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="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. -ts_dt 1e-3 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-dc-explicit.bin 26 //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. -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 27 //TESTARGS(name="adv_rotation_explicit_strong") -ceed {ceed_resource} -test -problem advection -strong_form 1 -degree 3 -dm_plex_box_faces 2,2,2 -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. -ts_dt 1e-3 -compare_final_state_atol 1E-11 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-rotation-explicit-strong.bin 28 //TESTARGS(name="adv_rotation_implicit_sharp_cylinder") -ceed {ceed_resource} -test -problem advection -bubble_type cylinder -bubble_continuity back_sharp -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_z 1,2 -bc_wall 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 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv-rotation-implicit-sharp-cylinder.bin 29 //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 -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 30 //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 -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 31 //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 32 //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 -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 33 //TESTARGS(name="adv2d_translation_implicit_stab_su") -ceed {ceed_resource} -test -problem advection2d -CtauS .3 -stab su -degree 3 -dm_plex_box_faces 1,1,2 -dm_plex_box_lower 0,0 -dm_plex_box_upper 125,125 -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 -ts_type alpha -wind_type translation -wind_translation .53,-1.33,0 -bc_inflow 1,2,3,4 -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-adv2d-translation-implicit-stab-su.bin 34 //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 -ts_type alpha -compare_final_state_atol 5E-4 -compare_final_state_filename examples/fluids/tests-output/fluids-navierstokes-euler-implicit.bin 35 //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 36 37 /// @file 38 /// Navier-Stokes example using PETSc 39 40 const char help[] = "Solve Navier-Stokes using PETSc and libCEED\n"; 41 42 #include "navierstokes.h" 43 44 int main(int argc, char **argv) { 45 // --------------------------------------------------------------------------- 46 // Initialize PETSc 47 // --------------------------------------------------------------------------- 48 PetscInt ierr; 49 ierr = PetscInitialize(&argc, &argv, NULL, help); 50 if (ierr) return ierr; 51 52 // --------------------------------------------------------------------------- 53 // Create structs 54 // --------------------------------------------------------------------------- 55 AppCtx app_ctx; 56 ierr = PetscCalloc1(1, &app_ctx); CHKERRQ(ierr); 57 58 ProblemData *problem = NULL; 59 ierr = PetscCalloc1(1, &problem); CHKERRQ(ierr); 60 61 User user; 62 ierr = PetscCalloc1(1, &user); CHKERRQ(ierr); 63 64 CeedData ceed_data; 65 ierr = PetscCalloc1(1, &ceed_data); CHKERRQ(ierr); 66 67 SimpleBC bc; 68 ierr = PetscCalloc1(1, &bc); CHKERRQ(ierr); 69 70 SetupContext setup_ctx; 71 ierr = PetscCalloc1(1, &setup_ctx); CHKERRQ(ierr); 72 73 Physics phys_ctx; 74 ierr = PetscCalloc1(1, &phys_ctx); CHKERRQ(ierr); 75 76 Units units; 77 ierr = PetscCalloc1(1, &units); CHKERRQ(ierr); 78 79 user->app_ctx = app_ctx; 80 user->units = units; 81 user->phys = phys_ctx; 82 83 // --------------------------------------------------------------------------- 84 // Process command line options 85 // --------------------------------------------------------------------------- 86 // -- Register problems to be available on the command line 87 ierr = RegisterProblems_NS(app_ctx); CHKERRQ(ierr); 88 89 // -- Process general command line options 90 MPI_Comm comm = PETSC_COMM_WORLD; 91 user->comm = comm; 92 ierr = ProcessCommandLineOptions(comm, app_ctx, bc); CHKERRQ(ierr); 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 ierr = CreateDM(comm, problem, &dm); CHKERRQ(ierr); 112 VecType vec_type = NULL; 113 switch (mem_type_backend) { 114 case CEED_MEM_HOST: vec_type = VECSTANDARD; break; 115 case CEED_MEM_DEVICE: { 116 const char *resolved; 117 CeedGetResource(ceed, &resolved); 118 if (strstr(resolved, "/gpu/cuda")) vec_type = VECCUDA; 119 else if (strstr(resolved, "/gpu/hip")) vec_type = VECHIP; 120 else vec_type = VECSTANDARD; 121 } 122 } 123 ierr = DMSetVecType(dm, vec_type); CHKERRQ(ierr); 124 user->dm = dm; 125 126 // --------------------------------------------------------------------------- 127 // Choose the problem from the list of registered problems 128 // --------------------------------------------------------------------------- 129 { 130 PetscErrorCode (*p)(ProblemData *, DM, void *, void *); 131 ierr = PetscFunctionListFind(app_ctx->problems, app_ctx->problem_name, &p); 132 CHKERRQ(ierr); 133 if (!p) SETERRQ(PETSC_COMM_SELF, 1, "Problem '%s' not found", 134 app_ctx->problem_name); 135 ierr = (*p)(problem, dm, &setup_ctx, &user); CHKERRQ(ierr); 136 } 137 138 // -- Set up DM 139 ierr = SetUpDM(dm, problem, app_ctx->degree, bc, phys_ctx, setup_ctx); 140 CHKERRQ(ierr); 141 142 // -- Refine DM for high-order viz 143 if (app_ctx->viz_refine) { 144 ierr = VizRefineDM(dm, user, problem, bc, phys_ctx, setup_ctx); 145 CHKERRQ(ierr); 146 } 147 148 // --------------------------------------------------------------------------- 149 // Set up libCEED 150 // --------------------------------------------------------------------------- 151 // -- Set up libCEED objects 152 ierr = SetupLibceed(ceed, ceed_data, dm, user, app_ctx, problem, bc, setup_ctx); 153 CHKERRQ(ierr); 154 155 // --------------------------------------------------------------------------- 156 // Set up ICs 157 // --------------------------------------------------------------------------- 158 // -- Set up global state vector Q 159 Vec Q; 160 ierr = DMCreateGlobalVector(dm, &Q); CHKERRQ(ierr); 161 ierr = VecZeroEntries(Q); CHKERRQ(ierr); 162 163 // -- Set up local state vector Q_loc 164 Vec Q_loc; 165 ierr = DMGetLocalVector(dm, &Q_loc); CHKERRQ(ierr); 166 167 // -- Fix multiplicity for ICs 168 ierr = ICs_FixMultiplicity(dm, ceed_data, Q_loc, Q, 0.0); CHKERRQ(ierr); 169 170 // --------------------------------------------------------------------------- 171 // Set up lumped mass matrix 172 // --------------------------------------------------------------------------- 173 // -- Set up global mass vector 174 ierr = VecDuplicate(Q, &user->M); CHKERRQ(ierr); 175 176 // -- Compute lumped mass matrix 177 ierr = ComputeLumpedMassMatrix(ceed, dm, ceed_data, user->M); CHKERRQ(ierr); 178 179 // --------------------------------------------------------------------------- 180 // Record boundary values from initial condition 181 // --------------------------------------------------------------------------- 182 // -- This overrides DMPlexInsertBoundaryValues(). 183 // We use this for the main simulation DM because the reference 184 // DMPlexInsertBoundaryValues() is very slow. If we disable this, we should 185 // still get the same results due to the problem->bc function, but with 186 // potentially much slower execution. 