1 static char help[] = "Pure advection with finite elements.\n\ 2 We solve the hyperbolic problem in a rectangular\n\ 3 domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n"; 4 5 /* 6 The continuity equation (https://en.wikipedia.org/wiki/Continuity_equation) for advection 7 (https://en.wikipedia.org/wiki/Advection) of a conserved scalar quantity phi, with source q, 8 9 phi_t + div (phi u) = q 10 11 if used with a solenoidal velocity field u (div u = 0) is given by 12 13 phi_t + u . grad phi = q 14 15 For a vector quantity a, we likewise have 16 17 a_t + u . grad a = q 18 */ 19 20 /* 21 r1: 8 SOR 22 r2: 1128 SOR 23 r3: > 10000 SOR 24 25 SOR is completely unreliable as a smoother, use Jacobi 26 r1: 8 MG 27 r2: 28 */ 29 30 #include <petscdmplex.h> 31 #include <petscts.h> 32 #include <petscds.h> 33 34 typedef enum {PRIMITIVE, INT_BY_PARTS} WeakFormType; 35 36 typedef struct { 37 /* Domain and mesh definition */ 38 PetscInt dim; /* The topological mesh dimension */ 39 PetscBool simplex; /* Use simplices or tensor product cells */ 40 /* Problem definition */ 41 WeakFormType formType; 42 PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx); 43 } AppCtx; 44 45 /* MMS1: 46 47 2D: 48 u = <1, 1> 49 phi = x + y - 2t 50 51 phi_t + u . grad phi = -2 + <1, 1> . <1, 1> = 0 52 53 3D: 54 u = <1, 1, 1> 55 phi = x + y + z - 3t 56 57 phi_t + u . grad phi = -3 + <1, 1, 1> . <1, 1, 1> = 0 58 */ 59 60 static PetscErrorCode analytic_phi(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) 61 { 62 PetscInt d; 63 64 *u = -dim*time; 65 for (d = 0; d < dim; ++d) *u += x[d]; 66 return 0; 67 } 68 69 static PetscErrorCode velocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) 70 { 71 PetscInt d; 72 for (d = 0; d < dim; ++d) u[d] = 1.0; 73 return 0; 74 } 75 76 /* <psi, phi_t> + <psi, u . grad phi> */ 77 static void f0_prim_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 78 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 79 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 80 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 81 { 82 PetscInt d; 83 84 f0[0] = u_t[0]; 85 for (d = 0; d < dim; ++d) f0[0] += a[d] * u_x[d]; 86 } 87 88 /* <psi, phi_t> */ 89 static void f0_ibp_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 90 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 91 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 92 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 93 { 94 f0[0] = u_t[0]; 95 } 96 97 /* <grad psi, u phi> */ 98 static void f1_ibp_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 99 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 100 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 101 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 102 { 103 PetscInt d; 104 for (d = 0; d < dim; ++d) f1[d] = a[d]*u[0]; 105 } 106 107 /* <psi, phi_t> */ 108 static void g0_prim_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 109 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 110 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 111 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 112 { 113 g0[0] = u_tShift*1.0; 114 } 115 116 /* <psi, u . grad phi> */ 117 static void g1_prim_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 118 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 119 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 120 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]) 121 { 122 PetscInt d; 123 for (d = 0; d < dim; ++d) g1[d] = a[d]; 124 } 125 126 /* <grad psi, u phi> */ 127 static void g2_ibp_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, 128 