xref: /libCEED/examples/petsc/bps.c (revision 6c5df90db8677641a04ff505ccfa313a57dff4e5)
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 // This function uses libCEED to compute the action of the mass matrix
262 static PetscErrorCode MatMult_Mass(Mat A, Vec X, Vec Y) {
263   PetscErrorCode ierr;
264   User user;
265   PetscScalar *x, *y;
266 
267   PetscFunctionBeginUser;
268   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
269   ierr = VecScatterBegin(user->ltog, X, user->Xloc, INSERT_VALUES,
270                          SCATTER_REVERSE); CHKERRQ(ierr);
271   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES, SCATTER_REVERSE);
272   CHKERRQ(ierr);
273   ierr = VecZeroEntries(user->Yloc); CHKERRQ(ierr);
274 
275   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
276   ierr = VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
277   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
278   CeedVectorSetArray(user->yceed, CEED_MEM_HOST, CEED_USE_POINTER, y);
279 
280   CeedOperatorApply(user->op, user->xceed, user->yceed,
281                     CEED_REQUEST_IMMEDIATE);
282   ierr = CeedVectorSyncArray(user->yceed, CEED_MEM_HOST); CHKERRQ(ierr);
283 
284   ierr = VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
285   ierr = VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
286 
287   if (Y) {
288     ierr = VecZeroEntries(Y); CHKERRQ(ierr);
289     ierr = VecScatterBegin(user->ltog, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
290     CHKERRQ(ierr);
291     ierr = VecScatterEnd(user->ltog, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
292     CHKERRQ(ierr);
293   }
294   PetscFunctionReturn(0);
295 }
296 
297 // This function uses libCEED to compute the action of the Laplacian with
298 // Dirichlet boundary conditions
299 static PetscErrorCode MatMult_Diff(Mat A, Vec X, Vec Y) {
300   PetscErrorCode ierr;
301   User user;
302   PetscScalar *x, *y;
303 
304   PetscFunctionBeginUser;
305   ierr = MatShellGetContext(A, &user); CHKERRQ(ierr);
306 
307   // Global-to-local
308   ierr = VecScatterBegin(user->ltog0, X, user->Xloc, INSERT_VALUES,
309                          SCATTER_REVERSE); CHKERRQ(ierr);
310   ierr = VecScatterEnd(user->ltog0, X, user->Xloc, INSERT_VALUES,
311                        SCATTER_REVERSE);
312   CHKERRQ(ierr);
313   ierr = VecZeroEntries(user->Yloc); CHKERRQ(ierr);
314 
315   // Setup CEED vectors
316   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
317   ierr = VecGetArray(user->Yloc, &y); CHKERRQ(ierr);
318   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
319   CeedVectorSetArray(user->yceed, CEED_MEM_HOST, CEED_USE_POINTER, y);
320 
321   // Apply CEED operator
322   CeedOperatorApply(user->op, user->xceed, user->yceed,
323                     CEED_REQUEST_IMMEDIATE);
324   ierr = CeedVectorSyncArray(user->yceed, CEED_MEM_HOST); CHKERRQ(ierr);
325 
326   // Restore PETSc vectors
327   ierr = VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
328   ierr = VecRestoreArray(user->Yloc, &y); CHKERRQ(ierr);
329 
330   // Local-to-global
331   ierr = VecZeroEntries(Y); CHKERRQ(ierr);
332   ierr = VecScatterBegin(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
333   CHKERRQ(ierr);
334   ierr = VecScatterEnd(user->gtogD, X, Y, INSERT_VALUES, SCATTER_FORWARD);
335   CHKERRQ(ierr);
336   ierr = VecScatterBegin(user->ltog0, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
337   CHKERRQ(ierr);
338   ierr = VecScatterEnd(user->ltog0, user->Yloc, Y, ADD_VALUES, SCATTER_FORWARD);
339   CHKERRQ(ierr);
340 
341   PetscFunctionReturn(0);
342 }
343 
344 // This function calculates the error in the final solution
