Actual source code: ex4.c
1: static char help[] = "Solves the incompressible, variable-viscosity Stokes equation in 2D or 3D, driven by buoyancy variations.\n"
2: "-dim: set dimension (2 or 3)\n"
3: "-nondimensional: replace dimensional domain and coefficients with nondimensional ones\n"
4: "-isoviscous: use constant viscosity\n"
5: "-levels: number of grids to create, by coarsening\n"
6: "-rediscretize: create operators for all grids and set up a FieldSplit/MG solver\n"
7: "-dump_solution: dump VTK files\n\n";
9: #include <petscdm.h>
10: #include <petscksp.h>
11: #include <petscdmstag.h>
12: #include <petscdmda.h>
14: /* Application context - grid-based data*/
15: typedef struct LevelCtxData_ {
16: DM dm_stokes, dm_coefficients, dm_faces;
17: Vec coeff;
18: PetscInt cells_x, cells_y, cells_z; /* redundant with DMs */
19: PetscReal hx_characteristic, hy_characteristic, hz_characteristic;
20: PetscScalar K_bound, K_cont;
21: } LevelCtxData;
22: typedef LevelCtxData *LevelCtx;
24: /* Application context - problem and grid(s) (but not solver-specific data) */
25: typedef struct CtxData_ {
26: MPI_Comm comm;
27: PetscInt dim; /* redundant with DMs */
28: PetscInt cells_x, cells_y, cells_z; /* Redundant with finest DMs */
29: PetscReal xmax, ymax, xmin, ymin, zmin, zmax;
30: PetscScalar eta1, eta2, rho1, rho2, gy, eta_characteristic;
31: PetscBool pin_pressure;
32: PetscScalar (*GetEta)(struct CtxData_ *, PetscScalar, PetscScalar, PetscScalar);
33: PetscScalar (*GetRho)(struct CtxData_ *, PetscScalar, PetscScalar, PetscScalar);
34: PetscInt n_levels;
35: LevelCtx *levels;
36: } CtxData;
37: typedef CtxData *Ctx;
39: /* Helper to pass system-creation parameters */
40: typedef struct SystemParameters_ {
41: Ctx ctx;
42: PetscInt level;
43: PetscBool include_inverse_visc, faces_only;
44: } SystemParametersData;
45: typedef SystemParametersData *SystemParameters;
47: /* Main logic */
48: static PetscErrorCode AttachNullspace(DM, Mat);
49: static PetscErrorCode CreateAuxiliaryOperator(Ctx, PetscInt, Mat *);
50: static PetscErrorCode CreateSystem(SystemParameters, Mat *, Vec *);
51: static PetscErrorCode CtxCreateAndSetFromOptions(Ctx *);
52: static PetscErrorCode CtxDestroy(Ctx *);
53: static PetscErrorCode DumpSolution(Ctx, PetscInt, Vec);
54: static PetscErrorCode OperatorInsertInverseViscosityPressureTerms(DM, DM, Vec, PetscScalar, Mat);
55: static PetscErrorCode PopulateCoefficientData(Ctx, PetscInt);
56: static PetscErrorCode SystemParametersCreate(SystemParameters *, Ctx);
57: static PetscErrorCode SystemParametersDestroy(SystemParameters *);
59: int main(int argc, char **argv)
60: {
61: Ctx ctx;
62: Mat A, *A_faces = NULL, S_hat = NULL, P = NULL;
63: Vec x, b;
64: KSP ksp;
65: DM dm_stokes, dm_coefficients;
66: PetscBool dump_solution, build_auxiliary_operator, rediscretize, custom_pc_mat;
68: PetscFunctionBeginUser;
69: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
71: /* Accept options for program behavior */
72: dump_solution = PETSC_FALSE;
73: PetscCall(PetscOptionsGetBool(NULL, NULL, "-dump_solution", &dump_solution, NULL));
74: rediscretize = PETSC_FALSE;
75: PetscCall(PetscOptionsGetBool(NULL, NULL, "-rediscretize", &rediscretize, NULL));
76: build_auxiliary_operator = rediscretize;
77: PetscCall(PetscOptionsGetBool(NULL, NULL, "-build_auxiliary_operator", &build_auxiliary_operator, NULL));
78: custom_pc_mat = PETSC_FALSE;
79: PetscCall(PetscOptionsGetBool(NULL, NULL, "-custom_pc_mat", &custom_pc_mat, NULL));
81: /* Populate application context */
82: PetscCall(CtxCreateAndSetFromOptions(&ctx));
84: /* Create two DMStag objects, corresponding to the same domain and parallel
85: decomposition ("topology"). Each defines a different set of fields on
86: the domain ("section"); the first the solution to the Stokes equations
87: (x- and y-velocities and scalar pressure), and the second holds coefficients
88: (viscosities on elements and viscosities+densities on corners/edges in 2d/3d) */
89: if (ctx->dim == 2) {
90: PetscCall(DMStagCreate2d(ctx->comm, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, ctx->cells_x, ctx->cells_y, /* Global element counts */
91: PETSC_DECIDE, PETSC_DECIDE, /* Determine parallel decomposition automatically */
92: 0, 1, 1, /* dof: 0 per vertex, 1 per edge, 1 per face/element */
93: DMSTAG_STENCIL_BOX, 1, /* elementwise stencil width */
94: NULL, NULL, &ctx->levels[ctx->n_levels - 1]->dm_stokes));
95: } else if (ctx->dim == 3) {
96: PetscCall(DMStagCreate3d(ctx->comm, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, ctx->cells_x, ctx->cells_y, ctx->cells_z, PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE, 0, 0, 1, 1, /* dof: 1 per face, 1 per element */
97: DMSTAG_STENCIL_BOX, 1, NULL, NULL, NULL, &ctx->levels[ctx->n_levels - 1]->dm_stokes));
98: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Unsupported dimension: %" PetscInt_FMT, ctx->dim);
99: dm_stokes = ctx->levels[ctx->n_levels - 1]->dm_stokes;
100: PetscCall(DMSetFromOptions(dm_stokes));
101: PetscCall(DMStagGetGlobalSizes(dm_stokes, &ctx->cells_x, &ctx->cells_y, &ctx->cells_z));
102: PetscCall(DMSetUp(dm_stokes));
103: PetscCall(DMStagSetUniformCoordinatesProduct(dm_stokes, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax, ctx->zmin, ctx->zmax));
105: if (ctx->dim == 2) PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 2, 0, 1, 0, &ctx->levels[ctx->n_levels - 1]->dm_coefficients));
106: else if (ctx->dim == 3) PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 2, 0, 1, &ctx->levels[ctx->n_levels - 1]->dm_coefficients));
107: else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Unsupported dimension: %" PetscInt_FMT, ctx->dim);
108: dm_coefficients = ctx->levels[ctx->n_levels - 1]->dm_coefficients;
109: PetscCall(DMSetUp(dm_coefficients));
110: PetscCall(DMStagSetUniformCoordinatesProduct(dm_coefficients, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax, ctx->zmin, ctx->zmax));
112: /* Create additional DMs by coarsening. 0 is the coarsest level */
113: for (PetscInt level = ctx->n_levels - 1; level > 0; --level) {
114: PetscCall(DMCoarsen(ctx->levels[level]->dm_stokes, MPI_COMM_NULL, &ctx->levels[level - 1]->dm_stokes));
115: PetscCall(DMCoarsen(ctx->levels[level]->dm_coefficients, MPI_COMM_NULL, &ctx->levels[level - 1]->dm_coefficients));
116: }
118: /* Compute scaling constants, knowing grid spacing */
119: ctx->eta_characteristic = PetscMin(PetscRealPart(ctx->eta1), PetscRealPart(ctx->eta2));
120: for (PetscInt level = 0; level < ctx->n_levels; ++level) {
121: PetscInt N[3];
122: PetscReal hx_avg_inv;
124: PetscCall(DMStagGetGlobalSizes(ctx->levels[level]->dm_stokes, &N[0], &N[1], &N[2]));
125: ctx->levels[level]->hx_characteristic = (ctx->xmax - ctx->xmin) / N[0];
126: ctx->levels[level]->hy_characteristic = (ctx->ymax - ctx->ymin) / N[1];
127: if (N[2]) ctx->levels[level]->hz_characteristic = (ctx->zmax - ctx->zmin) / N[2];
128: if (ctx->dim == 2) {
129: hx_avg_inv = 2.0 / (ctx->levels[level]->hx_characteristic + ctx->levels[level]->hy_characteristic);
130: } else if (ctx->dim == 3) {
131: hx_avg_inv = 3.0 / (ctx->levels[level]->hx_characteristic + ctx->levels[level]->hy_characteristic + ctx->levels[level]->hz_characteristic);
132: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not Implemented for dimension %" PetscInt_FMT, ctx->dim);
133: ctx->levels[level]->K_cont = ctx->eta_characteristic * hx_avg_inv;
134: ctx->levels[level]->K_bound = ctx->eta_characteristic * hx_avg_inv * hx_avg_inv;
135: }
137: /* Populate coefficient data */
138: for (PetscInt level = 0; level < ctx->n_levels; ++level) PetscCall(PopulateCoefficientData(ctx, level));
140: /* Construct main system */
141: {
142: SystemParameters system_parameters;
144: PetscCall(SystemParametersCreate(&system_parameters, ctx));
145: PetscCall(CreateSystem(system_parameters, &A, &b));
146: PetscCall(SystemParametersDestroy(&system_parameters));
147: }
149: /* Attach a constant-pressure nullspace to the fine-level operator */
150: if (!ctx->pin_pressure) PetscCall(AttachNullspace(dm_stokes, A));
152: /* Set up solver */
153: PetscCall(KSPCreate(ctx->comm, &ksp));
154: PetscCall(KSPSetType(ksp, KSPFGMRES));
155: {
156: /* Default to a direct solver, if a package is available */
157: PetscMPIInt size;
159: PetscCallMPI(MPI_Comm_size(ctx->comm, &size));
160: if (PetscDefined(HAVE_SUITESPARSE) && size == 1) {
161: PC pc;
163: PetscCall(KSPGetPC(ksp, &pc));
164: PetscCall(PCSetType(pc, PCLU));
165: PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERUMFPACK)); /* A default, requires SuiteSparse */
166: }
167: if (PetscDefined(HAVE_MUMPS) && size > 1) {
168: PC pc;
170: PetscCall(KSPGetPC(ksp, &pc));
171: PetscCall(PCSetType(pc, PCLU));
172: PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERMUMPS)); /* A default, requires MUMPS */
173: }
174: }
176: /* Create and set a custom preconditioning matrix */
177: if (custom_pc_mat) {
178: SystemParameters system_parameters;
180: PetscCall(SystemParametersCreate(&system_parameters, ctx));
181: system_parameters->include_inverse_visc = PETSC_TRUE;
182: PetscCall(CreateSystem(system_parameters, &P, NULL));
183: PetscCall(SystemParametersDestroy(&system_parameters));
184: PetscCall(KSPSetOperators(ksp, A, P));
185: } else {
186: PetscCall(KSPSetOperators(ksp, A, A));
187: }
189: PetscCall(KSPSetDM(ksp, dm_stokes));
190: PetscCall(KSPSetDMActive(ksp, PETSC_FALSE));
192: /* Finish setting up solver (can override options set above) */
193: PetscCall(KSPSetFromOptions(ksp));
195: /* Additional solver configuration that can involve setting up and CANNOT be
196: overridden from the command line */
198: /* Construct an auxiliary operator for use a Schur complement preconditioner,
199: and tell PCFieldSplit to use it (which has no effect if not using that PC) */
200: if (build_auxiliary_operator && !rediscretize) {
201: PC pc;
203: PetscCall(KSPGetPC(ksp, &pc));
204: PetscCall(CreateAuxiliaryOperator(ctx, ctx->n_levels - 1, &S_hat));
205: PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_USER, S_hat));
206: PetscCall(KSPSetFromOptions(ksp));
207: }
209: if (rediscretize) {
210: /* Set up an ABF solver with rediscretized geometric multigrid on the velocity-velocity block */
211: PC pc, pc_faces;
212: KSP ksp_faces;
214: if (ctx->n_levels < 2) PetscCall(PetscPrintf(ctx->comm, "Warning: not using multiple levels!\n"));
216: PetscCall(KSPGetPC(ksp, &pc));
217: PetscCall(PCSetType(pc, PCFIELDSPLIT));
218: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
219: PetscCall(PCFieldSplitSetSchurFactType(pc, PC_FIELDSPLIT_SCHUR_FACT_UPPER));
220: if (build_auxiliary_operator) {
221: PetscCall(CreateAuxiliaryOperator(ctx, ctx->n_levels - 1, &S_hat));
222: PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_USER, S_hat));
223: }
225: /* Create rediscretized velocity-only DMs and operators */
226: PetscCall(PetscMalloc1(ctx->n_levels, &A_faces));
227: for (PetscInt level = 0; level < ctx->n_levels; ++level) {
228: if (ctx->dim == 2) {
