xref: /libCEED/examples/petsc/bps.c (revision e6a04bf5cb06fd03ee882d1ea55149c09771081b)
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 bps [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
28 //
29 // Sample runs:
30 //
31 //     bps -problem bp1
32 //     bps -problem bp2 -ceed /cpu/self
33 //     bps -problem bp3 -ceed /gpu/occa
34 //     bps -problem bp4 -ceed /cpu/occa
35 //     bps -problem bp5 -ceed /omp/occa
36 //     bps -problem bp6 -ceed /ocl/occa
37 //
38 //TESTARGS -ceed {ceed_resource} -test -problem bp2 -degree 3
39 
40 /// @file
41 /// CEED BPs example using PETSc
42 /// See bpsdmplex.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/common.h"
50 #include "qfunctions/bp1.h"
51 #include "qfunctions/bp2.h"
52 #include "qfunctions/bp3.h"
53 #include "qfunctions/bp4.h"
54 
55 static void Split3(PetscInt size, PetscInt m[3], bool reverse) {
56   for (PetscInt d=0,sizeleft=size; d<3; d++) {
57     PetscInt try = (PetscInt)PetscCeilReal(PetscPowReal(sizeleft, 1./(3 - d)));
58     while (try * (sizeleft / try) != sizeleft) try++;
59     m[reverse ? 2-d : d] = try;
60     sizeleft /= try;
61   }
62 }
63 
64 static PetscInt Max3(const PetscInt a[3]) {
65   return PetscMax(a[0], PetscMax(a[1], a[2]));
66 }
67 static PetscInt Min3(const PetscInt a[3]) {
68   return PetscMin(a[0], PetscMin(a[1], a[2]));
69 }
70 static void GlobalNodes(const PetscInt p[3], const PetscInt irank[3],
71                         PetscInt degree, const PetscInt melem[3],
72                         PetscInt mnodes[3]) {
73   for (int d=0; d<3; d++)
74     mnodes[d] = degree*melem[d] + (irank[d] == p[d]-1);
75 }
76 static PetscInt GlobalStart(const PetscInt p[3], const PetscInt irank[3],
77                             PetscInt degree, const PetscInt melem[3]) {
78   PetscInt start = 0;
79   // Dumb brute-force is easier to read
80   for (PetscInt i=0; i<p[0]; i++) {
81     for (PetscInt j=0; j<p[1]; j++) {
82       for (PetscInt k=0; k<p[2]; k++) {
83         PetscInt mnodes[3], ijkrank[] = {i,j,k};
84         if (i == irank[0] && j == irank[1] && k == irank[2]) return start;
85         GlobalNodes(p, ijkrank, degree, melem, mnodes);
86         start += mnodes[0] * mnodes[1] * mnodes[2];
87       }
88     }
89   }
90   return -1;
91 }
92 static int CreateRestriction(Ceed ceed, const CeedInt melem[3],
93                              CeedInt P, CeedInt ncomp,
94                              CeedElemRestriction *Erestrict) {
95   const PetscInt nelem = melem[0]*melem[1]*melem[2];
96   PetscInt mnodes[3], *idx, *idxp;
97 
98   // Get indicies
99   for (int d=0; d<3; d++) mnodes[d] = melem[d]*(P-1) + 1;
100   idxp = idx = malloc(nelem*P*P*P*sizeof idx[0]);
101   for (CeedInt i=0; i<melem[0]; i++) {
102     for (CeedInt j=0; j<melem[1]; j++) {
103       for (CeedInt k=0; k<melem[2]; k++,idxp += P*P*P) {
104         for (CeedInt ii=0; ii<P; ii++) {
105           for (CeedInt jj=0; jj<P; jj++) {
106             for (CeedInt kk=0; kk<P; kk++) {
107               if (0) { // This is the C-style (i,j,k) ordering that I prefer
108                 idxp[(ii*P+jj)*P+kk] = (((i*(P-1)+ii)*mnodes[1]
109                                          + (j*(P-1)+jj))*mnodes[2]
110                                         + (k*(P-1)+kk));
111               } else { // (k,j,i) ordering for consistency with MFEM example
112                 idxp[ii+P*(jj+P*kk)] = (((i*(P-1)+ii)*mnodes[1]
113                                          + (j*(P-1)+jj))*mnodes[2]
114                                         + (k*(P-1)+kk));
115               }
116             }
117           }
118         }
119       }
120     }
121   }
122 
123   // Setup CEED restriction
124   CeedElemRestrictionCreate(ceed, nelem, P*P*P, mnodes[0]*mnodes[1]*mnodes[2],
125                             ncomp,
126                             CEED_MEM_HOST, CEED_OWN_POINTER, idx, Erestrict);
127 
128   PetscFunctionReturn(0);
129 }
130 
131 // Data for PETSc
132 typedef struct User_ *User;
133 struct User_ {
134   MPI_Comm comm;
135   VecScatter ltog;              // Scatter for all entries
136   VecScatter ltog0;             // Skip Dirichlet values
137   VecScatter gtogD;             // global-to-global; only Dirichlet values
138   Vec Xloc, Yloc;
139   CeedVector xceed, yceed;
140   CeedOperator op;
141   CeedVector qdata;
142   Ceed ceed;
143 };
144 
145 // BP Options
146 typedef enum {
147   CEED_BP1 = 0, CEED_BP2 = 1, CEED_BP3 = 2,
148   CEED_BP4 = 3, CEED_BP5 = 4, CEED_BP6 = 5
149 } bpType;
150 static const char *const bpTypes[] = {"bp1","bp2","bp3","bp4","bp5","bp6",
151                                       "bpType","CEED_BP",0
