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, NULL, 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 matrix from which the preconditioner is constructed */
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: PetscCheck(ctx->dim == 3, PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
515: ctx->GetRho = GetRho_blob3;
516: ctx->GetEta = GetEta_blob3;
517: }
518: if (is_sinker_box) {
519: if (ctx->dim == 2) {
520: ctx->GetRho = GetRho_sinker_box2;
521: ctx->GetEta = GetEta_sinker_box2;
522: } else if (ctx->dim == 3) {
523: ctx->GetRho = GetRho_sinker_box3;
524: ctx->GetEta = GetEta_sinker_box3;
525: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
526: }
527: if (is_sinker_sphere) {
528: PetscCheck(ctx->dim == 3, PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
529: ctx->GetRho = GetRho_sinker_sphere3;
530: ctx->GetEta = GetEta_sinker_sphere3;
531: }
532: }
534: /* Per-level data */
535: ctx->n_levels = 1;
536: PetscCall(PetscOptionsGetInt(NULL, NULL, "-levels", &ctx->n_levels, NULL));
537: PetscCall(PetscMalloc1(ctx->n_levels, &ctx->levels));
538: for (PetscInt i = 0; i < ctx->n_levels; ++i) PetscCall(LevelCtxCreate(&ctx->levels[i]));
539: PetscFunctionReturn(PETSC_SUCCESS);
540: }
542: static PetscErrorCode CtxDestroy(Ctx *p_ctx)
543: {
544: Ctx ctx;
546: PetscFunctionBeginUser;
547: ctx = *p_ctx;
548: for (PetscInt i = 0; i < ctx->n_levels; ++i) PetscCall(LevelCtxDestroy(&ctx->levels[i]));
549: PetscCall(PetscFree(ctx->levels));
550: PetscCall(PetscFree(*p_ctx));
551: PetscFunctionReturn(PETSC_SUCCESS);
552: }
554: static PetscErrorCode SystemParametersCreate(SystemParameters *parameters, Ctx ctx)
555: {
556: PetscFunctionBeginUser;
557: PetscCall(PetscMalloc1(1, parameters));
558: (*parameters)->ctx = ctx;
559: (*parameters)->level = ctx->n_levels - 1;
560: (*parameters)->include_inverse_visc = PETSC_FALSE;
561: (*parameters)->faces_only = PETSC_FALSE;
562: PetscFunctionReturn(PETSC_SUCCESS);
563: }
565: static PetscErrorCode SystemParametersDestroy(SystemParameters *parameters)
566: {
567: PetscFunctionBeginUser;
568: PetscCall(PetscFree(*parameters));
569: *parameters = NULL;
570: PetscFunctionReturn(PETSC_SUCCESS);
571: }
573: static PetscErrorCode CreateSystem2d(SystemParameters parameters, Mat *pA, Vec *pRhs)
574: {
575: PetscInt N[2];
576: PetscInt ex, ey, startx, starty, nx, ny;
577: Mat A;
578: Vec rhs;
579: PetscReal hx, hy, dv;
580: Vec coefficients_local;
581: PetscBool build_rhs;
582: DM dm_main, dm_coefficients;
583: PetscScalar K_cont, K_bound;
584: Ctx ctx = parameters->ctx;
585: PetscInt level = parameters->level;
587: PetscFunctionBeginUser;
588: if (parameters->faces_only) {
589: dm_main = ctx->levels[level]->dm_faces;
590: } else {
591: dm_main = ctx->levels[level]->dm_stokes;
592: }
593: dm_coefficients = ctx->levels[level]->dm_coefficients;
594: K_cont = ctx->levels[level]->K_cont;
595: K_bound = ctx->levels[level]->K_bound;
596: PetscCall(DMCreateMatrix(dm_main, pA));
597: A = *pA;
598: build_rhs = (PetscBool)(pRhs != NULL);
599: PetscCheck(!(parameters->faces_only && build_rhs), PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "RHS for faces-only not supported");
600: if (build_rhs) {
601: PetscCall(DMCreateGlobalVector(dm_main, pRhs));
602: rhs = *pRhs;
603: } else {
604: rhs = NULL;
605: }
606: PetscCall(DMStagGetCorners(dm_main, &startx, &starty, NULL, &nx, &ny, NULL, NULL, NULL, NULL));
607: PetscCall(DMStagGetGlobalSizes(dm_main, &N[0], &N[1], NULL));
608: hx = ctx->levels[level]->hx_characteristic;
609: hy = ctx->levels[level]->hy_characteristic;
610: dv = hx * hy;
611: PetscCall(DMGetLocalVector(dm_coefficients, &coefficients_local));
612: PetscCall(DMGlobalToLocal(dm_coefficients, ctx->levels[level]->coeff, INSERT_VALUES, coefficients_local));
614: /* Loop over all local elements */
615: for (ey = starty; ey < starty + ny; ++ey) { /* With DMStag, always iterate x fastest, y second fastest, z slowest */
616: for (ex = startx; ex < startx + nx; ++ex) {
617: const PetscBool left_boundary = (PetscBool)(ex == 0);
618: const PetscBool right_boundary = (PetscBool)(ex == N[0] - 1);
619: const PetscBool bottom_boundary = (PetscBool)(ey == 0);
620: const PetscBool top_boundary = (PetscBool)(ey == N[1] - 1);
622: if (ey == N[1] - 1) {
623: /* Top boundary velocity Dirichlet */
624: DMStagStencil row;
625: const PetscScalar val_rhs = 0.0;
626: const PetscScalar val_A = K_bound;
628: row.i = ex;
629: row.j = ey;
630: row.loc = DMSTAG_UP;
631: row.c = 0;
632: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
633: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
634: }
636: if (ey == 0) {
637: /* Bottom boundary velocity Dirichlet */
638: DMStagStencil row;
639: const PetscScalar val_rhs = 0.0;
640: const PetscScalar val_A = K_bound;
642: row.i = ex;
643: row.j = ey;
644: row.loc = DMSTAG_DOWN;
645: row.c = 0;
646: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
647: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
648: } else {
649: /* Y-momentum equation : (u_xx + u_yy) - p_y = f^y
650: includes non-zero forcing and free-slip boundary conditions */
651: PetscInt count;
652: DMStagStencil row, col[11];
653: PetscScalar val_A[11];
654: DMStagStencil rhoPoint[2];
655: PetscScalar rho[2], val_rhs;
656: DMStagStencil etaPoint[4];
657: PetscScalar eta[4], eta_left, eta_right, eta_up, eta_down;
659: row.i = ex;
660: row.j = ey;
661: row.loc = DMSTAG_DOWN;
662: row.c = 0;
664: /* get rho values and compute rhs value*/
665: rhoPoint[0].i = ex;
666: rhoPoint[0].j = ey;
667: rhoPoint[0].loc = DMSTAG_DOWN_LEFT;
668: rhoPoint[0].c = 1;
669: rhoPoint[1].i = ex;
670: rhoPoint[1].j = ey;
671: rhoPoint[1].loc = DMSTAG_DOWN_RIGHT;
672: rhoPoint[1].c = 1;
673: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 2, rhoPoint, rho));
674: val_rhs = -ctx->gy * dv * 0.5 * (rho[0] + rho[1]);
676: /* Get eta values */
677: etaPoint[0].i = ex;
678: etaPoint[0].j = ey;
679: etaPoint[0].loc = DMSTAG_DOWN_LEFT;
680: etaPoint[0].c = 0; /* Left */
681: etaPoint[1].i = ex;
682: etaPoint[1].j = ey;
683: etaPoint[1].loc = DMSTAG_DOWN_RIGHT;
684: etaPoint[1].c = 0; /* Right */
685: etaPoint[2].i = ex;
686: etaPoint[2].j = ey;
687: etaPoint[2].loc = DMSTAG_ELEMENT;
688: etaPoint[2].c = 0; /* Up */
689: etaPoint[3].i = ex;
690: etaPoint[3].j = ey - 1;
691: etaPoint[3].loc = DMSTAG_ELEMENT;
692: etaPoint[3].c = 0; /* Down */
693: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 4, etaPoint, eta));
694: eta_left = eta[0];
695: eta_right = eta[1];
696: eta_up = eta[2];
697: eta_down = eta[3];
699: count = 0;
701: col[count] = row;
702: val_A[count] = -2.0 * dv * (eta_down + eta_up) / (hy * hy);
703: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
704: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
705: ++count;
707: col[count].i = ex;
708: col[count].j = ey - 1;
709: col[count].loc = DMSTAG_DOWN;
710: col[count].c = 0;
711: val_A[count] = 2.0 * dv * eta_down / (hy * hy);
712: ++count;
713: col[count].i = ex;
714: col[count].j = ey + 1;
715: col[count].loc = DMSTAG_DOWN;
716: col[count].c = 0;
717: val_A[count] = 2.0 * dv * eta_up / (hy * hy);
718: ++count;
719: if (!left_boundary) {
720: col[count].i = ex - 1;
721: col[count].j = ey;
722: col[count].loc = DMSTAG_DOWN;
723: col[count].c = 0;
724: val_A[count] = dv * eta_left / (hx * hx);
725: ++count;
726: }
727: if (!right_boundary) {
728: col[count].i = ex + 1;
729: col[count].j = ey;
730: col[count].loc = DMSTAG_DOWN;
731: col[count].c = 0;
732: val_A[count] = dv * eta_right / (hx * hx);
733: ++count;
734: }
735: col[count].i = ex;
736: col[count].j = ey - 1;
737: col[count].loc = DMSTAG_LEFT;
738: col[count].c = 0;
739: val_A[count] = dv * eta_left / (hx * hy);
740: ++count; /* down left x edge */
741: col[count].i = ex;
742: col[count].j = ey - 1;
743: col[count].loc = DMSTAG_RIGHT;
744: col[count].c = 0;
745: val_A[count] = -1.0 * dv * eta_right / (hx * hy);
746: ++count; /* down right x edge */
747: col[count].i = ex;
748: col[count].j = ey;
749: col[count].loc = DMSTAG_LEFT;
750: col[count].c = 0;
751: val_A[count] = -1.0 * dv * eta_left / (hx * hy);
752: ++count; /* up left x edge */
753: col[count].i = ex;
754: col[count].j = ey;
755: col[count].loc = DMSTAG_RIGHT;
756: col[count].c = 0;
757: val_A[count] = dv * eta_right / (hx * hy);
758: ++count; /* up right x edge */
759: if (!parameters->faces_only) {
760: col[count].i = ex;
761: col[count].j = ey - 1;
762: col[count].loc = DMSTAG_ELEMENT;
763: col[count].c = 0;
764: val_A[count] = K_cont * dv / hy;
765: ++count;
766: col[count].i = ex;
767: col[count].j = ey;
