xref: /libCEED/examples/solids/elasticity.c (revision f7b4142eef27c8569cf480f31593e82c5a23ff6e)
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/occa
33 //
34 // Sample meshes can be found at https://github.com/jeremylt/ceedSampleMeshes
35 //
36 //TESTARGS -ceed {ceed_resource} -test -degree 2 -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   SNES           snes, snesCoarse = NULL;
62   Mat            *jacobMat, jacobMatCoarse, *prolongRestrMat;
63   // PETSc data
64   UserMult       resCtx, jacobCoarseCtx = NULL, *jacobCtx;
65   FormJacobCtx   formJacobCtx;
66   UserMultProlongRestr *prolongRestrCtx;
67   PCMGCycleType  pcmgCycleType = PC_MG_CYCLE_V;
68   // libCEED objects
69   Ceed           ceed, ceedFine = NULL;
70   CeedData       *ceedData;
71   CeedQFunction  qfRestrict = NULL, qfProlong = NULL;
72   // Parameters
73   PetscInt       ncompu = 3;             // 3 DoFs in 3D
74   PetscInt       ncompe = 1, ncompd = 2; // 1 energy output, 2 diagnostic
75   PetscInt       numLevels = 1, fineLevel = 0;
76   PetscInt       *Ugsz, *Ulsz, *Ulocsz;  // sz: size
77   PetscInt       snesIts = 0;
78   // Timing
79   double         startTime, elapsedTime, minTime, maxTime;
80 
81   ierr = PetscInitialize(&argc, &argv, NULL, help);
82   if (ierr)
83     return ierr;
84 
85   // ---------------------------------------------------------------------------
86   // Process command line options
87   // ---------------------------------------------------------------------------
88   comm = PETSC_COMM_WORLD;
89 
90   // -- Set mesh file, polynomial degree, problem type
91   ierr = PetscCalloc1(1, &appCtx); CHKERRQ(ierr);
92   ierr = ProcessCommandLineOptions(comm, appCtx); CHKERRQ(ierr);
93   numLevels = appCtx->numLevels;
94   fineLevel = numLevels - 1;
95 
96   // -- Set Poison's ratio, Young's Modulus
97   ierr = PetscMalloc1(1, &phys); CHKERRQ(ierr);
98   ierr = PetscMalloc1(1, &units); CHKERRQ(ierr);
99   ierr = ProcessPhysics(comm, phys, units); CHKERRQ(ierr);
100   if (fabs(appCtx->nuSmoother) > 1E-14) {
101     ierr = PetscMalloc1(1, &physSmoother); CHKERRQ(ierr);
102     ierr = PetscMemcpy(physSmoother, phys, sizeof(*phys)); CHKERRQ(ierr);
103     physSmoother->nu = appCtx->nuSmoother;
104   }
105 
106   // ---------------------------------------------------------------------------
107   // Setup DM
108   // ---------------------------------------------------------------------------
109   // Performance logging
110   ierr = PetscLogStageRegister("DM and Vector Setup Stage", &stageDMSetup);
111   CHKERRQ(ierr);
112   ierr = PetscLogStagePush(stageDMSetup); CHKERRQ(ierr);
113 
114   // -- Create distributed DM from mesh file
115   ierr = CreateDistributedDM(comm, appCtx, &dmOrig); CHKERRQ(ierr);
116 
117   // -- Setup DM by polynomial degree
118   ierr = PetscMalloc1(numLevels, &levelDMs); CHKERRQ(ierr);
119   for (PetscInt level = 0; level < numLevels; level++) {
120     ierr = DMClone(dmOrig, &levelDMs[level]); CHKERRQ(ierr);
121     ierr = SetupDMByDegree(levelDMs[level], appCtx, appCtx->levelDegrees[level],
122                            PETSC_TRUE, ncompu); CHKERRQ(ierr);
123     // -- Label field components for viewing
124     // Empty name for conserved field (because there is only one field)
125     PetscSection section;
126     ierr = DMGetLocalSection(levelDMs[level], &section); CHKERRQ(ierr);
127     ierr = PetscSectionSetFieldName(section, 0, "Displacement"); CHKERRQ(ierr);
128     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
129     CHKERRQ(ierr);
130     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
131     CHKERRQ(ierr);
132     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
133     CHKERRQ(ierr);
134   }
135 
136   // -- Setup postprocessing DMs
137   ierr = DMClone(dmOrig, &dmEnergy); CHKERRQ(ierr);
138   ierr = SetupDMByDegree(dmEnergy, appCtx, appCtx->levelDegrees[fineLevel],
139                          PETSC_FALSE, ncompe); CHKERRQ(ierr);
140   ierr = DMClone(dmOrig, &dmDiagnostic); CHKERRQ(ierr);
