xref: /libCEED/examples/solids/elasticity.c (revision 3fc8a154943bcd95936b4475143d7e8b037e7b11)
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 Linear -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 SS-NH -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 FSInitial-NH1 -forcing none -ceed /gpu/cuda
33 //
34 // Sample meshes can be found at https://github.com/jeremylt/ceedSampleMeshes
35 //
36 //TESTARGS(name="solids-Linear-MMS") -ceed {ceed_resource} -test -degree 3 -nu 0.3 -E 1 -dm_plex_box_faces 3,3,3
37 //TESTARGS(name="solids-NH1-1") -ceed {ceed_resource} -test -problem FSInitial-NH1 -E 2.8 -nu 0.4 -degree 2 -dm_plex_box_faces 2,2,2 -num_steps 1 -bc_clamp 6 -bc_traction 5 -bc_traction_5 0,0,-.5 -expect_final_strain_energy 2.124627916174e-01
38 //TESTARGS(name="solids-MR1-1") -ceed {ceed_resource} -test -problem FSInitial-MR1 -mu_1 .5 -mu_2 .5 -nu 0.4 -degree 2 -dm_plex_box_faces 2,2,2 -num_steps 1 -bc_clamp 6 -bc_traction 5 -bc_traction_5 0,0,-.5 -expect_final_strain_energy 2.339138880207e-01
39 
40 /// @file
41 /// CEED elasticity example using PETSc with DMPlex
42 
43 const char help[] = "Solve solid Problems with CEED and PETSc DMPlex\n";
44 
45 #include "elasticity.h"
46 
47 int main(int argc, char **argv) {
48   PetscInt       ierr;
49   MPI_Comm       comm;
50   // Context structs
51   AppCtx         app_ctx;                  // Contains problem options
52   ProblemFunctions problem_functions;      // Setup functions for each problem
53   Units          units;                    // Contains units scaling
54   // PETSc objects
55   PetscLogStage  stage_dm_setup, stage_libceed_setup,
56                  stage_snes_setup, stage_snes_solve;
57   DM             dm_orig;                  // Distributed DM to clone
58   DM             dm_energy, dm_diagnostic; // DMs for postprocessing
59   DM             *level_dms;
60   Vec            U, *U_g, *U_loc;          // U: solution, R: residual, F: forcing
61   Vec            R, R_loc, F, F_loc;       // g: global, loc: local
62   Vec            neumann_bcs = NULL, bcs_loc = NULL;
63   SNES           snes;
64   Mat            *jacob_mat, jacob_mat_coarse, *prolong_restr_mat;
65   // PETSc data
66   UserMult       res_ctx, jacob_coarse_ctx = NULL, *jacob_ctx;
67   FormJacobCtx   form_jacob_ctx;
68   UserMultProlongRestr *prolong_restr_ctx;
69   PCMGCycleType  pcmg_cycle_type = PC_MG_CYCLE_V;
70   // libCEED objects
71   Ceed           ceed;
72   CeedData       *ceed_data;
73   CeedQFunctionContext ctx_phys, ctx_phys_smoother = NULL;
74   // Parameters
75   PetscInt       num_comp_u = 3;                 // 3 DoFs in 3D
76   PetscInt       num_comp_e = 1, num_comp_d = 5; // 1 energy output, 5 diagnostic
77   PetscInt       num_levels = 1, fine_level = 0;
78   PetscInt       *U_g_size, *U_l_size, *U_loc_size;
79   PetscInt       snes_its = 0, ksp_its = 0;
80   double         start_time, elapsed_time, min_time, max_time;
81 
82   ierr = PetscInitialize(&argc, &argv, NULL, help);
83   if (ierr) 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, &app_ctx); CHKERRQ(ierr);
92   ierr = ProcessCommandLineOptions(comm, app_ctx); CHKERRQ(ierr);
93   ierr = PetscCalloc1(1, &problem_functions); CHKERRQ(ierr);
94   ierr = RegisterProblems(problem_functions); CHKERRQ(ierr);
95   num_levels = app_ctx->num_levels;
96   fine_level = num_levels - 1;
97 
98   // ---------------------------------------------------------------------------
99   // Initialize libCEED
100   // ---------------------------------------------------------------------------
101   // Initialize backend
102   CeedInit(app_ctx->ceed_resource, &ceed);
103 
104   // Check preferred MemType
105   CeedMemType mem_type_backend;
106   CeedGetPreferredMemType(ceed, &mem_type_backend);
107   // Setup physics context and wrap in libCEED object
108   {
109     PetscErrorCode (*SetupPhysics)(MPI_Comm, Ceed, Units *, CeedQFunctionContext *);
110     ierr = PetscFunctionListFind(problem_functions->setupPhysics, app_ctx->name,
111                                  &SetupPhysics); CHKERRQ(ierr);
112     if (!SetupPhysics)
113       SETERRQ(PETSC_COMM_SELF, 1, "Physics setup for '%s' not found",
114               app_ctx->name);
115     ierr = (*SetupPhysics)(comm, ceed, &units, &ctx_phys); CHKERRQ(ierr);
116     PetscErrorCode (*SetupSmootherPhysics)(MPI_Comm, Ceed, CeedQFunctionContext,
117                                            CeedQFunctionContext *);
118     ierr = PetscFunctionListFind(problem_functions->setupSmootherPhysics,
119                                  app_ctx->name, &SetupSmootherPhysics);
120     CHKERRQ(ierr);
121     if (!SetupSmootherPhysics)
122       SETERRQ(PETSC_COMM_SELF, 1, "Smoother physics setup for '%s' not found",
123               app_ctx->name);
124     ierr = (*SetupSmootherPhysics)(comm, ceed, ctx_phys, &ctx_phys_smoother);
125     CHKERRQ(ierr);
126   }
127 
128   // ---------------------------------------------------------------------------
129   // Setup DM
130   // ---------------------------------------------------------------------------
131   // Performance logging
132   ierr = PetscLogStageRegister("DM and Vector Setup Stage", &stage_dm_setup);
133   CHKERRQ(ierr);
134   ierr = PetscLogStagePush(stage_dm_setup); CHKERRQ(ierr);
135 
136   // -- Create distributed DM from mesh file
137   ierr = CreateDistributedDM(comm, app_ctx, &dm_orig); CHKERRQ(ierr);
138   VecType vectype;
139   switch (mem_type_backend) {
140   case CEED_MEM_HOST: vectype = VECSTANDARD; break;
141   case CEED_MEM_DEVICE: {
142     const char *resolved;
143     CeedGetResource(ceed, &resolved);
144     if (strstr(resolved, "/gpu/cuda")) vectype = VECCUDA;
145     else if (strstr(resolved, "/gpu/hip")) vectype = VECHIP;
