xref: /libCEED/examples/solids/elasticity.c (revision 7418ca8843e753bcb15a37dbebc7fe25f46df9c0)
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 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   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 = 5; // 1 energy output, 5 diagnostic
75   PetscInt       numLevels = 1, fineLevel = 0;
76   PetscInt       *Ugsz, *Ulsz, *Ulocsz;  // sz: size
77   PetscInt       snesIts = 0, kspIts = 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   // Initalize libCEED
108   // ---------------------------------------------------------------------------
109   // Initalize backend
110   CeedInit(appCtx->ceedResource, &ceed);
111   if (appCtx->degree > 4 && appCtx->ceedResourceFine[0])
112     CeedInit(appCtx->ceedResourceFine, &ceedFine);
113 
114   // Check preferred MemType
115   CeedMemType memTypeBackend;
116   CeedGetPreferredMemType(ceed, &memTypeBackend);
117   if (!appCtx->setMemTypeRequest)
118     appCtx->memTypeRequested = memTypeBackend;
119   else if (!appCtx->petscHaveCuda && appCtx->memTypeRequested == CEED_MEM_DEVICE)
120     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP_SYS,
121              "PETSc was not built with CUDA. "
122              "Requested MemType CEED_MEM_DEVICE is not supported.", NULL);
123 
124   // ---------------------------------------------------------------------------
125   // Setup DM
126   // ---------------------------------------------------------------------------
127   // Performance logging
128   ierr = PetscLogStageRegister("DM and Vector Setup Stage", &stageDMSetup);
129   CHKERRQ(ierr);
130   ierr = PetscLogStagePush(stageDMSetup); CHKERRQ(ierr);
131 
132   // -- Create distributed DM from mesh file
133   ierr = CreateDistributedDM(comm, appCtx, &dmOrig); CHKERRQ(ierr);
134 
135   // -- Setup DM by polynomial degree
136   ierr = PetscMalloc1(numLevels, &levelDMs); CHKERRQ(ierr);
137   for (PetscInt level = 0; level < numLevels; level++) {
138     ierr = DMClone(dmOrig, &levelDMs[level]); CHKERRQ(ierr);
139     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
140       ierr = DMSetVecType(levelDMs[level], VECCUDA); CHKERRQ(ierr);
141     }
142     ierr = SetupDMByDegree(levelDMs[level], appCtx, appCtx->levelDegrees[level],
143                            PETSC_TRUE, ncompu); CHKERRQ(ierr);
144     // -- Label field components for viewing
145     // Empty name for conserved field (because there is only one field)
146     PetscSection section;
147     ierr = DMGetLocalSection(levelDMs[level], &section); CHKERRQ(ierr);
148     ierr = PetscSectionSetFieldName(section, 0, "Displacement"); CHKERRQ(ierr);
149     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
150     CHKERRQ(ierr);
151     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
152     CHKERRQ(ierr);
153     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
154     CHKERRQ(ierr);
155   }
156 
157   // -- Setup postprocessing DMs
158   ierr = DMClone(dmOrig, &dmEnergy); CHKERRQ(ierr);
159   ierr = SetupDMByDegree(dmEnergy, appCtx, appCtx->levelDegrees[fineLevel],
160                          PETSC_FALSE, ncompe); CHKERRQ(ierr);
161   ierr = DMClone(dmOrig, &dmDiagnostic); CHKERRQ(ierr);
162   ierr = SetupDMByDegree(dmDiagnostic, appCtx, appCtx->levelDegrees[fineLevel],
163                          PETSC_FALSE, ncompu + ncompd); CHKERRQ(ierr);
164   if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
165     ierr = DMSetVecType(dmEnergy, VECCUDA); CHKERRQ(ierr);
166     ierr = DMSetVecType(dmDiagnostic, VECCUDA); CHKERRQ(ierr);
167   }
168   {
169     // -- Label field components for viewing
170     // Empty name for conserved field (because there is only one field)
171     PetscSection section;
172     ierr = DMGetLocalSection(dmDiagnostic, &section); CHKERRQ(ierr);
173     ierr = PetscSectionSetFieldName(section, 0, "Diagnostics"); CHKERRQ(ierr);
174     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
175     CHKERRQ(ierr);
176     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
177     CHKERRQ(ierr);
178     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
179     CHKERRQ(ierr);
180     ierr = PetscSectionSetComponentName(section, 0, 3, "Pressure");
181     CHKERRQ(ierr);
182     ierr = PetscSectionSetComponentName(section, 0, 4, "VolumentricStrain");