152                                      };
153 
154 // BP specific data
155 typedef struct {
156   CeedInt ncompu, qdatasize, qextra;
157   CeedQFunctionUser setupgeo, setuprhs, apply, error;
158   const char *setupgeofname, *setuprhsfname, *applyfname, *errorfname;
159   CeedEvalMode inmode, outmode;
160   CeedQuadMode qmode;
161 } bpData;
162 
163 bpData bpOptions[6] = {
164   [CEED_BP1] = {
165     .ncompu = 1,
166     .qdatasize = 1,
167     .qextra = 1,
168     .setupgeo = SetupMassGeo,
169     .setuprhs = SetupMassRhs,
170     .apply = Mass,
171     .error = Error,
172     .setupgeofname = SetupMassGeo_loc,
173     .setuprhsfname = SetupMassRhs_loc,
174     .applyfname = Mass_loc,
175     .errorfname = Error_loc,
176     .inmode = CEED_EVAL_INTERP,
177     .outmode = CEED_EVAL_INTERP,
178     .qmode = CEED_GAUSS
179   },
180   [CEED_BP2] = {
181     .ncompu = 3,
182     .qdatasize = 1,
183     .qextra = 1,
184     .setupgeo = SetupMassGeo,
185     .setuprhs = SetupMassRhs3,
186     .apply = Mass3,
187     .error = Error3,
188     .setupgeofname = SetupMassGeo_loc,
189     .setuprhsfname = SetupMassRhs3_loc,
190     .applyfname = Mass3_loc,
191     .errorfname = Error3_loc,
192     .inmode = CEED_EVAL_INTERP,
193     .outmode = CEED_EVAL_INTERP,
194     .qmode = CEED_GAUSS
195   },
196   [CEED_BP3] = {
197     .ncompu = 1,
198     .qdatasize = 6,
199     .qextra = 1,
200     .setupgeo = SetupDiffGeo,
201     .setuprhs = SetupDiffRhs,
202     .apply = Diff,
203     .error = Error,
204     .setupgeofname = SetupDiffGeo_loc,
205     .setuprhsfname = SetupDiffRhs_loc,
206     .applyfname = Diff_loc,
207     .errorfname = Error_loc,
208     .inmode = CEED_EVAL_GRAD,
209     .outmode = CEED_EVAL_GRAD,
210     .qmode = CEED_GAUSS
211   },
212   [CEED_BP4] = {
213     .ncompu = 3,
214     .qdatasize = 6,
215     .qextra = 1,
216     .setupgeo = SetupDiffGeo,
217     .setuprhs = SetupDiffRhs3,
218     .apply = Diff3,
219     .error = Error3,
220     .setupgeofname = SetupDiffGeo_loc,
221     .setuprhsfname = SetupDiffRhs3_loc,
222     .applyfname = Diff_loc,
223     .errorfname = Error3_loc,
224     .inmode = CEED_EVAL_GRAD,
225     .outmode = CEED_EVAL_GRAD,
226     .qmode = CEED_GAUSS
227   },
228   [CEED_BP5] = {
229     .ncompu = 1,
230     .qdatasize = 6,
231     .qextra = 0,
232     .setupgeo = SetupDiffGeo,
233     .setuprhs = SetupDiffRhs,
234     .apply = Diff,
235     .error = Error,
236     .setupgeofname = SetupDiffGeo_loc,
237     .setuprhsfname = SetupDiffRhs_loc,
238     .applyfname = Diff_loc,
239     .errorfname = Error_loc,
240     .inmode = CEED_EVAL_GRAD,
241     .outmode = CEED_EVAL_GRAD,
242     .qmode = CEED_GAUSS_LOBATTO
243   },
244   [CEED_BP6] = {
245     .ncompu = 3,
246     .qdatasize = 6,
247     .qextra = 0,
248     .setupgeo = SetupDiffGeo,
249     .setuprhs = SetupDiffRhs3,
250     .apply = Diff3,
251     .error = Error3,
252     .setupgeofname = SetupDiffGeo_loc,
253     .setuprhsfname = SetupDiffRhs3_loc,
254     .applyfname = Diff_loc,
255     .errorfname = Error3_loc,
256     .inmode = CEED_EVAL_GRAD,
257     .outmode = CEED_EVAL_GRAD,
258     .qmode = CEED_GAUSS_LOBATTO
259   }
260 };
261 
262 // This function uses libCEED to compute the action of the mass matrix
263 static PetscErrorCode MatMult_Mass(Mat A, Vec X, Vec Y) {
264   PetscErrorCode ierr;
265   User user;
266   PetscScalar *x, *y;
267 
268   PetscFunctionBeginUser;
269   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
270   ierr = VecScatterBegin(user->ltog, X, user->Xloc, INSERT_VALUES,
271                          SCATTER_REVERSE); CHKERRQ(ierr);
272   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES, SCATTER_REVERSE);
273   CHKERRQ(ierr);
274   ierr = VecZeroEntries(user->Yloc); CHKERRQ(ierr);
275 
276   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
277   ierr = VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
278   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
279   CeedVectorSetArray(user->yceed, CEED_MEM_HOST, CEED_USE_POINTER, y);
280 
281   CeedOperatorApply(user->op, user->xceed, user->yceed,
282                     CEED_REQUEST_IMMEDIATE);
283   ierr = CeedVectorSyncArray(user->yceed, CEED_MEM_HOST); CHKERRQ(ierr);
284 
285   ierr = VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
286   ierr = VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
287 
288   if (Y) {
289     ierr = VecZeroEntries(Y); CHKERRQ(ierr);
290     ierr = VecScatterBegin(user->ltog, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
291     CHKERRQ(ierr);
292     ierr = VecScatterEnd(user->ltog, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
