Actual source code: ex62.c

  1: static char help[] = "Stokes Problem discretized with finite elements,\n\
  2: using a parallel unstructured mesh (DMPLEX) to represent the domain.\n\n\n";

  4: /*
  5: For the isoviscous Stokes problem, which we discretize using the finite
  6: element method on an unstructured mesh, the weak form equations are

  8:   < \nabla v, \nabla u + {\nabla u}^T > - < \nabla\cdot v, p > - < v, f > = 0
  9:   < q, -\nabla\cdot u >                                                   = 0

 11: Viewing:

 13: To produce nice output, use

 15:   -dm_refine 3 -dm_view hdf5:sol1.h5 -error_vec_view hdf5:sol1.h5::append -snes_view_solution hdf5:sol1.h5::append -exact_vec_view hdf5:sol1.h5::append

 17: You can get a LaTeX view of the mesh, with point numbering using

 19:   -dm_view :mesh.tex:ascii_latex -dm_plex_view_scale 8.0

 21: The data layout can be viewed using

 23:   -dm_petscsection_view

 25: Lots of information about the FEM assembly can be printed using

 27:   -dm_plex_print_fem 3
 28: */

 30: #include <petscdmplex.h>
 31: #include <petscsnes.h>
 32: #include <petscds.h>
 33: #include <petscbag.h>

 35: // TODO: Plot residual by fields after each smoother iterate

 37: typedef enum {
 38:   SOL_QUADRATIC,
 39:   SOL_TRIG,
 40:   SOL_UNKNOWN
 41: } SolType;
 42: const char *SolTypes[] = {"quadratic", "trig", "unknown", "SolType", "SOL_", 0};

 44: typedef struct {
 45:   PetscScalar mu; /* dynamic shear viscosity */
 46: } Parameter;

 48: typedef struct {
 49:   PetscBag bag; /* Problem parameters */
 50:   SolType  sol; /* MMS solution */
 51: } AppCtx;

 53: static 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[])
 54: {
 55:   const PetscReal mu = PetscRealPart(constants[0]);
 56:   const PetscInt  Nc = uOff[1] - uOff[0];
 57:   PetscInt        c, d;

 59:   for (c = 0; c < Nc; ++c) {
 60:     for (d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
 61:     f1[c * dim + c] -= u[uOff[1]];
 62:   }
 63: }

 65: static 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[])
 66: {
 67:   PetscInt d;
 68:   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] -= u_x[d * dim + d];
 69: }

 71: static 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[])
 72: {
 73:   PetscInt d;
 74:   for (d = 0; d < dim; ++d) g1[d * dim + d] = -1.0; /* < q, -\nabla\cdot u > */
 75: }

 77: static 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[])
 78: {
 79:   PetscInt d;
 80:   for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0; /* -< \nabla\cdot v, p > */
 81: }

 83: static 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[])
 84: {
 85:   const PetscReal mu = PetscRealPart(constants[0]);
 86:   const PetscInt  Nc = uOff[1] - uOff[0];
 87:   PetscInt        c, d;

 89:   for (c = 0; c < Nc; ++c) {
 90:     for (d = 0; d < dim; ++d) {
 91:       g3[((c * Nc + c) * dim + d) * dim + d] += mu; /* < \nabla v, \nabla u > */
 92:       g3[((c * Nc + d) * dim + d) * dim + c] += mu; /* < \nabla v, {\nabla u}^T > */
 93:     }
 94:   }
 95: }

 97: static void g0_pp(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 g0[])
 98: {
 99:   const PetscReal mu = PetscRealPart(constants[0]);

101:   g0[0] = 1.0 / mu;
102: }

104: /* Quadratic MMS Solution
105:    2D:

107:      u = x^2 + y^2
108:      v = 2 x^2 - 2xy
109:      p = x + y - 1
110:      f = <1 - 4 mu, 1 - 4 mu>