141   ierr = SetupDMByDegree(dmDiagnostic, appCtx, appCtx->levelDegrees[fineLevel],
142                          PETSC_FALSE, ncompd); CHKERRQ(ierr);
143   {
144     // -- Label field components for viewing
145     // Empty name for conserved field (because there is only one field)
146     PetscSection section;
147     ierr = DMGetLocalSection(dmDiagnostic, &section); CHKERRQ(ierr);
148     ierr = PetscSectionSetFieldName(section, 0, "Diagnostics"); CHKERRQ(ierr);
149     ierr = PetscSectionSetComponentName(section, 0, 0, "CondensedPressure");
150     ierr = PetscSectionSetComponentName(section, 0, 1, "StrainEnergyDensity");
151     CHKERRQ(ierr);
152   }
153 
154   // ---------------------------------------------------------------------------
155   // Setup solution and work vectors
156   // ---------------------------------------------------------------------------
157   // Allocate arrays
158   ierr = PetscMalloc1(numLevels, &Ug); CHKERRQ(ierr);
159   ierr = PetscMalloc1(numLevels, &Uloc); CHKERRQ(ierr);
160   ierr = PetscMalloc1(numLevels, &Ugsz); CHKERRQ(ierr);
161   ierr = PetscMalloc1(numLevels, &Ulsz); CHKERRQ(ierr);
162   ierr = PetscMalloc1(numLevels, &Ulocsz); CHKERRQ(ierr);
163 
164   // -- Setup solution vectors for each level
165   for (PetscInt level = 0; level < numLevels; level++) {
166     // -- Create global unknown vector U
167     ierr = DMCreateGlobalVector(levelDMs[level], &Ug[level]); CHKERRQ(ierr);
168     ierr = VecGetSize(Ug[level], &Ugsz[level]); CHKERRQ(ierr);
169     // Note: Local size for matShell
170     ierr = VecGetLocalSize(Ug[level], &Ulsz[level]); CHKERRQ(ierr);
171 
172     // -- Create local unknown vector Uloc
173     ierr = DMCreateLocalVector(levelDMs[level], &Uloc[level]); CHKERRQ(ierr);
174     // Note: local size for libCEED
175     ierr = VecGetSize(Uloc[level], &Ulocsz[level]); CHKERRQ(ierr);
176   }
177 
178   // -- Create residual and forcing vectors
179   ierr = VecDuplicate(Ug[fineLevel], &U); CHKERRQ(ierr);
180   ierr = VecDuplicate(Ug[fineLevel], &R); CHKERRQ(ierr);
181   ierr = VecDuplicate(Ug[fineLevel], &F); CHKERRQ(ierr);
182   ierr = VecDuplicate(Uloc[fineLevel], &Rloc); CHKERRQ(ierr);
183   ierr = VecDuplicate(Uloc[fineLevel], &Floc); CHKERRQ(ierr);
184 
185   // Performance logging
186   ierr = PetscLogStagePop();
187 
188   // ---------------------------------------------------------------------------
189   // Set up libCEED
190   // ---------------------------------------------------------------------------
191   // Performance logging
192   ierr = PetscLogStageRegister("libCEED Setup Stage", &stageLibceedSetup);
193   CHKERRQ(ierr);
194   ierr = PetscLogStagePush(stageLibceedSetup); CHKERRQ(ierr);
195 
196   // Initalize backend
197   CeedInit(appCtx->ceedResource, &ceed);
198   if (appCtx->degree > 4 && appCtx->ceedResourceFine[0])
199     CeedInit(appCtx->ceedResourceFine, &ceedFine);
200 
201   // -- Create libCEED local forcing vector
202   CeedVector forceCeed;
203   CeedScalar *f;
204   if (appCtx->forcingChoice != FORCE_NONE) {
205     ierr = VecGetArray(Floc, &f); CHKERRQ(ierr);
206     CeedVectorCreate(ceed, Ulocsz[fineLevel], &forceCeed);
207     CeedVectorSetArray(forceCeed, CEED_MEM_HOST, CEED_USE_POINTER, f);
208   }
209 
210   // -- Restriction and prolongation QFunction
211   if (appCtx->multigridChoice != MULTIGRID_NONE) {
212     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
213                                 &qfRestrict);
214     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
215                                 &qfProlong);
216   }
217 
218   // -- Setup libCEED objects
219   ierr = PetscMalloc1(numLevels, &ceedData); CHKERRQ(ierr);
220   // ---- Setup residual evaluator and geometric information
221   ierr = PetscCalloc1(1, &ceedData[fineLevel]); CHKERRQ(ierr);
222   {
223     bool highOrder = (appCtx->levelDegrees[fineLevel] > 4 && ceedFine);
224     Ceed levelCeed = highOrder ? ceedFine : ceed;
225     ierr = SetupLibceedFineLevel(levelDMs[fineLevel], dmEnergy, dmDiagnostic,