293     CHKERRQ(ierr);
294   }
295   PetscFunctionReturn(0);
296 }
297 
298 // This function uses libCEED to compute the action of the Laplacian with
299 // Dirichlet boundary conditions
300 static PetscErrorCode MatMult_Diff(Mat A, Vec X, Vec Y) {
301   PetscErrorCode ierr;
302   User user;
303   PetscScalar *x, *y;
304 
305   PetscFunctionBeginUser;
306   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
307 
308   // Global-to-local
309   ierr = VecScatterBegin(user->ltog0, X, user->Xloc, INSERT_VALUES,
310                          SCATTER_REVERSE); CHKERRQ(ierr);
311   ierr = VecScatterEnd(user->ltog0, X, user->Xloc, INSERT_VALUES,
312                        SCATTER_REVERSE);
313   CHKERRQ(ierr);
314   ierr = VecZeroEntries(user->Yloc); CHKERRQ(ierr);
315 
316   // Setup CEED vectors
317   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
318   ierr = VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
319   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
320   CeedVectorSetArray(user->yceed, CEED_MEM_HOST, CEED_USE_POINTER, y);
321 
322   // Apply CEED operator
323   CeedOperatorApply(user->op, user->xceed, user->yceed,
324                     CEED_REQUEST_IMMEDIATE);
325   ierr = CeedVectorSyncArray(user->yceed, CEED_MEM_HOST); CHKERRQ(ierr);
326 
327   // Restore PETSc vectors
328   ierr = VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
329   ierr = VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
330 
331   // Local-to-global
332   ierr = VecZeroEntries(Y); CHKERRQ(ierr);
333   ierr = VecScatterBegin(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
334   CHKERRQ(ierr);
335   ierr = VecScatterEnd(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
336   CHKERRQ(ierr);
337   ierr = VecScatterBegin(user->ltog0, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
338   CHKERRQ(ierr);
339   ierr = VecScatterEnd(user->ltog0, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
340   CHKERRQ(ierr);
341 
342   PetscFunctionReturn(0);
343 }
344 
345 // This function calculates the error in the final solution
346 static PetscErrorCode ComputeErrorMax(User user, CeedOperator op_error, Vec X,
347                                       CeedVector target, PetscReal *maxerror) {
348   PetscErrorCode ierr;
349   PetscScalar *x;
350   CeedVector collocated_error;
351   CeedInt length;
352 
353   PetscFunctionBeginUser;
354   CeedVectorGetLength(target, &length);
355   CeedVectorCreate(user->ceed, length, &collocated_error);
356 
357   // Global-to-local
358   ierr = VecScatterBegin(user->ltog, X, user->Xloc, INSERT_VALUES,
359                          SCATTER_REVERSE); CHKERRQ(ierr);
360   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES, SCATTER_REVERSE);
361   CHKERRQ(ierr);
362 
363   // Setup CEED vector
364   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
365   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
366 
367   // Apply CEED operator
368   CeedOperatorApply(op_error, user->xceed, collocated_error,
369                     CEED_REQUEST_IMMEDIATE);
370 
371   // Restore PETSc vector
372   VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
373 
374   // Reduce max error
375   *maxerror = 0;
376   const CeedScalar *e;
377   CeedVectorGetArrayRead(collocated_error, CEED_MEM_HOST, &e);
378   for (CeedInt i=0; i<length; i++) {
379     *maxerror = PetscMax(*maxerror, PetscAbsScalar(e[i]));
380   }
381   CeedVectorRestoreArrayRead(collocated_error, &e);
382   ierr = MPI_Allreduce(MPI_IN_PLACE, maxerror,
383                        1, MPIU_REAL, MPIU_MAX, user->comm); CHKERRQ(ierr);
384 
385   // Cleanup
386   CeedVectorDestroy(&collocated_error);
387 
388   PetscFunctionReturn(0);
389 }
390 
391 int main(int argc, char **argv) {
392   PetscInt ierr;
393   MPI_Comm comm;
394   char ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self";
395   double my_rt_start, my_rt, rt_min, rt_max;
396   PetscInt degree, qextra, localnodes, localelem, melem[3], mnodes[3], p[3],
397            irank[3], lnodes[3], lsize, ncompu = 1;
398   PetscScalar *r;
399   PetscBool test_mode, benchmark_mode, write_solution;
400   PetscMPIInt size, rank;
401   Vec X, Xloc, rhs, rhsloc;
402   Mat mat;
403   KSP ksp;
404   VecScatter ltog, ltog0, gtogD;
405   User user;
406   Ceed ceed;
407   CeedBasis basisx, basisu;
408   CeedElemRestriction Erestrictx, Erestrictu, Erestrictxi, Erestrictui,
409                       Erestrictqdi;
410   CeedQFunction qf_setupgeo, qf_setuprhs, qf_apply, qf_error;
411   CeedOperator op_setupgeo, op_setuprhs, op_apply, op_error;