183     CHKERRQ(ierr);
184     ierr = PetscSectionSetComponentName(section, 0, 5, "TraceE2");
185     CHKERRQ(ierr);
186     ierr = PetscSectionSetComponentName(section, 0, 6, "detJ");
187     CHKERRQ(ierr);
188     ierr = PetscSectionSetComponentName(section, 0, 7, "StrainEnergyDensity");
189     CHKERRQ(ierr);
190   }
191 
192   // ---------------------------------------------------------------------------
193   // Setup solution and work vectors
194   // ---------------------------------------------------------------------------
195   // Allocate arrays
196   ierr = PetscMalloc1(numLevels, &Ug); CHKERRQ(ierr);
197   ierr = PetscMalloc1(numLevels, &Uloc); CHKERRQ(ierr);
198   ierr = PetscMalloc1(numLevels, &Ugsz); CHKERRQ(ierr);
199   ierr = PetscMalloc1(numLevels, &Ulsz); CHKERRQ(ierr);
200   ierr = PetscMalloc1(numLevels, &Ulocsz); CHKERRQ(ierr);
201 
202   // -- Setup solution vectors for each level
203   for (PetscInt level = 0; level < numLevels; level++) {
204     // -- Create global unknown vector U
205     ierr = DMCreateGlobalVector(levelDMs[level], &Ug[level]); CHKERRQ(ierr);
206     ierr = VecGetSize(Ug[level], &Ugsz[level]); CHKERRQ(ierr);
207     // Note: Local size for matShell
208     ierr = VecGetLocalSize(Ug[level], &Ulsz[level]); CHKERRQ(ierr);
209 
210     // -- Create local unknown vector Uloc
211     ierr = DMCreateLocalVector(levelDMs[level], &Uloc[level]); CHKERRQ(ierr);
212     // Note: local size for libCEED
213     ierr = VecGetSize(Uloc[level], &Ulocsz[level]); CHKERRQ(ierr);
214   }
215 
216   // -- Create residual and forcing vectors
217   ierr = VecDuplicate(Ug[fineLevel], &U); CHKERRQ(ierr);
218   ierr = VecDuplicate(Ug[fineLevel], &R); CHKERRQ(ierr);
219   ierr = VecDuplicate(Ug[fineLevel], &F); CHKERRQ(ierr);
220   ierr = VecDuplicate(Uloc[fineLevel], &Rloc); CHKERRQ(ierr);
221   ierr = VecDuplicate(Uloc[fineLevel], &Floc); CHKERRQ(ierr);
222 
223   // Performance logging
224   ierr = PetscLogStagePop();
225 
226   // ---------------------------------------------------------------------------
227   // Set up libCEED
228   // ---------------------------------------------------------------------------
229   // Performance logging
230   ierr = PetscLogStageRegister("libCEED Setup Stage", &stageLibceedSetup);
231   CHKERRQ(ierr);
232   ierr = PetscLogStagePush(stageLibceedSetup); CHKERRQ(ierr);
233 
234   // -- Create libCEED local forcing vector
235   CeedVector forceCeed;
236   CeedScalar *f;
237   if (appCtx->forcingChoice != FORCE_NONE) {
238     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
239       ierr = VecGetArray(Floc, &f); CHKERRQ(ierr);
240     } else {
241       ierr = VecCUDAGetArray(Floc, &f); CHKERRQ(ierr);
242     }
243     CeedVectorCreate(ceed, Ulocsz[fineLevel], &forceCeed);
244     CeedVectorSetArray(forceCeed, appCtx->memTypeRequested, CEED_USE_POINTER, f);
245   }
246 
247   // -- Restriction and prolongation QFunction
248   if (appCtx->multigridChoice != MULTIGRID_NONE) {
249     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_NONE, CEED_EVAL_INTERP,
250                                 &qfRestrict);
251     CeedQFunctionCreateIdentity(ceed, ncompu, CEED_EVAL_INTERP, CEED_EVAL_NONE,
252                                 &qfProlong);
253   }
254 
255   // -- Setup libCEED objects
256   ierr = PetscMalloc1(numLevels, &ceedData); CHKERRQ(ierr);
257   // ---- Setup residual evaluator and geometric information
258   ierr = PetscCalloc1(1, &ceedData[fineLevel]); CHKERRQ(ierr);
259   {
260     bool highOrder = (appCtx->levelDegrees[fineLevel] > 4 && ceedFine);
261     Ceed levelCeed = highOrder ? ceedFine : ceed;
262     ierr = SetupLibceedFineLevel(levelDMs[fineLevel], dmEnergy, dmDiagnostic,
263                                  levelCeed, appCtx, phys, ceedData, fineLevel,
264                                  ncompu, Ugsz[fineLevel], Ulocsz[fineLevel],
265                                  forceCeed, qfRestrict, qfProlong);
266     CHKERRQ(ierr);
267   }
268   // ---- Setup Jacobian evaluator and prolongation/restriction
269   for (PetscInt level = 0; level < numLevels; level++) {
270     if (level != fineLevel) {
271       ierr = PetscCalloc1(1, &ceedData[level]); CHKERRQ(ierr);
272     }
273 
274     // Note: use high order ceed, if specified and degree > 4
