Actual source code: ex62.c

petsc-master 2020-12-02
Report Typos and Errors
  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 {SOL_QUADRATIC, SOL_TRIG, SOL_UNKNOWN} SolType;
 38: const char *SolTypes[] = {"quadratic", "trig", "unknown", "SolType", "SOL_", 0};

 40: typedef struct {
 41:   PetscScalar mu; /* dynamic shear viscosity */
 42: } Parameter;

 44: typedef struct {
 45:   /* Domain and mesh definition */
 46:   char     filename[PETSC_MAX_PATH_LEN];
 47:   /* Problem definition */
 48:   PetscBag bag; /* Problem parameters */
 49:   SolType  sol; /* MMS solution */
 50: } AppCtx;

 52: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 53:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 54:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 55:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 56: {
 57:   const PetscReal mu = PetscRealPart(constants[0]);
 58:   const PetscInt  Nc = uOff[1]-uOff[0];
 59:   PetscInt        c, d;

 61:   for (c = 0; c < Nc; ++c) {
 62:     for (d = 0; d < dim; ++d) {
 63:       f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
 64:     }
 65:     f1[c*dim+c] -= u[uOff[1]];
 66:   }
 67: }

 69: static void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 70:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 71:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 72:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 73: {
 74:   PetscInt d;
 75:   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] -= u_x[d*dim+d];
 76: }

 78: static void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 79:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 80:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 81:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
 82: {
 83:   PetscInt d;
 84:   for (d = 0; d < dim; ++d) g1[d*dim+d] = -1.0; /* < q, -\nabla\cdot u > */
 85: }

 87: static void g2_up(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, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
 91: {
 92:   PetscInt d;
 93:   for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* -< \nabla\cdot v, p > */
 94: }

 96: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 97:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 98:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 99:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
100: {
101:   const PetscReal mu = PetscRealPart(constants[0]);
102:   const PetscInt  Nc = uOff[1]-uOff[0];
103:   PetscInt        c, d;

105:   for (c = 0; c < Nc; ++c) {
106:     for (d = 0; d < dim; ++d) {
107:       g3[((c*Nc+c)*dim+d)*dim+d] += mu; /* < \nabla v, \nabla u > */
108:       g3[((c*Nc+d)*dim+d)*dim+c] += mu; /* < \nabla v, {\nabla u}^T > */
109:     }
110:   }
111: }

113: static void g0_pp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
114:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
115:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
116:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
117: {
118:   const PetscReal mu = PetscRealPart(constants[0]);

120:   g0[0] = 1.0/mu;
121: }

123: /* Quadratic MMS Solution
124:    2D:

126:      u = x^2 + y^2
127:      v = 2 x^2 - 2xy
128:      p = x + y - 1
129:      f = <1 - 4 mu, 1 - 4 mu>

131:    so that

133:      e(u) = (grad u + grad u^T) = / 4x  4x \
134:                                   \ 4x -4x /
135:      div mu e(u) - \nabla p + f = mu <4, 4> - <1, 1> + <1 - 4 mu, 1 - 4 mu> = 0
136:      \nabla \cdot u             = 2x - 2x = 0

138:    3D:

140:      u = 2 x^2 + y^2 + z^2
141:      v = 2 x^2 - 2xy
142:      w = 2 x^2 - 2xz
143:      p = x + y + z - 3/2
144:      f = <1 - 8 mu, 1 - 4 mu, 1 - 4 mu>

146:    so that

148:      e(u) = (grad u + grad u^T) = / 8x  4x  4x \
149:                                   | 4x -4x  0  |
150:                                   \ 4x  0  -4x /
151:      div mu e(u) - \nabla p + f = mu <8, 4, 4> - <1, 1, 1> + <1 - 8 mu, 1 - 4 mu, 1 - 4 mu> = 0
152:      \nabla \cdot u             = 4x - 2x - 2x = 0
153: */
154: static PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
155: {
156:   PetscInt c;

158:   u[0] = (dim-1)*PetscSqr(x[0]);
159:   for (c = 1; c < Nc; ++c) {
160:     u[0] += PetscSqr(x[c]);
161:     u[c]  = 2.0*PetscSqr(x[0]) - 2.0*x[0]*x[c];
162:   }
163:   return 0;
164: }

166: static PetscErrorCode quadratic_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
167: {
168:   PetscInt d;