345 static PetscErrorCode ComputeErrorMax(User user, CeedOperator op_error, Vec X,
346                                       CeedVector target, PetscReal *maxerror) {
347   PetscErrorCode ierr;
348   PetscScalar *x;
349   CeedVector collocated_error;
350   CeedInt length;
351 
352   PetscFunctionBeginUser;
353   CeedVectorGetLength(target, &length);
354   CeedVectorCreate(user->ceed, length, &collocated_error);
355 
356   // Global-to-local
357   ierr = VecScatterBegin(user->ltog, X, user->Xloc, INSERT_VALUES,
358                          SCATTER_REVERSE); CHKERRQ(ierr);
359   ierr = VecScatterEnd(user->ltog, X, user->Xloc, INSERT_VALUES, SCATTER_REVERSE);
360   CHKERRQ(ierr);
361 
362   // Setup CEED vector
363   ierr = VecGetArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
364   CeedVectorSetArray(user->xceed, CEED_MEM_HOST, CEED_USE_POINTER, x);
365 
366   // Apply CEED operator
367   CeedOperatorApply(op_error, user->xceed, collocated_error,
368                     CEED_REQUEST_IMMEDIATE);
369 
370   // Restore PETSc vector
371   VecRestoreArrayRead(user->Xloc, (const PetscScalar **)&x); CHKERRQ(ierr);
372 
373   // Reduce max error
374   *maxerror = 0;
375   const CeedScalar *e;
376   CeedVectorGetArrayRead(collocated_error, CEED_MEM_HOST, &e);
377   for (CeedInt i=0; i<length; i++) {
378     *maxerror = PetscMax(*maxerror, PetscAbsScalar(e[i]));
379   }
380   CeedVectorRestoreArrayRead(collocated_error, &e);
381   ierr = MPI_Allreduce(MPI_IN_PLACE, maxerror,
382                        1, MPIU_REAL, MPIU_MAX, user->comm); CHKERRQ(ierr);
383 
384   // Cleanup
385   CeedVectorDestroy(&collocated_error);
386 
387   PetscFunctionReturn(0);
388 }
389 
390 int main(int argc, char **argv) {
391   PetscInt ierr;
392   MPI_Comm comm;
393   char ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self";
394   double my_rt_start, my_rt, rt_min, rt_max;
395   PetscInt degree, qextra, localnodes, localelem, melem[3], mnodes[3], p[3],
396            irank[3], lnodes[3], lsize, ncompu = 1;
397   PetscScalar *r;
398   PetscBool test_mode, benchmark_mode, write_solution;
399   PetscMPIInt size, rank;
400   Vec X, Xloc, rhs, rhsloc;
401   Mat mat;
402   KSP ksp;
403   VecScatter ltog, ltog0, gtogD;
404   User user;
405   Ceed ceed;
406   CeedBasis basisx, basisu;
407   CeedElemRestriction Erestrictx, Erestrictu, Erestrictxi, Erestrictui,
408                       Erestrictqdi;
409   CeedQFunction qf_setupgeo, qf_setuprhs, qf_apply, qf_error;
410   CeedOperator op_setupgeo, op_setuprhs, op_apply, op_error;
411   CeedVector xcoord, qdata, rhsceed, target;
412   CeedInt P, Q;
413   const CeedInt dim = 3, ncompx = 3;
414   bpType bpChoice;
415 
416   ierr = PetscInitialize(&argc, &argv, NULL, help);
417   if (ierr) return ierr;
418   comm = PETSC_COMM_WORLD;
419   ierr = PetscOptionsBegin(comm, NULL, "CEED BPs in PETSc", NULL); CHKERRQ(ierr);
420   bpChoice = CEED_BP1;
421   ierr = PetscOptionsEnum("-problem",
422                           "CEED benchmark problem to solve", NULL,
423                           bpTypes, (PetscEnum)bpChoice, (PetscEnum *)&bpChoice,
424                           NULL); CHKERRQ(ierr);
425   ncompu = bpOptions[bpChoice].ncompu;
426   test_mode = PETSC_FALSE;
427   ierr = PetscOptionsBool("-test",
428                           "Testing mode (do not print unless error is large)",
429                           NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr);
430   benchmark_mode = PETSC_FALSE;
431   ierr = PetscOptionsBool("-benchmark",
432                           "Benchmarking mode (prints benchmark statistics)",
433                           NULL, benchmark_mode, &benchmark_mode, NULL);