229: PetscCall(DMStagCreateCompatibleDMStag(ctx->levels[level]->dm_stokes, 0, 1, 0, 0, &ctx->levels[level]->dm_faces));
230: } else if (ctx->dim == 3) {
231: PetscCall(DMStagCreateCompatibleDMStag(ctx->levels[level]->dm_stokes, 0, 0, 1, 0, &ctx->levels[level]->dm_faces));
232: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not Implemented for dimension %" PetscInt_FMT, ctx->dim);
233: {
234: SystemParameters system_parameters;
236: PetscCall(SystemParametersCreate(&system_parameters, ctx));
237: system_parameters->faces_only = PETSC_TRUE;
238: system_parameters->level = level;
239: PetscCall(CreateSystem(system_parameters, &A_faces[level], NULL));
240: PetscCall(SystemParametersDestroy(&system_parameters));
241: }
242: }
244: /* Set up to populate enough to define the sub-solver */
245: PetscCall(KSPSetUp(ksp));
247: /* Set multigrid components and settings */
248: {
249: KSP *sub_ksp;
251: PetscCall(PCFieldSplitSchurGetSubKSP(pc, NULL, &sub_ksp));
252: ksp_faces = sub_ksp[0];
253: PetscCall(PetscFree(sub_ksp));
254: }
255: PetscCall(KSPSetType(ksp_faces, KSPGCR));
256: PetscCall(KSPGetPC(ksp_faces, &pc_faces));
257: PetscCall(PCSetType(pc_faces, PCMG));
258: PetscCall(PCMGSetLevels(pc_faces, ctx->n_levels, NULL));
259: for (PetscInt level = 0; level < ctx->n_levels; ++level) {
260: KSP ksp_level;
261: PC pc_level;
263: /* Smoothers */
264: PetscCall(PCMGGetSmoother(pc_faces, level, &ksp_level));
265: PetscCall(KSPGetPC(ksp_level, &pc_level));
266: PetscCall(KSPSetOperators(ksp_level, A_faces[level], A_faces[level]));
267: if (level > 0) PetscCall(PCSetType(pc_level, PCJACOBI));
269: /* Transfer Operators */
270: if (level > 0) {
271: Mat restriction, interpolation;
272: DM dm_level = ctx->levels[level]->dm_faces;
273: DM dm_coarser = ctx->levels[level - 1]->dm_faces;
275: PetscCall(DMCreateInterpolation(dm_coarser, dm_level, &interpolation, NULL));
276: PetscCall(PCMGSetInterpolation(pc_faces, level, interpolation));
277: PetscCall(MatDestroy(&interpolation));
278: PetscCall(DMCreateRestriction(dm_coarser, dm_level, &restriction));
279: PetscCall(PCMGSetRestriction(pc_faces, level, restriction));
280: PetscCall(MatDestroy(&restriction));
281: }
282: }
283: }
285: /* Solve */
286: PetscCall(VecDuplicate(b, &x));
287: PetscCall(KSPSolve(ksp, b, x));
288: {
289: KSPConvergedReason reason;
290: PetscCall(KSPGetConvergedReason(ksp, &reason));
291: PetscCheck(reason >= 0, PETSC_COMM_WORLD, PETSC_ERR_CONV_FAILED, "Linear solve failed");
292: }
294: /* Dump solution by converting to DMDAs and dumping */
295: if (dump_solution) PetscCall(DumpSolution(ctx, ctx->n_levels - 1, x));
297: /* Destroy PETSc objects and finalize */
298: PetscCall(MatDestroy(&A));
299: PetscCall(PetscFree(A));
300: if (A_faces) {
301: for (PetscInt level = 0; level < ctx->n_levels; ++level) {
302: if (A_faces[level]) PetscCall(MatDestroy(&A_faces[level]));
303: }
304: PetscCall(PetscFree(A_faces));
305: }
306: if (P) PetscCall(MatDestroy(&P));
307: PetscCall(VecDestroy(&x));
308: PetscCall(VecDestroy(&b));
309: PetscCall(MatDestroy(&S_hat));
310: PetscCall(KSPDestroy(&ksp));
311: PetscCall(CtxDestroy(&ctx));
312: PetscCall(PetscFinalize());
313: return 0;
314: }
316: static PetscScalar GetEta_constant(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
317: {
318: (void)ctx;
319: (void)x;
320: (void)y;
321: (void)z;
322: return 1.0;
323: }
325: static PetscScalar GetRho_layers(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
326: {
327: (void)y;
328: (void)z;
329: return PetscRealPart(x) < (ctx->xmax - ctx->xmin) / 2.0 ? ctx->rho1 : ctx->rho2;
330: }
332: static PetscScalar GetEta_layers(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
333: {
334: (void)y;
335: (void)z;
336: return PetscRealPart(x) < (ctx->xmax - ctx->xmin) / 2.0 ? ctx->eta1 : ctx->eta2;
337: }
339: static PetscScalar GetRho_sinker_box2(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
340: {
341: (void)z;
342: const PetscReal d = ctx->xmax - ctx->xmin;
343: const PetscReal xx = PetscRealPart(x) / d - 0.5;
344: const PetscReal yy = PetscRealPart(y) / d - 0.5;
345: return (xx * xx > 0.15 * 0.15 || yy * yy > 0.15 * 0.15) ? ctx->rho1 : ctx->rho2;
346: }
348: static PetscScalar GetEta_sinker_box2(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
349: {
350: (void)z;
351: const PetscReal d = ctx->xmax - ctx->xmin;
352: const PetscReal xx = PetscRealPart(x) / d - 0.5;
353: const PetscReal yy = PetscRealPart(y) / d - 0.5;
354: return (xx * xx > 0.15 * 0.15 || yy * yy > 0.15 * 0.15) ? ctx->eta1 : ctx->eta2;
355: }
357: static PetscScalar GetRho_sinker_box3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
358: {
359: const PetscReal d = ctx->xmax - ctx->xmin;
360: const PetscReal xx = PetscRealPart(x) / d - 0.5;
361: const PetscReal yy = PetscRealPart(y) / d - 0.5;
362: const PetscReal zz = PetscRealPart(z) / d - 0.5;
363: const PetscReal half_width = 0.15;
364: return (PetscAbsReal(xx) > half_width || PetscAbsReal(yy) > half_width || PetscAbsReal(zz) > half_width) ? ctx->rho1 : ctx->rho2;
365: }
367: static PetscScalar GetEta_sinker_box3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
368: {
369: const PetscReal d = ctx->xmax - ctx->xmin;
370: const PetscReal xx = PetscRealPart(x) / d - 0.5;
371: const PetscReal yy = PetscRealPart(y) / d - 0.5;
372: const PetscReal zz = PetscRealPart(z) / d - 0.5;
373: const PetscReal half_width = 0.15;
374: return (PetscAbsReal(xx) > half_width || PetscAbsReal(yy) > half_width || PetscAbsReal(zz) > half_width) ? ctx->eta1 : ctx->eta2;
375: }
377: static PetscScalar GetRho_sinker_sphere3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
378: {
379: const PetscReal d = ctx->xmax - ctx->xmin;
380: const PetscReal xx = PetscRealPart(x) / d - 0.5;
381: const PetscReal yy = PetscRealPart(y) / d - 0.5;
382: const PetscReal zz = PetscRealPart(z) / d - 0.5;
383: const PetscReal half_width = 0.3;
384: return (xx * xx + yy * yy + zz * zz > half_width * half_width) ? ctx->rho1 : ctx->rho2;
385: }
387: static PetscScalar GetEta_sinker_sphere3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
388: {
389: const PetscReal d = ctx->xmax - ctx->xmin;
390: const PetscReal xx = PetscRealPart(x) / d - 0.5;
391: const PetscReal yy = PetscRealPart(y) / d - 0.5;
392: const PetscReal zz = PetscRealPart(z) / d - 0.5;
393: const PetscReal half_width = 0.3;
394: return (xx * xx + yy * yy + zz * zz > half_width * half_width) ? ctx->eta1 : ctx->eta2;
395: }
397: static PetscScalar GetEta_blob3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
398: {
399: const PetscReal d = ctx->xmax - ctx->xmin;
400: const PetscReal xx = PetscRealPart(x) / d - 0.5;
401: const PetscReal yy = PetscRealPart(y) / d - 0.5;
402: const PetscReal zz = PetscRealPart(z) / d - 0.5;
403: return ctx->eta1 + ctx->eta2 * PetscExpScalar(-20.0 * (xx * xx + yy * yy + zz * zz));
404: }
406: static PetscScalar GetRho_blob3(Ctx ctx, PetscScalar x, PetscScalar y, PetscScalar z)
407: {
408: const PetscReal d = ctx->xmax - ctx->xmin;
409: const PetscReal xx = PetscRealPart(x) / d - 0.5;
410: const PetscReal yy = PetscRealPart(y) / d - 0.5;
411: const PetscReal zz = PetscRealPart(z) / d - 0.5;
412: return ctx->rho1 + ctx->rho2 * PetscExpScalar(-20.0 * (xx * xx + yy * yy + zz * zz));
413: }
415: static PetscErrorCode LevelCtxCreate(LevelCtx *p_level_ctx)
416: {
417: LevelCtx level_ctx;
419: PetscFunctionBeginUser;
420: PetscCall(PetscMalloc1(1, p_level_ctx));
421: level_ctx = *p_level_ctx;
422: level_ctx->dm_stokes = NULL;
423: level_ctx->dm_coefficients = NULL;
424: level_ctx->dm_faces = NULL;
425: PetscFunctionReturn(PETSC_SUCCESS);
426: }
428: static PetscErrorCode LevelCtxDestroy(LevelCtx *p_level_ctx)
429: {
430: LevelCtx level_ctx;
432: PetscFunctionBeginUser;
433: level_ctx = *p_level_ctx;
434: if (level_ctx->dm_stokes) PetscCall(DMDestroy(&level_ctx->dm_stokes));
435: if (level_ctx->dm_coefficients) PetscCall(DMDestroy(&level_ctx->dm_coefficients));
436: if (level_ctx->dm_faces) PetscCall(DMDestroy(&level_ctx->dm_faces));
437: if (level_ctx->coeff) PetscCall(VecDestroy(&level_ctx->coeff));
438: PetscCall(PetscFree(*p_level_ctx));
439: PetscFunctionReturn(PETSC_SUCCESS);
440: }
442: static PetscErrorCode CtxCreateAndSetFromOptions(Ctx *p_ctx)
443: {
444: Ctx ctx;
446: PetscFunctionBeginUser;
447: PetscCall(PetscMalloc1(1, p_ctx));
448: ctx = *p_ctx;
450: ctx->comm = PETSC_COMM_WORLD;
451: ctx->pin_pressure = PETSC_FALSE;
452: PetscCall(PetscOptionsGetBool(NULL, NULL, "-pin_pressure", &ctx->pin_pressure, NULL));
453: ctx->dim = 3;
454: PetscCall(PetscOptionsGetInt(NULL, NULL, "-dim", &ctx->dim, NULL));
455: if (ctx->dim <= 2) {
456: ctx->cells_x = 32;
457: } else {
458: ctx->cells_x = 16;
459: }
460: PetscCall(PetscOptionsGetInt(NULL, NULL, "-s", &ctx->cells_x, NULL)); /* shortcut. Usually, use -stag_grid_x etc. */
461: ctx->cells_z = ctx->cells_y = ctx->cells_x;
462: ctx->xmin = ctx->ymin = ctx->zmin = 0.0;
463: {
464: PetscBool nondimensional = PETSC_TRUE;
466: PetscCall(PetscOptionsGetBool(NULL, NULL, "-nondimensional", &nondimensional, NULL));
467: if (nondimensional) {
468: ctx->xmax = ctx->ymax = ctx->zmax = 1.0;
469: ctx->rho1 = 0.0;
470: ctx->rho2 = 1.0;
471: ctx->eta1 = 1.0;
472: ctx->eta2 = 1e2;
473: ctx->gy = -1.0; /* downwards */
474: } else {
475: ctx->xmax = 1e6;
476: ctx->ymax = 1.5e6;
477: ctx->zmax = 1e6;
478: ctx->rho1 = 3200;
479: ctx->rho2 = 3300;
480: ctx->eta1 = 1e20;
481: ctx->eta2 = 1e22;
482: ctx->gy = -10.0; /* downwards */
483: }
484: }
485: {
486: PetscBool isoviscous;
488: isoviscous = PETSC_FALSE;
489: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-eta1", &ctx->eta1, NULL));
490: PetscCall(PetscOptionsGetBool(NULL, NULL, "-isoviscous", &isoviscous, NULL));
491: if (isoviscous) {
492: ctx->eta2 = ctx->eta1;
493: ctx->GetEta = GetEta_constant; /* override */
494: } else {
495: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-eta2", &ctx->eta2, NULL));
496: }
497: }
498: {
499: char mode[1024] = "sinker";
500: PetscBool is_layers, is_blob, is_sinker_box, is_sinker_sphere;
502: PetscCall(PetscOptionsGetString(NULL, NULL, "-coefficients", mode, sizeof(mode), NULL));
503: PetscCall(PetscStrncmp(mode, "layers", sizeof(mode), &is_layers));
504: PetscCall(PetscStrncmp(mode, "sinker", sizeof(mode), &is_sinker_box));
505: if (!is_sinker_box) PetscCall(PetscStrncmp(mode, "sinker_box", sizeof(mode), &is_sinker_box));
506: PetscCall(PetscStrncmp(mode, "sinker_sphere", sizeof(mode), &is_sinker_sphere));
507: PetscCall(PetscStrncmp(mode, "blob", sizeof(mode), &is_blob));
509: if (is_layers) {
510: ctx->GetRho = GetRho_layers;
511: ctx->GetEta = GetEta_layers;
512: }
513: if (is_blob) {
514: if (ctx->dim == 3) {
515: ctx->GetRho = GetRho_blob3;
516: ctx->GetEta = GetEta_blob3;
517: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
518: }
519: if (is_sinker_box) {
520: if (ctx->dim == 2) {
521: ctx->GetRho = GetRho_sinker_box2;
522: ctx->GetEta = GetEta_sinker_box2;
523: } else if (ctx->dim == 3) {
