xref: /libCEED/examples/fluids/navierstokes.c (revision 10c9356ee76995d5baf54b243b957839f68a47f3)
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: Navier-Stokes
18 //
19 // This example demonstrates a simple usage of libCEED with PETSc to solve a
20 // Navier-Stokes problem.
21 //
22 // The code is intentionally "raw", using only low-level communication
23 // primitives.
24 //
25 // Build with:
26 //
27 //     make [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>] navierstokes
28 //
29 // Sample runs:
30 //
31 //     ./navierstokes -ceed /cpu/self -problem density_current -degree 1
32 //     ./navierstokes -ceed /gpu/occa -problem advection -degree 1
33 //
34 //TESTARGS suffix=-explicit; -ceed {ceed_resource} -test -degree 3 -dm_plex_box_faces 1,1,2 -lx 125 -ly 125 -lz 250 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -vec_view
35 //TESTARGS suffix=-implicit-nostab; -ceed {ceed_resource} -test -degree 3 -dm_plex_box_faces 1,1,2 -lx 125 -ly 125 -lz 250 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -ts_type alpha -vec_view
36 //TESTARGS suffix=-implicit-supgstab; -ceed {ceed_resource} -test -degree 3 -dm_plex_box_faces 1,1,2 -lx 125 -ly 125 -lz 250 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -ts_type alpha -stab supg -vec_view
37 
38 /// @file
39 /// Navier-Stokes example using PETSc
40 
41 const char help[] = "Solve Navier-Stokes using PETSc and libCEED\n";
42 
43 #include <petscts.h>
44 #include <petscdmplex.h>
45 #include <ceed.h>
46 #include <stdbool.h>
47 #include <petscsys.h>
48 #include "common.h"
49 #include "advection.h"
50 #include "advection2d.h"
51 #include "densitycurrent.h"
52 
53 // Problem Options
54 typedef enum {
55   NS_DENSITY_CURRENT = 0,
56   NS_ADVECTION = 1,
57   NS_ADVECTION2D = 2,
58 } problemType;
59 static const char *const problemTypes[] = {
60   "density_current",
61   "advection",
62   "advection2d",
63   "problemType","NS_",0
64 };
65 
66 typedef enum {
67   STAB_NONE = 0,
68   STAB_SU = 1,   // Streamline Upwind
69   STAB_SUPG = 2, // Streamline Upwind Petrov-Galerkin
70 } StabilizationType;
71 static const char *const StabilizationTypes[] = {
72   "NONE",
73   "SU",
74   "SUPG",
75   "StabilizationType", "STAB_", NULL
76 };
77 
78 // Problem specific data
79 typedef struct {
80   CeedInt dim, qdatasize;
81   CeedQFunctionUser setup, ics, apply_rhs, apply_ifunction;
82   PetscErrorCode (*bc)(PetscInt, PetscReal, const PetscReal[], PetscInt,
83                        PetscScalar[], void *);
84   const char *setup_loc, *ics_loc, *apply_rhs_loc, *apply_ifunction_loc;
85   const bool non_zero_time;
86 } problemData;
87 
88 problemData problemOptions[] = {
89   [NS_DENSITY_CURRENT] = {
90     .dim                 = 3,
91     .qdatasize           = 10,
92     .setup               = Setup,
93     .setup_loc           = Setup_loc,
94     .ics                 = ICsDC,
95     .ics_loc             = ICsDC_loc,
96     .apply_rhs           = DC,
97     .apply_rhs_loc       = DC_loc,
98     .apply_ifunction     = IFunction_DC,
99     .apply_ifunction_loc = IFunction_DC_loc,
100     .bc                  = Exact_DC,
101     .non_zero_time       = false,
102   },
103   [NS_ADVECTION] = {
104     .dim                 = 3,
105     .qdatasize           = 10,
106     .setup               = Setup,
107     .setup_loc           = Setup_loc,
108     .ics                 = ICsAdvection,
109     .ics_loc             = ICsAdvection_loc,
110     .apply_rhs           = Advection,
111     .apply_rhs_loc       = Advection_loc,
112     .apply_ifunction     = IFunction_Advection,
113     .apply_ifunction_loc = IFunction_Advection_loc,
114     .bc                  = Exact_Advection,
115     .non_zero_time       = false,
116   },
117   [NS_ADVECTION2D] = {
118     .dim                 = 2,
119     .qdatasize           = 5,
120     .setup               = Setup2d,
121     .setup_loc           = Setup2d_loc,
122     .ics                 = ICsAdvection2d,
123     .ics_loc             = ICsAdvection2d_loc,
124     .apply_rhs           = Advection2d,
125     .apply_rhs_loc       = Advection2d_loc,
126     .apply_ifunction     = IFunction_Advection2d,
127     .apply_ifunction_loc = IFunction_Advection2d_loc,
128     .bc                  = Exact_Advection2d,
129     .non_zero_time       = true,
130   },
131 };
132 
133 // PETSc user data
134 typedef struct User_ *User;
135 typedef struct Units_ *Units;
136 
137 struct User_ {
138   MPI_Comm comm;
139   PetscInt outputfreq;
140   DM dm;
141   DM dmviz;
142   Mat interpviz;
143   Ceed ceed;
144   Units units;
145   CeedVector qceed, qdotceed, gceed;
146   CeedOperator op_rhs, op_ifunction;
147   Vec M;
148   char outputfolder[PETSC_MAX_PATH_LEN];
149   PetscInt contsteps;
150 };
151 
152 struct Units_ {
153   // fundamental units
154   PetscScalar meter;
155   PetscScalar kilogram;
156   PetscScalar second;
157   PetscScalar Kelvin;
158   // derived units
159   PetscScalar Pascal;
160   PetscScalar JperkgK;
161   PetscScalar mpersquareds;
162   PetscScalar WpermK;
163   PetscScalar kgpercubicm;
164   PetscScalar kgpersquaredms;
165   PetscScalar Joulepercubicm;
166 };
167 
168 typedef struct SimpleBC_ *SimpleBC;
169 struct SimpleBC_ {
170   PetscInt nwall, nslip[3];
171   PetscInt walls[6], slips[3][6];
172   PetscBool userbc;
173 };
174 
175 // Essential BC dofs are encoded in closure indices as -(i+1).
176 static PetscInt Involute(PetscInt i) {
177   return i >= 0 ? i : -(i+1);
178 }
179 
180 // Utility function to create local CEED restriction
181 static PetscErrorCode CreateRestrictionFromPlex(Ceed ceed, DM dm, CeedInt P,
182     CeedElemRestriction *Erestrict) {
183 
184   PetscSection   section;
185   PetscInt       c, cStart, cEnd, Nelem, Ndof, *erestrict, eoffset, nfields, dim;
186   PetscErrorCode ierr;
187   Vec Uloc;
188 
189   PetscFunctionBeginUser;
190   ierr = DMGetDimension(dm, &dim); CHKERRQ(ierr);
191   ierr = DMGetLocalSection(dm,&section); CHKERRQ(ierr);
192   ierr = PetscSectionGetNumFields(section, &nfields); CHKERRQ(ierr);
193   PetscInt ncomp[nfields], fieldoff[nfields+1];
194   fieldoff[0] = 0;
195   for (PetscInt f=0; f<nfields; f++) {
196     ierr = PetscSectionGetFieldComponents(section, f, &ncomp[f]); CHKERRQ(ierr);
197     fieldoff[f+1] = fieldoff[f] + ncomp[f];
198   }
199 
200   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr);
201   Nelem = cEnd - cStart;
202   ierr = PetscMalloc1(Nelem*PetscPowInt(P, dim), &erestrict); CHKERRQ(ierr);
203   for (c=cStart,eoffset=0; c<cEnd; c++) {
204     PetscInt numindices, *indices, nnodes;
205     ierr = DMPlexGetClosureIndices(dm, section, section, c, &numindices,
206                                    &indices, NULL); CHKERRQ(ierr);
207     if (numindices % fieldoff[nfields]) SETERRQ1(PETSC_COMM_SELF,
208           PETSC_ERR_ARG_INCOMP, "Number of closure indices not compatible with Cell %D",
209           c);
210     nnodes = numindices / fieldoff[nfields];
211     for (PetscInt i=0; i<nnodes; i++) {
212       // Check that indices are blocked by node and thus can be coalesced as a single field with
213       // fieldoff[nfields] = sum(ncomp) components.
214       for (PetscInt f=0; f<nfields; f++) {
215         for (PetscInt j=0; j<ncomp[f]; j++) {
216           if (Involute(indices[fieldoff[f]*nnodes + i*ncomp[f] + j])
217               != Involute(indices[i*ncomp[0]]) + fieldoff[f] + j)
218             SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,
219                      "Cell %D closure indices not interlaced for node %D field %D component %D",
220                      c, i, f, j);
221         }
222       }
223       // Essential boundary conditions are encoded as -(loc+1), but we don't care so we decode.