112:    so that

114:      e(u) = (grad u + grad u^T) = / 4x  4x \
115:                                   \ 4x -4x /
116:      div mu e(u) - \nabla p + f = mu <4, 4> - <1, 1> + <1 - 4 mu, 1 - 4 mu> = 0
117:      \nabla \cdot u             = 2x - 2x = 0

119:    3D:

121:      u = 2 x^2 + y^2 + z^2
122:      v = 2 x^2 - 2xy
123:      w = 2 x^2 - 2xz
124:      p = x + y + z - 3/2
125:      f = <1 - 8 mu, 1 - 4 mu, 1 - 4 mu>

127:    so that

129:      e(u) = (grad u + grad u^T) = / 8x  4x  4x \
130:                                   | 4x -4x  0  |
131:                                   \ 4x  0  -4x /
132:      div mu e(u) - \nabla p + f = mu <8, 4, 4> - <1, 1, 1> + <1 - 8 mu, 1 - 4 mu, 1 - 4 mu> = 0
133:      \nabla \cdot u             = 4x - 2x - 2x = 0
134: */
135: static PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
136: {
137:   PetscInt c;

139:   u[0] = (dim - 1) * PetscSqr(x[0]);
140:   for (c = 1; c < Nc; ++c) {
141:     u[0] += PetscSqr(x[c]);
142:     u[c] = 2.0 * PetscSqr(x[0]) - 2.0 * x[0] * x[c];
143:   }
144:   return 0;
145: }

147: static PetscErrorCode quadratic_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
148: {
149:   PetscInt d;

151:   u[0] = -0.5 * dim;
152:   for (d = 0; d < dim; ++d) u[0] += x[d];
153:   return 0;
154: }

156: static void f0_quadratic_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 f0[])
157: {
158:   const PetscReal mu = PetscRealPart(constants[0]);
159:   PetscInt        d;

161:   f0[0] = (dim - 1) * 4.0 * mu - 1.0;
162:   for (d = 1; d < dim; ++d) f0[d] = 4.0 * mu - 1.0;
163: }

165: /* Trigonometric MMS Solution
166:    2D:

168:      u = sin(pi x) + sin(pi y)
169:      v = -pi cos(pi x) y
170:      p = sin(2 pi x) + sin(2 pi y)
171:      f = <2pi cos(2 pi x) + mu pi^2 sin(pi x) + mu pi^2 sin(pi y), 2pi cos(2 pi y) - mu pi^3 cos(pi x) y>

173:    so that

175:      e(u) = (grad u + grad u^T) = /        2pi cos(pi x)             pi cos(pi y) + pi^2 sin(pi x) y \
176:                                   \ pi cos(pi y) + pi^2 sin(pi x) y          -2pi cos(pi x)          /
177:      div mu e(u) - \nabla p + f = mu <-pi^2 sin(pi x) - pi^2 sin(pi y), pi^3 cos(pi x) y> - <2pi cos(2 pi x), 2pi cos(2 pi y)> + <f_x, f_y> = 0
178:      \nabla \cdot u             = pi cos(pi x) - pi cos(pi x) = 0

180:    3D:

182:      u = 2 sin(pi x) + sin(pi y) + sin(pi z)
183:      v = -pi cos(pi x) y
184:      w = -pi cos(pi x) z
185:      p = sin(2 pi x) + sin(2 pi y) + sin(2 pi z)
186:      f = <2pi cos(2 pi x) + mu 2pi^2 sin(pi x) + mu pi^2 sin(pi y) + mu pi^2 sin(pi z), 2pi cos(2 pi y) - mu pi^3 cos(pi x) y, 2pi cos(2 pi z) - mu pi^3 cos(pi x) z>

