xref: /libCEED/examples/solids/elasticity.c (revision b8eaa5f0210b478cc255b46a9a0e447345c58689)
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   Units          units;                  // Contains units scaling
52   // PETSc objects
53   PetscLogStage  stageDMSetup, stageLibceedSetup,
54                  stageSnesSetup, stageSnesSolve;
55   DM             dmOrig;                 // Distributed DM to clone
56   DM             dmEnergy, dmDiagnostic; // DMs for postprocessing
57   DM             *levelDMs;
58   Vec            U, *Ug, *Uloc;          // U: solution, R: residual, F: forcing
59   Vec            R, Rloc, F, Floc;       // g: global, loc: local
60   SNES           snes, snesCoarse = NULL;
61   Mat            *jacobMat, jacobMatCoarse, *prolongRestrMat;
62   // PETSc data
63   UserMult       resCtx, jacobCoarseCtx = NULL, *jacobCtx;
64   FormJacobCtx   formJacobCtx;
65   UserMultProlongRestr *prolongRestrCtx;
66   PCMGCycleType  pcmgCycleType = PC_MG_CYCLE_V;
67   // libCEED objects
68   Ceed           ceed, ceedFine = NULL;
69   CeedData       *ceedData;
70   CeedQFunction  qfRestrict = NULL, qfProlong = NULL;
71   // Parameters
72   PetscInt       ncompu = 3;             // 3 DoFs in 3D
73   PetscInt       ncompe = 1, ncompd = 2; // 1 energy output, 2 diagnostic
74   PetscInt       numLevels = 1, fineLevel = 0;
75   PetscInt       *Ugsz, *Ulsz, *Ulocsz;  // sz: size
76   PetscInt       snesIts = 0;
77   // Timing
78   double         startTime, elapsedTime, minTime, maxTime;
79 
80   ierr = PetscInitialize(&argc, &argv, NULL, help);
81   if (ierr)
82     return ierr;
83 
84   // ---------------------------------------------------------------------------
85   // Process command line options
86   // ---------------------------------------------------------------------------
87   comm = PETSC_COMM_WORLD;
88 
89   // -- Set mesh file, polynomial degree, problem type
90   ierr = PetscCalloc1(1, &appCtx); CHKERRQ(ierr);
91   ierr = ProcessCommandLineOptions(comm, appCtx); CHKERRQ(ierr);
92   numLevels = appCtx->numLevels;
93   fineLevel = numLevels - 1;
94 
95   // -- Set Poison's ratio, Young's Modulus
96   ierr = PetscMalloc1(1, &phys); CHKERRQ(ierr);
97   ierr = PetscMalloc1(1, &units); CHKERRQ(ierr);
98   ierr = ProcessPhysics(comm, phys, units); CHKERRQ(ierr);
99 
100   // ---------------------------------------------------------------------------
101   // Setup DM
102   // ---------------------------------------------------------------------------
103   // Performance logging
104   ierr = PetscLogStageRegister("DM and Vector Setup Stage", &stageDMSetup);
105   CHKERRQ(ierr);
106   ierr = PetscLogStagePush(stageDMSetup); CHKERRQ(ierr);
107 
108   // -- Create distributed DM from mesh file
109   ierr = CreateDistributedDM(comm, appCtx, &dmOrig); CHKERRQ(ierr);
110 
111   // -- Setup DM by polynomial degree
112   ierr = PetscMalloc1(numLevels, &levelDMs); CHKERRQ(ierr);
113   for (PetscInt level = 0; level < numLevels; level++) {
114     ierr = DMClone(dmOrig, &levelDMs[level]); CHKERRQ(ierr);
115     ierr = SetupDMByDegree(levelDMs[level], appCtx, appCtx->levelDegrees[level],
116                            PETSC_TRUE, ncompu); CHKERRQ(ierr);
117     // -- Label field components for viewing
118     // Empty name for conserved field (because there is only one field)
119     PetscSection section;
120     ierr = DMGetLocalSection(levelDMs[level], &section); CHKERRQ(ierr);
121     ierr = PetscSectionSetFieldName(section, 0, "Displacement"); CHKERRQ(ierr);
122     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
123     CHKERRQ(ierr);
124     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
125     CHKERRQ(ierr);
126     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
127     CHKERRQ(ierr);
128   }
129 
130   // -- Setup postprocessing DMs
131   ierr = DMClone(dmOrig, &dmEnergy); CHKERRQ(ierr);
132   ierr = SetupDMByDegree(dmEnergy, appCtx, appCtx->levelDegrees[fineLevel],
133                          PETSC_FALSE, ncompe); CHKERRQ(ierr);
134   ierr = DMClone(dmOrig, &dmDiagnostic); CHKERRQ(ierr);