170:   u[0] = -0.5*dim;
171:   for (d = 0; d < dim; ++d) u[0] += x[d];
172:   return 0;
173: }

175: static void f0_quadratic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
176:                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
177:                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
178:                            PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
179: {
180:   const PetscReal mu = PetscRealPart(constants[0]);
181:   PetscInt        d;

183:   f0[0] = (dim-1)*4.0*mu - 1.0;
184:   for (d = 1; d < dim; ++d) f0[d] = 4.0*mu - 1.0;
185: }

187: /* Trigonometric MMS Solution
188:    2D:

190:      u = sin(pi x) + sin(pi y)
191:      v = -pi cos(pi x) y
192:      p = sin(2 pi x) + sin(2 pi y)
193:      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>

195:    so that

197:      e(u) = (grad u + grad u^T) = /        2pi cos(pi x)             pi cos(pi y) + pi^2 sin(pi x) y \
198:                                   \ pi cos(pi y) + pi^2 sin(pi x) y          -2pi cos(pi x)          /
199:      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
200:      \nabla \cdot u             = pi cos(pi x) - pi cos(pi x) = 0

202:    3D:

204:      u = 2 sin(pi x) + sin(pi y) + sin(pi z)
205:      v = -pi cos(pi x) y
206:      w = -pi cos(pi x) z
207:      p = sin(2 pi x) + sin(2 pi y) + sin(2 pi z)
208:      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>

210:    so that

212:      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 \
213:                                   | pi cos(pi y) + pi^2 sin(pi x) y          -2pi cos(pi x)                        0                  |
214:                                   \ pi cos(pi z) + pi^2 sin(pi x) z               0                         -2pi cos(pi x)            /
215:      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
216:      \nabla \cdot u             = 2 pi cos(pi x) - pi cos(pi x) - pi cos(pi x) = 0
217: */
218: static PetscErrorCode trig_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
219: {
220:   PetscInt c;

222:   u[0] = (dim-1)*PetscSinReal(PETSC_PI*x[0]);
223:   for (c = 1; c < Nc; ++c) {
224:     u[0] += PetscSinReal(PETSC_PI*x[c]);
225:     u[c]  = -PETSC_PI*PetscCosReal(PETSC_PI*x[0]) * x[c];
226:   }
227:   return 0;
228: }

230: static PetscErrorCode trig_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
231: {
232:   PetscInt d;

234:   for (d = 0, u[0] = 0.0; d < dim; ++d) u[0] += PetscSinReal(2.0*PETSC_PI*x[d]);
235:   return 0;
236: }

238: static void f0_trig_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
239:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
240:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
241:                       PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
242: {
243:   const PetscReal mu = PetscRealPart(constants[0]);
244:   PetscInt        d;

246:   f0[0] = -2.0*PETSC_PI*PetscCosReal(2.0*PETSC_PI*x[0]) - (dim-1)*mu*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x[0]);
247:   for (d = 1; d < dim; ++d) {
248:     f0[0] -= mu*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x[d]);
249:     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];
250:   }
251: }

253: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
254: {
255:   PetscInt       sol;

259:   options->filename[0] = '\0';
260:   options->sol         = SOL_QUADRATIC;

262:   PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
263:   sol  = options->sol;
264:   PetscOptionsEList("-sol", "The MMS solution", "ex62.c", SolTypes, (sizeof(SolTypes)/sizeof(SolTypes[0]))-3, SolTypes[options->sol], &sol, NULL);
265:   options->sol = (SolType) sol;
266:   PetscOptionsEnd();
267:   return(0);
268: }

270: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
271: {
272:   size_t         len;

276:   PetscStrlen(user->filename, &len);
277:   if (len) {DMPlexCreateFromFile(comm, user->filename, PETSC_TRUE, dm);}
278:   else     {DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);}
279:   DMSetFromOptions(*dm);
280:   DMViewFromOptions(*dm, NULL, "-dm_view");
281:   return(0);
282: }

284: static PetscErrorCode SetupParameters(MPI_Comm comm, AppCtx *ctx)
285: {
286:   Parameter     *p;

290:   /* setup PETSc parameter bag */
291:   PetscBagCreate(PETSC_COMM_SELF, sizeof(Parameter), &ctx->bag);
292:   PetscBagGetData(ctx->bag, (void **) &p);
293:   PetscBagSetName(ctx->bag, "par", "Stokes Parameters");
294:   PetscBagRegisterScalar(ctx->bag, &p->mu, 1.0, "mu", "Dynamic Shear Viscosity, Pa s");
295:   PetscBagSetFromOptions(ctx->bag);
296:   {
297:     PetscViewer       viewer;
298:     PetscViewerFormat format;
299:     PetscBool         flg;

