xref: /libCEED/examples/solids/elasticity.c (revision 8a4ce0d78b95fffc485d7f6e76eabd31204930a1)
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: Elasticity
18 //
19 // This example demonstrates a simple usage of libCEED with PETSc to solve
20 //   elasticity problems.
21 //
22 // The code uses higher level communication protocols in DMPlex.
23 //
24 // Build with:
25 //
26 //     make elasticity [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>]
27 //
28 // Sample runs:
29 //
30 //     ./elasticity -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -problem linElas -forcing mms
31 //     ./elasticity -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -bc_clamp 998,999 -bc_clamp_998_translate 0.1,0.2,0.3 -problem hyperSS -forcing none -ceed /cpu/self
32 //     ./elasticity -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -bc_clamp 998,999 -bc_clamp_998_rotate 1,0,0,0.2 -problem hyperFS -forcing none -ceed /gpu/cuda
33 //
34 // Sample meshes can be found at https://github.com/jeremylt/ceedSampleMeshes
35 //
36 //TESTARGS -ceed {ceed_resource} -test -degree 3 -nu 0.3 -E 1 -dm_plex_box_faces 3,3,3
37 
38 /// @file
39 /// CEED elasticity example using PETSc with DMPlex
40 
41 const char help[] = "Solve solid Problems with CEED and PETSc DMPlex\n";
42 
43 #include "elasticity.h"
44 
45 int main(int argc, char **argv) {
46   PetscInt       ierr;
47   MPI_Comm       comm;
48   // Context structs
49   AppCtx         appCtx;                 // Contains problem options
50   Physics        phys;                   // Contains physical constants
51   Physics        physSmoother = NULL;    // Separate context if nuSmoother set
52   Units          units;                  // Contains units scaling
53   // PETSc objects
54   PetscLogStage  stageDMSetup, stageLibceedSetup,
55                  stageSnesSetup, stageSnesSolve;
56   DM             dmOrig;                 // Distributed DM to clone
57   DM             dmEnergy, dmDiagnostic; // DMs for postprocessing
58   DM             *levelDMs;
59   Vec            U, *Ug, *Uloc;          // U: solution, R: residual, F: forcing
60   Vec            R, Rloc, F, Floc;       // g: global, loc: local
61   Vec            NBCs = NULL, NBCsloc = NULL;
62   SNES           snes, snesCoarse = NULL;
63   Mat            *jacobMat, jacobMatCoarse, *prolongRestrMat;
64   // PETSc data
65   UserMult       resCtx, jacobCoarseCtx = NULL, *jacobCtx;
66   FormJacobCtx   formJacobCtx;
67   UserMultProlongRestr *prolongRestrCtx;
68   PCMGCycleType  pcmgCycleType = PC_MG_CYCLE_V;
69   // libCEED objects
70   Ceed           ceed;
71   CeedData       *ceedData;
72   CeedQFunctionContext ctxPhys, ctxPhysSmoother = NULL;
73   // Parameters
74   PetscInt       ncompu = 3;             // 3 DoFs in 3D
75   PetscInt       ncompe = 1, ncompd = 5; // 1 energy output, 5 diagnostic
76   PetscInt       numLevels = 1, fineLevel = 0;
77   PetscInt       *Ugsz, *Ulsz, *Ulocsz;  // sz: size
78   PetscInt       snesIts = 0, kspIts = 0;
79   // Timing
80   double         startTime, elapsedTime, minTime, maxTime;
81 
82   ierr = PetscInitialize(&argc, &argv, NULL, help);
83   if (ierr)
84     return ierr;
85 
86   // ---------------------------------------------------------------------------
87   // Process command line options
88   // ---------------------------------------------------------------------------
89   comm = PETSC_COMM_WORLD;
90 
91   // -- Set mesh file, polynomial degree, problem type
92   ierr = PetscCalloc1(1, &appCtx); CHKERRQ(ierr);
93   ierr = ProcessCommandLineOptions(comm, appCtx); CHKERRQ(ierr);
94   numLevels = appCtx->numLevels;
95   fineLevel = numLevels - 1;
96 
97   // -- Set Poison's ratio, Young's Modulus
98   ierr = PetscMalloc1(1, &phys); CHKERRQ(ierr);
99   ierr = PetscMalloc1(1, &units); CHKERRQ(ierr);
100   ierr = ProcessPhysics(comm, phys, units); CHKERRQ(ierr);
101   if (fabs(appCtx->nuSmoother) > 1E-14) {
102     ierr = PetscMalloc1(1, &physSmoother); CHKERRQ(ierr);
103     ierr = PetscMemcpy(physSmoother, phys, sizeof(*phys)); CHKERRQ(ierr);
104     physSmoother->nu = appCtx->nuSmoother;
105   }
106 
107   // ---------------------------------------------------------------------------
108   // Initalize libCEED
109   // ---------------------------------------------------------------------------
110   // Initalize backend
111   CeedInit(appCtx->ceedResource, &ceed);
112 
113   // Check preferred MemType
114   CeedMemType memTypeBackend;
115   CeedGetPreferredMemType(ceed, &memTypeBackend);
116   if (!appCtx->setMemTypeRequest)
117     appCtx->memTypeRequested = memTypeBackend;
118   else if (!appCtx->petscHaveCuda && appCtx->memTypeRequested == CEED_MEM_DEVICE)
119     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP_SYS,
120              "PETSc was not built with CUDA. "
121              "Requested MemType CEED_MEM_DEVICE is not supported.", NULL);
122 
123   // Wrap context in libCEED objects
124   CeedQFunctionContextCreate(ceed, &ctxPhys);
125   CeedQFunctionContextSetData(ctxPhys, CEED_MEM_HOST, CEED_USE_POINTER,
126                               sizeof(*phys), phys);
127   if (physSmoother) {
128     CeedQFunctionContextCreate(ceed, &ctxPhysSmoother);
129     CeedQFunctionContextSetData(ctxPhysSmoother, CEED_MEM_HOST, CEED_USE_POINTER,
130                                 sizeof(*physSmoother), physSmoother);
131   }
132 
133   // ---------------------------------------------------------------------------
134   // Setup DM
135   // ---------------------------------------------------------------------------