224       PetscInt loc = Involute(indices[i*ncomp[0]]);
225       erestrict[eoffset++] = loc / fieldoff[nfields];
226     }
227     ierr = DMPlexRestoreClosureIndices(dm, section, section, c, &numindices,
228                                        &indices, NULL); CHKERRQ(ierr);
229   }
230   if (eoffset != Nelem*PetscPowInt(P, dim)) SETERRQ3(PETSC_COMM_SELF,
231         PETSC_ERR_LIB, "ElemRestriction of size (%D,%D) initialized %D nodes", Nelem,
232         PetscPowInt(P, dim),eoffset);
233   ierr = DMGetLocalVector(dm, &Uloc); CHKERRQ(ierr);
234   ierr = VecGetLocalSize(Uloc, &Ndof); CHKERRQ(ierr);
235   ierr = DMRestoreLocalVector(dm, &Uloc); CHKERRQ(ierr);
236   CeedElemRestrictionCreate(ceed, CEED_INTERLACED, Nelem, PetscPowInt(P, dim),
237                             Ndof/fieldoff[nfields], fieldoff[nfields],
238                             CEED_MEM_HOST, CEED_COPY_VALUES, erestrict, Erestrict);
239   ierr = PetscFree(erestrict); CHKERRQ(ierr);
240   PetscFunctionReturn(0);
241 }
242 
243 static int CreateVectorFromPetscVec(Ceed ceed, Vec p, CeedVector *v) {
244   PetscErrorCode ierr;
245   PetscInt m;
246 
247   PetscFunctionBeginUser;
248   ierr = VecGetLocalSize(p, &m); CHKERRQ(ierr);
249   ierr = CeedVectorCreate(ceed, m, v); CHKERRQ(ierr);
250   PetscFunctionReturn(0);
251 }
252 
253 static int VectorPlacePetscVec(CeedVector c, Vec p) {
254   PetscErrorCode ierr;
255   PetscInt mceed,mpetsc;
256   PetscScalar *a;
257 
258   PetscFunctionBeginUser;
259   ierr = CeedVectorGetLength(c, &mceed); CHKERRQ(ierr);
260   ierr = VecGetLocalSize(p, &mpetsc); CHKERRQ(ierr);
261   if (mceed != mpetsc) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,
262                                   "Cannot place PETSc Vec of length %D in CeedVector of length %D",
263                                   mpetsc, mceed);
264   ierr = VecGetArray(p, &a); CHKERRQ(ierr);
265   CeedVectorSetArray(c, CEED_MEM_HOST, CEED_USE_POINTER, a);
266   PetscFunctionReturn(0);
267 }
268 
269 static PetscErrorCode DMPlexInsertBoundaryValues_NS(DM dm,
270     PetscBool insertEssential, Vec Qloc, PetscReal time, Vec faceGeomFVM,
271     Vec cellGeomFVM, Vec gradFVM) {
272   PetscErrorCode ierr;
273   Vec Qbc;
274 
275   PetscFunctionBegin;
276   ierr = DMGetNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
277   ierr = VecAXPY(Qloc, 1., Qbc); CHKERRQ(ierr);
278   ierr = DMRestoreNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
279   PetscFunctionReturn(0);
280 }
281 
282 // This is the RHS of the ODE, given as u_t = G(t,u)
283 // This function takes in a state vector Q and writes into G
284 static PetscErrorCode RHS_NS(TS ts, PetscReal t, Vec Q, Vec G, void *userData) {
285   PetscErrorCode ierr;
286   User user = *(User *)userData;
287   PetscScalar *q, *g;
288   Vec Qloc, Gloc;
289 
290   // Global-to-local
291   PetscFunctionBeginUser;
292   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
293   ierr = DMGetLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
294   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
295   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
296   ierr = DMPlexInsertBoundaryValues(user->dm, PETSC_TRUE, Qloc, 0.0,
297                                     NULL, NULL, NULL); CHKERRQ(ierr);
298   ierr = VecZeroEntries(Gloc); CHKERRQ(ierr);
299 
300   // Ceed Vectors
301   ierr = VecGetArrayRead(Qloc, (const PetscScalar **)&q); CHKERRQ(ierr);
302   ierr = VecGetArray(Gloc, &g); CHKERRQ(ierr);
303   CeedVectorSetArray(user->qceed, CEED_MEM_HOST, CEED_USE_POINTER, q);
304   CeedVectorSetArray(user->gceed, CEED_MEM_HOST, CEED_USE_POINTER, g);
305 
306   // Apply CEED operator
307   CeedOperatorApply(user->op_rhs, user->qceed, user->gceed,
308                     CEED_REQUEST_IMMEDIATE);
309 
310   // Restore vectors
311   ierr = VecRestoreArrayRead(Qloc, (const PetscScalar **)&q); CHKERRQ(ierr);
312   ierr = VecRestoreArray(Gloc, &g); CHKERRQ(ierr);
313 
314   ierr = VecZeroEntries(G); CHKERRQ(ierr);
315   ierr = DMLocalToGlobal(user->dm, Gloc, ADD_VALUES, G); CHKERRQ(ierr);
316 
317   // Inverse of the lumped mass matrix
318   ierr = VecPointwiseMult(G, G, user->M); // M is Minv
319   CHKERRQ(ierr);
320 
321   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
322   ierr = DMRestoreLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
323   PetscFunctionReturn(0);
324 }
325 
326 static PetscErrorCode IFunction_NS(TS ts, PetscReal t, Vec Q, Vec Qdot, Vec G,
327                                    void *userData) {
328   PetscErrorCode ierr;
329   User user = *(User *)userData;
330   const PetscScalar *q, *qdot;
331   PetscScalar *g;
332   Vec Qloc, Qdotloc, Gloc;
333 
334   // Global-to-local
335   PetscFunctionBeginUser;
336   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
337   ierr = DMGetLocalVector(user->dm, &Qdotloc); CHKERRQ(ierr);
338   ierr = DMGetLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
339   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
340   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
341   ierr = DMPlexInsertBoundaryValues(user->dm, PETSC_TRUE, Qloc, 0.0,
342                                     NULL, NULL, NULL); CHKERRQ(ierr);
343   ierr = VecZeroEntries(Qdotloc); CHKERRQ(ierr);
344   ierr = DMGlobalToLocal(user->dm, Qdot, INSERT_VALUES, Qdotloc); CHKERRQ(ierr);
345   ierr = VecZeroEntries(Gloc); CHKERRQ(ierr);
346 
347   // Ceed Vectors
348   ierr = VecGetArrayRead(Qloc, &q); CHKERRQ(ierr);
349   ierr = VecGetArrayRead(Qdotloc, &qdot); CHKERRQ(ierr);
350   ierr = VecGetArray(Gloc, &g); CHKERRQ(ierr);
351   CeedVectorSetArray(user->qceed, CEED_MEM_HOST, CEED_USE_POINTER,
352                      (PetscScalar *)q);
353   CeedVectorSetArray(user->qdotceed, CEED_MEM_HOST, CEED_USE_POINTER,
354                      (PetscScalar *)qdot);
355   CeedVectorSetArray(user->gceed, CEED_MEM_HOST, CEED_USE_POINTER, g);
356 
357   // Apply CEED operator
358   CeedOperatorApply(user->op_ifunction, user->qceed, user->gceed,
359                     CEED_REQUEST_IMMEDIATE);
360 
361   // Restore vectors
362   ierr = VecRestoreArrayRead(Qloc, &q); CHKERRQ(ierr);
363   ierr = VecRestoreArrayRead(Qdotloc, &qdot); CHKERRQ(ierr);
364   ierr = VecRestoreArray(Gloc, &g); CHKERRQ(ierr);
365 
366   ierr = VecZeroEntries(G); CHKERRQ(ierr);
367   ierr = DMLocalToGlobal(user->dm, Gloc, ADD_VALUES, G); CHKERRQ(ierr);
368 
369   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
370   ierr = DMRestoreLocalVector(user->dm, &Qdotloc); CHKERRQ(ierr);
371   ierr = DMRestoreLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
372   PetscFunctionReturn(0);
373 }
374 
375 // User provided TS Monitor
376 static PetscErrorCode TSMonitor_NS(TS ts, PetscInt stepno, PetscReal time,
377                                    Vec Q, void *ctx) {
378   User user = ctx;
379   Vec Qloc;
380   char filepath[PETSC_MAX_PATH_LEN];
381   PetscViewer viewer;
382   PetscErrorCode ierr;
383 
384   // Set up output
385   PetscFunctionBeginUser;
386   // Print every 'outputfreq' steps
387   if (stepno % user->outputfreq != 0)
388     PetscFunctionReturn(0);
389   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
390   ierr = PetscObjectSetName((PetscObject)Qloc, "StateVec"); CHKERRQ(ierr);
391   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
392   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
393 
394   // Output