135   ierr = SetupDMByDegree(dmDiagnostic, appCtx, appCtx->levelDegrees[fineLevel],
136                          PETSC_FALSE, ncompd); CHKERRQ(ierr);
137   {
138     // -- Label field components for viewing
139     // Empty name for conserved field (because there is only one field)
140     PetscSection section;
141     ierr = DMGetLocalSection(dmDiagnostic, &section); CHKERRQ(ierr);
142     ierr = PetscSectionSetFieldName(section, 0, "Diagnostics"); CHKERRQ(ierr);
143     ierr = PetscSectionSetComponentName(section, 0, 0, "CondensedPressure");
144     ierr = PetscSectionSetComponentName(section, 0, 1, "StrainEnergyDensity");
145     CHKERRQ(ierr);
146   }
147 
148   // ---------------------------------------------------------------------------
149   // Setup solution and work vectors
150   // ---------------------------------------------------------------------------
151   // Allocate arrays
152   ierr = PetscMalloc1(numLevels, &Ug); CHKERRQ(ierr);
153   ierr = PetscMalloc1(numLevels, &Uloc); CHKERRQ(ierr);
154   ierr = PetscMalloc1(numLevels, &Ugsz); CHKERRQ(ierr);
155   ierr = PetscMalloc1(numLevels, &Ulsz); CHKERRQ(ierr);
156   ierr = PetscMalloc1(numLevels, &Ulocsz); CHKERRQ(ierr);
157 
158   // -- Setup solution vectors for each level
159   for (PetscInt level = 0; level < numLevels; level++) {
160     // -- Create global unknown vector U
161     ierr = DMCreateGlobalVector(levelDMs[level], &Ug[level]); CHKERRQ(ierr);
162     ierr = VecGetSize(Ug[level], &Ugsz[level]); CHKERRQ(ierr);
163     // Note: Local size for matShell
164     ierr = VecGetLocalSize(Ug[level], &Ulsz[level]); CHKERRQ(ierr);
165 
166     // -- Create local unknown vector Uloc
167     ierr = DMCreateLocalVector(levelDMs[level], &Uloc[level]); CHKERRQ(ierr);
168     // Note: local size for libCEED
169     ierr = VecGetSize(Uloc[level], &Ulocsz[level]); CHKERRQ(ierr);
170   }
171 
172   // -- Create residual and forcing vectors
173   ierr = VecDuplicate(Ug[fineLevel], &U); CHKERRQ(ierr);
174   ierr = VecDuplicate(Ug[fineLevel], &R); CHKERRQ(ierr);
175   ierr = VecDuplicate(Ug[fineLevel], &F); CHKERRQ(ierr);
176   ierr = VecDuplicate(Uloc[fineLevel], &Rloc); CHKERRQ(ierr);
177   ierr = VecDuplicate(Uloc[fineLevel], &Floc); CHKERRQ(ierr);
178 
179   // Performance logging
180   ierr = PetscLogStagePop();
181 
182   // ---------------------------------------------------------------------------
183   // Set up libCEED
184   // ---------------------------------------------------------------------------
185   // Performance logging
186   ierr = PetscLogStageRegister("libCEED Setup Stage", &stageLibceedSetup);
187   CHKERRQ(ierr);
188   ierr = PetscLogStagePush(stageLibceedSetup); CHKERRQ(ierr);
189 
190   // Initalize backend
191   CeedInit(appCtx->ceedResource, &ceed);
192   if (appCtx->degree > 4 && appCtx->ceedResourceFine[0])
193     CeedInit(appCtx->ceedResourceFine, &ceedFine);
194 
195   // -- Create libCEED local forcing vector
196   CeedVector forceCeed;
197   CeedScalar *f;
198   if (appCtx->forcingChoice != FORCE_NONE) {
199     ierr = VecGetArray(Floc, &f); CHKERRQ(ierr);
200     CeedVectorCreate(ceed, Ulocsz[fineLevel], &forceCeed);
201     CeedVectorSetArray(forceCeed, CEED_MEM_HOST, CEED_USE_POINTER, f);
202   }
203 
204   // -- Restriction and prolongation QFunction
205   if (appCtx->multigridChoice != MULTIGRID_NONE) {
206     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
207                                 &qfRestrict);
208     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
209                                 &qfProlong);
210   }
211 
212   // -- Setup libCEED objects
213   ierr = PetscMalloc1(numLevels, &ceedData); CHKERRQ(ierr);
214   // ---- Setup residual evaluator and geometric information
215   ierr = PetscCalloc1(1, &ceedData[fineLevel]); CHKERRQ(ierr);
216   {
217     bool highOrder = (appCtx->levelDegrees[fineLevel] > 4 && ceedFine);
218     Ceed levelCeed = highOrder ? ceedFine : ceed;
219     ierr = SetupLibceedFineLevel(levelDMs[fineLevel], dmEnergy, dmDiagnostic,