524: ctx->GetRho = GetRho_sinker_box3;
525: ctx->GetEta = GetEta_sinker_box3;
526: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
527: }
528: if (is_sinker_sphere) {
529: if (ctx->dim == 3) {
530: ctx->GetRho = GetRho_sinker_sphere3;
531: ctx->GetEta = GetEta_sinker_sphere3;
532: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
533: }
534: }
536: /* Per-level data */
537: ctx->n_levels = 1;
538: PetscCall(PetscOptionsGetInt(NULL, NULL, "-levels", &ctx->n_levels, NULL));
539: PetscCall(PetscMalloc1(ctx->n_levels, &ctx->levels));
540: for (PetscInt i = 0; i < ctx->n_levels; ++i) PetscCall(LevelCtxCreate(&ctx->levels[i]));
541: PetscFunctionReturn(PETSC_SUCCESS);
542: }
544: static PetscErrorCode CtxDestroy(Ctx *p_ctx)
545: {
546: Ctx ctx;
548: PetscFunctionBeginUser;
549: ctx = *p_ctx;
550: for (PetscInt i = 0; i < ctx->n_levels; ++i) PetscCall(LevelCtxDestroy(&ctx->levels[i]));
551: PetscCall(PetscFree(ctx->levels));
552: PetscCall(PetscFree(*p_ctx));
553: PetscFunctionReturn(PETSC_SUCCESS);
554: }
556: static PetscErrorCode SystemParametersCreate(SystemParameters *parameters, Ctx ctx)
557: {
558: PetscFunctionBeginUser;
559: PetscCall(PetscMalloc1(1, parameters));
560: (*parameters)->ctx = ctx;
561: (*parameters)->level = ctx->n_levels - 1;
562: (*parameters)->include_inverse_visc = PETSC_FALSE;
563: (*parameters)->faces_only = PETSC_FALSE;
564: PetscFunctionReturn(PETSC_SUCCESS);
565: }
567: static PetscErrorCode SystemParametersDestroy(SystemParameters *parameters)
568: {
569: PetscFunctionBeginUser;
570: PetscCall(PetscFree(*parameters));
571: *parameters = NULL;
572: PetscFunctionReturn(PETSC_SUCCESS);
573: }
575: static PetscErrorCode CreateSystem2d(SystemParameters parameters, Mat *pA, Vec *pRhs)
576: {
577: PetscInt N[2];
578: PetscInt ex, ey, startx, starty, nx, ny;
579: Mat A;
580: Vec rhs;
581: PetscReal hx, hy, dv;
582: Vec coefficients_local;
583: PetscBool build_rhs;
584: DM dm_main, dm_coefficients;
585: PetscScalar K_cont, K_bound;
586: Ctx ctx = parameters->ctx;
587: PetscInt level = parameters->level;
589: PetscFunctionBeginUser;
590: if (parameters->faces_only) {
591: dm_main = ctx->levels[level]->dm_faces;
592: } else {
593: dm_main = ctx->levels[level]->dm_stokes;
594: }
595: dm_coefficients = ctx->levels[level]->dm_coefficients;
596: K_cont = ctx->levels[level]->K_cont;
597: K_bound = ctx->levels[level]->K_bound;
598: PetscCall(DMCreateMatrix(dm_main, pA));
599: A = *pA;
600: build_rhs = (PetscBool)(pRhs != NULL);
601: PetscCheck(!(parameters->faces_only && build_rhs), PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "RHS for faces-only not supported");
602: if (build_rhs) {
603: PetscCall(DMCreateGlobalVector(dm_main, pRhs));
604: rhs = *pRhs;
605: } else {
606: rhs = NULL;
607: }
608: PetscCall(DMStagGetCorners(dm_main, &startx, &starty, NULL, &nx, &ny, NULL, NULL, NULL, NULL));
609: PetscCall(DMStagGetGlobalSizes(dm_main, &N[0], &N[1], NULL));
610: hx = ctx->levels[level]->hx_characteristic;
611: hy = ctx->levels[level]->hy_characteristic;
612: dv = hx * hy;
613: PetscCall(DMGetLocalVector(dm_coefficients, &coefficients_local));
614: PetscCall(DMGlobalToLocal(dm_coefficients, ctx->levels[level]->coeff, INSERT_VALUES, coefficients_local));
616: /* Loop over all local elements */
617: for (ey = starty; ey < starty + ny; ++ey) { /* With DMStag, always iterate x fastest, y second fastest, z slowest */
618: for (ex = startx; ex < startx + nx; ++ex) {
619: const PetscBool left_boundary = (PetscBool)(ex == 0);
620: const PetscBool right_boundary = (PetscBool)(ex == N[0] - 1);
621: const PetscBool bottom_boundary = (PetscBool)(ey == 0);
622: const PetscBool top_boundary = (PetscBool)(ey == N[1] - 1);
624: if (ey == N[1] - 1) {
625: /* Top boundary velocity Dirichlet */
626: DMStagStencil row;
627: const PetscScalar val_rhs = 0.0;
628: const PetscScalar val_A = K_bound;
630: row.i = ex;
631: row.j = ey;
632: row.loc = DMSTAG_UP;
633: row.c = 0;
634: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
635: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
636: }
638: if (ey == 0) {
639: /* Bottom boundary velocity Dirichlet */
640: DMStagStencil row;
641: const PetscScalar val_rhs = 0.0;
642: const PetscScalar val_A = K_bound;
644: row.i = ex;
645: row.j = ey;
646: row.loc = DMSTAG_DOWN;
647: row.c = 0;
648: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
649: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
650: } else {
651: /* Y-momentum equation : (u_xx + u_yy) - p_y = f^y
652: includes non-zero forcing and free-slip boundary conditions */
653: PetscInt count;
654: DMStagStencil row, col[11];
655: PetscScalar val_A[11];
656: DMStagStencil rhoPoint[2];
657: PetscScalar rho[2], val_rhs;
658: DMStagStencil etaPoint[4];
659: PetscScalar eta[4], eta_left, eta_right, eta_up, eta_down;
661: row.i = ex;
662: row.j = ey;
663: row.loc = DMSTAG_DOWN;
664: row.c = 0;
666: /* get rho values and compute rhs value*/
667: rhoPoint[0].i = ex;
668: rhoPoint[0].j = ey;
669: rhoPoint[0].loc = DMSTAG_DOWN_LEFT;
670: rhoPoint[0].c = 1;
671: rhoPoint[1].i = ex;
672: rhoPoint[1].j = ey;
673: rhoPoint[1].loc = DMSTAG_DOWN_RIGHT;
674: rhoPoint[1].c = 1;
675: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 2, rhoPoint, rho));
676: val_rhs = -ctx->gy * dv * 0.5 * (rho[0] + rho[1]);
678: /* Get eta values */
679: etaPoint[0].i = ex;
680: etaPoint[0].j = ey;
681: etaPoint[0].loc = DMSTAG_DOWN_LEFT;
682: etaPoint[0].c = 0; /* Left */
683: etaPoint[1].i = ex;
684: etaPoint[1].j = ey;
685: etaPoint[1].loc = DMSTAG_DOWN_RIGHT;
686: etaPoint[1].c = 0; /* Right */
687: etaPoint[2].i = ex;
688: etaPoint[2].j = ey;
689: etaPoint[2].loc = DMSTAG_ELEMENT;
690: etaPoint[2].c = 0; /* Up */
691: etaPoint[3].i = ex;
692: etaPoint[3].j = ey - 1;
693: etaPoint[3].loc = DMSTAG_ELEMENT;
694: etaPoint[3].c = 0; /* Down */
695: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 4, etaPoint, eta));
696: eta_left = eta[0];
697: eta_right = eta[1];
698: eta_up = eta[2];
699: eta_down = eta[3];
701: count = 0;
703: col[count] = row;
704: val_A[count] = -2.0 * dv * (eta_down + eta_up) / (hy * hy);
705: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
706: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
707: ++count;
709: col[count].i = ex;
710: col[count].j = ey - 1;
711: col[count].loc = DMSTAG_DOWN;
712: col[count].c = 0;
713: val_A[count] = 2.0 * dv * eta_down / (hy * hy);
714: ++count;
715: col[count].i = ex;
716: col[count].j = ey + 1;
717: col[count].loc = DMSTAG_DOWN;
718: col[count].c = 0;
719: val_A[count] = 2.0 * dv * eta_up / (hy * hy);
720: ++count;
721: if (!left_boundary) {
722: col[count].i = ex - 1;
723: col[count].j = ey;
724: col[count].loc = DMSTAG_DOWN;
725: col[count].c = 0;
726: val_A[count] = dv * eta_left / (hx * hx);
727: ++count;
728: }
729: if (!right_boundary) {
730: col[count].i = ex + 1;
731: col[count].j = ey;
732: col[count].loc = DMSTAG_DOWN;
733: col[count].c = 0;
734: val_A[count] = dv * eta_right / (hx * hx);
735: ++count;
736: }
737: col[count].i = ex;
738: col[count].j = ey - 1;
739: col[count].loc = DMSTAG_LEFT;
740: col[count].c = 0;
741: val_A[count] = dv * eta_left / (hx * hy);
742: ++count; /* down left x edge */
743: col[count].i = ex;
744: col[count].j = ey - 1;
745: col[count].loc = DMSTAG_RIGHT;
746: col[count].c = 0;
747: val_A[count] = -1.0 * dv * eta_right / (hx * hy);
748: ++count; /* down right x edge */
749: col[count].i = ex;
750: col[count].j = ey;
751: col[count].loc = DMSTAG_LEFT;
752: col[count].c = 0;
753: val_A[count] = -1.0 * dv * eta_left / (hx * hy);
754: ++count; /* up left x edge */
755: col[count].i = ex;
756: col[count].j = ey;
757: col[count].loc = DMSTAG_RIGHT;
758: col[count].c = 0;
759: val_A[count] = dv * eta_right / (hx * hy);
760: ++count; /* up right x edge */
761: if (!parameters->faces_only) {
762: col[count].i = ex;
763: col[count].j = ey - 1;
764: col[count].loc = DMSTAG_ELEMENT;
765: col[count].c = 0;
766: val_A[count] = K_cont * dv / hy;
767: ++count;
768: col[count].i = ex;
769: col[count].j = ey;
770: col[count].loc = DMSTAG_ELEMENT;
771: col[count].c = 0;
772: val_A[count] = -1.0 * K_cont * dv / hy;
773: ++count;
774: }
776: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
777: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
778: }
780: if (ex == N[0] - 1) {
781: /* Right Boundary velocity Dirichlet */
782: /* Redundant in the corner */
783: DMStagStencil row;
784: const PetscScalar val_rhs = 0.0;
785: const PetscScalar val_A = K_bound;
787: row.i = ex;
788: row.j = ey;
789: row.loc = DMSTAG_RIGHT;
790: row.c = 0;
791: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
792: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
793: }
794: if (ex == 0) {
795: /* Left velocity Dirichlet */
796: DMStagStencil row;
797: const PetscScalar val_rhs = 0.0;
798: const PetscScalar val_A = K_bound;
800: row.i = ex;
801: row.j = ey;
802: row.loc = DMSTAG_LEFT;
803: row.c = 0;
804: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
805: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
806: } else {
807: /* X-momentum equation : (u_xx + u_yy) - p_x = f^x
808: zero RHS, including free-slip boundary conditions */
809: PetscInt count;
810: DMStagStencil row, col[11];
811: PetscScalar val_A[11];
812: DMStagStencil etaPoint[4];
813: PetscScalar eta[4], eta_left, eta_right, eta_up, eta_down;
814: const PetscScalar val_rhs = 0.0;
816: row.i = ex;
817: row.j = ey;
818: row.loc = DMSTAG_LEFT;
819: row.c = 0;
821: /* Get eta values */
822: etaPoint[0].i = ex - 1;
823: etaPoint[0].j = ey;
824: etaPoint[0].loc = DMSTAG_ELEMENT;
825: etaPoint[0].c = 0; /* Left */
826: etaPoint[1].i = ex;
827: etaPoint[1].j = ey;
828: etaPoint[1].loc = DMSTAG_ELEMENT;
829: etaPoint[1].c = 0; /* Right */
830: etaPoint[2].i = ex;
831: etaPoint[2].j = ey;
832: etaPoint[2].loc = DMSTAG_UP_LEFT;
833: etaPoint[2].c = 0; /* Up */
834: etaPoint[3].i = ex;
835: etaPoint[3].j = ey;
836: etaPoint[3].loc = DMSTAG_DOWN_LEFT;
837: etaPoint[3].c = 0; /* Down */
838: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 4, etaPoint, eta));
839: eta_left = eta[0];
840: eta_right = eta[1];
841: eta_up = eta[2];
842: eta_down = eta[3];
844: count = 0;
845: col[count] = row;
846: val_A[count] = -2.0 * dv * (eta_left + eta_right) / (hx * hx);
847: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
848: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
849: ++count;
851: if (!bottom_boundary) {
852: col[count].i = ex;
853: col[count].j = ey - 1;
854: col[count].loc = DMSTAG_LEFT;
855: col[count].c = 0;
856: val_A[count] = dv * eta_down / (hy * hy);
857: ++count;
858: }
859: if (!top_boundary) {
860: col[count].i = ex;
861: col[count].j = ey + 1;
862: col[count].loc = DMSTAG_LEFT;
863: col[count].c = 0;
864: val_A[count] = dv * eta_up / (hy * hy);
865: ++count;
866: }
867: col[count].i = ex - 1;
868: col[count].j = ey;
869: col[count].loc = DMSTAG_LEFT;
870: col[count].c = 0;
871: val_A[count] = 2.0 * dv * eta_left / (hx * hx);
