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 {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: PetscBag bag; /* Problem parameters */
46: SolType sol; /* MMS solution */
47: } AppCtx;
49: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
50: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
51: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
52: PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
53: {
54: const PetscReal mu = PetscRealPart(constants[0]);
55: const PetscInt Nc = uOff[1]-uOff[0];
56: PetscInt c, d;
58: for (c = 0; c < Nc; ++c) {
59: for (d = 0; d < dim; ++d) {
60: f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
61: }
62: f1[c*dim+c] -= u[uOff[1]];
63: }
64: }
66: static void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
67: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
68: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
69: PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
70: {
71: PetscInt d;
72: for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] -= u_x[d*dim+d];
73: }
75: static void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
76: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
77: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
78: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
79: {
80: PetscInt d;
81: for (d = 0; d < dim; ++d) g1[d*dim+d] = -1.0; /* < q, -\nabla\cdot u > */
82: }
84: static void g2_up(PetscInt dim, PetscInt Nf, PetscInt NfAux,
85: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
86: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
87: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
88: {
89: PetscInt d;
90: for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* -< \nabla\cdot v, p > */
91: }
93: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
94: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
95: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
96: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
97: {
98: const PetscReal mu = PetscRealPart(constants[0]);
99: const PetscInt Nc = uOff[1]-uOff[0];
100: PetscInt c, d;
102: for (c = 0; c < Nc; ++c) {
103: for (d = 0; d < dim; ++d) {
104: g3[((c*Nc+c)*dim+d)*dim+d] += mu; /* < \nabla v, \nabla u > */
105: g3[((c*Nc+d)*dim+d)*dim+c] += mu; /* < \nabla v, {\nabla u}^T > */
106: }
107: }
108: }
110: static void g0_pp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
111: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
112: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
113: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
114: {
115: const PetscReal mu = PetscRealPart(constants[0]);
117: g0[0] = 1.0/mu;
118: }
120: /* Quadratic MMS Solution
121: 2D:
123: u = x^2 + y^2
124: v = 2 x^2 - 2xy
125: p = x + y - 1
126: f = <1 - 4 mu, 1 - 4 mu>
128: so that
130: e(u) = (grad u + grad u^T) = / 4x 4x \
131: \ 4x -4x /
132: div mu e(u) - \nabla p + f = mu <4, 4> - <1, 1> + <1 - 4 mu, 1 - 4 mu> = 0
133: \nabla \cdot u = 2x - 2x = 0
135: 3D:
137: u = 2 x^2 + y^2 + z^2
138: v = 2 x^2 - 2xy
139: w = 2 x^2 - 2xz
140: p = x + y + z - 3/2
141: f = <1 - 8 mu, 1 - 4 mu, 1 - 4 mu>
143: so that
145: e(u) = (grad u + grad u^T) = / 8x 4x 4x \
146: | 4x -4x 0 |
147: \ 4x 0 -4x /
148: div mu e(u) - \nabla p + f = mu <8, 4, 4> - <1, 1, 1> + <1 - 8 mu, 1 - 4 mu, 1 - 4 mu> = 0
149: \nabla \cdot u = 4x - 2x - 2x = 0
150: */
151: static PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
152: {
153: PetscInt c;
155: u[0] = (dim-1)*PetscSqr(x[0]);
156: for (c = 1; c < Nc; ++c) {
157: u[0] += PetscSqr(x[c]);
158: u[c] = 2.0*PetscSqr(x[0]) - 2.0*x[0]*x[c];
159: }
160: return 0;
161: }
163: static PetscErrorCode quadratic_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
164: {
165: PetscInt d;
167: u[0] = -0.5*dim;
168: for (d = 0; d < dim; ++d) u[0] += x[d];
169: return 0;
170: }
172: static void f0_quadratic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
173: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
174: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
175: PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
176: {
177: const PetscReal mu = PetscRealPart(constants[0]);
178: PetscInt d;
180: f0[0] = (dim-1)*4.0*mu - 1.0;
181: for (d = 1; d < dim; ++d) f0[d] = 4.0*mu - 1.0;