412   CeedVector xcoord, qdata, rhsceed, target;
413   CeedInt P, Q;
414   const CeedInt dim = 3, ncompx = 3;
415   bpType bpChoice;
416 
417   ierr = PetscInitialize(&argc, &argv, NULL, help);
418   if (ierr) return ierr;
419   comm = PETSC_COMM_WORLD;
420   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
421   bpChoice = CEED_BP1;
422   ierr = PetscOptionsEnum("-problem",
423                           "CEED benchmark problem to solve", NULL,
424                           bpTypes, (PetscEnum)bpChoice, (PetscEnum *)&bpChoice,
425                           NULL); CHKERRQ(ierr);
426   ncompu = bpOptions[bpChoice].ncompu;
427   test_mode = PETSC_FALSE;
428   ierr = PetscOptionsBool("-test",
429                           "Testing mode (do not print unless error is large)",
430                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
431   benchmark_mode = PETSC_FALSE;
432   ierr = PetscOptionsBool("-benchmark",
433                           "Benchmarking mode (prints benchmark statistics)",
434                           NULL, benchmark_mode, &benchmark_mode, NULL);
435   CHKERRQ(ierr);
436   write_solution = PETSC_FALSE;
437   ierr = PetscOptionsBool("-write_solution",
438                           "Write solution for visualization",
439                           NULL, write_solution, &write_solution, NULL);
440   CHKERRQ(ierr);
441   degree = test_mode ? 3 : 1;
442   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
443                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
444   qextra = bpOptions[bpChoice].qextra;
445   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
446                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
447   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
448                             NULL, ceedresource, ceedresource,
449                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
450   localnodes = 1000;
451   ierr = PetscOptionsInt("-local",
452                          "Target number of locally owned nodes per process",
453                          NULL, localnodes, &localnodes, NULL); CHKERRQ(ierr);
454   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
455   P = degree + 1;
456   Q = P + qextra;
457 
458   // Determine size of process grid
459   ierr = MPI_Comm_size(comm, &size); CHKERRQ(ierr);
460   Split3(size, p, false);
461 
462   // Find a nicely composite number of elements no less than localnodes
463   for (localelem = PetscMax(1, localnodes / (degree*degree*degree)); ;
464        localelem++) {
465     Split3(localelem, melem, true);
466     if (Max3(melem) / Min3(melem) <= 2) break;
467   }
468 
469   // Find my location in the process grid
470   ierr = MPI_Comm_rank(comm, &rank); CHKERRQ(ierr);
471   for (int d=0,rankleft=rank; d<dim; d++) {
472     const int pstride[3] = {p[1] *p[2], p[2], 1};
473     irank[d] = rankleft / pstride[d];
474     rankleft -= irank[d] * pstride[d];
475   }
476 
477   GlobalNodes(p, irank, degree, melem, mnodes);
478 
479   // Setup global vector
480   ierr = VecCreate(comm, &X); CHKERRQ(ierr);
481   ierr = VecSetSizes(X, mnodes[0]*mnodes[1]*mnodes[2]*ncompu, PETSC_DECIDE);
482   CHKERRQ(ierr);
483   ierr = VecSetUp(X); CHKERRQ(ierr);
484 
485   // Print summary
486   if (!test_mode) {
487     CeedInt gsize;
488     ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
489     ierr = PetscPrintf(comm,
490                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc --\n"
491                        "  libCEED:\n"
492                        "    libCEED Backend                    : %s\n"
493                        "  Mesh:\n"
494                        "    Number of 1D Basis Nodes (p)       : %d\n"
495                        "    Number of 1D Quadrature Points (q) : %d\n"
496                        "    Global nodes                       : %D\n"
497                        "    Process Decomposition              : %D %D %D\n"
498                        "    Local Elements                     : %D = %D %D %D\n"
499                        "    Owned nodes                        : %D = %D %D %D\n",
500                        bpChoice+1, ceedresource, P, Q,  gsize/ncompu, p[0],
501                        p[1], p[2], localelem, melem[0], melem[1], melem[2],
502                        mnodes[0]*mnodes[1]*mnodes[2], mnodes[0], mnodes[1], mnodes[2]);
503     CHKERRQ(ierr);
504   }
505 
506   {
507     lsize = 1;
508     for (int d=0; d<dim; d++) {
509       lnodes[d] = melem[d]*degree + 1;
510       lsize *= lnodes[d];
511     }
512     ierr = VecCreate(PETSC_COMM_SELF, &Xloc); CHKERRQ(ierr);