220                                  levelCeed, appCtx, phys, ceedData, fineLevel,
221                                  ncompu, Ugsz[fineLevel], Ulocsz[fineLevel],
222                                  forceCeed, qfRestrict, qfProlong);
223     CHKERRQ(ierr);
224   }
225   // ---- Setup Jacobian evaluator and prolongation/restriction
226   for (PetscInt level = 0; level < numLevels; level++) {
227     if (level != fineLevel) {
228       ierr = PetscCalloc1(1, &ceedData[level]); CHKERRQ(ierr);
229     }
230 
231     // Note: use high order ceed, if specified and degree > 4
232     bool highOrder = (appCtx->levelDegrees[level] > 4 && ceedFine);
233     Ceed levelCeed = highOrder ? ceedFine : ceed;
234     ierr = SetupLibceedLevel(levelDMs[level], levelCeed, appCtx, phys,
235                              ceedData,  level, ncompu, Ugsz[level],
236                              Ulocsz[level], forceCeed, qfRestrict,
237                              qfProlong); CHKERRQ(ierr);
238   }
239 
240   // Performance logging
241   ierr = PetscLogStagePop();
242 
243   // ---------------------------------------------------------------------------
244   // Setup global forcing vector
245   // ---------------------------------------------------------------------------
246   ierr = VecZeroEntries(F); CHKERRQ(ierr);
247 
248   if (appCtx->forcingChoice != FORCE_NONE) {
249     ierr = VecRestoreArray(Floc, &f); CHKERRQ(ierr);
250     ierr = DMLocalToGlobal(levelDMs[fineLevel], Floc, ADD_VALUES, F);
251     CHKERRQ(ierr);
252     CeedVectorDestroy(&forceCeed);
253   }
254 
255   // ---------------------------------------------------------------------------
256   // Print problem summary
257   // ---------------------------------------------------------------------------
258   if (!appCtx->testMode) {
259     const char *usedresource;
260     CeedGetResource(ceed, &usedresource);
261 
262     ierr = PetscPrintf(comm,
263                        "\n-- Elastisticy Example - libCEED + PETSc --\n"
264                        "  libCEED:\n"
265                        "    libCEED Backend                    : %s\n",
266                        usedresource); CHKERRQ(ierr);
267 
268     if (ceedFine) {
269       ierr = PetscPrintf(comm,
270                          "    libCEED Backend - high order       : %s\n",
271                          appCtx->ceedResourceFine); CHKERRQ(ierr);
272     }
273 
274     ierr = PetscPrintf(comm,
275                        "  Problem:\n"
276                        "    Problem Name                       : %s\n"
277                        "    Forcing Function                   : %s\n"
278                        "  Mesh:\n"
279                        "    File                               : %s\n"
280                        "    Number of 1D Basis Nodes (p)       : %d\n"
281                        "    Number of 1D Quadrature Points (q) : %d\n"
282                        "    Global nodes                       : %D\n"
283                        "    Owned nodes                        : %D\n"
284                        "    DoF per node                       : %D\n"
285                        "  Multigrid:\n"
286                        "    Type                               : %s\n"
287                        "    Number of Levels                   : %d\n",
288                        problemTypesForDisp[appCtx->problemChoice],
289                        forcingTypesForDisp[appCtx->forcingChoice],
290                        appCtx->meshFile[0] ? appCtx->meshFile : "Box Mesh",
291                        appCtx->degree + 1, appCtx->degree + 1,
292                        Ugsz[fineLevel]/ncompu, Ulsz[fineLevel]/ncompu, ncompu,
293                        (appCtx->degree == 1 &&
294                         appCtx->multigridChoice != MULTIGRID_NONE) ?
295                        "Algebraic multigrid" :
296                        multigridTypesForDisp[appCtx->multigridChoice],
297                        (appCtx->degree == 1 ||
298                         appCtx->multigridChoice == MULTIGRID_NONE) ?
