xref: /libCEED/examples/solids/elasticity.c (revision 1c48f5db67f1a05a0c77b037a783d9df4fdf44be)
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 = 5; // 1 energy output, 5 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   // 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     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
293       ierr = VecRestoreArray(Floc, &f); CHKERRQ(ierr);
294     } else {
295       ierr = VecCUDARestoreArray(Floc, &f); CHKERRQ(ierr);
296     }
297     ierr = DMLocalToGlobal(levelDMs[fineLevel], Floc, ADD_VALUES, F);
298     CHKERRQ(ierr);
299     CeedVectorDestroy(&forceCeed);
300   }
301 
302   // ---------------------------------------------------------------------------
303   // Print problem summary
304   // ---------------------------------------------------------------------------
305   if (!appCtx->testMode) {
306     const char *usedresource;
307     CeedGetResource(ceed, &usedresource);
308 
309     ierr = PetscPrintf(comm,
310                        "\n-- Elasticity Example - libCEED + PETSc --\n"
311                        "  libCEED:\n"
312                        "    libCEED Backend                    : %s\n"
313                        "    libCEED Backend MemType            : %s\n"
314                        "    libCEED User Requested MemType     : %s\n",
315                        usedresource, CeedMemTypes[memTypeBackend],
316                        (appCtx->setMemTypeRequest) ?
317                        CeedMemTypes[appCtx->memTypeRequested] : "none");
318     CHKERRQ(ierr);
319 
320     if (ceedFine) {
321       ierr = PetscPrintf(comm,
322                          "    libCEED Backend - high order       : %s\n",
323                          appCtx->ceedResourceFine); CHKERRQ(ierr);
324     }
325 
326     VecType vecType;
327     ierr = VecGetType(U, &vecType); CHKERRQ(ierr);
328     ierr = PetscPrintf(comm,
329                        "  PETSc:\n"
330                        "    PETSc Vec Type                     : %s\n",
331                        vecType); CHKERRQ(ierr);
332 
333     ierr = PetscPrintf(comm,
334                        "  Problem:\n"
335                        "    Problem Name                       : %s\n"
336                        "    Forcing Function                   : %s\n"
337                        "  Mesh:\n"
338                        "    File                               : %s\n"
339                        "    Number of 1D Basis Nodes (p)       : %d\n"
340                        "    Number of 1D Quadrature Points (q) : %d\n"
341                        "    Global nodes                       : %D\n"
342                        "    Owned nodes                        : %D\n"
343                        "    DoF per node                       : %D\n"
344                        "  Multigrid:\n"
345                        "    Type                               : %s\n"
346                        "    Number of Levels                   : %d\n",
347                        problemTypesForDisp[appCtx->problemChoice],
348                        forcingTypesForDisp[appCtx->forcingChoice],
349                        appCtx->meshFile[0] ? appCtx->meshFile : "Box Mesh",
350                        appCtx->degree + 1, appCtx->degree + 1,
351                        Ugsz[fineLevel]/ncompu, Ulsz[fineLevel]/ncompu, ncompu,
352                        (appCtx->degree == 1 &&
353                         appCtx->multigridChoice != MULTIGRID_NONE) ?
354                        "Algebraic multigrid" :
355                        multigridTypesForDisp[appCtx->multigridChoice],
356                        (appCtx->degree == 1 ||
357                         appCtx->multigridChoice == MULTIGRID_NONE) ?