136   // Performance logging
137   ierr = PetscLogStageRegister("DM and Vector Setup Stage", &stageDMSetup);
138   CHKERRQ(ierr);
139   ierr = PetscLogStagePush(stageDMSetup); CHKERRQ(ierr);
140 
141   // -- Create distributed DM from mesh file
142   ierr = CreateDistributedDM(comm, appCtx, &dmOrig); CHKERRQ(ierr);
143 
144   // -- Setup DM by polynomial degree
145   ierr = PetscMalloc1(numLevels, &levelDMs); CHKERRQ(ierr);
146   for (PetscInt level = 0; level < numLevels; level++) {
147     ierr = DMClone(dmOrig, &levelDMs[level]); CHKERRQ(ierr);
148     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
149       ierr = DMSetVecType(levelDMs[level], VECCUDA); CHKERRQ(ierr);
150     }
151     ierr = SetupDMByDegree(levelDMs[level], appCtx, appCtx->levelDegrees[level],
152                            PETSC_TRUE, ncompu); CHKERRQ(ierr);
153     // -- Label field components for viewing
154     // Empty name for conserved field (because there is only one field)
155     PetscSection section;
156     ierr = DMGetLocalSection(levelDMs[level], &section); CHKERRQ(ierr);
157     ierr = PetscSectionSetFieldName(section, 0, "Displacement"); CHKERRQ(ierr);
158     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
159     CHKERRQ(ierr);
160     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
161     CHKERRQ(ierr);
162     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
163     CHKERRQ(ierr);
164   }
165 
166   // -- Setup postprocessing DMs
167   ierr = DMClone(dmOrig, &dmEnergy); CHKERRQ(ierr);
168   ierr = SetupDMByDegree(dmEnergy, appCtx, appCtx->levelDegrees[fineLevel],
169                          PETSC_FALSE, ncompe); CHKERRQ(ierr);
170   ierr = DMClone(dmOrig, &dmDiagnostic); CHKERRQ(ierr);
171   ierr = SetupDMByDegree(dmDiagnostic, appCtx, appCtx->levelDegrees[fineLevel],
172                          PETSC_FALSE, ncompu + ncompd); CHKERRQ(ierr);
173   if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
174     ierr = DMSetVecType(dmEnergy, VECCUDA); CHKERRQ(ierr);
175     ierr = DMSetVecType(dmDiagnostic, VECCUDA); CHKERRQ(ierr);
176   }
177   {
178     // -- Label field components for viewing
179     // Empty name for conserved field (because there is only one field)
180     PetscSection section;
181     ierr = DMGetLocalSection(dmDiagnostic, &section); CHKERRQ(ierr);
182     ierr = PetscSectionSetFieldName(section, 0, "Diagnostics"); CHKERRQ(ierr);
183     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
184     CHKERRQ(ierr);
185     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
186     CHKERRQ(ierr);
187     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
188     CHKERRQ(ierr);
189     ierr = PetscSectionSetComponentName(section, 0, 3, "Pressure");
190     CHKERRQ(ierr);
191     ierr = PetscSectionSetComponentName(section, 0, 4, "VolumentricStrain");
192     CHKERRQ(ierr);
193     ierr = PetscSectionSetComponentName(section, 0, 5, "TraceE2");
194     CHKERRQ(ierr);
195     ierr = PetscSectionSetComponentName(section, 0, 6, "detJ");
196     CHKERRQ(ierr);
197     ierr = PetscSectionSetComponentName(section, 0, 7, "StrainEnergyDensity");
198     CHKERRQ(ierr);
199   }
200 
201   // ---------------------------------------------------------------------------
202   // Setup solution and work vectors
203   // ---------------------------------------------------------------------------
204   // Allocate arrays
205   ierr = PetscMalloc1(numLevels, &Ug); CHKERRQ(ierr);
206   ierr = PetscMalloc1(numLevels, &Uloc); CHKERRQ(ierr);
207   ierr = PetscMalloc1(numLevels, &Ugsz); CHKERRQ(ierr);
208   ierr = PetscMalloc1(numLevels, &Ulsz); CHKERRQ(ierr);
209   ierr = PetscMalloc1(numLevels, &Ulocsz); CHKERRQ(ierr);
210 
211   // -- Setup solution vectors for each level
212   for (PetscInt level = 0; level < numLevels; level++) {
213     // -- Create global unknown vector U
214     ierr = DMCreateGlobalVector(levelDMs[level], &Ug[level]); CHKERRQ(ierr);
215     ierr = VecGetSize(Ug[level], &Ugsz[level]); CHKERRQ(ierr);
216     // Note: Local size for matShell
217     ierr = VecGetLocalSize(Ug[level], &Ulsz[level]); CHKERRQ(ierr);
218 
219     // -- Create local unknown vector Uloc
220     ierr = DMCreateLocalVector(levelDMs[level], &Uloc[level]); CHKERRQ(ierr);
221     // Note: local size for libCEED
222     ierr = VecGetSize(Uloc[level], &Ulocsz[level]); CHKERRQ(ierr);
223   }
224 
225   // -- Create residual and forcing vectors
226   ierr = VecDuplicate(Ug[fineLevel], &U); CHKERRQ(ierr);
227   ierr = VecDuplicate(Ug[fineLevel], &R); CHKERRQ(ierr);
228   ierr = VecDuplicate(Ug[fineLevel], &F); CHKERRQ(ierr);
229   ierr = VecDuplicate(Uloc[fineLevel], &Rloc); CHKERRQ(ierr);
230   ierr = VecDuplicate(Uloc[fineLevel], &Floc); CHKERRQ(ierr);
231 
232   // Performance logging
233   ierr = PetscLogStagePop();
234 
235   // ---------------------------------------------------------------------------
236   // Set up libCEED
237   // ---------------------------------------------------------------------------
238   // Performance logging
239   ierr = PetscLogStageRegister("libCEED Setup Stage", &stageLibceedSetup);
240   CHKERRQ(ierr);
241   ierr = PetscLogStagePush(stageLibceedSetup); CHKERRQ(ierr);
242 
243   // -- Create libCEED local forcing vector
244   CeedVector forceCeed;
245   CeedScalar *f;
246   if (appCtx->forcingChoice != FORCE_NONE) {
247     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
248       ierr = VecGetArray(Floc, &f); CHKERRQ(ierr);
249     } else {
250       ierr = VecCUDAGetArray(Floc, &f); CHKERRQ(ierr);