182: }
184: /* Trigonometric MMS Solution
185: 2D:
187: u = sin(pi x) + sin(pi y)
188: v = -pi cos(pi x) y
189: p = sin(2 pi x) + sin(2 pi y)
190: 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>
192: so that
194: e(u) = (grad u + grad u^T) = / 2pi cos(pi x) pi cos(pi y) + pi^2 sin(pi x) y \
195: \ pi cos(pi y) + pi^2 sin(pi x) y -2pi cos(pi x) /
196: 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
197: \nabla \cdot u = pi cos(pi x) - pi cos(pi x) = 0
199: 3D:
201: u = 2 sin(pi x) + sin(pi y) + sin(pi z)
202: v = -pi cos(pi x) y
203: w = -pi cos(pi x) z
204: p = sin(2 pi x) + sin(2 pi y) + sin(2 pi z)
205: 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>
207: so that
209: 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 \
210: | pi cos(pi y) + pi^2 sin(pi x) y -2pi cos(pi x) 0 |
211: \ pi cos(pi z) + pi^2 sin(pi x) z 0 -2pi cos(pi x) /
212: 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
213: \nabla \cdot u = 2 pi cos(pi x) - pi cos(pi x) - pi cos(pi x) = 0
214: */
215: static PetscErrorCode trig_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
216: {
217: PetscInt c;
219: u[0] = (dim-1)*PetscSinReal(PETSC_PI*x[0]);
220: for (c = 1; c < Nc; ++c) {
221: u[0] += PetscSinReal(PETSC_PI*x[c]);
222: u[c] = -PETSC_PI*PetscCosReal(PETSC_PI*x[0]) * x[c];
223: }
224: return 0;
225: }
227: static PetscErrorCode trig_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
228: {
229: PetscInt d;
231: for (d = 0, u[0] = 0.0; d < dim; ++d) u[0] += PetscSinReal(2.0*PETSC_PI*x[d]);
232: return 0;
233: }
235: static void f0_trig_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
236: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
237: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
238: PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
239: {
240: const PetscReal mu = PetscRealPart(constants[0]);
241: PetscInt d;
243: f0[0] = -2.0*PETSC_PI*PetscCosReal(2.0*PETSC_PI*x[0]) - (dim-1)*mu*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x[0]);
244: for (d = 1; d < dim; ++d) {
245: f0[0] -= mu*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x[d]);
246: 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];
247: }
248: }
250: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
251: {
252: PetscInt sol;
256: options->sol = SOL_QUADRATIC;
258: PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
259: sol = options->sol;
260: PetscOptionsEList("-sol", "The MMS solution", "ex62.c", SolTypes, (sizeof(SolTypes)/sizeof(SolTypes[0]))-3, SolTypes[options->sol], &sol, NULL);
261: options->sol = (SolType) sol;
262: PetscOptionsEnd();
263: return 0;
264: }
266: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
267: {
269: DMCreate(comm, dm);
270: DMSetType(*dm, DMPLEX);
271: DMSetFromOptions(*dm);
272: DMViewFromOptions(*dm, NULL, "-dm_view");
273: return 0;
274: }
276: static PetscErrorCode SetupParameters(MPI_Comm comm, AppCtx *ctx)
277: {
278: Parameter *p;
281: /* setup PETSc parameter bag */
282: PetscBagCreate(PETSC_COMM_SELF, sizeof(Parameter), &ctx->bag);
283: PetscBagGetData(ctx->bag, (void **) &p);
284: PetscBagSetName(ctx->bag, "par", "Stokes Parameters");
285: PetscBagRegisterScalar(ctx->bag, &p->mu, 1.0, "mu", "Dynamic Shear Viscosity, Pa s");
286: PetscBagSetFromOptions(ctx->bag);
287: {
288: PetscViewer viewer;
289: PetscViewerFormat format;
290: PetscBool flg;
292: PetscOptionsGetViewer(comm, NULL, NULL, "-param_view", &viewer, &format, &flg);
293: if (flg) {
294: PetscViewerPushFormat(viewer, format);
295: PetscBagView(ctx->bag, viewer);
296: PetscViewerFlush(viewer);
297: PetscViewerPopFormat(viewer);
298: PetscViewerDestroy(&viewer);
299: }
300: }
301: return 0;
302: }
304: static PetscErrorCode SetupEqn(DM dm, AppCtx *user)
305: {
306: PetscErrorCode (*exactFuncs[2])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *);
307: PetscDS ds;
308: DMLabel label;
309: const PetscInt id = 1;
312: DMGetDS(dm, &ds);
313: switch (user->sol) {
314: case SOL_QUADRATIC:
315: PetscDSSetResidual(ds, 0, f0_quadratic_u, f1_u);
316: exactFuncs[0] = quadratic_u;
317: exactFuncs[1] = quadratic_p;
318: break;
319: case SOL_TRIG:
320: PetscDSSetResidual(ds, 0, f0_trig_u, f1_u);
321: exactFuncs[0] = trig_u;
322: exactFuncs[1] = trig_p;