226                                  levelCeed, appCtx, phys, ceedData, fineLevel,
227                                  ncompu, Ugsz[fineLevel], Ulocsz[fineLevel],
228                                  forceCeed, qfRestrict, qfProlong);
229     CHKERRQ(ierr);
230   }
231   // ---- Setup Jacobian evaluator and prolongation/restriction
232   for (PetscInt level = 0; level < numLevels; level++) {
233     if (level != fineLevel) {
234       ierr = PetscCalloc1(1, &ceedData[level]); CHKERRQ(ierr);
235     }
236 
237     // Note: use high order ceed, if specified and degree > 4
238     bool highOrder = (appCtx->levelDegrees[level] > 4 && ceedFine);
239     Ceed levelCeed = highOrder ? ceedFine : ceed;
240     ierr = SetupLibceedLevel(levelDMs[level], levelCeed, appCtx, phys,
241                              ceedData,  level, ncompu, Ugsz[level],
242                              Ulocsz[level], forceCeed, qfRestrict,
243                              qfProlong); CHKERRQ(ierr);
244   }
245 
246   // Performance logging
247   ierr = PetscLogStagePop();
248 
249   // ---------------------------------------------------------------------------
250   // Setup global forcing vector
251   // ---------------------------------------------------------------------------
252   ierr = VecZeroEntries(F); CHKERRQ(ierr);
253 
254   if (appCtx->forcingChoice != FORCE_NONE) {
255     ierr = VecRestoreArray(Floc, &f); CHKERRQ(ierr);
256     ierr = DMLocalToGlobal(levelDMs[fineLevel], Floc, ADD_VALUES, F);
257     CHKERRQ(ierr);
258     CeedVectorDestroy(&forceCeed);
259   }
260 
261   // ---------------------------------------------------------------------------
262   // Print problem summary
263   // ---------------------------------------------------------------------------
264   if (!appCtx->testMode) {
265     const char *usedresource;
266     CeedGetResource(ceed, &usedresource);
267 
268     ierr = PetscPrintf(comm,
269                        "\n-- Elasticity Example - libCEED + PETSc --\n"
270                        "  libCEED:\n"
271                        "    libCEED Backend                    : %s\n",
272                        usedresource); CHKERRQ(ierr);
273 
274     if (ceedFine) {
275       ierr = PetscPrintf(comm,
276                          "    libCEED Backend - high order       : %s\n",
277                          appCtx->ceedResourceFine); CHKERRQ(ierr);
278     }
279 
280     ierr = PetscPrintf(comm,
281                        "  Problem:\n"
282                        "    Problem Name                       : %s\n"
283                        "    Forcing Function                   : %s\n"
284                        "  Mesh:\n"
285                        "    File                               : %s\n"
286                        "    Number of 1D Basis Nodes (p)       : %d\n"
287                        "    Number of 1D Quadrature Points (q) : %d\n"
288                        "    Global nodes                       : %D\n"
289                        "    Owned nodes                        : %D\n"
290                        "    DoF per node                       : %D\n"
291                        "  Multigrid:\n"
292                        "    Type                               : %s\n"
293                        "    Number of Levels                   : %d\n",
294                        problemTypesForDisp[appCtx->problemChoice],
295                        forcingTypesForDisp[appCtx->forcingChoice],
296                        appCtx->meshFile[0] ? appCtx->meshFile : "Box Mesh",
297                        appCtx->degree + 1, appCtx->degree + 1,
298                        Ugsz[fineLevel]/ncompu, Ulsz[fineLevel]/ncompu, ncompu,
299                        (appCtx->degree == 1 &&
300                         appCtx->multigridChoice != MULTIGRID_NONE) ?
301                        "Algebraic multigrid" :
302                        multigridTypesForDisp[appCtx->multigridChoice],
303                        (appCtx->degree == 1 ||
304                         appCtx->multigridChoice == MULTIGRID_NONE) ?