188:    so that

190:      e(u) = (grad u + grad u^T) = /        4pi cos(pi x)             pi cos(pi y) + pi^2 sin(pi x) y  pi cos(pi z) + pi^2 sin(pi x) z \
191:                                   | pi cos(pi y) + pi^2 sin(pi x) y          -2pi cos(pi x)                        0                  |
192:                                   \ pi cos(pi z) + pi^2 sin(pi x) z               0                         -2pi cos(pi x)            /
193:      div mu e(u) - \nabla p + f = mu <-2pi^2 sin(pi x) - pi^2 sin(pi y) - pi^2 sin(pi z), pi^3 cos(pi x) y, pi^3 cos(pi x) z> - <2pi cos(2 pi x), 2pi cos(2 pi y), 2pi cos(2 pi z)> + <f_x, f_y, f_z> = 0
194:      \nabla \cdot u             = 2 pi cos(pi x) - pi cos(pi x) - pi cos(pi x) = 0
195: */
196: static PetscErrorCode trig_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
197: {
198:   PetscInt c;

200:   u[0] = (dim - 1) * PetscSinReal(PETSC_PI * x[0]);
201:   for (c = 1; c < Nc; ++c) {
202:     u[0] += PetscSinReal(PETSC_PI * x[c]);
203:     u[c] = -PETSC_PI * PetscCosReal(PETSC_PI * x[0]) * x[c];
204:   }
205:   return 0;
206: }

208: static PetscErrorCode trig_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
209: {
210:   PetscInt d;

212:   for (d = 0, u[0] = 0.0; d < dim; ++d) u[0] += PetscSinReal(2.0 * PETSC_PI * x[d]);
213:   return 0;
214: }

216: static void f0_trig_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 f0[])
217: {
218:   const PetscReal mu = PetscRealPart(constants[0]);
219:   PetscInt        d;

221:   f0[0] = -2.0 * PETSC_PI * PetscCosReal(2.0 * PETSC_PI * x[0]) - (dim - 1) * mu * PetscSqr(PETSC_PI) * PetscSinReal(PETSC_PI * x[0]);
222:   for (d = 1; d < dim; ++d) {
223:     f0[0] -= mu * PetscSqr(PETSC_PI) * PetscSinReal(PETSC_PI * x[d]);
224:     f0[d] = -2.0 * PETSC_PI * PetscCosReal(2.0 * PETSC_PI * x[d]) + mu * PetscPowRealInt(PETSC_PI, 3) * PetscCosReal(PETSC_PI * x[0]) * x[d];
225:   }
226: }

228: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
229: {
230:   PetscInt sol;

233:   options->sol = SOL_QUADRATIC;
234:   PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
235:   sol = options->sol;
236:   PetscOptionsEList("-sol", "The MMS solution", "ex62.c", SolTypes, PETSC_STATIC_ARRAY_LENGTH(SolTypes) - 3, SolTypes[options->sol], &sol, NULL);
237:   options->sol = (SolType)sol;
238:   PetscOptionsEnd();
239:   return 0;
240: }

242: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
243: {
245:   DMCreate(comm, dm);
246:   DMSetType(*dm, DMPLEX);
247:   DMSetFromOptions(*dm);
248:   DMViewFromOptions(*dm, NULL, "-dm_view");
249:   return 0;
250: }

252: static PetscErrorCode SetupParameters(MPI_Comm comm, AppCtx *ctx)
253: {
254:   Parameter *p;

257:   /* setup PETSc parameter bag */
258:   PetscBagCreate(PETSC_COMM_SELF, sizeof(Parameter), &ctx->bag);
259:   PetscBagGetData(ctx->bag, (void **)&p);
260:   PetscBagSetName(ctx->bag, "par", "Stokes Parameters");
261:   PetscBagRegisterScalar(ctx->bag, &p->mu, 1.0, "mu", "Dynamic Shear Viscosity, Pa s");
262:   PetscBagSetFromOptions(ctx->bag);
263:   {
264:     PetscViewer       viewer;
265:     PetscViewerFormat format;
266:     PetscBool         flg;