358                        0 : numLevels); CHKERRQ(ierr);
359 
360     if (appCtx->multigridChoice != MULTIGRID_NONE) {
361       for (PetscInt i = 0; i < 2; i++) {
362         CeedInt level = i ? fineLevel : 0;
363         ierr = PetscPrintf(comm,
364                            "    Level %D (%s):\n"
365                            "      Number of 1D Basis Nodes (p)     : %d\n"
366                            "      Global Nodes                     : %D\n"
367                            "      Owned Nodes                      : %D\n",
368                            level, i ? "fine" : "coarse",
369                            appCtx->levelDegrees[level] + 1,
370                            Ugsz[level]/ncompu, Ulsz[level]/ncompu);
371         CHKERRQ(ierr);
372       }
373     }
374   }
375 
376   // ---------------------------------------------------------------------------
377   // Setup SNES
378   // ---------------------------------------------------------------------------
379   // Performance logging
380   ierr = PetscLogStageRegister("SNES Setup Stage", &stageSnesSetup);
381   CHKERRQ(ierr);
382   ierr = PetscLogStagePush(stageSnesSetup); CHKERRQ(ierr);
383 
384   // Create SNES
385   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
386   ierr = SNESSetDM(snes, levelDMs[fineLevel]); CHKERRQ(ierr);
387 
388   // -- Jacobian evaluators
389   ierr = PetscMalloc1(numLevels, &jacobCtx); CHKERRQ(ierr);
390   ierr = PetscMalloc1(numLevels, &jacobMat); CHKERRQ(ierr);
391   for (PetscInt level = 0; level < numLevels; level++) {
392     // -- Jacobian context for level
393     ierr = PetscMalloc1(1, &jacobCtx[level]); CHKERRQ(ierr);
394     ierr = SetupJacobianCtx(comm, appCtx, levelDMs[level], Ug[level],
395                             Uloc[level], ceedData[level], ceed, phys,
396                             physSmoother, jacobCtx[level]); CHKERRQ(ierr);
397 
398     // -- Form Action of Jacobian on delta_u
399     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level], Ugsz[level],
400                           Ugsz[level], jacobCtx[level], &jacobMat[level]);
401     CHKERRQ(ierr);
402     ierr = MatShellSetOperation(jacobMat[level], MATOP_MULT,
403                                 (void (*)(void))ApplyJacobian_Ceed);
404     CHKERRQ(ierr);
405     ierr = MatShellSetOperation(jacobMat[level], MATOP_GET_DIAGONAL,
406                                 (void(*)(void))GetDiag_Ceed);
407 
408   }
409   // Note: FormJacobian updates Jacobian matrices on each level
410   //   and assembles the Jpre matrix, if needed
411   ierr = PetscMalloc1(1, &formJacobCtx); CHKERRQ(ierr);
412   formJacobCtx->jacobCtx = jacobCtx;
413   formJacobCtx->numLevels = numLevels;
414   formJacobCtx->jacobMat = jacobMat;
415 
416   // -- Residual evaluation function
417   ierr = PetscMalloc1(1, &resCtx); CHKERRQ(ierr);
418   ierr = PetscMemcpy(resCtx, jacobCtx[fineLevel],
419                      sizeof(*jacobCtx[fineLevel])); CHKERRQ(ierr);
420   resCtx->op = ceedData[fineLevel]->opApply;
421   resCtx->qf = ceedData[fineLevel]->qfApply;
422   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, resCtx); CHKERRQ(ierr);
423 
424   // -- Prolongation/Restriction evaluation
425   ierr = PetscMalloc1(numLevels, &prolongRestrCtx); CHKERRQ(ierr);
426   ierr = PetscMalloc1(numLevels, &prolongRestrMat); CHKERRQ(ierr);
427   for (PetscInt level = 1; level < numLevels; level++) {
428     // ---- Prolongation/restriction context for level
429     ierr = PetscMalloc1(1, &prolongRestrCtx[level]); CHKERRQ(ierr);
430     ierr = SetupProlongRestrictCtx(comm, appCtx, levelDMs[level-1],
431                                    levelDMs[level], Ug[level], Uloc[level-1],
432                                    Uloc[level], ceedData[level-1],
433                                    ceedData[level], ceed,
434                                    prolongRestrCtx[level]); CHKERRQ(ierr);
435 
436     // ---- Form Action of Jacobian on delta_u
437     ierr = MatCreateShell(comm, Ulsz[level], Ulsz[level-1], Ugsz[level],