305                        0 : numLevels); CHKERRQ(ierr);
306 
307     if (appCtx->multigridChoice != MULTIGRID_NONE) {
308       for (PetscInt i = 0; i < 2; i++) {
309         CeedInt level = i ? fineLevel : 0;
310         ierr = PetscPrintf(comm,
311                            "    Level %D (%s):\n"
312                            "      Number of 1D Basis Nodes (p)     : %d\n"
313                            "      Global Nodes                     : %D\n"
314                            "      Owned Nodes                      : %D\n",
315                            level, i ? "fine" : "coarse",
316                            appCtx->levelDegrees[level] + 1,
317                            Ugsz[level]/ncompu, Ulsz[level]/ncompu);
318         CHKERRQ(ierr);
319       }
320     }
321   }
322 
323   // ---------------------------------------------------------------------------
324   // Setup SNES
325   // ---------------------------------------------------------------------------
326   // Performance logging
327   ierr = PetscLogStageRegister("SNES Setup Stage", &stageSnesSetup);
328   CHKERRQ(ierr);
329   ierr = PetscLogStagePush(stageSnesSetup); CHKERRQ(ierr);
330 
331   // Create SNES
332   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
333   ierr = SNESSetDM(snes, levelDMs[fineLevel]); CHKERRQ(ierr);
334 
335   // -- Jacobian evaluators
336   ierr = PetscMalloc1(numLevels, &jacobCtx); CHKERRQ(ierr);
337   ierr = PetscMalloc1(numLevels, &jacobMat); CHKERRQ(ierr);
338   for (PetscInt level = 0; level < numLevels; level++) {
339     // -- Jacobian context for level
340     ierr = PetscMalloc1(1, &jacobCtx[level]); CHKERRQ(ierr);
341     ierr = SetupJacobianCtx(comm, appCtx, levelDMs[level], Ug[level],
342                             Uloc[level], ceedData[level], ceed, phys,
343                             physSmoother, jacobCtx[level]); CHKERRQ(ierr);
344 
345     // -- Form Action of Jacobian on delta_u
346     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level], Ugsz[level],
347                           Ugsz[level], jacobCtx[level], &jacobMat[level]);
348     CHKERRQ(ierr);
349     ierr = MatShellSetOperation(jacobMat[level], MATOP_MULT,
350                                 (void (*)(void))ApplyJacobian_Ceed);
351     CHKERRQ(ierr);
352     ierr = MatShellSetOperation(jacobMat[level], MATOP_GET_DIAGONAL,
353                                 (void(*)(void))GetDiag_Ceed);
354 
355   }
356   // Note: FormJacobian updates Jacobian matrices on each level
357   //   and assembles the Jpre matrix, if needed
358   ierr = PetscMalloc1(1, &formJacobCtx); CHKERRQ(ierr);
359   formJacobCtx->jacobCtx = jacobCtx;
360   formJacobCtx->numLevels = numLevels;
361   formJacobCtx->jacobMat = jacobMat;
362 
363   // -- Residual evaluation function
364   ierr = PetscMalloc1(1, &resCtx); CHKERRQ(ierr);
365   ierr = PetscMemcpy(resCtx, jacobCtx[fineLevel],
366                      sizeof(*jacobCtx[fineLevel])); CHKERRQ(ierr);
367   resCtx->op = ceedData[fineLevel]->opApply;
368   resCtx->qf = ceedData[fineLevel]->qfApply;
369   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, resCtx); CHKERRQ(ierr);
370 
371   // -- Prolongation/Restriction evaluation
372   ierr = PetscMalloc1(numLevels, &prolongRestrCtx); CHKERRQ(ierr);
373   ierr = PetscMalloc1(numLevels, &prolongRestrMat); CHKERRQ(ierr);
374   for (PetscInt level = 1; level < numLevels; level++) {
375     // ---- Prolongation/restriction context for level
376     ierr = PetscMalloc1(1, &prolongRestrCtx[level]); CHKERRQ(ierr);
377     ierr = SetupProlongRestrictCtx(comm, levelDMs[level-1], levelDMs[level],
378                                    Ug[level], Uloc[level-1], Uloc[level],
379                                    ceedData[level-1], ceedData[level], ceed,
380                                    prolongRestrCtx[level]); CHKERRQ(ierr);
381 
382     // ---- Form Action of Jacobian on delta_u
383     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level-1], Ugsz[level],
384                           Ugsz[level-1], prolongRestrCtx[level],
385                           &prolongRestrMat[level]); CHKERRQ(ierr);
386     // Note: In PCMG, restriction is the transpose of prolongation
387     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT,
388                                 (void (*)(void))Prolong_Ceed);
389     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT_TRANSPOSE,
390                                 (void (*)(void))Restrict_Ceed);
391     CHKERRQ(ierr);
392   }
393 
394   // ---------------------------------------------------------------------------
395   // Setup dummy SNES for AMG coarse solve
396   // ---------------------------------------------------------------------------
