1 static char help[] = "Poisson Problem in 2d and 3d with finite elements.\n\ 2 We solve the Poisson problem in a rectangular\n\ 3 domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\ 4 This example supports automatic convergence estimation\n\ 5 and eventually adaptivity.\n\n\n"; 6 7 #include <petscdmplex.h> 8 #include <petscsnes.h> 9 #include <petscds.h> 10 #include <petscconvest.h> 11 12 typedef struct { 13 /* Domain and mesh definition */ 14 PetscBool spectral; /* Look at the spectrum along planes in the solution */ 15 PetscBool shear; /* Shear the domain */ 16 PetscBool adjoint; /* Solve the adjoint problem */ 17 PetscBool homogeneous; 18 } AppCtx; 19 20 static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 21 { 22 *u = 0.0; 23 return 0; 24 } 25 26 static PetscErrorCode trig_inhomogeneous_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 27 { 28 PetscInt d; 29 *u = 0.0; 30 for (d = 0; d < dim; ++d) *u += PetscSinReal(2.0*PETSC_PI*x[d]); 31 return 0; 32 } 33 34 static PetscErrorCode trig_homogeneous_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 35 { 36 PetscInt d; 37 *u = 1.0; 38 for (d = 0; d < dim; ++d) *u *= PetscSinReal(2.0*PETSC_PI*x[d]); 39 return 0; 40 } 41 42 /* Compute integral of (residual of solution)*(adjoint solution - projection of adjoint solution) */ 43 static void obj_error_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 44 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 45 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 46 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar obj[]) 47 { 48 obj[0] = a[aOff[0]]*(u[0] - a[aOff[1]]); 49 } 50 51 static void f0_trig_inhomogeneous_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 52 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 53 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 54 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 55 { 56 PetscInt d; 57 for (d = 0; d < dim; ++d) f0[0] += -4.0*PetscSqr(PETSC_PI)*PetscSinReal(2.0*PETSC_PI*x[d]); 58 } 59 60 static void f0_trig_homogeneous_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 61 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 62 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 63 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 64 { 65 PetscInt d; 66 for (d = 0; d < dim; ++d) { 67 PetscScalar v = 1.; 68 for (PetscInt e = 0; e < dim; e++) { 69 if (e == d) { 70 v *= -4.0*PetscSqr(PETSC_PI)*PetscSinReal(2.0*PETSC_PI*x[d]); 71 } else { 72 v *= PetscSinReal(2.0*PETSC_PI*x[d]); 73 } 74 } 75 f0[0] += v; 76 } 77 } 78 79 static void f0_unity_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 80 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 81 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 82 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 83 { 84 f0[0] = 1.0; 85 } 86 87 static void f0_identityaux_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 88 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 89 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 90 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 91 { 92 f0[0] = a[0]; 93 } 94 95 static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 96 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 97 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 98 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 99 { 100 PetscInt d; 101 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 102 } 103 104 static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 105 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 106 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 107 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 