513     ierr = VecSetSizes(Xloc, lsize*ncompu, PETSC_DECIDE); CHKERRQ(ierr);
514     ierr = VecSetUp(Xloc); CHKERRQ(ierr);
515 
516     // Create local-to-global scatter
517     PetscInt *ltogind, *ltogind0, *locind, l0count;
518     IS ltogis, ltogis0, locis;
519     PetscInt gstart[2][2][2], gmnodes[2][2][2][dim];
520 
521     for (int i=0; i<2; i++) {
522       for (int j=0; j<2; j++) {
523         for (int k=0; k<2; k++) {
524           PetscInt ijkrank[3] = {irank[0]+i, irank[1]+j, irank[2]+k};
525           gstart[i][j][k] = GlobalStart(p, ijkrank, degree, melem);
526           GlobalNodes(p, ijkrank, degree, melem, gmnodes[i][j][k]);
527         }
528       }
529     }
530 
531     ierr = PetscMalloc1(lsize, &ltogind); CHKERRQ(ierr);
532     ierr = PetscMalloc1(lsize, &ltogind0); CHKERRQ(ierr);
533     ierr = PetscMalloc1(lsize, &locind); CHKERRQ(ierr);
534     l0count = 0;
535     for (PetscInt i=0,ir,ii; ir=i>=mnodes[0], ii=i-ir*mnodes[0], i<lnodes[0]; i++)
536       for (PetscInt j=0,jr,jj; jr=j>=mnodes[1], jj=j-jr*mnodes[1], j<lnodes[1]; j++)
537         for (PetscInt k=0,kr,kk; kr=k>=mnodes[2], kk=k-kr*mnodes[2], k<lnodes[2]; k++) {
538           PetscInt here = (i*lnodes[1]+j)*lnodes[2]+k;
539           ltogind[here] =
540             gstart[ir][jr][kr] + (ii*gmnodes[ir][jr][kr][1]+jj)*gmnodes[ir][jr][kr][2]+kk;
541           if ((irank[0] == 0 && i == 0)
542               || (irank[1] == 0 && j == 0)
543               || (irank[2] == 0 && k == 0)
544               || (irank[0]+1 == p[0] && i+1 == lnodes[0])
545               || (irank[1]+1 == p[1] && j+1 == lnodes[1])
546               || (irank[2]+1 == p[2] && k+1 == lnodes[2]))
547             continue;
548           ltogind0[l0count] = ltogind[here];
549           locind[l0count++] = here;
550         }
551     ierr = ISCreateBlock(comm, ncompu, lsize, ltogind, PETSC_OWN_POINTER,
552                          &ltogis); CHKERRQ(ierr);
553     ierr = VecScatterCreate(Xloc, NULL, X, ltogis, &ltog); CHKERRQ(ierr);
554     CHKERRQ(ierr);
555     ierr = ISCreateBlock(comm, ncompu, l0count, ltogind0, PETSC_OWN_POINTER,
556                          &ltogis0); CHKERRQ(ierr);
557     ierr = ISCreateBlock(comm, ncompu, l0count, locind, PETSC_OWN_POINTER,
558                          &locis); CHKERRQ(ierr);
559     ierr = VecScatterCreate(Xloc, locis, X, ltogis0, &ltog0); CHKERRQ(ierr);
560     {
561       // Create global-to-global scatter for Dirichlet values (everything not in
562       // ltogis0, which is the range of ltog0)
563       PetscInt xstart, xend, *indD, countD = 0;
564       IS isD;
565       const PetscScalar *x;
566       ierr = VecZeroEntries(Xloc); CHKERRQ(ierr);
567       ierr = VecSet(X, 1.0); CHKERRQ(ierr);
568       ierr = VecScatterBegin(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
569       CHKERRQ(ierr);
570       ierr = VecScatterEnd(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
571       CHKERRQ(ierr);
572       ierr = VecGetOwnershipRange(X, &xstart, &xend); CHKERRQ(ierr);
573       ierr = PetscMalloc1(xend-xstart, &indD); CHKERRQ(ierr);
574       ierr = VecGetArrayRead(X, &x); CHKERRQ(ierr);
575       for (PetscInt i=0; i<xend-xstart; i++) {
576         if (x[i] == 1.) indD[countD++] = xstart + i;
577       }
578       ierr = VecRestoreArrayRead(X, &x); CHKERRQ(ierr);
579       ierr = ISCreateGeneral(comm, countD, indD, PETSC_COPY_VALUES, &isD);
580       CHKERRQ(ierr);
581       ierr = PetscFree(indD); CHKERRQ(ierr);
582       ierr = VecScatterCreate(X, isD, X, isD, &gtogD); CHKERRQ(ierr);
583       ierr = ISDestroy(&isD); CHKERRQ(ierr);
584     }
585     ierr = ISDestroy(&ltogis); CHKERRQ(ierr);
586     ierr = ISDestroy(&ltogis0); CHKERRQ(ierr);
587     ierr = ISDestroy(&locis); CHKERRQ(ierr);
588   }
589 
590   // Set up libCEED
591   CeedInit(ceedresource, &ceed);
592 
593   // CEED bases
594   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompu, P, Q,
595                                   bpOptions[bpChoice].qmode, &basisu);
596   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, Q,
597                                   bpOptions[bpChoice].qmode, &basisx);
598 
599   // CEED restrictions
600   CreateRestriction(ceed, melem, P, ncompu, &Erestrictu);
601   CreateRestriction(ceed, melem, 2, dim, &Erestrictx);
602   CeedInt nelem = melem[0]*melem[1]*melem[2];
603   CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q*Q, nelem*Q*Q*Q, ncompu,
604                                     &Erestrictui);
605   CeedElemRestrictionCreateIdentity(ceed, nelem,
606                                     Q*Q*Q,
607                                     nelem*Q*Q*Q,