299                        0 : numLevels); CHKERRQ(ierr);
300 
301     if (appCtx->multigridChoice != MULTIGRID_NONE) {
302       for (PetscInt i = 0; i < 2; i++) {
303         CeedInt level = i ? fineLevel : 0;
304         ierr = PetscPrintf(comm,
305                            "    Level %D (%s):\n"
306                            "      Number of 1D Basis Nodes (p)     : %d\n"
307                            "      Global Nodes                     : %D\n"
308                            "      Owned Nodes                      : %D\n",
309                            level, i ? "fine" : "coarse",
310                            appCtx->levelDegrees[level] + 1,
311                            Ugsz[level]/ncompu, Ulsz[level]/ncompu);
312         CHKERRQ(ierr);
313       }
314     }
315   }
316 
317   // ---------------------------------------------------------------------------
318   // Setup SNES
319   // ---------------------------------------------------------------------------
320   // Performance logging
321   ierr = PetscLogStageRegister("SNES Setup Stage", &stageSnesSetup);
322   CHKERRQ(ierr);
323   ierr = PetscLogStagePush(stageSnesSetup); CHKERRQ(ierr);
324 
325   // Create SNES
326   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
327   ierr = SNESSetDM(snes, levelDMs[fineLevel]); CHKERRQ(ierr);
328 
329   // -- Jacobian evaluators
330   ierr = PetscMalloc1(numLevels, &jacobCtx); CHKERRQ(ierr);
331   ierr = PetscMalloc1(numLevels, &jacobMat); CHKERRQ(ierr);
332   for (PetscInt level = 0; level < numLevels; level++) {
333     // -- Jacobian context for level
334     ierr = PetscMalloc1(1, &jacobCtx[level]); CHKERRQ(ierr);
335     ierr = SetupJacobianCtx(comm, appCtx, levelDMs[level], Ug[level],
336                             Uloc[level], ceedData[level], ceed,
337                             jacobCtx[level]); CHKERRQ(ierr);
338 
339     // -- Form Action of Jacobian on delta_u
340     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level], Ugsz[level],
341                           Ugsz[level], jacobCtx[level], &jacobMat[level]);
342     CHKERRQ(ierr);
343     ierr = MatShellSetOperation(jacobMat[level], MATOP_MULT,
344                                 (void (*)(void))ApplyJacobian_Ceed);
345     CHKERRQ(ierr);
346     ierr = MatShellSetOperation(jacobMat[level], MATOP_GET_DIAGONAL,
347                                 (void(*)(void))GetDiag_Ceed);
348 
349   }
350   // Note: FormJacobian updates Jacobian matrices on each level
351   //   and assembles the Jpre matrix, if needed
352   ierr = PetscMalloc1(1, &formJacobCtx); CHKERRQ(ierr);
353   formJacobCtx->jacobCtx = jacobCtx;
354   formJacobCtx->numLevels = numLevels;
355   formJacobCtx->jacobMat = jacobMat;
356 
357   // -- Residual evaluation function
358   ierr = PetscMalloc1(1, &resCtx); CHKERRQ(ierr);
359   ierr = PetscMemcpy(resCtx, jacobCtx[fineLevel],
360                      sizeof(*jacobCtx[fineLevel])); CHKERRQ(ierr);
361   resCtx->op = ceedData[fineLevel]->opApply;
362   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, resCtx); CHKERRQ(ierr);
363 
364   // -- Prolongation/Restriction evaluation
365   ierr = PetscMalloc1(numLevels, &prolongRestrCtx); CHKERRQ(ierr);
366   ierr = PetscMalloc1(numLevels, &prolongRestrMat); CHKERRQ(ierr);
367   for (PetscInt level = 1; level < numLevels; level++) {
368     // ---- Prolongation/restriction context for level
369     ierr = PetscMalloc1(1, &prolongRestrCtx[level]); CHKERRQ(ierr);
370     ierr = SetupProlongRestrictCtx(comm, levelDMs[level-1], levelDMs[level],
371                                    Ug[level], Uloc[level-1], Uloc[level],
372                                    ceedData[level-1], ceedData[level], ceed,
373                                    prolongRestrCtx[level]); CHKERRQ(ierr);
374 
375     // ---- Form Action of Jacobian on delta_u
376     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level-1], Ugsz[level],
377                           Ugsz[level-1], prolongRestrCtx[level],
378                           &prolongRestrMat[level]); CHKERRQ(ierr);
379     // Note: In PCMG, restriction is the transpose of prolongation
380     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT,
381                                 (void (*)(void))Prolong_Ceed);
382     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT_TRANSPOSE,
383                                 (void (*)(void))Restrict_Ceed);
384     CHKERRQ(ierr);
385   }
386 
387   // ---------------------------------------------------------------------------
388   // Setup dummy SNES for AMG coarse solve
389   // ---------------------------------------------------------------------------
390   if (appCtx->multigridChoice != MULTIGRID_NONE) {
391     // -- Jacobian Matrix