275     bool highOrder = (appCtx->levelDegrees[level] > 4 && ceedFine);
276     Ceed levelCeed = highOrder ? ceedFine : ceed;
277     ierr = SetupLibceedLevel(levelDMs[level], levelCeed, appCtx, phys,
278                              ceedData,  level, ncompu, Ugsz[level],
279                              Ulocsz[level], forceCeed, qfRestrict,
280                              qfProlong); CHKERRQ(ierr);
281   }
282 
283   // Performance logging
284   ierr = PetscLogStagePop();
285 
286   // ---------------------------------------------------------------------------
287   // Setup global forcing vector
288   // ---------------------------------------------------------------------------
289   ierr = VecZeroEntries(F); CHKERRQ(ierr);
290 
291   if (appCtx->forcingChoice != FORCE_NONE) {
292     CeedVectorTakeArray(forceCeed, appCtx->memTypeRequested, NULL);
293     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
294       ierr = VecRestoreArray(Floc, &f); CHKERRQ(ierr);
295     } else {
296       ierr = VecCUDARestoreArray(Floc, &f); CHKERRQ(ierr);
297     }
298     ierr = DMLocalToGlobal(levelDMs[fineLevel], Floc, ADD_VALUES, F);
299     CHKERRQ(ierr);
300     CeedVectorDestroy(&forceCeed);
301   }
302 
303   // ---------------------------------------------------------------------------
304   // Print problem summary
305   // ---------------------------------------------------------------------------
306   if (!appCtx->testMode) {
307     const char *usedresource;
308     CeedGetResource(ceed, &usedresource);
309 
310     ierr = PetscPrintf(comm,
311                        "\n-- Elasticity Example - libCEED + PETSc --\n"
312                        "  libCEED:\n"
313                        "    libCEED Backend                    : %s\n"
314                        "    libCEED Backend MemType            : %s\n"
315                        "    libCEED User Requested MemType     : %s\n",
316                        usedresource, CeedMemTypes[memTypeBackend],
317                        (appCtx->setMemTypeRequest) ?
318                        CeedMemTypes[appCtx->memTypeRequested] : "none");
319     CHKERRQ(ierr);
320 
321     if (ceedFine) {
322       ierr = PetscPrintf(comm,
323                          "    libCEED Backend - high order       : %s\n",
324                          appCtx->ceedResourceFine); CHKERRQ(ierr);
325     }
326 
327     VecType vecType;
328     ierr = VecGetType(U, &vecType); CHKERRQ(ierr);
329     ierr = PetscPrintf(comm,
330                        "  PETSc:\n"
331                        "    PETSc Vec Type                     : %s\n",
332                        vecType); CHKERRQ(ierr);
333 
334     ierr = PetscPrintf(comm,
335                        "  Problem:\n"
336                        "    Problem Name                       : %s\n"
337                        "    Forcing Function                   : %s\n"
338                        "  Mesh:\n"
339                        "    File                               : %s\n"
340                        "    Number of 1D Basis Nodes (p)       : %d\n"
341                        "    Number of 1D Quadrature Points (q) : %d\n"
342                        "    Global nodes                       : %D\n"
343                        "    Owned nodes                        : %D\n"
344                        "    DoF per node                       : %D\n"
345                        "  Multigrid:\n"
346                        "    Type                               : %s\n"
347                        "    Number of Levels                   : %d\n",
348                        problemTypesForDisp[appCtx->problemChoice],
349                        forcingTypesForDisp[appCtx->forcingChoice],
350                        appCtx->meshFile[0] ? appCtx->meshFile : "Box Mesh",
351                        appCtx->degree + 1, appCtx->degree + 1,
352                        Ugsz[fineLevel]/ncompu, Ulsz[fineLevel]/ncompu, ncompu,
353                        (appCtx->degree == 1 &&
354                         appCtx->multigridChoice != MULTIGRID_NONE) ?
355                        "Algebraic multigrid" :
356                        multigridTypesForDisp[appCtx->multigridChoice],
357                        (appCtx->degree == 1 ||
358                         appCtx->multigridChoice == MULTIGRID_NONE) ?