323: break;
324: default: SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%D)", SolTypes[PetscMin(user->sol, SOL_UNKNOWN)], user->sol);
325: }
326: PetscDSSetResidual(ds, 1, f0_p, NULL);
327: PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
328: PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_up, NULL);
329: PetscDSSetJacobian(ds, 1, 0, NULL, g1_pu, NULL, NULL);
330: PetscDSSetJacobianPreconditioner(ds, 0, 0, NULL, NULL, NULL, g3_uu);
331: PetscDSSetJacobianPreconditioner(ds, 1, 1, g0_pp, NULL, NULL, NULL);
333: PetscDSSetExactSolution(ds, 0, exactFuncs[0], user);
334: PetscDSSetExactSolution(ds, 1, exactFuncs[1], user);
336: DMGetLabel(dm, "marker", &label);
337: DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) exactFuncs[0], NULL, user, NULL);
339: /* Make constant values available to pointwise functions */
340: {
341: Parameter *param;
342: PetscScalar constants[1];
344: PetscBagGetData(user->bag, (void **) ¶m);
345: constants[0] = param->mu; /* dynamic shear viscosity, Pa s */
346: PetscDSSetConstants(ds, 1, constants);
347: }
348: return 0;
349: }
351: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
352: {
353: PetscInt c;
354: for (c = 0; c < Nc; ++c) u[c] = 0.0;
355: return 0;
356: }
357: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
358: {
359: PetscInt c;
360: for (c = 0; c < Nc; ++c) u[c] = 1.0;
361: return 0;
362: }
364: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
365: {
366: Vec vec;
367: PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, one};
371: funcs[field] = one;
372: {
373: PetscDS ds;
374: DMGetDS(dm, &ds);
375: PetscObjectViewFromOptions((PetscObject) ds, NULL, "-ds_view");
376: }
377: DMCreateGlobalVector(dm, &vec);
378: DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
379: VecNormalize(vec, NULL);
380: MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace);
381: VecDestroy(&vec);
382: /* New style for field null spaces */
383: {
384: PetscObject pressure;
385: MatNullSpace nullspacePres;
387: DMGetField(dm, field, NULL, &pressure);
388: MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);
389: PetscObjectCompose(pressure, "nullspace", (PetscObject) nullspacePres);
390: MatNullSpaceDestroy(&nullspacePres);
391: }
392: return 0;
393: }
395: static PetscErrorCode SetupProblem(DM dm, PetscErrorCode (*setupEqn)(DM, AppCtx *), AppCtx *user)
396: {
397: DM cdm = dm;
398: PetscQuadrature q = NULL;
399: PetscBool simplex;
400: PetscInt dim, Nf = 2, f, Nc[2];
401: const char *name[2] = {"velocity", "pressure"};
402: const char *prefix[2] = {"vel_", "pres_"};
404: DMGetDimension(dm, &dim);
405: DMPlexIsSimplex(dm, &simplex);
406: Nc[0] = dim;
407: Nc[1] = 1;
408: for (f = 0; f < Nf; ++f) {
409: PetscFE fe;
411: PetscFECreateDefault(PETSC_COMM_SELF, dim, Nc[f], simplex, prefix[f], -1, &fe);
412: PetscObjectSetName((PetscObject) fe, name[f]);
413: if (!q) PetscFEGetQuadrature(fe, &q);
414: PetscFESetQuadrature(fe, q);
415: DMSetField(dm, f, NULL, (PetscObject) fe);
416: PetscFEDestroy(&fe);
417: }
418: DMCreateDS(dm);
419: (*setupEqn)(dm, user);
420: while (cdm) {
421: DMCopyDisc(dm, cdm);
422: DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace);
423: DMGetCoarseDM(cdm, &cdm);
424: }
425: return 0;
426: }
428: int main(int argc, char **argv)
429: {
430: SNES snes;
431: DM dm;
432: Vec u;
433: AppCtx user;
435: PetscInitialize(&argc, &argv, NULL, help);
436: ProcessOptions(PETSC_COMM_WORLD, &user);
437: CreateMesh(PETSC_COMM_WORLD, &user, &dm);
438: SNESCreate(PetscObjectComm((PetscObject) dm), &snes);
439: SNESSetDM(snes, dm);
440: DMSetApplicationContext(dm, &user);
442: SetupParameters(PETSC_COMM_WORLD, &user);
443: SetupProblem(dm, SetupEqn, &user);
444: DMPlexCreateClosureIndex(dm, NULL);
446: DMCreateGlobalVector(dm, &u);
447: DMPlexSetSNESLocalFEM(dm, &user, &user, &user);
448: SNESSetFromOptions(snes);
449: DMSNESCheckFromOptions(snes, u);
450: PetscObjectSetName((PetscObject) u, "Solution");
451: {
452: Mat J;
453: MatNullSpace sp;
455: SNESSetUp(snes);
456: CreatePressureNullSpace(dm, 1, 1, &sp);
457: SNESGetJacobian(snes, &J, NULL, NULL, NULL);
458: MatSetNullSpace(J, sp);
459: MatNullSpaceDestroy(&sp);
460: PetscObjectSetName((PetscObject) J, "Jacobian");