768: col[count].loc = DMSTAG_ELEMENT;
769: col[count].c = 0;
770: val_A[count] = -1.0 * K_cont * dv / hy;
771: ++count;
772: }
774: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
775: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
776: }
778: if (ex == N[0] - 1) {
779: /* Right Boundary velocity Dirichlet */
780: /* Redundant in the corner */
781: DMStagStencil row;
782: const PetscScalar val_rhs = 0.0;
783: const PetscScalar val_A = K_bound;
785: row.i = ex;
786: row.j = ey;
787: row.loc = DMSTAG_RIGHT;
788: row.c = 0;
789: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
790: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
791: }
792: if (ex == 0) {
793: /* Left velocity Dirichlet */
794: DMStagStencil row;
795: const PetscScalar val_rhs = 0.0;
796: const PetscScalar val_A = K_bound;
798: row.i = ex;
799: row.j = ey;
800: row.loc = DMSTAG_LEFT;
801: row.c = 0;
802: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
803: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
804: } else {
805: /* X-momentum equation : (u_xx + u_yy) - p_x = f^x
806: zero RHS, including free-slip boundary conditions */
807: PetscInt count;
808: DMStagStencil row, col[11];
809: PetscScalar val_A[11];
810: DMStagStencil etaPoint[4];
811: PetscScalar eta[4], eta_left, eta_right, eta_up, eta_down;
812: const PetscScalar val_rhs = 0.0;
814: row.i = ex;
815: row.j = ey;
816: row.loc = DMSTAG_LEFT;
817: row.c = 0;
819: /* Get eta values */
820: etaPoint[0].i = ex - 1;
821: etaPoint[0].j = ey;
822: etaPoint[0].loc = DMSTAG_ELEMENT;
823: etaPoint[0].c = 0; /* Left */
824: etaPoint[1].i = ex;
825: etaPoint[1].j = ey;
826: etaPoint[1].loc = DMSTAG_ELEMENT;
827: etaPoint[1].c = 0; /* Right */
828: etaPoint[2].i = ex;
829: etaPoint[2].j = ey;
830: etaPoint[2].loc = DMSTAG_UP_LEFT;
831: etaPoint[2].c = 0; /* Up */
832: etaPoint[3].i = ex;
833: etaPoint[3].j = ey;
834: etaPoint[3].loc = DMSTAG_DOWN_LEFT;
835: etaPoint[3].c = 0; /* Down */
836: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coefficients_local, 4, etaPoint, eta));
837: eta_left = eta[0];
838: eta_right = eta[1];
839: eta_up = eta[2];
840: eta_down = eta[3];
842: count = 0;
843: col[count] = row;
844: val_A[count] = -2.0 * dv * (eta_left + eta_right) / (hx * hx);
845: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
846: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
847: ++count;
849: if (!bottom_boundary) {
850: col[count].i = ex;
851: col[count].j = ey - 1;
852: col[count].loc = DMSTAG_LEFT;
853: col[count].c = 0;
854: val_A[count] = dv * eta_down / (hy * hy);
855: ++count;
856: }
857: if (!top_boundary) {
858: col[count].i = ex;
859: col[count].j = ey + 1;
860: col[count].loc = DMSTAG_LEFT;
861: col[count].c = 0;
862: val_A[count] = dv * eta_up / (hy * hy);
863: ++count;
864: }
865: col[count].i = ex - 1;
866: col[count].j = ey;
867: col[count].loc = DMSTAG_LEFT;
868: col[count].c = 0;
869: val_A[count] = 2.0 * dv * eta_left / (hx * hx);
870: ++count;
871: col[count].i = ex + 1;
872: col[count].j = ey;
873: col[count].loc = DMSTAG_LEFT;
874: col[count].c = 0;
875: val_A[count] = 2.0 * dv * eta_right / (hx * hx);
876: ++count;
877: col[count].i = ex - 1;
878: col[count].j = ey;
879: col[count].loc = DMSTAG_DOWN;
880: col[count].c = 0;
881: val_A[count] = dv * eta_down / (hx * hy);
882: ++count; /* down left */
883: col[count].i = ex;
884: col[count].j = ey;
885: col[count].loc = DMSTAG_DOWN;
886: col[count].c = 0;
887: val_A[count] = -1.0 * dv * eta_down / (hx * hy);
888: ++count; /* down right */
889: col[count].i = ex - 1;
890: col[count].j = ey;
891: col[count].loc = DMSTAG_UP;
892: col[count].c = 0;
893: val_A[count] = -1.0 * dv * eta_up / (hx * hy);
894: ++count; /* up left */
895: col[count].i = ex;
896: col[count].j = ey;
897: col[count].loc = DMSTAG_UP;
898: col[count].c = 0;
899: val_A[count] = dv * eta_up / (hx * hy);
900: ++count; /* up right */
901: if (!parameters->faces_only) {
902: col[count].i = ex - 1;
903: col[count].j = ey;
904: col[count].loc = DMSTAG_ELEMENT;
905: col[count].c = 0;
906: val_A[count] = K_cont * dv / hx;
907: ++count;
908: col[count].i = ex;
909: col[count].j = ey;
910: col[count].loc = DMSTAG_ELEMENT;
911: col[count].c = 0;
912: val_A[count] = -1.0 * K_cont * dv / hx;
913: ++count;
914: }
916: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
917: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
918: }
920: /* P equation : u_x + v_y = 0
922: Note that this includes an explicit zero on the diagonal. This is only needed for
923: direct solvers (not required if using an iterative solver and setting the constant-pressure nullspace)
925: Note: the scaling by dv is not chosen in a principled way and is likely sub-optimal
926: */
927: if (!parameters->faces_only) {
928: if (ctx->pin_pressure && ex == 0 && ey == 0) { /* Pin the first pressure node to zero, if requested */
929: DMStagStencil row;
930: const PetscScalar val_A = K_bound;
931: const PetscScalar val_rhs = 0.0;
933: row.i = ex;
934: row.j = ey;
935: row.loc = DMSTAG_ELEMENT;
936: row.c = 0;
937: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
938: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
939: } else {
940: DMStagStencil row, col[5];
941: PetscScalar val_A[5];
942: const PetscScalar val_rhs = 0.0;
944: row.i = ex;
945: row.j = ey;
946: row.loc = DMSTAG_ELEMENT;
947: row.c = 0;
948: col[0].i = ex;
949: col[0].j = ey;
950: col[0].loc = DMSTAG_LEFT;
951: col[0].c = 0;
952: val_A[0] = -1.0 * K_cont * dv / hx;
953: col[1].i = ex;
954: col[1].j = ey;
955: col[1].loc = DMSTAG_RIGHT;
956: col[1].c = 0;
957: val_A[1] = K_cont * dv / hx;
958: col[2].i = ex;
959: col[2].j = ey;
960: col[2].loc = DMSTAG_DOWN;
961: col[2].c = 0;
962: val_A[2] = -1.0 * K_cont * dv / hy;
963: col[3].i = ex;
964: col[3].j = ey;
965: col[3].loc = DMSTAG_UP;
966: col[3].c = 0;
967: val_A[3] = K_cont * dv / hy;
968: col[4] = row;
969: val_A[4] = 0.0;
970: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 5, col, val_A, INSERT_VALUES));
971: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
972: }
973: }
974: }
975: }
976: PetscCall(DMRestoreLocalVector(dm_coefficients, &coefficients_local));
978: /* Add additional inverse viscosity terms (for use in building a matrix used to construct the preconditioner) */
979: if (parameters->include_inverse_visc) {
980: PetscCheck(!parameters->faces_only, PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "Does not make sense with faces only");
981: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_main, dm_coefficients, ctx->levels[level]->coeff, 1.0, A));
982: }
984: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
985: if (build_rhs) PetscCall(VecAssemblyBegin(rhs));
986: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
987: if (build_rhs) PetscCall(VecAssemblyEnd(rhs));
988: PetscFunctionReturn(PETSC_SUCCESS);
989: }
991: static PetscErrorCode CreateSystem3d(SystemParameters parameters, Mat *pA, Vec *pRhs)
992: {
993: PetscInt N[3];
994: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
995: Mat A;
996: PetscReal hx, hy, hz, dv;
997: PetscInt pinx, piny, pinz;
998: Vec coeff_local, rhs;
999: PetscBool build_rhs;
1000: DM dm_main, dm_coefficients;
1001: PetscScalar K_cont, K_bound;
1002: Ctx ctx = parameters->ctx;
1003: PetscInt level = parameters->level;
1005: PetscFunctionBeginUser;
1006: if (parameters->faces_only) {
1007: dm_main = ctx->levels[level]->dm_faces;
1008: } else {
1009: dm_main = ctx->levels[level]->dm_stokes;
1010: }
1011: dm_coefficients = ctx->levels[level]->dm_coefficients;
1012: K_cont = ctx->levels[level]->K_cont;
1013: K_bound = ctx->levels[level]->K_bound;
1014: PetscCall(DMCreateMatrix(dm_main, pA));
1015: A = *pA;
1016: build_rhs = (PetscBool)(pRhs != NULL);
1017: if (build_rhs) {
1018: PetscCall(DMCreateGlobalVector(dm_main, pRhs));
1019: rhs = *pRhs;
1020: } else {
1021: rhs = NULL;
1022: }
1023: PetscCall(DMStagGetCorners(dm_main, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
1024: PetscCall(DMStagGetGlobalSizes(dm_main, &N[0], &N[1], &N[2]));
1025: hx = ctx->levels[level]->hx_characteristic;
1026: hy = ctx->levels[level]->hy_characteristic;
1027: hz = ctx->levels[level]->hz_characteristic;
1028: dv = hx * hy * hz;
1029: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1030: PetscCall(DMGlobalToLocal(dm_coefficients, ctx->levels[level]->coeff, INSERT_VALUES, coeff_local));
1032: 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");
1033: pinx = 1;
1034: piny = 0;
1035: pinz = 0; /* Depends on assertion above that there are at least two element in the x direction */
1037: /* Loop over all local elements.