268:     PetscOptionsGetViewer(comm, NULL, NULL, "-param_view", &viewer, &format, &flg);
269:     if (flg) {
270:       PetscViewerPushFormat(viewer, format);
271:       PetscBagView(ctx->bag, viewer);
272:       PetscViewerFlush(viewer);
273:       PetscViewerPopFormat(viewer);
274:       PetscViewerDestroy(&viewer);
275:     }
276:   }
277:   return 0;
278: }

280: static PetscErrorCode SetupEqn(DM dm, AppCtx *user)
281: {
282:   PetscErrorCode (*exactFuncs[2])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *);
283:   PetscDS        ds;
284:   DMLabel        label;
285:   const PetscInt id = 1;

288:   DMGetDS(dm, &ds);
289:   switch (user->sol) {
290:   case SOL_QUADRATIC:
291:     PetscDSSetResidual(ds, 0, f0_quadratic_u, f1_u);
292:     exactFuncs[0] = quadratic_u;
293:     exactFuncs[1] = quadratic_p;
294:     break;
295:   case SOL_TRIG:
296:     PetscDSSetResidual(ds, 0, f0_trig_u, f1_u);
297:     exactFuncs[0] = trig_u;
298:     exactFuncs[1] = trig_p;
299:     break;
300:   default:
301:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%d)", SolTypes[PetscMin(user->sol, SOL_UNKNOWN)], user->sol);
302:   }
303:   PetscDSSetResidual(ds, 1, f0_p, NULL);
304:   PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
305:   PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_up, NULL);
306:   PetscDSSetJacobian(ds, 1, 0, NULL, g1_pu, NULL, NULL);
307:   PetscDSSetJacobianPreconditioner(ds, 0, 0, NULL, NULL, NULL, g3_uu);
308:   PetscDSSetJacobianPreconditioner(ds, 1, 1, g0_pp, NULL, NULL, NULL);

310:   PetscDSSetExactSolution(ds, 0, exactFuncs[0], user);
311:   PetscDSSetExactSolution(ds, 1, exactFuncs[1], user);

313:   DMGetLabel(dm, "marker", &label);
314:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], NULL, user, NULL);

316:   /* Make constant values available to pointwise functions */
317:   {
318:     Parameter  *param;
319:     PetscScalar constants[1];

321:     PetscBagGetData(user->bag, (void **)&param);
322:     constants[0] = param->mu; /* dynamic shear viscosity, Pa s */
323:     PetscDSSetConstants(ds, 1, constants);
324:   }
325:   return 0;
326: }

328: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
329: {
330:   PetscInt c;
331:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
332:   return 0;
333: }
334: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
335: {
336:   PetscInt c;
337:   for (c = 0; c < Nc; ++c) u[c] = 1.0;
338:   return 0;
339: }

341: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
342: {
343:   Vec vec;
344:   PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) = {zero, one};

348:   funcs[field] = one;
349:   {
350:     PetscDS ds;
351:     DMGetDS(dm, &ds);
352:     PetscObjectViewFromOptions((PetscObject)ds, NULL, "-ds_view");
353:   }
354:   DMCreateGlobalVector(dm, &vec);
355:   DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
356:   VecNormalize(vec, NULL);
357:   MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace);
358:   VecDestroy(&vec);
359:   /* New style for field null spaces */
360:   {
361:     PetscObject  pressure;
362:     MatNullSpace nullspacePres;

364:     DMGetField(dm, field, NULL, &pressure);
365:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);
366:     PetscObjectCompose(pressure, "nullspace", (PetscObject)nullspacePres);
367:     MatNullSpaceDestroy(&nullspacePres);
368:   }
369:   return 0;
370: }

372: static PetscErrorCode SetupProblem(DM dm, PetscErrorCode (*setupEqn)(DM, AppCtx *), AppCtx *user)
373: {
374:   DM              cdm = dm;
375:   PetscQuadrature q   = NULL;
376:   PetscBool       simplex;
377:   PetscInt        dim, Nf = 2, f, Nc[2];
378:   const char     *name[2]   = {"velocity", "pressure"};
379:   const char     *prefix[2] = {"vel_", "pres_"};