397   if (appCtx->multigridChoice != MULTIGRID_NONE) {
398     // -- Jacobian Matrix
399     ierr = DMSetMatType(levelDMs[0], MATAIJ); CHKERRQ(ierr);
400     ierr = DMCreateMatrix(levelDMs[0], &jacobMatCoarse); CHKERRQ(ierr);
401 
402     if (appCtx->degree > 1) {
403       ierr = SNESCreate(comm, &snesCoarse); CHKERRQ(ierr);
404       ierr = SNESSetDM(snesCoarse, levelDMs[0]); CHKERRQ(ierr);
405       ierr = SNESSetSolution(snesCoarse, Ug[0]); CHKERRQ(ierr);
406 
407       // -- Jacobian function
408       ierr = SNESSetJacobian(snesCoarse, jacobMatCoarse, jacobMatCoarse, NULL,
409                              NULL); CHKERRQ(ierr);
410 
411       // -- Residual evaluation function
412       ierr = PetscMalloc1(1, &jacobCoarseCtx); CHKERRQ(ierr);
413       ierr = PetscMemcpy(jacobCoarseCtx, jacobCtx[0], sizeof(*jacobCtx[0]));
414       CHKERRQ(ierr);
415       ierr = SNESSetFunction(snesCoarse, Ug[0], ApplyJacobianCoarse_Ceed,
416                              jacobCoarseCtx); CHKERRQ(ierr);
417 
418       // -- Update formJacobCtx
419       formJacobCtx->Ucoarse = Ug[0];
420       formJacobCtx->snesCoarse = snesCoarse;
421       formJacobCtx->jacobMatCoarse = jacobMatCoarse;
422     }
423   }
424 
425   // Set Jacobian function
426   if (appCtx->degree > 1) {
427     ierr = SNESSetJacobian(snes, jacobMat[fineLevel], jacobMat[fineLevel],
428                            FormJacobian, formJacobCtx); CHKERRQ(ierr);
429   } else {
430     ierr = SNESSetJacobian(snes, jacobMat[0], jacobMatCoarse,
431                            SNESComputeJacobianDefaultColor, NULL);
432     CHKERRQ(ierr);
433   }
434 
435   // ---------------------------------------------------------------------------
436   // Setup KSP
437   // ---------------------------------------------------------------------------
438   {
439     PC pc;
440     KSP ksp;
441 
442     // -- KSP
443     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
444     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
445     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
446     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
447                             PETSC_DEFAULT); CHKERRQ(ierr);
448     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
449 
450     // -- Preconditioning
451     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
452     ierr = PCSetDM(pc, levelDMs[fineLevel]); CHKERRQ(ierr);
453     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
454 
455     if (appCtx->multigridChoice == MULTIGRID_NONE) {
456       // ---- No Multigrid
457       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
458       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
459     } else if (appCtx->degree == 1) {
460       // ---- AMG for degree 1
461       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
462     } else {
463       // ---- PCMG
464       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
465 
466       // ------ PCMG levels
467       ierr = PCMGSetLevels(pc, numLevels, NULL); CHKERRQ(ierr);
468       for (PetscInt level = 0; level < numLevels; level++) {
469         // -------- Smoother
470         KSP kspSmoother, kspEst;
471         PC pcSmoother;
472 
473         // ---------- Smoother KSP
474         ierr = PCMGGetSmoother(pc, level, &kspSmoother); CHKERRQ(ierr);
475         ierr = KSPSetDM(kspSmoother, levelDMs[level]); CHKERRQ(ierr);
476         ierr = KSPSetDMActive(kspSmoother, PETSC_FALSE); CHKERRQ(ierr);
477 
478         // ---------- Chebyshev options
479         ierr = KSPSetType(kspSmoother, KSPCHEBYSHEV); CHKERRQ(ierr);
480         ierr = KSPChebyshevEstEigSet(kspSmoother, 0, 0.1, 0, 1.1);
481         CHKERRQ(ierr);
482         ierr = KSPChebyshevEstEigGetKSP(kspSmoother, &kspEst); CHKERRQ(ierr);
483         ierr = KSPSetType(kspEst, KSPCG); CHKERRQ(ierr);
484         ierr = KSPChebyshevEstEigSetUseNoisy(kspSmoother, PETSC_TRUE);
485         CHKERRQ(ierr);
486         ierr = KSPSetOperators(kspSmoother, jacobMat[level], jacobMat[level]);
487         CHKERRQ(ierr);
488 
489         // ---------- Smoother preconditioner
490         ierr = KSPGetPC(kspSmoother, &pcSmoother); CHKERRQ(ierr);
491         ierr = PCSetType(pcSmoother, PCJACOBI); CHKERRQ(ierr);
492         ierr = PCJacobiSetType(pcSmoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
493 
494         // -------- Work vector
495         if (level != fineLevel) {
496           ierr = PCMGSetX(pc, level, Ug[level]); CHKERRQ(ierr);
497         }
498 
499         // -------- Level prolongation/restriction operator
500         if (level > 0) {
501           ierr = PCMGSetInterpolation(pc, level, prolongRestrMat[level]);
502           CHKERRQ(ierr);
503           ierr = PCMGSetRestriction(pc, level, prolongRestrMat[level]);