438                           Ugsz[level-1], prolongRestrCtx[level],
439                           &prolongRestrMat[level]); CHKERRQ(ierr);
440     // Note: In PCMG, restriction is the transpose of prolongation
441     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT,
442                                 (void (*)(void))Prolong_Ceed);
443     ierr = MatShellSetOperation(prolongRestrMat[level], MATOP_MULT_TRANSPOSE,
444                                 (void (*)(void))Restrict_Ceed);
445     CHKERRQ(ierr);
446   }
447 
448   // ---------------------------------------------------------------------------
449   // Setup dummy SNES for AMG coarse solve
450   // ---------------------------------------------------------------------------
451   if (appCtx->multigridChoice != MULTIGRID_NONE) {
452     // -- Jacobian Matrix
453     ierr = DMSetMatType(levelDMs[0], MATAIJ); CHKERRQ(ierr);
454     ierr = DMCreateMatrix(levelDMs[0], &jacobMatCoarse); CHKERRQ(ierr);
455 
456     if (appCtx->degree > 1) {
457       ierr = SNESCreate(comm, &snesCoarse); CHKERRQ(ierr);
458       ierr = SNESSetDM(snesCoarse, levelDMs[0]); CHKERRQ(ierr);
459       ierr = SNESSetSolution(snesCoarse, Ug[0]); CHKERRQ(ierr);
460 
461       // -- Jacobian function
462       ierr = SNESSetJacobian(snesCoarse, jacobMatCoarse, jacobMatCoarse, NULL,
463                              NULL); CHKERRQ(ierr);
464 
465       // -- Residual evaluation function
466       ierr = PetscMalloc1(1, &jacobCoarseCtx); CHKERRQ(ierr);
467       ierr = PetscMemcpy(jacobCoarseCtx, jacobCtx[0], sizeof(*jacobCtx[0]));
468       CHKERRQ(ierr);
469       ierr = SNESSetFunction(snesCoarse, Ug[0], ApplyJacobianCoarse_Ceed,
470                              jacobCoarseCtx); CHKERRQ(ierr);
471 
472       // -- Update formJacobCtx
473       formJacobCtx->Ucoarse = Ug[0];
474       formJacobCtx->snesCoarse = snesCoarse;
475       formJacobCtx->jacobMatCoarse = jacobMatCoarse;
476     }
477   }
478 
479   // Set Jacobian function
480   if (appCtx->degree > 1) {
481     ierr = SNESSetJacobian(snes, jacobMat[fineLevel], jacobMat[fineLevel],
482                            FormJacobian, formJacobCtx); CHKERRQ(ierr);
483   } else {
484     ierr = SNESSetJacobian(snes, jacobMat[0], jacobMatCoarse,
485                            SNESComputeJacobianDefaultColor, NULL);
486     CHKERRQ(ierr);
487   }
488 
489   // ---------------------------------------------------------------------------
490   // Setup KSP
491   // ---------------------------------------------------------------------------
492   {
493     PC pc;
494     KSP ksp;
495 
496     // -- KSP
497     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
498     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
499     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
500     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
501                             PETSC_DEFAULT); CHKERRQ(ierr);
502     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
503 
504     // -- Preconditioning
505     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
506     ierr = PCSetDM(pc, levelDMs[fineLevel]); CHKERRQ(ierr);
507     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
508 
509     if (appCtx->multigridChoice == MULTIGRID_NONE) {
510       // ---- No Multigrid
511       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
512       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
513     } else if (appCtx->degree == 1) {
514       // ---- AMG for degree 1
515       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
516     } else {
517       // ---- PCMG
518       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
519 
520       // ------ PCMG levels
521       ierr = PCMGSetLevels(pc, numLevels, NULL); CHKERRQ(ierr);
522       for (PetscInt level = 0; level < numLevels; level++) {
523         // -------- Smoother
524         KSP kspSmoother, kspEst;
525         PC pcSmoother;
526 
527         // ---------- Smoother KSP