461: MatViewFromOptions(J, NULL, "-J_view");
462: }
463: SNESSolve(snes, NULL, u);
465: VecDestroy(&u);
466: SNESDestroy(&snes);
467: DMDestroy(&dm);
468: PetscBagDestroy(&user.bag);
469: PetscFinalize();
470: return 0;
471: }
472: /*TEST
474: test:
475: suffix: 2d_p2_p1_check
476: requires: triangle
477: args: -sol quadratic -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001
479: test:
480: suffix: 2d_p2_p1_check_parallel
481: nsize: {{2 3 5}}
482: requires: triangle
483: args: -sol quadratic -dm_refine 2 -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001
485: test:
486: suffix: 3d_p2_p1_check
487: requires: ctetgen
488: 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
490: test:
491: suffix: 3d_p2_p1_check_parallel
492: nsize: {{2 3 5}}
493: requires: ctetgen
494: args: -sol quadratic -dm_refine 2 -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
496: test:
497: suffix: 2d_p2_p1_conv
498: requires: triangle
499: # Using -dm_refine 3 gives L_2 convergence rate: [3.0, 2.1]
500: args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
501: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
502: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
503: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
505: test:
506: suffix: 2d_p2_p1_conv_gamg
507: requires: triangle
508: args: -sol trig -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2 \
509: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
510: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type gamg -fieldsplit_pressure_mg_coarse_pc_type svd
512: test:
513: suffix: 3d_p2_p1_conv
514: requires: ctetgen !single
515: # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.8]
516: 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 \
517: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
518: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
519: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
521: test:
522: suffix: 2d_q2_q1_check
523: args: -sol quadratic -dm_plex_simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001
525: test:
526: suffix: 3d_q2_q1_check
527: 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
529: test:
530: suffix: 2d_q2_q1_conv
531: # Using -dm_refine 3 -convest_num_refine 1 gives L_2 convergence rate: [3.0, 2.1]
532: 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 \
533: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
534: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
535: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
537: test:
538: suffix: 3d_q2_q1_conv
539: requires: !single
540: # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [2.8, 2.4]
541: 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 \
542: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
543: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
544: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
546: test:
547: suffix: 2d_p3_p2_check
548: requires: triangle
549: args: -sol quadratic -vel_petscspace_degree 3 -pres_petscspace_degree 2 -dmsnes_check 0.0001
551: test:
552: suffix: 3d_p3_p2_check
553: requires: ctetgen !single
554: 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
556: test:
557: suffix: 2d_p3_p2_conv
558: requires: triangle
559: # Using -dm_refine 2 gives L_2 convergence rate: [3.8, 3.0]
560: args: -sol trig -vel_petscspace_degree 3 -pres_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2 -ksp_error_if_not_converged \
561: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
562: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
563: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
565: test:
566: suffix: 3d_p3_p2_conv
567: requires: ctetgen long_runtime
568: # Using -dm_refine 1 -convest_num_refine 2 gives L_2 convergence rate: [3.6, 3.9]
569: 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 \
570: -ksp_atol 1e-10 -ksp_error_if_not_converged -pc_use_amat \
571: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition a11 -pc_fieldsplit_off_diag_use_amat \
572: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu
574: test:
575: suffix: 2d_q1_p0_conv
576: requires: !single
577: # Using -dm_refine 3 gives L_2 convergence rate: [1.9, 1.0]
578: args: -sol quadratic -dm_plex_simplex 0 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -snes_convergence_estimate -convest_num_refine 2 \