1039: For each element, fill 4-7 rows of the matrix, corresponding to
1040: - the pressure degree of freedom (dof), centered on the element
1041: - the 3 velocity dofs on left, bottom, and back faces of the element
1042: - velocity dof on the right, top, and front faces of the element (only on domain boundaries)
1044: */
1045: for (ez = startz; ez < startz + nz; ++ez) {
1046: for (ey = starty; ey < starty + ny; ++ey) {
1047: for (ex = startx; ex < startx + nx; ++ex) {
1048: const PetscBool left_boundary = (PetscBool)(ex == 0);
1049: const PetscBool right_boundary = (PetscBool)(ex == N[0] - 1);
1050: const PetscBool bottom_boundary = (PetscBool)(ey == 0);
1051: const PetscBool top_boundary = (PetscBool)(ey == N[1] - 1);
1052: const PetscBool back_boundary = (PetscBool)(ez == 0);
1053: const PetscBool front_boundary = (PetscBool)(ez == N[2] - 1);
1055: /* Note that below, we depend on the check above that there is never one
1056: element (globally) in a given direction. Thus, for example, an
1057: element is never both on the left and right boundary */
1059: /* X-faces - right boundary */
1060: if (right_boundary) {
1061: /* Right x-velocity Dirichlet */
1062: DMStagStencil row;
1063: const PetscScalar val_rhs = 0.0;
1064: const PetscScalar val_A = K_bound;
1066: row.i = ex;
1067: row.j = ey;
1068: row.k = ez;
1069: row.loc = DMSTAG_RIGHT;
1070: row.c = 0;
1071: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1072: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1073: }
1075: /* X faces - left*/
1076: {
1077: DMStagStencil row;
1079: row.i = ex;
1080: row.j = ey;
1081: row.k = ez;
1082: row.loc = DMSTAG_LEFT;
1083: row.c = 0;
1085: if (left_boundary) {
1086: /* Left x-velocity Dirichlet */
1087: const PetscScalar val_rhs = 0.0;
1088: const PetscScalar val_A = K_bound;
1090: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1091: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1092: } else {
1093: /* X-momentum equation */
1094: PetscInt count;
1095: DMStagStencil col[17];
1096: PetscScalar val_A[17];
1097: DMStagStencil eta_point[6];
1098: PetscScalar eta[6], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the left face */
1099: const PetscScalar val_rhs = 0.0;
1101: /* Get eta values */
1102: eta_point[0].i = ex - 1;
1103: eta_point[0].j = ey;
1104: eta_point[0].k = ez;
1105: eta_point[0].loc = DMSTAG_ELEMENT;
1106: eta_point[0].c = 0; /* Left */
1107: eta_point[1].i = ex;
1108: eta_point[1].j = ey;
1109: eta_point[1].k = ez;
1110: eta_point[1].loc = DMSTAG_ELEMENT;
1111: eta_point[1].c = 0; /* Right */
1112: eta_point[2].i = ex;
1113: eta_point[2].j = ey;
1114: eta_point[2].k = ez;
1115: eta_point[2].loc = DMSTAG_DOWN_LEFT;
1116: eta_point[2].c = 0; /* Down */
1117: eta_point[3].i = ex;
1118: eta_point[3].j = ey;
1119: eta_point[3].k = ez;
1120: eta_point[3].loc = DMSTAG_UP_LEFT;
1121: eta_point[3].c = 0; /* Up */
1122: eta_point[4].i = ex;
1123: eta_point[4].j = ey;
1124: eta_point[4].k = ez;
1125: eta_point[4].loc = DMSTAG_BACK_LEFT;
1126: eta_point[4].c = 0; /* Back */
1127: eta_point[5].i = ex;
1128: eta_point[5].j = ey;
1129: eta_point[5].k = ez;
1130: eta_point[5].loc = DMSTAG_FRONT_LEFT;
1131: eta_point[5].c = 0; /* Front */
1132: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1133: eta_left = eta[0];
1134: eta_right = eta[1];
1135: eta_down = eta[2];
1136: eta_up = eta[3];
1137: eta_back = eta[4];
1138: eta_front = eta[5];
1140: count = 0;
1142: col[count] = row;
1143: val_A[count] = -2.0 * dv * (eta_left + eta_right) / (hx * hx);
1144: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
1145: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
1146: if (!back_boundary) val_A[count] += -1.0 * dv * eta_back / (hz * hz);
1147: if (!front_boundary) val_A[count] += -1.0 * dv * eta_front / (hz * hz);
1148: ++count;
1150: col[count].i = ex - 1;
1151: col[count].j = ey;
1152: col[count].k = ez;
1153: col[count].loc = DMSTAG_LEFT;
1154: col[count].c = 0;
1155: val_A[count] = 2.0 * dv * eta_left / (hx * hx);
1156: ++count;
1157: col[count].i = ex + 1;
1158: col[count].j = ey;
1159: col[count].k = ez;
1160: col[count].loc = DMSTAG_LEFT;
1161: col[count].c = 0;
1162: val_A[count] = 2.0 * dv * eta_right / (hx * hx);
1163: ++count;
1164: if (!bottom_boundary) {
1165: col[count].i = ex;
1166: col[count].j = ey - 1;
1167: col[count].k = ez;
1168: col[count].loc = DMSTAG_LEFT;
1169: col[count].c = 0;
1170: val_A[count] = dv * eta_down / (hy * hy);
1171: ++count;
1172: }
1173: if (!top_boundary) {
1174: col[count].i = ex;
1175: col[count].j = ey + 1;
1176: col[count].k = ez;
1177: col[count].loc = DMSTAG_LEFT;
1178: col[count].c = 0;
1179: val_A[count] = dv * eta_up / (hy * hy);
1180: ++count;
1181: }
1182: if (!back_boundary) {
1183: col[count].i = ex;
1184: col[count].j = ey;
1185: col[count].k = ez - 1;
1186: col[count].loc = DMSTAG_LEFT;
1187: col[count].c = 0;
1188: val_A[count] = dv * eta_back / (hz * hz);
1189: ++count;
1190: }
1191: if (!front_boundary) {
1192: col[count].i = ex;
1193: col[count].j = ey;
1194: col[count].k = ez + 1;
1195: col[count].loc = DMSTAG_LEFT;
1196: col[count].c = 0;
1197: val_A[count] = dv * eta_front / (hz * hz);
1198: ++count;
1199: }
1201: col[count].i = ex - 1;
1202: col[count].j = ey;
1203: col[count].k = ez;
1204: col[count].loc = DMSTAG_DOWN;
1205: col[count].c = 0;
1206: val_A[count] = dv * eta_down / (hx * hy);
1207: ++count; /* down left */
1208: col[count].i = ex;
1209: col[count].j = ey;
1210: col[count].k = ez;
1211: col[count].loc = DMSTAG_DOWN;
1212: col[count].c = 0;
1213: val_A[count] = -1.0 * dv * eta_down / (hx * hy);
1214: ++count; /* down right */
1216: col[count].i = ex - 1;
1217: col[count].j = ey;
1218: col[count].k = ez;
1219: col[count].loc = DMSTAG_UP;
1220: col[count].c = 0;
1221: val_A[count] = -1.0 * dv * eta_up / (hx * hy);
1222: ++count; /* up left */
1223: col[count].i = ex;
1224: col[count].j = ey;
1225: col[count].k = ez;
1226: col[count].loc = DMSTAG_UP;
1227: col[count].c = 0;
1228: val_A[count] = dv * eta_up / (hx * hy);
1229: ++count; /* up right */
1231: col[count].i = ex - 1;
1232: col[count].j = ey;
1233: col[count].k = ez;
1234: col[count].loc = DMSTAG_BACK;
1235: col[count].c = 0;
1236: val_A[count] = dv * eta_back / (hx * hz);
1237: ++count; /* back left */
1238: col[count].i = ex;
1239: col[count].j = ey;
1240: col[count].k = ez;
1241: col[count].loc = DMSTAG_BACK;
1242: col[count].c = 0;
1243: val_A[count] = -1.0 * dv * eta_back / (hx * hz);
1244: ++count; /* back right */
1246: col[count].i = ex - 1;
1247: col[count].j = ey;
1248: col[count].k = ez;
1249: col[count].loc = DMSTAG_FRONT;
1250: col[count].c = 0;
1251: val_A[count] = -1.0 * dv * eta_front / (hx * hz);
1252: ++count; /* front left */
1253: col[count].i = ex;
1254: col[count].j = ey;
1255: col[count].k = ez;
1256: col[count].loc = DMSTAG_FRONT;
1257: col[count].c = 0;
1258: val_A[count] = dv * eta_front / (hx * hz);
1259: ++count; /* front right */
1261: if (!parameters->faces_only) {
1262: col[count].i = ex - 1;
1263: col[count].j = ey;
1264: col[count].k = ez;
1265: col[count].loc = DMSTAG_ELEMENT;
1266: col[count].c = 0;
1267: val_A[count] = K_cont * dv / hx;
1268: ++count;
1269: col[count].i = ex;
1270: col[count].j = ey;
1271: col[count].k = ez;
1272: col[count].loc = DMSTAG_ELEMENT;
1273: col[count].c = 0;
1274: val_A[count] = -1.0 * K_cont * dv / hx;
1275: ++count;
1276: }
1278: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1279: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1280: }
1281: }
1283: /* Y faces - top boundary */
