xref: /libCEED/examples/fluids/navierstokes.c (revision 2b730f8b5a9c809740a0b3b302db43a719c636b1)
1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 //                        libCEED + PETSc Example: Navier-Stokes
9 //
10 // This example demonstrates a simple usage of libCEED with PETSc to solve a
11 // Navier-Stokes problem.
12 //
13 // The code is intentionally "raw", using only low-level communication
14 // primitives.
15 //
16 // Build with:
17 //
18 //     make [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>] navierstokes
19 //
20 // Sample runs:
21 //
22 //     ./navierstokes -ceed /cpu/self -problem density_current -degree 1
23 //     ./navierstokes -ceed /gpu/cuda -problem advection -degree 1
24 //
25 //TESTARGS(name="blasius") -ceed {ceed_resource} -test -options_file examples/fluids/tests-output/blasius_test.yaml -compare_final_state_atol 2E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius.bin
26 //TESTARGS(name="blasius_STG") -ceed {ceed_resource} -test -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 2E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG.bin
27 //TESTARGS(name="blasius_STG_weakT") -ceed {ceed_resource} -test -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG_weakT.bin -weakT
28 //TESTARGS(name="blasius_STG_strongBC") -ceed {ceed_resource} -test -options_file examples/fluids/tests-output/blasius_stgtest.yaml -compare_final_state_atol 1E-10 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-blasius_STG_strongBC.bin -stg_strong true
29 //TESTARGS(name="channel") -ceed {ceed_resource} -test -options_file examples/fluids/channel.yaml -compare_final_state_atol 2e-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-channel.bin -dm_plex_box_faces 5,5,1 -ts_max_steps 5
30 //TESTARGS(name="channel-primitive") -ceed {ceed_resource} -test -options_file examples/fluids/channel.yaml -compare_final_state_atol 2e-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-channel-prim.bin -dm_plex_box_faces 5,5,1 -ts_max_steps 5 -state_var primitive
31 //TESTARGS(name="dc_explicit") -ceed {ceed_resource} -test -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -units_kilogram 1e-9 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -mu 75 -ts_dt 1e-3 -units_meter 1e-2 -units_second 1e-2 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-dc-explicit.bin
32 //TESTARGS(name="dc_implicit_stab_none") -ceed {ceed_resource} -test -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -units_kilogram 1e-9 -center 62.5,62.5,187.5 -rc 100. -thetaC -35. -mu 75 -units_meter 1e-2 -units_second 1e-2 -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-dc-implicit-stab-none.bin
33 //TESTARGS(name="adv_rotation_implicit_stab_supg") -ceed {ceed_resource} -test -problem advection -CtauS .3 -stab supg -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -bc_wall 1,2,3,4,5,6 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-rotation-implicit-stab-supg.bin
34 //TESTARGS(name="adv_translation_implicit_stab_su") -ceed {ceed_resource} -test -problem advection -CtauS .3 -stab su -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -wind_type translation -wind_translation .53,-1.33,-2.65 -bc_inflow 1,2,3,4,5,6 -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-translation-implicit-stab-su.bin
35 //TESTARGS(name="adv2d_rotation_explicit_strong") -ceed {ceed_resource} -test -problem advection2d -strong_form 1 -degree 3 -dm_plex_box_faces 2,2 -dm_plex_box_lower 0,0 -dm_plex_box_upper 125,125 -bc_wall 1,2,3,4 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ts_dt 1e-3 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv2d-rotation-explicit-strong.bin
