1 static char help[] = "Poiseuille Flow in 2d and 3d channels with finite elements.\n\ 2 We solve the Poiseuille flow problem in a rectangular\n\ 3 domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n"; 4 5 /*F 6 A Poiseuille flow is a steady-state isoviscous Stokes flow in a pipe of constant cross-section. We discretize using the 7 finite element method on an unstructured mesh. The weak form equations are 8 \begin{align*} 9 < \nabla v, \nu (\nabla u + {\nabla u}^T) > - < \nabla\cdot v, p > + < v, \Delta \hat n >_{\Gamma_o} = 0 10 < q, \nabla\cdot u > = 0 11 \end{align*} 12 where $\nu$ is the kinematic viscosity, $\Delta$ is the pressure drop per unit length, assuming that pressure is 0 on 13 the left edge, and $\Gamma_o$ is the outlet boundary at the right edge of the pipe. The normal velocity will be zero at 14 the wall, but we will allow a fixed tangential velocity $u_0$. 15 16 In order to test our global to local basis transformation, we will allow the pipe to be at an angle $\alpha$ to the 17 coordinate axes. 18 19 For visualization, use 20 21 -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append 22 F*/ 23 24 #include <petscdmplex.h> 25 #include <petscsnes.h> 26 #include <petscds.h> 27 #include <petscbag.h> 28 29 typedef struct { 30 PetscReal Delta; /* Pressure drop per unit length */ 31 PetscReal nu; /* Kinematic viscosity */ 32 PetscReal u_0; /* Tangential velocity at the wall */ 33 PetscReal alpha; /* Angle of pipe wall to x-axis */ 34 } Parameter; 35 36 typedef struct { 37 PetscBag bag; /* Holds problem parameters */ 38 } AppCtx; 39 40 /* 41 In 2D, plane Poiseuille flow has exact solution: 42 43 u = \Delta/(2 \nu) y (1 - y) + u_0 44 v = 0 45 p = -\Delta x 46 f = 0 47 48 so that 49 50 -\nu \Delta u + \nabla p + f = <\Delta, 0> + <-\Delta, 0> + <0, 0> = 0 51 \nabla \cdot u = 0 + 0 = 0 52 53 In 3D we use exact solution: 54 55 u = \Delta/(4 \nu) (y (1 - y) + z (1 - z)) + u_0 56 v = 0 57 w = 0 58 p = -\Delta x 59 f = 0 60 61 so that 62 63 -\nu \Delta u + \nabla p + f = <Delta, 0, 0> + <-Delta, 0, 0> + <0, 0, 0> = 0 64 \nabla \cdot u = 0 + 0 + 0 = 0 65 66 Note that these functions use coordinates X in the global (rotated) frame 67 */ 68 PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx) { 69 Parameter *param = (Parameter *)ctx; 70 PetscReal Delta = param->Delta; 71 PetscReal nu = param->nu; 72 PetscReal u_0 = param->u_0; 73 PetscReal fac = (PetscReal)(dim - 1); 74 PetscInt d; 75 76 u[0] = u_0; 77 for (d = 1; d < dim; ++d) u[0] += Delta / (fac * 2.0 * nu) * X[d] * (1.0 - X[d]); 78 for (d = 1; d < dim; ++d) u[d] = 0.0; 79 return 0; 80 } 81 82 PetscErrorCode linear_p(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx) { 83 Parameter *param = (Parameter *)ctx; 84 PetscReal Delta = param->Delta; 85 86 p[0] = -Delta * X[0]; 87 return 0; 88 } 89 90 PetscErrorCode wall_velocity(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx) { 91 Parameter *param = (Parameter *)ctx; 92 PetscReal u_0 = param->u_0; 93 PetscInt d; 94 95 u[0] = u_0; 96 for (d = 1; d < dim; ++d) u[d] = 0.0; 97 return 0; 98 } 99 100 /* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z} 101 u[Ncomp] = {p} */ 102 void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) { 103 const PetscReal nu = PetscRealPart(constants[1]); 104 const PetscInt Nc = dim; 105 PetscInt c, d; 106 107 for (c = 0; c < Nc; ++c) { 108 for (d = 0; d < dim; ++d) { 109 /* f1[c*dim+d] = 0.5*nu*(u_x[c*dim+d] + u_x[d*dim+c]); */ 110 f1[c * dim + d] = nu * u_x[c * dim + d]; 111 } 112 f1[c * dim + c] -= u[uOff[1]]; 113 } 114 } 115 116 /* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z} */ 117 void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) { 118 PetscInt d; 119 for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d * dim + d]; 120 } 121 122 /* Residual functions are in reference coordinates */ 123 static void f0_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) { 124 const PetscReal Delta = PetscRealPart(constants[0]); 