146     else vectype = VECSTANDARD;
147   }
148   }
149   ierr = DMSetVecType(dm_orig, vectype); CHKERRQ(ierr);
150   ierr = DMPlexDistributeSetDefault(dm_orig, PETSC_FALSE); CHKERRQ(ierr);
151   ierr = DMSetFromOptions(dm_orig); CHKERRQ(ierr);
152 
153   // -- Setup DM by polynomial degree
154   ierr = PetscMalloc1(num_levels, &level_dms); CHKERRQ(ierr);
155   for (PetscInt level = 0; level < num_levels; level++) {
156     ierr = DMClone(dm_orig, &level_dms[level]); CHKERRQ(ierr);
157     ierr = DMGetVecType(dm_orig, &vectype); CHKERRQ(ierr);
158     ierr = DMSetVecType(level_dms[level], vectype); CHKERRQ(ierr);
159     ierr = SetupDMByDegree(level_dms[level], app_ctx, app_ctx->level_degrees[level],
160                            PETSC_TRUE, num_comp_u); CHKERRQ(ierr);
161     // -- Label field components for viewing
162     // Empty name for conserved field (because there is only one field)
163     PetscSection section;
164     ierr = DMGetLocalSection(level_dms[level], &section); CHKERRQ(ierr);
165     ierr = PetscSectionSetFieldName(section, 0, "Displacement"); CHKERRQ(ierr);
166     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
167     CHKERRQ(ierr);
168     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
169     CHKERRQ(ierr);
170     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
171     CHKERRQ(ierr);
172   }
173 
174   // -- Setup postprocessing DMs
175   ierr = DMClone(dm_orig, &dm_energy); CHKERRQ(ierr);
176   ierr = SetupDMByDegree(dm_energy, app_ctx, app_ctx->level_degrees[fine_level],
177                          PETSC_FALSE, num_comp_e); CHKERRQ(ierr);
178   ierr = DMClone(dm_orig, &dm_diagnostic); CHKERRQ(ierr);
179   ierr = SetupDMByDegree(dm_diagnostic, app_ctx,
180                          app_ctx->level_degrees[fine_level],
181                          PETSC_FALSE, num_comp_u + num_comp_d); CHKERRQ(ierr);
182   ierr = DMSetVecType(dm_energy, vectype); CHKERRQ(ierr);
183   ierr = DMSetVecType(dm_diagnostic, vectype); CHKERRQ(ierr);
184   {
185     // -- Label field components for viewing
186     // Empty name for conserved field (because there is only one field)
187     PetscSection section;
188     ierr = DMGetLocalSection(dm_diagnostic, &section); CHKERRQ(ierr);
189     ierr = PetscSectionSetFieldName(section, 0, "Diagnostics"); CHKERRQ(ierr);
190     ierr = PetscSectionSetComponentName(section, 0, 0, "DisplacementX");
191     CHKERRQ(ierr);
192     ierr = PetscSectionSetComponentName(section, 0, 1, "DisplacementY");
193     CHKERRQ(ierr);
194     ierr = PetscSectionSetComponentName(section, 0, 2, "DisplacementZ");
195     CHKERRQ(ierr);
196     ierr = PetscSectionSetComponentName(section, 0, 3, "Pressure");
197     CHKERRQ(ierr);
198     ierr = PetscSectionSetComponentName(section, 0, 4, "VolumentricStrain");
199     CHKERRQ(ierr);
200     ierr = PetscSectionSetComponentName(section, 0, 5, "TraceE2");
201     CHKERRQ(ierr);
202     ierr = PetscSectionSetComponentName(section, 0, 6, "detJ");
203     CHKERRQ(ierr);
204     ierr = PetscSectionSetComponentName(section, 0, 7, "StrainEnergyDensity");
205     CHKERRQ(ierr);
206   }
207 
208   // ---------------------------------------------------------------------------
209   // Setup solution and work vectors
210   // ---------------------------------------------------------------------------
211   // Allocate arrays
212   ierr = PetscMalloc1(num_levels, &U_g); CHKERRQ(ierr);
213   ierr = PetscMalloc1(num_levels, &U_loc); CHKERRQ(ierr);
214   ierr = PetscMalloc1(num_levels, &U_g_size); CHKERRQ(ierr);
215   ierr = PetscMalloc1(num_levels, &U_l_size); CHKERRQ(ierr);
216   ierr = PetscMalloc1(num_levels, &U_loc_size); CHKERRQ(ierr);
217 
218   // -- Setup solution vectors for each level
219   for (PetscInt level = 0; level < num_levels; level++) {
220     // -- Create global unknown vector U
221     ierr = DMCreateGlobalVector(level_dms[level], &U_g[level]); CHKERRQ(ierr);
222     ierr = VecGetSize(U_g[level], &U_g_size[level]); CHKERRQ(ierr);
223     // Note: Local size for matShell
224     ierr = VecGetLocalSize(U_g[level], &U_l_size[level]); CHKERRQ(ierr);
225 
226     // -- Create local unknown vector U_loc
227     ierr = DMCreateLocalVector(level_dms[level], &U_loc[level]); CHKERRQ(ierr);
228     // Note: local size for libCEED
229     ierr = VecGetSize(U_loc[level], &U_loc_size[level]); CHKERRQ(ierr);
230   }
231 
232   // -- Create residual and forcing vectors
233   ierr = VecDuplicate(U_g[fine_level], &U); CHKERRQ(ierr);
234   ierr = VecDuplicate(U_g[fine_level], &R); CHKERRQ(ierr);
235   ierr = VecDuplicate(U_g[fine_level], &F); CHKERRQ(ierr);
236   ierr = VecDuplicate(U_loc[fine_level], &R_loc); CHKERRQ(ierr);
237   ierr = VecDuplicate(U_loc[fine_level], &F_loc); CHKERRQ(ierr);
238 
239   // Performance logging
240   ierr = PetscLogStagePop();
241 
242   // ---------------------------------------------------------------------------
243   // Set up libCEED
244   // ---------------------------------------------------------------------------
245   // Performance logging
246   ierr = PetscLogStageRegister("libCEED Setup Stage", &stage_libceed_setup);
247   CHKERRQ(ierr);
248   ierr = PetscLogStagePush(stage_libceed_setup); CHKERRQ(ierr);
249 
250   // -- Create libCEED local forcing vector
251   CeedVector force_ceed;
252   CeedScalar *f;
253   PetscMemType force_mem_type;
254   if (app_ctx->forcing_choice != FORCE_NONE) {
255     ierr = VecGetArrayAndMemType(F_loc, &f, &force_mem_type); CHKERRQ(ierr);
256     CeedVectorCreate(ceed, U_loc_size[fine_level], &force_ceed);
257     CeedVectorSetArray(force_ceed, MemTypeP2C(force_mem_type), CEED_USE_POINTER, f);
258   }
259 
260   // -- Create libCEED local Neumann BCs vector
261   CeedVector neumann_ceed;