395   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-%03D.vtu",
396                        user->outputfolder, stepno + user->contsteps);
397   CHKERRQ(ierr);
398   ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)Q), filepath,
399                             FILE_MODE_WRITE, &viewer); CHKERRQ(ierr);
400   ierr = VecView(Qloc, viewer); CHKERRQ(ierr);
401   if (user->dmviz) {
402     Vec Qrefined, Qrefined_loc;
403     char filepath_refined[PETSC_MAX_PATH_LEN];
404     PetscViewer viewer_refined;
405 
406     ierr = DMGetGlobalVector(user->dmviz, &Qrefined); CHKERRQ(ierr);
407     ierr = DMGetLocalVector(user->dmviz, &Qrefined_loc); CHKERRQ(ierr);
408     ierr = PetscObjectSetName((PetscObject)Qrefined_loc, "Refined");
409     CHKERRQ(ierr);
410     ierr = MatInterpolate(user->interpviz, Q, Qrefined); CHKERRQ(ierr);
411     ierr = VecZeroEntries(Qrefined_loc); CHKERRQ(ierr);
412     ierr = DMGlobalToLocal(user->dmviz, Qrefined, INSERT_VALUES, Qrefined_loc);
413     CHKERRQ(ierr);
414     ierr = PetscSNPrintf(filepath_refined, sizeof filepath_refined,
415                          "%s/nsrefined-%03D.vtu",
416                          user->outputfolder, stepno + user->contsteps);
417     CHKERRQ(ierr);
418     ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)Qrefined),
419                               filepath_refined,
420                               FILE_MODE_WRITE, &viewer_refined); CHKERRQ(ierr);
421     ierr = VecView(Qrefined_loc, viewer_refined); CHKERRQ(ierr);
422     ierr = DMRestoreLocalVector(user->dmviz, &Qrefined_loc); CHKERRQ(ierr);
423     ierr = DMRestoreGlobalVector(user->dmviz, &Qrefined); CHKERRQ(ierr);
424     ierr = PetscViewerDestroy(&viewer_refined); CHKERRQ(ierr);
425   }
426   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
427   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
428 
429   // Save data in a binary file for continuation of simulations
430   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-solution.bin",
431                        user->outputfolder); CHKERRQ(ierr);
432   ierr = PetscViewerBinaryOpen(user->comm, filepath, FILE_MODE_WRITE, &viewer);
433   CHKERRQ(ierr);
434   ierr = VecView(Q, viewer); CHKERRQ(ierr);
435   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
436 
437   // Save time stamp
438   // Dimensionalize time back
439   time /= user->units->second;
440   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-time.bin",
441                        user->outputfolder); CHKERRQ(ierr);
442   ierr = PetscViewerBinaryOpen(user->comm, filepath, FILE_MODE_WRITE, &viewer);
443   CHKERRQ(ierr);
444   #if PETSC_VERSION_GE(3,13,0)
445   ierr = PetscViewerBinaryWrite(viewer, &time, 1, PETSC_REAL);
446   #else
447   ierr = PetscViewerBinaryWrite(viewer, &time, 1, PETSC_REAL, true);
448   #endif
449   CHKERRQ(ierr);
450   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
451 
452   PetscFunctionReturn(0);
453 }
454 
455 static PetscErrorCode ICs_FixMultiplicity(CeedOperator op_ics,
456     CeedVector xcorners, CeedVector q0ceed, DM dm, Vec Qloc, Vec Q,
457     CeedElemRestriction restrictq, SetupContext ctxSetup, CeedScalar time) {
458   PetscErrorCode ierr;
459   CeedVector multlvec;
460   Vec Multiplicity, MultiplicityLoc;
461 
462   ctxSetup->time = time;
463   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
464   ierr = VectorPlacePetscVec(q0ceed, Qloc); CHKERRQ(ierr);
465   CeedOperatorApply(op_ics, xcorners, q0ceed, CEED_REQUEST_IMMEDIATE);
466   ierr = VecZeroEntries(Q); CHKERRQ(ierr);
467   ierr = DMLocalToGlobal(dm, Qloc, ADD_VALUES, Q); CHKERRQ(ierr);
468 
469   // Fix multiplicity for output of ICs
470   ierr = DMGetLocalVector(dm, &MultiplicityLoc); CHKERRQ(ierr);
471   CeedElemRestrictionCreateVector(restrictq, &multlvec, NULL);
472   ierr = VectorPlacePetscVec(multlvec, MultiplicityLoc); CHKERRQ(ierr);
473   CeedElemRestrictionGetMultiplicity(restrictq, multlvec);
474   CeedVectorDestroy(&multlvec);
475   ierr = DMGetGlobalVector(dm, &Multiplicity); CHKERRQ(ierr);
476   ierr = VecZeroEntries(Multiplicity); CHKERRQ(ierr);
477   ierr = DMLocalToGlobal(dm, MultiplicityLoc, ADD_VALUES, Multiplicity);
478   CHKERRQ(ierr);
479   ierr = VecPointwiseDivide(Q, Q, Multiplicity); CHKERRQ(ierr);
480   ierr = VecPointwiseDivide(Qloc, Qloc, MultiplicityLoc); CHKERRQ(ierr);
481   ierr = DMRestoreLocalVector(dm, &MultiplicityLoc); CHKERRQ(ierr);
482   ierr = DMRestoreGlobalVector(dm, &Multiplicity); CHKERRQ(ierr);
483 
484   PetscFunctionReturn(0);
485 }
486 
487 static PetscErrorCode ComputeLumpedMassMatrix(Ceed ceed, DM dm,
488     CeedElemRestriction restrictq, CeedBasis basisq,
489     CeedElemRestriction restrictqdi, CeedVector qdata, Vec M) {
490   PetscErrorCode ierr;
491   CeedQFunction qf_mass;
492   CeedOperator op_mass;
493   CeedVector mceed;
494   Vec Mloc;
495   CeedInt ncompq, qdatasize;
496 
497   PetscFunctionBeginUser;
498   CeedElemRestrictionGetNumComponents(restrictq, &ncompq);
499   CeedElemRestrictionGetNumComponents(restrictqdi, &qdatasize);
500   // Create the Q-function that defines the action of the mass operator
501   CeedQFunctionCreateInterior(ceed, 1, Mass, Mass_loc, &qf_mass);
502   CeedQFunctionAddInput(qf_mass, "q", ncompq, CEED_EVAL_INTERP);
503   CeedQFunctionAddInput(qf_mass, "qdata", qdatasize, CEED_EVAL_NONE);
504   CeedQFunctionAddOutput(qf_mass, "v", ncompq, CEED_EVAL_INTERP);
505 
506   // Create the mass operator
507   CeedOperatorCreate(ceed, qf_mass, NULL, NULL, &op_mass);
508   CeedOperatorSetField(op_mass, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
509   CeedOperatorSetField(op_mass, "qdata", restrictqdi,
510                        CEED_BASIS_COLLOCATED, qdata);
511   CeedOperatorSetField(op_mass, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
512 
513   ierr = DMGetLocalVector(dm, &Mloc); CHKERRQ(ierr);
514   ierr = VecZeroEntries(Mloc); CHKERRQ(ierr);
515   CeedElemRestrictionCreateVector(restrictq, &mceed, NULL);
516   ierr = VectorPlacePetscVec(mceed, Mloc); CHKERRQ(ierr);
517 
518   {
519     // Compute a lumped mass matrix
520     CeedVector onesvec;
521     CeedElemRestrictionCreateVector(restrictq, &onesvec, NULL);
522     CeedVectorSetValue(onesvec, 1.0);
523     CeedOperatorApply(op_mass, onesvec, mceed, CEED_REQUEST_IMMEDIATE);
524     CeedVectorDestroy(&onesvec);
525     CeedOperatorDestroy(&op_mass);
526     CeedVectorDestroy(&mceed);
527   }
528   CeedQFunctionDestroy(&qf_mass);
529 
530   ierr = VecZeroEntries(M); CHKERRQ(ierr);
531   ierr = DMLocalToGlobal(dm, Mloc, ADD_VALUES, M); CHKERRQ(ierr);
532   ierr = DMRestoreLocalVector(dm, &Mloc); CHKERRQ(ierr);
533 
534   // Invert diagonally lumped mass vector for RHS function
535   ierr = VecReciprocal(M); CHKERRQ(ierr);
536   PetscFunctionReturn(0);
537 }
538 
539 static PetscErrorCode SetUpDM(DM dm, problemData *problem, PetscInt degree,
540                               SimpleBC bc, void *ctxSetup) {
541   PetscErrorCode ierr;
542 
543   PetscFunctionBeginUser;
544   {
545     // Configure the finite element space and boundary conditions
546     PetscFE fe;
547     PetscInt ncompq = 5;
548     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, problem->dim, ncompq,
549                                  PETSC_FALSE, degree, PETSC_DECIDE,
550                                  &fe);
551     ierr = PetscObjectSetName((PetscObject)fe, "Q"); CHKERRQ(ierr);