251     }
252     CeedVectorCreate(ceed, Ulocsz[fineLevel], &forceCeed);
253     CeedVectorSetArray(forceCeed, appCtx->memTypeRequested, CEED_USE_POINTER, f);
254   }
255 
256   // -- Create libCEED local Neumann BCs vector
257   CeedVector neumannCeed;
258   CeedScalar *n;
259   if (appCtx->bcTractionCount > 0) {
260     ierr = VecDuplicate(U, &NBCs); CHKERRQ(ierr);
261     ierr = VecDuplicate(Uloc[fineLevel], &NBCsloc); CHKERRQ(ierr);
262     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
263       ierr = VecGetArray(NBCsloc, &n); CHKERRQ(ierr);
264     } else {
265       ierr = VecCUDAGetArray(NBCsloc, &n); CHKERRQ(ierr);
266     }
267     CeedVectorCreate(ceed, Ulocsz[fineLevel], &neumannCeed);
268     CeedVectorSetArray(neumannCeed, appCtx->memTypeRequested,
269                        CEED_USE_POINTER, n);
270   }
271 
272   // -- Setup libCEED objects
273   ierr = PetscMalloc1(numLevels, &ceedData); CHKERRQ(ierr);
274   // ---- Setup residual, Jacobian evaluator and geometric information
275   ierr = PetscCalloc1(1, &ceedData[fineLevel]); CHKERRQ(ierr);
276   {
277     ierr = SetupLibceedFineLevel(levelDMs[fineLevel], dmEnergy, dmDiagnostic,
278                                  ceed, appCtx, ctxPhys, ceedData, fineLevel,
279                                  ncompu, Ugsz[fineLevel], Ulocsz[fineLevel],
280                                  forceCeed, neumannCeed);
281     CHKERRQ(ierr);
282   }
283   // ---- Setup coarse Jacobian evaluator and prolongation/restriction
284   for (PetscInt level = numLevels - 2; level >= 0; level--) {
285     ierr = PetscCalloc1(1, &ceedData[level]); CHKERRQ(ierr);
286 
287     // Get global communication restriction
288     ierr = VecZeroEntries(Ug[level+1]); CHKERRQ(ierr);
289     ierr = VecSet(Uloc[level+1], 1.0); CHKERRQ(ierr);
290     ierr = DMLocalToGlobal(levelDMs[level+1], Uloc[level+1], ADD_VALUES,
291                            Ug[level+1]); CHKERRQ(ierr);
292     ierr = DMGlobalToLocal(levelDMs[level+1], Ug[level+1], INSERT_VALUES,
293                            Uloc[level+1]); CHKERRQ(ierr);
294 
295     // Place in libCEED array
296     const PetscScalar *m;
297     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
298       ierr = VecGetArrayRead(Uloc[level+1], &m); CHKERRQ(ierr);
299     } else {
300       ierr = VecCUDAGetArrayRead(Uloc[level+1], &m); CHKERRQ(ierr);
301     }
302     CeedVectorSetArray(ceedData[level+1]->xceed, appCtx->memTypeRequested,
303                        CEED_USE_POINTER, (CeedScalar *)m);
304 
305     // Note: use high order ceed, if specified and degree > 4
306     ierr = SetupLibceedLevel(levelDMs[level], ceed, appCtx,
307                              ceedData, level, ncompu, Ugsz[level],
308                              Ulocsz[level], ceedData[level+1]->xceed);
309     CHKERRQ(ierr);
310 
311     // Restore PETSc vector
312     CeedVectorTakeArray(ceedData[level+1]->xceed, appCtx->memTypeRequested,
313                         (CeedScalar **)&m);
314     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
315       ierr = VecRestoreArrayRead(Uloc[level+1], &m); CHKERRQ(ierr);
316     } else {
317       ierr = VecCUDARestoreArrayRead(Uloc[level+1], &m); CHKERRQ(ierr);
318     }
319     ierr = VecZeroEntries(Ug[level+1]); CHKERRQ(ierr);
320     ierr = VecZeroEntries(Uloc[level+1]); CHKERRQ(ierr);
321   }
322 
323   // Performance logging
324   ierr = PetscLogStagePop();
325 
326   // ---------------------------------------------------------------------------
327   // Setup global forcing and Neumann BC vectors
328   // ---------------------------------------------------------------------------
329   ierr = VecZeroEntries(F); CHKERRQ(ierr);
330 
331   if (appCtx->forcingChoice != FORCE_NONE) {
332     CeedVectorTakeArray(forceCeed, appCtx->memTypeRequested, NULL);
333     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
334       ierr = VecRestoreArray(Floc, &f); CHKERRQ(ierr);
335     } else {
336       ierr = VecCUDARestoreArray(Floc, &f); CHKERRQ(ierr);
337     }
338     ierr = DMLocalToGlobal(levelDMs[fineLevel], Floc, ADD_VALUES, F);
339     CHKERRQ(ierr);
340     CeedVectorDestroy(&forceCeed);
341   }
342 
343   if (appCtx->bcTractionCount > 0) {
344     ierr = VecZeroEntries(NBCs); CHKERRQ(ierr);
345     CeedVectorTakeArray(neumannCeed, appCtx->memTypeRequested, NULL);
346     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
347       ierr = VecRestoreArray(NBCsloc, &n); CHKERRQ(ierr);
348     } else {
349       ierr = VecCUDARestoreArray(NBCsloc, &n); CHKERRQ(ierr);
350     }
351     ierr = DMLocalToGlobal(levelDMs[fineLevel], NBCsloc, ADD_VALUES, NBCs);
352     CHKERRQ(ierr);
353     CeedVectorDestroy(&neumannCeed);
354   }
355 
356   // ---------------------------------------------------------------------------
357   // Print problem summary
358   // ---------------------------------------------------------------------------
359   if (!appCtx->testMode) {
360     const char *usedresource;
361     CeedGetResource(ceed, &usedresource);
362 
363     ierr = PetscPrintf(comm,
364                        "\n-- Elasticity Example - libCEED + PETSc --\n"
365                        "  libCEED:\n"
366                        "    libCEED Backend                    : %s\n"
367                        "    libCEED Backend MemType            : %s\n"
368                        "    libCEED User Requested MemType     : %s\n",
369                        usedresource, CeedMemTypes[memTypeBackend],
370                        (appCtx->setMemTypeRequest) ?