504           CHKERRQ(ierr);
505         }
506       }
507 
508       // ------ PCMG coarse solve
509       KSP kspCoarse;
510       PC pcCoarse;
511 
512       // -------- Coarse KSP
513       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
514       ierr = KSPSetType(kspCoarse, KSPPREONLY); CHKERRQ(ierr);
515       ierr = KSPSetOperators(kspCoarse, jacobMatCoarse, jacobMatCoarse);
516       CHKERRQ(ierr);
517       ierr = KSPSetOptionsPrefix(kspCoarse, "coarse_"); CHKERRQ(ierr);
518 
519       // -------- Coarse preconditioner
520       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
521       ierr = PCSetType(pcCoarse, PCGAMG); CHKERRQ(ierr);
522       ierr = PCSetOptionsPrefix(pcCoarse, "coarse_"); CHKERRQ(ierr);
523 
524       ierr = KSPSetFromOptions(kspCoarse); CHKERRQ(ierr);
525       ierr = PCSetFromOptions(pcCoarse); CHKERRQ(ierr);
526 
527       // ------ PCMG options
528       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
529       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
530       ierr = PCMGSetCycleType(pc, pcmgCycleType); CHKERRQ(ierr);
531     }
532     ierr = KSPSetFromOptions(ksp);
533     ierr = PCSetFromOptions(pc);
534   }
535   {
536     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
537     SNESLineSearch linesearch;
538 
539     ierr = SNESGetLineSearch(snes, &linesearch); CHKERRQ(ierr);
540     ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHCP); CHKERRQ(ierr);
541   }
542 
543   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
544 
545   // Performance logging
546   ierr = PetscLogStagePop();
547 
548   // ---------------------------------------------------------------------------
549   // Set initial guess
550   // ---------------------------------------------------------------------------
551   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
552 
553   // View solution
554   if (appCtx->viewSoln) {
555     ierr = ViewSolution(comm, U, 0, 0.0); CHKERRQ(ierr);
556   }
557 
558   // ---------------------------------------------------------------------------
559   // Solve SNES
560   // ---------------------------------------------------------------------------
561   PetscBool snesMonitor = PETSC_FALSE;
562   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snesMonitor);
563   CHKERRQ(ierr);
564 
565   // Performance logging
566   ierr = PetscLogStageRegister("SNES Solve Stage", &stageSnesSolve);
567   CHKERRQ(ierr);
568   ierr = PetscLogStagePush(stageSnesSolve); CHKERRQ(ierr);
569 
570   // Timing
571   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
572   startTime = MPI_Wtime();
573 
574   // Solve for each load increment
575   PetscInt increment;
576   for (increment = 1; increment <= appCtx->numIncrements; increment++) {
577     // -- Log increment count
578     if (snesMonitor) {
579       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
580       CHKERRQ(ierr);
581     }
582 
583     // -- Scale the problem
584     PetscScalar loadIncrement = 1.0*increment / appCtx->numIncrements,
585                 scalingFactor = loadIncrement /
586                                 (increment == 1 ? 1 : resCtx->loadIncrement);
587     resCtx->loadIncrement = loadIncrement;
588     if (appCtx->numIncrements > 1 && appCtx->forcingChoice != FORCE_NONE) {
589       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
590     }
591 
592     // -- Solve
593     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
594 
595     // -- View solution
596     if (appCtx->viewSoln) {
597       ierr = ViewSolution(comm, U, increment, loadIncrement); CHKERRQ(ierr);
598     }
599 
600     // -- Update SNES iteration count
601     PetscInt its;
602     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
603     snesIts += its;
604 
605     // -- Check for divergence
606     SNESConvergedReason reason;
607     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
608     if (reason < 0)
609       break;
610   }
611 
612   // Timing
613   elapsedTime = MPI_Wtime() - startTime;
614 
615   // Performance logging
616   ierr = PetscLogStagePop();
617 
618   // View solution
619   if (appCtx->viewFinalSoln && !appCtx->viewSoln) {
620     ierr = ViewSolution(comm, U, increment - 1, 1.0); CHKERRQ(ierr);
621   }
622 
623   // ---------------------------------------------------------------------------
624   // Output summary
625   // ---------------------------------------------------------------------------
626   if (!appCtx->testMode) {
627     // -- SNES
628     SNESType snesType;
629     SNESConvergedReason reason;
630     PetscReal rnorm;
631     ierr = SNESGetType(snes, &snesType); CHKERRQ(ierr);
632     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
633     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