552     ierr = DMAddField(dm,NULL,(PetscObject)fe); CHKERRQ(ierr);
553     ierr = DMCreateDS(dm); CHKERRQ(ierr);
554     {
555       PetscInt comps[1] = {1};
556       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipx", "Face Sets", 0,
557                            1, comps, (void(*)(void))NULL, bc->nslip[0],
558                            bc->slips[0], ctxSetup); CHKERRQ(ierr);
559       comps[0] = 2;
560       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipy", "Face Sets", 0,
561                            1, comps, (void(*)(void))NULL, bc->nslip[1],
562                            bc->slips[1], ctxSetup); CHKERRQ(ierr);
563       comps[0] = 3;
564       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipz", "Face Sets", 0,
565                            1, comps, (void(*)(void))NULL, bc->nslip[2],
566                            bc->slips[2], ctxSetup); CHKERRQ(ierr);
567     }
568     if (bc->userbc == PETSC_TRUE) {
569       for (PetscInt c = 0; c < 3; c++) {
570         for (PetscInt s = 0; s < bc->nslip[c]; s++) {
571           for (PetscInt w = 0; w < bc->nwall; w++) {
572             if (bc->slips[c][s] == bc->walls[w])
573               SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG,
574                        "Boundary condition already set on face %D!\n", bc->walls[w]);
575 
576           }
577         }
578       }
579     }
580     // Wall boundary conditions are zero energy density and zero flux for
581     //   velocity in advection/advection2d, and zero velocity and zero flux
582     //   for mass density and energy density in density_current
583     {
584       if (problem->bc == Exact_Advection || problem->bc == Exact_Advection2d) {
585         PetscInt comps[1] = {4};
586         ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "Face Sets", 0,
587                              1, comps, (void(*)(void))problem->bc,
588                              bc->nwall, bc->walls, ctxSetup); CHKERRQ(ierr);
589       } else if (problem->bc == Exact_DC) {
590         PetscInt comps[3] = {1, 2, 3};
591         ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "Face Sets", 0,
592                              3, comps, (void(*)(void))problem->bc,
593                              bc->nwall, bc->walls, ctxSetup); CHKERRQ(ierr);
594       } else
595         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_NULL,
596                 "Undefined boundary conditions for this problem");
597     }
598     ierr = DMPlexSetClosurePermutationTensor(dm, PETSC_DETERMINE, NULL);
599     CHKERRQ(ierr);
600     ierr = PetscFEDestroy(&fe); CHKERRQ(ierr);
601   }
602   {
603     // Empty name for conserved field (because there is only one field)
604     PetscSection section;
605     ierr = DMGetLocalSection(dm, &section); CHKERRQ(ierr);
606     ierr = PetscSectionSetFieldName(section, 0, ""); CHKERRQ(ierr);
607     ierr = PetscSectionSetComponentName(section, 0, 0, "Density");
608     CHKERRQ(ierr);
609     ierr = PetscSectionSetComponentName(section, 0, 1, "MomentumX");
610     CHKERRQ(ierr);
611     ierr = PetscSectionSetComponentName(section, 0, 2, "MomentumY");
612     CHKERRQ(ierr);
613     ierr = PetscSectionSetComponentName(section, 0, 3, "MomentumZ");
614     CHKERRQ(ierr);
615     ierr = PetscSectionSetComponentName(section, 0, 4, "EnergyDensity");
616     CHKERRQ(ierr);
617   }
618   PetscFunctionReturn(0);
619 }
620 
621 int main(int argc, char **argv) {
622   PetscInt ierr;
623   MPI_Comm comm;
624   DM dm, dmcoord, dmviz;
625   Mat interpviz;
626   TS ts;
627   TSAdapt adapt;
628   User user;
629   Units units;
630   char ceedresource[4096] = "/cpu/self";
631   PetscInt cStart, cEnd, localNelem, lnodes, steps;
632   const PetscInt ncompq = 5;
633   PetscMPIInt rank;
634   PetscScalar ftime;
635   Vec Q, Qloc, Xloc;
636   Ceed ceed;
637   CeedInt numP, numQ;
638   CeedVector xcorners, qdata, q0ceed;
639   CeedBasis basisx, basisxc, basisq;
640   CeedElemRestriction restrictx, restrictxcoord, restrictq, restrictqdi;
641   CeedQFunction qf_setup, qf_ics, qf_rhs, qf_ifunction;
642   CeedOperator op_setup, op_ics;
643   CeedScalar Rd;
644   PetscScalar WpermK, Pascal, JperkgK, mpersquareds, kgpercubicm,
645               kgpersquaredms, Joulepercubicm;
646   problemType problemChoice;
647   problemData *problem = NULL;
648   StabilizationType stab;
649   PetscBool   test, implicit;
650   PetscInt    viz_refine = 0;
651   struct SimpleBC_ bc = {
652     .nslip = {2, 2, 2},
653     .slips = {{5, 6}, {3, 4}, {1, 2}}
654   };
655   double start, cpu_time_used;
656 
657   // Create the libCEED contexts
658   PetscScalar meter     = 1e-2;     // 1 meter in scaled length units
659   PetscScalar second    = 1e-2;     // 1 second in scaled time units
660   PetscScalar kilogram  = 1e-6;     // 1 kilogram in scaled mass units
661   PetscScalar Kelvin    = 1;        // 1 Kelvin in scaled temperature units
662   CeedScalar theta0     = 300.;     // K
663   CeedScalar thetaC     = -15.;     // K
664   CeedScalar P0         = 1.e5;     // Pa
665   CeedScalar N          = 0.01;     // 1/s
666   CeedScalar cv         = 717.;     // J/(kg K)
667   CeedScalar cp         = 1004.;    // J/(kg K)
668   CeedScalar g          = 9.81;     // m/s^2
669   CeedScalar lambda     = -2./3.;   // -
670   CeedScalar mu         = 75.;      // Pa s, dynamic viscosity
671   // mu = 75 is not physical for air, but is good for numerical stability
672   CeedScalar k          = 0.02638;  // W/(m K)
673   CeedScalar CtauS      = 0.;       // dimensionless
674   CeedScalar strong_form = 0.;      // [0,1]
675   PetscScalar lx        = 8000.;    // m
676   PetscScalar ly        = 8000.;    // m
677   PetscScalar lz        = 4000.;    // m
678   CeedScalar rc         = 1000.;    // m (Radius of bubble)
679   PetscScalar resx      = 1000.;    // m (resolution in x)
680   PetscScalar resy      = 1000.;    // m (resolution in y)
681   PetscScalar resz      = 1000.;    // m (resolution in z)
682   PetscInt outputfreq   = 10;       // -
683   PetscInt contsteps    = 0;        // -
684   PetscInt degree       = 1;        // -
685   PetscInt qextra       = 2;        // -
686   PetscReal center[3], dc_axis[3] = {0, 0, 0};
687 
688   ierr = PetscInitialize(&argc, &argv, NULL, help);
689   if (ierr) return ierr;
690 
691   // Allocate PETSc context
692   ierr = PetscCalloc1(1, &user); CHKERRQ(ierr);
693   ierr = PetscMalloc1(1, &units); CHKERRQ(ierr);
694 
695   // Parse command line options
696   comm = PETSC_COMM_WORLD;
697   ierr = PetscOptionsBegin(comm, NULL, "Navier-Stokes in PETSc with libCEED",
698                            NULL); CHKERRQ(ierr);
699   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
700                             NULL, ceedresource, ceedresource,
701                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
702   ierr = PetscOptionsBool("-test", "Run in test mode",
703                           NULL, test=PETSC_FALSE, &test, NULL); CHKERRQ(ierr);
704   problemChoice = NS_DENSITY_CURRENT;
705   ierr = PetscOptionsEnum("-problem", "Problem to solve", NULL,
706                           problemTypes, (PetscEnum)problemChoice,
707                           (PetscEnum *)&problemChoice, NULL); CHKERRQ(ierr);
708   problem = &problemOptions[problemChoice];
709   ierr = PetscOptionsEnum("-stab", "Stabilization method", NULL,