36 //TESTARGS(name="adv2d_rotation_implicit_stab_supg") -ceed {ceed_resource} -test -problem advection2d -CtauS .3 -stab supg -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0 -dm_plex_box_upper 125,125 -bc_wall 1,2,3,4 -wall_comps 4 -units_kilogram 1e-9 -rc 100. -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv2d-rotation-implicit-stab-supg.bin
37 //TESTARGS(name="euler_implicit") -ceed {ceed_resource} -test -problem euler_vortex -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_meter 1e-4 -units_second 1e-4 -mean_velocity 1.4,-2.,0 -bc_inflow 4,6 -bc_outflow 3,5 -bc_slip_z 1,2 -vortex_strength 2 -ksp_atol 1e-4 -ksp_rtol 1e-3 -ksp_type bcgs -snes_atol 1e-3 -snes_lag_jacobian 100 -snes_lag_jacobian_persists -snes_mf_operator -ts_dt 1e-3 -implicit -dm_mat_preallocate_skip 0 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-euler-implicit.bin
38 //TESTARGS(name="euler_explicit") -ceed {ceed_resource} -test -problem euler_vortex -degree 3 -dm_plex_box_faces 2,2,1 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 125,125,250 -dm_plex_dim 3 -units_meter 1e-4 -units_second 1e-4 -mean_velocity 1.4,-2.,0 -bc_inflow 4,6 -bc_outflow 3,5 -bc_slip_z 1,2 -vortex_strength 2 -ts_dt 1e-7 -ts_rk_type 5bs -ts_rtol 1e-10 -ts_atol 1e-10 -compare_final_state_atol 1E-7 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-euler-explicit.bin
39 //TESTARGS(name="shocktube_explicit_su_yzb") -ceed {ceed_resource} -test -problem shocktube -degree 1 -dm_plex_box_faces 50,1,1 -units_meter 1e-2 units_second 1e-2 -dm_plex_box_lower 0,0,0 -dm_plex_box_upper 1000,20,20 -dm_plex_dim 3 -bc_slip_x 5,6 -bc_slip_y 3,4 -bc_Slip_z 1,2 -yzb -stab su -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-shocktube-explicit-su-yzb.bin
40 
41 /// @file
42 /// Navier-Stokes example using PETSc
43 
44 const char help[] = "Solve Navier-Stokes using PETSc and libCEED\n";
45 
46 #include "navierstokes.h"
47 
48 int main(int argc, char **argv) {
49   // ---------------------------------------------------------------------------
50   // Initialize PETSc
51   // ---------------------------------------------------------------------------
52   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
53 
54   // ---------------------------------------------------------------------------
55   // Create structs
56   // ---------------------------------------------------------------------------
57   AppCtx app_ctx;
58   PetscCall(PetscCalloc1(1, &app_ctx));
59 
60   ProblemData *problem = NULL;
61   PetscCall(PetscCalloc1(1, &problem));
62 
63   User user;
64   PetscCall(PetscCalloc1(1, &user));
65 
66   CeedData ceed_data;
67   PetscCall(PetscCalloc1(1, &ceed_data));
68 
69   SimpleBC bc;
70   PetscCall(PetscCalloc1(1, &bc));
71 
72   Physics phys_ctx;
73   PetscCall(PetscCalloc1(1, &phys_ctx));
74 
75   Units units;
76   PetscCall(PetscCalloc1(1, &units));
77 
78   user->app_ctx        = app_ctx;
79   user->units          = units;
80   user->phys           = phys_ctx;
81   problem->bc_from_ics = PETSC_TRUE;
82 
83   // ---------------------------------------------------------------------------
84   // Process command line options
85   // ---------------------------------------------------------------------------
86   // -- Register problems to be available on the command line
87   PetscCall(RegisterProblems_NS(app_ctx));
88 
89   // -- Process general command line options
90   MPI_Comm comm = PETSC_COMM_WORLD;
91   user->comm    = comm;
92   PetscCall(ProcessCommandLineOptions(comm, app_ctx, bc));
93 
94   // ---------------------------------------------------------------------------
95   // Initialize libCEED
96   // ---------------------------------------------------------------------------
97   // -- Initialize backend
98   Ceed ceed;
99   CeedInit(app_ctx->ceed_resource, &ceed);
100   user->ceed = ceed;
101 
102   // -- Check preferred MemType
103   CeedMemType mem_type_backend;
104   CeedGetPreferredMemType(ceed, &mem_type_backend);