359                        0 : numLevels); CHKERRQ(ierr);
360 
361     if (appCtx->multigridChoice != MULTIGRID_NONE) {
362       for (PetscInt i = 0; i < 2; i++) {
363         CeedInt level = i ? fineLevel : 0;
364         ierr = PetscPrintf(comm,
365                            "    Level %D (%s):\n"
366                            "      Number of 1D Basis Nodes (p)     : %d\n"
367                            "      Global Nodes                     : %D\n"
368                            "      Owned Nodes                      : %D\n",
369                            level, i ? "fine" : "coarse",
370                            appCtx->levelDegrees[level] + 1,
371                            Ugsz[level]/ncompu, Ulsz[level]/ncompu);
372         CHKERRQ(ierr);
373       }
374     }
375   }
376 
377   // ---------------------------------------------------------------------------
378   // Setup SNES
379   // ---------------------------------------------------------------------------
380   // Performance logging
381   ierr = PetscLogStageRegister("SNES Setup Stage", &stageSnesSetup);
382   CHKERRQ(ierr);
383   ierr = PetscLogStagePush(stageSnesSetup); CHKERRQ(ierr);
384 
385   // Create SNES
386   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
387   ierr = SNESSetDM(snes, levelDMs[fineLevel]); CHKERRQ(ierr);
388 
389   // -- Jacobian evaluators
390   ierr = PetscMalloc1(numLevels, &jacobCtx); CHKERRQ(ierr);
391   ierr = PetscMalloc1(numLevels, &jacobMat); CHKERRQ(ierr);
392   for (PetscInt level = 0; level < numLevels; level++) {
393     // -- Jacobian context for level
394     ierr = PetscMalloc1(1, &jacobCtx[level]); CHKERRQ(ierr);
395     ierr = SetupJacobianCtx(comm, appCtx, levelDMs[level], Ug[level],
396                             Uloc[level], ceedData[level], ceed, phys,
397                             physSmoother, jacobCtx[level]); CHKERRQ(ierr);
398 
399     // -- Form Action of Jacobian on delta_u
400     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level], Ugsz[level],
401                           Ugsz[level], jacobCtx[level], &jacobMat[level]);
402     CHKERRQ(ierr);
403     ierr = MatShellSetOperation(jacobMat[level], MATOP_MULT,
404                                 (void (*)(void))ApplyJacobian_Ceed);
405     CHKERRQ(ierr);
406     ierr = MatShellSetOperation(jacobMat[level], MATOP_GET_DIAGONAL,
407                                 (void(*)(void))GetDiag_Ceed);
408     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
409       ierr = MatShellSetVecType(jacobMat[level], VECCUDA); CHKERRQ(ierr);
410     }
411   }
412   // Note: FormJacobian updates Jacobian matrices on each level
413   //   and assembles the Jpre matrix, if needed
414   ierr = PetscMalloc1(1, &formJacobCtx); CHKERRQ(ierr);
415   formJacobCtx->jacobCtx = jacobCtx;
416   formJacobCtx->numLevels = numLevels;
417   formJacobCtx->jacobMat = jacobMat;
418 
419   // -- Residual evaluation function
420   ierr = PetscMalloc1(1, &resCtx); CHKERRQ(ierr);
421   ierr = PetscMemcpy(resCtx, jacobCtx[fineLevel],
422                      sizeof(*jacobCtx[fineLevel])); CHKERRQ(ierr);
423   resCtx->op = ceedData[fineLevel]->opApply;
424   resCtx->qf = ceedData[fineLevel]->qfApply;
425   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, resCtx); CHKERRQ(ierr);
426 
427   // -- Prolongation/Restriction evaluation
428   ierr = PetscMalloc1(numLevels, &prolongRestrCtx); CHKERRQ(ierr);
429   ierr = PetscMalloc1(numLevels, &prolongRestrMat); CHKERRQ(ierr);
430   for (PetscInt level = 1; level < numLevels; level++) {
431     // ---- Prolongation/restriction context for level
432     ierr = PetscMalloc1(1, &prolongRestrCtx[level]); CHKERRQ(ierr);
433     ierr = SetupProlongRestrictCtx(comm, appCtx, levelDMs[level-1],
434                                    levelDMs[level], Ug[level], Uloc[level-1],
435                                    Uloc[level], ceedData[level-1],
436                                    ceedData[level], ceed,
437                                    prolongRestrCtx[level]); CHKERRQ(ierr);
438 
439     // ---- Form Action of Jacobian on delta_u
440     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level-1], Ugsz[level],
441                           Ugsz[level-1], prolongRestrCtx[level],
442                           &prolongRestrMat[level]); CHKERRQ(ierr);
443     // Note: In PCMG, restriction is the transpose of prolongation
444     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT,
445                                 (void (*)(void))Prolong_Ceed);
446     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT_TRANSPOSE,
447                                 (void (*)(void))Restrict_Ceed);
448     CHKERRQ(ierr);
449     if (appCtx->memTypeRequested == CEED_MEM_DEVICE) {
450       ierr = MatShellSetVecType(prolongRestrMat[level], VECCUDA); CHKERRQ(ierr);
451     }
452   }
453 
454   // ---------------------------------------------------------------------------