710                           StabilizationTypes, (PetscEnum)(stab = STAB_NONE),
711                           (PetscEnum *)&stab, NULL); CHKERRQ(ierr);
712   ierr = PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation",
713                           NULL, implicit=PETSC_FALSE, &implicit, NULL);
714   CHKERRQ(ierr);
715   if (!implicit && stab != STAB_NONE) {
716     ierr = PetscPrintf(comm, "Warning! Use -stab only with -implicit\n");
717     CHKERRQ(ierr);
718   }
719   {
720     PetscInt len;
721     PetscBool flg;
722     ierr = PetscOptionsIntArray("-bc_wall",
723                                 "Use wall boundary conditions on this list of faces",
724                                 NULL, bc.walls,
725                                 (len = sizeof(bc.walls) / sizeof(bc.walls[0]),
726                                  &len), &flg); CHKERRQ(ierr);
727     if (flg) bc.nwall = len;
728     for (PetscInt j=0; j<3; j++) {
729       const char *flags[3] = {"-bc_slip_x", "-bc_slip_y", "-bc_slip_z"};
730       ierr = PetscOptionsIntArray(flags[j],
731                                   "Use slip boundary conditions on this list of faces",
732                                   NULL, bc.slips[j],
733                                   (len = sizeof(bc.slips[j]) / sizeof(bc.slips[j][0]),
734                                    &len), &flg);
735       CHKERRQ(ierr);
736       if (flg) {
737         bc.nslip[j] = len;
738         bc.userbc = PETSC_TRUE;
739       }
740     }
741   }
742   ierr = PetscOptionsInt("-viz_refine",
743                          "Regular refinement levels for visualization",
744                          NULL, viz_refine, &viz_refine, NULL);
745   CHKERRQ(ierr);
746   ierr = PetscOptionsScalar("-units_meter", "1 meter in scaled length units",
747                             NULL, meter, &meter, NULL); CHKERRQ(ierr);
748   meter = fabs(meter);
749   ierr = PetscOptionsScalar("-units_second","1 second in scaled time units",
750                             NULL, second, &second, NULL); CHKERRQ(ierr);
751   second = fabs(second);
752   ierr = PetscOptionsScalar("-units_kilogram","1 kilogram in scaled mass units",
753                             NULL, kilogram, &kilogram, NULL); CHKERRQ(ierr);
754   kilogram = fabs(kilogram);
755   ierr = PetscOptionsScalar("-units_Kelvin",
756                             "1 Kelvin in scaled temperature units",
757                             NULL, Kelvin, &Kelvin, NULL); CHKERRQ(ierr);
758   Kelvin = fabs(Kelvin);
759   ierr = PetscOptionsScalar("-theta0", "Reference potential temperature",
760                             NULL, theta0, &theta0, NULL); CHKERRQ(ierr);
761   ierr = PetscOptionsScalar("-thetaC", "Perturbation of potential temperature",
762                             NULL, thetaC, &thetaC, NULL); CHKERRQ(ierr);
763   ierr = PetscOptionsScalar("-P0", "Atmospheric pressure",
764                             NULL, P0, &P0, NULL); CHKERRQ(ierr);
765   ierr = PetscOptionsScalar("-N", "Brunt-Vaisala frequency",
766                             NULL, N, &N, NULL); CHKERRQ(ierr);
767   ierr = PetscOptionsScalar("-cv", "Heat capacity at constant volume",
768                             NULL, cv, &cv, NULL); CHKERRQ(ierr);
769   ierr = PetscOptionsScalar("-cp", "Heat capacity at constant pressure",
770                             NULL, cp, &cp, NULL); CHKERRQ(ierr);
771   ierr = PetscOptionsScalar("-g", "Gravitational acceleration",
772                             NULL, g, &g, NULL); CHKERRQ(ierr);
773   ierr = PetscOptionsScalar("-lambda",
774                             "Stokes hypothesis second viscosity coefficient",
775                             NULL, lambda, &lambda, NULL); CHKERRQ(ierr);
776   ierr = PetscOptionsScalar("-mu", "Shear dynamic viscosity coefficient",
777                             NULL, mu, &mu, NULL); CHKERRQ(ierr);
778   ierr = PetscOptionsScalar("-k", "Thermal conductivity",
779                             NULL, k, &k, NULL); CHKERRQ(ierr);
780   ierr = PetscOptionsScalar("-CtauS",
781                             "Scale coefficient for tau (nondimensional)",
782                             NULL, CtauS, &CtauS, NULL); CHKERRQ(ierr);
783   if (stab == STAB_NONE && CtauS != 0) {
784     ierr = PetscPrintf(comm,
785                        "Warning! Use -CtauS only with -stab su or -stab supg\n");
786     CHKERRQ(ierr);
787   }
788   ierr = PetscOptionsScalar("-strong_form",
789                             "Strong (1) or weak/integrated by parts (0) advection residual",
790                             NULL, strong_form, &strong_form, NULL);
791   CHKERRQ(ierr);
792   ierr = PetscOptionsScalar("-lx", "Length scale in x direction",
793                             NULL, lx, &lx, NULL); CHKERRQ(ierr);
794   ierr = PetscOptionsScalar("-ly", "Length scale in y direction",
795                             NULL, ly, &ly, NULL); CHKERRQ(ierr);
796   ierr = PetscOptionsScalar("-lz", "Length scale in z direction",
797                             NULL, lz, &lz, NULL); CHKERRQ(ierr);
798   ierr = PetscOptionsScalar("-rc", "Characteristic radius of thermal bubble",
799                             NULL, rc, &rc, NULL); CHKERRQ(ierr);
800   ierr = PetscOptionsScalar("-resx","Target resolution in x",
801                             NULL, resx, &resx, NULL); CHKERRQ(ierr);
802   ierr = PetscOptionsScalar("-resy","Target resolution in y",
803                             NULL, resy, &resy, NULL); CHKERRQ(ierr);
804   ierr = PetscOptionsScalar("-resz","Target resolution in z",
805                             NULL, resz, &resz, NULL); CHKERRQ(ierr);
806   PetscInt n = problem->dim;
807   center[0] = 0.5 * lx;
808   center[1] = 0.5 * ly;
809   center[2] = 0.5 * lz;
810   ierr = PetscOptionsRealArray("-center", "Location of bubble center",
811                                NULL, center, &n, NULL); CHKERRQ(ierr);
812   n = problem->dim;
813   ierr = PetscOptionsRealArray("-dc_axis",
814                                "Axis of density current cylindrical anomaly, or {0,0,0} for spherically symmetric",
815                                NULL, dc_axis, &n, NULL); CHKERRQ(ierr);
816   {
817     PetscReal norm = PetscSqrtReal(PetscSqr(dc_axis[0]) +
818                                    PetscSqr(dc_axis[1]) + PetscSqr(dc_axis[2]));
819     if (norm > 0) {
820       for (int i=0; i<3; i++) dc_axis[i] /= norm;
821     }
822   }
823   ierr = PetscOptionsInt("-output_freq",
824                          "Frequency of output, in number of steps",
825                          NULL, outputfreq, &outputfreq, NULL); CHKERRQ(ierr);
826   ierr = PetscOptionsInt("-continue", "Continue from previous solution",
827                          NULL, contsteps, &contsteps, NULL); CHKERRQ(ierr);
828   ierr = PetscOptionsInt("-degree", "Polynomial degree of finite elements",
829                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
830   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
831                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
832   PetscStrncpy(user->outputfolder, ".", 2);
833   ierr = PetscOptionsString("-of", "Output folder",
834                             NULL, user->outputfolder, user->outputfolder,
835                             sizeof(user->outputfolder), NULL); CHKERRQ(ierr);
836   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
837 
838   // Define derived units
839   Pascal = kilogram / (meter * PetscSqr(second));