105 
106   // ---------------------------------------------------------------------------
107   // Set up global mesh
108   // ---------------------------------------------------------------------------
109   // -- Create DM
110   DM      dm;
111   VecType vec_type = NULL;
112   MatType mat_type = NULL;
113   switch (mem_type_backend) {
114     case CEED_MEM_HOST:
115       vec_type = VECSTANDARD;
116       break;
117     case CEED_MEM_DEVICE: {
118       const char *resolved;
119       CeedGetResource(ceed, &resolved);
120       if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA;
121       else if (strstr(resolved, "/gpu/hip")) vec_type = VECKOKKOS;
122       else vec_type = VECSTANDARD;
123     }
124   }
125   if (strstr(vec_type, VECCUDA)) mat_type = MATAIJCUSPARSE;
126   else if (strstr(vec_type, VECKOKKOS)) mat_type = MATAIJKOKKOS;
127   else mat_type = MATAIJ;
128   PetscCall(CreateDM(comm, problem, mat_type, vec_type, &dm));
129   user->dm = dm;
130   PetscCall(DMSetApplicationContext(dm, user));
131 
132   // ---------------------------------------------------------------------------
133   // Choose the problem from the list of registered problems
134   // ---------------------------------------------------------------------------
135   {
136     PetscErrorCode (*p)(ProblemData *, DM, void *);
137     PetscCall(PetscFunctionListFind(app_ctx->problems, app_ctx->problem_name, &p));
138     if (!p) SETERRQ(PETSC_COMM_SELF, 1, "Problem '%s' not found", app_ctx->problem_name);
139     PetscCall((*p)(problem, dm, &user));
140   }
141 
142   // -- Set up DM
143   PetscCall(SetUpDM(dm, problem, app_ctx->degree, bc, phys_ctx));
144 
145   // -- Refine DM for high-order viz
146   if (app_ctx->viz_refine) {
147     PetscCall(VizRefineDM(dm, user, problem, bc, phys_ctx));
148   }
149 
150   // ---------------------------------------------------------------------------
151   // Set up libCEED
152   // ---------------------------------------------------------------------------
153   // -- Set up libCEED objects
154   PetscCall(SetupLibceed(ceed, ceed_data, dm, user, app_ctx, problem, bc));
155 
156   // ---------------------------------------------------------------------------
157   // Set up ICs
158   // ---------------------------------------------------------------------------
159   // -- Set up global state vector Q
160   Vec Q;
161   PetscCall(DMCreateGlobalVector(dm, &Q));
162   PetscCall(VecZeroEntries(Q));
163 
164   // -- Set up local state vectors Q_loc, Q_dot_loc
165   PetscCall(DMCreateLocalVector(dm, &user->Q_loc));
166   PetscCall(DMCreateLocalVector(dm, &user->Q_dot_loc));
167   PetscCall(VecZeroEntries(user->Q_dot_loc));
168 
169   // -- Fix multiplicity for ICs
170   PetscCall(ICs_FixMultiplicity(dm, ceed_data, user, user->Q_loc, Q, 0.0));
171 
172   // ---------------------------------------------------------------------------
173   // Set up lumped mass matrix
174   // ---------------------------------------------------------------------------
175   // -- Set up global mass vector
176   PetscCall(VecDuplicate(Q, &user->M));
177 
178   // -- Compute lumped mass matrix
179   PetscCall(ComputeLumpedMassMatrix(ceed, dm, ceed_data, user->M));
180 
181   // ---------------------------------------------------------------------------
182   // Record boundary values from initial condition
183   // ---------------------------------------------------------------------------
184   // -- This overrides DMPlexInsertBoundaryValues().
185   //    We use this for the main simulation DM because the reference
186   //    DMPlexInsertBoundaryValues() is very slow. If we disable this, we should
187   //    still get the same results due to the problem->bc function, but with
188   //    potentially much slower execution.