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 129 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 130 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]) 131 { 132 PetscInt d; 133 for (d = 0; d < dim; ++d) g2[d] = a[d]; 134 } 135 136 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 137 { 138 const char *formTypes[2] = {"primitive", "int_by_parts"}; 139 PetscInt form; 140 PetscErrorCode ierr; 141 142 PetscFunctionBeginUser; 143 options->dim = 2; 144 options->simplex = PETSC_TRUE; 145 options->formType = PRIMITIVE; 146 147 ierr = PetscOptionsBegin(comm, "", "Advection Equation Options", "DMPLEX");CHKERRQ(ierr); 148 ierr = PetscOptionsInt("-dim", "The topological mesh dimension", "ex47.c", options->dim, &options->dim, NULL);CHKERRQ(ierr); 149 ierr = PetscOptionsBool("-simplex", "Simplicial (true) or tensor (false) mesh", "ex47.c", options->simplex, &options->simplex, NULL);CHKERRQ(ierr); 150 form = options->formType; 151 ierr = PetscOptionsEList("-form_type", "The weak form type", "ex47.c", formTypes, 2, formTypes[options->formType], &form, NULL);CHKERRQ(ierr); 152 options->formType = (WeakFormType) form; 153 ierr = PetscOptionsEnd();CHKERRQ(ierr); 154 PetscFunctionReturn(0); 155 } 156 157 static PetscErrorCode CreateBCLabel(DM dm, const char name[]) 158 { 159 DM plex; 160 DMLabel label; 161 PetscErrorCode ierr; 162 163 PetscFunctionBeginUser; 164 ierr = DMCreateLabel(dm, name);CHKERRQ(ierr); 165 ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr); 166 ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr); 167 ierr = DMPlexMarkBoundaryFaces(dm, 1, label);CHKERRQ(ierr); 168 ierr = DMDestroy(&plex);CHKERRQ(ierr); 169 PetscFunctionReturn(0); 170 } 171 172 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *ctx) 173 { 174 DM pdm = NULL; 175 const PetscInt dim = ctx->dim; 176 PetscBool hasLabel; 177 PetscErrorCode ierr; 178 179 PetscFunctionBeginUser; 180 ierr = DMPlexCreateBoxMesh(comm, dim, ctx->simplex, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr); 181 ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr); 182 /* If no boundary marker exists, mark the whole boundary */ 183 ierr = DMHasLabel(*dm, "marker", &hasLabel);CHKERRQ(ierr); 184 if (!hasLabel) {ierr = CreateBCLabel(*dm, "marker");CHKERRQ(ierr);} 185 /* Distribute mesh over processes */ 186 ierr = DMPlexDistribute(*dm, 0, NULL, &pdm);CHKERRQ(ierr); 187 if (pdm) { 188 ierr = DMDestroy(dm);CHKERRQ(ierr); 189 *dm = pdm; 190 } 191 ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); 192 ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr); 193 PetscFunctionReturn(0); 194 } 195 196 static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx) 197 { 198 PetscDS ds; 199 DMLabel label; 200 const PetscInt id = 1; 201 PetscErrorCode ierr; 202 203 PetscFunctionBeginUser; 204 ierr = DMGetDS(dm, &ds);CHKERRQ(ierr); 205 switch (ctx->formType) { 206 case PRIMITIVE: 207 ierr = PetscDSSetResidual(ds, 0, f0_prim_phi, NULL);CHKERRQ(ierr); 208 ierr = PetscDSSetJacobian(ds, 0, 0, g0_prim_phi, g1_prim_phi, NULL, NULL);CHKERRQ(ierr); 209 break; 210 case INT_BY_PARTS: 211 ierr = PetscDSSetResidual(ds, 0, f0_ibp_phi, f1_ibp_phi);CHKERRQ(ierr); 212 ierr = PetscDSSetJacobian(ds, 0, 0, g0_prim_phi, NULL, g2_ibp_phi, NULL);CHKERRQ(ierr); 213 break; 214 } 215 ctx->exactFuncs[0] = analytic_phi; 216 ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr); 217 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) ctx->exactFuncs[0], NULL, ctx, NULL);CHKERRQ(ierr); 218 PetscFunctionReturn(0); 219 } 220 221 static PetscErrorCode SetupVelocity(DM dm, DM dmAux, AppCtx *user) 222 { 223 