371                        CeedMemTypes[appCtx->memTypeRequested] : "none");
372     CHKERRQ(ierr);
373 
374     VecType vecType;
375     ierr = VecGetType(U, &vecType); CHKERRQ(ierr);
376     ierr = PetscPrintf(comm,
377                        "  PETSc:\n"
378                        "    PETSc Vec Type                     : %s\n",
379                        vecType); CHKERRQ(ierr);
380 
381     ierr = PetscPrintf(comm,
382                        "  Problem:\n"
383                        "    Problem Name                       : %s\n"
384                        "    Forcing Function                   : %s\n"
385                        "  Mesh:\n"
386                        "    File                               : %s\n"
387                        "    Number of 1D Basis Nodes (p)       : %d\n"
388                        "    Number of 1D Quadrature Points (q) : %d\n"
389                        "    Global nodes                       : %D\n"
390                        "    Owned nodes                        : %D\n"
391                        "    DoF per node                       : %D\n"
392                        "  Multigrid:\n"
393                        "    Type                               : %s\n"
394                        "    Number of Levels                   : %d\n",
395                        problemTypesForDisp[appCtx->problemChoice],
396                        forcingTypesForDisp[appCtx->forcingChoice],
397                        appCtx->meshFile[0] ? appCtx->meshFile : "Box Mesh",
398                        appCtx->degree + 1, appCtx->degree + 1,
399                        Ugsz[fineLevel]/ncompu, Ulsz[fineLevel]/ncompu, ncompu,
400                        (appCtx->degree == 1 &&
401                         appCtx->multigridChoice != MULTIGRID_NONE) ?
402                        "Algebraic multigrid" :
403                        multigridTypesForDisp[appCtx->multigridChoice],
404                        (appCtx->degree == 1 ||
405                         appCtx->multigridChoice == MULTIGRID_NONE) ?
406                        0 : numLevels); CHKERRQ(ierr);
407 
408     if (appCtx->multigridChoice != MULTIGRID_NONE) {
409       for (PetscInt i = 0; i < 2; i++) {
410         CeedInt level = i ? fineLevel : 0;
411         ierr = PetscPrintf(comm,
412                            "    Level %D (%s):\n"
413                            "      Number of 1D Basis Nodes (p)     : %d\n"
414                            "      Global Nodes                     : %D\n"
415                            "      Owned Nodes                      : %D\n",
416                            level, i ? "fine" : "coarse",
417                            appCtx->levelDegrees[level] + 1,
418                            Ugsz[level]/ncompu, Ulsz[level]/ncompu);
419         CHKERRQ(ierr);
420       }
421     }
422   }
423 
424   // ---------------------------------------------------------------------------
425   // Setup SNES
426   // ---------------------------------------------------------------------------
427   // Performance logging
428   ierr = PetscLogStageRegister("SNES Setup Stage", &stageSnesSetup);
429   CHKERRQ(ierr);
430   ierr = PetscLogStagePush(stageSnesSetup); CHKERRQ(ierr);
431 
432   // Create SNES
433   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
434   ierr = SNESSetDM(snes, levelDMs[fineLevel]); CHKERRQ(ierr);
435 
436   // -- Jacobian evaluators
437   ierr = PetscMalloc1(numLevels, &jacobCtx); CHKERRQ(ierr);
438   ierr = PetscMalloc1(numLevels, &jacobMat); CHKERRQ(ierr);
439   for (PetscInt level = 0; level < numLevels; level++) {
440     // -- Jacobian context for level
441     ierr = PetscMalloc1(1, &jacobCtx[level]); CHKERRQ(ierr);
442     ierr = SetupJacobianCtx(comm, appCtx, levelDMs[level], Ug[level],
443                             Uloc[level], ceedData[level], ceed, ctxPhys,
444                             ctxPhysSmoother, jacobCtx[level]); CHKERRQ(ierr);
445 
446     // -- Form Action of Jacobian on delta_u
447     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level], Ugsz[level],
448                           Ugsz[level], jacobCtx[level], &jacobMat[level]);
449     CHKERRQ(ierr);
450     ierr = MatShellSetOperation(jacobMat[level], MATOP_MULT,
451                                 (void (*)(void))ApplyJacobian_Ceed);
452     CHKERRQ(ierr);
453     ierr = MatShellSetOperation(jacobMat[level], MATOP_GET_DIAGONAL,
454                                 (void(*)(void))GetDiag_Ceed);
455     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
456       ierr = MatShellSetVecType(jacobMat[level], VECCUDA); CHKERRQ(ierr);
457     }
458   }
459   // Note: FormJacobian updates Jacobian matrices on each level
460   //   and assembles the Jpre matrix, if needed
461   ierr = PetscMalloc1(1, &formJacobCtx); CHKERRQ(ierr);
462   formJacobCtx->jacobCtx = jacobCtx;
463   formJacobCtx->numLevels = numLevels;
464   formJacobCtx->jacobMat = jacobMat;
465 
466   // -- Residual evaluation function
467   ierr = PetscCalloc1(1, &resCtx); CHKERRQ(ierr);
468   ierr = PetscMemcpy(resCtx, jacobCtx[fineLevel],
469                      sizeof(*jacobCtx[fineLevel])); CHKERRQ(ierr);
470   resCtx->op = ceedData[fineLevel]->opApply;
471   resCtx->qf = ceedData[fineLevel]->qfApply;
472   if (appCtx->bcTractionCount > 0)
473     resCtx->NBCs = NBCs;
474   else
475     resCtx->NBCs = NULL;