455   // Setup dummy SNES for AMG coarse solve
456   // ---------------------------------------------------------------------------
457   if (appCtx->multigridChoice != MULTIGRID_NONE) {
458     // -- Jacobian Matrix
459     ierr = DMSetMatType(levelDMs[0], MATAIJ); CHKERRQ(ierr);
460     ierr = DMCreateMatrix(levelDMs[0], &jacobMatCoarse); CHKERRQ(ierr);
461 
462     if (appCtx->degree > 1) {
463       ierr = SNESCreate(comm, &snesCoarse); CHKERRQ(ierr);
464       ierr = SNESSetDM(snesCoarse, levelDMs[0]); CHKERRQ(ierr);
465       ierr = SNESSetSolution(snesCoarse, Ug[0]); CHKERRQ(ierr);
466 
467       // -- Jacobian function
468       ierr = SNESSetJacobian(snesCoarse, jacobMatCoarse, jacobMatCoarse, NULL,
469                              NULL); CHKERRQ(ierr);
470 
471       // -- Residual evaluation function
472       ierr = PetscMalloc1(1, &jacobCoarseCtx); CHKERRQ(ierr);
473       ierr = PetscMemcpy(jacobCoarseCtx, jacobCtx[0], sizeof(*jacobCtx[0]));
474       CHKERRQ(ierr);
475       ierr = SNESSetFunction(snesCoarse, Ug[0], ApplyJacobianCoarse_Ceed,
476                              jacobCoarseCtx); CHKERRQ(ierr);
477 
478       // -- Update formJacobCtx
479       formJacobCtx->Ucoarse = Ug[0];
480       formJacobCtx->snesCoarse = snesCoarse;
481       formJacobCtx->jacobMatCoarse = jacobMatCoarse;
482     }
483   }
484 
485   // Set Jacobian function
486   if (appCtx->degree > 1) {
487     ierr = SNESSetJacobian(snes, jacobMat[fineLevel], jacobMat[fineLevel],
488                            FormJacobian, formJacobCtx); CHKERRQ(ierr);
489   } else {
490     ierr = SNESSetJacobian(snes, jacobMat[0], jacobMatCoarse,
491                            SNESComputeJacobianDefaultColor, NULL);
492     CHKERRQ(ierr);
493   }
494 
495   // ---------------------------------------------------------------------------
496   // Setup KSP
497   // ---------------------------------------------------------------------------
498   {
499     PC pc;
500     KSP ksp;
501 
502     // -- KSP
503     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
504     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
505     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
506     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
507                             PETSC_DEFAULT); CHKERRQ(ierr);
508     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
509 
510     // -- Preconditioning
511     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
512     ierr = PCSetDM(pc, levelDMs[fineLevel]); CHKERRQ(ierr);
513     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
514 
515     if (appCtx->multigridChoice == MULTIGRID_NONE) {
516       // ---- No Multigrid
517       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
518       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
519     } else if (appCtx->degree == 1) {
520       // ---- AMG for degree 1
521       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
522     } else {
523       // ---- PCMG
524       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
525 
526       // ------ PCMG levels
527       ierr = PCMGSetLevels(pc, numLevels, NULL); CHKERRQ(ierr);
528       for (PetscInt level = 0; level < numLevels; level++) {
529         // -------- Smoother
530         KSP kspSmoother, kspEst;
531         PC pcSmoother;
532 
533         // ---------- Smoother KSP
534         ierr = PCMGGetSmoother(pc, level, &kspSmoother); CHKERRQ(ierr);
535         ierr = KSPSetDM(kspSmoother, levelDMs[level]); CHKERRQ(ierr);
536         ierr = KSPSetDMActive(kspSmoother, PETSC_FALSE); CHKERRQ(ierr);
537 
538         // ---------- Chebyshev options
539         ierr = KSPSetType(kspSmoother, KSPCHEBYSHEV); CHKERRQ(ierr);
540         ierr = KSPChebyshevEstEigSet(kspSmoother, 0, 0.1, 0, 1.1);
541         CHKERRQ(ierr);
542         ierr = KSPChebyshevEstEigGetKSP(kspSmoother, &kspEst); CHKERRQ(ierr);
543         ierr = KSPSetType(kspEst, KSPCG); CHKERRQ(ierr);
544         ierr = KSPChebyshevEstEigSetUseNoisy(kspSmoother, PETSC_TRUE);
545         CHKERRQ(ierr);
546         ierr = KSPSetOperators(kspSmoother, jacobMat[level], jacobMat[level]);
547         CHKERRQ(ierr);
548 
549         // ---------- Smoother preconditioner
550         ierr = KSPGetPC(kspSmoother, &pcSmoother); CHKERRQ(ierr);
551         ierr = PCSetType(pcSmoother, PCJACOBI); CHKERRQ(ierr);
552         ierr = PCJacobiSetType(pcSmoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
553 
554         // -------- Work vector
555         if (level != fineLevel) {
556           ierr = PCMGSetX(pc, level, Ug[level]); CHKERRQ(ierr);
557         }
558 
559         // -------- Level prolongation/restriction operator
560         if (level > 0) {
561           ierr = PCMGSetInterpolation(pc, level, prolongRestrMat[level]);
562           CHKERRQ(ierr);
563           ierr = PCMGSetRestriction(pc, level, prolongRestrMat[level]);
564           CHKERRQ(ierr);
565         }
566       }
567 