840   JperkgK =  PetscSqr(meter) / (PetscSqr(second) * Kelvin);
841   mpersquareds = meter / PetscSqr(second);
842   WpermK = kilogram * meter / (pow(second,3) * Kelvin);
843   kgpercubicm = kilogram / pow(meter,3);
844   kgpersquaredms = kilogram / (PetscSqr(meter) * second);
845   Joulepercubicm = kilogram / (meter * PetscSqr(second));
846 
847   // Scale variables to desired units
848   theta0 *= Kelvin;
849   thetaC *= Kelvin;
850   P0 *= Pascal;
851   N *= (1./second);
852   cv *= JperkgK;
853   cp *= JperkgK;
854   Rd = cp - cv;
855   g *= mpersquareds;
856   mu *= Pascal * second;
857   k *= WpermK;
858   lx = fabs(lx) * meter;
859   ly = fabs(ly) * meter;
860   lz = fabs(lz) * meter;
861   rc = fabs(rc) * meter;
862   resx = fabs(resx) * meter;
863   resy = fabs(resy) * meter;
864   resz = fabs(resz) * meter;
865   for (int i=0; i<3; i++) center[i] *= meter;
866 
867   const CeedInt dim = problem->dim, ncompx = problem->dim,
868                 qdatasize = problem->qdatasize;
869   // Set up the libCEED context
870   struct SetupContext_ ctxSetup = {
871     .theta0 = theta0,
872     .thetaC = thetaC,
873     .P0 = P0,
874     .N = N,
875     .cv = cv,
876     .cp = cp,
877     .Rd = Rd,
878     .g = g,
879     .rc = rc,
880     .lx = lx,
881     .ly = ly,
882     .lz = lz,
883     .center[0] = center[0],
884     .center[1] = center[1],
885     .center[2] = center[2],
886     .dc_axis[0] = dc_axis[0],
887     .dc_axis[1] = dc_axis[1],
888     .dc_axis[2] = dc_axis[2],
889     .time = 0,
890   };
891 
892   // Create the mesh
893   {
894     const PetscReal scale[3] = {lx, ly, lz};
895     ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, NULL, NULL, scale,
896                                NULL, PETSC_TRUE, &dm);
897     CHKERRQ(ierr);
898   }
899 
900   // Distribute the mesh over processes
901   {
902     DM               dmDist = NULL;
903     PetscPartitioner part;
904 
905     ierr = DMPlexGetPartitioner(dm, &part); CHKERRQ(ierr);
906     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
907     ierr = DMPlexDistribute(dm, 0, NULL, &dmDist); CHKERRQ(ierr);
908     if (dmDist) {
909       ierr = DMDestroy(&dm); CHKERRQ(ierr);
910       dm  = dmDist;
911     }
912   }
913   ierr = DMViewFromOptions(dm, NULL, "-dm_view"); CHKERRQ(ierr);
914 
915   // Setup DM
916   ierr = DMLocalizeCoordinates(dm); CHKERRQ(ierr);
917   ierr = DMSetFromOptions(dm); CHKERRQ(ierr);
918   ierr = SetUpDM(dm, problem, degree, &bc, &ctxSetup); CHKERRQ(ierr);
919 
920   // Print FEM space information
921   if (!test) {
922     ierr = PetscPrintf(PETSC_COMM_WORLD,
923                        "Degree of FEM space: %D\n",
924                        degree); CHKERRQ(ierr);
925   }
926 
927   // Refine DM for high-order viz
928   dmviz = NULL;
929   interpviz = NULL;
930   if (viz_refine) {
931     DM dmhierarchy[viz_refine+1];
932 
933     ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE); CHKERRQ(ierr);
934     dmhierarchy[0] = dm;
935     for (PetscInt i = 0, d = degree; i < viz_refine; i++) {
936       Mat interp_next;
937 
938       ierr = DMRefine(dmhierarchy[i], MPI_COMM_NULL, &dmhierarchy[i+1]);
939       CHKERRQ(ierr);
940       ierr = DMSetCoarseDM(dmhierarchy[i+1], dmhierarchy[i]); CHKERRQ(ierr);
941       d = (d + 1) / 2;
942       if (i + 1 == viz_refine) d = 1;
943       ierr = SetUpDM(dmhierarchy[i+1], problem, d, &bc, &ctxSetup); CHKERRQ(ierr);
944       ierr = DMCreateInterpolation(dmhierarchy[i], dmhierarchy[i+1],
945                                    &interp_next, NULL); CHKERRQ(ierr);
946       if (!i) interpviz = interp_next;
947       else {
948         Mat C;
949         ierr = MatMatMult(interp_next, interpviz, MAT_INITIAL_MATRIX,
950                           PETSC_DECIDE, &C); CHKERRQ(ierr);
951         ierr = MatDestroy(&interp_next); CHKERRQ(ierr);
952         ierr = MatDestroy(&interpviz); CHKERRQ(ierr);
953         interpviz = C;
954       }
955     }
956     for (PetscInt i=1; i<viz_refine; i++) {
957       ierr = DMDestroy(&dmhierarchy[i]); CHKERRQ(ierr);
958     }
959     dmviz = dmhierarchy[viz_refine];
960   }
961   ierr = DMCreateGlobalVector(dm, &Q); CHKERRQ(ierr);
962   ierr = DMGetLocalVector(dm, &Qloc); CHKERRQ(ierr);
963   ierr = VecGetSize(Qloc, &lnodes); CHKERRQ(ierr);
964   lnodes /= ncompq;
965 
966   {
967     // Print grid information
968     CeedInt gdofs, odofs;
969     int comm_size;
970     char box_faces_str[PETSC_MAX_PATH_LEN] = "NONE";
971     ierr = VecGetSize(Q, &gdofs); CHKERRQ(ierr);
972     ierr = VecGetLocalSize(Q, &odofs); CHKERRQ(ierr);
973     ierr = MPI_Comm_size(comm, &comm_size); CHKERRQ(ierr);
974     ierr = PetscOptionsGetString(NULL, NULL, "-dm_plex_box_faces", box_faces_str,
975                                  sizeof(box_faces_str), NULL); CHKERRQ(ierr);
976     if (!test) {
977       ierr = PetscPrintf(comm, "Global FEM dofs: %D (%D owned) on %d rank(s)\n",
978                          gdofs, odofs, comm_size); CHKERRQ(ierr);
979       ierr = PetscPrintf(comm, "Local FEM nodes: %D\n", lnodes); CHKERRQ(ierr);
980       ierr = PetscPrintf(comm, "dm_plex_box_faces: %s\n", box_faces_str);
981       CHKERRQ(ierr);
982     }
983 
984   }
985 
986   // Set up global mass vector
987   ierr = VecDuplicate(Q, &user->M); CHKERRQ(ierr);
988 
989   // Set up CEED
990   // CEED Bases
991   CeedInit(ceedresource, &ceed);
992   numP = degree + 1;
993   numQ = numP + qextra;
994   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompq, numP, numQ, CEED_GAUSS,
995                                   &basisq);
996   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, numQ, CEED_GAUSS,
997                                   &basisx);
998   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, numP,
999                                   CEED_GAUSS_LOBATTO, &basisxc);
1000 
1001   ierr = DMGetCoordinateDM(dm, &dmcoord); CHKERRQ(ierr);
1002   ierr = DMPlexSetClosurePermutationTensor(dmcoord, PETSC_DETERMINE, NULL);
1003   CHKERRQ(ierr);
1004 
1005   // CEED Restrictions
1006   ierr = CreateRestrictionFromPlex(ceed, dm, degree+1, &restrictq);
1007   CHKERRQ(ierr);
1008   ierr = CreateRestrictionFromPlex(ceed, dmcoord, 2, &restrictx); CHKERRQ(ierr);
1009   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr);
1010   localNelem = cEnd - cStart;
1011   CeedInt numQdim = CeedIntPow(numQ, dim);
1012   CeedElemRestrictionCreateStrided(ceed, localNelem, numQdim,
1013                                    localNelem*numQdim, qdatasize,
1014                                    CEED_STRIDES_BACKEND, &restrictqdi);
1015   CeedElemRestrictionCreateStrided(ceed, localNelem, PetscPowInt(numP, dim),
1016                                    localNelem*PetscPowInt(numP, dim), ncompx,
1017                                    CEED_STRIDES_BACKEND, &restrictxcoord);
1018 
1019   ierr = DMGetCoordinatesLocal(dm, &Xloc); CHKERRQ(ierr);
1020   ierr = CreateVectorFromPetscVec(ceed, Xloc, &xcorners); CHKERRQ(ierr);
1021 
1022   // Create the CEED vectors that will be needed in setup
1023   CeedInt Nqpts;
1024   CeedBasisGetNumQuadraturePoints(basisq, &Nqpts);
1025   CeedVectorCreate(ceed, qdatasize*localNelem*Nqpts, &qdata);
1026   CeedElemRestrictionCreateVector(restrictq, &q0ceed, NULL);
1027 
1028   // Create the Q-function that builds the quadrature data for the NS operator
1029   CeedQFunctionCreateInterior(ceed, 1, problem->setup, problem->setup_loc,