1284: if (top_boundary) {
1285: /* Top y-velocity Dirichlet */
1286: DMStagStencil row;
1287: const PetscScalar val_rhs = 0.0;
1288: const PetscScalar val_A = K_bound;
1290: row.i = ex;
1291: row.j = ey;
1292: row.k = ez;
1293: row.loc = DMSTAG_UP;
1294: row.c = 0;
1295: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1296: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1297: }
1299: /* Y faces - down */
1300: {
1301: DMStagStencil row;
1303: row.i = ex;
1304: row.j = ey;
1305: row.k = ez;
1306: row.loc = DMSTAG_DOWN;
1307: row.c = 0;
1309: if (bottom_boundary) {
1310: /* Bottom y-velocity Dirichlet */
1311: const PetscScalar val_rhs = 0.0;
1312: const PetscScalar val_A = K_bound;
1314: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1315: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1316: } else {
1317: /* Y-momentum equation (including non-zero forcing) */
1318: PetscInt count;
1319: DMStagStencil col[17];
1320: PetscScalar val_rhs, val_A[17];
1321: DMStagStencil eta_point[6], rho_point[4];
1322: PetscScalar eta[6], rho[4], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the bottom face */
1324: if (build_rhs) {
1325: /* get rho values (note .c = 1) */
1326: /* Note that we have rho at perhaps strange points (edges not corners) */
1327: rho_point[0].i = ex;
1328: rho_point[0].j = ey;
1329: rho_point[0].k = ez;
1330: rho_point[0].loc = DMSTAG_DOWN_LEFT;
1331: rho_point[0].c = 1;
1332: rho_point[1].i = ex;
1333: rho_point[1].j = ey;
1334: rho_point[1].k = ez;
1335: rho_point[1].loc = DMSTAG_DOWN_RIGHT;
1336: rho_point[1].c = 1;
1337: rho_point[2].i = ex;
1338: rho_point[2].j = ey;
1339: rho_point[2].k = ez;
1340: rho_point[2].loc = DMSTAG_BACK_DOWN;
1341: rho_point[2].c = 1;
1342: rho_point[3].i = ex;
1343: rho_point[3].j = ey;
1344: rho_point[3].k = ez;
1345: rho_point[3].loc = DMSTAG_FRONT_DOWN;
1346: rho_point[3].c = 1;
1347: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 4, rho_point, rho));
1349: /* Compute forcing */
1350: val_rhs = ctx->gy * dv * (0.25 * (rho[0] + rho[1] + rho[2] + rho[3]));
1351: }
1353: /* Get eta values */
1354: eta_point[0].i = ex;
1355: eta_point[0].j = ey;
1356: eta_point[0].k = ez;
1357: eta_point[0].loc = DMSTAG_DOWN_LEFT;
1358: eta_point[0].c = 0; /* Left */
1359: eta_point[1].i = ex;
1360: eta_point[1].j = ey;
1361: eta_point[1].k = ez;
1362: eta_point[1].loc = DMSTAG_DOWN_RIGHT;
1363: eta_point[1].c = 0; /* Right */
1364: eta_point[2].i = ex;
1365: eta_point[2].j = ey - 1;
1366: eta_point[2].k = ez;
1367: eta_point[2].loc = DMSTAG_ELEMENT;
1368: eta_point[2].c = 0; /* Down */
1369: eta_point[3].i = ex;
1370: eta_point[3].j = ey;
1371: eta_point[3].k = ez;
1372: eta_point[3].loc = DMSTAG_ELEMENT;
1373: eta_point[3].c = 0; /* Up */
1374: eta_point[4].i = ex;
1375: eta_point[4].j = ey;
1376: eta_point[4].k = ez;
1377: eta_point[4].loc = DMSTAG_BACK_DOWN;
1378: eta_point[4].c = 0; /* Back */
1379: eta_point[5].i = ex;
1380: eta_point[5].j = ey;
1381: eta_point[5].k = ez;
1382: eta_point[5].loc = DMSTAG_FRONT_DOWN;
1383: eta_point[5].c = 0; /* Front */
1384: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1385: eta_left = eta[0];
1386: eta_right = eta[1];
1387: eta_down = eta[2];
1388: eta_up = eta[3];
1389: eta_back = eta[4];
1390: eta_front = eta[5];
1392: count = 0;
1394: col[count] = row;
1395: val_A[count] = -2.0 * dv * (eta_up + eta_down) / (hy * hy);
1396: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
1397: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
1398: if (!back_boundary) val_A[count] += -1.0 * dv * eta_back / (hz * hz);
1399: if (!front_boundary) val_A[count] += -1.0 * dv * eta_front / (hz * hz);
1400: ++count;
1402: col[count].i = ex;
1403: col[count].j = ey - 1;
1404: col[count].k = ez;
1405: col[count].loc = DMSTAG_DOWN;
1406: col[count].c = 0;
1407: val_A[count] = 2.0 * dv * eta_down / (hy * hy);
1408: ++count;
1409: col[count].i = ex;
1410: col[count].j = ey + 1;
1411: col[count].k = ez;
1412: col[count].loc = DMSTAG_DOWN;
1413: col[count].c = 0;
1414: val_A[count] = 2.0 * dv * eta_up / (hy * hy);
1415: ++count;
1417: if (!left_boundary) {
1418: col[count].i = ex - 1;
1419: col[count].j = ey;
1420: col[count].k = ez;
1421: col[count].loc = DMSTAG_DOWN;
1422: col[count].c = 0;
1423: val_A[count] = dv * eta_left / (hx * hx);
1424: ++count;
1425: }
1426: if (!right_boundary) {
1427: col[count].i = ex + 1;
1428: col[count].j = ey;
1429: col[count].k = ez;
1430: col[count].loc = DMSTAG_DOWN;
1431: col[count].c = 0;
1432: val_A[count] = dv * eta_right / (hx * hx);
1433: ++count;
1434: }
1435: if (!back_boundary) {
1436: col[count].i = ex;
1437: col[count].j = ey;
1438: col[count].k = ez - 1;
1439: col[count].loc = DMSTAG_DOWN;
1440: col[count].c = 0;
1441: val_A[count] = dv * eta_back / (hz * hz);
1442: ++count;
1443: }
1444: if (!front_boundary) {
1445: col[count].i = ex;
1446: col[count].j = ey;
1447: col[count].k = ez + 1;
1448: col[count].loc = DMSTAG_DOWN;
1449: col[count].c = 0;
1450: val_A[count] = dv * eta_front / (hz * hz);
1451: ++count;
1452: }
1454: col[count].i = ex;
1455: col[count].j = ey - 1;
1456: col[count].k = ez;
1457: col[count].loc = DMSTAG_LEFT;
1458: col[count].c = 0;
1459: val_A[count] = dv * eta_left / (hx * hy);
1460: ++count; /* down left*/
1461: col[count].i = ex;
1462: col[count].j = ey;
1463: col[count].k = ez;
1464: col[count].loc = DMSTAG_LEFT;
1465: col[count].c = 0;
1466: val_A[count] = -1.0 * dv * eta_left / (hx * hy);
1467: ++count; /* up left*/
1469: col[count].i = ex;
1470: col[count].j = ey - 1;
1471: col[count].k = ez;
1472: col[count].loc = DMSTAG_RIGHT;
1473: col[count].c = 0;
1474: val_A[count] = -1.0 * dv * eta_right / (hx * hy);
1475: ++count; /* down right*/
1476: col[count].i = ex;
1477: col[count].j = ey;
1478: col[count].k = ez;
1479: col[count].loc = DMSTAG_RIGHT;
1480: col[count].c = 0;
1481: val_A[count] = dv * eta_right / (hx * hy);
1482: ++count; /* up right*/
1484: col[count].i = ex;
1485: col[count].j = ey - 1;
1486: col[count].k = ez;
1487: col[count].loc = DMSTAG_BACK;
1488: col[count].c = 0;
1489: val_A[count] = dv * eta_back / (hy * hz);
1490: ++count; /* back down */
1491: col[count].i = ex;
1492: col[count].j = ey;
1493: col[count].k = ez;
1494: col[count].loc = DMSTAG_BACK;
1495: col[count].c = 0;
1496: val_A[count] = -1.0 * dv * eta_back / (hy * hz);
1497: ++count; /* back up */
1499: col[count].i = ex;
1500: col[count].j = ey - 1;
1501: col[count].k = ez;
1502: col[count].loc = DMSTAG_FRONT;
1503: col[count].c = 0;
1504: val_A[count] = -1.0 * dv * eta_front / (hy * hz);
1505: ++count; /* front down */
1506: col[count].i = ex;
1507: col[count].j = ey;
1508: col[count].k = ez;
1509: col[count].loc = DMSTAG_FRONT;
1510: col[count].c = 0;
1511: val_A[count] = dv * eta_front / (hy * hz);
1512: ++count; /* front up */
1514: if (!parameters->faces_only) {
1515: col[count].i = ex;
1516: col[count].j = ey - 1;
1517: col[count].k = ez;
1518: col[count].loc = DMSTAG_ELEMENT;
1519: col[count].c = 0;
1520: val_A[count] = K_cont * dv / hy;
1521: ++count;
1522: col[count].i = ex;
1523: col[count].j = ey;
1524: col[count].k = ez;
1525: col[count].loc = DMSTAG_ELEMENT;
1526: col[count].c = 0;
1527: val_A[count] = -1.0 * K_cont * dv / hy;
1528: ++count;
1529: }
1531: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1532: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1533: }
1534: }
1536: if (front_boundary) {
1537: /* Front z-velocity Dirichlet */
1538: DMStagStencil row;
1539: const PetscScalar val_rhs = 0.0;