301:     PetscOptionsGetViewer(comm, NULL, NULL, "-param_view", &viewer, &format, &flg);
302:     if (flg) {
303:       PetscViewerPushFormat(viewer, format);
304:       PetscBagView(ctx->bag, viewer);
305:       PetscViewerFlush(viewer);
306:       PetscViewerPopFormat(viewer);
307:       PetscViewerDestroy(&viewer);
308:     }
309:   }
310:   return(0);
311: }

313: static PetscErrorCode SetupEqn(DM dm, AppCtx *user)
314: {
315:   PetscErrorCode (*exactFuncs[2])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *);
316:   PetscDS          ds;
317:   const PetscInt   id = 1;
318:   PetscErrorCode   ierr;

321:   DMGetDS(dm, &ds);
322:   switch (user->sol) {
323:     case SOL_QUADRATIC:
324:       PetscDSSetResidual(ds, 0, f0_quadratic_u, f1_u);
325:       exactFuncs[0] = quadratic_u;
326:       exactFuncs[1] = quadratic_p;
327:       break;
328:     case SOL_TRIG:
329:       PetscDSSetResidual(ds, 0, f0_trig_u, f1_u);
330:       exactFuncs[0] = trig_u;
331:       exactFuncs[1] = trig_p;
332:       break;
333:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%D)", SolTypes[PetscMin(user->sol, SOL_UNKNOWN)], user->sol);
334:   }
335:   PetscDSSetResidual(ds, 1, f0_p, NULL);
336:   PetscDSSetJacobian(ds, 0, 0, NULL, NULL,  NULL,  g3_uu);
337:   PetscDSSetJacobian(ds, 0, 1, NULL, NULL,  g2_up, NULL);
338:   PetscDSSetJacobian(ds, 1, 0, NULL, g1_pu, NULL,  NULL);
339:   PetscDSSetJacobianPreconditioner(ds, 0, 0, NULL, NULL, NULL, g3_uu);
340:   PetscDSSetJacobianPreconditioner(ds, 1, 1, g0_pp, NULL, NULL, NULL);

342:   PetscDSSetExactSolution(ds, 0, exactFuncs[0], user);
343:   PetscDSSetExactSolution(ds, 1, exactFuncs[1], user);

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

347:   /* Make constant values available to pointwise functions */
348:   {
349:     Parameter  *param;
350:     PetscScalar constants[1];

352:     PetscBagGetData(user->bag, (void **) &param);
353:     constants[0] = param->mu; /* dynamic shear viscosity, Pa s */
354:     PetscDSSetConstants(ds, 1, constants);
355:   }
356:   return(0);
357: }

359: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
360: {
361:   PetscInt c;
362:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
363:   return 0;
364: }
365: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
366: {
367:   PetscInt c;
368:   for (c = 0; c < Nc; ++c) u[c] = 1.0;
369:   return 0;
370: }

372: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
373: {
374:   Vec              vec;
375:   PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, one};
376:   PetscErrorCode   ierr;

379:   if (origField != 1) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Field %D should be 1 for pressure", origField);
380:   funcs[field] = one;
381:   {
382:     PetscDS ds;
383:     DMGetDS(dm, &ds);
384:     PetscObjectViewFromOptions((PetscObject) ds, NULL, "-ds_view");
385:   }
386:   DMCreateGlobalVector(dm, &vec);
387:   DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
388:   VecNormalize(vec, NULL);
389:   MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace);
390:   VecDestroy(&vec);
391:   /* New style for field null spaces */
392:   {
393:     PetscObject  pressure;
394:     MatNullSpace nullspacePres;

396:     DMGetField(dm, field, NULL, &pressure);
397:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);
398:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nullspacePres);
399:     MatNullSpaceDestroy(&nullspacePres);
400:   }
401:   return(0);
402: }

404: static PetscErrorCode SetupProblem(DM dm, PetscErrorCode (*setupEqn)(DM, AppCtx *), AppCtx *user)
405: {
406:   DM              cdm = dm;
407:   PetscQuadrature q   = NULL;
408:   DMPolytopeType  ct;
409:   PetscBool       simplex;
410:   PetscInt        dim, Nf = 2, f, Nc[2], cStart;
411:   const char     *name[2]   = {"velocity", "pressure"};
412:   const char     *prefix[2] = {"vel_",     "pres_"};
413:   PetscErrorCode  ierr;