434   CHKERRQ(ierr);
435   write_solution = PETSC_FALSE;
436   ierr = PetscOptionsBool("-write_solution",
437                           "Write solution for visualization",
438                           NULL, write_solution, &write_solution, NULL);
439   CHKERRQ(ierr);
440   degree = test_mode ? 3 : 1;
441   ierr = PetscOptionsInt("-degree", "Polynomial degree of tensor product basis",
442                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
443   qextra = bpOptions[bpChoice].qextra;
444   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
445                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
446   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
447                             NULL, ceedresource, ceedresource,
448                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
449   localnodes = 1000;
450   ierr = PetscOptionsInt("-local",
451                          "Target number of locally owned nodes per process",
452                          NULL, localnodes, &localnodes, NULL); CHKERRQ(ierr);
453   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
454   P = degree + 1;
455   Q = P + qextra;
456 
457   // Determine size of process grid
458   ierr = MPI_Comm_size(comm, &size); CHKERRQ(ierr);
459   Split3(size, p, false);
460 
461   // Find a nicely composite number of elements no less than localnodes
462   for (localelem = PetscMax(1, localnodes / (degree*degree*degree)); ;
463        localelem++) {
464     Split3(localelem, melem, true);
465     if (Max3(melem) / Min3(melem) <= 2) break;
466   }
467 
468   // Find my location in the process grid
469   ierr = MPI_Comm_rank(comm, &rank); CHKERRQ(ierr);
470   for (int d=0,rankleft=rank; d<dim; d++) {
471     const int pstride[3] = {p[1] *p[2], p[2], 1};
472     irank[d] = rankleft / pstride[d];
473     rankleft -= irank[d] * pstride[d];
474   }
475 
476   GlobalNodes(p, irank, degree, melem, mnodes);
477 
478   // Setup global vector
479   ierr = VecCreate(comm, &X); CHKERRQ(ierr);
480   ierr = VecSetSizes(X, mnodes[0]*mnodes[1]*mnodes[2]*ncompu, PETSC_DECIDE);
481   CHKERRQ(ierr);
482   ierr = VecSetUp(X); CHKERRQ(ierr);
483 
484   // Print summary
485   if (!test_mode) {
486     CeedInt gsize;
487     ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
488     ierr = PetscPrintf(comm,
489                        "\n-- CEED Benchmark Problem %d -- libCEED + PETSc --\n"
490                        "  libCEED:\n"
491                        "    libCEED Backend                    : %s\n"
492                        "  Mesh:\n"
493                        "    Number of 1D Basis Nodes (p)       : %d\n"
494                        "    Number of 1D Quadrature Points (q) : %d\n"
495                        "    Global nodes                       : %D\n"
496                        "    Process Decomposition              : %D %D %D\n"
497                        "    Local Elements                     : %D = %D %D %D\n"
498                        "    Owned nodes                        : %D = %D %D %D\n",
499                        bpChoice+1, ceedresource, P, Q,  gsize/ncompu, p[0],
500                        p[1], p[2], localelem, melem[0], melem[1], melem[2],
501                        mnodes[0]*mnodes[1]*mnodes[2], mnodes[0], mnodes[1], mnodes[2]);
502     CHKERRQ(ierr);
503   }
504 
505   {
506     lsize = 1;
507     for (int d=0; d<dim; d++) {
508       lnodes[d] = melem[d]*degree + 1;
509       lsize *= lnodes[d];
510     }
511     ierr = VecCreate(PETSC_COMM_SELF, &Xloc); CHKERRQ(ierr);
512     ierr = VecSetSizes(Xloc, lsize*ncompu, PETSC_DECIDE); CHKERRQ(ierr);
513     ierr = VecSetUp(Xloc); CHKERRQ(ierr);
514 