108 { 109 PetscInt d; 110 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 111 } 112 113 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 114 { 115 PetscErrorCode ierr; 116 117 PetscFunctionBeginUser; 118 options->shear = PETSC_FALSE; 119 options->spectral = PETSC_FALSE; 120 options->adjoint = PETSC_FALSE; 121 options->homogeneous = PETSC_FALSE; 122 123 ierr = PetscOptionsBegin(comm, "", "Poisson Problem Options", "DMPLEX");CHKERRQ(ierr); 124 ierr = PetscOptionsBool("-shear", "Shear the domain", "ex13.c", options->shear, &options->shear, NULL);CHKERRQ(ierr); 125 ierr = PetscOptionsBool("-spectral", "Look at the spectrum along planes of the solution", "ex13.c", options->spectral, &options->spectral, NULL);CHKERRQ(ierr); 126 ierr = PetscOptionsBool("-adjoint", "Solve the adjoint problem", "ex13.c", options->adjoint, &options->adjoint, NULL);CHKERRQ(ierr); 127 ierr = PetscOptionsBool("-homogeneous", "Use homogeneous boundary conditions", "ex13.c", options->homogeneous, &options->homogeneous, NULL);CHKERRQ(ierr); 128 ierr = PetscOptionsEnd(); 129 PetscFunctionReturn(0); 130 } 131 132 static PetscErrorCode CreateSpectralPlanes(DM dm, PetscInt numPlanes, const PetscInt planeDir[], const PetscReal planeCoord[], AppCtx *user) 133 { 134 PetscSection coordSection; 135 Vec coordinates; 136 const PetscScalar *coords; 137 PetscInt dim, p, vStart, vEnd, v; 138 PetscErrorCode ierr; 139 140 PetscFunctionBeginUser; 141 ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr); 142 ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr); 143 ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr); 144 ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr); 145 ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr); 146 for (p = 0; p < numPlanes; ++p) { 147 DMLabel label; 148 char name[PETSC_MAX_PATH_LEN]; 149 150 ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN, "spectral_plane_%D", p);CHKERRQ(ierr); 151 ierr = DMCreateLabel(dm, name);CHKERRQ(ierr); 152 ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr); 153 ierr = DMLabelAddStratum(label, 1);CHKERRQ(ierr); 154 for (v = vStart; v < vEnd; ++v) { 155 PetscInt off; 156 157 ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr); 158 if (PetscAbsReal(planeCoord[p] - PetscRealPart(coords[off+planeDir[p]])) < PETSC_SMALL) { 159 ierr = DMLabelSetValue(label, v, 1);CHKERRQ(ierr); 160 } 161 } 162 } 163 ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr); 164 PetscFunctionReturn(0); 165 } 166 167 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) 168 { 169 PetscErrorCode ierr; 170 171 PetscFunctionBeginUser; 172 ierr = DMCreate(comm, dm);CHKERRQ(ierr); 173 ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr); 174 ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); 175 if (user->shear) {ierr = DMPlexShearGeometry(*dm, DM_X, NULL);CHKERRQ(ierr);} 176 ierr = DMSetApplicationContext(*dm, user);CHKERRQ(ierr); 177 ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr); 178 if (user->spectral) { 179 PetscInt planeDir[2] = {0, 1}; 180 PetscReal planeCoord[2] = {0., 1.}; 181 182 ierr = CreateSpectralPlanes(*dm, 2, planeDir, planeCoord, user);CHKERRQ(ierr); 183 } 184 PetscFunctionReturn(0); 185 } 186 187 static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user) 188 { 189 PetscDS ds; 190 DMLabel label; 191 const PetscInt id = 1; 192 PetscPointFunc f0 = user->homogeneous ? f0_trig_homogeneous_u : f0_trig_inhomogeneous_u; 193 PetscErrorCode (*ex)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *) = user->homogeneous ? trig_homogeneous_u : trig_inhomogeneous_u; 194 PetscErrorCode ierr; 195 196 PetscFunctionBeginUser; 197 ierr = DMGetDS(dm, &ds);CHKERRQ(ierr); 