634     ierr = PetscPrintf(comm,
635                        "  SNES:\n"
636                        "    SNES Type                          : %s\n"
637                        "    SNES Convergence                   : %s\n"
638                        "    Number of Load Increments          : %d\n"
639                        "    Completed Load Increments          : %d\n"
640                        "    Total SNES Iterations              : %D\n"
641                        "    Final rnorm                        : %e\n",
642                        snesType, SNESConvergedReasons[reason],
643                        appCtx->numIncrements, increment - 1,
644                        snesIts, (double)rnorm); CHKERRQ(ierr);
645 
646     // -- KSP
647     KSP ksp;
648     KSPType kspType;
649     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
650     ierr = KSPGetType(ksp, &kspType); CHKERRQ(ierr);
651     ierr = PetscPrintf(comm,
652                        "  Linear Solver:\n"
653                        "    KSP Type                           : %s\n",
654                        kspType); CHKERRQ(ierr);
655 
656     // -- PC
657     PC pc;
658     PCType pcType;
659     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
660     ierr = PCGetType(pc, &pcType); CHKERRQ(ierr);
661     ierr = PetscPrintf(comm,
662                        "    PC Type                            : %s\n",
663                        pcType); CHKERRQ(ierr);
664 
665     if (!strcmp(pcType, PCMG)) {
666       PCMGType pcmgType;
667       ierr = PCMGGetType(pc, &pcmgType); CHKERRQ(ierr);
668       ierr = PetscPrintf(comm,
669                          "  P-Multigrid:\n"
670                          "    PCMG Type                          : %s\n"
671                          "    PCMG Cycle Type                    : %s\n",
672                          PCMGTypes[pcmgType],
673                          PCMGCycleTypes[pcmgCycleType]); CHKERRQ(ierr);
674 
675       // -- Coarse Solve
676       KSP kspCoarse;
677       PC pcCoarse;
678       PCType pcType;
679 
680       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
681       ierr = KSPGetType(kspCoarse, &kspType); CHKERRQ(ierr);
682       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
683       ierr = PCGetType(pcCoarse, &pcType); CHKERRQ(ierr);
684       ierr = PetscPrintf(comm,
685                          "    Coarse Solve:\n"
686                          "      KSP Type                         : %s\n"
687                          "      PC Type                          : %s\n",
688                          kspType, pcType); CHKERRQ(ierr);
689     }
690   }
691 
692   // ---------------------------------------------------------------------------
693   // Compute solve time
694   // ---------------------------------------------------------------------------
695   if (!appCtx->testMode) {
696     ierr = MPI_Allreduce(&elapsedTime, &minTime, 1, MPI_DOUBLE, MPI_MIN, comm);
697     CHKERRQ(ierr);
698     ierr = MPI_Allreduce(&elapsedTime, &maxTime, 1, MPI_DOUBLE, MPI_MAX, comm);
699     CHKERRQ(ierr);
700     ierr = PetscPrintf(comm,
701                        "  Performance:\n"
702                        "    SNES Solve Time                    : %g (%g) sec\n",
703                        maxTime, minTime); CHKERRQ(ierr);
704   }
705 
706   // ---------------------------------------------------------------------------
707   // Compute error
708   // ---------------------------------------------------------------------------
709   if (appCtx->forcingChoice == FORCE_MMS) {
710     CeedScalar l2Error = 1., l2Unorm = 1.;
711     const CeedScalar *truearray;
712     Vec errorVec, trueVec;
713 
714     // -- Work vectors
715     ierr = VecDuplicate(U, &errorVec); CHKERRQ(ierr);
716     ierr = VecSet(errorVec, 0.0); CHKERRQ(ierr);
717     ierr = VecDuplicate(U, &trueVec); CHKERRQ(ierr);
718     ierr = VecSet(trueVec, 0.0); CHKERRQ(ierr);
719 
720     // -- Assemble global true solution vector
721     CeedVectorGetArrayRead(ceedData[fineLevel]->truesoln, CEED_MEM_HOST,
722                            &truearray);
723     ierr = VecPlaceArray(resCtx->Yloc, truearray); CHKERRQ(ierr);
724     ierr = DMLocalToGlobal(resCtx->dm, resCtx->Yloc, INSERT_VALUES, trueVec);
725     CHKERRQ(ierr);
726     ierr = VecResetArray(resCtx->Yloc); CHKERRQ(ierr);
727     CeedVectorRestoreArrayRead(ceedData[fineLevel]->truesoln, &truearray);
728 
729     // -- Compute L2 error
730     ierr = VecWAXPY(errorVec, -1.0, U, trueVec); CHKERRQ(ierr);
731     ierr = VecNorm(errorVec, NORM_2, &l2Error); CHKERRQ(ierr);
732     ierr = VecNorm(U, NORM_2, &l2Unorm); CHKERRQ(ierr);
733     l2Error /= l2Unorm;
734 
735     // -- Output
736     if (!appCtx->testMode || l2Error > 0.05) {