515     // Create local-to-global scatter
516     PetscInt *ltogind, *ltogind0, *locind, l0count;
517     IS ltogis, ltogis0, locis;
518     PetscInt gstart[2][2][2], gmnodes[2][2][2][dim];
519 
520     for (int i=0; i<2; i++) {
521       for (int j=0; j<2; j++) {
522         for (int k=0; k<2; k++) {
523           PetscInt ijkrank[3] = {irank[0]+i, irank[1]+j, irank[2]+k};
524           gstart[i][j][k] = GlobalStart(p, ijkrank, degree, melem);
525           GlobalNodes(p, ijkrank, degree, melem, gmnodes[i][j][k]);
526         }
527       }
528     }
529 
530     ierr = PetscMalloc1(lsize, &ltogind); CHKERRQ(ierr);
531     ierr = PetscMalloc1(lsize, &ltogind0); CHKERRQ(ierr);
532     ierr = PetscMalloc1(lsize, &locind); CHKERRQ(ierr);
533     l0count = 0;
534     for (PetscInt i=0,ir,ii; ir=i>=mnodes[0], ii=i-ir*mnodes[0], i<lnodes[0]; i++)
535       for (PetscInt j=0,jr,jj; jr=j>=mnodes[1], jj=j-jr*mnodes[1], j<lnodes[1]; j++)
536         for (PetscInt k=0,kr,kk; kr=k>=mnodes[2], kk=k-kr*mnodes[2], k<lnodes[2]; k++) {
537           PetscInt here = (i*lnodes[1]+j)*lnodes[2]+k;
538           ltogind[here] =
539             gstart[ir][jr][kr] + (ii*gmnodes[ir][jr][kr][1]+jj)*gmnodes[ir][jr][kr][2]+kk;
540           if ((irank[0] == 0 && i == 0)
541               || (irank[1] == 0 && j == 0)
542               || (irank[2] == 0 && k == 0)
543               || (irank[0]+1 == p[0] && i+1 == lnodes[0])
544               || (irank[1]+1 == p[1] && j+1 == lnodes[1])
545               || (irank[2]+1 == p[2] && k+1 == lnodes[2]))
546             continue;
547           ltogind0[l0count] = ltogind[here];
548           locind[l0count++] = here;
549         }
550     ierr = ISCreateBlock(comm, ncompu, lsize, ltogind, PETSC_OWN_POINTER,
551                          &ltogis); CHKERRQ(ierr);
552     ierr = VecScatterCreate(Xloc, NULL, X, ltogis, &ltog); CHKERRQ(ierr);
553     CHKERRQ(ierr);
554     ierr = ISCreateBlock(comm, ncompu, l0count, ltogind0, PETSC_OWN_POINTER,
555                          &ltogis0); CHKERRQ(ierr);
556     ierr = ISCreateBlock(comm, ncompu, l0count, locind, PETSC_OWN_POINTER,
557                          &locis); CHKERRQ(ierr);
558     ierr = VecScatterCreate(Xloc, locis, X, ltogis0, &ltog0); CHKERRQ(ierr);
559     {
560       // Create global-to-global scatter for Dirichlet values (everything not in
561       // ltogis0, which is the range of ltog0)
562       PetscInt xstart, xend, *indD, countD = 0;
563       IS isD;
564       const PetscScalar *x;
565       ierr = VecZeroEntries(Xloc); CHKERRQ(ierr);
566       ierr = VecSet(X, 1.0); CHKERRQ(ierr);
567       ierr = VecScatterBegin(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
568       CHKERRQ(ierr);
569       ierr = VecScatterEnd(ltog0, Xloc, X, INSERT_VALUES, SCATTER_FORWARD);
570       CHKERRQ(ierr);
571       ierr = VecGetOwnershipRange(X, &xstart, &xend); CHKERRQ(ierr);
572       ierr = PetscMalloc1(xend-xstart, &indD); CHKERRQ(ierr);
573       ierr = VecGetArrayRead(X, &x); CHKERRQ(ierr);
574       for (PetscInt i=0; i<xend-xstart; i++) {
575         if (x[i] == 1.) indD[countD++] = xstart + i;
576       }
577       ierr = VecRestoreArrayRead(X, &x); CHKERRQ(ierr);
578       ierr = ISCreateGeneral(comm, countD, indD, PETSC_COPY_VALUES, &isD);
579       CHKERRQ(ierr);
580       ierr = PetscFree(indD); CHKERRQ(ierr);
581       ierr = VecScatterCreate(X, isD, X, isD, &gtogD); CHKERRQ(ierr);
582       ierr = ISDestroy(&isD); CHKERRQ(ierr);
583     }
584     ierr = ISDestroy(&ltogis); CHKERRQ(ierr);
585     ierr = ISDestroy(&ltogis0); CHKERRQ(ierr);
586     ierr = ISDestroy(&locis); CHKERRQ(ierr);
587   }
588 
589   // Set up libCEED