416:   DMGetDimension(dm, &dim);
417:   DMPlexGetHeightStratum(dm, 0, &cStart, NULL);
418:   DMPlexGetCellType(dm, cStart, &ct);
419:   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE;
420:   Nc[0] = dim;
421:   Nc[1] = 1;
422:   for (f = 0; f < Nf; ++f) {
423:     PetscFE fe;

425:     PetscFECreateDefault(PETSC_COMM_SELF, dim, Nc[f], simplex, prefix[f], -1, &fe);
426:     PetscObjectSetName((PetscObject) fe, name[f]);
427:     if (!q) {PetscFEGetQuadrature(fe, &q);}
428:     PetscFESetQuadrature(fe, q);
429:     DMSetField(dm, f, NULL, (PetscObject) fe);
430:     PetscFEDestroy(&fe);
431:   }
432:   DMCreateDS(dm);
433:   (*setupEqn)(dm, user);
434:   while (cdm) {
435:     DMCopyDisc(dm, cdm);
436:     DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace);
437:     DMGetCoarseDM(cdm, &cdm);
438:   }
439:   return(0);
440: }

442: int main(int argc, char **argv)
443: {
444:   SNES           snes;
445:   DM             dm;
446:   Vec            u;
447:   AppCtx         user;

450:   PetscInitialize(&argc, &argv, NULL, help);if (ierr) return ierr;
451:   ProcessOptions(PETSC_COMM_WORLD, &user);
452:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
453:   SNESCreate(PetscObjectComm((PetscObject) dm), &snes);
454:   SNESSetDM(snes, dm);
455:   DMSetApplicationContext(dm, &user);

457:   SetupParameters(PETSC_COMM_WORLD, &user);
458:   SetupProblem(dm, SetupEqn, &user);
459:   DMPlexCreateClosureIndex(dm, NULL);

461:   DMCreateGlobalVector(dm, &u);
462:   DMPlexSetSNESLocalFEM(dm, &user, &user, &user);
463:   SNESSetFromOptions(snes);
464:   DMSNESCheckFromOptions(snes, u);
465:   PetscObjectSetName((PetscObject) u, "Solution");
466:   {
467:     Mat          J;
468:     MatNullSpace sp;

470:     SNESSetUp(snes);
471:     CreatePressureNullSpace(dm, 1, 1, &sp);
472:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
473:     MatSetNullSpace(J, sp);
474:     MatNullSpaceDestroy(&sp);
475:     PetscObjectSetName((PetscObject) J, "Jacobian");
476:     MatViewFromOptions(J, NULL, "-J_view");
477:   }
478:   SNESSolve(snes, NULL, u);

480:   VecDestroy(&u);
481:   SNESDestroy(&snes);
482:   DMDestroy(&dm);
483:   PetscBagDestroy(&user.bag);
484:   PetscFinalize();
485:   return ierr;
486: }
487: /*TEST

489:   test:
490:     suffix: 2d_p2_p1_check
491:     requires: triangle
492:     args: -sol quadratic -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

494:   test:
495:     suffix: 2d_p2_p1_check_parallel
496:     nsize: {{2 3 5}}
497:     requires: triangle
498:     args: -sol quadratic -dm_refine 2 -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

500:   test:
501:     suffix: 3d_p2_p1_check
502:     requires: ctetgen
503:     args: -sol quadratic -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

505:   test:
506:     suffix: 3d_p2_p1_check_parallel
507:     nsize: {{2 3 5}}
508:     requires: ctetgen
509:     args: -sol quadratic -dm_refine 2 -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

511:   test:
512:     suffix: 2d_p2_p1_conv
513:     requires: triangle
514:     # Using -dm_refine 3 gives L_2 convergence rate: [3.0, 2.1]
515:     args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
516:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
517:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
518:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

520:   test:
521:     suffix: 2d_p2_p1_conv_gamg
522:     requires: triangle
523:     args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
524:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
525:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_coarse_pc_type svd

527:   test:
528:     suffix: 3d_p2_p1_conv
529:     requires: ctetgen !single
530:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.8]
531:     args: -sol trig -dm_plex_box_dim 3 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 \
532:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
533:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
534:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

