qdata);
758   CeedVectorCreate(ceed, nelem*nqpts*ncompu, &target);
759   CeedVectorCreate(ceed, lsize*ncompu, &rhsceed);
760 
761   // Create the operator that builds the quadrature data for the ceed operator
762   CeedOperatorCreate(ceed, qfsetupgeo, CEED_QFUNCTION_NONE,
763                      CEED_QFUNCTION_NONE, &opsetupgeo);
764   CeedOperatorSetField(opsetupgeo, "dx", Erestrictx, basisx,
765                        CEED_VECTOR_ACTIVE);
766   CeedOperatorSetField(opsetupgeo, "weight", CEED_ELEMRESTRICTION_NONE, basisx,
767                        CEED_VECTOR_NONE);
768   CeedOperatorSetField(opsetupgeo, "qdata", Erestrictqdi,
769                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
770 
771   // Create the operator that builds the RHS and true solution
772   CeedOperatorCreate(ceed, qfsetuprhs, CEED_QFUNCTION_NONE,
773                      CEED_QFUNCTION_NONE, &opsetuprhs);
774   CeedOperatorSetField(opsetuprhs, "x", Erestrictx, basisx,
775                        CEED_VECTOR_ACTIVE);
776   CeedOperatorSetField(opsetuprhs, "dx", Erestrictx, basisx,
777                        CEED_VECTOR_ACTIVE);
778   CeedOperatorSetField(opsetuprhs, "weight", CEED_ELEMRESTRICTION_NONE, basisx,
779                        CEED_VECTOR_NONE);
780   CeedOperatorSetField(opsetuprhs, "true_soln", Erestrictui,
781                        CEED_BASIS_COLLOCATED, target);
782   CeedOperatorSetField(opsetuprhs, "rhs", Erestrictu, basisu,
783                        CEED_VECTOR_ACTIVE);
784 
785   // Create the mass or diff operator
786   CeedOperatorCreate(ceed, qfapply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
787                      &opapply);
788   CeedOperatorSetField(opapply, "u", Erestrictu, basisu, CEED_VECTOR_ACTIVE);
789   CeedOperatorSetField(opapply, "qdata", Erestrictqdi, CEED_BASIS_COLLOCATED,
790                        qdata);
791   CeedOperatorSetField(opapply, "v", Erestrictu, basisu, CEED_VECTOR_ACTIVE);
792 
793   // Create the error operator
794   CeedOperatorCreate(ceed, qferror, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
795                      &operror);
796   CeedOperatorSetField(operror, "u", Erestrictu, basisu, CEED_VECTOR_ACTIVE);
797   CeedOperatorSetField(operror, "true_soln", Erestrictui,
798                        CEED_BASIS_COLLOCATED, target);
799   CeedOperatorSetField(operror, "error", Erestrictui, CEED_BASIS_COLLOCATED,
800                        CEED_VECTOR_ACTIVE);
801 
802   // Set up Mat
803   ierr = PetscMalloc1(1, &user); CHKERRQ(ierr);
804   user->comm = comm;
805   user->ltog = ltog;
806   if (bpchoice != CEED_BP1 && bpchoice != CEED_BP2) {
807     user->ltog0 = ltog0;
808     user->gtogD = gtogD;
809   }
810   user->Xloc = Xloc;
811   ierr = VecDuplicate(Xloc, &user->Yloc); CHKERRQ(ierr);
812   CeedVectorCreate(ceed, lsize*ncompu, &user->xceed);
813   CeedVectorCreate(ceed, lsize*ncompu, &user->yceed);
814   user->op = opapply;
815   user->qdata = qdata;
816   user->ceed = ceed;
817   user->memtype = memtyperequested;
818   if (memtyperequested == CEED_MEM_HOST) {
819     user->VecGetArray = VecGetArray;
820     user->VecGetArrayRead = VecGetArrayRead;
821     user->VecRestoreArray = VecRestoreArray;
822     user->VecRestoreArrayRead = VecRestoreArrayRead;
823   } else {
824     user->VecGetArray = VecCUDAGetArray;
825     user->VecGetArrayRead = VecCUDAGetArrayRead;
826     user->VecRestoreArray = VecCUDARestoreArray;
827     user->VecRestoreArrayRead = VecCUDARestoreArrayRead;
828   }
829 
830   ierr = MatCreateShell(comm, mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
831                         mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