392     ierr = DMSetMatType(levelDMs[0], MATAIJ); CHKERRQ(ierr);
393     ierr = DMCreateMatrix(levelDMs[0], &jacobMatCoarse); CHKERRQ(ierr);
394 
395     if (appCtx->degree > 1) {
396       ierr = SNESCreate(comm, &snesCoarse); CHKERRQ(ierr);
397       ierr = SNESSetDM(snesCoarse, levelDMs[0]); CHKERRQ(ierr);
398       ierr = SNESSetSolution(snesCoarse, Ug[0]); CHKERRQ(ierr);
399 
400       // -- Jacobian function
401       ierr = SNESSetJacobian(snesCoarse, jacobMatCoarse, jacobMatCoarse, NULL,
402                              NULL); CHKERRQ(ierr);
403 
404       // -- Residual evaluation function
405       ierr = PetscMalloc1(1, &jacobCoarseCtx); CHKERRQ(ierr);
406       ierr = PetscMemcpy(jacobCoarseCtx, jacobCtx[0], sizeof(*jacobCtx[0]));
407       CHKERRQ(ierr);
408       ierr = SNESSetFunction(snesCoarse, Ug[0], ApplyJacobianCoarse_Ceed,
409                              jacobCoarseCtx); CHKERRQ(ierr);
410 
411       // -- Update formJacobCtx
412       formJacobCtx->Ucoarse = Ug[0];
413       formJacobCtx->snesCoarse = snesCoarse;
414       formJacobCtx->jacobMatCoarse = jacobMatCoarse;
415     }
416   }
417 
418   // Set Jacobian function
419   if (appCtx->degree > 1) {
420     ierr = SNESSetJacobian(snes, jacobMat[fineLevel], jacobMat[fineLevel],
421                            FormJacobian, formJacobCtx); CHKERRQ(ierr);
422   } else {
423     ierr = SNESSetJacobian(snes, jacobMat[0], jacobMatCoarse,
424                            SNESComputeJacobianDefaultColor, NULL);
425     CHKERRQ(ierr);
426   }
427 
428   // ---------------------------------------------------------------------------
429   // Setup KSP
430   // ---------------------------------------------------------------------------
431   {
432     PC pc;
433     KSP ksp;
434 
435     // -- KSP
436     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
437     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
438     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
439     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
440                             PETSC_DEFAULT); CHKERRQ(ierr);
441     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
442 
443     // -- Preconditioning
444     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
445     ierr = PCSetDM(pc, levelDMs[fineLevel]); CHKERRQ(ierr);
446     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
447 
448     if (appCtx->multigridChoice == MULTIGRID_NONE) {
449       // ---- No Multigrid
450       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
451       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
452     } else if (appCtx->degree == 1) {
453       // ---- AMG for degree 1
454       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
455     } else {
456       // ---- PCMG
457       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
458 
459       // ------ PCMG levels
460       ierr = PCMGSetLevels(pc, numLevels, NULL); CHKERRQ(ierr);
461       for (PetscInt level = 0; level < numLevels; level++) {
462         // -------- Smoother
463         KSP kspSmoother, kspEst;
464         PC pcSmoother;
465 
466         // ---------- Smoother KSP
467         ierr = PCMGGetSmoother(pc, level, &kspSmoother); CHKERRQ(ierr);
468         ierr = KSPSetDM(kspSmoother, levelDMs[level]); CHKERRQ(ierr);
469         ierr = KSPSetDMActive(kspSmoother, PETSC_FALSE); CHKERRQ(ierr);
470 
471         // ---------- Chebyshev options
472         ierr = KSPSetType(kspSmoother, KSPCHEBYSHEV); CHKERRQ(ierr);
473         ierr = KSPChebyshevEstEigSet(kspSmoother, 0, 0.1, 0, 1.1);
474         CHKERRQ(ierr);
475         ierr = KSPChebyshevEstEigGetKSP(kspSmoother, &kspEst); CHKERRQ(ierr);
476         ierr = KSPSetType(kspEst, KSPCG); CHKERRQ(ierr);
477         ierr = KSPChebyshevEstEigSetUseNoisy(kspSmoother, PETSC_TRUE);
478         CHKERRQ(ierr);
479         ierr = KSPSetOperators(kspSmoother, jacobMat[level], jacobMat[level]);
480         CHKERRQ(ierr);
481 
482         // ---------- Smoother preconditioner
483         ierr = KSPGetPC(kspSmoother, &pcSmoother); CHKERRQ(ierr);
484         ierr = PCSetType(pcSmoother, PCJACOBI); CHKERRQ(ierr);
485         ierr = PCJacobiSetType(pcSmoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
486 
487         // -------- Work vector
488         if (level != fineLevel) {
489           ierr = PCMGSetX(pc, level, Ug[level]); CHKERRQ(ierr);
490         }
491 
492         // -------- Level prolongation/restriction operator
493         if (level > 0) {
494           ierr = PCMGSetInterpolation(pc, level, prolongRestrMat[level]);
495           CHKERRQ(ierr);
496           ierr = PCMGSetRestriction(pc, level, prolongRestrMat[level]);
497           CHKERRQ(ierr);