262   CeedScalar *n;
263   PetscMemType nummann_mem_type;
264   if (app_ctx->bc_traction_count > 0) {
265     ierr = VecDuplicate(U, &neumann_bcs); CHKERRQ(ierr);
266     ierr = VecDuplicate(U_loc[fine_level], &bcs_loc); CHKERRQ(ierr);
267     ierr = VecGetArrayAndMemType(bcs_loc, &n, &nummann_mem_type); CHKERRQ(ierr);
268     CeedVectorCreate(ceed, U_loc_size[fine_level], &neumann_ceed);
269     CeedVectorSetArray(neumann_ceed, MemTypeP2C(nummann_mem_type),
270                        CEED_USE_POINTER, n);
271   }
272 
273   // -- Setup libCEED objects
274   ierr = PetscMalloc1(num_levels, &ceed_data); CHKERRQ(ierr);
275   // ---- Setup residual, Jacobian evaluator and geometric information
276   ierr = PetscCalloc1(1, &ceed_data[fine_level]); CHKERRQ(ierr);
277   {
278     PetscErrorCode (*SetupLibceedFineLevel)(DM, DM, DM, Ceed, AppCtx,
279                                             CeedQFunctionContext, PetscInt,
280                                             PetscInt, PetscInt, PetscInt,
281                                             CeedVector, CeedVector, CeedData *);
282     ierr = PetscFunctionListFind(problem_functions->setupLibceedFineLevel,
283                                  app_ctx->name, &SetupLibceedFineLevel);
284     CHKERRQ(ierr);
285     if (!SetupLibceedFineLevel)
286       SETERRQ(PETSC_COMM_SELF, 1, "Fine grid setup for '%s' not found",
287               app_ctx->name);
288     ierr = (*SetupLibceedFineLevel)(level_dms[fine_level], dm_energy, dm_diagnostic,
289                                     ceed, app_ctx, ctx_phys, fine_level,
290                                     num_comp_u, U_g_size[fine_level],
291                                     U_loc_size[fine_level],
292                                     force_ceed, neumann_ceed, ceed_data);
293     CHKERRQ(ierr);
294   }
295   // ---- Setup coarse Jacobian evaluator and prolongation/restriction
296   for (PetscInt level = num_levels - 2; level >= 0; level--) {
297     ierr = PetscCalloc1(1, &ceed_data[level]); CHKERRQ(ierr);
298 
299     // Get global communication restriction
300     ierr = VecZeroEntries(U_g[level+1]); CHKERRQ(ierr);
301     ierr = VecSet(U_loc[level+1], 1.0); CHKERRQ(ierr);
302     ierr = DMLocalToGlobal(level_dms[level+1], U_loc[level+1], ADD_VALUES,
303                            U_g[level+1]); CHKERRQ(ierr);
304     ierr = DMGlobalToLocal(level_dms[level+1], U_g[level+1], INSERT_VALUES,
305                            U_loc[level+1]); CHKERRQ(ierr);
306 
307     // Place in libCEED array
308     const PetscScalar *m;
309     PetscMemType m_mem_type;
310     ierr = VecGetArrayReadAndMemType(U_loc[level+1], &m, &m_mem_type);
311     CHKERRQ(ierr);
312     CeedVectorSetArray(ceed_data[level+1]->x_ceed, MemTypeP2C(m_mem_type),
313                        CEED_USE_POINTER, (CeedScalar *)m);
314 
315     // Note: use high order ceed, if specified and degree > 4
316     PetscErrorCode (*SetupLibceedLevel)(DM, Ceed, AppCtx, PetscInt,
317                                         PetscInt, PetscInt, PetscInt, CeedVector, CeedData *);
318     ierr = PetscFunctionListFind(problem_functions->setupLibceedLevel,
319                                  app_ctx->name, &SetupLibceedLevel);
320     CHKERRQ(ierr);
321     if (!SetupLibceedLevel)
322       SETERRQ(PETSC_COMM_SELF, 1, "Coarse grid setup for '%s' not found",
323               app_ctx->name);
324     ierr = (*SetupLibceedLevel)(level_dms[level], ceed, app_ctx,
325                                 level, num_comp_u, U_g_size[level],
326                                 U_loc_size[level], ceed_data[level+1]->x_ceed,
327                                 ceed_data);
328     CHKERRQ(ierr);
329 
330     // Restore PETSc vector
331     CeedVectorTakeArray(ceed_data[level+1]->x_ceed, MemTypeP2C(m_mem_type),
332                         (CeedScalar **)&m);
333     ierr = VecRestoreArrayReadAndMemType(U_loc[level+1], &m); CHKERRQ(ierr);
334     ierr = VecZeroEntries(U_g[level+1]); CHKERRQ(ierr);
335     ierr = VecZeroEntries(U_loc[level+1]); CHKERRQ(ierr);
336   }
337 
338   // Performance logging
339   ierr = PetscLogStagePop();
340 
341   // ---------------------------------------------------------------------------
342   // Setup global forcing and Neumann BC vectors
343   // ---------------------------------------------------------------------------
344   ierr = VecZeroEntries(F); CHKERRQ(ierr);
345 
346   if (app_ctx->forcing_choice != FORCE_NONE) {
347     CeedVectorTakeArray(force_ceed, MemTypeP2C(force_mem_type), NULL);
348     ierr = VecRestoreArrayAndMemType(F_loc, &f); CHKERRQ(ierr);
349     ierr = DMLocalToGlobal(level_dms[fine_level], F_loc, ADD_VALUES, F);
350     CHKERRQ(ierr);
351     CeedVectorDestroy(&force_ceed);
352   }
353 
354   if (app_ctx->bc_traction_count > 0) {
355     ierr = VecZeroEntries(neumann_bcs); CHKERRQ(ierr);
356     CeedVectorTakeArray(neumann_ceed, MemTypeP2C(nummann_mem_type), NULL);
357     ierr = VecRestoreArrayAndMemType(bcs_loc, &n); CHKERRQ(ierr);
358     ierr = DMLocalToGlobal(level_dms[fine_level], bcs_loc, ADD_VALUES, neumann_bcs);
359     CHKERRQ(ierr);
360     CeedVectorDestroy(&neumann_ceed);
361   }
362 
363   // ---------------------------------------------------------------------------
364   // Print problem summary
365   // ---------------------------------------------------------------------------
366   if (!app_ctx->test_mode) {
367     const char *usedresource;
368     CeedGetResource(ceed, &usedresource);
369     char hostname[PETSC_MAX_PATH_LEN];
370     ierr = PetscGetHostName(hostname, sizeof hostname); CHKERRQ(ierr);
371     PetscInt comm_size;
372     ierr = MPI_Comm_size(comm, &comm_size); CHKERRQ(ierr);
373 
374     ierr = PetscPrintf(comm,