381:   DMGetDimension(dm, &dim);
382:   DMPlexIsSimplex(dm, &simplex);
383:   Nc[0] = dim;
384:   Nc[1] = 1;
385:   for (f = 0; f < Nf; ++f) {
386:     PetscFE fe;

388:     PetscFECreateDefault(PETSC_COMM_SELF, dim, Nc[f], simplex, prefix[f], -1, &fe);
389:     PetscObjectSetName((PetscObject)fe, name[f]);
390:     if (!q) PetscFEGetQuadrature(fe, &q);
391:     PetscFESetQuadrature(fe, q);
392:     DMSetField(dm, f, NULL, (PetscObject)fe);
393:     PetscFEDestroy(&fe);
394:   }
395:   DMCreateDS(dm);
396:   (*setupEqn)(dm, user);
397:   while (cdm) {
398:     DMCopyDisc(dm, cdm);
399:     DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace);
400:     DMGetCoarseDM(cdm, &cdm);
401:   }
402:   return 0;
403: }

405: int main(int argc, char **argv)
406: {
407:   SNES   snes;
408:   DM     dm;
409:   Vec    u;
410:   AppCtx user;

413:   PetscInitialize(&argc, &argv, NULL, help);
414:   ProcessOptions(PETSC_COMM_WORLD, &user);
415:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
416:   SNESCreate(PetscObjectComm((PetscObject)dm), &snes);
417:   SNESSetDM(snes, dm);
418:   DMSetApplicationContext(dm, &user);

420:   SetupParameters(PETSC_COMM_WORLD, &user);
421:   SetupProblem(dm, SetupEqn, &user);
422:   DMPlexCreateClosureIndex(dm, NULL);

424:   DMCreateGlobalVector(dm, &u);
425:   DMPlexSetSNESLocalFEM(dm, &user, &user, &user);
426:   SNESSetFromOptions(snes);
427:   DMSNESCheckFromOptions(snes, u);
428:   PetscObjectSetName((PetscObject)u, "Solution");
429:   {
430:     Mat          J;
431:     MatNullSpace sp;

433:     SNESSetUp(snes);
434:     CreatePressureNullSpace(dm, 1, 1, &sp);
435:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
436:     MatSetNullSpace(J, sp);
437:     MatNullSpaceDestroy(&sp);
438:     PetscObjectSetName((PetscObject)J, "Jacobian");
439:     MatViewFromOptions(J, NULL, "-J_view");
440:   }
441:   SNESSolve(snes, NULL, u);

443:   VecDestroy(&u);
444:   SNESDestroy(&snes);
445:   DMDestroy(&dm);
446:   PetscBagDestroy(&user.bag);
447:   PetscFinalize();
448:   return 0;
449: }
450: /*TEST

452:   test:
453:     suffix: 2d_p2_p1_check
454:     requires: triangle
455:     args: -sol quadratic -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

457:   test:
458:     suffix: 2d_p2_p1_check_parallel
459:     nsize: {{2 3 5}}
460:     requires: triangle
461:     args: -sol quadratic -dm_refine 2 -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

463:   test:
464:     suffix: 3d_p2_p1_check
465:     requires: ctetgen
466:     args: -sol quadratic -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

468:   test:
469:     suffix: 3d_p2_p1_check_parallel
470:     nsize: {{2 3 5}}
471:     requires: ctetgen
472:     args: -sol quadratic -dm_refine 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

474:   test:
475:     suffix: 2d_p2_p1_conv
476:     requires: triangle
477:     # Using -dm_refine 3 gives L_2 convergence rate: [3.0, 2.1]
478:     args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
479:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
480:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
481:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

483:   test:
484:     suffix: 2d_p2_p1_conv_gamg
485:     requires: triangle
486:     args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2  \
487:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
488:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_coarse_pc_type svd