498         }
499       }
500 
501       // ------ PCMG coarse solve
502       KSP kspCoarse;
503       PC pcCoarse;
504 
505       // -------- Coarse KSP
506       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
507       ierr = KSPSetType(kspCoarse, KSPPREONLY); CHKERRQ(ierr);
508       ierr = KSPSetOperators(kspCoarse, jacobMatCoarse, jacobMatCoarse);
509       CHKERRQ(ierr);
510       ierr = KSPSetOptionsPrefix(kspCoarse, "coarse_"); CHKERRQ(ierr);
511 
512       // -------- Coarse preconditioner
513       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
514       ierr = PCSetType(pcCoarse, PCGAMG); CHKERRQ(ierr);
515       ierr = PCSetOptionsPrefix(pcCoarse, "coarse_"); CHKERRQ(ierr);
516 
517       ierr = KSPSetFromOptions(kspCoarse); CHKERRQ(ierr);
518       ierr = PCSetFromOptions(pcCoarse); CHKERRQ(ierr);
519 
520       // ------ PCMG options
521       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
522       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
523       ierr = PCMGSetCycleType(pc, pcmgCycleType); CHKERRQ(ierr);
524     }
525     ierr = KSPSetFromOptions(ksp);
526     ierr = PCSetFromOptions(pc);
527   }
528   {
529     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
530     SNESLineSearch linesearch;
531 
532     ierr = SNESGetLineSearch(snes, &linesearch); CHKERRQ(ierr);
533     ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHCP); CHKERRQ(ierr);
534   }
535 
536   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
537 
538   // Performance logging
539   ierr = PetscLogStagePop();
540 
541   // ---------------------------------------------------------------------------
542   // Set initial guess
543   // ---------------------------------------------------------------------------
544   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
545 
546   // View solution
547   if (appCtx->viewSoln) {
548     ierr = ViewSolution(comm, U, 0, 0.0); CHKERRQ(ierr);
549   }
550 
551   // ---------------------------------------------------------------------------
552   // Solve SNES
553   // ---------------------------------------------------------------------------
554   PetscBool snesMonitor = PETSC_FALSE;
555   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snesMonitor);
556   CHKERRQ(ierr);
557 
558   // Performance logging
559   ierr = PetscLogStageRegister("SNES Solve Stage", &stageSnesSolve);
560   CHKERRQ(ierr);
561   ierr = PetscLogStagePush(stageSnesSolve); CHKERRQ(ierr);
562 
563   // Timing
564   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
565   startTime = MPI_Wtime();
566 
567   // Solve for each load increment
568   PetscInt increment;
569   for (increment = 1; increment <= appCtx->numIncrements; increment++) {
570     // -- Log increment count
571     if (snesMonitor) {
572       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
573       CHKERRQ(ierr);
574     }
575 
576     // -- Scale the problem
577     PetscScalar loadIncrement = 1.0*increment / appCtx->numIncrements,
578                 scalingFactor = loadIncrement /
579                                 (increment == 1 ? 1 : resCtx->loadIncrement);
580     resCtx->loadIncrement = loadIncrement;
581     if (appCtx->numIncrements > 1 && appCtx->forcingChoice != FORCE_NONE) {
582       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
583     }
584 
585     // -- Solve
586     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
587 
588     // -- View solution
589     if (appCtx->viewSoln) {
590       ierr = ViewSolution(comm, U, increment, loadIncrement); CHKERRQ(ierr);
591     }
592 
593     // -- Update SNES iteration count
594     PetscInt its;
595     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
596     snesIts += its;
597 
598     // -- Check for divergence
599     SNESConvergedReason reason;
600     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
601     if (reason < 0)
602       break;
603   }
604 
605   // Timing
606   elapsedTime = MPI_Wtime() - startTime;
607 
608   // Performance logging
609   ierr = PetscLogStagePop();
610 
611   // View solution
612   if (appCtx->viewFinalSoln && !appCtx->viewSoln) {
613     ierr = ViewSolution(comm, U, increment - 1, 1.0); CHKERRQ(ierr);
614   }
615 
616   // ---------------------------------------------------------------------------
617   // Output summary
618   // ---------------------------------------------------------------------------
619   if (!appCtx->testMode) {
620     // -- SNES
621     SNESType snesType;
622     SNESConvergedReason reason;
623     PetscReal rnorm;
624     ierr = SNESGetType(snes, &snesType); CHKERRQ(ierr);
625     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
626     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