1030                               &qf_setup);
1031   CeedQFunctionAddInput(qf_setup, "dx", ncompx*dim, CEED_EVAL_GRAD);
1032   CeedQFunctionAddInput(qf_setup, "weight", 1, CEED_EVAL_WEIGHT);
1033   CeedQFunctionAddOutput(qf_setup, "qdata", qdatasize, CEED_EVAL_NONE);
1034 
1035   // Create the Q-function that sets the ICs of the operator
1036   CeedQFunctionCreateInterior(ceed, 1, problem->ics, problem->ics_loc, &qf_ics);
1037   CeedQFunctionAddInput(qf_ics, "x", ncompx, CEED_EVAL_INTERP);
1038   CeedQFunctionAddOutput(qf_ics, "q0", ncompq, CEED_EVAL_NONE);
1039 
1040   qf_rhs = NULL;
1041   if (problem->apply_rhs) { // Create the Q-function that defines the action of the RHS operator
1042     CeedQFunctionCreateInterior(ceed, 1, problem->apply_rhs,
1043                                 problem->apply_rhs_loc, &qf_rhs);
1044     CeedQFunctionAddInput(qf_rhs, "q", ncompq, CEED_EVAL_INTERP);
1045     CeedQFunctionAddInput(qf_rhs, "dq", ncompq*dim, CEED_EVAL_GRAD);
1046     CeedQFunctionAddInput(qf_rhs, "qdata", qdatasize, CEED_EVAL_NONE);
1047     CeedQFunctionAddInput(qf_rhs, "x", ncompx, CEED_EVAL_INTERP);
1048     CeedQFunctionAddOutput(qf_rhs, "v", ncompq, CEED_EVAL_INTERP);
1049     CeedQFunctionAddOutput(qf_rhs, "dv", ncompq*dim, CEED_EVAL_GRAD);
1050   }
1051 
1052   qf_ifunction = NULL;
1053   if (problem->apply_ifunction) { // Create the Q-function that defines the action of the IFunction
1054     CeedQFunctionCreateInterior(ceed, 1, problem->apply_ifunction,
1055                                 problem->apply_ifunction_loc, &qf_ifunction);
1056     CeedQFunctionAddInput(qf_ifunction, "q", ncompq, CEED_EVAL_INTERP);
1057     CeedQFunctionAddInput(qf_ifunction, "dq", ncompq*dim, CEED_EVAL_GRAD);
1058     CeedQFunctionAddInput(qf_ifunction, "qdot", ncompq, CEED_EVAL_INTERP);
1059     CeedQFunctionAddInput(qf_ifunction, "qdata", qdatasize, CEED_EVAL_NONE);
1060     CeedQFunctionAddInput(qf_ifunction, "x", ncompx, CEED_EVAL_INTERP);
1061     CeedQFunctionAddOutput(qf_ifunction, "v", ncompq, CEED_EVAL_INTERP);
1062     CeedQFunctionAddOutput(qf_ifunction, "dv", ncompq*dim, CEED_EVAL_GRAD);
1063   }
1064 
1065   // Create the operator that builds the quadrature data for the NS operator
1066   CeedOperatorCreate(ceed, qf_setup, NULL, NULL, &op_setup);
1067   CeedOperatorSetField(op_setup, "dx", restrictx, basisx, CEED_VECTOR_ACTIVE);
1068   CeedOperatorSetField(op_setup, "weight", CEED_ELEMRESTRICTION_NONE,
1069                        basisx, CEED_VECTOR_NONE);
1070   CeedOperatorSetField(op_setup, "qdata", restrictqdi,
1071                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
1072 
1073   // Create the operator that sets the ICs
1074   CeedOperatorCreate(ceed, qf_ics, NULL, NULL, &op_ics);
1075   CeedOperatorSetField(op_ics, "x", restrictx, basisxc, CEED_VECTOR_ACTIVE);
1076   CeedOperatorSetField(op_ics, "q0", restrictq,
1077                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
1078 
1079   CeedElemRestrictionCreateVector(restrictq, &user->qceed, NULL);
1080   CeedElemRestrictionCreateVector(restrictq, &user->qdotceed, NULL);
1081   CeedElemRestrictionCreateVector(restrictq, &user->gceed, NULL);
1082 
1083   if (qf_rhs) { // Create the RHS physics operator
1084     CeedOperator op;
1085     CeedOperatorCreate(ceed, qf_rhs, NULL, NULL, &op);
1086     CeedOperatorSetField(op, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
1087     CeedOperatorSetField(op, "dq", restrictq, basisq, CEED_VECTOR_ACTIVE);
1088     CeedOperatorSetField(op, "qdata", restrictqdi,
1089                          CEED_BASIS_COLLOCATED, qdata);
1090     CeedOperatorSetField(op, "x", restrictx, basisx, xcorners);
1091     CeedOperatorSetField(op, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
1092     CeedOperatorSetField(op, "dv", restrictq, basisq, CEED_VECTOR_ACTIVE);
1093     user->op_rhs = op;
1094   }
1095 
1096   if (qf_ifunction) { // Create the IFunction operator
1097     CeedOperator op;
1098     CeedOperatorCreate(ceed, qf_ifunction, NULL, NULL, &op);
1099     CeedOperatorSetField(op, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
1100     CeedOperatorSetField(op, "dq", restrictq, basisq, CEED_VECTOR_ACTIVE);
1101     CeedOperatorSetField(op, "qdot", restrictq, basisq, user->qdotceed);
1102     CeedOperatorSetField(op, "qdata", restrictqdi,
1103                          CEED_BASIS_COLLOCATED, qdata);
1104     CeedOperatorSetField(op, "x", restrictx, basisx, xcorners);
1105     CeedOperatorSetField(op, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
1106     CeedOperatorSetField(op, "dv", restrictq, basisq, CEED_VECTOR_ACTIVE);
1107     user->op_ifunction = op;
1108   }
1109 
1110   CeedQFunctionSetContext(qf_ics, &ctxSetup, sizeof ctxSetup);
1111   CeedScalar ctxNS[8] = {lambda, mu, k, cv, cp, g, Rd};
1112   struct Advection2dContext_ ctxAdvection2d = {
1113     .CtauS = CtauS,
1114     .strong_form = strong_form,
1115     .stabilization = stab,
1116   };
1117   switch (problemChoice) {
1118   case NS_DENSITY_CURRENT:
1119     if (qf_rhs) CeedQFunctionSetContext(qf_rhs, &ctxNS, sizeof ctxNS);
1120     if (qf_ifunction) CeedQFunctionSetContext(qf_ifunction, &ctxNS,
1121           sizeof ctxNS);
1122     break;
1123   case NS_ADVECTION:
1124   case NS_ADVECTION2D:
1125     if (qf_rhs) CeedQFunctionSetContext(qf_rhs, &ctxAdvection2d,
1126                                           sizeof ctxAdvection2d);
1127     if (qf_ifunction) CeedQFunctionSetContext(qf_ifunction, &ctxAdvection2d,
1128           sizeof ctxAdvection2d);
1129   }
1130 
1131   // Set up PETSc context
1132   // Set up units structure
1133   units->meter = meter;
1134   units->kilogram = kilogram;
1135   units->second = second;
1136   units->Kelvin = Kelvin;
1137   units->Pascal = Pascal;
1138   units->JperkgK = JperkgK;
1139   units->mpersquareds = mpersquareds;
1140   units->WpermK = WpermK;
1141   units->kgpercubicm = kgpercubicm;
1142   units->kgpersquaredms = kgpersquaredms;
1143   units->Joulepercubicm = Joulepercubicm;
1144 
1145   // Set up user structure
1146   user->comm = comm;
1147   user->outputfreq = outputfreq;
1148   user->contsteps = contsteps;
1149   user->units = units;
1150   user->dm = dm;
1151   user->dmviz = dmviz;
1152   user->interpviz = interpviz;
1153   user->ceed = ceed;
1154 
1155   // Calculate qdata and ICs
1156   // Set up state global and local vectors
1157   ierr = VecZeroEntries(Q); CHKERRQ(ierr);
1158 
1159   ierr = VectorPlacePetscVec(q0ceed, Qloc); CHKERRQ(ierr);
1160 
1161   // Apply Setup Ceed Operators
1162   ierr = VectorPlacePetscVec(xcorners, Xloc); CHKERRQ(ierr);
1163   CeedOperatorApply(op_setup, xcorners, qdata, CEED_REQUEST_IMMEDIATE);
1164   ierr = ComputeLumpedMassMatrix(ceed, dm, restrictq, basisq, restrictqdi, qdata,
1165                                  user->M); CHKERRQ(ierr);
1166 
1167   ierr = ICs_FixMultiplicity(op_ics, xcorners, q0ceed, dm, Qloc, Q, restrictq,
1168                              &ctxSetup, 0.0);
1169   if (1) { // Record boundary values from initial condition and override DMPlexInsertBoundaryValues()
1170     // We use this for the main simulation DM because the reference DMPlexInsertBoundaryValues() is very slow.  If we
1171     // disable this, we should still get the same results due to the problem->bc function, but with potentially much
1172     // slower execution.