375                        "\n-- Elasticity Example - libCEED + PETSc --\n"
376                        "  MPI:\n"
377                        "    Hostname                           : %s\n"
378                        "    Total ranks                        : %d\n"
379                        "  libCEED:\n"
380                        "    libCEED Backend                    : %s\n"
381                        "    libCEED Backend MemType            : %s\n",
382                        hostname, comm_size, usedresource, CeedMemTypes[mem_type_backend]);
383     CHKERRQ(ierr);
384 
385     VecType vecType;
386     ierr = VecGetType(U, &vecType); CHKERRQ(ierr);
387     ierr = PetscPrintf(comm,
388                        "  PETSc:\n"
389                        "    PETSc Vec Type                     : %s\n",
390                        vecType); CHKERRQ(ierr);
391 
392     ierr = PetscPrintf(comm,
393                        "  Problem:\n"
394                        "    Problem Name                       : %s\n"
395                        "    Forcing Function                   : %s\n"
396                        "  Mesh:\n"
397                        "    File                               : %s\n"
398                        "    Number of 1D Basis Nodes (p)       : %d\n"
399                        "    Number of 1D Quadrature Points (q) : %d\n"
400                        "    Global nodes                       : %D\n"
401                        "    Owned nodes                        : %D\n"
402                        "    DoF per node                       : %D\n"
403                        "  Multigrid:\n"
404                        "    Type                               : %s\n"
405                        "    Number of Levels                   : %d\n",
406                        app_ctx->name_for_disp,
407                        forcing_types_for_disp[app_ctx->forcing_choice],
408                        app_ctx->mesh_file[0] ? app_ctx->mesh_file : "Box Mesh",
409                        app_ctx->degree + 1, app_ctx->degree + 1,
410                        U_g_size[fine_level]/num_comp_u, U_l_size[fine_level]/num_comp_u,
411                        num_comp_u,
412                        (app_ctx->degree == 1 &&
413                         app_ctx->multigrid_choice != MULTIGRID_NONE) ?
414                        "Algebraic multigrid" :
415                        multigrid_types_for_disp[app_ctx->multigrid_choice],
416                        (app_ctx->degree == 1 ||
417                         app_ctx->multigrid_choice == MULTIGRID_NONE) ?
418                        0 : num_levels); CHKERRQ(ierr);
419 
420     if (app_ctx->multigrid_choice != MULTIGRID_NONE) {
421       for (PetscInt i = 0; i < 2; i++) {
422         CeedInt level = i ? fine_level : 0;
423         ierr = PetscPrintf(comm,
424                            "    Level %D (%s):\n"
425                            "      Number of 1D Basis Nodes (p)     : %d\n"
426                            "      Global Nodes                     : %D\n"
427                            "      Owned Nodes                      : %D\n",
428                            level, i ? "fine" : "coarse",
429                            app_ctx->level_degrees[level] + 1,
430                            U_g_size[level]/num_comp_u, U_l_size[level]/num_comp_u);
431         CHKERRQ(ierr);
432       }
433     }
434   }
435 
436   // ---------------------------------------------------------------------------
437   // Setup SNES
438   // ---------------------------------------------------------------------------
439   // Performance logging
440   ierr = PetscLogStageRegister("SNES Setup Stage", &stage_snes_setup);
441   CHKERRQ(ierr);
442   ierr = PetscLogStagePush(stage_snes_setup); CHKERRQ(ierr);
443 
444   // Create SNES
445   ierr = SNESCreate(comm, &snes); CHKERRQ(ierr);
446   ierr = SNESSetDM(snes, level_dms[fine_level]); CHKERRQ(ierr);
447 
448   // -- Jacobian evaluators
449   ierr = PetscMalloc1(num_levels, &jacob_ctx); CHKERRQ(ierr);
450   ierr = PetscMalloc1(num_levels, &jacob_mat); CHKERRQ(ierr);
451   for (PetscInt level = 0; level < num_levels; level++) {
452     // -- Jacobian context for level
453     ierr = PetscMalloc1(1, &jacob_ctx[level]); CHKERRQ(ierr);
454     ierr = SetupJacobianCtx(comm, app_ctx, level_dms[level], U_g[level],
455                             U_loc[level], ceed_data[level], ceed, ctx_phys,
456                             ctx_phys_smoother, jacob_ctx[level]); CHKERRQ(ierr);
457 
458     // -- Form Action of Jacobian on delta_u
459     ierr = MatCreateShell(comm, U_l_size[level], U_l_size[level], U_g_size[level],
460                           U_g_size[level], jacob_ctx[level], &jacob_mat[level]);
461     CHKERRQ(ierr);
462     ierr = MatShellSetOperation(jacob_mat[level], MATOP_MULT,
463                                 (void (*)(void))ApplyJacobian_Ceed);
464     CHKERRQ(ierr);
465     ierr = MatShellSetOperation(jacob_mat[level], MATOP_GET_DIAGONAL,
466                                 (void(*)(void))GetDiag_Ceed);
467     ierr = MatShellSetVecType(jacob_mat[level], vectype); CHKERRQ(ierr);
468   }
469   // Note: FormJacobian updates Jacobian matrices on each level
470   //   and assembles the Jpre matrix, if needed
471   ierr = PetscMalloc1(1, &form_jacob_ctx); CHKERRQ(ierr);
472   form_jacob_ctx->jacob_ctx = jacob_ctx;
473   form_jacob_ctx->num_levels = num_levels;
474   form_jacob_ctx->jacob_mat = jacob_mat;
475 
476   // -- Residual evaluation function
477   ierr = PetscCalloc1(1, &res_ctx); CHKERRQ(ierr);
478   ierr = PetscMemcpy(res_ctx, jacob_ctx[fine_level],
479                      sizeof(*jacob_ctx[fine_level])); CHKERRQ(ierr);
480   res_ctx->op = ceed_data[fine_level]->op_residual;