568       // ------ PCMG coarse solve
569       KSP kspCoarse;
570       PC pcCoarse;
571 
572       // -------- Coarse KSP
573       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
574       ierr = KSPSetType(kspCoarse, KSPPREONLY); CHKERRQ(ierr);
575       ierr = KSPSetOperators(kspCoarse, jacobMatCoarse, jacobMatCoarse);
576       CHKERRQ(ierr);
577       ierr = KSPSetOptionsPrefix(kspCoarse, "coarse_"); CHKERRQ(ierr);
578 
579       // -------- Coarse preconditioner
580       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
581       ierr = PCSetType(pcCoarse, PCGAMG); CHKERRQ(ierr);
582       ierr = PCSetOptionsPrefix(pcCoarse, "coarse_"); CHKERRQ(ierr);
583 
584       ierr = KSPSetFromOptions(kspCoarse); CHKERRQ(ierr);
585       ierr = PCSetFromOptions(pcCoarse); CHKERRQ(ierr);
586 
587       // ------ PCMG options
588       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
589       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
590       ierr = PCMGSetCycleType(pc, pcmgCycleType); CHKERRQ(ierr);
591     }
592     ierr = KSPSetFromOptions(ksp);
593     ierr = PCSetFromOptions(pc);
594   }
595   {
596     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
597     SNESLineSearch linesearch;
598 
599     ierr = SNESGetLineSearch(snes, &linesearch); CHKERRQ(ierr);
600     ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHCP); CHKERRQ(ierr);
601   }
602 
603   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
604 
605   // Performance logging
606   ierr = PetscLogStagePop();
607 
608   // ---------------------------------------------------------------------------
609   // Set initial guess
610   // ---------------------------------------------------------------------------
611   ierr = PetscObjectSetName((PetscObject)U, ""); CHKERRQ(ierr);
612   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
613 
614   // View solution
615   if (appCtx->viewSoln) {
616     ierr = ViewSolution(comm, U, 0, 0.0); CHKERRQ(ierr);
617   }
618 
619   // ---------------------------------------------------------------------------
620   // Solve SNES
621   // ---------------------------------------------------------------------------
622   PetscBool snesMonitor = PETSC_FALSE;
623   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snesMonitor);
624   CHKERRQ(ierr);
625 
626   // Performance logging
627   ierr = PetscLogStageRegister("SNES Solve Stage", &stageSnesSolve);
628   CHKERRQ(ierr);
629   ierr = PetscLogStagePush(stageSnesSolve); CHKERRQ(ierr);
630 
631   // Timing
632   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
633   startTime = MPI_Wtime();
634 
635   // Solve for each load increment
636   PetscInt increment;
637   for (increment = 1; increment <= appCtx->numIncrements; increment++) {
638     // -- Log increment count
639     if (snesMonitor) {
640       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
641       CHKERRQ(ierr);
642     }
643 
644     // -- Scale the problem
645     PetscScalar loadIncrement = 1.0*increment / appCtx->numIncrements,
646                 scalingFactor = loadIncrement /
647                                 (increment == 1 ? 1 : resCtx->loadIncrement);
648     resCtx->loadIncrement = loadIncrement;
649     if (appCtx->numIncrements > 1 && appCtx->forcingChoice != FORCE_NONE) {
650       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
651     }
652 
653     // -- Solve
654     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
655 
656     // -- View solution
657     if (appCtx->viewSoln) {
658       ierr = ViewSolution(comm, U, increment, loadIncrement); CHKERRQ(ierr);
659     }
660 
661     // -- Update SNES iteration count
662     PetscInt its;
663     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
664     snesIts += its;
665     ierr = SNESGetLinearSolveIterations(snes, &its); CHKERRQ(ierr);
666     kspIts += its;
667 
668     // -- Check for divergence
669     SNESConvergedReason reason;
670     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
671     if (reason < 0)
672       break;
673   }
674 
675   // Timing
676   elapsedTime = MPI_Wtime() - startTime;
677 
678   // Performance logging
679   ierr = PetscLogStagePop();
680 
681   // ---------------------------------------------------------------------------
682   // Output summary
683   // ---------------------------------------------------------------------------
684   if (!appCtx->testMode) {
685     // -- SNES
686     SNESType snesType;
687     SNESConvergedReason reason;
688     PetscReal rnorm;
689     ierr = SNESGetType(snes, &snesType); CHKERRQ(ierr);
690     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
691     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
692     ierr = PetscPrintf(comm,
693                        "  SNES:\n"
694                        "    SNES Type                          : %s\n"
695                        "    SNES Convergence                   : %s\n"