198 ierr = PetscDSSetResidual(ds, 0, f0, f1_u);CHKERRQ(ierr); 199 ierr = PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);CHKERRQ(ierr); 200 ierr = PetscDSSetExactSolution(ds, 0, ex, user);CHKERRQ(ierr); 201 ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr); 202 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) ex, NULL, user, NULL);CHKERRQ(ierr); 203 PetscFunctionReturn(0); 204 } 205 206 static PetscErrorCode SetupAdjointProblem(DM dm, AppCtx *user) 207 { 208 PetscDS ds; 209 DMLabel label; 210 const PetscInt id = 1; 211 PetscErrorCode ierr; 212 213 PetscFunctionBeginUser; 214 ierr = DMGetDS(dm, &ds);CHKERRQ(ierr); 215 ierr = PetscDSSetResidual(ds, 0, f0_unity_u, f1_u);CHKERRQ(ierr); 216 ierr = PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);CHKERRQ(ierr); 217 ierr = PetscDSSetObjective(ds, 0, obj_error_u);CHKERRQ(ierr); 218 ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr); 219 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) zero, NULL, user, NULL);CHKERRQ(ierr); 220 PetscFunctionReturn(0); 221 } 222 223 static PetscErrorCode SetupErrorProblem(DM dm, AppCtx *user) 224 { 225 PetscDS prob; 226 PetscErrorCode ierr; 227 228 PetscFunctionBeginUser; 229 ierr = DMGetDS(dm, &prob);CHKERRQ(ierr); 230 PetscFunctionReturn(0); 231 } 232 233 static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user) 234 { 235 DM cdm = dm; 236 PetscFE fe; 237 DMPolytopeType ct; 238 PetscBool simplex; 239 PetscInt dim, cStart; 240 char prefix[PETSC_MAX_PATH_LEN]; 241 PetscErrorCode ierr; 242 243 PetscFunctionBeginUser; 244 ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr); 245 ierr = DMPlexGetHeightStratum(dm, 0, &cStart, NULL);CHKERRQ(ierr); 246 ierr = DMPlexGetCellType(dm, cStart, &ct);CHKERRQ(ierr); 247 simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE; 248 /* Create finite element */ 249 ierr = PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name);CHKERRQ(ierr); 250 ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, name ? prefix : NULL, -1, &fe);CHKERRQ(ierr); 251 ierr = PetscObjectSetName((PetscObject) fe, name);CHKERRQ(ierr); 252 /* Set discretization and boundary conditions for each mesh */ 253 ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr); 254 ierr = DMCreateDS(dm);CHKERRQ(ierr); 255 ierr = (*setup)(dm, user);CHKERRQ(ierr); 256 while (cdm) { 257 ierr = DMCopyDisc(dm,cdm);CHKERRQ(ierr); 258 /* TODO: Check whether the boundary of coarse meshes is marked */ 259 ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); 260 } 261 ierr = PetscFEDestroy(&fe);CHKERRQ(ierr); 262 PetscFunctionReturn(0); 263 } 264 265 static PetscErrorCode ComputeSpectral(DM dm, Vec u, PetscInt numPlanes, const PetscInt planeDir[], const PetscReal planeCoord[], AppCtx *user) 266 { 267 MPI_Comm comm; 268 PetscSection coordSection, section; 269 Vec coordinates, uloc; 270 const PetscScalar *coords, *array; 271 PetscInt p; 272 PetscMPIInt size, rank; 273 PetscErrorCode ierr; 274 275 PetscFunctionBeginUser; 276 ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr); 277 ierr = MPI_Comm_size(comm, &size);CHKERRMPI(ierr); 278 ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr); 279 ierr = DMGetLocalVector(dm, &uloc);CHKERRQ(ierr); 280 ierr = DMGlobalToLocalBegin(dm, u, INSERT_VALUES, uloc);CHKERRQ(ierr); 281 ierr = DMGlobalToLocalEnd(dm, u, INSERT_VALUES, uloc);CHKERRQ(ierr); 282 ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, uloc, 0.0, NULL, NULL, NULL);CHKERRQ(ierr); 283 ierr = VecViewFromOptions(uloc, NULL, "-sol_view");CHKERRQ(ierr); 284 ierr = DMGetLocalSection(dm, §ion);CHKERRQ(ierr); 285 ierr = VecGetArrayRead(uloc, &array);CHKERRQ(ierr); 286 ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr); 287 ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr); 288 ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr); 289 for (p = 0; p < numPlanes; ++p) { 290 DMLabel label; 291 char name[PETSC_MAX_PATH_LEN]; 292 Mat F; 293 Vec x, y; 294 IS stratum; 295 PetscReal *ray, *gray; 296 PetscScalar *rvals, *svals, *gsvals; 297 PetscInt *perm, *nperm; 298 PetscInt n, N, i, j, off, offu; 299 const PetscInt *points; 300 301 ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN, "spectral_plane_%D", p);CHKERRQ(ierr); 302 ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr); 303 ierr = DMLabelGetStratumIS(label, 1, &stratum);CHKERRQ(ierr); 304 ierr = ISGetLocalSize(stratum, &n);CHKERRQ(ierr); 305 ierr = ISGetIndices(stratum, &points);CHKERRQ(ierr); 306 ierr = PetscMalloc2(n, &ray, n, &svals);CHKERRQ(ierr); 307 for (i = 0; i < n; ++i) { 308 ierr = PetscSectionGetOffset(coordSection, points[i], &off);CHKERRQ(ierr); 309 ierr = PetscSectionGetOffset(section, points[i], &offu);CHKERRQ(ierr); 310 ray[i] = PetscRealPart(coords[off+((planeDir[p]+1)%2)]); 311 svals[i] = array[offu]; 312 } 313 /* Gather the ray data to proc 0 */ 314 if (size > 1) { 315 PetscMPIInt *cnt, *displs, p; 316 317 ierr = PetscCalloc2(size, &cnt, size, &displs);CHKERRQ(ierr); 318 ierr = MPI_Gather(&n, 1, MPIU_INT, cnt, 1, MPIU_INT, 0, comm);CHKERRMPI(ierr); 319 for (p = 1; p < size; ++p) displs[p] = displs[p-1] + cnt[p-1]; 320 N = displs[size-1] + cnt[size-1]; 321 ierr = PetscMalloc2(N, &gray, N, &gsvals);CHKERRQ(ierr); 322 ierr = MPI_Gatherv(ray, n, MPIU_REAL, gray, cnt, displs, MPIU_REAL, 0, comm);CHKERRMPI(ierr); 323 ierr = MPI_Gatherv(svals, n, MPIU_SCALAR, gsvals, cnt, displs, MPIU_SCALAR, 0, comm);CHKERRMPI(ierr); 324 ierr = PetscFree2(cnt, displs);CHKERRQ(ierr); 325 } else { 326 N = n; 327 gray = ray; 328 gsvals = svals; 329 } 330 if (!rank) { 331 /* Sort point along ray */ 332 ierr = PetscMalloc2(N, &perm, N, &nperm);CHKERRQ(ierr); 333 for (i = 0; i < N; ++i) {perm[i] = i;} 334 ierr = PetscSortRealWithPermutation(N, gray, perm);CHKERRQ(ierr); 335 /* Count duplicates and squish mapping */ 336 nperm[0] = perm[0]; 337 for (i = 1, j = 1; i < N; ++i) { 338 if (PetscAbsReal(gray[perm[i]] - gray[perm[i-1]]) > PETSC_SMALL) nperm[j++] = perm[i]; 339 } 340 /* Create FFT structs */ 341 ierr = MatCreateFFT(PETSC_COMM_SELF, 1, &j, MATFFTW, &F);CHKERRQ(ierr); 342 ierr = MatCreateVecs(F, &x, &y);CHKERRQ(ierr); 343 ierr = PetscObjectSetName((PetscObject) y, name);CHKERRQ(ierr); 344 ierr = VecGetArray(x, &rvals);CHKERRQ(ierr); 345 for (i = 0, j = 0; i < N; ++i) { 346 if (i > 0 && PetscAbsReal(gray[perm[i]] - gray[perm[i-1]]) < PETSC_SMALL) continue; 347 rvals[j] = gsvals[nperm[j]]; 348 ++j; 349 } 350 ierr = PetscFree2(perm, nperm);CHKERRQ(ierr); 351 if (size > 1) {ierr = PetscFree2(gray, gsvals);CHKERRQ(ierr);} 352 ierr = VecRestoreArray(x, &rvals);CHKERRQ(ierr); 353 /* Do FFT along the ray */ 354 ierr = MatMult(F, x, y);CHKERRQ(ierr); 355 /* Chop FFT */ 356 ierr = VecChop(y, PETSC_SMALL);CHKERRQ(ierr); 357 ierr = VecViewFromOptions(x, NULL, "-real_view");CHKERRQ(ierr); 358 ierr = VecViewFromOptions(y, NULL, "-fft_view");CHKERRQ(ierr); 359 ierr = VecDestroy(&x);CHKERRQ(ierr); 360 ierr = VecDestroy(&y);CHKERRQ(ierr); 361 ierr = MatDestroy(&F);CHKERRQ(ierr); 362 } 363 ierr = ISRestoreIndices(stratum, &points);CHKERRQ(ierr); 364 ierr = ISDestroy(&stratum);CHKERRQ(ierr); 365 ierr = PetscFree2(ray, svals);CHKERRQ(ierr); 366 } 367 ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr); 368 ierr = VecRestoreArrayRead(uloc, &array);CHKERRQ(ierr); 369 ierr = DMRestoreLocalVector(dm, &uloc);CHKERRQ(ierr); 370 