590   CeedInit(ceedresource, &ceed);
591 
592   // CEED bases
593   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompu, P, Q,
594                                   bpOptions[bpChoice].qmode, &basisu);
595   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, Q,
596                                   bpOptions[bpChoice].qmode, &basisx);
597 
598   // CEED restrictions
599   CreateRestriction(ceed, melem, P, ncompu, &Erestrictu);
600   CreateRestriction(ceed, melem, 2, dim, &Erestrictx);
601   CeedInt nelem = melem[0]*melem[1]*melem[2];
602   CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q*Q, nelem*Q*Q*Q, ncompu,
603                                     &Erestrictui);
604   CeedElemRestrictionCreateIdentity(ceed, nelem,
605                                     Q*Q*Q,
606                                     nelem*Q*Q*Q,
607                                     bpOptions[bpChoice].qdatasize, &Erestrictqdi);
608   CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q*Q, nelem*Q*Q*Q, 1,
609                                     &Erestrictxi);
610   {
611     CeedScalar *xloc;
612     CeedInt shape[3] = {melem[0]+1, melem[1]+1, melem[2]+1}, len =
613                          shape[0]*shape[1]*shape[2];
614     xloc = malloc(len*ncompx*sizeof xloc[0]);
615     for (CeedInt i=0; i<shape[0]; i++) {
616       for (CeedInt j=0; j<shape[1]; j++) {
617         for (CeedInt k=0; k<shape[2]; k++) {
618           xloc[((i*shape[1]+j)*shape[2]+k) + 0*len] = 1.*(irank[0]*melem[0]+i) /
619               (p[0]*melem[0]);
620           xloc[((i*shape[1]+j)*shape[2]+k) + 1*len] = 1.*(irank[1]*melem[1]+j) /
621               (p[1]*melem[1]);
622           xloc[((i*shape[1]+j)*shape[2]+k) + 2*len] = 1.*(irank[2]*melem[2]+k) /
623               (p[2]*melem[2]);
624         }
625       }
626     }
627     CeedVectorCreate(ceed, len*ncompx, &xcoord);
628     CeedVectorSetArray(xcoord, CEED_MEM_HOST, CEED_OWN_POINTER, xloc);
629   }
630 
631   // Create the Qfunction that builds the operator quadrature data
632   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].setupgeo,
633                               bpOptions[bpChoice].setupgeofname, &qf_setupgeo);
634   CeedQFunctionAddInput(qf_setupgeo, "dx", ncompx*dim, CEED_EVAL_GRAD);
635   CeedQFunctionAddInput(qf_setupgeo, "weight", 1, CEED_EVAL_WEIGHT);
636   CeedQFunctionAddOutput(qf_setupgeo, "qdata", bpOptions[bpChoice].qdatasize,
637                          CEED_EVAL_NONE);
638 
639   // Create the Qfunction that sets up the RHS and true solution
640   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].setuprhs,
641                               bpOptions[bpChoice].setuprhsfname, &qf_setuprhs);
642   CeedQFunctionAddInput(qf_setuprhs, "x", ncompx, CEED_EVAL_INTERP);
643   CeedQFunctionAddInput(qf_setuprhs, "dx", ncompx*dim, CEED_EVAL_GRAD);
644   CeedQFunctionAddInput(qf_setuprhs, "weight", 1, CEED_EVAL_WEIGHT);
645   CeedQFunctionAddOutput(qf_setuprhs, "true_soln", ncompu, CEED_EVAL_NONE);
646   CeedQFunctionAddOutput(qf_setuprhs, "rhs", ncompu, CEED_EVAL_INTERP);
647 
648   // Set up PDE operator
649   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].apply,
650                               bpOptions[bpChoice].applyfname, &qf_apply);
651   // Add inputs and outputs
652   CeedInt inscale = bpOptions[bpChoice].inmode==CEED_EVAL_GRAD ? 3 : 1;
653   CeedInt outscale = bpOptions[bpChoice].outmode==CEED_EVAL_GRAD ? 3 : 1;
654   CeedQFunctionAddInput(qf_apply, "u", ncompu*inscale,
655                         bpOptions[bpChoice].inmode);
656   CeedQFunctionAddInput(qf_apply, "qdata", bpOptions[bpChoice].qdatasize,
657                         CEED_EVAL_NONE);