481   res_ctx->qf = ceed_data[fine_level]->qf_residual;
482   if (app_ctx->bc_traction_count > 0)
483     res_ctx->neumann_bcs = neumann_bcs;
484   else
485     res_ctx->neumann_bcs = NULL;
486   ierr = SNESSetFunction(snes, R, FormResidual_Ceed, res_ctx); CHKERRQ(ierr);
487 
488   // -- Prolongation/Restriction evaluation
489   ierr = PetscMalloc1(num_levels, &prolong_restr_ctx); CHKERRQ(ierr);
490   ierr = PetscMalloc1(num_levels, &prolong_restr_mat); CHKERRQ(ierr);
491   for (PetscInt level = 1; level < num_levels; level++) {
492     // ---- Prolongation/restriction context for level
493     ierr = PetscMalloc1(1, &prolong_restr_ctx[level]); CHKERRQ(ierr);
494     ierr = SetupProlongRestrictCtx(comm, app_ctx, level_dms[level-1],
495                                    level_dms[level], U_g[level], U_loc[level-1],
496                                    U_loc[level], ceed_data[level-1],
497                                    ceed_data[level], ceed,
498                                    prolong_restr_ctx[level]); CHKERRQ(ierr);
499 
500     // ---- Form Action of Jacobian on delta_u
501     ierr = MatCreateShell(comm, U_l_size[level], U_l_size[level-1], U_g_size[level],
502                           U_g_size[level-1], prolong_restr_ctx[level],
503                           &prolong_restr_mat[level]); CHKERRQ(ierr);
504     // Note: In PCMG, restriction is the transpose of prolongation
505     ierr = MatShellSetOperation(prolong_restr_mat[level], MATOP_MULT,
506                                 (void (*)(void))Prolong_Ceed);
507     ierr = MatShellSetOperation(prolong_restr_mat[level], MATOP_MULT_TRANSPOSE,
508                                 (void (*)(void))Restrict_Ceed);
509     CHKERRQ(ierr);
510     ierr = MatShellSetVecType(prolong_restr_mat[level], vectype); CHKERRQ(ierr);
511   }
512 
513   // ---------------------------------------------------------------------------
514   // Setup for AMG coarse solve
515   // ---------------------------------------------------------------------------
516   if (app_ctx->multigrid_choice != MULTIGRID_NONE) {
517     // -- Jacobian Matrix
518     ierr = DMCreateMatrix(level_dms[0], &jacob_mat_coarse); CHKERRQ(ierr);
519 
520     if (app_ctx->degree > 1) {
521       // -- Assemble sparsity pattern
522       CeedInt num_entries, *rows, *cols;
523       CeedVector coo_values;
524       CeedOperatorLinearAssembleSymbolic(ceed_data[0]->op_jacobian, &num_entries,
525                                          &rows, &cols);
526       ISLocalToGlobalMapping ltog_row, ltog_col;
527       ierr = MatGetLocalToGlobalMapping(jacob_mat_coarse, &ltog_row, &ltog_col);
528       CHKERRQ(ierr);
529       ierr = ISLocalToGlobalMappingApply(ltog_row, num_entries, rows, rows);
530       CHKERRQ(ierr);
531       ierr = ISLocalToGlobalMappingApply(ltog_col, num_entries, cols, cols);
532       CHKERRQ(ierr);
533       ierr = MatSetPreallocationCOO(jacob_mat_coarse, num_entries, rows, cols);
534       CHKERRQ(ierr);
535       free(rows);
536       free(cols);
537       CeedVectorCreate(ceed, num_entries, &coo_values);
538 
539       // -- Update form_jacob_ctx
540       form_jacob_ctx->coo_values = coo_values;
541       form_jacob_ctx->op_coarse = ceed_data[0]->op_jacobian;
542       form_jacob_ctx->jacob_mat_coarse = jacob_mat_coarse;
543     }
544   }
545 
546   // Set Jacobian function
547   if (app_ctx->degree > 1) {
548     ierr = SNESSetJacobian(snes, jacob_mat[fine_level], jacob_mat[fine_level],
549                            FormJacobian, form_jacob_ctx); CHKERRQ(ierr);
550   } else {
551     ierr = SNESSetJacobian(snes, jacob_mat[0], jacob_mat_coarse,
552                            SNESComputeJacobianDefaultColor, NULL);
553     CHKERRQ(ierr);
554   }
555 
556   // ---------------------------------------------------------------------------
557   // Setup KSP
558   // ---------------------------------------------------------------------------
559   {
560     PC pc;
561     KSP ksp;
562 
563     // -- KSP
564     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
565     ierr = KSPSetType(ksp, KSPCG); CHKERRQ(ierr);
566     ierr = KSPSetNormType(ksp, KSP_NORM_NATURAL); CHKERRQ(ierr);
567     ierr = KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT,
568                             PETSC_DEFAULT); CHKERRQ(ierr);
569     ierr = KSPSetOptionsPrefix(ksp, "outer_"); CHKERRQ(ierr);
570 
571     // -- Preconditioning
572     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
573     ierr = PCSetDM(pc, level_dms[fine_level]); CHKERRQ(ierr);
574     ierr = PCSetOptionsPrefix(pc, "outer_"); CHKERRQ(ierr);
575 
576     if (app_ctx->multigrid_choice == MULTIGRID_NONE) {
577       // ---- No Multigrid
578       ierr = PCSetType(pc, PCJACOBI); CHKERRQ(ierr);
579       ierr = PCJacobiSetType(pc, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
580     } else if (app_ctx->degree == 1) {
581       // ---- AMG for degree 1
582       ierr = PCSetType(pc, PCGAMG); CHKERRQ(ierr);
583     } else {
584       // ---- PCMG
585       ierr = PCSetType(pc, PCMG); CHKERRQ(ierr);
586 
587       // ------ PCMG levels
588       ierr = PCMGSetLevels(pc, num_levels, NULL); CHKERRQ(ierr);
589       for (PetscInt level = 0; level < num_levels; level++) {
590         // -------- Smoother
591         KSP ksp_smoother, ksp_est;
592         PC pc_smoother;
593 
594         // ---------- Smoother KSP
595         ierr = PCMGGetSmoother(pc, level, &ksp_smoother); CHKERRQ(ierr);
596         ierr = KSPSetDM(ksp_smoother, level_dms[level]); CHKERRQ(ierr);
597         ierr = KSPSetDMActive(ksp_smoother, PETSC_FALSE); CHKERRQ(ierr);
598 
599         // ---------- Chebyshev options
600         ierr = KSPSetType(ksp_smoother, KSPCHEBYSHEV); CHKERRQ(ierr);