PetscFunctionReturn(0); 371 } 372 373 int main(int argc, char **argv) 374 { 375 DM dm; /* Problem specification */ 376 SNES snes; /* Nonlinear solver */ 377 Vec u; /* Solutions */ 378 AppCtx user; /* User-defined work context */ 379 PetscErrorCode ierr; 380 381 ierr = PetscInitialize(&argc, &argv, NULL, help);if (ierr) return ierr; 382 ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr); 383 /* Primal system */ 384 ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr); 385 ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr); 386 ierr = SNESSetDM(snes, dm);CHKERRQ(ierr); 387 ierr = SetupDiscretization(dm, "potential", SetupPrimalProblem, &user);CHKERRQ(ierr); 388 ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr); 389 ierr = VecSet(u, 0.0);CHKERRQ(ierr); 390 ierr = PetscObjectSetName((PetscObject) u, "potential");CHKERRQ(ierr); 391 ierr = DMPlexSetSNESLocalFEM(dm, &user, &user, &user);CHKERRQ(ierr); 392 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 393 ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr); 394 ierr = SNESGetSolution(snes, &u);CHKERRQ(ierr); 395 ierr = VecViewFromOptions(u, NULL, "-potential_view");CHKERRQ(ierr); 396 if (user.spectral) { 397 PetscInt planeDir[2] = {0, 1}; 398 PetscReal planeCoord[2] = {0., 1.}; 399 400 ierr = ComputeSpectral(dm, u, 2, planeDir, planeCoord, &user);CHKERRQ(ierr); 401 } 402 /* Adjoint system */ 403 if (user.adjoint) { 404 DM dmAdj; 405 SNES snesAdj; 406 Vec uAdj; 407 408 ierr = SNESCreate(PETSC_COMM_WORLD, &snesAdj);CHKERRQ(ierr); 409 ierr = PetscObjectSetOptionsPrefix((PetscObject) snesAdj, "adjoint_");CHKERRQ(ierr); 410 ierr = DMClone(dm, &dmAdj);CHKERRQ(ierr); 411 ierr = SNESSetDM(snesAdj, dmAdj);CHKERRQ(ierr); 412 ierr = SetupDiscretization(dmAdj, "adjoint", SetupAdjointProblem, &user);CHKERRQ(ierr); 413 ierr = DMCreateGlobalVector(dmAdj, &uAdj);CHKERRQ(ierr); 414 ierr = VecSet(uAdj, 0.0);CHKERRQ(ierr); 415 ierr = PetscObjectSetName((PetscObject) uAdj, "adjoint");CHKERRQ(ierr); 416 ierr = DMPlexSetSNESLocalFEM(dmAdj, &user, &user, &user);CHKERRQ(ierr); 417 ierr = SNESSetFromOptions(snesAdj);CHKERRQ(ierr); 418 ierr = SNESSolve(snesAdj, NULL, uAdj);CHKERRQ(ierr); 419 ierr = SNESGetSolution(snesAdj, &uAdj);CHKERRQ(ierr); 420 ierr = VecViewFromOptions(uAdj, NULL, "-adjoint_view");CHKERRQ(ierr); 421 /* Error representation */ 422 { 423 DM dmErr, dmErrAux, dms[2]; 424 Vec errorEst, errorL2, uErr, uErrLoc, uAdjLoc, uAdjProj; 425 IS *subis; 426 PetscReal errorEstTot, errorL2Norm, errorL2Tot; 427 PetscInt N, i; 428 PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *) = {user.homogeneous ? trig_homogeneous_u : trig_inhomogeneous_u}; 429 void (*identity[1])(PetscInt, PetscInt, PetscInt, 430 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], 431 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], 432 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]) = {f0_identityaux_u}; 433 void *ctxs[1] = {0}; 434 435 ctxs[0] = &user; 436 ierr = DMClone(dm, &dmErr);CHKERRQ(ierr); 437 ierr = SetupDiscretization(dmErr, "error", SetupErrorProblem, &user);CHKERRQ(ierr); 438 ierr = DMGetGlobalVector(dmErr, &errorEst);CHKERRQ(ierr); 439 ierr = DMGetGlobalVector(dmErr, &errorL2);CHKERRQ(ierr); 440 /* Compute auxiliary data (solution and projection of adjoint solution) */ 441 ierr = DMGetLocalVector(dmAdj, &uAdjLoc);CHKERRQ(ierr); 442 ierr = DMGlobalToLocalBegin(dmAdj, uAdj, INSERT_VALUES, uAdjLoc);CHKERRQ(ierr); 443 ierr = DMGlobalToLocalEnd(dmAdj, uAdj, INSERT_VALUES, uAdjLoc);CHKERRQ(ierr); 444 ierr = DMGetGlobalVector(dm, &uAdjProj);CHKERRQ(ierr); 445 ierr = DMSetAuxiliaryVec(dm, NULL, 0, uAdjLoc);CHKERRQ(ierr); 446 ierr = DMProjectField(dm, 