1173     Vec Qbc;
1174     ierr = DMGetNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
1175     ierr = VecCopy(Qloc, Qbc); CHKERRQ(ierr);
1176     ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
1177     ierr = DMGlobalToLocal(dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
1178     ierr = VecAXPY(Qbc, -1., Qloc); CHKERRQ(ierr);
1179     ierr = DMRestoreNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
1180     ierr = PetscObjectComposeFunction((PetscObject)dm,
1181                                       "DMPlexInsertBoundaryValues_C", DMPlexInsertBoundaryValues_NS);
1182     CHKERRQ(ierr);
1183   }
1184 
1185   MPI_Comm_rank(comm, &rank);
1186   if (!rank) {ierr = PetscMkdir(user->outputfolder); CHKERRQ(ierr);}
1187   // Gather initial Q values
1188   // In case of continuation of simulation, set up initial values from binary file
1189   if (contsteps) { // continue from existent solution
1190     PetscViewer viewer;
1191     char filepath[PETSC_MAX_PATH_LEN];
1192     // Read input
1193     ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-solution.bin",
1194                          user->outputfolder);
1195     CHKERRQ(ierr);
1196     ierr = PetscViewerBinaryOpen(comm, filepath, FILE_MODE_READ, &viewer);
1197     CHKERRQ(ierr);
1198     ierr = VecLoad(Q, viewer); CHKERRQ(ierr);
1199     ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
1200   }
1201   ierr = DMRestoreLocalVector(dm, &Qloc); CHKERRQ(ierr);
1202 
1203   // Create and setup TS
1204   ierr = TSCreate(comm, &ts); CHKERRQ(ierr);
1205   ierr = TSSetDM(ts, dm); CHKERRQ(ierr);
1206   if (implicit) {
1207     ierr = TSSetType(ts, TSBDF); CHKERRQ(ierr);
1208     if (user->op_ifunction) {
1209       ierr = TSSetIFunction(ts, NULL, IFunction_NS, &user); CHKERRQ(ierr);
1210     } else {                    // Implicit integrators can fall back to using an RHSFunction
1211       ierr = TSSetRHSFunction(ts, NULL, RHS_NS, &user); CHKERRQ(ierr);
1212     }
1213   } else {
1214     if (!user->op_rhs) SETERRQ(comm,PETSC_ERR_ARG_NULL,
1215                                  "Problem does not provide RHSFunction");
1216     ierr = TSSetType(ts, TSRK); CHKERRQ(ierr);
1217     ierr = TSRKSetType(ts, TSRK5F); CHKERRQ(ierr);
1218     ierr = TSSetRHSFunction(ts, NULL, RHS_NS, &user); CHKERRQ(ierr);
1219   }
1220   ierr = TSSetMaxTime(ts, 500. * units->second); CHKERRQ(ierr);
1221   ierr = TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER); CHKERRQ(ierr);
1222   ierr = TSSetTimeStep(ts, 1.e-2 * units->second); CHKERRQ(ierr);
1223   if (test) {ierr = TSSetMaxSteps(ts, 10); CHKERRQ(ierr);}
1224   ierr = TSGetAdapt(ts, &adapt); CHKERRQ(ierr);
1225   ierr = TSAdaptSetStepLimits(adapt,
1226                               1.e-12 * units->second,
1227                               1.e2 * units->second); CHKERRQ(ierr);
1228   ierr = TSSetFromOptions(ts); CHKERRQ(ierr);
1229   if (!contsteps) { // print initial condition
1230     if (!test) {
1231       ierr = TSMonitor_NS(ts, 0, 0., Q, user); CHKERRQ(ierr);
1232     }
1233   } else { // continue from time of last output
1234     PetscReal time;
1235     PetscInt count;
1236     PetscViewer viewer;
1237     char filepath[PETSC_MAX_PATH_LEN];
1238     ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-time.bin",
1239                          user->outputfolder); CHKERRQ(ierr);
1240     ierr = PetscViewerBinaryOpen(comm, filepath, FILE_MODE_READ, &viewer);
1241     CHKERRQ(ierr);
1242     ierr = PetscViewerBinaryRead(viewer, &time, 1, &count, PETSC_REAL);
1243     CHKERRQ(ierr);
1244     ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
1245     ierr = TSSetTime(ts, time * user->units->second); CHKERRQ(ierr);
1246   }
1247   if (!test) {
1248     ierr = TSMonitorSet(ts, TSMonitor_NS, user, NULL); CHKERRQ(ierr);
1249   }
1250 
1251   // Solve
1252   start = MPI_Wtime();
1253   ierr = PetscBarrier((PetscObject)ts); CHKERRQ(ierr);
1254   ierr = TSSolve(ts, Q); CHKERRQ(ierr);
1255   cpu_time_used = MPI_Wtime() - start;
1256   ierr = TSGetSolveTime(ts, &ftime); CHKERRQ(ierr);
1257   ierr = MPI_Allreduce(MPI_IN_PLACE, &cpu_time_used, 1, MPI_DOUBLE, MPI_MIN,
1258                        comm); CHKERRQ(ierr);
1259   if (!test) {
1260     ierr = PetscPrintf(PETSC_COMM_WORLD,
1261                        "Time taken for solution (sec): %g\n",
1262                        (double)cpu_time_used); CHKERRQ(ierr);
1263   }
1264 
1265   // Get error
1266   if (problem->non_zero_time && !test) {
1267     Vec Qexact, Qexactloc;
1268     PetscReal norm;
1269     ierr = DMCreateGlobalVector(dm, &Qexact); CHKERRQ(ierr);
1270     ierr = DMGetLocalVector(dm, &Qexactloc); CHKERRQ(ierr);
1271     ierr = VecGetSize(Qexactloc, &lnodes); CHKERRQ(ierr);
1272 
1273     ierr = ICs_FixMultiplicity(op_ics, xcorners, q0ceed, dm, Qexactloc, Qexact,
1274                                restrictq, &ctxSetup, ftime); CHKERRQ(ierr);
1275 
1276     ierr = VecAXPY(Q, -1.0, Qexact);  CHKERRQ(ierr);
1277     ierr = VecNorm(Q, NORM_MAX, &norm); CHKERRQ(ierr);
1278     CeedVectorDestroy(&q0ceed);
1279     ierr = PetscPrintf(PETSC_COMM_WORLD,
1280                        "Max Error: %g\n",
1281                        (double)norm); CHKERRQ(ierr);
1282     // Clean up vectors
1283     ierr = DMRestoreLocalVector(dm, &Qexactloc); CHKERRQ(ierr);
1284     ierr = VecDestroy(&Qexact); CHKERRQ(ierr);
1285   }
1286 
1287   // Output Statistics
1288   ierr = TSGetStepNumber(ts,&steps); CHKERRQ(ierr);
1289   if (!test) {
1290     ierr = PetscPrintf(PETSC_COMM_WORLD,
1291                        "Time integrator took %D time steps to reach final time %g\n",
1292                        steps, (double)ftime); CHKERRQ(ierr);
1293   }
1294   // Output numerical values from command line
1295   ierr = VecViewFromOptions(Q, NULL, "-vec_view"); CHKERRQ(ierr);
1296 
1297   // Clean up libCEED
1298   CeedVectorDestroy(&qdata);
1299   CeedVectorDestroy(&user->qceed);
1300   CeedVectorDestroy(&user->qdotceed);
1301   CeedVectorDestroy(&user->gceed);
1302   CeedVectorDestroy(&xcorners);
1303   CeedBasisDestroy(&basisq);
1304   CeedBasisDestroy(&basisx);
1305   CeedBasisDestroy(&basisxc);
1306   CeedElemRestrictionDestroy(&restrictq);
1307   CeedElemRestrictionDestroy(&restrictx);
1308   CeedElemRestrictionDestroy(&restrictqdi);
1309   CeedElemRestrictionDestroy(&restrictxcoord);
1310   CeedQFunctionDestroy(&qf_setup);
1311   CeedQFunctionDestroy(&qf_ics);
1312   CeedQFunctionDestroy(&qf_rhs);
1313   CeedQFunctionDestroy(&qf_ifunction);
1314   CeedOperatorDestroy(&op_setup);
1315   CeedOperatorDestroy(&op_ics);
1316   CeedOperatorDestroy(&user->op_rhs);
1317   CeedOperatorDestroy(&user->op_ifunction);
1318   CeedDestroy(&ceed);
1319 
1320   // Clean up PETSc
1321   ierr = VecDestroy(&Q); CHKERRQ(ierr);
1322   ierr = VecDestroy(&user->M); CHKERRQ(ierr);
1323   ierr = MatDestroy(&interpviz); CHKERRQ(ierr);
1324   ierr = DMDestroy(&dmviz); CHKERRQ(ierr);
1325   ierr = TSDestroy(&ts); CHKERRQ(ierr);
1326   ierr = DMDestroy(&dm); CHKERRQ(ierr);
1327   ierr = PetscFree(units); CHKERRQ(ierr);
1328   ierr = PetscFree(user); CHKERRQ(ierr);
1329   return PetscFinalize();
1330 }
1331 
1332