658   CeedQFunctionAddOutput(qf_apply, "v", ncompu*outscale,
659                          bpOptions[bpChoice].outmode);
660 
661   // Create the error qfunction
662   CeedQFunctionCreateInterior(ceed, 1, bpOptions[bpChoice].error,
663                               bpOptions[bpChoice].errorfname, &qf_error);
664   CeedQFunctionAddInput(qf_error, "u", ncompu, CEED_EVAL_INTERP);
665   CeedQFunctionAddInput(qf_error, "true_soln", ncompu, CEED_EVAL_NONE);
666   CeedQFunctionAddOutput(qf_error, "error", ncompu, CEED_EVAL_NONE);
667 
668   // Create the persistent vectors that will be needed in setup
669   CeedInt nqpts;
670   CeedBasisGetNumQuadraturePoints(basisu, &nqpts);
671   CeedVectorCreate(ceed, bpOptions[bpChoice].qdatasize*nelem*nqpts, &qdata);
672   CeedVectorCreate(ceed, nelem*nqpts*ncompu, &target);
673   CeedVectorCreate(ceed, lsize*ncompu, &rhsceed);
674 
675   // Create the operator that builds the quadrature data for the ceed operator
676   CeedOperatorCreate(ceed, qf_setupgeo, NULL, NULL, &op_setupgeo);
677   CeedOperatorSetField(op_setupgeo, "dx", Erestrictx, CEED_NOTRANSPOSE,
678                        basisx, CEED_VECTOR_ACTIVE);
679   CeedOperatorSetField(op_setupgeo, "weight", Erestrictxi, CEED_NOTRANSPOSE,
680                        basisx, CEED_VECTOR_NONE);
681   CeedOperatorSetField(op_setupgeo, "qdata", Erestrictqdi, CEED_NOTRANSPOSE,
682                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
683 
684   // Create the operator that builds the RHS and true solution
685   CeedOperatorCreate(ceed, qf_setuprhs, NULL, NULL, &op_setuprhs);
686   CeedOperatorSetField(op_setuprhs, "x", Erestrictx, CEED_NOTRANSPOSE,
687                        basisx, CEED_VECTOR_ACTIVE);
688   CeedOperatorSetField(op_setuprhs, "dx", Erestrictx, CEED_NOTRANSPOSE,
689                        basisx, CEED_VECTOR_ACTIVE);
690   CeedOperatorSetField(op_setuprhs, "weight", Erestrictxi, CEED_NOTRANSPOSE,
691                        basisx, CEED_VECTOR_NONE);
692   CeedOperatorSetField(op_setuprhs, "true_soln", Erestrictui, CEED_NOTRANSPOSE,
693                        CEED_BASIS_COLLOCATED, target);
694   CeedOperatorSetField(op_setuprhs, "rhs", Erestrictu, CEED_TRANSPOSE,
695                        basisu, CEED_VECTOR_ACTIVE);
696 
697   // Create the mass or diff operator
698   CeedOperatorCreate(ceed, qf_apply, NULL, NULL, &op_apply);
699   CeedOperatorSetField(op_apply, "u", Erestrictu, CEED_TRANSPOSE,
700                        basisu, CEED_VECTOR_ACTIVE);
701   CeedOperatorSetField(op_apply, "qdata", Erestrictqdi, CEED_NOTRANSPOSE,
702                        CEED_BASIS_COLLOCATED, qdata);
703   CeedOperatorSetField(op_apply, "v", Erestrictu, CEED_TRANSPOSE,
704                        basisu, CEED_VECTOR_ACTIVE);
705 
706   // Create the error operator
707   CeedOperatorCreate(ceed, qf_error, NULL, NULL, &op_error);
708   CeedOperatorSetField(op_error, "u", Erestrictu, CEED_TRANSPOSE,
709                        basisu, CEED_VECTOR_ACTIVE);
710   CeedOperatorSetField(op_error, "true_soln", Erestrictui, CEED_NOTRANSPOSE,
711                        CEED_BASIS_COLLOCATED, target);
712   CeedOperatorSetField(op_error, "error", Erestrictui, CEED_NOTRANSPOSE,
713                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
714 
715   // Set up Mat
716   ierr = PetscMalloc1(1, &user); CHKERRQ(ierr);
717   user->comm = comm;
718   user->ltog = ltog;
719   if (bpChoice != CEED_BP1 && bpChoice != CEED_BP2) {
720     user->ltog0 = ltog0;
721     user->gtogD = gtogD;
722   }
723   user->Xloc = Xloc;
724   ierr = VecDuplicate(Xloc, &user->Yloc); CHKERRQ(ierr);
725   CeedVectorCreate(ceed, lsize*ncompu, &user->xceed);