601         ierr = KSPChebyshevEstEigSet(ksp_smoother, 0, 0.1, 0, 1.1);
602         CHKERRQ(ierr);
603         ierr = KSPChebyshevEstEigGetKSP(ksp_smoother, &ksp_est); CHKERRQ(ierr);
604         ierr = KSPSetType(ksp_est, KSPCG); CHKERRQ(ierr);
605         ierr = KSPChebyshevEstEigSetUseNoisy(ksp_smoother, PETSC_TRUE);
606         CHKERRQ(ierr);
607         ierr = KSPSetOperators(ksp_smoother, jacob_mat[level], jacob_mat[level]);
608         CHKERRQ(ierr);
609 
610         // ---------- Smoother preconditioner
611         ierr = KSPGetPC(ksp_smoother, &pc_smoother); CHKERRQ(ierr);
612         ierr = PCSetType(pc_smoother, PCJACOBI); CHKERRQ(ierr);
613         ierr = PCJacobiSetType(pc_smoother, PC_JACOBI_DIAGONAL); CHKERRQ(ierr);
614 
615         // -------- Work vector
616         if (level != fine_level) {
617           ierr = PCMGSetX(pc, level, U_g[level]); CHKERRQ(ierr);
618         }
619 
620         // -------- Level prolongation/restriction operator
621         if (level > 0) {
622           ierr = PCMGSetInterpolation(pc, level, prolong_restr_mat[level]);
623           CHKERRQ(ierr);
624           ierr = PCMGSetRestriction(pc, level, prolong_restr_mat[level]);
625           CHKERRQ(ierr);
626         }
627       }
628 
629       // ------ PCMG coarse solve
630       KSP ksp_coarse;
631       PC pc_coarse;
632 
633       // -------- Coarse KSP
634       ierr = PCMGGetCoarseSolve(pc, &ksp_coarse); CHKERRQ(ierr);
635       ierr = KSPSetType(ksp_coarse, KSPPREONLY); CHKERRQ(ierr);
636       ierr = KSPSetOperators(ksp_coarse, jacob_mat_coarse, jacob_mat_coarse);
637       CHKERRQ(ierr);
638       ierr = KSPSetOptionsPrefix(ksp_coarse, "coarse_"); CHKERRQ(ierr);
639 
640       // -------- Coarse preconditioner
641       ierr = KSPGetPC(ksp_coarse, &pc_coarse); CHKERRQ(ierr);
642       ierr = PCSetType(pc_coarse, PCGAMG); CHKERRQ(ierr);
643       ierr = PCSetOptionsPrefix(pc_coarse, "coarse_"); CHKERRQ(ierr);
644 
645       ierr = KSPSetFromOptions(ksp_coarse); CHKERRQ(ierr);
646       ierr = PCSetFromOptions(pc_coarse); CHKERRQ(ierr);
647 
648       // ------ PCMG options
649       ierr = PCMGSetType(pc, PC_MG_MULTIPLICATIVE); CHKERRQ(ierr);
650       ierr = PCMGSetNumberSmooth(pc, 3); CHKERRQ(ierr);
651       ierr = PCMGSetCycleType(pc, pcmg_cycle_type); CHKERRQ(ierr);
652     }
653     ierr = KSPSetFromOptions(ksp);
654     ierr = PCSetFromOptions(pc);
655   }
656   {
657     // Default to critical-point (CP) line search (related to Wolfe's curvature condition)
658     SNESLineSearch line_search;
659 
660     ierr = SNESGetLineSearch(snes, &line_search); CHKERRQ(ierr);
661     ierr = SNESLineSearchSetType(line_search, SNESLINESEARCHCP); CHKERRQ(ierr);
662   }
663 
664   ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
665 
666   // Performance logging
667   ierr = PetscLogStagePop();
668 
669   // ---------------------------------------------------------------------------
670   // Set initial guess
671   // ---------------------------------------------------------------------------
672   ierr = PetscObjectSetName((PetscObject)U, ""); CHKERRQ(ierr);
673   ierr = VecSet(U, 0.0); CHKERRQ(ierr);
674 
675   // View solution
676   if (app_ctx->view_soln) {
677     ierr = ViewSolution(comm, app_ctx, U, 0, 0.0); CHKERRQ(ierr);
678   }
679 
680   // ---------------------------------------------------------------------------
681   // Solve SNES
682   // ---------------------------------------------------------------------------
683   PetscBool snes_monitor = PETSC_FALSE;
684   ierr = PetscOptionsHasName(NULL, NULL, "-snes_monitor", &snes_monitor);
685   CHKERRQ(ierr);
686 
687   // Performance logging
688   ierr = PetscLogStageRegister("SNES Solve Stage", &stage_snes_solve);
689   CHKERRQ(ierr);
690   ierr = PetscLogStagePush(stage_snes_solve); CHKERRQ(ierr);
691 
692   // Timing
693   ierr = PetscBarrier((PetscObject)snes); CHKERRQ(ierr);
694   start_time = MPI_Wtime();
695 
696   // Solve for each load increment
697   PetscInt increment;
698   for (increment = 1; increment <= app_ctx->num_increments; increment++) {
699     // -- Log increment count
700     if (snes_monitor) {
701       ierr = PetscPrintf(comm, "%d Load Increment\n", increment - 1);
702       CHKERRQ(ierr);
703     }
704 
705     // -- Scale the problem
706     PetscScalar load_increment = 1.0*increment / app_ctx->num_increments,
707                 scalingFactor = load_increment /
708                                 (increment == 1 ? 1 : res_ctx->load_increment);
709     res_ctx->load_increment = load_increment;
710     if (app_ctx->num_increments > 1 && app_ctx->forcing_choice != FORCE_NONE) {
711       ierr = VecScale(F, scalingFactor); CHKERRQ(ierr);
712     }
713 
714     // -- Solve
715     ierr = SNESSolve(snes, F, U); CHKERRQ(ierr);
716 
717     // -- View solution
718     if (app_ctx->view_soln) {
719       ierr = ViewSolution(comm, app_ctx, U, increment, load_increment); CHKERRQ(ierr);
720     }
721 
722     // -- Update SNES iteration count
723     PetscInt its;
724     ierr = SNESGetIterationNumber(snes, &its); CHKERRQ(ierr);
725     snes_its += its;
726     ierr = SNESGetLinearSolveIterations(snes, &its); CHKERRQ(ierr);
727     ksp_its += its;
728 
729     // -- Check for divergence
730     SNESConvergedReason reason;
731     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
732     if (reason < 0)
733       break;
734     if (app_ctx->energy_viewer) {
735       // -- Log strain energy for current load increment
736       CeedScalar energy;
737       ierr = ComputeStrainEnergy(dm_energy, res_ctx, ceed_data[fine_level]->op_energy,
738                                  U, &energy); CHKERRQ(ierr);
739 
740       if (!app_ctx->test_mode) {