1540: const PetscScalar val_A = K_bound;
1542: row.i = ex;
1543: row.j = ey;
1544: row.k = ez;
1545: row.loc = DMSTAG_FRONT;
1546: row.c = 0;
1547: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1548: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1549: }
1551: /* Z faces - back */
1552: {
1553: DMStagStencil row;
1555: row.i = ex;
1556: row.j = ey;
1557: row.k = ez;
1558: row.loc = DMSTAG_BACK;
1559: row.c = 0;
1561: if (back_boundary) {
1562: /* Back z-velocity Dirichlet */
1563: const PetscScalar val_rhs = 0.0;
1564: const PetscScalar val_A = K_bound;
1566: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1567: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1568: } else {
1569: /* Z-momentum equation */
1570: PetscInt count;
1571: DMStagStencil col[17];
1572: PetscScalar val_A[17];
1573: DMStagStencil eta_point[6];
1574: PetscScalar eta[6], eta_left, eta_right, eta_up, eta_down, eta_back, eta_front; /* relative to the back face */
1575: const PetscScalar val_rhs = 0.0;
1577: /* Get eta values */
1578: eta_point[0].i = ex;
1579: eta_point[0].j = ey;
1580: eta_point[0].k = ez;
1581: eta_point[0].loc = DMSTAG_BACK_LEFT;
1582: eta_point[0].c = 0; /* Left */
1583: eta_point[1].i = ex;
1584: eta_point[1].j = ey;
1585: eta_point[1].k = ez;
1586: eta_point[1].loc = DMSTAG_BACK_RIGHT;
1587: eta_point[1].c = 0; /* Right */
1588: eta_point[2].i = ex;
1589: eta_point[2].j = ey;
1590: eta_point[2].k = ez;
1591: eta_point[2].loc = DMSTAG_BACK_DOWN;
1592: eta_point[2].c = 0; /* Down */
1593: eta_point[3].i = ex;
1594: eta_point[3].j = ey;
1595: eta_point[3].k = ez;
1596: eta_point[3].loc = DMSTAG_BACK_UP;
1597: eta_point[3].c = 0; /* Up */
1598: eta_point[4].i = ex;
1599: eta_point[4].j = ey;
1600: eta_point[4].k = ez - 1;
1601: eta_point[4].loc = DMSTAG_ELEMENT;
1602: eta_point[4].c = 0; /* Back */
1603: eta_point[5].i = ex;
1604: eta_point[5].j = ey;
1605: eta_point[5].k = ez;
1606: eta_point[5].loc = DMSTAG_ELEMENT;
1607: eta_point[5].c = 0; /* Front */
1608: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 6, eta_point, eta));
1609: eta_left = eta[0];
1610: eta_right = eta[1];
1611: eta_down = eta[2];
1612: eta_up = eta[3];
1613: eta_back = eta[4];
1614: eta_front = eta[5];
1616: count = 0;
1618: col[count] = row;
1619: val_A[count] = -2.0 * dv * (eta_back + eta_front) / (hz * hz);
1620: if (!left_boundary) val_A[count] += -1.0 * dv * eta_left / (hx * hx);
1621: if (!right_boundary) val_A[count] += -1.0 * dv * eta_right / (hx * hx);
1622: if (!top_boundary) val_A[count] += -1.0 * dv * eta_up / (hy * hy);
1623: if (!bottom_boundary) val_A[count] += -1.0 * dv * eta_down / (hy * hy);
1624: ++count;
1626: col[count].i = ex;
1627: col[count].j = ey;
1628: col[count].k = ez - 1;
1629: col[count].loc = DMSTAG_BACK;
1630: col[count].c = 0;
1631: val_A[count] = 2.0 * dv * eta_back / (hz * hz);
1632: ++count;
1633: col[count].i = ex;
1634: col[count].j = ey;
1635: col[count].k = ez + 1;
1636: col[count].loc = DMSTAG_BACK;
1637: col[count].c = 0;
1638: val_A[count] = 2.0 * dv * eta_front / (hz * hz);
1639: ++count;
1641: if (!left_boundary) {
1642: col[count].i = ex - 1;
1643: col[count].j = ey;
1644: col[count].k = ez;
1645: col[count].loc = DMSTAG_BACK;
1646: col[count].c = 0;
1647: val_A[count] = dv * eta_left / (hx * hx);
1648: ++count;
1649: }
1650: if (!right_boundary) {
1651: col[count].i = ex + 1;
1652: col[count].j = ey;
1653: col[count].k = ez;
1654: col[count].loc = DMSTAG_BACK;
1655: col[count].c = 0;
1656: val_A[count] = dv * eta_right / (hx * hx);
1657: ++count;
1658: }
1659: if (!bottom_boundary) {
1660: col[count].i = ex;
1661: col[count].j = ey - 1;
1662: col[count].k = ez;
1663: col[count].loc = DMSTAG_BACK;
1664: col[count].c = 0;
1665: val_A[count] = dv * eta_down / (hy * hy);
1666: ++count;
1667: }
1668: if (!top_boundary) {
1669: col[count].i = ex;
1670: col[count].j = ey + 1;
1671: col[count].k = ez;
1672: col[count].loc = DMSTAG_BACK;
1673: col[count].c = 0;
1674: val_A[count] = dv * eta_up / (hy * hy);
1675: ++count;
1676: }
1678: col[count].i = ex;
1679: col[count].j = ey;
1680: col[count].k = ez - 1;
1681: col[count].loc = DMSTAG_LEFT;
1682: col[count].c = 0;
1683: val_A[count] = dv * eta_left / (hx * hz);
1684: ++count; /* back left*/
1685: col[count].i = ex;
1686: col[count].j = ey;
1687: col[count].k = ez;
1688: col[count].loc = DMSTAG_LEFT;
1689: col[count].c = 0;
1690: val_A[count] = -1.0 * dv * eta_left / (hx * hz);
1691: ++count; /* front left*/
1693: col[count].i = ex;
1694: col[count].j = ey;
1695: col[count].k = ez - 1;
1696: col[count].loc = DMSTAG_RIGHT;
1697: col[count].c = 0;
1698: val_A[count] = -1.0 * dv * eta_right / (hx * hz);
1699: ++count; /* back right */
1700: col[count].i = ex;
1701: col[count].j = ey;
1702: col[count].k = ez;
1703: col[count].loc = DMSTAG_RIGHT;
1704: col[count].c = 0;
1705: val_A[count] = dv * eta_right / (hx * hz);
1706: ++count; /* front right*/
1708: col[count].i = ex;
1709: col[count].j = ey;
1710: col[count].k = ez - 1;
1711: col[count].loc = DMSTAG_DOWN;
1712: col[count].c = 0;
1713: val_A[count] = dv * eta_down / (hy * hz);
1714: ++count; /* back down */
1715: col[count].i = ex;
1716: col[count].j = ey;
1717: col[count].k = ez;
1718: col[count].loc = DMSTAG_DOWN;
1719: col[count].c = 0;
1720: val_A[count] = -1.0 * dv * eta_down / (hy * hz);
1721: ++count; /* back down */
1723: col[count].i = ex;
1724: col[count].j = ey;
1725: col[count].k = ez - 1;
1726: col[count].loc = DMSTAG_UP;
1727: col[count].c = 0;
1728: val_A[count] = -1.0 * dv * eta_up / (hy * hz);
1729: ++count; /* back up */
1730: col[count].i = ex;
1731: col[count].j = ey;
1732: col[count].k = ez;
1733: col[count].loc = DMSTAG_UP;
1734: col[count].c = 0;
1735: val_A[count] = dv * eta_up / (hy * hz);
1736: ++count; /* back up */
1738: if (!parameters->faces_only) {
1739: col[count].i = ex;
1740: col[count].j = ey;
1741: col[count].k = ez - 1;
1742: col[count].loc = DMSTAG_ELEMENT;
1743: col[count].c = 0;
1744: val_A[count] = K_cont * dv / hz;
1745: ++count;
1746: col[count].i = ex;
1747: col[count].j = ey;
1748: col[count].k = ez;
1749: col[count].loc = DMSTAG_ELEMENT;
1750: col[count].c = 0;
1751: val_A[count] = -1.0 * K_cont * dv / hz;
1752: ++count;
1753: }
1755: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, count, col, val_A, INSERT_VALUES));
1756: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1757: }
1758: }
1760: /* Elements */
1761: if (!parameters->faces_only) {
1762: DMStagStencil row;
1764: row.i = ex;
1765: row.j = ey;
1766: row.k = ez;
1767: row.loc = DMSTAG_ELEMENT;
1768: row.c = 0;
1770: if (ctx->pin_pressure && ex == pinx && ey == piny && ez == pinz) {
1771: /* Pin a pressure node to zero, if requested */
1772: const PetscScalar val_A = K_bound;
1773: const PetscScalar val_rhs = 0.0;
1775: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 1, &row, &val_A, INSERT_VALUES));
1776: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1777: } else {
1778: /* Continuity equation */
1779: /* Note that this includes an explicit zero on the diagonal. This is only needed for
1780: some direct solvers (not required if using an iterative solver and setting a constant-pressure nullspace) */
1781: /* Note: the scaling by dv is not chosen in a principled way and is likely sub-optimal */
1782: DMStagStencil col[7];
1783: PetscScalar val_A[7];
1784: const PetscScalar val_rhs = 0.0;
1786: col[0].i = ex;
1787: col[0].j = ey;
1788: col[0].k = ez;
1789: col[0].loc = DMSTAG_LEFT;
1790: col[0].c = 0;
1791: val_A[0] = -1.0 * K_cont * dv / hx;
1792: col[1].i = ex;