726   CeedVectorCreate(ceed, lsize*ncompu, &user->yceed);
727   user->op = op_apply;
728   user->qdata = qdata;
729   user->ceed = ceed;
730 
731   ierr = MatCreateShell(comm, mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
732                         mnodes[0]*mnodes[1]*mnodes[2]*ncompu,
733                         PETSC_DECIDE, PETSC_DECIDE, user, &mat); CHKERRQ(ierr);
734   if (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) {
735     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Mass);
736     CHKERRQ(ierr);
737   } else {
738     ierr = MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))MatMult_Diff);
739     CHKERRQ(ierr);
740   }
741   ierr = MatCreateVecs(mat, &rhs, NULL); CHKERRQ(ierr);
742 
743   // Get RHS vector
744   ierr = VecDuplicate(Xloc, &rhsloc); CHKERRQ(ierr);
745   ierr = VecZeroEntries(rhsloc); CHKERRQ(ierr);
746   ierr = VecGetArray(rhsloc, &r); CHKERRQ(ierr);
747   CeedVectorSetArray(rhsceed, CEED_MEM_HOST, CEED_USE_POINTER, r);
748 
749   // Setup qdata, rhs, and target
750   CeedOperatorApply(op_setupgeo, xcoord, qdata, CEED_REQUEST_IMMEDIATE);
751   CeedOperatorApply(op_setuprhs, xcoord, rhsceed, CEED_REQUEST_IMMEDIATE);
752   ierr = CeedVectorSyncArray(rhsceed, CEED_MEM_HOST); CHKERRQ(ierr);
753   CeedVectorDestroy(&xcoord);
754 
755   // Gather RHS
756   ierr = VecRestoreArray(rhsloc, &r); CHKERRQ(ierr);
757   ierr = VecZeroEntries(rhs); CHKERRQ(ierr);
758   ierr = VecScatterBegin(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
759   CHKERRQ(ierr);
760   ierr = VecScatterEnd(ltog, rhsloc, rhs, ADD_VALUES, SCATTER_FORWARD);
761   CHKERRQ(ierr);
762   CeedVectorDestroy(&rhsceed);
763 
764   ierr = KSPCreate(comm, &ksp); CHKERRQ(ierr);
765   {
766     PC pc;
767     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
768     if (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) {
769       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
770       ierr = PCJacobiSetType(pc, PC_JACOBI_ROWSUM); CHKERRQ(ierr);
771     } else {
772       ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
773     }
774     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
775     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
776     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
777                             PETSC_DEFAULT); CHKERRQ(ierr);
778   }
779   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
780   ierr = KSPSetOperators(ksp, mat, mat); CHKERRQ(ierr);
781   // First run, if benchmarking
782   if (benchmark_mode) {
783     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 1);
784     CHKERRQ(ierr);
785     my_rt_start = MPI_Wtime();
786     ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
787     my_rt = MPI_Wtime() - my_rt_start;
788     ierr = MPI_Allreduce(MPI_IN_PLACE, &my_rt, 1, MPI_DOUBLE, MPI_MIN, comm);
789     CHKERRQ(ierr);
790     // Set maxits based on first iteration timing
791     if (my_rt > 0.02) {
792       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 5);
793       CHKERRQ(ierr);
794     } else {
795       ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, 20);
796       CHKERRQ(ierr);
797     }
798   }
799   // Timed solve
800   ierr = PetscBarrier((PetscObject)ksp); CHKERRQ(ierr);
801   my_rt_start = MPI_Wtime();
802   ierr = KSPSolve(ksp, rhs, X); CHKERRQ(ierr);
803   my_rt = MPI_Wtime() - my_rt_start;
804   {
805     KSPType ksptype;
806     KSPConvergedReason reason;
807     PetscReal rnorm;
808     PetscInt its;
809     ierr = KSPGetType(ksp, &ksptype); CHKERRQ(ierr);
810     ierr = KSPGetConvergedReason(ksp, &reason); CHKERRQ(ierr);
811     ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