125 PetscReal alpha = PetscRealPart(constants[3]); 126 PetscReal X = PetscCosReal(alpha) * x[0] + PetscSinReal(alpha) * x[1]; 127 PetscInt d; 128 129 for (d = 0; d < dim; ++d) { f0[d] = -Delta * X * n[d]; } 130 } 131 132 /* < q, \nabla\cdot u > 133 NcompI = 1, NcompJ = dim */ 134 void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]) { 135 PetscInt d; 136 for (d = 0; d < dim; ++d) g1[d * dim + d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */ 137 } 138 139 /* -< \nabla\cdot v, p > 140 NcompI = dim, NcompJ = 1 */ 141 void g2_up(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]) { 142 PetscInt d; 143 for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */ 144 } 145 146 /* < \nabla v, \nabla u + {\nabla u}^T > 147 This just gives \nabla u, give the perdiagonal for the transpose */ 148 void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) { 149 const PetscReal nu = PetscRealPart(constants[1]); 150 const PetscInt Nc = dim; 151 PetscInt c, d; 152 153 for (c = 0; c < Nc; ++c) { 154 for (d = 0; d < dim; ++d) { g3[((c * Nc + c) * dim + d) * dim + d] = nu; } 155 } 156 } 157 158 static PetscErrorCode SetupParameters(AppCtx *user) { 159 PetscBag bag; 160 Parameter *p; 161 162 PetscFunctionBeginUser; 163 /* setup PETSc parameter bag */ 164 PetscCall(PetscBagGetData(user->bag, (void **)&p)); 165 PetscCall(PetscBagSetName(user->bag, "par", "Poiseuille flow parameters")); 166 bag = user->bag; 167 PetscCall(PetscBagRegisterReal(bag, &p->Delta, 1.0, "Delta", "Pressure drop per unit length")); 168 PetscCall(PetscBagRegisterReal(bag, &p->nu, 1.0, "nu", "Kinematic viscosity")); 169 PetscCall(PetscBagRegisterReal(bag, &p->u_0, 0.0, "u_0", "Tangential velocity at the wall")); 170 PetscCall(PetscBagRegisterReal(bag, &p->alpha, 0.0, "alpha", "Angle of pipe wall to x-axis")); 171 PetscFunctionReturn(0); 172 } 173 174 PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) { 175 PetscFunctionBeginUser; 176 PetscCall(DMCreate(comm, dm)); 177 PetscCall(DMSetType(*dm, DMPLEX)); 178 PetscCall(DMSetFromOptions(*dm)); 179 { 180 Parameter *param; 181 Vec coordinates; 182 PetscScalar *coords; 183 PetscReal alpha; 184 PetscInt cdim, N, bs, i; 185 186 PetscCall(DMGetCoordinateDim(*dm, &cdim)); 187 PetscCall(DMGetCoordinates(*dm, &coordinates)); 188 PetscCall(VecGetLocalSize(coordinates, &N)); 189 PetscCall(VecGetBlockSize(coordinates, &bs)); 190 PetscCheck(bs == cdim, comm, PETSC_ERR_ARG_WRONG, "Invalid coordinate blocksize %" PetscInt_FMT " != embedding dimension %" PetscInt_FMT, bs, cdim); 191 PetscCall(VecGetArray(coordinates, &coords)); 192 PetscCall(PetscBagGetData(user->bag, (void **)¶m)); 193 alpha = param->alpha; 194 for (i = 0; i < N; i += cdim) { 195 PetscScalar x = coords[i + 0]; 196 PetscScalar y = coords[i + 1]; 197 198 coords[i + 0] = PetscCosReal(alpha) * x - PetscSinReal(alpha) * y; 199 coords[i + 1] = PetscSinReal(alpha) * x + PetscCosReal(alpha) * y; 200 } 201 PetscCall(VecRestoreArray(coordinates, &coords)); 202 PetscCall(DMSetCoordinates(*dm, coordinates)); 203 } 204 PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view")); 205 PetscFunctionReturn(0); 206 } 207 208 PetscErrorCode SetupProblem(DM dm, AppCtx *user) { 209 PetscDS ds; 210 PetscWeakForm wf; 211 DMLabel label; 212 Parameter *ctx; 213 PetscInt id, bd; 214 215 PetscFunctionBeginUser; 216 PetscCall(PetscBagGetData(user->bag, (void **)&ctx)); 217 PetscCall(DMGetDS(dm, &ds)); 218 PetscCall(PetscDSSetResidual(ds, 0, NULL, f1_u)); 219 PetscCall(PetscDSSetResidual(ds, 1, f0_p, NULL)); 220 PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu)); 221 PetscCall(PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_up, NULL)); 222 PetscCall(PetscDSSetJacobian(ds, 1, 0, NULL, g1_pu, NULL, NULL)); 223 224 id = 2; 225 PetscCall(DMGetLabel(dm, "marker", &label)); 226 PetscCall(DMAddBoundary(dm, DM_BC_NATURAL, "right wall", label, 1, &id, 0, 0, NULL, NULL, NULL, ctx, &bd)); 227 PetscCall(PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)); 