696                        "    Number of Load Increments          : %d\n"
697                        "    Completed Load Increments          : %d\n"
698                        "    Total SNES Iterations              : %D\n"
699                        "    Final rnorm                        : %e\n",
700                        snesType, SNESConvergedReasons[reason],
701                        appCtx->numIncrements, increment - 1,
702                        snesIts, (double)rnorm); CHKERRQ(ierr);
703 
704     // -- KSP
705     KSP ksp;
706     KSPType kspType;
707     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
708     ierr = KSPGetType(ksp, &kspType); CHKERRQ(ierr);
709     ierr = PetscPrintf(comm,
710                        "  Linear Solver:\n"
711                        "    KSP Type                           : %s\n"
712                        "    Total KSP Iterations               : %D\n",
713                        kspType, kspIts); CHKERRQ(ierr);
714 
715     // -- PC
716     PC pc;
717     PCType pcType;
718     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
719     ierr = PCGetType(pc, &pcType); CHKERRQ(ierr);
720     ierr = PetscPrintf(comm,
721                        "    PC Type                            : %s\n",
722                        pcType); CHKERRQ(ierr);
723 
724     if (!strcmp(pcType, PCMG)) {
725       PCMGType pcmgType;
726       ierr = PCMGGetType(pc, &pcmgType); CHKERRQ(ierr);
727       ierr = PetscPrintf(comm,
728                          "  P-Multigrid:\n"
729                          "    PCMG Type                          : %s\n"
730                          "    PCMG Cycle Type                    : %s\n",
731                          PCMGTypes[pcmgType],
732                          PCMGCycleTypes[pcmgCycleType]); CHKERRQ(ierr);
733 
734       // -- Coarse Solve
735       KSP kspCoarse;
736       PC pcCoarse;
737       PCType pcType;
738 
739       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
740       ierr = KSPGetType(kspCoarse, &kspType); CHKERRQ(ierr);
741       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
742       ierr = PCGetType(pcCoarse, &pcType); CHKERRQ(ierr);
743       ierr = PetscPrintf(comm,
744                          "    Coarse Solve:\n"
745                          "      KSP Type                         : %s\n"
746                          "      PC Type                          : %s\n",
747                          kspType, pcType); CHKERRQ(ierr);
748     }
749   }
750 
751   // ---------------------------------------------------------------------------
752   // Compute solve time
753   // ---------------------------------------------------------------------------
754   if (!appCtx->testMode) {
755     ierr = MPI_Allreduce(&elapsedTime, &minTime, 1, MPI_DOUBLE, MPI_MIN, comm);
756     CHKERRQ(ierr);
757     ierr = MPI_Allreduce(&elapsedTime, &maxTime, 1, MPI_DOUBLE, MPI_MAX, comm);
758     CHKERRQ(ierr);
759     ierr = PetscPrintf(comm,
760                        "  Performance:\n"
761                        "    SNES Solve Time                    : %g (%g) sec\n"
762                        "    DoFs/Sec in SNES                   : %g (%g) million\n",
763                        maxTime, minTime, 1e-6*Ugsz[fineLevel]*kspIts/maxTime,
764                        1e-6*Ugsz[fineLevel]*kspIts/minTime); CHKERRQ(ierr);
765   }
766 
767   // ---------------------------------------------------------------------------
768   // Compute error
769   // ---------------------------------------------------------------------------
770   if (appCtx->forcingChoice == FORCE_MMS) {
771     CeedScalar l2Error = 1., l2Unorm = 1.;
772     const CeedScalar *truearray;
773     Vec errorVec, trueVec;
774 
775     // -- Work vectors
776     ierr = VecDuplicate(U, &errorVec); CHKERRQ(ierr);
777     ierr = VecSet(errorVec, 0.0); CHKERRQ(ierr);
778     ierr = VecDuplicate(U, &trueVec); CHKERRQ(ierr);
779     ierr = VecSet(trueVec, 0.0); CHKERRQ(ierr);
780 
781     // -- Assemble global true solution vector
782     CeedVectorGetArrayRead(ceedData[fineLevel]->truesoln,
783                            appCtx->memTypeRequested, &truearray);
784     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
785       ierr = VecPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
786       CHKERRQ(ierr);
787     } else {
788       ierr = VecCUDAPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
789       CHKERRQ(ierr);
790     }
791     ierr = DMLocalToGlobal(resCtx->dm, resCtx->Yloc, INSERT_VALUES, trueVec);
792     CHKERRQ(ierr);
793     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
794       ierr = VecResetArray(resCtx->Yloc); CHKERRQ(ierr);
795     } else {
796       ierr = VecCUDAResetArray(resCtx->Yloc); CHKERRQ(ierr);
797     }
798     CeedVectorRestoreArrayRead(ceedData[fineLevel]->truesoln, &truearray);
799 
800     // -- Compute L2 error
801     ierr = VecWAXPY(errorVec, -1.0, U, trueVec); CHKERRQ(ierr);