737       ierr = PetscPrintf(comm,
738                          "    L2 Error                           : %e\n",
739                          l2Error); CHKERRQ(ierr);
740     }
741 
742     // -- Cleanup
743     ierr = VecDestroy(&errorVec); CHKERRQ(ierr);
744     ierr = VecDestroy(&trueVec); CHKERRQ(ierr);
745   }
746 
747   // ---------------------------------------------------------------------------
748   // Compute energy
749   // ---------------------------------------------------------------------------
750   if (!appCtx->testMode) {
751     // -- Compute L2 error
752     CeedScalar energy;
753     ierr = ComputeStrainEnergy(dmEnergy, resCtx, ceedData[fineLevel]->opEnergy,
754                                U, &energy); CHKERRQ(ierr);
755 
756     // -- Output
757     ierr = PetscPrintf(comm,
758                        "    Strain Energy                      : %e\n",
759                        energy); CHKERRQ(ierr);
760   }
761 
762   // ---------------------------------------------------------------------------
763   // Output diagnostic quantities
764   // ---------------------------------------------------------------------------
765   if (appCtx->viewSoln || appCtx->viewFinalSoln) {
766     // -- Setup context
767     UserMult diagnosticCtx;
768     ierr = PetscMalloc1(1, &diagnosticCtx); CHKERRQ(ierr);
769     ierr = PetscMemcpy(diagnosticCtx, resCtx, sizeof(*resCtx)); CHKERRQ(ierr);
770     diagnosticCtx->dm = dmDiagnostic;
771     diagnosticCtx->op = ceedData[fineLevel]->opDiagnostic;
772 
773     // -- Compute and output
774     ierr = ViewDiagnosticQuantities(comm, levelDMs[fineLevel], diagnosticCtx, U,
775                                     ceedData[fineLevel]->ErestrictDiagnostic);
776     CHKERRQ(ierr);
777 
778     // -- Cleanup
779     ierr = PetscFree(diagnosticCtx); CHKERRQ(ierr);
780   }
781 
782   // ---------------------------------------------------------------------------
783   // Free objects
784   // ---------------------------------------------------------------------------
785   // Data in arrays per level
786   for (PetscInt level = 0; level < numLevels; level++) {
787     // Vectors
788     ierr = VecDestroy(&Ug[level]); CHKERRQ(ierr);
789     ierr = VecDestroy(&Uloc[level]); CHKERRQ(ierr);
790 
791     // Jacobian matrix and data
792     ierr = VecDestroy(&jacobCtx[level]->Yloc); CHKERRQ(ierr);
793     ierr = MatDestroy(&jacobMat[level]); CHKERRQ(ierr);
794     ierr = PetscFree(jacobCtx[level]); CHKERRQ(ierr);
795 
796     // Prolongation/Restriction matrix and data
797     if (level > 0) {
798       ierr = VecDestroy(&prolongRestrCtx[level]->multVec); CHKERRQ(ierr);
799       ierr = PetscFree(prolongRestrCtx[level]); CHKERRQ(ierr);
800       ierr = MatDestroy(&prolongRestrMat[level]); CHKERRQ(ierr);
801     }
802 
803     // DM
804     ierr = DMDestroy(&levelDMs[level]); CHKERRQ(ierr);
805 
806     // libCEED objects
807     ierr = CeedDataDestroy(level, ceedData[level]); CHKERRQ(ierr);
808   }
809 
810   // Arrays
811   ierr = PetscFree(Ug); CHKERRQ(ierr);
812   ierr = PetscFree(Uloc); CHKERRQ(ierr);
813   ierr = PetscFree(Ugsz); CHKERRQ(ierr);
814   ierr = PetscFree(Ulsz); CHKERRQ(ierr);
815   ierr = PetscFree(Ulocsz); CHKERRQ(ierr);
816   ierr = PetscFree(jacobCtx); CHKERRQ(ierr);
817   ierr = PetscFree(jacobMat); CHKERRQ(ierr);
818   ierr = PetscFree(prolongRestrCtx); CHKERRQ(ierr);
819   ierr = PetscFree(prolongRestrMat); CHKERRQ(ierr);
820   ierr = PetscFree(appCtx->levelDegrees); CHKERRQ(ierr);
821   ierr = PetscFree(ceedData); CHKERRQ(ierr);
822 
823   // libCEED objects
824   CeedQFunctionDestroy(&qfRestrict);
825   CeedQFunctionDestroy(&qfProlong);
826   CeedDestroy(&ceed);
827   CeedDestroy(&ceedFine);
828 
829   // PETSc objects
830   ierr = VecDestroy(&U); CHKERRQ(ierr);
831   ierr = VecDestroy(&R); CHKERRQ(ierr);
832   ierr = VecDestroy(&Rloc); CHKERRQ(ierr);
833   ierr = VecDestroy(&F); CHKERRQ(ierr);
834   ierr = VecDestroy(&Floc); CHKERRQ(ierr);
835   ierr = MatDestroy(&jacobMatCoarse); CHKERRQ(ierr);
836   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
837   ierr = SNESDestroy(&snesCoarse); CHKERRQ(ierr);
838   ierr = DMDestroy(&dmOrig); CHKERRQ(ierr);
839   ierr = DMDestroy(&dmEnergy); CHKERRQ(ierr);
840   ierr = DMDestroy(&dmDiagnostic); CHKERRQ(ierr);
841   ierr = PetscFree(levelDMs); CHKERRQ(ierr);
842 
843   // Structs
844   ierr = PetscFree(resCtx); CHKERRQ(ierr);
845   ierr = PetscFree(formJacobCtx); CHKERRQ(ierr);
846   ierr = PetscFree(jacobCoarseCtx); CHKERRQ(ierr);
847   ierr = PetscFree(appCtx); CHKERRQ(ierr);
848   ierr = PetscFree(phys); CHKERRQ(ierr);
849   ierr = PetscFree(physSmoother); CHKERRQ(ierr);
850   ierr = PetscFree(units); CHKERRQ(ierr);
851 
852   return PetscFinalize();
853 }
854