189   if (problem->bc_from_ics) {
190     PetscCall(SetBCsFromICs_NS(dm, Q, user->Q_loc));
191   }
192 
193   // ---------------------------------------------------------------------------
194   // Create output directory
195   // ---------------------------------------------------------------------------
196   PetscMPIInt rank;
197   MPI_Comm_rank(comm, &rank);
198   if (!rank) {
199     PetscCall(PetscMkdir(app_ctx->output_dir));
200   }
201 
202   // ---------------------------------------------------------------------------
203   // Gather initial Q values in case of continuation of simulation
204   // ---------------------------------------------------------------------------
205   // -- Set up initial values from binary file
206   if (app_ctx->cont_steps) {
207     PetscCall(SetupICsFromBinary(comm, app_ctx, Q));
208   }
209 
210   // ---------------------------------------------------------------------------
211   // Print problem summary
212   // ---------------------------------------------------------------------------
213   if (!app_ctx->test_mode) {
214     // Header and rank
215     char host_name[PETSC_MAX_PATH_LEN];
216     int  comm_size;
217     PetscCall(PetscGetHostName(host_name, sizeof host_name));
218     PetscCall(MPI_Comm_size(comm, &comm_size));
219     PetscCall(PetscPrintf(comm,
220                           "\n-- Navier-Stokes solver - libCEED + PETSc --\n"
221                           "  MPI:\n"
222                           "    Host Name                          : %s\n"
223                           "    Total ranks                        : %d\n",
224                           host_name, comm_size));
225 
226     // Problem specific info
227     PetscCall(problem->print_info(problem, app_ctx));
228 
229     // libCEED
230     const char *used_resource;
231     CeedGetResource(ceed, &used_resource);
232     PetscCall(PetscPrintf(comm,
233                           "  libCEED:\n"
234                           "    libCEED Backend                    : %s\n"
235                           "    libCEED Backend MemType            : %s\n",
236                           used_resource, CeedMemTypes[mem_type_backend]));
237     // PETSc
238     char box_faces_str[PETSC_MAX_PATH_LEN] = "3,3,3";
239     if (problem->dim == 2) box_faces_str[3] = '\0';
240     PetscCall(PetscOptionsGetString(NULL, NULL, "-dm_plex_box_faces", box_faces_str, sizeof(box_faces_str), NULL));
241     MatType mat_type;
242     VecType vec_type;
243     PetscCall(DMGetMatType(dm, &mat_type));
244     PetscCall(DMGetVecType(dm, &vec_type));
245     PetscCall(PetscPrintf(comm,
246                           "  PETSc:\n"
247                           "    Box Faces                          : %s\n"
248                           "    DM MatType                         : %s\n"
249                           "    DM VecType                         : %s\n"
250                           "    Time Stepping Scheme               : %s\n",
251                           box_faces_str, mat_type, vec_type, phys_ctx->implicit ? "implicit" : "explicit"));
252     // Mesh
253     const PetscInt num_comp_q = 5;
254     CeedInt        glob_dofs, owned_dofs;
255     PetscInt       glob_nodes, owned_nodes;
256     const CeedInt  num_P = app_ctx->degree + 1, num_Q = num_P + app_ctx->q_extra;
257     // -- Get global size
258     PetscCall(VecGetSize(Q, &glob_dofs));
259     PetscCall(VecGetLocalSize(Q, &owned_dofs));
260     glob_nodes = glob_dofs / num_comp_q;
261     // -- Get local size
262     PetscCall(VecGetSize(user->Q_loc, &owned_nodes));
263     owned_nodes /= num_comp_q;
264     PetscCall(PetscPrintf(comm,
265                           "  Mesh:\n"
266                           "    Number of 1D Basis Nodes (P)       : %" CeedInt_FMT "\n"
267                           "    Number of 1D Quadrature Points (Q) : %" CeedInt_FMT "\n"
268                           "    Global DoFs                        : %" PetscInt_FMT "\n"
269                           "    Owned DoFs                         : %" PetscInt_FMT "\n"