832                         PETSC_DECIDE, PETSC_DECIDE, user, &mat); CHKERRQ(ierr);
833   if (bpchoice == CEED_BP1 || bpchoice == CEED_BP2) {
834     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Mass);
835     CHKERRQ(ierr);
836   } else {
837     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Diff);
838     CHKERRQ(ierr);
839   }
840   if (user->memtype == CEED_MEM_DEVICE) {
841     ierr = MatShellSetVecType(mat, VECCUDA); CHKERRQ(ierr);
842   }
843 
844   // Get RHS vector
845   ierr = VecDuplicate(X, &rhs); CHKERRQ(ierr);
846   ierr = VecDuplicate(Xloc, &rhsloc); CHKERRQ(ierr);
847   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
848   ierr = user->VecGetArray(rhsloc, &r); CHKERRQ(ierr);
849   CeedVectorSetArray(rhsceed, user->memtype, CEED_USE_POINTER, r);
850 
851   // Setup qdata, rhs, and target
852   CeedOperatorApply(opsetupgeo, xcoord, qdata, CEED_REQUEST_IMMEDIATE);
853   CeedOperatorApply(opsetuprhs, xcoord, rhsceed, CEED_REQUEST_IMMEDIATE);
854   ierr = CeedVectorSyncArray(rhsceed, user->memtype); CHKERRQ(ierr);
855   CeedVectorDestroy(&xcoord);
856 
857   // Gather RHS
858   ierr = user->VecRestoreArray(rhsloc, &r); CHKERRQ(ierr);
859   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
860   ierr = VecScatterBegin(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
861   CHKERRQ(ierr);
862   ierr = VecScatterEnd(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
863   CHKERRQ(ierr);
864   CeedVectorDestroy(&rhsceed);
865 
866   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
867   {
868     PC pc;
869     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
870     if (bpchoice == CEED_BP1 || bpchoice == CEED_BP2) {
871       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
872       ierr = PCJacobiSetType(pc, PC_JACOBI_ROWSUM); CHKERRQ(ierr);
873     } else {
874       ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
875     }
876     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
877     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
878     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
879                             PETSC_DEFAULT); CHKERRQ(ierr);
880   }
881   ierr = KSPSetOperators(ksp, mat, mat); CHKERRQ(ierr);
882   // First run's performance log is not considered for benchmarking purposes
883   ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
884   CHKERRQ(ierr);
885   my_rt_start = MPI_Wtime();
886   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
887   my_rt = MPI_Wtime() - my_rt_start;
888   ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
889   CHKERRQ(ierr);
890   // Set maxits based on first iteration timing
891   if (my_rt > 0.02) {
892     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
893                             ksp_max_it_clip[0]); CHKERRQ(ierr);
894   } else {
895     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
896                             ksp_max_it_clip[1]); CHKERRQ(ierr);
897   }
898   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
899 
900   // Timed solve
901   ierr = VecZeroEntries(X); CHKERRQ(ierr);
902   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
903 
904   // -- Performance logging
905   ierr = PetscLogStageRegister("Solve Stage", &solvestage); CHKERRQ(ierr);
906   ierr = PetscLogStagePush(solvestage); CHKERRQ(ierr);
907 
908   // -- Solve
909   my_rt_start = MPI_Wtime();
910   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
911   my_rt = MPI_Wtime() - my_rt_start;
912 
913   // -- Performance logging
914   ierr = PetscLogStagePop();
915 
916   // Output results
917   {
918     KSPType ksptype;
919     KSPConvergedReason reason;
920     PetscReal rnorm;
921     PetscInt its;