0.0, u, identity, INSERT_VALUES, uAdjProj);CHKERRQ(ierr); 447 ierr = DMSetAuxiliaryVec(dm, NULL, 0, NULL);CHKERRQ(ierr); 448 ierr = DMRestoreLocalVector(dmAdj, &uAdjLoc);CHKERRQ(ierr); 449 /* Attach auxiliary data */ 450 dms[0] = dm; dms[1] = dm; 451 ierr = DMCreateSuperDM(dms, 2, &subis, &dmErrAux);CHKERRQ(ierr); 452 if (0) { 453 PetscSection sec; 454 455 ierr = DMGetLocalSection(dms[0], &sec);CHKERRQ(ierr); 456 ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 457 ierr = DMGetLocalSection(dms[1], &sec);CHKERRQ(ierr); 458 ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 459 ierr = DMGetLocalSection(dmErrAux, &sec);CHKERRQ(ierr); 460 ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 461 } 462 ierr = DMViewFromOptions(dmErrAux, NULL, "-dm_err_view");CHKERRQ(ierr); 463 ierr = ISViewFromOptions(subis[0], NULL, "-super_is_view");CHKERRQ(ierr); 464 ierr = ISViewFromOptions(subis[1], NULL, "-super_is_view");CHKERRQ(ierr); 465 ierr = DMGetGlobalVector(dmErrAux, &uErr);CHKERRQ(ierr); 466 ierr = VecViewFromOptions(u, NULL, "-map_vec_view");CHKERRQ(ierr); 467 ierr = VecViewFromOptions(uAdjProj, NULL, "-map_vec_view");CHKERRQ(ierr); 468 ierr = VecViewFromOptions(uErr, NULL, "-map_vec_view");CHKERRQ(ierr); 469 ierr = VecISCopy(uErr, subis[0], SCATTER_FORWARD, u);CHKERRQ(ierr); 470 ierr = VecISCopy(uErr, subis[1], SCATTER_FORWARD, uAdjProj);CHKERRQ(ierr); 471 ierr = DMRestoreGlobalVector(dm, &uAdjProj);CHKERRQ(ierr); 472 for (i = 0; i < 2; ++i) {ierr = ISDestroy(&subis[i]);CHKERRQ(ierr);} 473 ierr = PetscFree(subis);CHKERRQ(ierr); 474 ierr = DMGetLocalVector(dmErrAux, &uErrLoc);CHKERRQ(ierr); 475 ierr = DMGlobalToLocalBegin(dm, uErr, INSERT_VALUES, uErrLoc);CHKERRQ(ierr); 476 ierr = DMGlobalToLocalEnd(dm, uErr, INSERT_VALUES, uErrLoc);CHKERRQ(ierr); 477 ierr = DMRestoreGlobalVector(dmErrAux, &uErr);CHKERRQ(ierr); 478 ierr = DMSetAuxiliaryVec(dmAdj, NULL, 0, uErrLoc);CHKERRQ(ierr); 479 /* Compute cellwise error estimate */ 480 ierr = VecSet(errorEst, 0.0);CHKERRQ(ierr); 481 ierr = DMPlexComputeCellwiseIntegralFEM(dmAdj, uAdj, errorEst, &user);CHKERRQ(ierr); 482 ierr = DMSetAuxiliaryVec(dmAdj, NULL, 0, NULL);CHKERRQ(ierr); 483 ierr = DMRestoreLocalVector(dmErrAux, &uErrLoc);CHKERRQ(ierr); 484 ierr = DMDestroy(&dmErrAux);CHKERRQ(ierr); 485 /* Plot cellwise error vector */ 486 ierr = VecViewFromOptions(errorEst, NULL, "-error_view");CHKERRQ(ierr); 487 /* Compute ratio of estimate (sum over cells) with actual L_2 error */ 488 ierr = DMComputeL2Diff(dm, 0.0, funcs, ctxs, u, &errorL2Norm);CHKERRQ(ierr); 489 ierr = DMPlexComputeL2DiffVec(dm, 0.0, funcs, ctxs, u, errorL2);CHKERRQ(ierr); 490 ierr = VecViewFromOptions(errorL2, NULL, "-l2_error_view");CHKERRQ(ierr); 491 ierr = VecNorm(errorL2, NORM_INFINITY, &errorL2Tot);CHKERRQ(ierr); 492 ierr = VecNorm(errorEst, NORM_INFINITY, &errorEstTot);CHKERRQ(ierr); 493 ierr = VecGetSize(errorEst, &N);CHKERRQ(ierr); 494 ierr = VecPointwiseDivide(errorEst, errorEst, errorL2);CHKERRQ(ierr); 495 ierr = PetscObjectSetName((PetscObject) errorEst, "Error ratio");CHKERRQ(ierr); 496 ierr = VecViewFromOptions(errorEst, NULL, "-error_ratio_view");CHKERRQ(ierr); 497 ierr = PetscPrintf(PETSC_COMM_WORLD, "N: %D L2 error: %g Error Ratio: %g/%g = %g\n", N, (double) errorL2Norm, (double) errorEstTot, (double) PetscSqrtReal(errorL2Tot), (double) errorEstTot/PetscSqrtReal(errorL2Tot));CHKERRQ(ierr); 498 ierr = DMRestoreGlobalVector(dmErr, &errorEst);CHKERRQ(ierr); 499 ierr = DMRestoreGlobalVector(dmErr, &errorL2);CHKERRQ(ierr); 500 ierr = DMDestroy(&dmErr);CHKERRQ(ierr); 501 } 502 ierr = DMDestroy(&dmAdj);CHKERRQ(ierr); 503 ierr = VecDestroy(&uAdj);CHKERRQ(ierr); 504 ierr = SNESDestroy(&snesAdj);CHKERRQ(ierr); 