536:   test:
537:     suffix: 2d_q2_q1_check
538:     args: -sol quadratic -dm_plex_box_simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

540:   test:
541:     suffix: 3d_q2_q1_check
542:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001

544:   test:
545:     suffix: 2d_q2_q1_conv
546:     # Using -dm_refine 3 -convest_num_refine 1 gives L_2 convergence rate: [3.0, 2.1]
547:     args: -sol trig -dm_plex_box_simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 -ksp_error_if_not_converged \
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: 3d_q2_q1_conv
554:     requires: !single
555:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.4]
556:     args: -sol trig -dm_plex_box_simplex 0 -dm_plex_box_dim 3 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1 \
557:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
558:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
559:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

561:   test:
562:     suffix: 2d_p3_p2_check
563:     requires: triangle
564:     args: -sol quadratic -vel_petscspace_degree 3 -pres_petscspace_degree 2 -dmsnes_check 0.0001

566:   test:
567:     suffix: 3d_p3_p2_check
568:     requires: ctetgen !single
569:     args: -sol quadratic -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -vel_petscspace_degree 3 -pres_petscspace_degree 2 -dmsnes_check 0.0001

571:   test:
572:     suffix: 2d_p3_p2_conv
573:     requires: triangle
574:     # Using -dm_refine 2 gives L_2 convergence rate: [3.8, 3.0]
575:     args: -sol trig -vel_petscspace_degree 3 -pres_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
576:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
577:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
578:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

580:   test:
581:     suffix: 3d_p3_p2_conv
582:     requires: ctetgen long_runtime
583:     # Using -dm_refine 1 -convest_num_refine 2 gives L_2 convergence rate: [3.6, 3.9]
584:     args: -sol trig -dm_plex_box_dim 3 -dm_refine 1 -vel_petscspace_degree 3 -pres_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 \
585:       -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
586:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
587:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu

589:   test:
590:     suffix: 2d_q1_p0_conv
591:     requires: !single
592:     # Using -dm_refine 3 gives L_2 convergence rate: [1.9, 1.0]
593:     args: -sol quadratic -dm_plex_box_simplex 0 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -snes_convergence_estimate -convest_num_refine 2 \
594:       -ksp_atol 1e-10 -ksp_error_if_not_converged -petscds_jac_pre 0 \
595:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
596:         -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

598:   test:
599:     suffix: 3d_q1_p0_conv
600:     requires: !single
601:     # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [1.7, 1.0]
602:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_plex_box_dim 3 -dm_refine 1 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -snes_convergence_estimate -convest_num_refine 1 \
603:       -ksp_atol 1e-10 -ksp_error_if_not_converged -petscds_jac_pre 0 \
604:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
605:         -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