1793: col[1].j = ey;
1794: col[1].k = ez;
1795: col[1].loc = DMSTAG_RIGHT;
1796: col[1].c = 0;
1797: val_A[1] = K_cont * dv / hx;
1798: col[2].i = ex;
1799: col[2].j = ey;
1800: col[2].k = ez;
1801: col[2].loc = DMSTAG_DOWN;
1802: col[2].c = 0;
1803: val_A[2] = -1.0 * K_cont * dv / hy;
1804: col[3].i = ex;
1805: col[3].j = ey;
1806: col[3].k = ez;
1807: col[3].loc = DMSTAG_UP;
1808: col[3].c = 0;
1809: val_A[3] = K_cont * dv / hy;
1810: col[4].i = ex;
1811: col[4].j = ey;
1812: col[4].k = ez;
1813: col[4].loc = DMSTAG_BACK;
1814: col[4].c = 0;
1815: val_A[4] = -1.0 * K_cont * dv / hz;
1816: col[5].i = ex;
1817: col[5].j = ey;
1818: col[5].k = ez;
1819: col[5].loc = DMSTAG_FRONT;
1820: col[5].c = 0;
1821: val_A[5] = K_cont * dv / hz;
1822: col[6] = row;
1823: val_A[6] = 0.0;
1824: PetscCall(DMStagMatSetValuesStencil(dm_main, A, 1, &row, 7, col, val_A, INSERT_VALUES));
1825: if (build_rhs) PetscCall(DMStagVecSetValuesStencil(dm_main, rhs, 1, &row, &val_rhs, INSERT_VALUES));
1826: }
1827: }
1828: }
1829: }
1830: }
1831: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
1833: /* Add additional inverse viscosity terms (for use in building a matrix used to construct the preconditioner) */
1834: if (parameters->include_inverse_visc) {
1835: PetscCheck(!parameters->faces_only, PetscObjectComm((PetscObject)dm_main), PETSC_ERR_SUP, "Does not make sense with faces only");
1836: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_main, dm_coefficients, ctx->levels[level]->coeff, 1.0, A));
1837: }
1839: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1840: if (build_rhs) PetscCall(VecAssemblyBegin(rhs));
1841: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1842: if (build_rhs) PetscCall(VecAssemblyEnd(rhs));
1843: PetscFunctionReturn(PETSC_SUCCESS);
1844: }
1846: static PetscErrorCode CreateSystem(SystemParameters parameters, Mat *pA, Vec *pRhs)
1847: {
1848: PetscFunctionBeginUser;
1849: if (parameters->ctx->dim == 2) {
1850: PetscCall(CreateSystem2d(parameters, pA, pRhs));
1851: } else if (parameters->ctx->dim == 3) {
1852: PetscCall(CreateSystem3d(parameters, pA, pRhs));
1853: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT, parameters->ctx->dim);
1854: PetscFunctionReturn(PETSC_SUCCESS);
1855: }
1857: PetscErrorCode PopulateCoefficientData(Ctx ctx, PetscInt level)
1858: {
1859: PetscInt dim;
1860: PetscInt N[3];
1861: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
1862: PetscInt slot_prev, slot_center;
1863: PetscInt slot_rho_downleft, slot_rho_backleft, slot_rho_backdown, slot_eta_element, slot_eta_downleft, slot_eta_backleft, slot_eta_backdown;
1864: Vec coeff_local;
1865: PetscReal **arr_coordinates_x, **arr_coordinates_y, **arr_coordinates_z;
1866: DM dm_coefficients;
1867: Vec coeff;
1869: PetscFunctionBeginUser;
1870: dm_coefficients = ctx->levels[level]->dm_coefficients;
1871: PetscCall(DMGetDimension(dm_coefficients, &dim));
1873: /* Create global coefficient vector */
1874: PetscCall(DMCreateGlobalVector(dm_coefficients, &ctx->levels[level]->coeff));
1875: coeff = ctx->levels[level]->coeff;
1877: /* Get temporary access to a local representation of the coefficient data */
1878: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1879: PetscCall(DMGlobalToLocal(dm_coefficients, coeff, INSERT_VALUES, coeff_local));
1881: /* Use direct array access to coefficient and coordinate arrays, to popoulate coefficient data */
1882: PetscCall(DMStagGetGhostCorners(dm_coefficients, &startx, &starty, &startz, &nx, &ny, &nz));
1883: PetscCall(DMStagGetGlobalSizes(dm_coefficients, &N[0], &N[1], &N[2]));
1884: PetscCall(DMStagGetProductCoordinateArraysRead(dm_coefficients, &arr_coordinates_x, &arr_coordinates_y, &arr_coordinates_z));
1885: PetscCall(DMStagGetProductCoordinateLocationSlot(dm_coefficients, DMSTAG_ELEMENT, &slot_center));
1886: PetscCall(DMStagGetProductCoordinateLocationSlot(dm_coefficients, DMSTAG_LEFT, &slot_prev));
1887: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_ELEMENT, 0, &slot_eta_element));
1888: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_DOWN_LEFT, 0, &slot_eta_downleft));
1889: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_DOWN_LEFT, 1, &slot_rho_downleft));
1890: if (dim == 2) {
1891: PetscScalar ***arr_coefficients;
1893: PetscCall(DMStagVecGetArray(dm_coefficients, coeff_local, &arr_coefficients));
1894: /* Note that these ranges are with respect to the local representation */
1895: for (ey = starty; ey < starty + ny; ++ey) {
1896: for (ex = startx; ex < startx + nx; ++ex) {
1897: arr_coefficients[ey][ex][slot_eta_element] = ctx->GetEta(ctx, arr_coordinates_x[ex][slot_center], arr_coordinates_y[ey][slot_center], 0.0);
1898: arr_coefficients[ey][ex][slot_eta_downleft] = ctx->GetEta(ctx, arr_coordinates_x[ex][slot_prev], arr_coordinates_y[ey][slot_prev], 0.0);
1899: arr_coefficients[ey][ex][slot_rho_downleft] = ctx->GetRho(ctx, arr_coordinates_x[ex][slot_prev], arr_coordinates_y[ey][slot_prev], 0.0);
1900: }
1901: }
1902: PetscCall(DMStagVecRestoreArray(dm_coefficients, coeff_local, &arr_coefficients));
1903: } else if (dim == 3) {
1904: PetscScalar ****arr_coefficients;
1906: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_LEFT, 0, &slot_eta_backleft));
1907: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_LEFT, 1, &slot_rho_backleft));
1908: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_DOWN, 0, &slot_eta_backdown));
1909: PetscCall(DMStagGetLocationSlot(dm_coefficients, DMSTAG_BACK_DOWN, 1, &slot_rho_backdown));
1910: PetscCall(DMStagVecGetArray(dm_coefficients, coeff_local, &arr_coefficients));
1911: /* Note that these are with respect to the entire local representation, including ghosts */
1912: for (ez = startz; ez < startz + nz; ++ez) {
1913: for (ey = starty; ey < starty + ny; ++ey) {
1914: for (ex = startx; ex < startx + nx; ++ex) {
1915: const PetscScalar x_prev = arr_coordinates_x[ex][slot_prev];
1916: const PetscScalar y_prev = arr_coordinates_y[ey][slot_prev];
1917: const PetscScalar z_prev = arr_coordinates_z[ez][slot_prev];
1918: const PetscScalar x_center = arr_coordinates_x[ex][slot_center];
1919: const PetscScalar y_center = arr_coordinates_y[ey][slot_center];
1920: const PetscScalar z_center = arr_coordinates_z[ez][slot_center];
1922: arr_coefficients[ez][ey][ex][slot_eta_element] = ctx->GetEta(ctx, x_center, y_center, z_center);
1923: arr_coefficients[ez][ey][ex][slot_eta_downleft] = ctx->GetEta(ctx, x_prev, y_prev, z_center);
1924: arr_coefficients[ez][ey][ex][slot_rho_downleft] = ctx->GetRho(ctx, x_prev, y_prev, z_center);
1925: arr_coefficients[ez][ey][ex][slot_eta_backleft] = ctx->GetEta(ctx, x_prev, y_center, z_prev);
1926: arr_coefficients[ez][ey][ex][slot_rho_backleft] = ctx->GetRho(ctx, x_prev, y_center, z_prev);
1927: arr_coefficients[ez][ey][ex][slot_eta_backdown] = ctx->GetEta(ctx, x_center, y_prev, z_prev);
1928: arr_coefficients[ez][ey][ex][slot_rho_backdown] = ctx->GetRho(ctx, x_center, y_prev, z_prev);
1929: }
1930: }
1931: }
1932: PetscCall(DMStagVecRestoreArray(dm_coefficients, coeff_local, &arr_coefficients));
1933: } else SETERRQ(PetscObjectComm((PetscObject)dm_coefficients), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT, dim);
1934: PetscCall(DMStagRestoreProductCoordinateArraysRead(dm_coefficients, &arr_coordinates_x, &arr_coordinates_y, &arr_coordinates_z));
1935: PetscCall(DMLocalToGlobal(dm_coefficients, coeff_local, INSERT_VALUES, coeff));
1936: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
1937: PetscFunctionReturn(PETSC_SUCCESS);
1938: }