922     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
923     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
924     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
925     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
926     if (!test_mode || reason < 0 || rnorm > 1e-9) {
927       ierr = PetscPrintf(comm,
928                          "  KSP:\n"
929                          "    KSP Type                           : %s\n"
930                          "    KSP Convergence                    : %s\n"
931                          "    Total KSP Iterations               : %D\n"
932                          "    Final rnorm                        : %e\n",
933                          ksptype, KSPConvergedReasons[reason], its,
934                          (double)rnorm); CHKERRQ(ierr);
935     }
936     if (!test_mode) {
937       ierr = PetscPrintf(comm,"  Performance:\n"); CHKERRQ(ierr);
938     }
939     {
940       PetscReal maxerror;
941       ierr = ComputeErrorMax(user, operror, X, target, &maxerror);
942       CHKERRQ(ierr);
943       PetscReal tol = 5e-2;
944       if (!test_mode || maxerror > tol) {
945         ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
946         CHKERRQ(ierr);
947         ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
948         CHKERRQ(ierr);
949         ierr = PetscPrintf(comm,
950                            "    Pointwise Error (max)              : %e\n"
951                            "    CG Solve Time                      : %g (%g) sec\n",
952                            (double)maxerror, rt_max, rt_min); CHKERRQ(ierr);
953       }
954     }
955     if (!test_mode) {
956       ierr = PetscPrintf(comm,
957                          "    DoFs/Sec in CG                     : %g (%g) million\n",
958                          1e-6*gsize*its/rt_max,
959                          1e-6*gsize*its/rt_min); CHKERRQ(ierr);
960     }
961   }
962 
963   if (write_solution) {
964     PetscViewer vtkviewersoln;
965 
966     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
967     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
968     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtk"); CHKERRQ(ierr);
969     ierr = VecView(X, vtkviewersoln); CHKERRQ(ierr);
970     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
971   }
972 
973   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
974   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
975   ierr = VecDestroy(&X); CHKERRQ(ierr);
976   ierr = VecDestroy(&user->Xloc); CHKERRQ(ierr);
977   ierr = VecDestroy(&user->Yloc); CHKERRQ(ierr);
978   ierr = VecScatterDestroy(&ltog); CHKERRQ(ierr);
979   ierr = VecScatterDestroy(&ltog0); CHKERRQ(ierr);
980   ierr = VecScatterDestroy(&gtogD); CHKERRQ(ierr);
981   ierr = MatDestroy(&mat); CHKERRQ(ierr);
982   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
983 
984   CeedVectorDestroy(&user->xceed);
985   CeedVectorDestroy(&user->yceed);
986   CeedVectorDestroy(&user->qdata);
987   CeedVectorDestroy(&target);
988   CeedOperatorDestroy(&opsetupgeo);
989   CeedOperatorDestroy(&opsetuprhs);
990   CeedOperatorDestroy(&opapply);
991   CeedOperatorDestroy(&operror);
992   CeedElemRestrictionDestroy(&Erestrictu);
993   CeedElemRestrictionDestroy(&Erestrictx);
994   CeedElemRestrictionDestroy(&Erestrictui);
995   CeedElemRestrictionDestroy(&Erestrictqdi);
996   CeedQFunctionDestroy(&qfsetupgeo);
997   CeedQFunctionDestroy(&qfsetuprhs);
998   CeedQFunctionDestroy(&qfapply);
999   CeedQFunctionDestroy(&qferror);
1000   CeedBasisDestroy(&basisu);
1001   CeedBasisDestroy(&basisx);
1002   CeedDestroy(&ceed);
1003   ierr = PetscFree(user); CHKERRQ(ierr);
1004   return PetscFinalize();
1005 }
1006