476   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, resCtx); CHKERRQ(ierr);
477 
478   // -- Prolongation/Restriction evaluation
479   ierr = PetscMalloc1(numLevels, &prolongRestrCtx); CHKERRQ(ierr);
480   ierr = PetscMalloc1(numLevels, &prolongRestrMat); CHKERRQ(ierr);
481   for (PetscInt level = 1; level < numLevels; level++) {
482     // ---- Prolongation/restriction context for level
483     ierr = PetscMalloc1(1, &prolongRestrCtx[level]); CHKERRQ(ierr);
484     ierr = SetupProlongRestrictCtx(comm, appCtx, levelDMs[level-1],
485                                    levelDMs[level], Ug[level], Uloc[level-1],
486                                    Uloc[level], ceedData[level-1],
487                                    ceedData[level], ceed,
488                                    prolongRestrCtx[level]); CHKERRQ(ierr);
489 
490     // ---- Form Action of Jacobian on delta_u
491     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level-1], Ugsz[level],
492                           Ugsz[level-1], prolongRestrCtx[level],
493                           &prolongRestrMat[level]); CHKERRQ(ierr);
494     // Note: In PCMG, restriction is the transpose of prolongation
495     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT,
496                                 (void (*)(void))Prolong_Ceed);
497     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT_TRANSPOSE,
498                                 (void (*)(void))Restrict_Ceed);
499     CHKERRQ(ierr);
500     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
501       ierr = MatShellSetVecType(prolongRestrMat[level], VECCUDA); CHKERRQ(ierr);
502     }
503   }
504 
505   // ---------------------------------------------------------------------------
506   // Setup dummy SNES for AMG coarse solve
507   // ---------------------------------------------------------------------------
508   if (appCtx->multigridChoice != MULTIGRID_NONE) {
509     // -- Jacobian Matrix
510     ierr = DMSetMatType(levelDMs[0], MATAIJ); CHKERRQ(ierr);
511     ierr = DMCreateMatrix(levelDMs[0], &jacobMatCoarse); CHKERRQ(ierr);
512 
513     if (appCtx->degree > 1) {
514       ierr = SNESCreate(comm, &snesCoarse); CHKERRQ(ierr);
515       ierr = SNESSetDM(snesCoarse, levelDMs[0]); CHKERRQ(ierr);
516       ierr = SNESSetSolution(snesCoarse, Ug[0]); CHKERRQ(ierr);
517 
518       // -- Jacobian function
519       ierr = SNESSetJacobian(snesCoarse, jacobMatCoarse, jacobMatCoarse, NULL,
520                              NULL); CHKERRQ(ierr);
521 
522       // -- Residual evaluation function
523       ierr = PetscMalloc1(1, &jacobCoarseCtx); CHKERRQ(ierr);
524       ierr = PetscMemcpy(jacobCoarseCtx, jacobCtx[0], sizeof(*jacobCtx[0]));
525       CHKERRQ(ierr);
526       ierr = SNESSetFunction(snesCoarse, Ug[0], ApplyJacobianCoarse_Ceed,
527                              jacobCoarseCtx); CHKERRQ(ierr);
528 
529       // -- Update formJacobCtx
530       formJacobCtx->Ucoarse = Ug[0];
531       formJacobCtx->snesCoarse = snesCoarse;
532       formJacobCtx->jacobMatCoarse = jacobMatCoarse;
533     }
534   }
535 
536   // Set Jacobian function
537   if (appCtx->degree > 1) {
538     ierr = SNESSetJacobian(snes, jacobMat[fineLevel], jacobMat[fineLevel],
539                            FormJacobian, formJacobCtx); CHKERRQ(ierr);
540   } else {
541     ierr = SNESSetJacobian(snes, jacobMat[0], jacobMatCoarse,
542                            SNESComputeJacobianDefaultColor, NULL);
543     CHKERRQ(ierr);
544   }
545 
546   // ---------------------------------------------------------------------------
547   // Setup KSP
548   // ---------------------------------------------------------------------------
549   {
550     PC pc;
551     KSP ksp;
552 
553     // -- KSP
554     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
555     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
556     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
557     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
558                             PETSC_DEFAULT); CHKERRQ(ierr);
559     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
560 
561     // -- Preconditioning
562     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
563     ierr = PCSetDM(pc, levelDMs[fineLevel]); CHKERRQ(ierr);
564     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
565 
566     if (appCtx->multigridChoice == MULTIGRID_NONE) {
567       // ---- No Multigrid
568       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
569       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
570     } else if (appCtx->degree == 1) {
571       // ---- AMG for degree 1
572       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
573     } else {
574       // ---- PCMG
575       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
576 
577       // ------ PCMG levels
578       ierr = PCMGSetLevels(pc, numLevels, NULL); CHKERRQ(ierr);
579       for (PetscInt level = 0; level < numLevels; level++) {
580         // -------- Smoother
581         KSP kspSmoother, kspEst;
582         PC pcSmoother;
583 
584         // ---------- Smoother KSP
585         ierr = PCMGGetSmoother(pc, level, &kspSmoother); CHKERRQ(ierr);
586         ierr = KSPSetDM(kspSmoother, levelDMs[level]); CHKERRQ(ierr);
587         ierr = KSPSetDMActive(kspSmoother, PETSC_FALSE); CHKERRQ(ierr);
588 
589         // ---------- Chebyshev options