187 if (1) {ierr = SetBCsFromICs_NS(dm, Q, Q_loc); CHKERRQ(ierr);} 188 189 // --------------------------------------------------------------------------- 190 // Create output directory 191 // --------------------------------------------------------------------------- 192 PetscMPIInt rank; 193 MPI_Comm_rank(comm, &rank); 194 if (!rank) {ierr = PetscMkdir(app_ctx->output_dir); CHKERRQ(ierr);} 195 196 // --------------------------------------------------------------------------- 197 // Gather initial Q values in case of continuation of simulation 198 // --------------------------------------------------------------------------- 199 // -- Set up initial values from binary file 200 if (app_ctx->cont_steps) { 201 ierr = SetupICsFromBinary(comm, app_ctx, Q); CHKERRQ(ierr); 202 } 203 204 // --------------------------------------------------------------------------- 205 // Print problem summary 206 // --------------------------------------------------------------------------- 207 if (!app_ctx->test_mode) { 208 // Header and rank 209 char host_name[PETSC_MAX_PATH_LEN]; 210 int comm_size; 211 ierr = PetscGetHostName(host_name, sizeof host_name); CHKERRQ(ierr); 212 ierr = MPI_Comm_size(comm, &comm_size); CHKERRQ(ierr); 213 ierr = PetscPrintf(comm, 214 "\n-- Navier-Stokes solver - libCEED + PETSc --\n" 215 " MPI:\n" 216 " Host Name : %s\n" 217 " Total ranks : %d\n", 218 host_name, comm_size); CHKERRQ(ierr); 219 220 // Problem specific info 221 ierr = problem->print_info(phys_ctx, setup_ctx, app_ctx); CHKERRQ(ierr); 222 223 // libCEED 224 const char *used_resource; 225 CeedGetResource(ceed, &used_resource); 226 ierr = PetscPrintf(comm, 227 " libCEED:\n" 228 " libCEED Backend : %s\n" 229 " libCEED Backend MemType : %s\n", 230 used_resource, CeedMemTypes[mem_type_backend]); CHKERRQ(ierr); 231 // PETSc 232 char box_faces_str[PETSC_MAX_PATH_LEN] = "3,3,3"; 233 if (problem->dim == 2) box_faces_str[3] = '\0'; 234 ierr = PetscOptionsGetString(NULL, NULL, "-dm_plex_box_faces", box_faces_str, 235 sizeof(box_faces_str), NULL); CHKERRQ(ierr); 236 ierr = PetscPrintf(comm, 237 " PETSc:\n" 238 " Box Faces : %s\n" 239 " Time Stepping Scheme : %s\n", 240 box_faces_str, phys_ctx->implicit ? "implicit" : "explicit"); CHKERRQ(ierr); 241 // Mesh 242 const PetscInt num_comp_q = 5; 243 CeedInt glob_dofs, owned_dofs; 244 PetscInt glob_nodes, owned_nodes; 245 const CeedInt num_P = app_ctx->degree + 1, 246 num_Q = num_P + app_ctx->q_extra; 247 // -- Get global size 248 ierr = VecGetSize(Q, &glob_dofs); CHKERRQ(ierr); 249 ierr = VecGetLocalSize(Q, &owned_dofs); CHKERRQ(ierr); 250 glob_nodes = glob_dofs/num_comp_q; 251 // -- Get local size 252 ierr = VecGetSize(Q_loc, &owned_nodes); CHKERRQ(ierr); 253 owned_nodes /= num_comp_q; 254 ierr = PetscPrintf(comm, 255 " Mesh:\n" 256 " Number of 1D Basis Nodes (P) : %d\n" 257 " Number of 1D Quadrature Points (Q) : %d\n" 258 " Global DoFs : %" PetscInt_FMT "\n" 259 " Owned DoFs : %" PetscInt_FMT "\n" 260 " DoFs per node : %" PetscInt_FMT "\n" 261 " Global nodes : %" PetscInt_FMT "\n" 262 " Owned nodes : %" PetscInt_FMT "\n", 263 num_P, num_Q, glob_dofs, owned_dofs, num_comp_q, 264 glob_nodes, owned_nodes); CHKERRQ(ierr); 265 } 266 // -- Restore Q_loc 267 ierr = DMRestoreLocalVector(dm, &Q_loc); CHKERRQ(ierr); 268 269 // --------------------------------------------------------------------------- 270 // TS: Create, setup, and solve 271 // --------------------------------------------------------------------------- 