607:   # Stokes preconditioners
608:   #   Block diagonal \begin{pmatrix} A & 0 \\ 0 & I \end{pmatrix}
609:   test:
610:     suffix: 2d_p2_p1_block_diagonal
611:     requires: triangle
612:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
613:       -snes_error_if_not_converged \
614:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-4 -ksp_error_if_not_converged \
615:       -pc_type fieldsplit -pc_fieldsplit_type additive -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
616:   #   Block triangular \begin{pmatrix} A & B \\ 0 & I \end{pmatrix}
617:   test:
618:     suffix: 2d_p2_p1_block_triangular
619:     requires: triangle
620:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
621:       -snes_error_if_not_converged \
622:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
623:       -pc_type fieldsplit -pc_fieldsplit_type multiplicative -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
624:   #   Diagonal Schur complement \begin{pmatrix} A & 0 \\ 0 & S \end{pmatrix}
625:   test:
626:     suffix: 2d_p2_p1_schur_diagonal
627:     requires: triangle
628:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
629:       -snes_error_if_not_converged \
630:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
631:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type diag -pc_fieldsplit_off_diag_use_amat \
632:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
633:   #   Upper triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
634:   test:
635:     suffix: 2d_p2_p1_schur_upper
636:     requires: triangle
637:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001 \
638:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
639:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -pc_fieldsplit_off_diag_use_amat \
640:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
641:   #   Lower triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
642:   test:
643:     suffix: 2d_p2_p1_schur_lower
644:     requires: triangle
645:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
646:       -snes_error_if_not_converged \
647:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
648:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type lower -pc_fieldsplit_off_diag_use_amat \
649:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
650:   #   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}
651:   test:
652:     suffix: 2d_p2_p1_schur_full
653:     requires: triangle
654:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
655:       -snes_error_if_not_converged \
656:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
657:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_off_diag_use_amat \
658:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
659:   #   Full Schur + Velocity GMG
660:   test:
661:     suffix: 2d_p2_p1_gmg_vcycle
662:     requires: triangle
663:     args: -sol quadratic -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
664:       -snes_error_if_not_converged \
665:       -ksp_type fgmres -ksp_atol 1e-9 -ksp_error_if_not_converged -pc_use_amat \
666:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_off_diag_use_amat \
667:         -fieldsplit_velocity_pc_type mg -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_coarse_pc_type svd
668:   #   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}
669:   test:
670:     suffix: 2d_p2_p1_simple
671:     requires: triangle
672:     args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
673:       -snes_error_if_not_converged \
674:       -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
675:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
676:         -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
677:         -fieldsplit_pressure_inner_ksp_type preonly -fieldsplit_pressure_inner_pc_type jacobi -fieldsplit_pressure_upper_ksp_type preonly -fieldsplit_pressure_upper_pc_type jacobi
678:   #   FETI-DP solvers (these solvers are quite inefficient, they are here to exercise the code)
679:   test:
680:     suffix: 2d_p2_p1_fetidp
681:     requires: triangle mumps
682:     nsize: 5
683:     args: -sol quadratic -dm_refine 2 -dm_mat_type is -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
684:       -snes_error_if_not_converged \
685:       -ksp_type fetidp -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
686:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
687:         -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 \
688:         -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
689:   test:
690:     suffix: 2d_q2_q1_fetidp
691:     requires: mumps
692:     nsize: 5
693:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_refine 2 -dm_mat_type is -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
694:       -snes_error_if_not_converged \
695:       -ksp_type fetidp -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
696:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
697:         -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 \
698:         -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
699:   test:
700:     suffix: 3d_p2_p1_fetidp
701:     requires: ctetgen mumps suitesparse
702:     nsize: 5
703:     args: -sol quadratic -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
704:       -snes_error_if_not_converged \
705:       -ksp_type fetidp -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
706:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
707:         -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 \
708:         -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_benign_trick -fetidp_bddc_pc_bddc_deluxe_singlemat \
709:         -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
710:         -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 \
711:         -fetidp_bddelta_pc_factor_mat_ordering_type external \
712:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
713:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
714:   test:
715:     suffix: 3d_q2_q1_fetidp
716:     requires: suitesparse
717:     nsize: 5
718:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_plex_box_dim 3 -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
719:       -snes_error_if_not_converged \
720:       -ksp_type fetidp -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
721:       -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
722:         -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 \
723:         -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
724:         -fetidp_bddc_pc_bddc_symmetric -fetidp_fieldsplit_lag_ksp_type preonly \
725:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
726:         -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
727:   #   BDDC solvers (these solvers are quite inefficient, they are here to exercise the code)
728:   test:
729:     suffix: 2d_p2_p1_bddc
730:     nsize: 2
731:     requires: triangle !single
732:     args: -sol quadratic -dm_plex_box_faces 2,2,2 -dm_refine 1 -dm_mat_type is -dm_distribute -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
733:       -snes_error_if_not_converged \
734:       -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
735:         -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
736:   #   Vanka
737:   test:
738:     suffix: 2d_q1_p0_vanka
739:     requires: double !complex
740:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
741:       -snes_rtol 1.0e-4 \
742:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
743:       -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
744:         -sub_ksp_type preonly -sub_pc_type lu
745:   test:
746:     suffix: 2d_q1_p0_vanka_denseinv
747:     requires: double !complex
748:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
749:       -snes_rtol 1.0e-4 \
750:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
751:       -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
752:         -pc_patch_dense_inverse -pc_patch_sub_mat_type seqdense
753:   #   Vanka smoother
754:   test:
755:     suffix: 2d_q1_p0_gmg_vanka
756:     requires: double !complex
757:     args: -sol quadratic -dm_plex_box_simplex 0 -dm_refine_hierarchy 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
758:       -snes_rtol 1.0e-4 \
759:       -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
760:       -pc_type mg \
761:         -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 30 \
762:         -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 \
763:           -mg_levels_sub_ksp_type preonly -mg_levels_sub_pc_type lu \
764:         -mg_coarse_pc_type svd

766: TEST*/