627     ierr = PetscPrintf(comm,
628                        "  SNES:\n"
629                        "    SNES Type                          : %s\n"
630                        "    SNES Convergence                   : %s\n"
631                        "    Number of Load Increments          : %d\n"
632                        "    Completed Load Increments          : %d\n"
633                        "    Total SNES Iterations              : %D\n"
634                        "    Final rnorm                        : %e\n",
635                        snesType, SNESConvergedReasons[reason],
636                        appCtx->numIncrements, increment - 1,
637                        snesIts, (double)rnorm); CHKERRQ(ierr);
638 
639     // -- KSP
640     KSP ksp;
641     KSPType kspType;
642     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
643     ierr = KSPGetType(ksp, &kspType); CHKERRQ(ierr);
644     ierr = PetscPrintf(comm,
645                        "  Linear Solver:\n"
646                        "    KSP Type                           : %s\n",
647                        kspType); CHKERRQ(ierr);
648 
649     // -- PC
650     PC pc;
651     PCType pcType;
652     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
653     ierr = PCGetType(pc, &pcType); CHKERRQ(ierr);
654     ierr = PetscPrintf(comm,
655                        "    PC Type                            : %s\n",
656                        pcType); CHKERRQ(ierr);
657 
658     if (!strcmp(pcType, PCMG)) {
659       PCMGType pcmgType;
660       ierr = PCMGGetType(pc, &pcmgType); CHKERRQ(ierr);
661       ierr = PetscPrintf(comm,
662                          "  P-Multigrid:\n"
663                          "    PCMG Type                          : %s\n"
664                          "    PCMG Cycle Type                    : %s\n",
665                          PCMGTypes[pcmgType],
666                          PCMGCycleTypes[pcmgCycleType]); CHKERRQ(ierr);
667 
668       // -- Coarse Solve
669       KSP kspCoarse;
670       PC pcCoarse;
671       PCType pcType;
672 
673       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
674       ierr = KSPGetType(kspCoarse, &kspType); CHKERRQ(ierr);
675       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
676       ierr = PCGetType(pcCoarse, &pcType); CHKERRQ(ierr);
677       ierr = PetscPrintf(comm,
678                          "    Coarse Solve:\n"
679                          "      KSP Type                         : %s\n"
680                          "      PC Type                          : %s\n",
681                          kspType, pcType); CHKERRQ(ierr);
682     }
683   }
684 
685   // ---------------------------------------------------------------------------
686   // Compute solve time
687   // ---------------------------------------------------------------------------
688   if (!appCtx->testMode) {
689     ierr = MPI_Allreduce(&elapsedTime, &minTime, 1, MPI_DOUBLE, MPI_MIN, comm);
690     CHKERRQ(ierr);
691     ierr = MPI_Allreduce(&elapsedTime, &maxTime, 1, MPI_DOUBLE, MPI_MAX, comm);
692     CHKERRQ(ierr);
693     ierr = PetscPrintf(comm,
694                        "  Performance:\n"
695                        "    SNES Solve Time                    : %g (%g) sec\n",
696                        maxTime, minTime); CHKERRQ(ierr);
697   }
698 
699   // ---------------------------------------------------------------------------
700   // Compute error
701   // ---------------------------------------------------------------------------
702   if (appCtx->forcingChoice == FORCE_MMS) {
703     CeedScalar l2Error = 1., l2Unorm = 1.;
704     const CeedScalar *truearray;
705     Vec errorVec, trueVec;
706 
707     // -- Work vectors
708     ierr = VecDuplicate(U, &errorVec); CHKERRQ(ierr);
709     ierr = VecSet(errorVec, 0.0); CHKERRQ(ierr);
710     ierr = VecDuplicate(U, &trueVec); CHKERRQ(ierr);
711     ierr = VecSet(trueVec, 0.0); CHKERRQ(ierr);
712 
713     // -- Assemble global true solution vector
714     CeedVectorGetArrayRead(ceedData[fineLevel]->truesoln, CEED_MEM_HOST,
715                            &truearray);
716     ierr = VecPlaceArray(resCtx->Yloc, truearray); CHKERRQ(ierr);
717     ierr = DMLocalToGlobal(resCtx->dm, resCtx->Yloc, INSERT_VALUES, trueVec);
718     CHKERRQ(ierr);
719     ierr = VecResetArray(resCtx->Yloc); CHKERRQ(ierr);
720     CeedVectorRestoreArrayRead(ceedData[fineLevel]->truesoln, &truearray);
721 
722     // -- Compute L2 error
723     ierr = VecWAXPY(errorVec, -1.0, U, trueVec); CHKERRQ(ierr);
724     ierr = VecNorm(errorVec, NORM_2, &l2Error); CHKERRQ(ierr);
725     ierr = VecNorm(U, NORM_2, &l2Unorm); CHKERRQ(ierr);
726     l2Error /= l2Unorm;
727 
728     // -- Output