528         ierr = PCMGGetSmoother(pc, level, &kspSmoother); CHKERRQ(ierr);
529         ierr = KSPSetDM(kspSmoother, levelDMs[level]); CHKERRQ(ierr);
530         ierr = KSPSetDMActive(kspSmoother, PETSC_FALSE); CHKERRQ(ierr);
531 
532         // ---------- Chebyshev options
533         ierr = KSPSetType(kspSmoother, KSPCHEBYSHEV); CHKERRQ(ierr);
534         ierr = KSPChebyshevEstEigSet(kspSmoother, 0, 0.1, 0, 1.1);
535         CHKERRQ(ierr);
536         ierr = KSPChebyshevEstEigGetKSP(kspSmoother, &kspEst); CHKERRQ(ierr);
537         ierr = KSPSetType(kspEst, KSPCG); CHKERRQ(ierr);
538         ierr = KSPChebyshevEstEigSetUseNoisy(kspSmoother, PETSC_TRUE);
539         CHKERRQ(ierr);
540         ierr = KSPSetOperators(kspSmoother, jacobMat[level], jacobMat[level]);
541         CHKERRQ(ierr);
542 
543         // ---------- Smoother preconditioner
544         ierr = KSPGetPC(kspSmoother, &pcSmoother); CHKERRQ(ierr);
545         ierr = PCSetType(pcSmoother, PCJACOBI); CHKERRQ(ierr);
546         ierr = PCJacobiSetType(pcSmoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
547 
548         // -------- Work vector
549         if (level != fineLevel) {
550           ierr = PCMGSetX(pc, level, Ug[level]); CHKERRQ(ierr);
551         }
552 
553         // -------- Level prolongation/restriction operator
554         if (level > 0) {
555           ierr = PCMGSetInterpolation(pc, level, prolongRestrMat[level]);
556           CHKERRQ(ierr);
557           ierr = PCMGSetRestriction(pc, level, prolongRestrMat[level]);
558           CHKERRQ(ierr);
559         }
560       }
561 
562       // ------ PCMG coarse solve
563       KSP kspCoarse;
564       PC pcCoarse;
565 
566       // -------- Coarse KSP
567       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
568       ierr = KSPSetType(kspCoarse, KSPPREONLY); CHKERRQ(ierr);
569       ierr = KSPSetOperators(kspCoarse, jacobMatCoarse, jacobMatCoarse);
570       CHKERRQ(ierr);
571       ierr = KSPSetOptionsPrefix(kspCoarse, "coarse_"); CHKERRQ(ierr);
572 
573       // -------- Coarse preconditioner
574       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
575       ierr = PCSetType(pcCoarse, PCGAMG); CHKERRQ(ierr);
576       ierr = PCSetOptionsPrefix(pcCoarse, "coarse_"); CHKERRQ(ierr);
577 
578       ierr = KSPSetFromOptions(kspCoarse); CHKERRQ(ierr);
579       ierr = PCSetFromOptions(pcCoarse); CHKERRQ(ierr);
580 
581       // ------ PCMG options
582       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
583       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
584       ierr = PCMGSetCycleType(pc, pcmgCycleType); CHKERRQ(ierr);
585     }
586     ierr = KSPSetFromOptions(ksp);
587     ierr = PCSetFromOptions(pc);
588   }
589   {
590     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
591     SNESLineSearch linesearch;
592 
593     ierr = SNESGetLineSearch(snes, &linesearch); CHKERRQ(ierr);
594     ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHCP); CHKERRQ(ierr);
595   }
596 
597   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
598 
599   // Performance logging
600   ierr = PetscLogStagePop();
601 
602   // ---------------------------------------------------------------------------
603   // Set initial guess
604   // ---------------------------------------------------------------------------
605   ierr = PetscObjectSetName((PetscObject)U, ""); CHKERRQ(ierr);
606   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
607 
608   // View solution
609   if (appCtx->viewSoln) {
610     ierr = ViewSolution(comm, U, 0, 0.0); CHKERRQ(ierr);
611   }
612 
613   // ---------------------------------------------------------------------------
614   // Solve SNES
615   // ---------------------------------------------------------------------------
616   PetscBool snesMonitor = PETSC_FALSE;
617   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snesMonitor);
618   CHKERRQ(ierr);
619 
620   // Performance logging
621   ierr = PetscLogStageRegister("SNES Solve Stage", &stageSnesSolve);
622   CHKERRQ(ierr);