812     ierr = KSPGetResidualNorm(ksp, &rnorm); CHKERRQ(ierr);
813     if (!test_mode || reason < 0 || rnorm > 1e-8) {
814       ierr = PetscPrintf(comm,
815                          "  KSP:\n"
816                          "    KSP Type                           : %s\n"
817                          "    KSP Convergence                    : %s\n"
818                          "    Total KSP Iterations               : %D\n"
819                          "    Final rnorm                        : %e\n",
820                          ksptype, KSPConvergedReasons[reason], its,
821                          (double)rnorm); CHKERRQ(ierr);
822     }
823     if (benchmark_mode && (!test_mode)) {
824       CeedInt gsize;
825       ierr = VecGetSize(X, &gsize); CHKERRQ(ierr);
826       ierr = MPI_Allreduce(&my_rt, &rt_min, 1, MPI_DOUBLE, MPI_MIN, comm);
827       CHKERRQ(ierr);
828       ierr = MPI_Allreduce(&my_rt, &rt_max, 1, MPI_DOUBLE, MPI_MAX, comm);
829       CHKERRQ(ierr);
830       ierr = PetscPrintf(comm,
831                          "  Performance:\n"
832                          "    CG Solve Time                      : %g (%g) sec\n"
833                          "    DoFs/Sec in CG                     : %g (%g) million\n",
834                          rt_max, rt_min, 1e-6*gsize*its/rt_max,
835                          1e-6*gsize*its/rt_min); CHKERRQ(ierr);
836     }
837   }
838 
839   {
840     PetscReal maxerror;
841     ierr = ComputeErrorMax(user, op_error, X, target, &maxerror); CHKERRQ(ierr);
842     PetscReal tol = (bpChoice == CEED_BP1 || bpChoice == CEED_BP2) ? 5e-3 : 5e-2;
843     if (!test_mode || maxerror > tol) {
844       ierr = PetscPrintf(comm,
845                          "    Pointwise Error (max)              : %e\n",
846                          (double)maxerror); CHKERRQ(ierr);
847     }
848   }
849 
850   if (write_solution) {
851     PetscViewer vtkviewersoln;
852 
853     ierr = PetscViewerCreate(comm, &vtkviewersoln); CHKERRQ(ierr);
854     ierr = PetscViewerSetType(vtkviewersoln, PETSCVIEWERVTK); CHKERRQ(ierr);
855     ierr = PetscViewerFileSetName(vtkviewersoln, "solution.vtk"); CHKERRQ(ierr);
856     ierr = VecView(X, vtkviewersoln); CHKERRQ(ierr);
857     ierr = PetscViewerDestroy(&vtkviewersoln); CHKERRQ(ierr);
858   }
859 
860   ierr = VecDestroy(&rhs); CHKERRQ(ierr);
861   ierr = VecDestroy(&rhsloc); CHKERRQ(ierr);
862   ierr = VecDestroy(&X); CHKERRQ(ierr);
863   ierr = VecDestroy(&user->Xloc); CHKERRQ(ierr);
864   ierr = VecDestroy(&user->Yloc); CHKERRQ(ierr);
865   ierr = VecScatterDestroy(&ltog); CHKERRQ(ierr);
866   ierr = VecScatterDestroy(&ltog0); CHKERRQ(ierr);
867   ierr = VecScatterDestroy(&gtogD); CHKERRQ(ierr);
868   ierr = MatDestroy(&mat); CHKERRQ(ierr);
869   ierr = KSPDestroy(&ksp); CHKERRQ(ierr);
870 
871   CeedVectorDestroy(&user->xceed);
872   CeedVectorDestroy(&user->yceed);
873   CeedVectorDestroy(&user->qdata);
874   CeedVectorDestroy(&target);
875   CeedOperatorDestroy(&op_setupgeo);
876   CeedOperatorDestroy(&op_setuprhs);
877   CeedOperatorDestroy(&op_apply);
878   CeedOperatorDestroy(&op_error);
879   CeedElemRestrictionDestroy(&Erestrictu);
880   CeedElemRestrictionDestroy(&Erestrictx);
881   CeedElemRestrictionDestroy(&Erestrictui);
882   CeedElemRestrictionDestroy(&Erestrictxi);
883   CeedElemRestrictionDestroy(&Erestrictqdi);
884   CeedQFunctionDestroy(&qf_setupgeo);
885   CeedQFunctionDestroy(&qf_setuprhs);
886   CeedQFunctionDestroy(&qf_apply);
887   CeedQFunctionDestroy(&qf_error);
888   CeedBasisDestroy(&basisu);
889   CeedBasisDestroy(&basisx);
890   CeedDestroy(&ceed);
891   ierr = PetscFree(user); CHKERRQ(ierr);
892   return PetscFinalize();
893 }
894