872: ++count;
873: col[count].i = ex + 1;
874: col[count].j = ey;
875: col[count].loc = DMSTAG_LEFT;
876: col[count].c = 0;
877: val_A[count] = 2.0 * dv * eta_right / (hx * hx);
878: ++count;
879: col[count].i = ex - 1;
880: col[count].j = ey;
881: col[count].loc = DMSTAG_DOWN;
882: col[count].c = 0;
883: val_A[count] = dv * eta_down / (hx * hy);
884: ++count; /* down left */
885: col[count].i = ex;
886: col[count].j = ey;
887: col[count].loc = DMSTAG_DOWN;
888: col[count].c = 0;
889: val_A[count] = -1.0 * dv * eta_down / (hx * hy);
890: ++count; /* down right */
891: col[count].i = ex - 1;
892: col[count].j = ey;
893: col[count].loc = DMSTAG_UP;
894: col[count].c = 0;
895: val_A[count] = -1.0 * dv * eta_up / (hx * hy);
896: ++count; /* up left */
897: col[count].i = ex;
898: col[count].j = ey;
899: col[count].loc = DMSTAG_UP;
900: col[count].c = 0;
901: val_A[count] = dv * eta_up / (hx * hy);
902: ++count; /* up right */
903: if (!parameters->faces_only) {
904: col[count].i = ex - 1;
905: col[count].j = ey;
906: col[count].loc = DMSTAG_ELEMENT;
907: col[count].c = 0;
908: val_A[count] = K_cont * dv / hx;
909: ++count;
910: col[count].i = ex;
911: col[count].j = ey;
912: col[count].loc = DMSTAG_ELEMENT;
913: col[count].c = 0;
914: val_A[count] = -1.0 * K_cont * dv / hx;
915: ++count;
916: }
918: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
919: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
920: }
922: /* P equation : u_x + v_y = 0
924: Note that this includes an explicit zero on the diagonal. This is only needed for
925: direct solvers (not required if using an iterative solver and setting the constant-pressure nullspace)
927: Note: the scaling by dv is not chosen in a principled way and is likely sub-optimal
928: */
929: if (!parameters->faces_only) {
930: if (ctx->pin_pressure && ex == 0 && ey == 0) { /* Pin the first pressure node to zero, if requested */
931: DMStagStencil row;
932: const PetscScalar val_A = K_bound;
933: const PetscScalar val_rhs = 0.0;
935: row.i = ex;
936: row.j = ey;
937: row.loc = DMSTAG_ELEMENT;
938: row.c = 0;
939: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
940: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
941: } else {
942: DMStagStencil row, col[5];
943: PetscScalar val_A[5];
944: const PetscScalar val_rhs = 0.0;
946: row.i = ex;
947: row.j = ey;
948: row.loc = DMSTAG_ELEMENT;
949: row.c = 0;
950: col[0].i = ex;
951: col[0].j = ey;
952: col[0].loc = DMSTAG_LEFT;
953: col[0].c = 0;
954: val_A[0] = -1.0 * K_cont * dv / hx;
955: col[1].i = ex;
956: col[1].j = ey;
957: col[1].loc = DMSTAG_RIGHT;
958: col[1].c = 0;
959: val_A[1] = K_cont * dv / hx;
960: col[2].i = ex;
961: col[2].j = ey;
962: col[2].loc = DMSTAG_DOWN;
963: col[2].c = 0;
964: val_A[2] = -1.0 * K_cont * dv / hy;
965: col[3].i = ex;
966: col[3].j = ey;
967: col[3].loc = DMSTAG_UP;
968: col[3].c = 0;
969: val_A[3] = K_cont * dv / hy;
970: col[4] = row;
971: val_A[4] = 0.0;
972: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 5, col, val_A, INSERT_VALUES));
973: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
974: }
975: }
976: }
977: }
978: PetscCall(DMRestoreLocalVector(dm_coefficients, &coefficients_local));
980: /* Add additional inverse viscosity terms (for use in building a preconditioning matrix) */
981: if (parameters->include_inverse_visc) {
982: PetscCheck(!parameters->faces_only, PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "Does not make sense with faces only");
983: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_main, dm_coefficients, ctx->levels[level]->coeff, 1.0, A));
984: }
986: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
987: if (build_rhs) PetscCall(VecAssemblyBegin(rhs));
988: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
989: if (build_rhs) PetscCall(VecAssemblyEnd(rhs));
990: PetscFunctionReturn(PETSC_SUCCESS);
991: }
993: static PetscErrorCode CreateSystem3d(SystemParameters parameters, Mat *pA, Vec *pRhs)
994: {
995: PetscInt N[3];
996: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
997: Mat A;
998: PetscReal hx, hy, hz, dv;
999: PetscInt pinx, piny, pinz;
1000: Vec coeff_local, rhs;
1001: PetscBool build_rhs;
1002: DM dm_main, dm_coefficients;
1003: PetscScalar K_cont, K_bound;
1004: Ctx ctx = parameters->ctx;
1005: PetscInt level = parameters->level;
1007: PetscFunctionBeginUser;
1008: if (parameters->faces_only) {
1009: dm_main = ctx->levels[level]->dm_faces;
1010: } else {
1011: dm_main = ctx->levels[level]->dm_stokes;
1012: }
1013: dm_coefficients = ctx->levels[level]->dm_coefficients;
1014: K_cont = ctx->levels[level]->K_cont;
1015: K_bound = ctx->levels[level]->K_bound;
1016: PetscCall(DMCreateMatrix(dm_main, pA));
1017: A = *pA;
1018: build_rhs = (PetscBool)(pRhs != NULL);
1019: if (build_rhs) {
1020: PetscCall(DMCreateGlobalVector(dm_main, pRhs));
1021: rhs = *pRhs;
1022: } else {
1023: rhs = NULL;
1024: }
1025: PetscCall(DMStagGetCorners(dm_main, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
1026: PetscCall(DMStagGetGlobalSizes(dm_main, &N[0], &N[1], &N[2]));
1027: hx = ctx->levels[level]->hx_characteristic;
1028: hy = ctx->levels[level]->hy_characteristic;
1029: hz = ctx->levels[level]->hz_characteristic;
1030: dv = hx * hy * hz;
1031: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1032: PetscCall(DMGlobalToLocal(dm_coefficients, ctx->levels[level]->coeff, INSERT_VALUES, coeff_local));
1034: PetscCheck(N[0] >= 2 && N[1] >= 2 && N[2] >= 2, PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for less than 2 elements in any direction");
1035: pinx = 1;
1036: piny = 0;
1037: pinz = 0; /* Depends on assertion above that there are at least two element in the x direction */
1039: /* Loop over all local elements.
1041: For each element, fill 4-7 rows of the matrix, corresponding to
1042: - the pressure degree of freedom (dof), centered on the element
1043: - the 3 velocity dofs on left, bottom, and back faces of the element
1044: - velocity dof on the right, top, and front faces of the element (only on domain boundaries)
1046: */
1047: for (ez = startz; ez < startz + nz; ++ez) {
1048: for (ey = starty; ey < starty + ny; ++ey) {
1049: for (ex = startx; ex < startx + nx; ++ex) {
1050: const PetscBool left_boundary = (PetscBool)(ex == 0);
1051: const PetscBool right_boundary = (PetscBool)(ex == N[0] - 1);
1052: const PetscBool bottom_boundary = (PetscBool)(ey == 0);
1053: const PetscBool top_boundary = (PetscBool)(ey == N[1] - 1);
1054: const PetscBool back_boundary = (PetscBool)(ez == 0);
1055: const PetscBool front_boundary = (PetscBool)(ez == N[2] - 1);
1057: /* Note that below, we depend on the check above that there is never one
1058: element (globally) in a given direction. Thus, for example, an
1059: element is never both on the left and right boundary */
1061: /* X-faces - right boundary */
1062: if (right_boundary) {
1063: /* Right x-velocity Dirichlet */
1064: DMStagStencil row;
1065: const PetscScalar val_rhs = 0.0;
1066: const PetscScalar val_A = K_bound;
1068: row.i = ex;
1069: row.j = ey;
1070: row.k = ez;
1071: row.loc = DMSTAG_RIGHT;
1072: row.c = 0;
1073: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1074: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1075: }
1077: /* X faces - left*/
1078: {
1079: DMStagStencil row;
1081: row.i = ex;
1082: row.j = ey;
1083: row.k = ez;
1084: row.loc = DMSTAG_LEFT;
1085: row.c = 0;
1087: if (left_boundary) {
1088: /* Left x-velocity Dirichlet */
1089: const PetscScalar val_rhs = 0.0;
1090: const PetscScalar val_A = K_bound;
1092: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1093: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1094: } else {
1095: /* X-momentum equation */
1096: PetscInt count;
1097: DMStagStencil col[17];
1098: PetscScalar val_A[17];
1099: DMStagStencil eta_point[6];
1100: PetscScalar eta[6], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the left face */
1101: const PetscScalar val_rhs = 0.0;
1103: /* Get eta values */
1104: eta_point[0].i = ex - 1;
1105: eta_point[0].j = ey;
1106: eta_point[0].k = ez;
1107: eta_point[0].loc = DMSTAG_ELEMENT;
1108: eta_point[0].c = 0; /* Left */
1109: eta_point[1].i = ex;
1110: eta_point[1].j = ey;
1111: eta_point[1].k = ez;
1112: eta_point[1].loc = DMSTAG_ELEMENT;
1113: eta_point[1].c = 0; /* Right */
1114: eta_point[2].i = ex;
1115: eta_point[2].j = ey;
1116: eta_point[2].k = ez;
1117: eta_point[2].loc = DMSTAG_DOWN_LEFT;
1118: eta_point[2].c = 0; /* Down */
1119: eta_point[3].i = ex;
1120: eta_point[3].j = ey;
1121: eta_point[3].k = ez;
1122: eta_point[3].loc = DMSTAG_UP_LEFT;
1123: eta_point[3].c = 0; /* Up */
1124: eta_point[4].i = ex;
1125: eta_point[4].j = ey;
1126: eta_point[4].k = ez;
1127: eta_point[4].loc = DMSTAG_BACK_LEFT;
1128: eta_point[4].c = 0; /* Back */
1129: eta_point[5].i = ex;
1130: eta_point[5].j = ey;
1131: eta_point[5].k = ez;
1132: eta_point[5].loc = DMSTAG_FRONT_LEFT;
1133: eta_point[5].c = 0; /* Front */
1134: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1135: eta_left = eta[0];
1136: eta_right = eta[1];
1137: eta_down = eta[2];
1138: eta_up = eta[3];
1139: eta_back = eta[4];
1140: eta_front = eta[5];
1142: count = 0;
1144: col[count] = row;
1145: val_A[count] = -2.0 * dv * (eta_left + eta_right) / (hx * hx);
1146: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
1147: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
1148: if (!back_boundary) val_A[count] += -1.0 * dv * eta_back / (hz * hz);
1149: if (!front_boundary) val_A[count] += -1.0 * dv * eta_front / (hz * hz);
1150: ++count;
1152: col[count].i = ex - 1;
1153: col[count].j = ey;
1154: col[count].k = ez;
1155: col[count].loc = DMSTAG_LEFT;
1156: col[count].c = 0;
1157: val_A[count] = 2.0 * dv * eta_left / (hx * hx);
1158: ++count;
1159: col[count].i = ex + 1;
1160: col[count].j = ey;
1161: col[count].k = ez;
1162: col[count].loc = DMSTAG_LEFT;
1163: col[count].c = 0;
1164: val_A[count] = 2.0 * dv * eta_right / (hx * hx);
1165: ++count;
1166: if (!bottom_boundary) {
1167: col[count].i = ex;
1168: col[count].j = ey - 1;
1169: col[count].k = ez;
1170: col[count].loc = DMSTAG_LEFT;
1171: col[count].c = 0;
1172: val_A[count] = dv * eta_down / (hy * hy);
1173: ++count;
1174: }
1175: if (!top_boundary) {
1176: col[count].i = ex;
1177: col[count].j = ey + 1;
1178: col[count].k = ez;
1179: col[count].loc = DMSTAG_LEFT;
1180: col[count].c = 0;
1181: val_A[count] = dv * eta_up / (hy * hy);
1182: ++count;
1183: }
1184: if (!back_boundary) {
1185: col[count].i = ex;
1186: col[count].j = ey;
1187: col[count].k = ez - 1;
1188: col[count].loc = DMSTAG_LEFT;
1189: col[count].c = 0;
1190: val_A[count] = dv * eta_back / (hz * hz);
1191: ++count;
1192: }
1193: if (!front_boundary) {
1194: col[count].i = ex;
1195: col[count].j = ey;
1196: col[count].k = ez + 1;
1197: col[count].loc = DMSTAG_LEFT;
1198: col[count].c = 0;
1199: val_A[count] = dv * eta_front / (hz * hz);
1200: ++count;
1201: }
1203: col[count].i = ex - 1;
1204: col[count].j = ey;