623   ierr = PetscLogStagePush(stageSnesSolve); CHKERRQ(ierr);
624 
625   // Timing
626   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
627   startTime = MPI_Wtime();
628 
629   // Solve for each load increment
630   PetscInt increment;
631   for (increment = 1; increment <= appCtx->numIncrements; increment++) {
632     // -- Log increment count
633     if (snesMonitor) {
634       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
635       CHKERRQ(ierr);
636     }
637 
638     // -- Scale the problem
639     PetscScalar loadIncrement = 1.0*increment / appCtx->numIncrements,
640                 scalingFactor = loadIncrement /
641                                 (increment == 1 ? 1 : resCtx->loadIncrement);
642     resCtx->loadIncrement = loadIncrement;
643     if (appCtx->numIncrements > 1 && appCtx->forcingChoice != FORCE_NONE) {
644       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
645     }
646 
647     // -- Solve
648     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
649 
650     // -- View solution
651     if (appCtx->viewSoln) {
652       ierr = ViewSolution(comm, U, increment, loadIncrement); CHKERRQ(ierr);
653     }
654 
655     // -- Update SNES iteration count
656     PetscInt its;
657     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
658     snesIts += its;
659 
660     // -- Check for divergence
661     SNESConvergedReason reason;
662     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
663     if (reason < 0)
664       break;
665   }
666 
667   // Timing
668   elapsedTime = MPI_Wtime() - startTime;
669 
670   // Performance logging
671   ierr = PetscLogStagePop();
672 
673   // ---------------------------------------------------------------------------
674   // Output summary
675   // ---------------------------------------------------------------------------
676   if (!appCtx->testMode) {
677     // -- SNES
678     SNESType snesType;
679     SNESConvergedReason reason;
680     PetscReal rnorm;
681     ierr = SNESGetType(snes, &snesType); CHKERRQ(ierr);
682     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
683     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
684     ierr = PetscPrintf(comm,
685                        "  SNES:\n"
686                        "    SNES Type                          : %s\n"
687                        "    SNES Convergence                   : %s\n"
688                        "    Number of Load Increments          : %d\n"
689                        "    Completed Load Increments          : %d\n"
690                        "    Total SNES Iterations              : %D\n"
691                        "    Final rnorm                        : %e\n",
692                        snesType, SNESConvergedReasons[reason],
693                        appCtx->numIncrements, increment - 1,
694                        snesIts, (double)rnorm); CHKERRQ(ierr);
695 
696     // -- KSP
697     KSP ksp;
698     KSPType kspType;
699     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
700     ierr = KSPGetType(ksp, &kspType); CHKERRQ(ierr);
701     ierr = PetscPrintf(comm,
702                        "  Linear Solver:\n"
703                        "    KSP Type                           : %s\n",
704                        kspType); CHKERRQ(ierr);
705 
706     // -- PC
707     PC pc;
708     PCType pcType;
709     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
710     ierr = PCGetType(pc, &pcType); CHKERRQ(ierr);
711     ierr = PetscPrintf(comm,
712                        "    PC Type                            : %s\n",
713                        pcType); CHKERRQ(ierr);
714 
715     if (!strcmp(pcType, PCMG)) {
716       PCMGType pcmgType;
717       ierr = PCMGGetType(pc, &pcmgType); CHKERRQ(ierr);
718       ierr = PetscPrintf(comm,
719                          "  P-Multigrid:\n"
720                          "    PCMG Type                          : %s\n"
721                          "    PCMG Cycle Type                    : %s\n",
722                          PCMGTypes[pcmgType],