1940: static PetscErrorCode CreateAuxiliaryOperator(Ctx ctx, PetscInt level, Mat *p_S_hat)
1941: {
1942: DM dm_element;
1943: Mat S_hat;
1944: DM dm_stokes, dm_coefficients;
1945: Vec coeff;
1947: PetscFunctionBeginUser;
1948: dm_stokes = ctx->levels[level]->dm_stokes;
1949: dm_coefficients = ctx->levels[level]->dm_coefficients;
1950: coeff = ctx->levels[level]->coeff;
1951: if (ctx->dim == 2) {
1952: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 1, 0, &dm_element));
1953: } else if (ctx->dim == 3) {
1954: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 0, 1, &dm_element));
1955: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not implemented for dimension %" PetscInt_FMT, ctx->dim);
1956: PetscCall(DMCreateMatrix(dm_element, p_S_hat));
1957: S_hat = *p_S_hat;
1958: PetscCall(OperatorInsertInverseViscosityPressureTerms(dm_element, dm_coefficients, coeff, 1.0, S_hat));
1959: PetscCall(MatAssemblyBegin(S_hat, MAT_FINAL_ASSEMBLY));
1960: PetscCall(MatAssemblyEnd(S_hat, MAT_FINAL_ASSEMBLY));
1961: PetscCall(DMDestroy(&dm_element));
1962: PetscFunctionReturn(PETSC_SUCCESS);
1963: }
1965: static PetscErrorCode OperatorInsertInverseViscosityPressureTerms(DM dm, DM dm_coefficients, Vec coefficients, PetscScalar scale, Mat mat)
1966: {
1967: PetscInt dim, ex, ey, ez, startx, starty, startz, nx, ny, nz;
1968: Vec coeff_local;
1970: PetscFunctionBeginUser;
1971: PetscCall(DMGetDimension(dm, &dim));
1972: PetscCall(DMGetLocalVector(dm_coefficients, &coeff_local));
1973: PetscCall(DMGlobalToLocal(dm_coefficients, coefficients, INSERT_VALUES, coeff_local));
1974: PetscCall(DMStagGetCorners(dm, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
1975: if (dim == 2) { /* Trick to have one loop nest */
1976: startz = 0;
1977: nz = 1;
1978: }
1979: for (ez = startz; ez < startz + nz; ++ez) {
1980: for (ey = starty; ey < starty + ny; ++ey) {
1981: for (ex = startx; ex < startx + nx; ++ex) {
1982: DMStagStencil from, to;
1983: PetscScalar val;
1985: /* component 0 on element is viscosity */
1986: from.i = ex;
1987: from.j = ey;
1988: from.k = ez;
1989: from.c = 0;
1990: from.loc = DMSTAG_ELEMENT;
1991: PetscCall(DMStagVecGetValuesStencil(dm_coefficients, coeff_local, 1, &from, &val));
1992: val = scale / val; /* inverse viscosity, scaled */
1993: to = from;
1994: PetscCall(DMStagMatSetValuesStencil(dm, mat, 1, &to, 1, &to, &val, INSERT_VALUES));
1995: }
1996: }
1997: }
1998: PetscCall(DMRestoreLocalVector(dm_coefficients, &coeff_local));
1999: /* Note that this function does not call MatAssembly{Begin,End} */
2000: PetscFunctionReturn(PETSC_SUCCESS);
2001: }
2003: /* Create a pressure-only DMStag and use it to generate a nullspace vector
2004: - Create a compatible DMStag with one dof per element (and nothing else).
2005: - Create a constant vector and normalize it
2006: - Migrate it to a vector on the original dmSol (making use of the fact
2007: that this will fill in zeros for "extra" dof)
2008: - Set the nullspace for the operator
2009: - Destroy everything (the operator keeps the references it needs) */
2010: static PetscErrorCode AttachNullspace(DM dmSol, Mat A)
2011: {
2012: DM dmPressure;
2013: Vec constantPressure, basis;
2014: PetscReal nrm;
2015: MatNullSpace matNullSpace;
2017: PetscFunctionBeginUser;
2018: PetscCall(DMStagCreateCompatibleDMStag(dmSol, 0, 0, 1, 0, &dmPressure));
2019: PetscCall(DMGetGlobalVector(dmPressure, &constantPressure));
2020: PetscCall(VecSet(constantPressure, 1.0));
2021: PetscCall(VecNorm(constantPressure, NORM_2, &nrm));
2022: PetscCall(VecScale(constantPressure, 1.0 / nrm));
2023: PetscCall(DMCreateGlobalVector(dmSol, &basis));
2024: PetscCall(DMStagMigrateVec(dmPressure, constantPressure, dmSol, basis));
2025: PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dmSol), PETSC_FALSE, 1, &basis, &matNullSpace));
2026: PetscCall(VecDestroy(&basis));
2027: PetscCall(MatSetNullSpace(A, matNullSpace));
2028: PetscCall(MatNullSpaceDestroy(&matNullSpace));
2029: PetscCall(DMRestoreGlobalVector(dmPressure, &constantPressure));
2030: PetscCall(DMDestroy(&dmPressure));
2031: PetscFunctionReturn(PETSC_SUCCESS);
2032: }
2034: static PetscErrorCode DumpSolution(Ctx ctx, PetscInt level, Vec x)
2035: {
2036: DM dm_stokes, dm_coefficients;
2037: Vec coeff;
2038: DM dm_vel_avg;
2039: Vec vel_avg;
2040: DM da_vel_avg, da_p, da_eta_element;
2041: Vec vec_vel_avg, vec_p, vec_eta_element;
2042: 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;
2043: 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;
2044: PetscInt ex, ey, ez, startx, starty, startz, nx, ny, nz;
2045: Vec stokesLocal;
2047: PetscFunctionBeginUser;
2048: dm_stokes = ctx->levels[level]->dm_stokes;
2049: dm_coefficients = ctx->levels[level]->dm_coefficients;
2050: coeff = ctx->levels[level]->coeff;
2052: /* For convenience, create a new DM and Vec which will hold averaged velocities
2053: Note that this could also be accomplished with direct array access, using
2054: DMStagVecGetArray() and related functions */
2055: if (ctx->dim == 2) {
2056: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 2, 0, &dm_vel_avg)); /* 2 dof per element */
2057: } else if (ctx->dim == 3) {
2058: PetscCall(DMStagCreateCompatibleDMStag(dm_stokes, 0, 0, 0, 3, &dm_vel_avg)); /* 3 dof per element */
2059: } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Not Implemented for dimension %" PetscInt_FMT, ctx->dim);
2060: PetscCall(DMSetUp(dm_vel_avg));
2061: PetscCall(DMStagSetUniformCoordinatesProduct(dm_vel_avg, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax, ctx->zmin, ctx->zmax));
2062: PetscCall(DMCreateGlobalVector(dm_vel_avg, &vel_avg));
2063: PetscCall(DMGetLocalVector(dm_stokes, &stokesLocal));
2064: PetscCall(DMGlobalToLocal(dm_stokes, x, INSERT_VALUES, stokesLocal));
2065: PetscCall(DMStagGetCorners(dm_vel_avg, &startx, &starty, &startz, &nx, &ny, &nz, NULL, NULL, NULL));
2066: if (ctx->dim == 2) {
2067: for (ey = starty; ey < starty + ny; ++ey) {
2068: for (ex = startx; ex < startx + nx; ++ex) {
2069: DMStagStencil from[4], to[2];
2070: PetscScalar valFrom[4], valTo[2];
2072: from[0].i = ex;
2073: from[0].j = ey;
2074: from[0].loc = DMSTAG_UP;
2075: from[0].c = 0;
2076: from[1].i = ex;
2077: from[1].j = ey;
2078: from[1].loc = DMSTAG_DOWN;
2079: from[1].c = 0;
2080: from[2].i = ex;
2081: from[2].j = ey;
2082: from[2].loc = DMSTAG_LEFT;
2083: from[2].c = 0;
2084: from[3].i = ex;
2085: from[3].j = ey;
2086: from[3].loc = DMSTAG_RIGHT;
2087: from[3].c = 0;
2088: PetscCall(DMStagVecGetValuesStencil(dm_stokes, stokesLocal, 4, from, valFrom));
2089: to[0].i = ex;
2090: to[0].j = ey;
2091: to[0].loc = DMSTAG_ELEMENT;
2092: to[0].c = 0;
2093: valTo[0] = 0.5 * (valFrom[2] + valFrom[3]);
2094: to[1].i = ex;
2095: to[1].j = ey;
2096: to[1].loc = DMSTAG_ELEMENT;
2097: to[1].c = 1;
2098: valTo[1] = 0.5 * (valFrom[0] + valFrom[1]);
2099: PetscCall(DMStagVecSetValuesStencil(dm_vel_avg, vel_avg, 2, to, valTo, INSERT_VALUES));
2100: }
2101: }
2102: } else if (ctx->dim == 3) {
2103: for (ez = startz; ez < startz + nz; ++ez) {
2104: for (ey = starty; ey < starty + ny; ++ey) {
2105: for (ex = startx; ex < startx + nx; ++ex) {
2106: DMStagStencil from[6], to[3];
2107: PetscScalar valFrom[6], valTo[3];
2109: from[0].i = ex;
2110: from[0].j = ey;
2111: from[0].k = ez;
2112: from[0].loc = DMSTAG_UP;
2113: from[0].c = 0;
2114: from[1].i = ex;
2115: from[1].j = ey;
2116: from[1].k = ez;
2117: from[1].loc = DMSTAG_DOWN;
2118: from[1].c = 0;
2119: from[2].i = ex;
2120: from[2].j = ey;
2121: from[2].k = ez;
2122: from[2].loc = DMSTAG_LEFT;