228 PetscCall(PetscWeakFormSetIndexBdResidual(wf, label, id, 0, 0, 0, f0_bd_u, 0, NULL)); 229 /* Setup constants */ 230 { 231 Parameter *param; 232 PetscScalar constants[4]; 233 234 PetscCall(PetscBagGetData(user->bag, (void **)¶m)); 235 236 constants[0] = param->Delta; 237 constants[1] = param->nu; 238 constants[2] = param->u_0; 239 constants[3] = param->alpha; 240 PetscCall(PetscDSSetConstants(ds, 4, constants)); 241 } 242 /* Setup Boundary Conditions */ 243 id = 3; 244 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "top wall", label, 1, &id, 0, 0, NULL, (void (*)(void))wall_velocity, NULL, ctx, NULL)); 245 id = 1; 246 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "bottom wall", label, 1, &id, 0, 0, NULL, (void (*)(void))wall_velocity, NULL, ctx, NULL)); 247 /* Setup exact solution */ 248 PetscCall(PetscDSSetExactSolution(ds, 0, quadratic_u, ctx)); 249 PetscCall(PetscDSSetExactSolution(ds, 1, linear_p, ctx)); 250 PetscFunctionReturn(0); 251 } 252 253 PetscErrorCode SetupDiscretization(DM dm, AppCtx *user) { 254 DM cdm = dm; 255 PetscFE fe[2]; 256 Parameter *param; 257 PetscBool simplex; 258 PetscInt dim; 259 MPI_Comm comm; 260 261 PetscFunctionBeginUser; 262 PetscCall(DMGetDimension(dm, &dim)); 263 PetscCall(DMPlexIsSimplex(dm, &simplex)); 264 PetscCall(PetscObjectGetComm((PetscObject)dm, &comm)); 265 PetscCall(PetscFECreateDefault(comm, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0])); 266 PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity")); 267 PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1])); 268 PetscCall(PetscFECopyQuadrature(fe[0], fe[1])); 269 PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure")); 270 /* Set discretization and boundary conditions for each mesh */ 271 PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0])); 272 PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1])); 273 PetscCall(DMCreateDS(dm)); 274 PetscCall(SetupProblem(dm, user)); 275 PetscCall(PetscBagGetData(user->bag, (void **)¶m)); 276 while (cdm) { 277 PetscCall(DMCopyDisc(dm, cdm)); 278 PetscCall(DMPlexCreateBasisRotation(cdm, param->alpha, 0.0, 0.0)); 279 PetscCall(DMGetCoarseDM(cdm, &cdm)); 280 } 281 PetscCall(PetscFEDestroy(&fe[0])); 282 PetscCall(PetscFEDestroy(&fe[1])); 283 PetscFunctionReturn(0); 284 } 285 286 int main(int argc, char **argv) { 287 SNES snes; /* nonlinear solver */ 288 DM dm; /* problem definition */ 289 Vec u, r; /* solution and residual */ 290 AppCtx user; /* user-defined work context */ 291 292 PetscFunctionBeginUser; 293 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 294 PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag)); 295 PetscCall(SetupParameters(&user)); 296 PetscCall(PetscBagSetFromOptions(user.bag)); 297 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 298 PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm)); 299 PetscCall(SNESSetDM(snes, dm)); 300 PetscCall(DMSetApplicationContext(dm, &user)); 301 /* Setup problem */ 302 PetscCall(SetupDiscretization(dm, &user)); 303 PetscCall(DMPlexCreateClosureIndex(dm, NULL)); 304 305 PetscCall(DMCreateGlobalVector(dm, &u)); 306 PetscCall(VecDuplicate(u, &r)); 307 308 PetscCall(DMPlexSetSNESLocalFEM(dm, &user, &user, &user)); 309 310 PetscCall(SNESSetFromOptions(snes)); 311 312 { 313 PetscDS ds; 314 PetscSimplePointFunc exactFuncs[2]; 315 void *ctxs[2]; 316 317 PetscCall(DMGetDS(dm, &ds)); 318 PetscCall(PetscDSGetExactSolution(ds, 0, &exactFuncs[0], &ctxs[0])); 319 PetscCall(PetscDSGetExactSolution(ds, 1, &exactFuncs[1], &ctxs[1])); 320 PetscCall(DMProjectFunction(dm, 0.0, exactFuncs, ctxs, INSERT_ALL_VALUES, u)); 321 PetscCall(PetscObjectSetName((PetscObject)u, "Exact Solution")); 322 PetscCall(VecViewFromOptions(u, NULL, "-exact_vec_view")); 323 } 324 PetscCall(DMSNESCheckFromOptions(snes, u)); 325 PetscCall(VecSet(u, 0.0)); 326 PetscCall(PetscObjectSetName((PetscObject)u, "Solution")); 327 PetscCall(SNESSolve(snes, NULL, u)); 328 PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view")); 329 330 PetscCall(VecDestroy(&u)); 331 PetscCall(VecDestroy(&r)); 332 PetscCall(DMDestroy(&dm)); 333 PetscCall(SNESDestroy(&snes)); 334 PetscCall(PetscBagDestroy(&user.bag)); 335 PetscCall(PetscFinalize()); 336 return 0; 337 } 338 339 /*TEST 340 341 # Convergence 342 test: 343 suffix: 2d_quad_q1_p0_conv 344 requires: !single 345 args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine 1 \ 346 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \ 347 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \ 348 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 349 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 350 -fieldsplit_velocity_pc_type lu \ 351 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 352 test: 353 suffix: 2d_quad_q1_p0_conv_u0 354 requires: !single 355 args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 \ 356 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \ 357 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \ 358 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 359 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 360 -fieldsplit_velocity_pc_type lu \ 361 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 362 test: 363 suffix: 2d_quad_q1_p0_conv_u0_alpha 364 requires: !single 365 args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 -alpha 0.3927 \ 366 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \ 367 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \ 368 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 369 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 370 -fieldsplit_velocity_pc_type lu \ 371 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 372 test: 373 suffix: 2d_quad_q1_p0_conv_gmg_vanka 374 requires: !single long_runtime 375 args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_plex_box_faces 2,2 -dm_refine_hierarchy 1 \ 376 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \ 377 -snes_convergence_estimate -convest_num_refine 1 -snes_error_if_not_converged \ 378 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 379 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 380 -fieldsplit_velocity_pc_type mg \ 381 -fieldsplit_velocity_mg_levels_pc_type patch -fieldsplit_velocity_mg_levels_pc_patch_exclude_subspaces 1 \ 382 -fieldsplit_velocity_mg_levels_pc_patch_construct_codim 0 -fieldsplit_velocity_mg_levels_pc_patch_construct_type vanka \ 383 -fieldsplit_pressure_ksp_rtol 1e-5 -fieldsplit_pressure_pc_type jacobi 384 test: 385 suffix: 2d_tri_p2_p1_conv 386 requires: triangle !single 387 args: -dm_plex_separate_marker -dm_refine 1 \ 388 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \ 389 -dmsnes_check .001 -snes_error_if_not_converged \ 390 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 391 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 392 -fieldsplit_velocity_pc_type lu \ 393 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 394 test: 395 suffix: 2d_tri_p2_p1_conv_u0_alpha 396 requires: triangle !single 397 args: -dm_plex_separate_marker -dm_refine 0 -u_0 0.125 -alpha 0.3927 \ 398 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \ 399 -dmsnes_check .001 -snes_error_if_not_converged \ 400 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 401 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 402 -fieldsplit_velocity_pc_type lu \ 403 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 404 test: 405 suffix: 2d_tri_p2_p1_conv_gmg_vcycle 406 requires: triangle !single 407 args: -dm_plex_separate_marker -dm_plex_box_faces 2,2 -dm_refine_hierarchy 1 \ 408 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \ 409 -dmsnes_check .001 -snes_error_if_not_converged \ 410 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \ 411 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \ 412 -fieldsplit_velocity_pc_type mg \ 413 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi 414 TEST*/ 415