1205: col[count].k = ez;
1206: col[count].loc = DMSTAG_DOWN;
1207: col[count].c = 0;
1208: val_A[count] = dv * eta_down / (hx * hy);
1209: ++count; /* down left */
1210: col[count].i = ex;
1211: col[count].j = ey;
1212: col[count].k = ez;
1213: col[count].loc = DMSTAG_DOWN;
1214: col[count].c = 0;
1215: val_A[count] = -1.0 * dv * eta_down / (hx * hy);
1216: ++count; /* down right */
1218: col[count].i = ex - 1;
1219: col[count].j = ey;
1220: col[count].k = ez;
1221: col[count].loc = DMSTAG_UP;
1222: col[count].c = 0;
1223: val_A[count] = -1.0 * dv * eta_up / (hx * hy);
1224: ++count; /* up left */
1225: col[count].i = ex;
1226: col[count].j = ey;
1227: col[count].k = ez;
1228: col[count].loc = DMSTAG_UP;
1229: col[count].c = 0;
1230: val_A[count] = dv * eta_up / (hx * hy);
1231: ++count; /* up right */
1233: col[count].i = ex - 1;
1234: col[count].j = ey;
1235: col[count].k = ez;
1236: col[count].loc = DMSTAG_BACK;
1237: col[count].c = 0;
1238: val_A[count] = dv * eta_back / (hx * hz);
1239: ++count; /* back left */
1240: col[count].i = ex;
1241: col[count].j = ey;
1242: col[count].k = ez;
1243: col[count].loc = DMSTAG_BACK;
1244: col[count].c = 0;
1245: val_A[count] = -1.0 * dv * eta_back / (hx * hz);
1246: ++count; /* back right */
1248: col[count].i = ex - 1;
1249: col[count].j = ey;
1250: col[count].k = ez;
1251: col[count].loc = DMSTAG_FRONT;
1252: col[count].c = 0;
1253: val_A[count] = -1.0 * dv * eta_front / (hx * hz);
1254: ++count; /* front left */
1255: col[count].i = ex;
1256: col[count].j = ey;
1257: col[count].k = ez;
1258: col[count].loc = DMSTAG_FRONT;
1259: col[count].c = 0;
1260: val_A[count] = dv * eta_front / (hx * hz);
1261: ++count; /* front right */
1263: if (!parameters->faces_only) {
1264: col[count].i = ex - 1;
1265: col[count].j = ey;
1266: col[count].k = ez;
1267: col[count].loc = DMSTAG_ELEMENT;
1268: col[count].c = 0;
1269: val_A[count] = K_cont * dv / hx;
1270: ++count;
1271: col[count].i = ex;
1272: col[count].j = ey;
1273: col[count].k = ez;
1274: col[count].loc = DMSTAG_ELEMENT;
1275: col[count].c = 0;
1276: val_A[count] = -1.0 * K_cont * dv / hx;
1277: ++count;
1278: }
1280: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1281: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1282: }
1283: }
1285: /* Y faces - top boundary */
1286: if (top_boundary) {
1287: /* Top y-velocity Dirichlet */
1288: DMStagStencil row;
1289: const PetscScalar val_rhs = 0.0;
1290: const PetscScalar val_A = K_bound;
1292: row.i = ex;
1293: row.j = ey;
1294: row.k = ez;
1295: row.loc = DMSTAG_UP;
1296: row.c = 0;
1297: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1298: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1299: }
1301: /* Y faces - down */
1302: {
1303: DMStagStencil row;
1305: row.i = ex;
1306: row.j = ey;
1307: row.k = ez;
1308: row.loc = DMSTAG_DOWN;
1309: row.c = 0;
1311: if (bottom_boundary) {
1312: /* Bottom y-velocity Dirichlet */
1313: const PetscScalar val_rhs = 0.0;
1314: const PetscScalar val_A = K_bound;
1316: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1317: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1318: } else {
1319: /* Y-momentum equation (including non-zero forcing) */
1320: PetscInt count;
1321: DMStagStencil col[17];
1322: PetscScalar val_rhs, val_A[17];
1323: DMStagStencil eta_point[6], rho_point[4];
1324: PetscScalar eta[6], rho[4], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the bottom face */
1326: if (build_rhs) {
1327: /* get rho values (note .c = 1) */
1328: /* Note that we have rho at perhaps strange points (edges not corners) */
1329: rho_point[0].i = ex;
1330: rho_point[0].j = ey;
1331: rho_point[0].k = ez;
1332: rho_point[0].loc = DMSTAG_DOWN_LEFT;
1333: rho_point[0].c = 1;
1334: rho_point[1].i = ex;
1335: rho_point[1].j = ey;
1336: rho_point[1].k = ez;
1337: rho_point[1].loc = DMSTAG_DOWN_RIGHT;
1338: rho_point[1].c = 1;
1339: rho_point[2].i = ex;
1340: rho_point[2].j = ey;
1341: rho_point[2].k = ez;
1342: rho_point[2].loc = DMSTAG_BACK_DOWN;
1343: rho_point[2].c = 1;
1344: rho_point[3].i = ex;
1345: rho_point[3].j = ey;
1346: rho_point[3].k = ez;
1347: rho_point[3].loc = DMSTAG_FRONT_DOWN;
1348: rho_point[3].c = 1;
1349: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 4, rho_point, rho));
1351: /* Compute forcing */
1352: val_rhs = ctx->gy * dv * (0.25 * (rho[0] + rho[1] + rho[2] + rho[3]));
1353: }
1355: /* Get eta values */
1356: eta_point[0].i = ex;
1357: eta_point[0].j = ey;
1358: eta_point[0].k = ez;
1359: eta_point[0].loc = DMSTAG_DOWN_LEFT;
1360: eta_point[0].c = 0; /* Left */
1361: eta_point[1].i = ex;
1362: eta_point[1].j = ey;
1363: eta_point[1].k = ez;
1364: eta_point[1].loc = DMSTAG_DOWN_RIGHT;
1365: eta_point[1].c = 0; /* Right */
1366: eta_point[2].i = ex;
1367: eta_point[2].j = ey - 1;
1368: eta_point[2].k = ez;
1369: eta_point[2].loc = DMSTAG_ELEMENT;
1370: eta_point[2].c = 0; /* Down */
1371: eta_point[3].i = ex;
1372: eta_point[3].j = ey;
1373: eta_point[3].k = ez;
1374: eta_point[3].loc = DMSTAG_ELEMENT;
1375: eta_point[3].c = 0; /* Up */
1376: eta_point[4].i = ex;
1377: eta_point[4].j = ey;
1378: eta_point[4].k = ez;
1379: eta_point[4].loc = DMSTAG_BACK_DOWN;
1380: eta_point[4].c = 0; /* Back */
1381: eta_point[5].i = ex;
1382: eta_point[5].j = ey;
1383: eta_point[5].k = ez;
1384: eta_point[5].loc = DMSTAG_FRONT_DOWN;
1385: eta_point[5].c = 0; /* Front */
1386: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1387: eta_left = eta[0];
1388: eta_right = eta[1];
1389: eta_down = eta[2];
1390: eta_up = eta[3];
1391: eta_back = eta[4];
1392: eta_front = eta[5];
1394: count = 0;
1396: col[count] = row;
1397: val_A[count] = -2.0 * dv * (eta_up + eta_down) / (hy * hy);
1398: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
1399: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
1400: if (!back_boundary) val_A[count] += -1.0 * dv * eta_back / (hz * hz);
1401: if (!front_boundary) val_A[count] += -1.0 * dv * eta_front / (hz * hz);
1402: ++count;
1404: col[count].i = ex;
1405: col[count].j = ey - 1;
1406: col[count].k = ez;
1407: col[count].loc = DMSTAG_DOWN;
1408: col[count].c = 0;
1409: val_A[count] = 2.0 * dv * eta_down / (hy * hy);
1410: ++count;
1411: col[count].i = ex;
1412: col[count].j = ey + 1;
1413: col[count].k = ez;
1414: col[count].loc = DMSTAG_DOWN;
1415: col[count].c = 0;
1416: val_A[count] = 2.0 * dv * eta_up / (hy * hy);
1417: ++count;
1419: if (!left_boundary) {
1420: col[count].i = ex - 1;
1421: col[count].j = ey;
1422: col[count].k = ez;
1423: col[count].loc = DMSTAG_DOWN;
1424: col[count].c = 0;
1425: val_A[count] = dv * eta_left / (hx * hx);
1426: ++count;
1427: }
1428: if (!right_boundary) {
1429: col[count].i = ex + 1;
1430: col[count].j = ey;
1431: col[count].k = ez;
1432: col[count].loc = DMSTAG_DOWN;
1433: col[count].c = 0;
1434: val_A[count] = dv * eta_right / (hx * hx);
1435: ++count;
1436: }
1437: if (!back_boundary) {
1438: col[count].i = ex;
1439: col[count].j = ey;
1440: col[count].k = ez - 1;
1441: col[count].loc = DMSTAG_DOWN;
1442: col[count].c = 0;
1443: val_A[count] = dv * eta_back / (hz * hz);
1444: ++count;
1445: }
1446: if (!front_boundary) {
1447: col[count].i = ex;
1448: col[count].j = ey;
1449: col[count].k = ez + 1;
1450: col[count].loc = DMSTAG_DOWN;
1451: col[count].c = 0;
1452: val_A[count] = dv * eta_front / (hz * hz);
1453: ++count;
1454: }
1456: col[count].i = ex;
1457: col[count].j = ey - 1;
1458: col[count].k = ez;
1459: col[count].loc = DMSTAG_LEFT;
1460: col[count].c = 0;
1461: val_A[count] = dv * eta_left / (hx * hy);
1462: ++count; /* down left*/
1463: col[count].i = ex;
1464: col[count].j = ey;
1465: col[count].k = ez;
1466: col[count].loc = DMSTAG_LEFT;
1467: col[count].c = 0;
1468: val_A[count] = -1.0 * dv * eta_left / (hx * hy);
1469: ++count; /* up left*/
1471: col[count].i = ex;
1472: col[count].j = ey - 1;
1473: col[count].k = ez;
1474: col[count].loc = DMSTAG_RIGHT;
1475: col[count].c = 0;
1476: val_A[count] = -1.0 * dv * eta_right / (hx * hy);
1477: ++count; /* down right*/
1478: col[count].i = ex;
1479: col[count].j = ey;
1480: col[count].k = ez;
1481: col[count].loc = DMSTAG_RIGHT;
1482: col[count].c = 0;
1483: val_A[count] = dv * eta_right / (hx * hy);
1484: ++count; /* up right*/
1486: col[count].i = ex;
1487: col[count].j = ey - 1;
1488: col[count].k = ez;
1489: col[count].loc = DMSTAG_BACK;
1490: col[count].c = 0;
1491: val_A[count] = dv * eta_back / (hy * hz);
1492: ++count; /* back down */
1493: col[count].i = ex;
1494: col[count].j = ey;
1495: col[count].k = ez;
1496: col[count].loc = DMSTAG_BACK;
1497: col[count].c = 0;
1498: val_A[count] = -1.0 * dv * eta_back / (hy * hz);
1499: ++count; /* back up */
1501: col[count].i = ex;
1502: col[count].j = ey - 1;
1503: col[count].k = ez;
1504: col[count].loc = DMSTAG_FRONT;
1505: col[count].c = 0;
1506: val_A[count] = -1.0 * dv * eta_front / (hy * hz);
1507: ++count; /* front down */
1508: col[count].i = ex;
1509: col[count].j = ey;
1510: col[count].k = ez;
1511: col[count].loc = DMSTAG_FRONT;
1512: col[count].c = 0;
1513: val_A[count] = dv * eta_front / (hy * hz);
1514: ++count; /* front up */
1516: if (!parameters->faces_only) {
1517: col[count].i = ex;
1518: col[count].j = ey - 1;
1519: col[count].k = ez;
1520: col[count].loc = DMSTAG_ELEMENT;
1521: col[count].c = 0;
1522: val_A[count] = K_cont * dv / hy;
1523: ++count;
1524: col[count].i = ex;
1525: col[count].j = ey;
1526: col[count].k = ez;
1527: col[count].loc = DMSTAG_ELEMENT;
1528: col[count].c = 0;
1529: val_A[count] = -1.0 * K_cont * dv / hy;
1530: ++count;
1531: }
1533: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1534: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1535: }
1536: }
1538: if (front_boundary) {
1539: /* Front z-velocity Dirichlet */
1540: DMStagStencil row;
1541: const PetscScalar val_rhs = 0.0;
1542: const PetscScalar val_A = K_bound;
1544: row.i = ex;
1545: row.j = ey;
1546: row.k = ez;
1547: row.loc = DMSTAG_FRONT;
1548: row.c = 0;
1549: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1550: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1551: }
1553: /* Z faces - back */
1554: {
1555: DMStagStencil row;
1557: row.i = ex;
1558: row.j = ey;
1559: row.k = ez;
1560: row.loc = DMSTAG_BACK;
1561: row.c = 0;
1563: if (back_boundary) {
1564: /* Back z-velocity Dirichlet */
1565: const PetscScalar val_rhs = 0.0;
1566: const PetscScalar val_A = K_bound;
1568: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1569: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1570: } else {
1571: /* Z-momentum equation */
1572: PetscInt count;
1573: DMStagStencil col[17];
1574: PetscScalar val_A[17];
1575: DMStagStencil eta_point[6];
1576: PetscScalar eta[6], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the back face */
1577: const PetscScalar val_rhs = 0.0;
1579: /* Get eta values */
1580: eta_point[0].i = ex;
1581: eta_point[0].j = ey;
1582: eta_point[0].k = ez;
1583: eta_point[0].loc = DMSTAG_BACK_LEFT;
1584: eta_point[0].c = 0; /* Left */