505 } 506 /* Cleanup */ 507 ierr = VecDestroy(&u);CHKERRQ(ierr); 508 ierr = SNESDestroy(&snes);CHKERRQ(ierr); 509 ierr = DMDestroy(&dm);CHKERRQ(ierr); 510 ierr = PetscFinalize(); 511 return ierr; 512 } 513 514 /*TEST 515 516 test: 517 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9 518 suffix: 2d_p1_conv 519 requires: triangle 520 args: -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 521 test: 522 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9 523 suffix: 2d_p2_conv 524 requires: triangle 525 args: -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 526 test: 527 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9 528 suffix: 2d_p3_conv 529 requires: triangle 530 args: -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2 531 test: 532 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9 533 suffix: 2d_q1_conv 534 args: -dm_plex_simplex 0 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 535 test: 536 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9 537 suffix: 2d_q2_conv 538 args: -dm_plex_simplex 0 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 539 test: 540 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9 541 suffix: 2d_q3_conv 542 args: -dm_plex_simplex 0 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2 543 test: 544 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9 545 suffix: 2d_q1_shear_conv 546 args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 547 test: 548 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9 549 suffix: 2d_q2_shear_conv 550 args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 551 test: 552 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9 553 suffix: 2d_q3_shear_conv 554 args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2 555 test: 556 # Using -convest_num_refine 3 we get L_2 convergence rate: 1.7 557 suffix: 3d_p1_conv 558 requires: ctetgen 559 args: -dm_plex_dim 3 -dm_refine 1 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 560 test: 561 # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 2.8 562 suffix: 3d_p2_conv 563 requires: ctetgen 564 args: -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 1 565 test: 566 # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 4.0 567 suffix: 3d_p3_conv 568 requires: ctetgen 569 args: -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 1 570 test: 571 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.8 572 suffix: 3d_q1_conv 573 args: -dm_plex_dim 3 -dm_plex_simplex 0 -dm_refine 1 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 574 test: 575 # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.8 576 suffix: 3d_q2_conv 577 args: -dm_plex_dim 3 -dm_plex_simplex 0 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 1 578 test: 579 # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 3.8 580 suffix: 3d_q3_conv 581 args: -dm_plex_dim 3 -dm_plex_simplex 0 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 1 582 test: 583 suffix: 2d_p1_fas_full 584 requires: triangle 585 args: -potential_petscspace_degree 1 -dm_refine_hierarchy 5 -dm_distribute \ 586 -snes_max_it 1 -snes_type fas -snes_fas_levels 5 -snes_fas_type full -snes_fas_full_total \ 587 -fas_coarse_snes_monitor -fas_coarse_snes_max_it 1 -fas_coarse_ksp_atol 1.e-13 \ 588 -fas_levels_snes_monitor -fas_levels_snes_max_it 1 -fas_levels_snes_type newtonls \ 589 -fas_levels_pc_type none -fas_levels_ksp_max_it 2 -fas_levels_ksp_converged_maxits -fas_levels_ksp_type chebyshev \ 590 -fas_levels_esteig_ksp_type cg -fas_levels_ksp_chebyshev_esteig 0,0.25,0,1.05 -fas_levels_esteig_ksp_max_it 10 591 test: 592 suffix: 2d_p1_fas_full_homogeneous 593 requires: triangle 594 args: -homogeneous -potential_petscspace_degree 1 -dm_refine_hierarchy 5 -dm_distribute \ 595 -snes_max_it 1 -snes_type fas -snes_fas_levels 5 -snes_fas_type full \ 596 -fas_coarse_snes_monitor -fas_coarse_snes_max_it 1 -fas_coarse_ksp_atol 1.e-13 \ 597 -fas_levels_snes_monitor -fas_levels_snes_max_it 1 -fas_levels_snes_type newtonls \ 598 -fas_levels_pc_type none -fas_levels_ksp_max_it 2 -fas_levels_ksp_converged_maxits -fas_levels_ksp_type chebyshev \ 599 -fas_levels_esteig_ksp_type cg -fas_levels_ksp_chebyshev_esteig 0,0.25,0,1.05 -fas_levels_esteig_ksp_max_it 10 600 601 test: 602 suffix: 2d_p1_scalable 603 requires: triangle 604 args: -potential_petscspace_degree 1 -dm_refine 3 \ 605 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned \ 606 -pc_type gamg \ 607 -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 \ 608 -pc_gamg_coarse_eq_limit 1000 \ 609 -pc_gamg_square_graph 1 \ 610 -pc_gamg_threshold 0.05 \ 611 -pc_gamg_threshold_scale .0 \ 612 -mg_levels_ksp_type chebyshev \ 613 -mg_levels_ksp_max_it 1 \ 614 -mg_levels_esteig_ksp_type cg \ 615 -mg_levels_esteig_ksp_max_it 10 \ 616 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 \ 617 -mg_levels_pc_type jacobi \ 618 -matptap_via scalable 619 test: 620 suffix: 2d_p1_gmg_vcycle 621 requires: triangle 622 args: -potential_petscspace_degree 1 -dm_plex_box_faces 2,2 -dm_refine_hierarchy 3 \ 623 -ksp_rtol 5e-10 -pc_type mg \ 624 -mg_levels_ksp_max_it 1 \ 625 -mg_levels_esteig_ksp_type cg \ 626 -mg_levels_esteig_ksp_max_it 10 \ 627 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 \ 628 -mg_levels_pc_type jacobi 629 test: 630 suffix: 2d_p1_gmg_fcycle 631 requires: triangle 632 args: -potential_petscspace_degree 1 -dm_plex_box_faces 2,2 -dm_refine_hierarchy 3 \ 633 -ksp_rtol 5e-10 -pc_type mg -pc_mg_type full \ 634 -mg_levels_ksp_max_it 2 \ 635 -mg_levels_esteig_ksp_type cg \ 636 -mg_levels_esteig_ksp_max_it 10 \ 637 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 \ 638 -mg_levels_pc_type jacobi 639 test: 640 suffix: 2d_p1_gmg_vcycle_adapt 641 requires: triangle bamg 642 args: -potential_petscspace_degree 1 -dm_plex_box_faces 2,2 -dm_refine_hierarchy 3 \ 643 -ksp_rtol 5e-10 -pc_type mg -pc_mg_galerkin -pc_mg_adapt_interp -pc_mg_adapt_interp_coarse_space harmonic -pc_mg_adapt_interp_n 8 \ 644 -mg_levels_ksp_max_it 1 \ 645 -mg_levels_esteig_ksp_type cg \ 646 -mg_levels_esteig_ksp_max_it 10 \ 647 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 \ 648 -mg_levels_pc_type jacobi 649 test: 650 suffix: 2d_p1_spectral_0 651 requires: triangle fftw !complex 652 args: -dm_plex_box_faces 1,1 -potential_petscspace_degree 1 -dm_refine 6 -spectral -fft_view 653 test: 654 suffix: 2d_p1_spectral_1 655 requires: triangle fftw !complex 656 nsize: 2 657 args: -dm_plex_box_faces 4,4 -dm_distribute -potential_petscspace_degree 1 -spectral -fft_view 658 test: 659 suffix: 2d_p1_adj_0 660 requires: triangle 661 args: -potential_petscspace_degree 1 -dm_refine 1 -adjoint -adjoint_petscspace_degree 1 -error_petscspace_degree 0 662 test: 663 nsize: 2 664 requires: kokkos_kernels 665 suffix: kokkos 666 args: -dm_plex_dim 3 -dm_plex_box_faces 2,3,6 -dm_distribute -petscpartitioner_type simple -dm_plex_simplex 0 -potential_petscspace_degree 1 \ 667 -dm_refine 0 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -pc_type gamg -pc_gamg_coarse_eq_limit 1000 -pc_gamg_threshold 0.0 \ 668 -pc_gamg_threshold_scale .5 -mg_levels_ksp_type chebyshev -mg_levels_ksp_max_it 2 -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 \ 669 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -ksp_monitor -snes_monitor -dm_view -dm_mat_type aijkokkos -dm_vec_type kokkos 670 671 TEST*/ 672