590         ierr = KSPSetType(kspSmoother, KSPCHEBYSHEV); CHKERRQ(ierr);
591         ierr = KSPChebyshevEstEigSet(kspSmoother, 0, 0.1, 0, 1.1);
592         CHKERRQ(ierr);
593         ierr = KSPChebyshevEstEigGetKSP(kspSmoother, &kspEst); CHKERRQ(ierr);
594         ierr = KSPSetType(kspEst, KSPCG); CHKERRQ(ierr);
595         ierr = KSPChebyshevEstEigSetUseNoisy(kspSmoother, PETSC_TRUE);
596         CHKERRQ(ierr);
597         ierr = KSPSetOperators(kspSmoother, jacobMat[level], jacobMat[level]);
598         CHKERRQ(ierr);
599 
600         // ---------- Smoother preconditioner
601         ierr = KSPGetPC(kspSmoother, &pcSmoother); CHKERRQ(ierr);
602         ierr = PCSetType(pcSmoother, PCJACOBI); CHKERRQ(ierr);
603         ierr = PCJacobiSetType(pcSmoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
604 
605         // -------- Work vector
606         if (level != fineLevel) {
607           ierr = PCMGSetX(pc, level, Ug[level]); CHKERRQ(ierr);
608         }
609 
610         // -------- Level prolongation/restriction operator
611         if (level > 0) {
612           ierr = PCMGSetInterpolation(pc, level, prolongRestrMat[level]);
613           CHKERRQ(ierr);
614           ierr = PCMGSetRestriction(pc, level, prolongRestrMat[level]);
615           CHKERRQ(ierr);
616         }
617       }
618 
619       // ------ PCMG coarse solve
620       KSP kspCoarse;
621       PC pcCoarse;
622 
623       // -------- Coarse KSP
624       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
625       ierr = KSPSetType(kspCoarse, KSPPREONLY); CHKERRQ(ierr);
626       ierr = KSPSetOperators(kspCoarse, jacobMatCoarse, jacobMatCoarse);
627       CHKERRQ(ierr);
628       ierr = KSPSetOptionsPrefix(kspCoarse, "coarse_"); CHKERRQ(ierr);
629 
630       // -------- Coarse preconditioner
631       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
632       ierr = PCSetType(pcCoarse, PCGAMG); CHKERRQ(ierr);
633       ierr = PCSetOptionsPrefix(pcCoarse, "coarse_"); CHKERRQ(ierr);
634 
635       ierr = KSPSetFromOptions(kspCoarse); CHKERRQ(ierr);
636       ierr = PCSetFromOptions(pcCoarse); CHKERRQ(ierr);
637 
638       // ------ PCMG options
639       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
640       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
641       ierr = PCMGSetCycleType(pc, pcmgCycleType); CHKERRQ(ierr);
642     }
643     ierr = KSPSetFromOptions(ksp);
644     ierr = PCSetFromOptions(pc);
645   }
646   {
647     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
648     SNESLineSearch linesearch;
649 
650     ierr = SNESGetLineSearch(snes, &linesearch); CHKERRQ(ierr);
651     ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHCP); CHKERRQ(ierr);
652   }
653 
654   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
655 
656   // Performance logging
657   ierr = PetscLogStagePop();
658 
659   // ---------------------------------------------------------------------------
660   // Set initial guess
661   // ---------------------------------------------------------------------------
662   ierr = PetscObjectSetName((PetscObject)U, ""); CHKERRQ(ierr);
663   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
664 
665   // View solution
666   if (appCtx->viewSoln) {
667     ierr = ViewSolution(comm, U, 0, 0.0); CHKERRQ(ierr);
668   }
669 
670   // ---------------------------------------------------------------------------
671   // Solve SNES
672   // ---------------------------------------------------------------------------
673   PetscBool snesMonitor = PETSC_FALSE;
674   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snesMonitor);
675   CHKERRQ(ierr);
676 
677   // Performance logging
678   ierr = PetscLogStageRegister("SNES Solve Stage", &stageSnesSolve);
679   CHKERRQ(ierr);
680   ierr = PetscLogStagePush(stageSnesSolve); CHKERRQ(ierr);
681 
682   // Timing
683   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
684   startTime = MPI_Wtime();
685 
686   // Solve for each load increment
687   PetscInt increment;
688   for (increment = 1; increment <= appCtx->numIncrements; increment++) {
689     // -- Log increment count
690     if (snesMonitor) {
691       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
692       CHKERRQ(ierr);
693     }
694 
695     // -- Scale the problem
696     PetscScalar loadIncrement = 1.0*increment / appCtx->numIncrements,
697                 scalingFactor = loadIncrement /
698                                 (increment == 1 ? 1 : resCtx->loadIncrement);
699     resCtx->loadIncrement = loadIncrement;
700     if (appCtx->numIncrements > 1 && appCtx->forcingChoice != FORCE_NONE) {
701       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
702     }
703 
704     // -- Solve
705     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
706 
707     // -- View solution
708     if (appCtx->viewSoln) {
709       ierr = ViewSolution(comm, U, increment, loadIncrement); CHKERRQ(ierr);
710     }
711 
712     // -- Update SNES iteration count
713     PetscInt its;
714     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
715     snesIts += its;
716     ierr = SNESGetLinearSolveIterations(snes, &its); CHKERRQ(ierr);
717     kspIts += its;
718 
719     // -- Check for divergence
720     SNESConvergedReason reason;
721     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
722     if (reason < 0)
723       break;
724   }
725 
726   // Timing
727   elapsedTime = MPI_Wtime() - startTime;