490:   test:
491:     suffix: 3d_p2_p1_conv
492:     requires: ctetgen !single
493:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.8]
494:     args: -sol trig -dm_plex_dim 3 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 \
495:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
496:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
497:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

499:   test:
500:     suffix: 2d_q2_q1_check
501:     args: -sol quadratic -dm_plex_simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

503:   test:
504:     suffix: 3d_q2_q1_check
505:     args: -sol quadratic -dm_plex_simplex 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

507:   test:
508:     suffix: 2d_q2_q1_conv
509:     # Using -dm_refine 3 -convest_num_refine 1 gives L_2 convergence rate: [3.0, 2.1]
510:     args: -sol trig -dm_plex_simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 -ksp_error_if_not_converged \
511:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
512:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
513:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

515:   test:
516:     suffix: 3d_q2_q1_conv
517:     requires: !single
518:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.4]
519:     args: -sol trig -dm_plex_simplex 0 -dm_plex_dim 3 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 \
520:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
521:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
522:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

524:   test:
525:     suffix: 2d_p3_p2_check
526:     requires: triangle
527:     args: -sol quadratic -vel_petscspace_degree 3 -pres_petscspace_degree 2 -dmsnes_check 0.0001

529:   test:
530:     suffix: 3d_p3_p2_check
531:     requires: ctetgen !single
532:     args: -sol quadratic -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 3 -pres_petscspace_degree 2 -dmsnes_check 0.0001

534:   test:
535:     suffix: 2d_p3_p2_conv
536:     requires: triangle
537:     # Using -dm_refine 2 gives L_2 convergence rate: [3.8, 3.0]
538:     args: -sol trig -vel_petscspace_degree 3 -pres_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
539:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
540:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
541:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

543:   test:
544:     suffix: 3d_p3_p2_conv
545:     requires: ctetgen long_runtime
546:     # Using -dm_refine 1 -convest_num_refine 2 gives L_2 convergence rate: [3.6, 3.9]
547:     args: -sol trig -dm_plex_dim 3 -dm_refine 1 -vel_petscspace_degree 3 -pres_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 \
548:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
549:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
550:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

552:   test:
553:     suffix: 2d_q1_p0_conv
554:     requires: !single
555:     # Using -dm_refine 3 gives L_2 convergence rate: [1.9, 1.0]
556:     args: -sol quadratic -dm_plex_simplex 0 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -snes_convergence_estimate -convest_num_refine 2 \
557:       -ksp_atol 1e-10 -petscds_jac_pre 0 \
558:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
559:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_levels_pc_type jacobi -fieldsplit_pressure_mg_coarse_pc_type svd -fieldsplit_pressure_pc_gamg_aggressive_coarsening 0

561:   test:
562:     suffix: 3d_q1_p0_conv
563:     requires: !single
564:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [1.7, 1.0]
565:     args: -sol quadratic -dm_plex_simplex 0 -dm_plex_dim 3 -dm_refine 1 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -snes_convergence_estimate -convest_num_refine 1 \
566:       -ksp_atol 1e-10 -petscds_jac_pre 0 \
567:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
568:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_levels_pc_type jacobi -fieldsplit_pressure_mg_coarse_pc_type svd -fieldsplit_pressure_pc_gamg_aggressive_coarsening 0