272 TS ts; 273 PetscScalar final_time; 274 ierr = TSSolve_NS(dm, user, app_ctx, phys_ctx, &Q, &final_time, &ts); 275 CHKERRQ(ierr); 276 277 // --------------------------------------------------------------------------- 278 // Post-processing 279 // --------------------------------------------------------------------------- 280 ierr = PostProcess_NS(ts, ceed_data, dm, problem, app_ctx, Q, final_time); 281 CHKERRQ(ierr); 282 283 // --------------------------------------------------------------------------- 284 // Destroy libCEED objects 285 // --------------------------------------------------------------------------- 286 // -- Vectors 287 CeedVectorDestroy(&ceed_data->x_coord); 288 CeedVectorDestroy(&ceed_data->q_data); 289 CeedVectorDestroy(&user->q_ceed); 290 CeedVectorDestroy(&user->q_dot_ceed); 291 CeedVectorDestroy(&user->g_ceed); 292 293 // -- Contexts 294 CeedQFunctionContextDestroy(&ceed_data->setup_context); 295 CeedQFunctionContextDestroy(&ceed_data->newt_ig_context); 296 CeedQFunctionContextDestroy(&ceed_data->advection_context); 297 CeedQFunctionContextDestroy(&ceed_data->euler_context); 298 299 // -- QFunctions 300 CeedQFunctionDestroy(&ceed_data->qf_setup_vol); 301 CeedQFunctionDestroy(&ceed_data->qf_ics); 302 CeedQFunctionDestroy(&ceed_data->qf_rhs_vol); 303 CeedQFunctionDestroy(&ceed_data->qf_ifunction_vol); 304 CeedQFunctionDestroy(&ceed_data->qf_setup_sur); 305 CeedQFunctionDestroy(&ceed_data->qf_apply_inflow); 306 CeedQFunctionDestroy(&ceed_data->qf_apply_outflow); 307 308 // -- Bases 309 CeedBasisDestroy(&ceed_data->basis_q); 310 CeedBasisDestroy(&ceed_data->basis_x); 311 CeedBasisDestroy(&ceed_data->basis_xc); 312 CeedBasisDestroy(&ceed_data->basis_q_sur); 313 CeedBasisDestroy(&ceed_data->basis_x_sur); 314 315 // -- Restrictions 316 CeedElemRestrictionDestroy(&ceed_data->elem_restr_q); 317 CeedElemRestrictionDestroy(&ceed_data->elem_restr_x); 318 CeedElemRestrictionDestroy(&ceed_data->elem_restr_qd_i); 319 320 // -- Operators 321 CeedOperatorDestroy(&ceed_data->op_setup_vol); 322 CeedOperatorDestroy(&ceed_data->op_ics); 323 CeedOperatorDestroy(&user->op_rhs_vol); 324 CeedOperatorDestroy(&user->op_ifunction_vol); 325 CeedOperatorDestroy(&user->op_rhs); 326 CeedOperatorDestroy(&user->op_ifunction); 327 328 // -- Ceed 329 CeedDestroy(&ceed); 330 331 // --------------------------------------------------------------------------- 332 // Clean up PETSc 333 // --------------------------------------------------------------------------- 334 // -- Vectors 335 ierr = VecDestroy(&Q); CHKERRQ(ierr); 336 ierr = VecDestroy(&user->M); CHKERRQ(ierr); 337 338 // -- Matrices 339 ierr = MatDestroy(&user->interp_viz); CHKERRQ(ierr); 340 341 // -- DM 342 ierr = DMDestroy(&dm); CHKERRQ(ierr); 343 ierr = DMDestroy(&user->dm_viz); CHKERRQ(ierr); 344 345 // -- TS 346 ierr = TSDestroy(&ts); CHKERRQ(ierr); 347 348 // -- Function list 349 ierr = PetscFunctionListDestroy(&app_ctx->problems); CHKERRQ(ierr); 350 351 // -- Structs 352 ierr = PetscFree(units); CHKERRQ(ierr); 353 ierr = PetscFree(user); CHKERRQ(ierr); 354 ierr = PetscFree(problem); CHKERRQ(ierr); 355 ierr = PetscFree(bc); CHKERRQ(ierr); 356 ierr = PetscFree(setup_ctx); CHKERRQ(ierr); 357 ierr = PetscFree(phys_ctx->newtonian_ig_ctx); CHKERRQ(ierr); 358 ierr = PetscFree(phys_ctx->euler_ctx); CHKERRQ(ierr); 359 ierr = PetscFree(phys_ctx->advection_ctx); CHKERRQ(ierr); 360 ierr = PetscFree(phys_ctx); CHKERRQ(ierr); 361 ierr = PetscFree(app_ctx); CHKERRQ(ierr); 362 ierr = PetscFree(ceed_data); CHKERRQ(ierr); 363 364 return PetscFinalize(); 365 } 366