723                          PCMGCycleTypes[pcmgCycleType]); CHKERRQ(ierr);
724 
725       // -- Coarse Solve
726       KSP kspCoarse;
727       PC pcCoarse;
728       PCType pcType;
729 
730       ierr = PCMGGetCoarseSolve(pc, &kspCoarse); CHKERRQ(ierr);
731       ierr = KSPGetType(kspCoarse, &kspType); CHKERRQ(ierr);
732       ierr = KSPGetPC(kspCoarse, &pcCoarse); CHKERRQ(ierr);
733       ierr = PCGetType(pcCoarse, &pcType); CHKERRQ(ierr);
734       ierr = PetscPrintf(comm,
735                          "    Coarse Solve:\n"
736                          "      KSP Type                         : %s\n"
737                          "      PC Type                          : %s\n",
738                          kspType, pcType); CHKERRQ(ierr);
739     }
740   }
741 
742   // ---------------------------------------------------------------------------
743   // Compute solve time
744   // ---------------------------------------------------------------------------
745   if (!appCtx->testMode) {
746     ierr = MPI_Allreduce(&elapsedTime, &minTime, 1, MPI_DOUBLE, MPI_MIN, comm);
747     CHKERRQ(ierr);
748     ierr = MPI_Allreduce(&elapsedTime, &maxTime, 1, MPI_DOUBLE, MPI_MAX, comm);
749     CHKERRQ(ierr);
750     ierr = PetscPrintf(comm,
751                        "  Performance:\n"
752                        "    SNES Solve Time                    : %g (%g) sec\n",
753                        maxTime, minTime); CHKERRQ(ierr);
754   }
755 
756   // ---------------------------------------------------------------------------
757   // Compute error
758   // ---------------------------------------------------------------------------
759   if (appCtx->forcingChoice == FORCE_MMS) {
760     CeedScalar l2Error = 1., l2Unorm = 1.;
761     const CeedScalar *truearray;
762     Vec errorVec, trueVec;
763 
764     // -- Work vectors
765     ierr = VecDuplicate(U, &errorVec); CHKERRQ(ierr);
766     ierr = VecSet(errorVec, 0.0); CHKERRQ(ierr);
767     ierr = VecDuplicate(U, &trueVec); CHKERRQ(ierr);
768     ierr = VecSet(trueVec, 0.0); CHKERRQ(ierr);
769 
770     // -- Assemble global true solution vector
771     CeedVectorGetArrayRead(ceedData[fineLevel]->truesoln,
772                            appCtx->memTypeRequested, &truearray);
773     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
774       ierr = VecPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
775       CHKERRQ(ierr);
776     } else {
777       ierr = VecCUDAPlaceArray(resCtx->Yloc, (PetscScalar *)truearray);
778       CHKERRQ(ierr);
779     }
780     ierr = DMLocalToGlobal(resCtx->dm, resCtx->Yloc, INSERT_VALUES, trueVec);
781     CHKERRQ(ierr);
782     if (appCtx->memTypeRequested == CEED_MEM_HOST) {
783       ierr = VecResetArray(resCtx->Yloc); CHKERRQ(ierr);
784     } else {
785       ierr = VecCUDAResetArray(resCtx->Yloc); CHKERRQ(ierr);
786     }
787     CeedVectorRestoreArrayRead(ceedData[fineLevel]->truesoln, &truearray);
788 
789     // -- Compute L2 error
790     ierr = VecWAXPY(errorVec, -1.0, U, trueVec); CHKERRQ(ierr);
791     ierr = VecNorm(errorVec, NORM_2, &l2Error); CHKERRQ(ierr);
792     ierr = VecNorm(U, NORM_2, &l2Unorm); CHKERRQ(ierr);
793     l2Error /= l2Unorm;
794 
795     // -- Output
796     if (!appCtx->testMode || l2Error > 0.05) {
797       ierr = PetscPrintf(comm,
798                          "    L2 Error                           : %e\n",
799                          l2Error); CHKERRQ(ierr);
800     }
801 
802     // -- Cleanup
803     ierr = VecDestroy(&errorVec); CHKERRQ(ierr);
804     ierr = VecDestroy(&trueVec); CHKERRQ(ierr);
805   }
806 
807   // ---------------------------------------------------------------------------
808   // Compute energy
809   // ---------------------------------------------------------------------------
810   if (!appCtx->testMode) {
811     // -- Compute L2 error
812     CeedScalar energy;
813     ierr = ComputeStrainEnergy(dmEnergy, resCtx, ceedData[fineLevel]->opEnergy,
814                                U, &energy); CHKERRQ(ierr);