728 
729   // Performance logging
730   ierr = PetscLogStagePop();
731 
732   // ---------------------------------------------------------------------------
733   // Output summary
734   // ---------------------------------------------------------------------------
735   if (!appCtx->testMode) {
736     // -- SNES
737     SNESType snesType;
738     SNESConvergedReason reason;
739     PetscReal rnorm;
740     ierr = SNESGetType(snes, &snesType); CHKERRQ(ierr);
741     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
742     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
743     ierr = PetscPrintf(comm,
744                        "  SNES:\n"
745                        "    SNES Type                          : %s\n"
746                        "    SNES Convergence                   : %s\n"
747                        "    Number of Load Increments          : %d\n"
748                        "    Completed Load Increments          : %d\n"
749                        "    Total SNES Iterations              : %D\n"
750                        "    Final rnorm                        : %e\n",
751                        snesType, SNESConvergedReasons[reason],
752                        appCtx->numIncrements, increment - 1,
753                        snesIts, (double)rnorm); CHKERRQ(ierr);
754 
755     // -- KSP
756     KSP ksp;
757     KSPType kspType;
758     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
759     ierr = KSPGetType(ksp, &kspType); CHKERRQ(ierr);
760     ierr = PetscPrintf(comm,
761                        "  Linear Solver:\n"
762                        "    KSP Type                           : %s\n"
763                        "    Total KSP Iterations               : %D\n",
764                        kspType, kspIts); CHKERRQ(ierr);
765 
766     // -- PC
767     PC pc;
768     PCType pcType;
769     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
770     ierr = PCGetType(pc, &pcType); CHKERRQ(ierr);
771     ierr = PetscPrintf(comm,
772                        "    PC Type                            : %s\n",
773                        pcType); CHKERRQ(ierr);
774 
775     if (!strcmp(pcType, PCMG)) {
776       PCMGType pcmgType;
777       ierr = PCMGGetType(pc, &pcmgType); CHKERRQ(ierr);
778       ierr = PetscPrintf(comm,
779                          "  P-Multigrid:\n"
780                          "    PCMG Type                          : %s\n"
781                          "    PCMG Cycle Type                    : %s\n",
782                          PCMGTypes[pcmgType],
783                          PCMGCycleTypes[pcmgCycleType]); CHKERRQ(ierr);
784 
785       // -- Coarse Solve
786       KSP kspCoarse;
787       PC pcCoarse;
788       PCType pcType;
789 
790       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
791       ierr = KSPGetType(kspCoarse, &kspType); CHKERRQ(ierr);
792       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
793       ierr = PCGetType(pcCoarse, &pcType); CHKERRQ(ierr);
794       ierr = PetscPrintf(comm,
795                          "    Coarse Solve:\n"
796                          "      KSP Type                         : %s\n"
797                          "      PC Type                          : %s\n",
798                          kspType, pcType); CHKERRQ(ierr);
799     }
800   }
801 
802   // ---------------------------------------------------------------------------
803   // Compute solve time
804   // ---------------------------------------------------------------------------
805   if (!appCtx->testMode) {
806     ierr = MPI_Allreduce(&elapsedTime, &minTime, 1, MPI_DOUBLE, MPI_MIN, comm);
807     CHKERRQ(ierr);
808     ierr = MPI_Allreduce(&elapsedTime, &maxTime, 1, MPI_DOUBLE, MPI_MAX, comm);
809     CHKERRQ(ierr);
810     ierr = PetscPrintf(comm,
811                        "  Performance:\n"
812                        "    SNES Solve Time                    : %g (%g) sec\n"
813                        "    DoFs/Sec in SNES                   : %g (%g) million\n",
814                        maxTime, minTime, 1e-6*Ugsz[fineLevel]*kspIts/maxTime,
815                        1e-6*Ugsz[fineLevel]*kspIts/minTime); CHKERRQ(ierr);
816   }
817 
818   // ---------------------------------------------------------------------------
819   // Compute error
820   // ---------------------------------------------------------------------------
821   if (appCtx->forcingChoice == FORCE_MMS) {
822     CeedScalar l2Error = 1., l2Unorm = 1.;
823     const CeedScalar *truearray;
824     Vec errorVec, trueVec;
825 
826     // -- Work vectors
827     ierr = VecDuplicate(U, &errorVec); CHKERRQ(ierr);
828     ierr = VecSet(errorVec, 0.0); CHKERRQ(ierr);
829     ierr = VecDuplicate(U, &trueVec); CHKERRQ(ierr);
830     ierr = VecSet(trueVec, 0.0); CHKERRQ(ierr);
831 
832     // -- Assemble global true solution vector
833     CeedVectorGetArrayRead(ceedData[fineLevel]->truesoln,
834                            appCtx->memTypeRequested, &truearray);
835     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
836       ierr = VecPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
837       CHKERRQ(ierr);
838     } else {
839       ierr = VecCUDAPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
840       CHKERRQ(ierr);
841     }
842     ierr = DMLocalToGlobal(resCtx->dm, resCtx->Yloc, INSERT_VALUES, trueVec);
843     CHKERRQ(ierr);