802     ierr = VecNorm(errorVec, NORM_2, &l2Error); CHKERRQ(ierr);
803     ierr = VecNorm(U, NORM_2, &l2Unorm); CHKERRQ(ierr);
804     l2Error /= l2Unorm;
805 
806     // -- Output
807     if (!appCtx->testMode || l2Error > 0.05) {
808       ierr = PetscPrintf(comm,
809                          "    L2 Error                           : %e\n",
810                          l2Error); CHKERRQ(ierr);
811     }
812 
813     // -- Cleanup
814     ierr = VecDestroy(&errorVec); CHKERRQ(ierr);
815     ierr = VecDestroy(&trueVec); CHKERRQ(ierr);
816   }
817 
818   // ---------------------------------------------------------------------------
819   // Compute energy
820   // ---------------------------------------------------------------------------
821   if (!appCtx->testMode) {
822     // -- Compute L2 error
823     CeedScalar energy;
824     ierr = ComputeStrainEnergy(dmEnergy, resCtx, ceedData[fineLevel]->opEnergy,
825                                U, &energy); CHKERRQ(ierr);
826 
827     // -- Output
828     ierr = PetscPrintf(comm,
829                        "    Strain Energy                      : %e\n",
830                        energy); CHKERRQ(ierr);
831   }
832 
833   // ---------------------------------------------------------------------------
834   // Output diagnostic quantities
835   // ---------------------------------------------------------------------------
836   if (appCtx->viewSoln || appCtx->viewFinalSoln) {
837     // -- Setup context
838     UserMult diagnosticCtx;
839     ierr = PetscMalloc1(1, &diagnosticCtx); CHKERRQ(ierr);
840     ierr = PetscMemcpy(diagnosticCtx, resCtx, sizeof(*resCtx)); CHKERRQ(ierr);
841     diagnosticCtx->dm = dmDiagnostic;
842     diagnosticCtx->op = ceedData[fineLevel]->opDiagnostic;
843 
844     // -- Compute and output
845     ierr = ViewDiagnosticQuantities(comm, levelDMs[fineLevel], diagnosticCtx, U,
846                                     ceedData[fineLevel]->ErestrictDiagnostic);
847     CHKERRQ(ierr);
848 
849     // -- Cleanup
850     ierr = PetscFree(diagnosticCtx); CHKERRQ(ierr);
851   }
852 
853   // ---------------------------------------------------------------------------
854   // Free objects
855   // ---------------------------------------------------------------------------
856   // Data in arrays per level
857   for (PetscInt level = 0; level < numLevels; level++) {
858     // Vectors
859     ierr = VecDestroy(&Ug[level]); CHKERRQ(ierr);
860     ierr = VecDestroy(&Uloc[level]); CHKERRQ(ierr);
861 
862     // Jacobian matrix and data
863     ierr = VecDestroy(&jacobCtx[level]->Yloc); CHKERRQ(ierr);
864     ierr = MatDestroy(&jacobMat[level]); CHKERRQ(ierr);
865     ierr = PetscFree(jacobCtx[level]); CHKERRQ(ierr);
866 
867     // Prolongation/Restriction matrix and data
868     if (level > 0) {
869       ierr = VecDestroy(&prolongRestrCtx[level]->multVec); CHKERRQ(ierr);
870       ierr = PetscFree(prolongRestrCtx[level]); CHKERRQ(ierr);
871       ierr = MatDestroy(&prolongRestrMat[level]); CHKERRQ(ierr);
872     }
873 
874     // DM
875     ierr = DMDestroy(&levelDMs[level]); CHKERRQ(ierr);
876 
877     // libCEED objects
878     ierr = CeedDataDestroy(level, ceedData[level]); CHKERRQ(ierr);
879   }
880 
881   // Arrays
882   ierr = PetscFree(Ug); CHKERRQ(ierr);
883   ierr = PetscFree(Uloc); CHKERRQ(ierr);
884   ierr = PetscFree(Ugsz); CHKERRQ(ierr);
885   ierr = PetscFree(Ulsz); CHKERRQ(ierr);
886   ierr = PetscFree(Ulocsz); CHKERRQ(ierr);
887   ierr = PetscFree(jacobCtx); CHKERRQ(ierr);
888   ierr = PetscFree(jacobMat); CHKERRQ(ierr);
889   ierr = PetscFree(prolongRestrCtx); CHKERRQ(ierr);
890   ierr = PetscFree(prolongRestrMat); CHKERRQ(ierr);
891   ierr = PetscFree(appCtx->levelDegrees); CHKERRQ(ierr);
892   ierr = PetscFree(ceedData); CHKERRQ(ierr);
893 
894   // libCEED objects
895   CeedQFunctionDestroy(&qfRestrict);
896   CeedQFunctionDestroy(&qfProlong);
897   CeedDestroy(&ceed);
898   CeedDestroy(&ceedFine);
899 
900   // PETSc objects
901   ierr = VecDestroy(&U); CHKERRQ(ierr);
902   ierr = VecDestroy(&R); CHKERRQ(ierr);
903   ierr = VecDestroy(&Rloc); CHKERRQ(ierr);
904   ierr = VecDestroy(&F); CHKERRQ(ierr);
905   ierr = VecDestroy(&Floc); CHKERRQ(ierr);
906   ierr = MatDestroy(&jacobMatCoarse); CHKERRQ(ierr);
907   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
908   ierr = SNESDestroy(&snesCoarse); CHKERRQ(ierr);
909   ierr = DMDestroy(&dmOrig); CHKERRQ(ierr);
910   ierr = DMDestroy(&dmEnergy); CHKERRQ(ierr);
911   ierr = DMDestroy(&dmDiagnostic); CHKERRQ(ierr);
912   ierr = PetscFree(levelDMs); CHKERRQ(ierr);
913 
914   // Structs
915   ierr = PetscFree(resCtx); CHKERRQ(ierr);
916   ierr = PetscFree(formJacobCtx); CHKERRQ(ierr);
917   ierr = PetscFree(jacobCoarseCtx); CHKERRQ(ierr);
918   ierr = PetscFree(appCtx); CHKERRQ(ierr);
919   ierr = PetscFree(phys); CHKERRQ(ierr);
920   ierr = PetscFree(physSmoother); CHKERRQ(ierr);
921   ierr = PetscFree(units); CHKERRQ(ierr);
922 
923   return PetscFinalize();
924 }
925