815 
816     // -- Output
817     ierr = PetscPrintf(comm,
818                        "    Strain Energy                      : %e\n",
819                        energy); CHKERRQ(ierr);
820   }
821 
822   // ---------------------------------------------------------------------------
823   // Output diagnostic quantities
824   // ---------------------------------------------------------------------------
825   if (appCtx->viewSoln || appCtx->viewFinalSoln) {
826     // -- Setup context
827     UserMult diagnosticCtx;
828     ierr = PetscMalloc1(1, &diagnosticCtx); CHKERRQ(ierr);
829     ierr = PetscMemcpy(diagnosticCtx, resCtx, sizeof(*resCtx)); CHKERRQ(ierr);
830     diagnosticCtx->dm = dmDiagnostic;
831     diagnosticCtx->op = ceedData[fineLevel]->opDiagnostic;
832 
833     // -- Compute and output
834     ierr = ViewDiagnosticQuantities(comm, levelDMs[fineLevel], diagnosticCtx, U,
835                                     ceedData[fineLevel]->ErestrictDiagnostic);
836     CHKERRQ(ierr);
837 
838     // -- Cleanup
839     ierr = PetscFree(diagnosticCtx); CHKERRQ(ierr);
840   }
841 
842   // ---------------------------------------------------------------------------
843   // Free objects
844   // ---------------------------------------------------------------------------
845   // Data in arrays per level
846   for (PetscInt level = 0; level < numLevels; level++) {
847     // Vectors
848     ierr = VecDestroy(&Ug[level]); CHKERRQ(ierr);
849     ierr = VecDestroy(&Uloc[level]); CHKERRQ(ierr);
850 
851     // Jacobian matrix and data
852     ierr = VecDestroy(&jacobCtx[level]->Yloc); CHKERRQ(ierr);
853     ierr = MatDestroy(&jacobMat[level]); CHKERRQ(ierr);
854     ierr = PetscFree(jacobCtx[level]); CHKERRQ(ierr);
855 
856     // Prolongation/Restriction matrix and data
857     if (level > 0) {
858       ierr = VecDestroy(&prolongRestrCtx[level]->multVec); CHKERRQ(ierr);
859       ierr = PetscFree(prolongRestrCtx[level]); CHKERRQ(ierr);
860       ierr = MatDestroy(&prolongRestrMat[level]); CHKERRQ(ierr);
861     }
862 
863     // DM
864     ierr = DMDestroy(&levelDMs[level]); CHKERRQ(ierr);
865 
866     // libCEED objects
867     ierr = CeedDataDestroy(level, ceedData[level]); CHKERRQ(ierr);
868   }
869 
870   // Arrays
871   ierr = PetscFree(Ug); CHKERRQ(ierr);
872   ierr = PetscFree(Uloc); CHKERRQ(ierr);
873   ierr = PetscFree(Ugsz); CHKERRQ(ierr);
874   ierr = PetscFree(Ulsz); CHKERRQ(ierr);
875   ierr = PetscFree(Ulocsz); CHKERRQ(ierr);
876   ierr = PetscFree(jacobCtx); CHKERRQ(ierr);
877   ierr = PetscFree(jacobMat); CHKERRQ(ierr);
878   ierr = PetscFree(prolongRestrCtx); CHKERRQ(ierr);
879   ierr = PetscFree(prolongRestrMat); CHKERRQ(ierr);
880   ierr = PetscFree(appCtx->levelDegrees); CHKERRQ(ierr);
881   ierr = PetscFree(ceedData); CHKERRQ(ierr);
882 
883   // libCEED objects
884   CeedQFunctionDestroy(&qfRestrict);
885   CeedQFunctionDestroy(&qfProlong);
886   CeedDestroy(&ceed);
887   CeedDestroy(&ceedFine);
888 
889   // PETSc objects
890   ierr = VecDestroy(&U); CHKERRQ(ierr);
891   ierr = VecDestroy(&R); CHKERRQ(ierr);
892   ierr = VecDestroy(&Rloc); CHKERRQ(ierr);
893   ierr = VecDestroy(&F); CHKERRQ(ierr);
894   ierr = VecDestroy(&Floc); CHKERRQ(ierr);
895   ierr = MatDestroy(&jacobMatCoarse); CHKERRQ(ierr);
896   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
897   ierr = SNESDestroy(&snesCoarse); CHKERRQ(ierr);
898   ierr = DMDestroy(&dmOrig); CHKERRQ(ierr);
899   ierr = DMDestroy(&dmEnergy); CHKERRQ(ierr);
900   ierr = DMDestroy(&dmDiagnostic); CHKERRQ(ierr);
901   ierr = PetscFree(levelDMs); CHKERRQ(ierr);
902 
903   // Structs
904   ierr = PetscFree(resCtx); CHKERRQ(ierr);
905   ierr = PetscFree(formJacobCtx); CHKERRQ(ierr);
906   ierr = PetscFree(jacobCoarseCtx); CHKERRQ(ierr);
907   ierr = PetscFree(appCtx); CHKERRQ(ierr);
908   ierr = PetscFree(phys); CHKERRQ(ierr);
909   ierr = PetscFree(physSmoother); CHKERRQ(ierr);
910   ierr = PetscFree(units); CHKERRQ(ierr);
911 
912   return PetscFinalize();
913 }
914