741         // -- Output
742         ierr = PetscPrintf(comm,
743                            "    Strain Energy                      : %.12e\n",
744                            energy); CHKERRQ(ierr);
745       }
746       ierr = PetscViewerASCIIPrintf(app_ctx->energy_viewer, "%f,%e\n", load_increment,
747                                     energy); CHKERRQ(ierr);
748     }
749   }
750 
751   // Timing
752   elapsed_time = MPI_Wtime() - start_time;
753 
754   // Performance logging
755   ierr = PetscLogStagePop();
756 
757   // ---------------------------------------------------------------------------
758   // Output summary
759   // ---------------------------------------------------------------------------
760   if (!app_ctx->test_mode) {
761     // -- SNES
762     SNESType snes_type;
763     SNESConvergedReason reason;
764     PetscReal rnorm;
765     ierr = SNESGetType(snes, &snes_type); CHKERRQ(ierr);
766     ierr = SNESGetConvergedReason(snes, &reason); CHKERRQ(ierr);
767     ierr = SNESGetFunctionNorm(snes, &rnorm); CHKERRQ(ierr);
768     ierr = PetscPrintf(comm,
769                        "  SNES:\n"
770                        "    SNES Type                          : %s\n"
771                        "    SNES Convergence                   : %s\n"
772                        "    Number of Load Increments          : %d\n"
773                        "    Completed Load Increments          : %d\n"
774                        "    Total SNES Iterations              : %D\n"
775                        "    Final rnorm                        : %e\n",
776                        snes_type, SNESConvergedReasons[reason],
777                        app_ctx->num_increments, increment - 1,
778                        snes_its, (double)rnorm); CHKERRQ(ierr);
779 
780     // -- KSP
781     KSP ksp;
782     KSPType ksp_type;
783     ierr = SNESGetKSP(snes, &ksp); CHKERRQ(ierr);
784     ierr = KSPGetType(ksp, &ksp_type); CHKERRQ(ierr);
785     ierr = PetscPrintf(comm,
786                        "  Linear Solver:\n"
787                        "    KSP Type                           : %s\n"
788                        "    Total KSP Iterations               : %D\n",
789                        ksp_type, ksp_its); CHKERRQ(ierr);
790 
791     // -- PC
792     PC pc;
793     PCType pc_type;
794     ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
795     ierr = PCGetType(pc, &pc_type); CHKERRQ(ierr);
796     ierr = PetscPrintf(comm,
797                        "    PC Type                            : %s\n",
798                        pc_type); CHKERRQ(ierr);
799 
800     if (!strcmp(pc_type, PCMG)) {
801       PCMGType pcmg_type;
802       ierr = PCMGGetType(pc, &pcmg_type); CHKERRQ(ierr);
803       ierr = PetscPrintf(comm,
804                          "  P-Multigrid:\n"
805                          "    PCMG Type                          : %s\n"
806                          "    PCMG Cycle Type                    : %s\n",
807                          PCMGTypes[pcmg_type],
808                          PCMGCycleTypes[pcmg_cycle_type]); CHKERRQ(ierr);
809 
810       // -- Coarse Solve
811       KSP ksp_coarse;
812       PC pc_coarse;
813       PCType pc_type;
814 
815       ierr = PCMGGetCoarseSolve(pc, &ksp_coarse); CHKERRQ(ierr);
816       ierr = KSPGetType(ksp_coarse, &ksp_type); CHKERRQ(ierr);
817       ierr = KSPGetPC(ksp_coarse, &pc_coarse); CHKERRQ(ierr);
818       ierr = PCGetType(pc_coarse, &pc_type); CHKERRQ(ierr);
819       ierr = PetscPrintf(comm,
820                          "    Coarse Solve:\n"
821                          "      KSP Type                         : %s\n"
822                          "      PC Type                          : %s\n",
823                          ksp_type, pc_type); CHKERRQ(ierr);
824     }
825   }
826 
827   // ---------------------------------------------------------------------------
828   // Compute solve time
829   // ---------------------------------------------------------------------------
830   if (!app_ctx->test_mode) {
831     ierr = MPI_Allreduce(&elapsed_time, &min_time, 1, MPI_DOUBLE, MPI_MIN, comm);
832     CHKERRQ(ierr);
833     ierr = MPI_Allreduce(&elapsed_time, &max_time, 1, MPI_DOUBLE, MPI_MAX, comm);
834     CHKERRQ(ierr);
835     ierr = PetscPrintf(comm,
836                        "  Performance:\n"
837                        "    SNES Solve Time                    : %g (%g) sec\n"
838                        "    DoFs/Sec in SNES                   : %g (%g) million\n",
839                        max_time, min_time, 1e-6*U_g_size[fine_level]*ksp_its/max_time,
840                        1e-6*U_g_size[fine_level]*ksp_its/min_time); CHKERRQ(ierr);
841   }
842 
843   // ---------------------------------------------------------------------------
844   // Compute error
845   // ---------------------------------------------------------------------------
846   if (app_ctx->forcing_choice == FORCE_MMS) {
847     CeedScalar l2_error = 1., l2_U_norm = 1.;
848     const CeedScalar *true_array;
849     Vec error_vec, true_vec;
850 
851     // -- Work vectors
852     ierr = VecDuplicate(U, &error_vec); CHKERRQ(ierr);
853     ierr = VecSet(error_vec, 0.0); CHKERRQ(ierr);
854     ierr = VecDuplicate(U, &true_vec); CHKERRQ(ierr);
855     ierr = VecSet(true_vec, 0.0); CHKERRQ(ierr);
856 
857     // -- Assemble global true solution vector
858     CeedVectorGetArrayRead(ceed_data[fine_level]->true_soln,
859                            CEED_MEM_HOST, &true_array);
860     ierr = VecPlaceArray(res_ctx->Y_loc, (PetscScalar *)true_array);
861     CHKERRQ(ierr);
862     ierr = DMLocalToGlobal(res_ctx->dm, res_ctx->Y_loc, INSERT_VALUES, true_vec);
863     CHKERRQ(ierr);
864     ierr = VecResetArray(res_ctx->Y_loc); CHKERRQ(ierr);