579: -ksp_atol 1e-10 -petscds_jac_pre 0 \
580: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
581: -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
583: test:
584: suffix: 3d_q1_p0_conv
585: requires: !single
586: # Using -dm_refine 2 -convest_num_refine 2 gives L_2 convergence rate: [1.7, 1.0]
587: 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 \
588: -ksp_atol 1e-10 -petscds_jac_pre 0 \
589: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition full \
590: -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
592: # Stokes preconditioners
593: # Block diagonal \begin{pmatrix} A & 0 \\ 0 & I \end{pmatrix}
594: test:
595: suffix: 2d_p2_p1_block_diagonal
596: requires: triangle
597: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
598: -snes_error_if_not_converged \
599: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-4 -ksp_error_if_not_converged \
600: -pc_type fieldsplit -pc_fieldsplit_type additive -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
601: # Block triangular \begin{pmatrix} A & B \\ 0 & I \end{pmatrix}
602: test:
603: suffix: 2d_p2_p1_block_triangular
604: requires: triangle
605: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
606: -snes_error_if_not_converged \
607: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
608: -pc_type fieldsplit -pc_fieldsplit_type multiplicative -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type jacobi
609: # Diagonal Schur complement \begin{pmatrix} A & 0 \\ 0 & S \end{pmatrix}
610: test:
611: suffix: 2d_p2_p1_schur_diagonal
612: requires: triangle
613: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
614: -snes_error_if_not_converged \
615: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
616: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type diag -pc_fieldsplit_off_diag_use_amat \
617: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
618: # Upper triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
619: test:
620: suffix: 2d_p2_p1_schur_upper
621: requires: triangle
622: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -dmsnes_check 0.0001 \
623: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
624: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -pc_fieldsplit_off_diag_use_amat \
625: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
626: # Lower triangular Schur complement \begin{pmatrix} A & B \\ 0 & S \end{pmatrix}
627: test:
628: suffix: 2d_p2_p1_schur_lower
629: requires: triangle
630: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
631: -snes_error_if_not_converged \
632: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
633: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type lower -pc_fieldsplit_off_diag_use_amat \
634: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
635: # 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}
636: test:
637: suffix: 2d_p2_p1_schur_full
638: requires: triangle
639: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
640: -snes_error_if_not_converged \
641: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged -pc_use_amat \
642: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_off_diag_use_amat \
643: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
644: # Full Schur + Velocity GMG
645: test:
646: suffix: 2d_p2_p1_gmg_vcycle
647: requires: triangle
648: args: -sol quadratic -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
649: -ksp_type fgmres -ksp_atol 1e-9 -snes_error_if_not_converged -pc_use_amat \
650: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_off_diag_use_amat \
651: -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
652: # 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}
653: test:
654: suffix: 2d_p2_p1_simple
655: requires: triangle
656: args: -sol quadratic -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscds_jac_pre 0 \
657: -snes_error_if_not_converged \
658: -ksp_type fgmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
659: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
660: -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
661: -fieldsplit_pressure_inner_ksp_type preonly -fieldsplit_pressure_inner_pc_type jacobi -fieldsplit_pressure_upper_ksp_type preonly -fieldsplit_pressure_upper_pc_type jacobi