608                                     bpOptions[bpChoice].qdatasize, &Erestrictqdi);
609   CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q*Q, nelem*Q*Q*Q, 1,
610                                     &Erestrictxi);
611   {
612     CeedScalar *xloc;
613     CeedInt shape[3] = {melem[0]+1, melem[1]+1, melem[2]+1}, len =
614                          shape[0]*shape[1]*shape[2];
615     xloc = malloc(len*ncompx*sizeof xloc[0]);
616     for (CeedInt i=0; i<shape[0]; i++) {
617       for (CeedInt j=0; j<shape[1]; j++) {
618         for (CeedInt k=0; k<shape[2]; k++) {
619           xloc[((i*shape[1]+j)*shape[2]+k) + 0*len] = 1.*(irank[0]*melem[0]+i) /
620               (p[0]*melem[0]);
621           xloc[((i*shape[1]+j)*shape[2]+k) + 1*len] = 1.*(irank[1]*melem[1]+j) /
622               (p[1]*melem[1]);
623           xloc[((i*shape[1]+j)*shape[2]+k) + 2*len] = 1.*(irank[2]*melem[2]+k) /
624               (p[2]*melem[2]);
625         }
626       }
627     }
628     CeedVectorCreate(ceed, len*ncompx, &xcoord);
629     CeedVectorSetArray(xcoord, CEED_MEM_HOST, CEED_OWN_POINTER, xloc);
630   }
631 
632   // Create the Qfunction that builds the operator quadrature data
633   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].setupgeo,
634                               bpOptions[bpChoice].setupgeofname, &qf_setupgeo);
635   CeedQFunctionAddInput(qf_setupgeo, "dx", ncompx*dim, CEED_EVAL_GRAD);
636   CeedQFunctionAddInput(qf_setupgeo, "weight", 1, CEED_EVAL_WEIGHT);
637   CeedQFunctionAddOutput(qf_setupgeo, "qdata", bpOptions[bpChoice].qdatasize,
638                          CEED_EVAL_NONE);
639 
640   // Create the Qfunction that sets up the RHS and true solution
641   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].setuprhs,
642                               bpOptions[bpChoice].setuprhsfname, &qf_setuprhs);
643   CeedQFunctionAddInput(qf_setuprhs, "x", ncompx, CEED_EVAL_INTERP);
644   CeedQFunctionAddInput(qf_setuprhs, "dx", ncompx*dim, CEED_EVAL_GRAD);
645   CeedQFunctionAddInput(qf_setuprhs, "weight", 1, CEED_EVAL_WEIGHT);
646   CeedQFunctionAddOutput(qf_setuprhs, "true_soln", ncompu, CEED_EVAL_NONE);
647   CeedQFunctionAddOutput(qf_setuprhs, "rhs", ncompu, CEED_EVAL_INTERP);
648 
649   // Set up PDE operator
650   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].apply,
651                               bpOptions[bpChoice].applyfname, &qf_apply);
652   // Add inputs and outputs
653   CeedInt inscale = bpOptions[bpChoice].inmode==CEED_EVAL_GRAD ? 3 : 1;
654   CeedInt outscale = bpOptions[bpChoice].outmode==CEED_EVAL_GRAD ? 3 : 1;
655   CeedQFunctionAddInput(qf_apply, "u", ncompu*inscale,
656                         bpOptions[bpChoice].inmode);
657   CeedQFunctionAddInput(qf_apply, "qdata", bpOptions[bpChoice].qdatasize,
658                         CEED_EVAL_NONE);
659   CeedQFunctionAddOutput(qf_apply, "v", ncompu*outscale,
660                          bpOptions[bpChoice].outmode);
661 
662   // Create the error qfunction
663   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].error,
664                               bpOptions[bpChoice].errorfname, &qf_error);
665   CeedQFunctionAddInput(qf_error, "u", ncompu, CEED_EVAL_INTERP);
666   CeedQFunctionAddInput(qf_error, "true_soln", ncompu, CEED_EVAL_NONE);
667   CeedQFunctionAddOutput(qf_error, "error", ncompu, CEED_EVAL_NONE);
668 
669   // Create the persistent vectors that will be needed in setup
670   CeedInt nqpts;
671   CeedBasisGetNumQuadraturePoints(basisu, &nqpts);
672   CeedVectorCreate(ceed, bpOptions[bpChoice].qdatasize*nelem*nqpts, &qdata);
673   CeedVectorCreate(ceed, nelem*nqpts*ncompu, &target);
674   CeedVectorCreate(ceed, lsize*ncompu, &rhsceed);
675 
676   // Create the operator that builds the quadrature data for the ceed operator
677   CeedOperatorCreate(ceed, qf_setupgeo, NULL, NULL, &op_setupgeo);
678   CeedOperatorSetField(op_setupgeo, "dx", Erestrictx, CEED_NOTRANSPOSE,
679                        basisx, CEED_VECTOR_ACTIVE);
680   CeedOperatorSetField(op_setupgeo, "weight", Erestrictxi, CEED_NOTRANSPOSE,
681                        basisx, CEED_VECTOR_NONE);
682   CeedOperatorSetField(op_setupgeo, "qdata", Erestrictqdi, CEED_NOTRANSPOSE,
683                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
684 
685   // Create the operator that builds the RHS and true solution
686   CeedOperatorCreate(ceed, qf_setuprhs, NULL, NULL, &op_setuprhs);
687   CeedOperatorSetField(op_setuprhs, "x", Erestrictx, CEED_NOTRANSPOSE,
688                        basisx, CEED_VECTOR_ACTIVE);
689   CeedOperatorSetField(op_setuprhs, "dx", Erestrictx, CEED_NOTRANSPOSE,