570:   # Stokes preconditioners
571:   #   Block diagonal \begin{pmatrix} A & 0 \\ 0 & I \end{pmatrix}
572:   test:
573:     suffix: 2d_p2_p1_block_diagonal
574:     requires: triangle
575:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
576:       -snes_error_if_not_converged \
577:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-4 -ksp_error_if_not_converged \
578:       -pc_type fieldsplit -pc_fieldsplit_type additive -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
579:   #   Block triangular \begin{pmatrix} A & B \\ 0 & I \end{pmatrix}
580:   test:
581:     suffix: 2d_p2_p1_block_triangular
582:     requires: triangle
583:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
584:       -snes_error_if_not_converged \
585:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
586:       -pc_type fieldsplit -pc_fieldsplit_type multiplicative -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
587:   #   Diagonal Schur complement \begin{pmatrix} A & 0 \\ 0 & S \end{pmatrix}
588:   test:
589:     suffix: 2d_p2_p1_schur_diagonal
590:     requires: triangle
591:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
592:       -snes_error_if_not_converged \
593:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
594:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type diag -pc_fieldsplit_off_diag_use_amat \
595:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
596:   #   Upper triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
597:   test:
598:     suffix: 2d_p2_p1_schur_upper
599:     requires: triangle
600:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001 \
601:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
602:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -pc_fieldsplit_off_diag_use_amat \
603:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
604:   #   Lower triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
605:   test:
606:     suffix: 2d_p2_p1_schur_lower
607:     requires: triangle
608:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
609:       -snes_error_if_not_converged \
610:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
611:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type lower -pc_fieldsplit_off_diag_use_amat \
612:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
613:   #   Full Schur complement \begin{pmatrix} I & 0 \\ B^T A^{-1} & I \end{pmatrix} \begin{pmatrix} A & 0 \\ 0 & S \end{pmatrix} \begin{pmatrix} I & A^{-1} B \\ 0 & I \end{pmatrix}
614:   test:
615:     suffix: 2d_p2_p1_schur_full
616:     requires: triangle
617:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
618:       -snes_error_if_not_converged \
619:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
620:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_off_diag_use_amat \
621:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
622:   #   Full Schur + Velocity GMG
623:   test:
624:     suffix: 2d_p2_p1_gmg_vcycle
625:     requires: triangle
626:     args: -sol quadratic -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
627:       -ksp_type fgmres -ksp_atol 1e-9 -snes_error_if_not_converged -pc_use_amat \
628:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_off_diag_use_amat \
629:         -fieldsplit_velocity_pc_type mg -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_pc_gamg_esteig_ksp_max_it 10 -fieldsplit_pressure_mg_levels_pc_type sor -fieldsplit_pressure_mg_coarse_pc_type svd
630:   #   SIMPLE \begin{pmatrix} I & 0 \\ B^T A^{-1} & I \end{pmatrix} \begin{pmatrix} A & 0 \\ 0 & B^T diag(A)^{-1} B \end{pmatrix} \begin{pmatrix} I & diag(A)^{-1} B \\ 0 & I \end{pmatrix}
631:   test:
632:     suffix: 2d_p2_p1_simple
633:     requires: triangle
634:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
635:       -snes_error_if_not_converged \
636:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
637:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
638:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
639:         -fieldsplit_pressure_inner_ksp_type preonly -fieldsplit_pressure_inner_pc_type jacobi -fieldsplit_pressure_upper_ksp_type preonly -fieldsplit_pressure_upper_pc_type jacobi
640:   #   FETI-DP solvers (these solvers are quite inefficient, they are here to exercise the code)
641:   test:
642:     suffix: 2d_p2_p1_fetidp
643:     requires: triangle mumps
644:     nsize: 5
645:     args: -sol quadratic -dm_refine 2 -dm_mat_type is -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
646:       -snes_error_if_not_converged \
647:       -ksp_type fetidp -ksp_rtol 1.0e-8 \
648:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
649:         -fetidp_fieldsplit_p_ksp_max_it 1 -fetidp_fieldsplit_p_ksp_type richardson -fetidp_fieldsplit_p_ksp_richardson_scale 200 -fetidp_fieldsplit_p_pc_type none \
650:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type mumps -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type mumps -fetidp_fieldsplit_lag_ksp_type preonly
651:   test:
652:     suffix: 2d_q2_q1_fetidp
653:     requires: mumps
654:     nsize: 5
655:     args: -sol quadratic -dm_plex_simplex 0 -dm_refine 2 -dm_mat_type is -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
656:       -ksp_type fetidp -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
657:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
658:         -fetidp_fieldsplit_p_ksp_max_it 1 -fetidp_fieldsplit_p_ksp_type richardson -fetidp_fieldsplit_p_ksp_richardson_scale 200 -fetidp_fieldsplit_p_pc_type none \
659:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type mumps -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type mumps -fetidp_fieldsplit_lag_ksp_type preonly
660:   test:
661:     suffix: 3d_p2_p1_fetidp
662:     requires: ctetgen mumps suitesparse
663:     nsize: 5
664:     args: -sol quadratic -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
665:       -snes_error_if_not_converged \
666:       -ksp_type fetidp -ksp_rtol 1.0e-9  \
667:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
668:         -fetidp_fieldsplit_p_ksp_max_it 1 -fetidp_fieldsplit_p_ksp_type richardson -fetidp_fieldsplit_p_ksp_richardson_scale 1000 -fetidp_fieldsplit_p_pc_type none \
669:         -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_benign_trick -fetidp_bddc_pc_bddc_deluxe_singlemat \
670:         -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
671:         -fetidp_bddelta_pc_factor_mat_solver_type umfpack -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 100000 \
672:         -fetidp_bddelta_pc_factor_mat_ordering_type external \
673:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
674:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
675:   test:
676:     suffix: 3d_q2_q1_fetidp
677:     requires: suitesparse
678:     nsize: 5
679:     args: -sol quadratic -dm_plex_simplex 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
680:       -snes_error_if_not_converged \
681:       -ksp_type fetidp -ksp_rtol 1.0e-8 \
682:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
683:         -fetidp_fieldsplit_p_ksp_max_it 1 -fetidp_fieldsplit_p_ksp_type richardson -fetidp_fieldsplit_p_ksp_richardson_scale 2000 -fetidp_fieldsplit_p_pc_type none \
684:         -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
685:         -fetidp_bddc_pc_bddc_symmetric -fetidp_fieldsplit_lag_ksp_type preonly \
686:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
687:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
688:   #   BDDC solvers (these solvers are quite inefficient, they are here to exercise the code)
689:   test:
690:     suffix: 2d_p2_p1_bddc
691:     nsize: 2
692:     requires: triangle !single
693:     args: -sol quadratic -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
694:       -snes_error_if_not_converged \
695:       -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
696:         -pc_type bddc -pc_bddc_corner_selection -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd -pc_bddc_coarse_redundant_pc_type svd
697:   #   Vanka
698:   test:
699:     suffix: 2d_q1_p0_vanka
700:     requires: double !complex
701:     args: -sol quadratic -dm_plex_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
702:       -snes_rtol 1.0e-4 \
703:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
704:       -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
705:         -sub_ksp_type preonly -sub_pc_type lu
706:   test:
707:     suffix: 2d_q1_p0_vanka_denseinv
708:     requires: double !complex
709:     args: -sol quadratic -dm_plex_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
710:       -snes_rtol 1.0e-4 \
711:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
712:       -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
713:         -pc_patch_dense_inverse -pc_patch_sub_mat_type seqdense
714:   #   Vanka smoother
715:   test:
716:     suffix: 2d_q1_p0_gmg_vanka
717:     requires: double !complex
718:     args: -sol quadratic -dm_plex_simplex 0 -dm_refine_hierarchy 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
719:       -snes_rtol 1.0e-4 \
720:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
721:       -pc_type mg \
722:         -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 30 \
723:         -mg_levels_pc_type patch -mg_levels_pc_patch_partition_of_unity 0 -mg_levels_pc_patch_construct_codim 0 -mg_levels_pc_patch_construct_type vanka \
724:           -mg_levels_sub_ksp_type preonly -mg_levels_sub_pc_type lu \
725:         -mg_coarse_pc_type svd

727: TEST*/