662: # FETI-DP solvers (these solvers are quite inefficient, they are here to exercise the code)
663: test:
664: suffix: 2d_p2_p1_fetidp
665: requires: triangle mumps
666: nsize: 5
667: 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 \
668: -snes_error_if_not_converged \
669: -ksp_type fetidp -ksp_rtol 1.0e-8 \
670: -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
671: -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 \
672: -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
673: test:
674: suffix: 2d_q2_q1_fetidp
675: requires: mumps
676: nsize: 5
677: 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 \
678: -ksp_type fetidp -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
679: -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
680: -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 \
681: -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
682: test:
683: suffix: 3d_p2_p1_fetidp
684: requires: ctetgen mumps suitesparse
685: nsize: 5
686: 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 \
687: -snes_error_if_not_converged \
688: -ksp_type fetidp -ksp_rtol 1.0e-9 \
689: -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
690: -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 \
691: -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_benign_trick -fetidp_bddc_pc_bddc_deluxe_singlemat \
692: -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
693: -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 \
694: -fetidp_bddelta_pc_factor_mat_ordering_type external \
695: -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
696: -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
697: test:
698: suffix: 3d_q2_q1_fetidp
699: requires: suitesparse
700: nsize: 5
701: 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 \
702: -snes_error_if_not_converged \
703: -ksp_type fetidp -ksp_rtol 1.0e-8 \
704: -ksp_fetidp_saddlepoint -fetidp_ksp_type cg \
705: -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 \
706: -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_factor_mat_solver_type petsc -fetidp_harmonic_pc_type cholesky \
707: -fetidp_bddc_pc_bddc_symmetric -fetidp_fieldsplit_lag_ksp_type preonly \
708: -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_solver_type umfpack -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_solver_type umfpack \
709: -fetidp_bddc_pc_bddc_dirichlet_pc_factor_mat_ordering_type external -fetidp_bddc_pc_bddc_neumann_pc_factor_mat_ordering_type external
710: # BDDC solvers (these solvers are quite inefficient, they are here to exercise the code)
711: test:
712: suffix: 2d_p2_p1_bddc
713: nsize: 2
714: requires: triangle !single
715: 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 \
716: -snes_error_if_not_converged \
717: -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-8 -ksp_error_if_not_converged \
718: -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
719: # Vanka
720: test:
721: suffix: 2d_q1_p0_vanka
722: requires: double !complex
723: args: -sol quadratic -dm_plex_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
724: -snes_rtol 1.0e-4 \
725: -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
726: -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
727: -sub_ksp_type preonly -sub_pc_type lu
728: test:
729: suffix: 2d_q1_p0_vanka_denseinv
730: requires: double !complex
731: args: -sol quadratic -dm_plex_simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -petscds_jac_pre 0 \
732: -snes_rtol 1.0e-4 \
733: -ksp_type fgmres -ksp_atol 1e-5 -ksp_error_if_not_converged \
734: -pc_type patch -pc_patch_partition_of_unity 0 -pc_patch_construct_codim 0 -pc_patch_construct_type vanka \
735: -pc_patch_dense_inverse -pc_patch_sub_mat_type seqdense
736: # Vanka smoother
737: test:
738: suffix: 2d_q1_p0_gmg_vanka
739: requires: double !complex
740: args: -sol quadratic -dm_plex_simplex 0 -dm_refine_hierarchy 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 mg \
744: -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 30 \
745: -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 \
746: -mg_levels_sub_ksp_type preonly -mg_levels_sub_pc_type lu \
747: -mg_coarse_pc_type svd
749: TEST*/