1585: eta_point[1].i = ex;
1586: eta_point[1].j = ey;
1587: eta_point[1].k = ez;
1588: eta_point[1].loc = DMSTAG_BACK_RIGHT;
1589: eta_point[1].c = 0; /* Right */
1590: eta_point[2].i = ex;
1591: eta_point[2].j = ey;
1592: eta_point[2].k = ez;
1593: eta_point[2].loc = DMSTAG_BACK_DOWN;
1594: eta_point[2].c = 0; /* Down */
1595: eta_point[3].i = ex;
1596: eta_point[3].j = ey;
1597: eta_point[3].k = ez;
1598: eta_point[3].loc = DMSTAG_BACK_UP;
1599: eta_point[3].c = 0; /* Up */
1600: eta_point[4].i = ex;
1601: eta_point[4].j = ey;
1602: eta_point[4].k = ez - 1;
1603: eta_point[4].loc = DMSTAG_ELEMENT;
1604: eta_point[4].c = 0; /* Back */
1605: eta_point[5].i = ex;
1606: eta_point[5].j = ey;
1607: eta_point[5].k = ez;
1608: eta_point[5].loc = DMSTAG_ELEMENT;
1609: eta_point[5].c = 0; /* Front */
1610: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1611: eta_left = eta[0];
1612: eta_right = eta[1];
1613: eta_down = eta[2];
1614: eta_up = eta[3];
1615: eta_back = eta[4];
1616: eta_front = eta[5];
1618: count = 0;
1620: col[count] = row;
1621: val_A[count] = -2.0 * dv * (eta_back + eta_front) / (hz * hz);
1622: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
1623: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
1624: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
1625: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
1626: ++count;
1628: col[count].i = ex;
1629: col[count].j = ey;
1630: col[count].k = ez - 1;
1631: col[count].loc = DMSTAG_BACK;
1632: col[count].c = 0;
1633: val_A[count] = 2.0 * dv * eta_back / (hz * hz);
1634: ++count;
1635: col[count].i = ex;
1636: col[count].j = ey;
1637: col[count].k = ez + 1;
1638: col[count].loc = DMSTAG_BACK;
1639: col[count].c = 0;
1640: val_A[count] = 2.0 * dv * eta_front / (hz * hz);
1641: ++count;
1643: if (!left_boundary) {
1644: col[count].i = ex - 1;
1645: col[count].j = ey;
1646: col[count].k = ez;
1647: col[count].loc = DMSTAG_BACK;
1648: col[count].c = 0;
1649: val_A[count] = dv * eta_left / (hx * hx);
1650: ++count;
1651: }
1652: if (!right_boundary) {
1653: col[count].i = ex + 1;
1654: col[count].j = ey;
1655: col[count].k = ez;
1656: col[count].loc = DMSTAG_BACK;
1657: col[count].c = 0;
1658: val_A[count] = dv * eta_right / (hx * hx);
1659: ++count;
1660: }
1661: if (!bottom_boundary) {
1662: col[count].i = ex;
1663: col[count].j = ey - 1;
1664: col[count].k = ez;
1665: col[count].loc = DMSTAG_BACK;
1666: col[count].c = 0;
1667: val_A[count] = dv * eta_down / (hy * hy);
1668: ++count;
1669: }
1670: if (!top_boundary) {
1671: col[count].i = ex;
1672: col[count].j = ey + 1;
1673: col[count].k = ez;
1674: col[count].loc = DMSTAG_BACK;
1675: col[count].c = 0;
1676: val_A[count] = dv * eta_up / (hy * hy);
1677: ++count;
1678: }
1680: col[count].i = ex;
1681: col[count].j = ey;
1682: col[count].k = ez - 1;
1683: col[count].loc = DMSTAG_LEFT;
1684: col[count].c = 0;
1685: val_A[count] = dv * eta_left / (hx * hz);
1686: ++count; /* back left*/
1687: col[count].i = ex;
1688: col[count].j = ey;
1689: col[count].k = ez;
1690: col[count].loc = DMSTAG_LEFT;
1691: col[count].c = 0;
1692: val_A[count] = -1.0 * dv * eta_left / (hx * hz);
1693: ++count; /* front left*/
1695: col[count].i = ex;
1696: col[count].j = ey;
1697: col[count].k = ez - 1;
1698: col[count].loc = DMSTAG_RIGHT;
1699: col[count].c = 0;
1700: val_A[count] = -1.0 * dv * eta_right / (hx * hz);
1701: ++count; /* back right */
1702: col[count].i = ex;
1703: col[count].j = ey;
1704: col[count].k = ez;
1705: col[count].loc = DMSTAG_RIGHT;
1706: col[count].c = 0;
1707: val_A[count] = dv * eta_right / (hx * hz);
1708: ++count; /* front right*/
1710: col[count].i = ex;
1711: col[count].j = ey;
1712: col[count].k = ez - 1;
1713: col[count].loc = DMSTAG_DOWN;
1714: col[count].c = 0;
1715: val_A[count] = dv * eta_down / (hy * hz);
1716: ++count; /* back down */
1717: col[count].i = ex;
1718: col[count].j = ey;
1719: col[count].k = ez;
1720: col[count].loc = DMSTAG_DOWN;
1721: col[count].c = 0;
1722: val_A[count] = -1.0 * dv * eta_down / (hy * hz);
1723: ++count; /* back down */
1725: col[count].i = ex;
1726: col[count].j = ey;
1727: col[count].k = ez - 1;
1728: col[count].loc = DMSTAG_UP;
1729: col[count].c = 0;
1730: val_A[count] = -1.0 * dv * eta_up / (hy * hz);
1731: ++count; /* back up */
1732: col[count].i = ex;
1733: col[count].j = ey;
1734: col[count].k = ez;
1735: col[count].loc = DMSTAG_UP;
1736: col[count].c = 0;
1737: val_A[count] = dv * eta_up / (hy * hz);
1738: ++count; /* back up */
1740: if (!parameters->faces_only) {
1741: col[count].i = ex;
1742: col[count].j = ey;
1743: col[count].k = ez - 1;
1744: col[count].loc = DMSTAG_ELEMENT;
1745: col[count].c = 0;
1746: val_A[count] = K_cont * dv / hz;
1747: ++count;
1748: col[count].i = ex;
1749: col[count].j = ey;
1750: col[count].k = ez;
1751: col[count].loc = DMSTAG_ELEMENT;
1752: col[count].c = 0;
1753: val_A[count] = -1.0 * K_cont * dv / hz;
1754: ++count;
1755: }
1757: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1758: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1759: }
1760: }
1762: /* Elements */
1763: if (!parameters->faces_only) {
1764: DMStagStencil row;
1766: row.i = ex;
1767: row.j = ey;
1768: row.k = ez;
1769: row.loc = DMSTAG_ELEMENT;
1770: row.c = 0;
1772: if (ctx->pin_pressure && ex == pinx && ey == piny && ez == pinz) {
1773: /* Pin a pressure node to zero, if requested */
1774: const PetscScalar val_A = K_bound;
1775: const PetscScalar val_rhs = 0.0;
1777: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1778: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1779: } else {
1780: /* Continuity equation */
1781: /* Note that this includes an explicit zero on the diagonal. This is only needed for
1782: some direct solvers (not required if using an iterative solver and setting a constant-pressure nullspace) */
1783: /* Note: the scaling by dv is not chosen in a principled way and is likely sub-optimal */
1784: DMStagStencil col[7];
1785: PetscScalar val_A[7];
1786: const PetscScalar val_rhs = 0.0;
1788: col[0].i = ex;
1789: col[0].j = ey;
1790: col[0].k = ez;
1791: col[0].loc = DMSTAG_LEFT;
1792: col[0].c = 0;
1793: val_A[0] = -1.0 * K_cont * dv / hx;
1794: col[1].i = ex;
1795: col[1].j = ey;
1796: col[1].k = ez;
1797: col[1].loc = DMSTAG_RIGHT;
1798: col[1].c = 0;
1799: val_A[1] = K_cont * dv / hx;
1800: col[2].i = ex;
1801: col[2].j = ey;
1802: col[2].k = ez;
1803: col[2].loc = DMSTAG_DOWN;
1804: col[2].c = 0;
1805: val_A[2] = -1.0 * K_cont * dv / hy;
1806: col[3].i = ex;
1807: col[3].j = ey;
1808: col[3].k = ez;
1809: col[3].loc = DMSTAG_UP;
1810: col[3].c = 0;
1811: val_A[3] = K_cont * dv / hy;
1812: col[4].i = ex;
1813: col[4].j = ey;
1814: col[4].k = ez;
1815: col[4].loc = DMSTAG_BACK;
1816: col[4].c = 0;
1817: val_A[4] = -1.0 * K_cont * dv / hz;
1818: col[5].i = ex;
1819: col[5].j = ey;
1820: col[5].k = ez;
1821: col[5].loc = DMSTAG_FRONT;
1822: col[5].c = 0;
1823: val_A[5] = K_cont * dv / hz;
1824: col[6] = row;
1825: val_A[6] = 0.0;
1826: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 7, col, val_A, INSERT_VALUES));
1827: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1828: }
1829: }
1830: }
1831: }
1832: }
1833: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
1835: /* Add additional inverse viscosity terms (for use in building a preconditioning matrix) */
1836: if (parameters->include_inverse_visc) {
1837: PetscCheck(!parameters->faces_only, PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "Does not make sense with faces only");
1838: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_main, dm_coefficients, ctx->levels[level]->coeff, 1.0, A));
1839: }
1841: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1842: if (build_rhs) PetscCall(VecAssemblyBegin(rhs));
1843: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1844: if (build_rhs) PetscCall(VecAssemblyEnd(rhs));
1845: PetscFunctionReturn(PETSC_SUCCESS);
1846: }
1848: static PetscErrorCode CreateSystem(SystemParameters parameters, Mat *pA, Vec *pRhs)
1849: {
1850: PetscFunctionBeginUser;
1851: if (parameters->ctx->dim == 2) {
1852: PetscCall(CreateSystem2d(parameters, pA, pRhs));
1853: } else if (parameters->ctx->dim == 3) {
1854: PetscCall(CreateSystem3d(parameters, pA, pRhs));
1855: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT, parameters->ctx->dim);
1856: PetscFunctionReturn(PETSC_SUCCESS);
1857: }
1859: PetscErrorCode PopulateCoefficientData(Ctx ctx, PetscInt level)
1860: {
1861: PetscInt dim;
1862: PetscInt N[3];
1863: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
1864: PetscInt slot_prev, slot_center;
1865: PetscInt slot_rho_downleft, slot_rho_backleft, slot_rho_backdown, slot_eta_element, slot_eta_downleft, slot_eta_backleft, slot_eta_backdown;
1866: Vec coeff_local;
1867: PetscReal **arr_coordinates_x, **arr_coordinates_y, **arr_coordinates_z;
1868: DM dm_coefficients;
1869: Vec coeff;
1871: PetscFunctionBeginUser;
1872: dm_coefficients = ctx->levels[level]->dm_coefficients;
1873: PetscCall(DMGetDimension(dm_coefficients, &dim));
1875: /* Create global coefficient vector */
1876: PetscCall(DMCreateGlobalVector(dm_coefficients, &ctx->levels[level]->coeff));
1877: coeff = ctx->levels[level]->coeff;
1879: /* Get temporary access to a local representation of the coefficient data */
1880: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1881: PetscCall(DMGlobalToLocal(dm_coefficients, coeff, INSERT_VALUES, coeff_local));
1883: /* Use direct array access to coefficient and coordinate arrays, to popoulate coefficient data */
1884: PetscCall(DMStagGetGhostCorners(dm_coefficients, &startx, &starty, &startz, &nx, &ny, &nz));
1885: PetscCall(DMStagGetGlobalSizes(dm_coefficients, &N[0], &N[1], &N[2]));
1886: PetscCall(DMStagGetProductCoordinateArraysRead(dm_coefficients, &arr_coordinates_x, &arr_coordinates_y, &arr_coordinates_z));
1887: PetscCall(DMStagGetProductCoordinateLocationSlot(dm_coefficients, DMSTAG_ELEMENT, &slot_center));
1888: PetscCall(DMStagGetProductCoordinateLocationSlot(dm_coefficients, DMSTAG_LEFT, &slot_prev));
1889: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_ELEMENT, 0, &slot_eta_element));
1890: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_DOWN_LEFT, 0, &slot_eta_downleft));
1891: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_DOWN_LEFT, 1, &slot_rho_downleft));
1892: if (dim == 2) {
1893: PetscScalar ***arr_coefficients;
1895: PetscCall(DMStagVecGetArray(dm_coefficients, coeff_local, &arr_coefficients));
1896: /* Note that these ranges are with respect to the local representation */
1897: for (ey = starty; ey < starty + ny; ++ey) {
1898: for (ex = startx; ex < startx + nx; ++ex) {
1899: arr_coefficients[ey][ex][slot_eta_element] = ctx->GetEta(ctx, arr_coordinates_x[ex][slot_center], arr_coordinates_y[ey][slot_center], 0.0);
1900: arr_coefficients[ey][ex][slot_eta_downleft] = ctx->GetEta(ctx, arr_coordinates_x[ex][slot_prev], arr_coordinates_y[ey][slot_prev], 0.0);