270                           "    DoFs per node                      : %" PetscInt_FMT "\n"
271                           "    Global nodes                       : %" PetscInt_FMT "\n"
272                           "    Owned nodes                        : %" PetscInt_FMT "\n",
273                           num_P, num_Q, glob_dofs, owned_dofs, num_comp_q, glob_nodes, owned_nodes));
274   }
275   // -- Zero Q_loc
276   PetscCall(VecZeroEntries(user->Q_loc));
277 
278   // ---------------------------------------------------------------------------
279   // TS: Create, setup, and solve
280   // ---------------------------------------------------------------------------
281   TS          ts;
282   PetscScalar final_time;
283   PetscCall(TSSolve_NS(dm, user, app_ctx, phys_ctx, &Q, &final_time, &ts));
284 
285   // ---------------------------------------------------------------------------
286   // Post-processing
287   // ---------------------------------------------------------------------------
288   PetscCall(PostProcess_NS(ts, ceed_data, dm, problem, user, Q, final_time));
289 
290   // ---------------------------------------------------------------------------
291   // Destroy libCEED objects
292   // ---------------------------------------------------------------------------
293   // -- Vectors
294   CeedVectorDestroy(&ceed_data->x_coord);
295   CeedVectorDestroy(&ceed_data->q_data);
296   CeedVectorDestroy(&user->q_ceed);
297   CeedVectorDestroy(&user->q_dot_ceed);
298   CeedVectorDestroy(&user->g_ceed);
299   CeedVectorDestroy(&user->coo_values_amat);
300   CeedVectorDestroy(&user->coo_values_pmat);
301 
302   // -- QFunctions
303   CeedQFunctionDestroy(&ceed_data->qf_setup_vol);
304   CeedQFunctionDestroy(&ceed_data->qf_ics);
305   CeedQFunctionDestroy(&ceed_data->qf_rhs_vol);
306   CeedQFunctionDestroy(&ceed_data->qf_ifunction_vol);
307   CeedQFunctionDestroy(&ceed_data->qf_setup_sur);
308   CeedQFunctionDestroy(&ceed_data->qf_apply_inflow);
309   CeedQFunctionDestroy(&ceed_data->qf_apply_inflow_jacobian);
310   CeedQFunctionDestroy(&ceed_data->qf_apply_outflow);
311   CeedQFunctionDestroy(&ceed_data->qf_apply_outflow_jacobian);
312 
313   // -- Bases
314   CeedBasisDestroy(&ceed_data->basis_q);
315   CeedBasisDestroy(&ceed_data->basis_x);
316   CeedBasisDestroy(&ceed_data->basis_xc);
317   CeedBasisDestroy(&ceed_data->basis_q_sur);
318   CeedBasisDestroy(&ceed_data->basis_x_sur);
319 
320   // -- Restrictions
321   CeedElemRestrictionDestroy(&ceed_data->elem_restr_q);
322   CeedElemRestrictionDestroy(&ceed_data->elem_restr_x);
323   CeedElemRestrictionDestroy(&ceed_data->elem_restr_qd_i);
324 
325   // -- Operators
326   CeedOperatorDestroy(&ceed_data->op_setup_vol);
327   CeedOperatorDestroy(&ceed_data->op_ics);
328   CeedOperatorDestroy(&user->op_rhs_vol);
329   CeedOperatorDestroy(&user->op_ifunction_vol);
330   CeedOperatorDestroy(&user->op_rhs);
331   CeedOperatorDestroy(&user->op_ifunction);
332   CeedOperatorDestroy(&user->op_ijacobian);
333 
334   // -- Ceed
335   CeedDestroy(&ceed);
336 
337   // ---------------------------------------------------------------------------
338   // Clean up PETSc
339   // ---------------------------------------------------------------------------
340   // -- Vectors
341   PetscCall(VecDestroy(&Q));
342   PetscCall(VecDestroy(&user->M));
343   PetscCall(VecDestroy(&user->Q_loc));
344   PetscCall(VecDestroy(&user->Q_dot_loc));
345 
346   // -- Matrices
347   PetscCall(MatDestroy(&user->interp_viz));
348 
349   // -- DM
350   PetscCall(DMDestroy(&dm));
351   PetscCall(DMDestroy(&user->dm_viz));
352 
353   // -- TS
354   PetscCall(TSDestroy(&ts));
355 
356   // -- Function list
357   PetscCall(PetscFunctionListDestroy(&app_ctx->problems));
358 
359   PetscCall(PetscFree(app_ctx->amat_type));
360 
361   // -- Structs
362   PetscCall(PetscFree(units));
363   PetscCall(PetscFree(user));
364   PetscCall(PetscFree(problem));
365   PetscCall(PetscFree(bc));
366   PetscCall(PetscFree(phys_ctx));
367   PetscCall(PetscFree(app_ctx));
368   PetscCall(PetscFree(ceed_data));
369 
370   return PetscFinalize();
371 }
372