690                        basisx, CEED_VECTOR_ACTIVE);
691   CeedOperatorSetField(op_setuprhs, "weight", Erestrictxi, CEED_NOTRANSPOSE,
692                        basisx, CEED_VECTOR_NONE);
693   CeedOperatorSetField(op_setuprhs, "true_soln", Erestrictui, CEED_NOTRANSPOSE,
694                        CEED_BASIS_COLLOCATED, target);
695   CeedOperatorSetField(op_setuprhs, "rhs", Erestrictu, CEED_TRANSPOSE,
696                        basisu, CEED_VECTOR_ACTIVE);
697 
698   // Create the mass or diff operator
699   CeedOperatorCreate(ceed, qf_apply, NULL, NULL, &op_apply);
700   CeedOperatorSetField(op_apply, "u", Erestrictu, CEED_TRANSPOSE,
701                        basisu, CEED_VECTOR_ACTIVE);
702   CeedOperatorSetField(op_apply, "qdata", Erestrictqdi, CEED_NOTRANSPOSE,
703                        CEED_BASIS_COLLOCATED, qdata);
704   CeedOperatorSetField(op_apply, "v", Erestrictu, CEED_TRANSPOSE,
705                        basisu, CEED_VECTOR_ACTIVE);
706 
707   // Create the error operator
708   CeedOperatorCreate(ceed, qf_error, NULL, NULL, &op_error);
709   CeedOperatorSetField(op_error, "u", Erestrictu, CEED_TRANSPOSE,
710                        basisu, CEED_VECTOR_ACTIVE);
711   CeedOperatorSetField(op_error, "true_soln", Erestrictui, CEED_NOTRANSPOSE,
712                        CEED_BASIS_COLLOCATED, target);
713   CeedOperatorSetField(op_error, "error", Erestrictui, CEED_NOTRANSPOSE,
714                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
715 
716   // Set up Mat
717   ierr = PetscMalloc1(1, &user); CHKERRQ(ierr);
718   user->comm = comm;
719   user->ltog = ltog;
720   if (bpChoice != CEED_BP1 && bpChoice != CEED_BP2) {
721     user->ltog0 = ltog0;
722     user->gtogD = gtogD;
723   }
724   user->Xloc = Xloc;
725   ierr = VecDuplicate(Xloc, &user->Yloc); CHKERRQ(ierr);
726   CeedVectorCreate(ceed, lsize*ncompu, &user->xceed);
727   CeedVectorCreate(ceed, lsize*ncompu, &user->yceed);
728   user->op = op_apply;
729   user->qdata = qdata;
730   user->ceed = ceed;
731 
732   ierr = MatCreateShell(comm, mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
733                         mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
734                         PETSC_DECIDE, PETSC_DECIDE, user, &mat); CHKERRQ(ierr);
735   if (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) {
736     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Mass);
737     CHKERRQ(ierr);
738   } else {
739     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Diff);
740     CHKERRQ(ierr);
741   }
742   ierr = MatCreateVecs(mat, &rhs, NULL); CHKERRQ(ierr);
743 
744   // Get RHS vector
745   ierr = VecDuplicate(Xloc, &rhsloc); CHKERRQ(ierr);
746   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
747   ierr = VecGetArray(rhsloc, &r); CHKERRQ(ierr);
748   CeedVectorSetArray(rhsceed, CEED_MEM_HOST, CEED_USE_POINTER, r);
749 
750   // Setup qdata, rhs, and target
751   CeedOperatorApply(op_setupgeo, xcoord, qdata, CEED_REQUEST_IMMEDIATE);
752   CeedOperatorApply(op_setuprhs, xcoord, rhsceed, CEED_REQUEST_IMMEDIATE);
753   ierr = CeedVectorSyncArray(rhsceed, CEED_MEM_HOST); CHKERRQ(ierr);
754   CeedVectorDestroy(&xcoord);
755 
756   // Gather RHS
757   ierr = VecRestoreArray(rhsloc, &r); CHKERRQ(ierr);
758   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
759   ierr = VecScatterBegin(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
760   CHKERRQ(ierr);
761   ierr = VecScatterEnd(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
762   CHKERRQ(ierr);
763   CeedVectorDestroy(&rhsceed);
764 
765   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
766   {
767     PC pc;
768     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
769     if (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) {
770       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
771       ierr = PCJacobiSetType(pc, PC_JACOBI_ROWSUM); CHKERRQ(ierr);
772     } else {
773       ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
774     }
775     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
776     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
777     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
778                             PETSC_DEFAULT); CHKERRQ(ierr);
779   }
780   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
781   ierr = KSPSetOperators(ksp, mat, mat); CHKERRQ(ierr);
782   // First run, if benchmarking
783   if (benchmark_mode) {
784     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
785     CHKERRQ(ierr);
786     my_rt_start = MPI_Wtime();
787     ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