1901: arr_coefficients[ey][ex][slot_rho_downleft] = ctx->GetRho(ctx, arr_coordinates_x[ex][slot_prev], arr_coordinates_y[ey][slot_prev], 0.0);
1902: }
1903: }
1904: PetscCall(DMStagVecRestoreArray(dm_coefficients, coeff_local, &arr_coefficients));
1905: } else if (dim == 3) {
1906: PetscScalar ****arr_coefficients;
1908: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_LEFT, 0, &slot_eta_backleft));
1909: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_LEFT, 1, &slot_rho_backleft));
1910: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_DOWN, 0, &slot_eta_backdown));
1911: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_DOWN, 1, &slot_rho_backdown));
1912: PetscCall(DMStagVecGetArray(dm_coefficients, coeff_local, &arr_coefficients));
1913: /* Note that these are with respect to the entire local representation, including ghosts */
1914: for (ez = startz; ez < startz + nz; ++ez) {
1915: for (ey = starty; ey < starty + ny; ++ey) {
1916: for (ex = startx; ex < startx + nx; ++ex) {
1917: const PetscScalar x_prev = arr_coordinates_x[ex][slot_prev];
1918: const PetscScalar y_prev = arr_coordinates_y[ey][slot_prev];
1919: const PetscScalar z_prev = arr_coordinates_z[ez][slot_prev];
1920: const PetscScalar x_center = arr_coordinates_x[ex][slot_center];
1921: const PetscScalar y_center = arr_coordinates_y[ey][slot_center];
1922: const PetscScalar z_center = arr_coordinates_z[ez][slot_center];
1924: arr_coefficients[ez][ey][ex][slot_eta_element] = ctx->GetEta(ctx, x_center, y_center, z_center);
1925: arr_coefficients[ez][ey][ex][slot_eta_downleft] = ctx->GetEta(ctx, x_prev, y_prev, z_center);
1926: arr_coefficients[ez][ey][ex][slot_rho_downleft] = ctx->GetRho(ctx, x_prev, y_prev, z_center);
1927: arr_coefficients[ez][ey][ex][slot_eta_backleft] = ctx->GetEta(ctx, x_prev, y_center, z_prev);
1928: arr_coefficients[ez][ey][ex][slot_rho_backleft] = ctx->GetRho(ctx, x_prev, y_center, z_prev);
1929: arr_coefficients[ez][ey][ex][slot_eta_backdown] = ctx->GetEta(ctx, x_center, y_prev, z_prev);
1930: arr_coefficients[ez][ey][ex][slot_rho_backdown] = ctx->GetRho(ctx, x_center, y_prev, z_prev);
1931: }
1932: }
1933: }
1934: PetscCall(DMStagVecRestoreArray(dm_coefficients, coeff_local, &arr_coefficients));
1935: } else SETERRQ(PetscObjectComm((PetscObject)dm_coefficients), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT, dim);
1936: PetscCall(DMStagRestoreProductCoordinateArraysRead(dm_coefficients, &arr_coordinates_x, &arr_coordinates_y, &arr_coordinates_z));
1937: PetscCall(DMLocalToGlobal(dm_coefficients, coeff_local, INSERT_VALUES, coeff));
1938: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
1939: PetscFunctionReturn(PETSC_SUCCESS);
1940: }
1942: static PetscErrorCode CreateAuxiliaryOperator(Ctx ctx, PetscInt level, Mat *p_S_hat)
1943: {
1944: DM dm_element;
1945: Mat S_hat;
1946: DM dm_stokes, dm_coefficients;
1947: Vec coeff;
1949: PetscFunctionBeginUser;
1950: dm_stokes = ctx->levels[level]->dm_stokes;
1951: dm_coefficients = ctx->levels[level]->dm_coefficients;
1952: coeff = ctx->levels[level]->coeff;
1953: if (ctx->dim == 2) {
1954: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 1, 0, &dm_element));
1955: } else if (ctx->dim == 3) {
1956: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 0, 1, &dm_element));
1957: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
1958: PetscCall(DMCreateMatrix(dm_element, p_S_hat));
1959: S_hat = *p_S_hat;
1960: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_element, dm_coefficients, coeff, 1.0, S_hat));
1961: PetscCall(MatAssemblyBegin(S_hat, MAT_FINAL_ASSEMBLY));
1962: PetscCall(MatAssemblyEnd(S_hat, MAT_FINAL_ASSEMBLY));
1963: PetscCall(DMDestroy(&dm_element));
1964: PetscFunctionReturn(PETSC_SUCCESS);
1965: }
1967: static PetscErrorCode OperatorInsertInverseViscosityPressureTerms(DM dm, DM dm_coefficients, Vec coefficients, PetscScalar scale, Mat mat)
1968: {
1969: PetscInt dim, ex, ey, ez, startx, starty, startz, nx, ny, nz;
1970: Vec coeff_local;
1972: PetscFunctionBeginUser;
1973: PetscCall(DMGetDimension(dm, &dim));
1974: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1975: PetscCall(DMGlobalToLocal(dm_coefficients, coefficients, INSERT_VALUES, coeff_local));
1976: PetscCall(DMStagGetCorners(dm, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
1977: if (dim == 2) { /* Trick to have one loop nest */
1978: startz = 0;
1979: nz = 1;
1980: }
1981: for (ez = startz; ez < startz + nz; ++ez) {
1982: for (ey = starty; ey < starty + ny; ++ey) {
1983: for (ex = startx; ex < startx + nx; ++ex) {
1984: DMStagStencil from, to;
1985: PetscScalar val;
1987: /* component 0 on element is viscosity */
1988: from.i = ex;
1989: from.j = ey;
1990: from.k = ez;
1991: from.c = 0;
1992: from.loc = DMSTAG_ELEMENT;
1993: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 1, &from, &val));
1994: val = scale / val; /* inverse viscosity, scaled */
1995: to = from;
1996: PetscCall(DMStagMatSetValuesStencil(dm, mat, 1, &to, 1, &to, &val, INSERT_VALUES));
1997: }
1998: }
1999: }
2000: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
2001: /* Note that this function does not call MatAssembly{Begin,End} */
2002: PetscFunctionReturn(PETSC_SUCCESS);
2003: }
2005: /* Create a pressure-only DMStag and use it to generate a nullspace vector
2006: - Create a compatible DMStag with one dof per element (and nothing else).
2007: - Create a constant vector and normalize it
2008: - Migrate it to a vector on the original dmSol (making use of the fact
2009: that this will fill in zeros for "extra" dof)
2010: - Set the nullspace for the operator
2011: - Destroy everything (the operator keeps the references it needs) */
2012: static PetscErrorCode AttachNullspace(DM dmSol, Mat A)
2013: {
2014: DM dmPressure;
2015: Vec constantPressure, basis;
2016: PetscReal nrm;
2017: MatNullSpace matNullSpace;
2019: PetscFunctionBeginUser;
2020: PetscCall(DMStagCreateCompatibleDMStag(dmSol, 0, 0, 1, 0, &dmPressure));
2021: PetscCall(DMGetGlobalVector(dmPressure, &constantPressure));
2022: PetscCall(VecSet(constantPressure, 1.0));
2023: PetscCall(VecNorm(constantPressure, NORM_2, &nrm));
2024: PetscCall(VecScale(constantPressure, 1.0 / nrm));
2025: PetscCall(DMCreateGlobalVector(dmSol, &basis));
2026: PetscCall(DMStagMigrateVec(dmPressure, constantPressure, dmSol, basis));
2027: PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dmSol), PETSC_FALSE, 1, &basis, &matNullSpace));
2028: PetscCall(VecDestroy(&basis));
2029: PetscCall(MatSetNullSpace(A, matNullSpace));
2030: PetscCall(MatNullSpaceDestroy(&matNullSpace));
2031: PetscCall(DMRestoreGlobalVector(dmPressure, &constantPressure));
2032: PetscCall(DMDestroy(&dmPressure));
2033: PetscFunctionReturn(PETSC_SUCCESS);
2034: }
2036: static PetscErrorCode DumpSolution(Ctx ctx, PetscInt level, Vec x)
2037: {
2038: DM dm_stokes, dm_coefficients;
2039: Vec coeff;
2040: DM dm_vel_avg;
2041: Vec vel_avg;
2042: DM da_vel_avg, da_p, da_eta_element;
2043: Vec vec_vel_avg, vec_p, vec_eta_element;
2044: DM da_eta_down_left, da_rho_down_left, da_eta_back_left, da_rho_back_left, da_eta_back_down, da_rho_back_down;
2045: Vec vec_eta_down_left, vec_rho_down_left, vec_eta_back_left, vec_rho_back_left, vec_eta_back_down, vec_rho_back_down;
2046: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
2047: Vec stokesLocal;
2049: PetscFunctionBeginUser;
2050: dm_stokes = ctx->levels[level]->dm_stokes;
2051: dm_coefficients = ctx->levels[level]->dm_coefficients;
2052: coeff = ctx->levels[level]->coeff;
2054: /* For convenience, create a new DM and Vec which will hold averaged velocities
2055: Note that this could also be accomplished with direct array access, using
2056: DMStagVecGetArray() and related functions */
2057: if (ctx->dim == 2) {
2058: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 2, 0, &dm_vel_avg)); /* 2 dof per element */
2059: } else if (ctx->dim == 3) {
2060: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 0, 3, &dm_vel_avg)); /* 3 dof per element */
2061: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not Implemented for dimension %" PetscInt_FMT, ctx->dim);
2062: PetscCall(DMSetUp(dm_vel_avg));
2063: PetscCall(DMStagSetUniformCoordinatesProduct(dm_vel_avg, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax, ctx->zmin, ctx->zmax));
2064: PetscCall(DMCreateGlobalVector(dm_vel_avg, &vel_avg));
2065: PetscCall(DMGetLocalVector(dm_stokes, &stokesLocal));
2066: PetscCall(DMGlobalToLocal(dm_stokes, x, INSERT_VALUES, stokesLocal));
2067: PetscCall(DMStagGetCorners(dm_vel_avg, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
2068: if (ctx->dim == 2) {
2069: for (ey = starty; ey < starty + ny; ++ey) {
2070: for (ex = startx; ex < startx + nx; ++ex) {
2071: DMStagStencil from[4], to[2];
2072: PetscScalar valFrom[4], valTo[2];
2074: from[0].i = ex;
2075: from[0].j = ey;
2076: from[0].loc = DMSTAG_UP;
2077: from[0].c = 0;
2078: from[1].i = ex;
2079: from[1].j = ey;
2080: from[1].loc = DMSTAG_DOWN;
2081: from[1].c = 0;
2082: from[2].i = ex;
2083: from[2].j = ey;
2084: from[2].loc = DMSTAG_LEFT;
2085: from[2].c = 0;
2086: from[3].i = ex;
2087: from[3].j = ey;
2088: from[3].loc = DMSTAG_RIGHT;
2089: from[3].c = 0;
2090: PetscCall(DMStagVecGetValuesStencil(dm_stokes, stokesLocal, 4, from, valFrom));
2091: to[0].i = ex;
2092: to[0].j = ey;
2093: to[0].loc = DMSTAG_ELEMENT;
2094: to[0].c = 0;
2095: valTo[0] = 0.5 * (valFrom[2] + valFrom[3]);
2096: to[1].i = ex;
2097: to[1].j = ey;
2098: to[1].loc = DMSTAG_ELEMENT;
2099: to[1].c = 1;
2100: valTo[1] = 0.5 * (valFrom[0] + valFrom[1]);
2101: PetscCall(DMStagVecSetValuesStencil(dm_vel_avg, vel_avg, 2, to, valTo, INSERT_VALUES));
2102: }
2103: }
2104: } else if (ctx->dim == 3) {
2105: for (ez = startz; ez < startz + nz; ++ez) {
2106: for (ey = starty; ey < starty + ny; ++ey) {
2107: for (ex = startx; ex < startx + nx; ++ex) {
2108: DMStagStencil from[6], to[3];
2109: PetscScalar valFrom[6], valTo[3];
2111: from[0].i = ex;
2112: from[0].j = ey;
2113: from[0].k = ez;
2114: from[0].loc = DMSTAG_UP;
2115: from[0].c = 0;
2116: from[1].i = ex;
2117: from[1].j = ey;
2118: from[1].k = ez;
2119: from[1].loc = DMSTAG_DOWN;
2120: from[1].c = 0;
2121: from[2].i = ex;
2122: from[2].j = ey;
2123: from[2].k = ez;
2124: from[2].loc = DMSTAG_LEFT;
2125: from[2].c = 0;
2126: from[3].i = ex;
2127: from[3].j = ey;
2128: from[3].k = ez;
2129: from[3].loc = DMSTAG_RIGHT;
2130: from[3].c = 0;
2131: from[4].i = ex;
2132: from[4].j = ey;
2133: from[4].k = ez;
2134: from[4].loc = DMSTAG_BACK;
2135: from[4].c = 0;
2136: from[5].i = ex;
2137: from[5].j = ey;
2138: from[5].k = ez;
2139: from[5].loc = DMSTAG_FRONT;
2140: from[5].c = 0;
2141: PetscCall(DMStagVecGetValuesStencil(dm_stokes, stokesLocal, 6, from, valFrom));
2142: to[0].i = ex;
2143: to[0].j = ey;
2144: to[0].k = ez;
2145: to[0].loc = DMSTAG_ELEMENT;
2146: to[0].c = 0;
2147: valTo[0] = 0.5 * (valFrom[2] + valFrom[3]);
2148: to[1].i = ex;
2149: to[1].j = ey;
2150: to[1].k = ez;
2151: to[1].loc = DMSTAG_ELEMENT;
2152: to[1].c = 1;