2123: from[2].c = 0;
2124: from[3].i = ex;
2125: from[3].j = ey;
2126: from[3].k = ez;
2127: from[3].loc = DMSTAG_RIGHT;
2128: from[3].c = 0;
2129: from[4].i = ex;
2130: from[4].j = ey;
2131: from[4].k = ez;
2132: from[4].loc = DMSTAG_BACK;
2133: from[4].c = 0;
2134: from[5].i = ex;
2135: from[5].j = ey;
2136: from[5].k = ez;
2137: from[5].loc = DMSTAG_FRONT;
2138: from[5].c = 0;
2139: PetscCall(DMStagVecGetValuesStencil(dm_stokes, stokesLocal, 6, from, valFrom));
2140: to[0].i = ex;
2141: to[0].j = ey;
2142: to[0].k = ez;
2143: to[0].loc = DMSTAG_ELEMENT;
2144: to[0].c = 0;
2145: valTo[0] = 0.5 * (valFrom[2] + valFrom[3]);
2146: to[1].i = ex;
2147: to[1].j = ey;
2148: to[1].k = ez;
2149: to[1].loc = DMSTAG_ELEMENT;
2150: to[1].c = 1;
2151: valTo[1] = 0.5 * (valFrom[0] + valFrom[1]);
2152: to[2].i = ex;
2153: to[2].j = ey;
2154: to[2].k = ez;
2155: to[2].loc = DMSTAG_ELEMENT;
2156: to[2].c = 2;
2157: valTo[2] = 0.5 * (valFrom[4] + valFrom[5]);
2158: PetscCall(DMStagVecSetValuesStencil(dm_vel_avg, vel_avg, 3, to, valTo, INSERT_VALUES));
2159: }
2160: }
2161: }
2162: }
2163: PetscCall(VecAssemblyBegin(vel_avg));
2164: PetscCall(VecAssemblyEnd(vel_avg));
2165: PetscCall(DMRestoreLocalVector(dm_stokes, &stokesLocal));
2167: /* Create individual DMDAs for sub-grids of our DMStag objects. This is
2168: somewhat inefficient, but allows use of the DMDA API without re-implementing
2169: all utilities for DMStag */
2171: PetscCall(DMStagVecSplitToDMDA(dm_stokes, x, DMSTAG_ELEMENT, 0, &da_p, &vec_p));
2172: PetscCall(PetscObjectSetName((PetscObject)vec_p, "p (scaled)"));
2174: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_ELEMENT, 0, &da_eta_element, &vec_eta_element));
2175: PetscCall(PetscObjectSetName((PetscObject)vec_eta_element, "eta"));
2177: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_DOWN_LEFT, 0, &da_eta_down_left, &vec_eta_down_left));
2178: PetscCall(PetscObjectSetName((PetscObject)vec_eta_down_left, "eta"));
2180: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_DOWN_LEFT, 1, &da_rho_down_left, &vec_rho_down_left));
2181: PetscCall(PetscObjectSetName((PetscObject)vec_rho_down_left, "density"));
2183: if (ctx->dim == 3) {
2184: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_LEFT, 0, &da_eta_back_left, &vec_eta_back_left));
2185: PetscCall(PetscObjectSetName((PetscObject)vec_eta_back_left, "eta"));
2187: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_LEFT, 1, &da_rho_back_left, &vec_rho_back_left));
2188: PetscCall(PetscObjectSetName((PetscObject)vec_rho_back_left, "rho"));
2190: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_DOWN, 0, &da_eta_back_down, &vec_eta_back_down));
2191: PetscCall(PetscObjectSetName((PetscObject)vec_eta_back_down, "eta"));
2193: PetscCall(DMStagVecSplitToDMDA(dm_coefficients, coeff, DMSTAG_BACK_DOWN, 1, &da_rho_back_down, &vec_rho_back_down));
2194: PetscCall(PetscObjectSetName((PetscObject)vec_rho_back_down, "rho"));
2195: }
2197: PetscCall(DMStagVecSplitToDMDA(dm_vel_avg, vel_avg, DMSTAG_ELEMENT, -3, &da_vel_avg, &vec_vel_avg)); /* note -3 : pad with zero */
2198: PetscCall(PetscObjectSetName((PetscObject)vec_vel_avg, "Velocity (Averaged)"));
2200: /* Dump element-based fields to a .vtr file */
2201: {
2202: PetscViewer viewer;
2204: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_vel_avg), "ex4_element.vtr", FILE_MODE_WRITE, &viewer));
2205: PetscCall(VecView(vec_vel_avg, viewer));
2206: PetscCall(VecView(vec_p, viewer));
2207: PetscCall(VecView(vec_eta_element, viewer));
2208: PetscCall(PetscViewerDestroy(&viewer));
2209: }
2211: /* Dump vertex- or edge-based fields to a second .vtr file */
2212: {
2213: PetscViewer viewer;
2215: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_down_left), "ex4_down_left.vtr", FILE_MODE_WRITE, &viewer));
2216: PetscCall(VecView(vec_eta_down_left, viewer));
2217: PetscCall(VecView(vec_rho_down_left, viewer));
2218: PetscCall(PetscViewerDestroy(&viewer));
2219: }
2220: if (ctx->dim == 3) {
2221: PetscViewer viewer;
2223: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_back_left), "ex4_back_left.vtr", FILE_MODE_WRITE, &viewer));
2224: PetscCall(VecView(vec_eta_back_left, viewer));
2225: PetscCall(VecView(vec_rho_back_left, viewer));
2226: PetscCall(PetscViewerDestroy(&viewer));
2227: }
2228: if (ctx->dim == 3) {
2229: PetscViewer viewer;
2231: PetscCall(PetscViewerVTKOpen(PetscObjectComm((PetscObject)da_eta_back_down), "ex4_back_down.vtr", FILE_MODE_WRITE, &viewer));
2232: PetscCall(VecView(vec_eta_back_down, viewer));
2233: PetscCall(VecView(vec_rho_back_down, viewer));
2234: PetscCall(PetscViewerDestroy(&viewer));
2235: }
2237: /* Destroy DMDAs and Vecs */
2238: PetscCall(VecDestroy(&vec_vel_avg));
2239: PetscCall(VecDestroy(&vec_p));
2240: PetscCall(VecDestroy(&vec_eta_element));
2241: PetscCall(VecDestroy(&vec_eta_down_left));
2242: if (ctx->dim == 3) {
2243: PetscCall(VecDestroy(&vec_eta_back_left));
2244: PetscCall(VecDestroy(&vec_eta_back_down));
2245: }
2246: PetscCall(VecDestroy(&vec_rho_down_left));
2247: if (ctx->dim == 3) {
2248: PetscCall(VecDestroy(&vec_rho_back_left));
2249: PetscCall(VecDestroy(&vec_rho_back_down));
2250: }
2251: PetscCall(DMDestroy(&da_vel_avg));
2252: PetscCall(DMDestroy(&da_p));
2253: PetscCall(DMDestroy(&da_eta_element));
2254: PetscCall(DMDestroy(&da_eta_down_left));
2255: if (ctx->dim == 3) {
2256: PetscCall(DMDestroy(&da_eta_back_left));
2257: PetscCall(DMDestroy(&da_eta_back_down));
2258: }
2259: PetscCall(DMDestroy(&da_rho_down_left));
2260: if (ctx->dim == 3) {
2261: PetscCall(DMDestroy(&da_rho_back_left));
2262: PetscCall(DMDestroy(&da_rho_back_down));
2263: }
2264: PetscCall(VecDestroy(&vel_avg));
2265: PetscCall(DMDestroy(&dm_vel_avg));
2266: PetscFunctionReturn(PETSC_SUCCESS);
2267: }
2269: /*TEST
2271: test:
2272: suffix: direct_umfpack
2273: requires: suitesparse !complex
2274: nsize: 1
2275: 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
2277: test:
2278: suffix: direct_mumps
2279: requires: mumps !complex !single
2280: nsize: 9
2281: 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
2283: test:
2284: suffix: isovisc_nondim_abf_mg
2285: nsize: 1
2286: 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
2288: test:
2289: suffix: isovisc_nondim_abf_mg_2
2290: nsize: 1
2291: 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
2293: test:
2294: suffix: nondim_abf_mg
2295: requires: suitesparse !complex
2296: nsize: 4
2297: 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
2299: test:
2300: suffix: nondim_abf_lu
2301: requires: suitesparse !complex
2302: nsize: 1
2303: 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
2305: test:
2306: suffix: 3d_nondim_isovisc_abf_mg
2307: requires: !single
2308: nsize: 1
2309: 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
2311: test:
2312: TODO: unstable across systems
2313: suffix: monolithic
2314: nsize: 1
2315: requires: double !complex
2316: 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
2318: test:
2319: suffix: 3d_nondim_isovisc_sinker_abf_mg
2320: requires: !complex !single
2321: nsize: 1
2322: 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
2324: test:
2325: TODO: unstable across systems
2326: suffix: 3d_nondim_mono_mg_lamemstyle
2327: nsize: 1
2328: requires: suitesparse
2329: 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
2331: test:
2332: suffix: 3d_isovisc_blob_cuda
2333: requires: cuda defined(PETSC_USE_LOG)
2334: nsize: 2
2335: 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
2336: filter: awk "/MGInterp/ {print \$NF}"
2338: TEST*/