729     if (!appCtx->testMode || l2Error > 0.05) {
730       ierr = PetscPrintf(comm,
731                          "    L2 Error                           : %e\n",
732                          l2Error); CHKERRQ(ierr);
733     }
734 
735     // -- Cleanup
736     ierr = VecDestroy(&errorVec); CHKERRQ(ierr);
737     ierr = VecDestroy(&trueVec); CHKERRQ(ierr);
738   }
739 
740   // ---------------------------------------------------------------------------
741   // Compute energy
742   // ---------------------------------------------------------------------------
743   if (!appCtx->testMode) {
744     // -- Compute L2 error
745     CeedScalar energy;
746     ierr = ComputeStrainEnergy(dmEnergy, resCtx, ceedData[fineLevel]->opEnergy,
747                                U, &energy); CHKERRQ(ierr);
748 
749     // -- Output
750     ierr = PetscPrintf(comm,
751                        "    Strain Energy                      : %e\n",
752                        energy); CHKERRQ(ierr);
753   }
754 
755   // ---------------------------------------------------------------------------
756   // Output diagnostic quantities
757   // ---------------------------------------------------------------------------
758   if (appCtx->viewSoln || appCtx->viewFinalSoln) {
759     // -- Setup context
760     UserMult diagnosticCtx;
761     ierr = PetscMalloc1(1, &diagnosticCtx); CHKERRQ(ierr);
762     ierr = PetscMemcpy(diagnosticCtx, resCtx, sizeof(*resCtx)); CHKERRQ(ierr);
763     diagnosticCtx->dm = dmDiagnostic;
764     diagnosticCtx->op = ceedData[fineLevel]->opDiagnostic;
765 
766     // -- Compute and output
767     ierr = ViewDiagnosticQuantities(comm, levelDMs[fineLevel], diagnosticCtx, U,
768                                     ceedData[fineLevel]->ErestrictDiagnostic);
769     CHKERRQ(ierr);
770 
771     // -- Cleanup
772     ierr = PetscFree(diagnosticCtx); CHKERRQ(ierr);
773   }
774 
775   // ---------------------------------------------------------------------------
776   // Free objects
777   // ---------------------------------------------------------------------------
778   // Data in arrays per level
779   for (PetscInt level = 0; level < numLevels; level++) {
780     // Vectors
781     ierr = VecDestroy(&Ug[level]); CHKERRQ(ierr);
782     ierr = VecDestroy(&Uloc[level]); CHKERRQ(ierr);
783 
784     // Jacobian matrix and data
785     ierr = VecDestroy(&jacobCtx[level]->Yloc); CHKERRQ(ierr);
786     ierr = MatDestroy(&jacobMat[level]); CHKERRQ(ierr);
787     ierr = PetscFree(jacobCtx[level]); CHKERRQ(ierr);
788 
789     // Prolongation/Restriction matrix and data
790     if (level > 0) {
791       ierr = VecDestroy(&prolongRestrCtx[level]->multVec); CHKERRQ(ierr);
792       ierr = PetscFree(prolongRestrCtx[level]); CHKERRQ(ierr);
793       ierr = MatDestroy(&prolongRestrMat[level]); CHKERRQ(ierr);
794     }
795 
796     // DM
797     ierr = DMDestroy(&levelDMs[level]); CHKERRQ(ierr);
798 
799     // libCEED objects
800     ierr = CeedDataDestroy(level, ceedData[level]); CHKERRQ(ierr);
801   }
802 
803   // Arrays
804   ierr = PetscFree(Ug); CHKERRQ(ierr);
805   ierr = PetscFree(Uloc); CHKERRQ(ierr);
806   ierr = PetscFree(Ugsz); CHKERRQ(ierr);
807   ierr = PetscFree(Ulsz); CHKERRQ(ierr);
808   ierr = PetscFree(Ulocsz); CHKERRQ(ierr);
809   ierr = PetscFree(jacobCtx); CHKERRQ(ierr);
810   ierr = PetscFree(jacobMat); CHKERRQ(ierr);
811   ierr = PetscFree(prolongRestrCtx); CHKERRQ(ierr);
812   ierr = PetscFree(prolongRestrMat); CHKERRQ(ierr);
813   ierr = PetscFree(appCtx->levelDegrees); CHKERRQ(ierr);
814   ierr = PetscFree(ceedData); CHKERRQ(ierr);
815 
816   // libCEED objects
817   CeedQFunctionDestroy(&qfRestrict);
818   CeedQFunctionDestroy(&qfProlong);
819   CeedDestroy(&ceed);
820   CeedDestroy(&ceedFine);
821 
822   // PETSc objects
823   ierr = VecDestroy(&U); CHKERRQ(ierr);
824   ierr = VecDestroy(&R); CHKERRQ(ierr);
825   ierr = VecDestroy(&Rloc); CHKERRQ(ierr);
826   ierr = VecDestroy(&F); CHKERRQ(ierr);
827   ierr = VecDestroy(&Floc); CHKERRQ(ierr);
828   ierr = MatDestroy(&jacobMatCoarse); CHKERRQ(ierr);
829   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
830   ierr = SNESDestroy(&snesCoarse); CHKERRQ(ierr);
831   ierr = DMDestroy(&dmOrig); CHKERRQ(ierr);
832   ierr = DMDestroy(&dmEnergy); CHKERRQ(ierr);
833   ierr = DMDestroy(&dmDiagnostic); CHKERRQ(ierr);
834   ierr = PetscFree(levelDMs); CHKERRQ(ierr);
835 
836   // Structs
837   ierr = PetscFree(resCtx); CHKERRQ(ierr);
838   ierr = PetscFree(formJacobCtx); CHKERRQ(ierr);
839   ierr = PetscFree(jacobCoarseCtx); CHKERRQ(ierr);
840   ierr = PetscFree(appCtx); CHKERRQ(ierr);
841   ierr = PetscFree(phys); CHKERRQ(ierr);
842   ierr = PetscFree(units); CHKERRQ(ierr);
843 
844   return PetscFinalize();
845 }
846