844     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
845       ierr = VecResetArray(resCtx->Yloc); CHKERRQ(ierr);
846     } else {
847       ierr = VecCUDAResetArray(resCtx->Yloc); CHKERRQ(ierr);
848     }
849     CeedVectorRestoreArrayRead(ceedData[fineLevel]->truesoln, &truearray);
850 
851     // -- Compute L2 error
852     ierr = VecWAXPY(errorVec, -1.0, U, trueVec); CHKERRQ(ierr);
853     ierr = VecNorm(errorVec, NORM_2, &l2Error); CHKERRQ(ierr);
854     ierr = VecNorm(U, NORM_2, &l2Unorm); CHKERRQ(ierr);
855     l2Error /= l2Unorm;
856 
857     // -- Output
858     if (!appCtx->testMode || l2Error > 0.05) {
859       ierr = PetscPrintf(comm,
860                          "    L2 Error                           : %e\n",
861                          l2Error); CHKERRQ(ierr);
862     }
863 
864     // -- Cleanup
865     ierr = VecDestroy(&errorVec); CHKERRQ(ierr);
866     ierr = VecDestroy(&trueVec); CHKERRQ(ierr);
867   }
868 
869   // ---------------------------------------------------------------------------
870   // Compute energy
871   // ---------------------------------------------------------------------------
872   if (!appCtx->testMode) {
873     // -- Compute L2 error
874     CeedScalar energy;
875     ierr = ComputeStrainEnergy(dmEnergy, resCtx, ceedData[fineLevel]->opEnergy,
876                                U, &energy); CHKERRQ(ierr);
877 
878     // -- Output
879     ierr = PetscPrintf(comm,
880                        "    Strain Energy                      : %e\n",
881                        energy); CHKERRQ(ierr);
882   }
883 
884   // ---------------------------------------------------------------------------
885   // Output diagnostic quantities
886   // ---------------------------------------------------------------------------
887   if (appCtx->viewSoln || appCtx->viewFinalSoln) {
888     // -- Setup context
889     UserMult diagnosticCtx;
890     ierr = PetscMalloc1(1, &diagnosticCtx); CHKERRQ(ierr);
891     ierr = PetscMemcpy(diagnosticCtx, resCtx, sizeof(*resCtx)); CHKERRQ(ierr);
892     diagnosticCtx->dm = dmDiagnostic;
893     diagnosticCtx->op = ceedData[fineLevel]->opDiagnostic;
894 
895     // -- Compute and output
896     ierr = ViewDiagnosticQuantities(comm, levelDMs[fineLevel], diagnosticCtx, U,
897                                     ceedData[fineLevel]->ErestrictDiagnostic);
898     CHKERRQ(ierr);
899 
900     // -- Cleanup
901     ierr = PetscFree(diagnosticCtx); CHKERRQ(ierr);
902   }
903 
904   // ---------------------------------------------------------------------------
905   // Free objects
906   // ---------------------------------------------------------------------------
907   // Data in arrays per level
908   for (PetscInt level = 0; level < numLevels; level++) {
909     // Vectors
910     ierr = VecDestroy(&Ug[level]); CHKERRQ(ierr);
911     ierr = VecDestroy(&Uloc[level]); CHKERRQ(ierr);
912 
913     // Jacobian matrix and data
914     ierr = VecDestroy(&jacobCtx[level]->Yloc); CHKERRQ(ierr);
915     ierr = MatDestroy(&jacobMat[level]); CHKERRQ(ierr);
916     ierr = PetscFree(jacobCtx[level]); CHKERRQ(ierr);
917 
918     // Prolongation/Restriction matrix and data
919     if (level > 0) {
920       ierr = PetscFree(prolongRestrCtx[level]); CHKERRQ(ierr);
921       ierr = MatDestroy(&prolongRestrMat[level]); CHKERRQ(ierr);
922     }
923 
924     // DM
925     ierr = DMDestroy(&levelDMs[level]); CHKERRQ(ierr);
926 
927     // libCEED objects
928     ierr = CeedDataDestroy(level, ceedData[level]); CHKERRQ(ierr);
929   }
930 
931   // Arrays
932   ierr = PetscFree(Ug); CHKERRQ(ierr);
933   ierr = PetscFree(Uloc); CHKERRQ(ierr);
934   ierr = PetscFree(Ugsz); CHKERRQ(ierr);
935   ierr = PetscFree(Ulsz); CHKERRQ(ierr);
936   ierr = PetscFree(Ulocsz); CHKERRQ(ierr);
937   ierr = PetscFree(jacobCtx); CHKERRQ(ierr);
938   ierr = PetscFree(jacobMat); CHKERRQ(ierr);
939   ierr = PetscFree(prolongRestrCtx); CHKERRQ(ierr);
940   ierr = PetscFree(prolongRestrMat); CHKERRQ(ierr);
941   ierr = PetscFree(appCtx->levelDegrees); CHKERRQ(ierr);
942   ierr = PetscFree(ceedData); CHKERRQ(ierr);
943 
944   // libCEED objects
945   CeedQFunctionContextDestroy(&ctxPhys);
946   CeedQFunctionContextDestroy(&ctxPhysSmoother);
947   CeedDestroy(&ceed);
948 
949   // PETSc objects
950   ierr = VecDestroy(&U); CHKERRQ(ierr);
951   ierr = VecDestroy(&R); CHKERRQ(ierr);
952   ierr = VecDestroy(&Rloc); CHKERRQ(ierr);
953   ierr = VecDestroy(&F); CHKERRQ(ierr);
954   ierr = VecDestroy(&Floc); CHKERRQ(ierr);
955   ierr = VecDestroy(&NBCs); CHKERRQ(ierr);
956   ierr = VecDestroy(&NBCsloc); CHKERRQ(ierr);
957   ierr = MatDestroy(&jacobMatCoarse); CHKERRQ(ierr);
958   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
959   ierr = SNESDestroy(&snesCoarse); CHKERRQ(ierr);
960   ierr = DMDestroy(&dmOrig); CHKERRQ(ierr);
961   ierr = DMDestroy(&dmEnergy); CHKERRQ(ierr);
962   ierr = DMDestroy(&dmDiagnostic); CHKERRQ(ierr);
963   ierr = PetscFree(levelDMs); CHKERRQ(ierr);
964 
965   // Structs
966   ierr = PetscFree(resCtx); CHKERRQ(ierr);
967   ierr = PetscFree(formJacobCtx); CHKERRQ(ierr);
968   ierr = PetscFree(jacobCoarseCtx); CHKERRQ(ierr);
969   ierr = PetscFree(appCtx); CHKERRQ(ierr);
970   ierr = PetscFree(phys); CHKERRQ(ierr);
971   ierr = PetscFree(physSmoother); CHKERRQ(ierr);
972   ierr = PetscFree(units); CHKERRQ(ierr);
973 
974   return PetscFinalize();
975 }
976