PetscErrorCode (*funcs[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx) = {velocity}; 224 Vec v; 225 PetscErrorCode ierr; 226 227 PetscFunctionBeginUser; 228 ierr = DMCreateLocalVector(dmAux, &v);CHKERRQ(ierr); 229 ierr = DMProjectFunctionLocal(dmAux, 0.0, funcs, NULL, INSERT_ALL_VALUES, v);CHKERRQ(ierr); 230 ierr = DMSetAuxiliaryVec(dm, NULL, 0, v);CHKERRQ(ierr); 231 ierr = VecDestroy(&v);CHKERRQ(ierr); 232 PetscFunctionReturn(0); 233 } 234 235 static PetscErrorCode SetupAuxDM(DM dm, PetscFE feAux, AppCtx *user) 236 { 237 DM dmAux, coordDM; 238 PetscErrorCode ierr; 239 240 PetscFunctionBegin; 241 /* MUST call DMGetCoordinateDM() in order to get p4est setup if present */ 242 ierr = DMGetCoordinateDM(dm, &coordDM);CHKERRQ(ierr); 243 if (!feAux) PetscFunctionReturn(0); 244 ierr = DMClone(dm, &dmAux);CHKERRQ(ierr); 245 ierr = DMSetCoordinateDM(dmAux, coordDM);CHKERRQ(ierr); 246 ierr = DMSetField(dmAux, 0, NULL, (PetscObject) feAux);CHKERRQ(ierr); 247 ierr = DMCreateDS(dmAux);CHKERRQ(ierr); 248 ierr = SetupVelocity(dm, dmAux, user);CHKERRQ(ierr); 249 ierr = DMDestroy(&dmAux);CHKERRQ(ierr); 250 PetscFunctionReturn(0); 251 } 252 253 static PetscErrorCode SetupDiscretization(DM dm, AppCtx* ctx) 254 { 255 DM cdm = dm; 256 const PetscInt dim = ctx->dim; 257 PetscFE fe, feAux; 258 MPI_Comm comm; 259 PetscErrorCode ierr; 260 261 PetscFunctionBeginUser; 262 /* Create finite element */ 263 ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr); 264 ierr = PetscFECreateDefault(comm, dim, 1, ctx->simplex, "phi_", -1, &fe);CHKERRQ(ierr); 265 ierr = PetscObjectSetName((PetscObject) fe, "phi");CHKERRQ(ierr); 266 /* Create velocity */ 267 ierr = PetscFECreateDefault(comm, dim, dim, ctx->simplex, "vel_", -1, &feAux);CHKERRQ(ierr); 268 ierr = PetscFECopyQuadrature(fe, feAux);CHKERRQ(ierr); 269 /* Set discretization and boundary conditions for each mesh */ 270 ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr); 271 ierr = DMCreateDS(dm);CHKERRQ(ierr); 272 ierr = SetupProblem(dm, ctx);CHKERRQ(ierr); 273 while (cdm) { 274 PetscBool hasLabel; 275 276 ierr = SetupAuxDM(cdm, feAux, ctx);CHKERRQ(ierr); 277 ierr = DMHasLabel(cdm, "marker", &hasLabel);CHKERRQ(ierr); 278 if (!hasLabel) {ierr = CreateBCLabel(cdm, "marker");CHKERRQ(ierr);} 279 ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr); 280 ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); 281 } 282 ierr = PetscFEDestroy(&fe);CHKERRQ(ierr); 283 ierr = PetscFEDestroy(&feAux);CHKERRQ(ierr); 284 PetscFunctionReturn(0); 285 } 286 287 static PetscErrorCode MonitorError(KSP ksp, PetscInt it, PetscReal rnorm, void *ctx) 288 { 289 AppCtx *user = (AppCtx *) ctx; 290 DM dm; 291 Vec u, r, error; 292 PetscReal time = 0.5, res; 293 PetscErrorCode ierr; 294 295 PetscFunctionBeginUser; 296 ierr = KSPGetDM(ksp, &dm);CHKERRQ(ierr); 297 ierr = DMSetOutputSequenceNumber(dm, it, time);CHKERRQ(ierr); 298 /* Calculate residual */ 299 ierr = KSPBuildResidual(ksp, NULL, NULL, &r);CHKERRQ(ierr); 300 ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr); 301 ierr = DMSetOutputSequenceNumber(dm, it, res);CHKERRQ(ierr); 302 ierr = PetscObjectSetName((PetscObject) r, "residual");CHKERRQ(ierr); 303 ierr = VecViewFromOptions(r, NULL, "-res_vec_view");CHKERRQ(ierr); 304 ierr = VecDestroy(&r);CHKERRQ(ierr); 305 /* Calculate error */ 306 ierr = KSPBuildSolution(ksp, NULL, &u);CHKERRQ(ierr); 307 ierr = DMGetGlobalVector(dm, &error);CHKERRQ(ierr); 308 ierr = DMProjectFunction(dm, time, user->exactFuncs, NULL, INSERT_ALL_VALUES, error);CHKERRQ(ierr); 309 ierr = VecAXPY(error, -1.0, u);CHKERRQ(ierr); 310 ierr = PetscObjectSetName((PetscObject) error, "error");CHKERRQ(ierr); 311 ierr = VecViewFromOptions(error, NULL, "-err_vec_view");CHKERRQ(ierr); 312 ierr = DMRestoreGlobalVector(dm, &error);CHKERRQ(ierr); 313 PetscFunctionReturn(0); 314 } 315 316 static PetscErrorCode MyTSMonitorError(TS ts, PetscInt step, PetscReal crtime, Vec u, void *ctx) 317 { 318 AppCtx *user = (AppCtx *) ctx; 319 DM dm; 320 PetscReal error; 321 PetscErrorCode ierr; 322 323 PetscFunctionBeginUser; 324 ierr = TSGetDM(ts, &dm);CHKERRQ(ierr); 325 ierr = DMComputeL2Diff(dm, crtime, user->exactFuncs, NULL, u, &error);CHKERRQ(ierr); 326 ierr = PetscPrintf(PETSC_COMM_WORLD, "Timestep: %04d time = %-8.4g \t L_2 Error: %2.5g\n", (int) step, (double) crtime, (double) error);CHKERRQ(ierr); 327 PetscFunctionReturn(0); 328 } 329 330 int main(int argc, char **argv) 331 { 332 AppCtx ctx; 333 DM dm; 334 TS ts; 335 Vec u, r; 336 PetscReal t = 0.0; 337 PetscErrorCode ierr; 338 339 ierr = PetscInitialize(&argc, &argv, NULL, help);if (ierr) return ierr; 340 ierr = ProcessOptions(PETSC_COMM_WORLD, &ctx);CHKERRQ(ierr); 341 ierr = CreateMesh(PETSC_COMM_WORLD, &dm, &ctx);CHKERRQ(ierr); 342 ierr = DMSetApplicationContext(dm, &ctx);CHKERRQ(ierr); 343 ierr = PetscMalloc1(1, &ctx.exactFuncs);CHKERRQ(ierr); 344 ierr = SetupDiscretization(dm, &ctx);CHKERRQ(ierr); 345 346 ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr); 347 ierr = PetscObjectSetName((PetscObject) u, "phi");CHKERRQ(ierr); 348 ierr = VecDuplicate(u, &r);CHKERRQ(ierr); 349 350 ierr = TSCreate(PETSC_COMM_WORLD, &ts);CHKERRQ(ierr); 351 ierr = TSMonitorSet(ts, MyTSMonitorError, &ctx, NULL);CHKERRQ(ierr); 352 ierr = TSSetDM(ts, dm);CHKERRQ(ierr); 353 ierr = DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx);CHKERRQ(ierr); 354 ierr = DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx);CHKERRQ(ierr); 355 ierr = DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx);CHKERRQ(ierr); 356 ierr = TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 357 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 358 359 ierr = DMProjectFunction(dm, t, ctx.exactFuncs, NULL, INSERT_ALL_VALUES, u);CHKERRQ(ierr); 360 { 361 SNES snes; 362 KSP ksp; 363 364 ierr = TSGetSNES(ts, &snes);CHKERRQ(ierr); 365 ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr); 366 ierr = KSPMonitorSet(ksp, MonitorError, &ctx, NULL);CHKERRQ(ierr); 367 } 368 ierr = TSSolve(ts, u);CHKERRQ(ierr); 369 ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr); 370 371 ierr = VecDestroy(&u);CHKERRQ(ierr); 372 ierr = VecDestroy(&r);CHKERRQ(ierr); 373 ierr = TSDestroy(&ts);CHKERRQ(ierr); 374 ierr = DMDestroy(&dm);CHKERRQ(ierr); 375 ierr = PetscFree(ctx.exactFuncs);CHKERRQ(ierr); 376 ierr = PetscFinalize(); 377 return ierr; 378 } 379 380 /*TEST 381 382 # Full solves 383 test: 384 suffix: 2d_p1p1_r1 385 requires: triangle 386 args: -dm_refine 1 -phi_petscspace_degree 1 -vel_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -pc_type lu -snes_monitor_short -snes_converged_reason -ts_monitor 387 388 test: 389 suffix: 2d_p1p1_sor_r1 390 requires: triangle !single 391 args: -dm_refine 1 -phi_petscspace_degree 1 -vel_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -ksp_rtol 1.0e-9 -pc_type sor -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ts_monitor 392 393 test: 394 suffix: 2d_p1p1_mg_r1 395 requires: triangle !single 396 args: -dm_refine_hierarchy 1 -phi_petscspace_degree 1 -vel_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -ksp_type fgmres -ksp_rtol 1.0e-9 -pc_type mg -pc_mg_levels 2 -snes_monitor_short -snes_converged_reason -snes_view -ksp_monitor_true_residual -ts_monitor 397 398 TEST*/ 399