788     my_rt = MPI_Wtime() - my_rt_start;
789     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
790     CHKERRQ(ierr);
791     // Set maxits based on first iteration timing
792     if (my_rt > 0.02) {
793       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
794       CHKERRQ(ierr);
795     } else {
796       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
797       CHKERRQ(ierr);
798     }
799   }
800   // Timed solve
801   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
802   my_rt_start = MPI_Wtime();
803   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
804   my_rt = MPI_Wtime() - my_rt_start;
805   {
806     KSPType ksptype;
807     KSPConvergedReason reason;
808     PetscReal rnorm;
809     PetscInt its;
810     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
811     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
812     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
813     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
814     if (!test_mode || reason < 0 || rnorm > 1e-8) {
815       ierr = PetscPrintf(comm,
816                          "  KSP:\n"
817                          "    KSP Type                           : %s\n"
818                          "    KSP Convergence                    : %s\n"
819                          "    Total KSP Iterations               : %D\n"
820                          "    Final rnorm                        : %e\n",
821                          ksptype, KSPConvergedReasons[reason], its,
822                          (double)rnorm); CHKERRQ(ierr);
823     }
824     if (benchmark_mode && (!test_mode)) {
825       CeedInt gsize;
826       ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
827       ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
828       CHKERRQ(ierr);
829       ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
830       CHKERRQ(ierr);
831       ierr = PetscPrintf(comm,
832                          "  Performance:\n"
833                          "    CG Solve Time                      : %g (%g) sec\n"
834                          "    DoFs/Sec in CG                     : %g (%g) million\n",
835                          rt_max, rt_min, 1e-6*gsize*its/rt_max,
836                          1e-6*gsize*its/rt_min); CHKERRQ(ierr);
837     }
838   }
839 
840   {
841     PetscReal maxerror;
842     ierr = ComputeErrorMax(user, op_error, X, target, &maxerror); CHKERRQ(ierr);
843     PetscReal tol = (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) ? 5e-3 : 5e-2;
844     if (!test_mode || maxerror > tol) {
845       ierr = PetscPrintf(comm,
846                          "    Pointwise Error (max)              : %e\n",
847                          (double)maxerror); CHKERRQ(ierr);
848     }
849   }
850 
851   if (write_solution) {
852     PetscViewer vtkviewersoln;
853 
854     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
855     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
856     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtk"); CHKERRQ(ierr);
857     ierr = VecView(X, vtkviewersoln); CHKERRQ(ierr);
858     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
859   }
860 
861   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
862   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
863   ierr = VecDestroy(&X); CHKERRQ(ierr);
864   ierr = VecDestroy(&user->Xloc); CHKERRQ(ierr);
865   ierr = VecDestroy(&user->Yloc); CHKERRQ(ierr);
866   ierr = VecScatterDestroy(&ltog); CHKERRQ(ierr);
867   ierr = VecScatterDestroy(&ltog0); CHKERRQ(ierr);
868   ierr = VecScatterDestroy(&gtogD); CHKERRQ(ierr);
869   ierr = MatDestroy(&mat); CHKERRQ(ierr);
870   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
871 
872   CeedVectorDestroy(&user->xceed);
873   CeedVectorDestroy(&user->yceed);
874   CeedVectorDestroy(&user->qdata);
875   CeedVectorDestroy(&target);
876   CeedOperatorDestroy(&op_setupgeo);
877   CeedOperatorDestroy(&op_setuprhs);
878   CeedOperatorDestroy(&op_apply);
879   CeedOperatorDestroy(&op_error);
880   CeedElemRestrictionDestroy(&Erestrictu);
881   CeedElemRestrictionDestroy(&Erestrictx);
882   CeedElemRestrictionDestroy(&Erestrictui);
883   CeedElemRestrictionDestroy(&Erestrictxi);
884   CeedElemRestrictionDestroy(&Erestrictqdi);
885   CeedQFunctionDestroy(&qf_setupgeo);
886   CeedQFunctionDestroy(&qf_setuprhs);
887   CeedQFunctionDestroy(&qf_apply);
888   CeedQFunctionDestroy(&qf_error);
889   CeedBasisDestroy(&basisu);
890   CeedBasisDestroy(&basisx);
891   CeedDestroy(&ceed);
892   ierr = PetscFree(user); CHKERRQ(ierr);
893   return PetscFinalize();
894 }
895