2153: valTo[1] = 0.5 * (valFrom[0] + valFrom[1]);
2154: to[2].i = ex;
2155: to[2].j = ey;
2156: to[2].k = ez;
2157: to[2].loc = DMSTAG_ELEMENT;
2158: to[2].c = 2;
2159: valTo[2] = 0.5 * (valFrom[4] + valFrom[5]);
2160: PetscCall(DMStagVecSetValuesStencil(dm_vel_avg, vel_avg, 3, to, valTo, INSERT_VALUES));
2161: }
2162: }
2163: }
2164: }
2165: PetscCall(VecAssemblyBegin(vel_avg));
2166: PetscCall(VecAssemblyEnd(vel_avg));
2167: PetscCall(DMRestoreLocalVector(dm_stokes, &stokesLocal));
2169: /* Create individual DMDAs for sub-grids of our DMStag objects. This is
2170: somewhat inefficient, but allows use of the DMDA API without re-implementing
2171: all utilities for DMStag */
2173: PetscCall(DMStagVecSplitToDMDA(dm_stokes, x, DMSTAG_ELEMENT, 0, &da_p, &vec_p));
2174: PetscCall(PetscObjectSetName((PetscObject)vec_p, "p (scaled)"));
2176: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_ELEMENT, 0, &da_eta_element, &vec_eta_element));
2177: PetscCall(PetscObjectSetName((PetscObject)vec_eta_element, "eta"));
2179: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_DOWN_LEFT, 0, &da_eta_down_left, &vec_eta_down_left));
2180: PetscCall(PetscObjectSetName((PetscObject)vec_eta_down_left, "eta"));
2182: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_DOWN_LEFT, 1, &da_rho_down_left, &vec_rho_down_left));
2183: PetscCall(PetscObjectSetName((PetscObject)vec_rho_down_left, "density"));
2185: if (ctx->dim == 3) {
2186: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_LEFT, 0, &da_eta_back_left, &vec_eta_back_left));
2187: PetscCall(PetscObjectSetName((PetscObject)vec_eta_back_left, "eta"));
2189: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_LEFT, 1, &da_rho_back_left, &vec_rho_back_left));
2190: PetscCall(PetscObjectSetName((PetscObject)vec_rho_back_left, "rho"));
2192: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_DOWN, 0, &da_eta_back_down, &vec_eta_back_down));
2193: PetscCall(PetscObjectSetName((PetscObject)vec_eta_back_down, "eta"));
2195: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_DOWN, 1, &da_rho_back_down, &vec_rho_back_down));
2196: PetscCall(PetscObjectSetName((PetscObject)vec_rho_back_down, "rho"));
2197: }
2199: PetscCall(DMStagVecSplitToDMDA(dm_vel_avg, vel_avg, DMSTAG_ELEMENT, -3, &da_vel_avg, &vec_vel_avg)); /* note -3 : pad with zero */
2200: PetscCall(PetscObjectSetName((PetscObject)vec_vel_avg, "Velocity (Averaged)"));
2202: /* Dump element-based fields to a .vtr file */
2203: {
2204: PetscViewer viewer;
2206: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_vel_avg), "ex4_element.vtr", FILE_MODE_WRITE, &viewer));
2207: PetscCall(VecView(vec_vel_avg, viewer));
2208: PetscCall(VecView(vec_p, viewer));
2209: PetscCall(VecView(vec_eta_element, viewer));
2210: PetscCall(PetscViewerDestroy(&viewer));
2211: }
2213: /* Dump vertex- or edge-based fields to a second .vtr file */
2214: {
2215: PetscViewer viewer;
2217: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_down_left), "ex4_down_left.vtr", FILE_MODE_WRITE, &viewer));
2218: PetscCall(VecView(vec_eta_down_left, viewer));
2219: PetscCall(VecView(vec_rho_down_left, viewer));
2220: PetscCall(PetscViewerDestroy(&viewer));
2221: }
2222: if (ctx->dim == 3) {
2223: PetscViewer viewer;
2225: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_back_left), "ex4_back_left.vtr", FILE_MODE_WRITE, &viewer));
2226: PetscCall(VecView(vec_eta_back_left, viewer));
2227: PetscCall(VecView(vec_rho_back_left, viewer));
2228: PetscCall(PetscViewerDestroy(&viewer));
2229: }
2230: if (ctx->dim == 3) {
2231: PetscViewer viewer;
2233: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_back_down), "ex4_back_down.vtr", FILE_MODE_WRITE, &viewer));
2234: PetscCall(VecView(vec_eta_back_down, viewer));
2235: PetscCall(VecView(vec_rho_back_down, viewer));
2236: PetscCall(PetscViewerDestroy(&viewer));
2237: }
2239: /* Destroy DMDAs and Vecs */
2240: PetscCall(VecDestroy(&vec_vel_avg));
2241: PetscCall(VecDestroy(&vec_p));
2242: PetscCall(VecDestroy(&vec_eta_element));
2243: PetscCall(VecDestroy(&vec_eta_down_left));
2244: if (ctx->dim == 3) {
2245: PetscCall(VecDestroy(&vec_eta_back_left));
2246: PetscCall(VecDestroy(&vec_eta_back_down));
2247: }
2248: PetscCall(VecDestroy(&vec_rho_down_left));
2249: if (ctx->dim == 3) {
2250: PetscCall(VecDestroy(&vec_rho_back_left));
2251: PetscCall(VecDestroy(&vec_rho_back_down));
2252: }
2253: PetscCall(DMDestroy(&da_vel_avg));
2254: PetscCall(DMDestroy(&da_p));
2255: PetscCall(DMDestroy(&da_eta_element));
2256: PetscCall(DMDestroy(&da_eta_down_left));
2257: if (ctx->dim == 3) {
2258: PetscCall(DMDestroy(&da_eta_back_left));
2259: PetscCall(DMDestroy(&da_eta_back_down));
2260: }
2261: PetscCall(DMDestroy(&da_rho_down_left));
2262: if (ctx->dim == 3) {
2263: PetscCall(DMDestroy(&da_rho_back_left));
2264: PetscCall(DMDestroy(&da_rho_back_down));
2265: }
2266: PetscCall(VecDestroy(&vel_avg));
2267: PetscCall(DMDestroy(&dm_vel_avg));
2268: PetscFunctionReturn(PETSC_SUCCESS);
2269: }
2271: /*TEST
2273: test:
2274: suffix: direct_umfpack
2275: requires: suitesparse !complex
2276: nsize: 1
2277: args: -dim 2 -coefficients layers -nondimensional 0 -stag_grid_x 12 -stag_grid_y 7 -pc_type lu -pc_factor_mat_solver_type umfpack -ksp_converged_reason
2279: test:
2280: suffix: direct_mumps
2281: requires: mumps !complex
2282: nsize: 9
2283: args: -dim 2 -coefficients layers -nondimensional 0 -stag_grid_x 13 -stag_grid_y 8 -pc_type lu -pc_factor_mat_solver_type mumps -ksp_converged_reason
2285: test:
2286: suffix: isovisc_nondim_abf_mg
2287: nsize: 1
2288: args: -dim 2 -coefficients layers -nondimensional 1 -pc_type fieldsplit -pc_fieldsplit_type schur -ksp_converged_reason -fieldsplit_element_ksp_type preonly -pc_fieldsplit_detect_saddle_point false -fieldsplit_face_pc_type mg -fieldsplit_face_pc_mg_levels 3 -stag_grid_x 24 -stag_grid_y 24 -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_ksp_converged_reason -ksp_type fgmres -fieldsplit_element_pc_type none -fieldsplit_face_mg_levels_ksp_max_it 6 -pc_fieldsplit_schur_fact_type upper -isoviscous
2290: test:
2291: suffix: isovisc_nondim_abf_mg_2
2292: nsize: 1
2293: args: -dim 2 -coefficients layers -nondimensional -isoviscous -eta1 1.0 -stag_grid_x 32 -stag_grid_y 32 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type upper -build_auxiliary_operator -fieldsplit_element_ksp_type preonly -fieldsplit_element_pc_type jacobi -fieldsplit_face_pc_type mg -fieldsplit_face_pc_mg_levels 3 -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_mg_levels_pc_type jacobi -fieldsplit_face_mg_levels_ksp_type chebyshev -ksp_converged_reason
2295: test:
2296: suffix: nondim_abf_mg
2297: requires: suitesparse !complex
2298: nsize: 4
2299: args: -dim 2 -coefficients layers -pc_type fieldsplit -pc_fieldsplit_type schur -ksp_converged_reason -fieldsplit_element_ksp_type preonly -pc_fieldsplit_detect_saddle_point false -fieldsplit_face_pc_type mg -fieldsplit_face_pc_mg_levels 3 -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_mg_coarse_pc_type redundant -fieldsplit_face_mg_coarse_redundant_pc_type lu -fieldsplit_face_mg_coarse_redundant_pc_factor_mat_solver_type umfpack -ksp_type fgmres -fieldsplit_element_pc_type none -fieldsplit_face_mg_levels_ksp_max_it 6 -pc_fieldsplit_schur_fact_type upper -nondimensional -eta1 1e-2 -eta2 1.0 -ksp_monitor -fieldsplit_face_mg_levels_pc_type jacobi -fieldsplit_face_mg_levels_ksp_type gmres -fieldsplit_element_pc_type jacobi -pc_fieldsplit_schur_precondition selfp -stag_grid_x 32 -stag_grid_y 32 -fieldsplit_face_ksp_monitor
2301: test:
2302: suffix: nondim_abf_lu
2303: requires: suitesparse !complex
2304: nsize: 1
2305: args: -dim 2 -coefficients layers -pc_type fieldsplit -pc_fieldsplit_type schur -ksp_converged_reason -fieldsplit_element_ksp_type preonly -pc_fieldsplit_detect_saddle_point false -ksp_type fgmres -fieldsplit_element_pc_type none -pc_fieldsplit_schur_fact_type upper -nondimensional -eta1 1e-2 -eta2 1.0 -isoviscous 0 -ksp_monitor -fieldsplit_element_pc_type jacobi -build_auxiliary_operator -fieldsplit_face_pc_type lu -fieldsplit_face_pc_factor_mat_solver_type umfpack -stag_grid_x 32 -stag_grid_y 32
2307: test:
2308: suffix: 3d_nondim_isovisc_abf_mg
2309: requires: !single
2310: nsize: 1
2311: args: -dim 3 -coefficients layers -isoviscous -nondimensional -build_auxiliary_operator -pc_type fieldsplit -pc_fieldsplit_type schur -ksp_converged_reason -fieldsplit_element_ksp_type preonly -pc_fieldsplit_detect_saddle_point false -fieldsplit_face_pc_type mg -fieldsplit_face_pc_mg_levels 3 -s 16 -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_ksp_converged_reason -ksp_type fgmres -fieldsplit_element_pc_type none -fieldsplit_face_mg_levels_ksp_max_it 6 -pc_fieldsplit_schur_fact_type upper
2313: test:
2314: TODO: unstable across systems
2315: suffix: monolithic
2316: nsize: 1
2317: requires: double !complex
2318: args: -dim {{2 3}separate output} -s 16 -custom_pc_mat -pc_type mg -pc_mg_levels 3 -pc_mg_galerkin -mg_levels_ksp_type gmres -mg_levels_ksp_norm_type unpreconditioned -mg_levels_ksp_max_it 10 -mg_levels_pc_type jacobi -ksp_converged_reason
2320: test:
2321: suffix: 3d_nondim_isovisc_sinker_abf_mg
2322: requires: !complex !single
2323: nsize: 1
2324: args: -dim 3 -coefficients sinker -isoviscous -nondimensional -pc_type fieldsplit -pc_fieldsplit_type schur -ksp_converged_reason -fieldsplit_element_ksp_type preonly -pc_fieldsplit_detect_saddle_point false -fieldsplit_face_pc_type mg -fieldsplit_face_pc_mg_levels 3 -s 16 -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_ksp_converged_reason -ksp_type fgmres -fieldsplit_element_pc_type none -fieldsplit_face_mg_levels_ksp_max_it 6 -pc_fieldsplit_schur_fact_type upper
2326: test:
2327: TODO: unstable across systems
2328: suffix: 3d_nondim_mono_mg_lamemstyle
2329: nsize: 1
2330: requires: suitesparse
2331: args: -dim 3 -coefficients layers -nondimensional -s 16 -custom_pc_mat -pc_type mg -pc_mg_galerkin -pc_mg_levels 2 -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -mg_levels_ksp_richardson_scale 0.5 -mg_levels_ksp_max_it 20 -mg_coarse_pc_type lu -mg_coarse_pc_factor_mat_solver_type umfpack -ksp_converged_reason
2333: test:
2334: suffix: 3d_isovisc_blob_cuda
2335: requires: cuda defined(PETSC_USE_LOG)
2336: nsize: 2
2337: args: -dim 3 -coefficients blob -isoviscous -s 8 -build_auxiliary_operator -fieldsplit_element_ksp_type preonly -fieldsplit_element_pc_type jacobi -fieldsplit_face_ksp_type fgmres -fieldsplit_face_mg_levels_ksp_max_it 6 -fieldsplit_face_mg_levels_ksp_norm_type none -fieldsplit_face_mg_levels_ksp_type chebyshev -fieldsplit_face_mg_levels_pc_type jacobi -fieldsplit_face_pc_mg_galerkin -fieldsplit_face_pc_mg_levels 3 -fieldsplit_face_pc_type mg -pc_fieldsplit_schur_fact_type upper -pc_fieldsplit_schur_precondition user -pc_fieldsplit_type schur -pc_type fieldsplit -dm_mat_type aijcusparse -dm_vec_type cuda -log_view -fieldsplit_face_pc_mg_log
2338: filter: awk "/MGInterp/ {print \$NF}"
2340: TEST*/