865     CeedVectorRestoreArrayRead(ceed_data[fine_level]->true_soln, &true_array);
866 
867     // -- Compute L2 error
868     ierr = VecWAXPY(error_vec, -1.0, U, true_vec); CHKERRQ(ierr);
869     ierr = VecNorm(error_vec, NORM_2, &l2_error); CHKERRQ(ierr);
870     ierr = VecNorm(U, NORM_2, &l2_U_norm); CHKERRQ(ierr);
871     l2_error /= l2_U_norm;
872 
873     // -- Output
874     if (!app_ctx->test_mode || l2_error > 0.05) {
875       ierr = PetscPrintf(comm,
876                          "    L2 Error                           : %e\n",
877                          l2_error); CHKERRQ(ierr);
878     }
879 
880     // -- Cleanup
881     ierr = VecDestroy(&error_vec); CHKERRQ(ierr);
882     ierr = VecDestroy(&true_vec); CHKERRQ(ierr);
883   }
884 
885   // ---------------------------------------------------------------------------
886   // Compute energy
887   // ---------------------------------------------------------------------------
888   PetscReal energy;
889   ierr = ComputeStrainEnergy(dm_energy, res_ctx, ceed_data[fine_level]->op_energy,
890                              U, &energy); CHKERRQ(ierr);
891   if (!app_ctx->test_mode) {
892     // -- Output
893     ierr = PetscPrintf(comm,
894                        "    Strain Energy                      : %.12e\n",
895                        energy); CHKERRQ(ierr);
896   }
897   ierr = RegressionTests_solids(app_ctx, energy); CHKERRQ(ierr);
898 
899   // ---------------------------------------------------------------------------
900   // Output diagnostic quantities
901   // ---------------------------------------------------------------------------
902   if (app_ctx->view_soln || app_ctx->view_final_soln) {
903     // -- Setup context
904     UserMult diagnostic_ctx;
905     ierr = PetscMalloc1(1, &diagnostic_ctx); CHKERRQ(ierr);
906     ierr = PetscMemcpy(diagnostic_ctx, res_ctx, sizeof(*res_ctx)); CHKERRQ(ierr);
907     diagnostic_ctx->dm = dm_diagnostic;
908     diagnostic_ctx->op = ceed_data[fine_level]->op_diagnostic;
909 
910     // -- Compute and output
911     ierr = ViewDiagnosticQuantities(comm, level_dms[fine_level], diagnostic_ctx,
912                                     app_ctx, U,
913                                     ceed_data[fine_level]->elem_restr_diagnostic);
914     CHKERRQ(ierr);
915 
916     // -- Cleanup
917     ierr = PetscFree(diagnostic_ctx); CHKERRQ(ierr);
918   }
919 
920   // ---------------------------------------------------------------------------
921   // Free objects
922   // ---------------------------------------------------------------------------
923   // Data in arrays per level
924   for (PetscInt level = 0; level < num_levels; level++) {
925     // Vectors
926     ierr = VecDestroy(&U_g[level]); CHKERRQ(ierr);
927     ierr = VecDestroy(&U_loc[level]); CHKERRQ(ierr);
928 
929     // Jacobian matrix and data
930     ierr = VecDestroy(&jacob_ctx[level]->Y_loc); CHKERRQ(ierr);
931     ierr = MatDestroy(&jacob_mat[level]); CHKERRQ(ierr);
932     ierr = PetscFree(jacob_ctx[level]); CHKERRQ(ierr);
933 
934     // Prolongation/Restriction matrix and data
935     if (level > 0) {
936       ierr = PetscFree(prolong_restr_ctx[level]); CHKERRQ(ierr);
937       ierr = MatDestroy(&prolong_restr_mat[level]); CHKERRQ(ierr);
938     }
939 
940     // DM
941     ierr = DMDestroy(&level_dms[level]); CHKERRQ(ierr);
942 
943     // libCEED objects
944     ierr = CeedDataDestroy(level, ceed_data[level]); CHKERRQ(ierr);
945   }
946 
947   ierr = PetscViewerDestroy(&app_ctx->energy_viewer); CHKERRQ(ierr);
948 
949   // Arrays
950   ierr = PetscFree(U_g); CHKERRQ(ierr);
951   ierr = PetscFree(U_loc); CHKERRQ(ierr);
952   ierr = PetscFree(U_g_size); CHKERRQ(ierr);
953   ierr = PetscFree(U_l_size); CHKERRQ(ierr);
954   ierr = PetscFree(U_loc_size); CHKERRQ(ierr);
955   ierr = PetscFree(jacob_ctx); CHKERRQ(ierr);
956   ierr = PetscFree(jacob_mat); CHKERRQ(ierr);
957   ierr = PetscFree(prolong_restr_ctx); CHKERRQ(ierr);
958   ierr = PetscFree(prolong_restr_mat); CHKERRQ(ierr);
959   ierr = PetscFree(app_ctx->level_degrees); CHKERRQ(ierr);
960   ierr = PetscFree(ceed_data); CHKERRQ(ierr);
961 
962   // libCEED objects
963   CeedVectorDestroy(&form_jacob_ctx->coo_values);
964   CeedQFunctionContextDestroy(&ctx_phys);
965   CeedQFunctionContextDestroy(&ctx_phys_smoother);
966   CeedDestroy(&ceed);
967 
968   // PETSc objects
969   ierr = VecDestroy(&U); CHKERRQ(ierr);
970   ierr = VecDestroy(&R); CHKERRQ(ierr);
971   ierr = VecDestroy(&R_loc); CHKERRQ(ierr);
972   ierr = VecDestroy(&F); CHKERRQ(ierr);
973   ierr = VecDestroy(&F_loc); CHKERRQ(ierr);
974   ierr = VecDestroy(&neumann_bcs); CHKERRQ(ierr);
975   ierr = VecDestroy(&bcs_loc); CHKERRQ(ierr);
976   ierr = MatDestroy(&jacob_mat_coarse); CHKERRQ(ierr);
977   ierr = SNESDestroy(&snes); CHKERRQ(ierr);
978   ierr = DMDestroy(&dm_orig); CHKERRQ(ierr);
979   ierr = DMDestroy(&dm_energy); CHKERRQ(ierr);
980   ierr = DMDestroy(&dm_diagnostic); CHKERRQ(ierr);
981   ierr = PetscFree(level_dms); CHKERRQ(ierr);
982 
983   // -- Function list
984   ierr = PetscFunctionListDestroy(&problem_functions->setupPhysics);
985   CHKERRQ(ierr);
986   ierr = PetscFunctionListDestroy(&problem_functions->setupLibceedFineLevel);
987   CHKERRQ(ierr);
988   ierr = PetscFunctionListDestroy(&problem_functions->setupLibceedLevel);
989   CHKERRQ(ierr);
990 
991   // Structs
992   ierr = PetscFree(res_ctx); CHKERRQ(ierr);
993   ierr = PetscFree(form_jacob_ctx); CHKERRQ(ierr);
994   ierr = PetscFree(jacob_coarse_ctx); CHKERRQ(ierr);
995   ierr = PetscFree(app_ctx); CHKERRQ(ierr);
996   ierr = PetscFree(problem_functions); CHKERRQ(ierr);
997   ierr = PetscFree(units); CHKERRQ(ierr);
998 
999   return PetscFinalize();
1000 }
1001